Citation
Pharmacokinetics of buprenorphine in dogs

Material Information

Title:
Pharmacokinetics of buprenorphine in dogs
Creator:
Chandran, V. Ravi, 1955-
Publication Date:
Language:
English
Physical Description:
v, 325 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Bile ( jstor )
Dogs ( jstor )
Dosage ( jstor )
Excretion ( jstor )
Half lives ( jstor )
Metabolites ( jstor )
Plasmas ( jstor )
Renal clearance ( jstor )
Urine ( jstor )
Urine specimen collection ( jstor )
Buprenorphine -- administration & dosage ( mesh )
Buprenorphine -- metabolism ( mesh )
Dogs ( mesh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1986.
Bibliography:
Includes bibliographical references (leaves 348-351).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by V. Ravi Chandran.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
16849862 ( OCLC )
ocm16849862

Downloads

This item has the following downloads:

ES79KV2GS_NNJFCT.xml

pharmacokinetics00chan.pdf

pharmacokinetics00chan_0049.txt

pharmacokinetics00chan_0023.txt

pharmacokinetics00chan_0193.txt

pharmacokinetics00chan_0199.txt

pharmacokinetics00chan_0200.txt

pharmacokinetics00chan_0085.txt

pharmacokinetics00chan_0074.txt

pharmacokinetics00chan_0171.txt

pharmacokinetics00chan_0290.txt

pharmacokinetics00chan_0145.txt

pharmacokinetics00chan_0013.txt

pharmacokinetics00chan_0102.txt

pharmacokinetics00chan_0106.txt

pharmacokinetics00chan_0136.txt

pharmacokinetics00chan_0161.txt

pharmacokinetics00chan_0131.txt

pharmacokinetics00chan_0116.txt

pharmacokinetics00chan_0129.txt

pharmacokinetics00chan_0033.txt

pharmacokinetics00chan_0108.txt

pharmacokinetics00chan_0169.txt

pharmacokinetics00chan_0284.txt

pharmacokinetics00chan_0202.txt

pharmacokinetics00chan_0087.txt

pharmacokinetics00chan_0077.txt

pharmacokinetics00chan_0232.txt

pharmacokinetics00chan_0047.txt

pharmacokinetics00chan_0082.txt

pharmacokinetics00chan_0239.txt

pharmacokinetics00chan_0342.txt

pharmacokinetics00chan_0079.txt

pharmacokinetics00chan_0122.txt

pharmacokinetics00chan_0257.txt

pharmacokinetics00chan_0057.txt

pharmacokinetics00chan_0301.txt

pharmacokinetics00chan_0083.txt

pharmacokinetics00chan_0030.txt

pharmacokinetics00chan_0285.txt

pharmacokinetics00chan_0000.txt

pharmacokinetics00chan_0117.txt

pharmacokinetics00chan_0347.txt

pharmacokinetics00chan_0109.txt

pharmacokinetics00chan_0024.txt

pharmacokinetics00chan_0309.txt

pharmacokinetics00chan_0104.txt

pharmacokinetics00chan_0213.txt

pharmacokinetics00chan_0227.txt

pharmacokinetics00chan_0197.txt

pharmacokinetics00chan_0051.txt

pharmacokinetics00chan_0317.txt

pharmacokinetics00chan_0072.txt

pharmacokinetics00chan_0293.txt

pharmacokinetics00chan_0071.txt

pharmacokinetics00chan_0050.txt

pharmacokinetics00chan_0256.txt

pharmacokinetics00chan_0014.txt

pharmacokinetics00chan_0067.txt

pharmacokinetics00chan_0311.txt

pharmacokinetics00chan_0345.txt

pharmacokinetics00chan_0005.txt

pharmacokinetics00chan_0012.txt

pharmacokinetics00chan_0235.txt

pharmacokinetics00chan_0125.txt

pharmacokinetics00chan_0036.txt

pharmacokinetics00chan_0192.txt

pharmacokinetics00chan_0340.txt

pharmacokinetics00chan_0142.txt

pharmacokinetics00chan_0305.txt

pharmacokinetics00chan_0265.txt

pharmacokinetics00chan_0141.txt

pharmacokinetics00chan_0289.txt

pharmacokinetics00chan_0278.txt

pharmacokinetics00chan_0212.txt

pharmacokinetics00chan_0133.txt

pharmacokinetics00chan_0064.txt

pharmacokinetics00chan_0230.txt

pharmacokinetics00chan_0100.txt

pharmacokinetics00chan_0027.txt

pharmacokinetics00chan_0246.txt

pharmacokinetics00chan_0038.txt

pharmacokinetics00chan_0162.txt

pharmacokinetics00chan_0251.txt

pharmacokinetics00chan_0172.txt

pharmacokinetics00chan_0180.txt

pharmacokinetics00chan_0154.txt

pharmacokinetics00chan_0130.txt

pharmacokinetics00chan_0228.txt

pharmacokinetics00chan_0356.txt

pharmacokinetics00chan_0323.txt

pharmacokinetics00chan_0292.txt

pharmacokinetics00chan_0247.txt

pharmacokinetics00chan_0173.txt

pharmacokinetics00chan_0346.txt

pharmacokinetics00chan_0209.txt

pharmacokinetics00chan_0063.txt

pharmacokinetics00chan_0221.txt

pharmacokinetics00chan_0026.txt

pharmacokinetics00chan_0194.txt

pharmacokinetics00chan_0270.txt

pharmacokinetics00chan_0303.txt

pharmacokinetics00chan_0214.txt

pharmacokinetics00chan_0279.txt

pharmacokinetics00chan_0078.txt

pharmacokinetics00chan_0052.txt

pharmacokinetics00chan_0354.txt

pharmacokinetics00chan_0271.txt

pharmacokinetics00chan_0334.txt

pharmacokinetics00chan_0121.txt

pharmacokinetics00chan_0355.txt

pharmacokinetics00chan_0211.txt

pharmacokinetics00chan_0054.txt

pharmacokinetics00chan_0287.txt

pharmacokinetics00chan_0147.txt

pharmacokinetics00chan_0220.txt

pharmacokinetics00chan_0263.txt

pharmacokinetics00chan_0112.txt

pharmacokinetics00chan_0098.txt

pharmacokinetics00chan_0149.txt

pharmacokinetics00chan_0195.txt

pharmacokinetics00chan_0260.txt

pharmacokinetics00chan_0330.txt

pharmacokinetics00chan_0034.txt

pharmacokinetics00chan_0208.txt

pharmacokinetics00chan_0324.txt

pharmacokinetics00chan_0352.txt

pharmacokinetics00chan_0156.txt

pharmacokinetics00chan_0244.txt

pharmacokinetics00chan_0093.txt

pharmacokinetics00chan_0143.txt

pharmacokinetics00chan_0165.txt

pharmacokinetics00chan_0163.txt

pharmacokinetics00chan_0349.txt

pharmacokinetics00chan_0010.txt

pharmacokinetics00chan_0152.txt

pharmacokinetics00chan_0191.txt

pharmacokinetics00chan_0297.txt

pharmacokinetics00chan_0315.txt

pharmacokinetics00chan_0097.txt

pharmacokinetics00chan_0300.txt

pharmacokinetics00chan_0304.txt

pharmacokinetics00chan_0312.txt

pharmacokinetics00chan_0022.txt

pharmacokinetics00chan_0280.txt

pharmacokinetics00chan_0333.txt

pharmacokinetics00chan_0015.txt

pharmacokinetics00chan_0188.txt

pharmacokinetics00chan_0269.txt

pharmacokinetics00chan_0103.txt

pharmacokinetics00chan_0002.txt

pharmacokinetics00chan_0322.txt

pharmacokinetics00chan_0110.txt

pharmacokinetics00chan_0167.txt

pharmacokinetics00chan_0040.txt

pharmacokinetics00chan_0267.txt

pharmacokinetics00chan_0140.txt

pharmacokinetics00chan_0073.txt

pharmacokinetics00chan_0043.txt

pharmacokinetics00chan_0032.txt

pharmacokinetics00chan_0325.txt

pharmacokinetics00chan_0198.txt

pharmacokinetics00chan_0053.txt

pharmacokinetics00chan_0225.txt

pharmacokinetics00chan_0234.txt

pharmacokinetics00chan_0181.txt

pharmacokinetics00chan_0153.txt

pharmacokinetics00chan_0331.txt

pharmacokinetics00chan_0041.txt

pharmacokinetics00chan_0061.txt

pharmacokinetics00chan_0157.txt

pharmacokinetics00chan_0037.txt

pharmacokinetics00chan_0204.txt

pharmacokinetics00chan_0224.txt

pharmacokinetics00chan_0242.txt

pharmacokinetics00chan_0135.txt

pharmacokinetics00chan_0019.txt

pharmacokinetics00chan_0185.txt

pharmacokinetics00chan_0158.txt

pharmacokinetics00chan_0339.txt

pharmacokinetics00chan_0178.txt

pharmacokinetics00chan_0028.txt

pharmacokinetics00chan_0281.txt

pharmacokinetics00chan_0268.txt

pharmacokinetics00chan_0264.txt

pharmacokinetics00chan_0344.txt

pharmacokinetics00chan_0176.txt

pharmacokinetics00chan_0299.txt

pharmacokinetics00chan_0168.txt

pharmacokinetics00chan_0183.txt

pharmacokinetics00chan_0008.txt

pharmacokinetics00chan_0126.txt

pharmacokinetics00chan_0205.txt

pharmacokinetics00chan_0187.txt

pharmacokinetics00chan_0056.txt

pharmacokinetics00chan_0189.txt

pharmacokinetics00chan_0092.txt

pharmacokinetics00chan_0343.txt

pharmacokinetics00chan_0070.txt

pharmacokinetics00chan_0124.txt

pharmacokinetics00chan_0350.txt

pharmacokinetics00chan_0286.txt

pharmacokinetics00chan_0335.txt

pharmacokinetics00chan_0321.txt

pharmacokinetics00chan_0313.txt

pharmacokinetics00chan_0353.txt

pharmacokinetics00chan_0351.txt

pharmacokinetics00chan_0348.txt

pharmacokinetics00chan_0080.txt

pharmacokinetics00chan_0190.txt

pharmacokinetics00chan_0003.txt

pharmacokinetics00chan_0090.txt

pharmacokinetics00chan_0060.txt

pharmacokinetics00chan_0283.txt

pharmacokinetics00chan_0236.txt

pharmacokinetics00chan_0302.txt

pharmacokinetics00chan_0025.txt

pharmacokinetics00chan_0006.txt

pharmacokinetics00chan_0166.txt

pharmacokinetics00chan_0058.txt

pharmacokinetics00chan_0275.txt

pharmacokinetics00chan_0016.txt

pharmacokinetics00chan_0175.txt

pharmacokinetics00chan_0240.txt

pharmacokinetics00chan_0177.txt

pharmacokinetics00chan_0196.txt

AA00010255_00001.pdf

pharmacokinetics00chan_0282.txt

pharmacokinetics00chan_0245.txt

pharmacokinetics00chan_pdf.txt

pharmacokinetics00chan_0274.txt

pharmacokinetics00chan_0155.txt

pharmacokinetics00chan_0320.txt

pharmacokinetics00chan_0307.txt

pharmacokinetics00chan_0115.txt

pharmacokinetics00chan_0055.txt

pharmacokinetics00chan_0081.txt

pharmacokinetics00chan_0139.txt

pharmacokinetics00chan_0203.txt

pharmacokinetics00chan_0237.txt

pharmacokinetics00chan_0327.txt

pharmacokinetics00chan_0358.txt

pharmacokinetics00chan_0255.txt

pharmacokinetics00chan_0341.txt

pharmacokinetics00chan_0035.txt

pharmacokinetics00chan_0218.txt

pharmacokinetics00chan_0113.txt

pharmacokinetics00chan_0272.txt

pharmacokinetics00chan_0044.txt

pharmacokinetics00chan_0065.txt

pharmacokinetics00chan_0243.txt

pharmacokinetics00chan_0123.txt

pharmacokinetics00chan_0159.txt

pharmacokinetics00chan_0148.txt

pharmacokinetics00chan_0207.txt

pharmacokinetics00chan_0144.txt

pharmacokinetics00chan_0105.txt

pharmacokinetics00chan_0182.txt

pharmacokinetics00chan_0137.txt

pharmacokinetics00chan_0306.txt

pharmacokinetics00chan_0252.txt

pharmacokinetics00chan_0262.txt

pharmacokinetics00chan_0288.txt

pharmacokinetics00chan_0096.txt

AA00010255_00001_pdf.txt

pharmacokinetics00chan_0298.txt

pharmacokinetics00chan_0127.txt

pharmacokinetics00chan_0001.txt

pharmacokinetics00chan_0128.txt

pharmacokinetics00chan_0357.txt

pharmacokinetics00chan_0326.txt

pharmacokinetics00chan_0138.txt

pharmacokinetics00chan_0329.txt

pharmacokinetics00chan_0291.txt

pharmacokinetics00chan_0107.txt

pharmacokinetics00chan_0186.txt

pharmacokinetics00chan_0091.txt

pharmacokinetics00chan_0217.txt

pharmacokinetics00chan_0059.txt

pharmacokinetics00chan_0095.txt

pharmacokinetics00chan_0316.txt

pharmacokinetics00chan_0248.txt

pharmacokinetics00chan_0229.txt

pharmacokinetics00chan_0170.txt

pharmacokinetics00chan_0314.txt

pharmacokinetics00chan_0253.txt

pharmacokinetics00chan_0114.txt

pharmacokinetics00chan_0336.txt

pharmacokinetics00chan_0222.txt

pharmacokinetics00chan_0318.txt

pharmacokinetics00chan_0094.txt

pharmacokinetics00chan_0146.txt

pharmacokinetics00chan_0068.txt

pharmacokinetics00chan_0160.txt

pharmacokinetics00chan_0132.txt

pharmacokinetics00chan_0042.txt

pharmacokinetics00chan_0216.txt

pharmacokinetics00chan_0201.txt

pharmacokinetics00chan_0164.txt

pharmacokinetics00chan_0062.txt

pharmacokinetics00chan_0066.txt

pharmacokinetics00chan_0226.txt

pharmacokinetics00chan_0219.txt

pharmacokinetics00chan_0086.txt

pharmacokinetics00chan_0241.txt

pharmacokinetics00chan_0179.txt

pharmacokinetics00chan_0007.txt

pharmacokinetics00chan_0151.txt

pharmacokinetics00chan_0215.txt

pharmacokinetics00chan_0045.txt

pharmacokinetics00chan_0259.txt

pharmacokinetics00chan_0276.txt

pharmacokinetics00chan_0295.txt

pharmacokinetics00chan_0359.txt

pharmacokinetics00chan_0223.txt

pharmacokinetics00chan_0076.txt

pharmacokinetics00chan_0099.txt

pharmacokinetics00chan_0174.txt

pharmacokinetics00chan_0120.txt

pharmacokinetics00chan_0266.txt

pharmacokinetics00chan_0328.txt

pharmacokinetics00chan_0118.txt

pharmacokinetics00chan_0111.txt

pharmacokinetics00chan_0004.txt

pharmacokinetics00chan_0009.txt

pharmacokinetics00chan_0046.txt

pharmacokinetics00chan_0210.txt

pharmacokinetics00chan_0261.txt

pharmacokinetics00chan_0084.txt

pharmacokinetics00chan_0031.txt

pharmacokinetics00chan_0277.txt

pharmacokinetics00chan_0150.txt

pharmacokinetics00chan_0048.txt

pharmacokinetics00chan_0069.txt

pharmacokinetics00chan_0089.txt

pharmacokinetics00chan_0231.txt

pharmacokinetics00chan_0029.txt

pharmacokinetics00chan_0249.txt

pharmacokinetics00chan_0338.txt

pharmacokinetics00chan_0319.txt

pharmacokinetics00chan_0337.txt

pharmacokinetics00chan_0206.txt

pharmacokinetics00chan_0360.txt

pharmacokinetics00chan_0011.txt

pharmacokinetics00chan_0250.txt

pharmacokinetics00chan_0254.txt

pharmacokinetics00chan_0020.txt

pharmacokinetics00chan_0233.txt

pharmacokinetics00chan_0134.txt

pharmacokinetics00chan_0332.txt

pharmacokinetics00chan_0294.txt

pharmacokinetics00chan_0088.txt

pharmacokinetics00chan_0184.txt

pharmacokinetics00chan_0075.txt

ES79KV2GS_NNJFCT_xml.txt

pharmacokinetics00chan_0101.txt

pharmacokinetics00chan_0258.txt

pharmacokinetics00chan_0039.txt

pharmacokinetics00chan_0273.txt

pharmacokinetics00chan_0308.txt

pharmacokinetics00chan_0296.txt

pharmacokinetics00chan_0017.txt

pharmacokinetics00chan_0018.txt

pharmacokinetics00chan_0310.txt

pharmacokinetics00chan_0119.txt

pharmacokinetics00chan_0021.txt

pharmacokinetics00chan_0238.txt


Full Text












PHARMACOKINEICS OF BUPRENORPHINE IN DOGS


By

V. RAVI CHANDRAN




















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FIDRIDA IN
PARTIAL FULF~IIDGET OF THE RIEQUIREMENTS
FOR THE DEGREEE OF DOCTOR OF PHIID~SOPHY



UNIVERSITY OF~ FIDRIDA


1986




PHARMACOKINETICS OF BUPRENORPHINE IN DOGS
By
V. RAVI CHANDRAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986


ACKNOWLEDGEMENT
I gratefully acknowledge Dr. Edward R. Garrett for his numerous and
varied contributions. I also thank him for his guidance, training,
support and facilities during my graduate career, which made this
dissertation possible.
My special thanks are extended to Dr. Jurgen Venitz for his time,
fruitful discussions and helpful suggestions, and to Dr. Larry J. Peters
and Dr. August H. Battles for animal preparations.
I wish to thank the current and past members of the "Beehive" for
their help, support, advice and friendship.
I acknowledge the members of my supervisory committee,
Dr. John H. Perrin, Dr. Hartmut C. Derendorf, Dr. James W. Simpkins,
Dr. Michael J. Katovich, Dr. C. Lindsay Devane, Dr. John A. Zoltewicz
for their contributions.
I take this opportunity to express my sincere appreciation to
Dr. Bernard Desoize, Dr. Peter Langguth, Mrs. Marjorie Rigby, Mrs. Kathy
Eberst, Mr. George Perry and Mr. Thomas Miller for their valuble help.
li


TABLE OF CONTENTS
ACKNOWLEDGEMENTS
ABSTRACT iv
INTRODUCTION 1
EXPERIMENTAL 20
IV BOLUS STUDIES 30
URINARY EXCRETION OF BUPRENORPHINE 86
IV INFUSION STUDIES 131
PHARMACOKINETICS OF THE IV ADMINISTERED METABOLITE 214
SUMMARY AND CONCLUSIONS 241
APPENDIX I PROGRAM "MULTI" 247
APPENDIX II FITTING OF DATA TO EQUATIONS 251
APPENDIX III KRUSKAL-WALLIS TEST 258
APPENDIX IV TABLES OF RAW DATA 261
GLOSSARY OF TERMS 346
REFERENCES 348
BIOGRAPHICAL SKETCH 352
iii


Abstract of Dissertation presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PHARMACOKINETICS OF BUPRENORPHINE IN DOGS
By
V. Ravi Chandran
December 1986
Chairman: Dr. Edward R. Garrett
Cochairman: Dr. John H. Perrin
Major Department: Pharmaceutical Sciences
Specific and sensitive reverse-phase HPLC assays of buprenorphine
and its metabolite in biological fluids were developed with
sensitivities of 2-6 ng/ml using fluorimetric detection. Upon acute
bolus administration of buprenorphine in six dogs within the 0.7-2.6
mg/kg dose range, accurate estimation of the terminal rate constant and
the derived total body clearance were not feasible due to the lack of
sufficient quantifiable terminal plasma points at less than 5 ng/ml
sensitivity. The terminal plasma concentrations could not be increased
by increasing the bolus dose since such high doses would have
significant toxicity. This toxicity was circumvented and the terminal
plasma concentrations were increased by infusing 3.7-4.8 mg/kg doses of
buprenorphine over 3 h in six studies in six dogs. The terminal rate
IV


constants of the IV infusion studies averaged 34 +_ 3.7 h with an
averaged total body clearance of 212 _+ 35 ml/min. The apprent volumes of
distribution of buprenorphine referenced to the total plasma
concentration were 35 L (V central compartment volume) and 617 L
(Vj, total body volume), indicative of a highly bound, sequestered or
lipophilic drug.
Unchanged buprenorphine is insignificantly renally (<0.5% of the
dose) and biliary (<0.5%) excreted. The major route of buprenorphine
disposition is by hepatic conjugation to glucuronide which is eliminated
into the bile (about 95%) with only small amounts appearing in urine
(<1% as metabolite). Minor metabolites excreted in the bile accounted
for about 3% of the administered dose.
Direct IV administration of the metabolite gave a terminal
half-life of 6 h. Unlike intravenously administered morphine glucuronide
which was not excreted in the bile, more than 90% of the systemically
circulating metabolite was excreted in bile and only 10% in urine.
The oral bioavailability estimated from the areas under the
buprenorphine plasma concentration-time curve following TV and oral
administration of buprenorphine in the dogs was 3-6%. In a bile
cannulated dog, intraduodenally administered metabolite demonstrated 6%
enterohepatic recirculation of the conjugate.
There were no apparent correlations of the buprenorphine time
course with cardiovascular parameters such as heart rate, ECG and blood
pressure. Miotic effect was significant. Respiratory depression was
observed during the first 4 h after IV bolus injection, but not during
the infusion studies.
v


INTRODUCTION
Buprenorphine (1) is a derivative of the morphine alkaloid
thebaine. It is a strong analgesic with marked narcotic activity. Since
the mid-sixties, its therapeutic potential as a morphine-type analgesic
at low doses and antagonistic activity at high doses, has been well
documented.^ Buprenorphine has been claimed to have an advantage over
morphine in that the dose does not need to be increased during several
2
weeks of chronic administration.
Pharmacodynamic and Therapeutic Studies
Buprenorphine has displayed narcotic agonist and antagonist
properties in animals and man. Agonistic effects often exhibited a bell
3
shaped dose-response curve, as occurs with pentazocine, and subjective
opiate-like effects reached a maximum at a dose of about 0.2 to 0.8 mg
4
subcutaneously in man. The onset of agonistic effects (peak effects
about 6 h after subcutaneous or IM injection) in man was slower than
with morphine but the duration of such effects was longer (about 72
5
hours) than with morphine. Also, the analgesic potency of
buprenorphine was about 25 times that of morphine (on a per unit weight
basis)
Therapeutic Trials
In a comparative study of the treatment of chronic pain of
malignant origin by intramuscularly administered buprenorphine and
morphine, 27 patients received buprenorphine (0.3 mg) and morphine (10
7
mg) in a double-blind, single-dose within-patient study. There were no
1


2
significant differences in the intensity of analgesic effect or the time
7
to reach it. However, buprenorphine had a significantly longer
duration of action than morphine. Sedation was the most frequent side
7
effect but dizziness, nausea and vomiting were also seen. Compared to
morphine, buprenorphine showed significantly higher incidences of side
effects, greater severity and earlier onset, and longer duration.^
Following both treatments there were small but significant decreases in
7
pulse rate, blood pressure and respiratory rate.
Antinociceptive actions (blockade of impulses at the peripheral
pain sensitive nerves) of buprenorphine and morphine given intrathecally
g
in conscious rats were compared. After intrathecal injection the peak
(30 min) antinociceptive potencies of buprenorphine or morphine were
g
similar. The analgesic profiles of buprenorphine and morphine (0.3 mg
and 10 mg respectively) were compared in a double-blind non-crossover
9
multiple dose study (IM administration) in man. When the patient
complained of moderate to severe post-operative pain after upper
abdominal surgery, the first test dose of either drug was given. The
drugs gave an equal decrease in pain intensity, suggesting a relative
g
potency of 33:1. An average of 0.51 mg of buprenorphine or 16 mg of
morphine had to be administered for satisfactory initial analgesia. A
faster decrease in the rate of respiration was observed after
buprenorphine than after morphine, but ultimately both the drugs gave
9
the same minimum rate of respiration. These results were comparable to
7
those reported elsewhere.
An oral combination of buprenorphine and paracetamol was compared
to paracetamol in a single-dose double-blind study in man for the
initial acute treatment of post-operative pain.^ One hundred and


3
twenty patients undergoing orthopedic operations were divided into four
groups of 30 patients each. The four treatments were 1, 1.5 or 2 mg of
buprenorphine combined with paracetamol 1000 mg or paracetamol (1000 mg)
alone. There were no significant differences among the groups in
analgesia measured by the observer and by the pain intensity scoring by
the patients over the first six hour. The oral combinations of
buprenorphine and paracetamol produced a significant increase in
duration of analgesia beyond 6 hours over that of paracetamol alone at
all three dose concentrations. A significant increase in side effects
was seen only at the highest dose of buprenorphine-paracetamol
combination compared with paracetamol alone.1
In a study designed to assess the development of drug dependence,
rats were chronically treated subcutaneously for 4 days with
buprenorphine.11 These rats showed only weak signs of withdrawal upon
cessation of a treatment or upon challenge with naloxone.11 More
intense withdrawal symptoms were induced when morphine was substituted
for buprenorphine. Even one injection of morphine, given 12 h after the
last buprenorphine treatment, led to withdrawal symptoms with naloxone.
Naloxone did not cause withdrawal in naive rats treated with this dose
of morphine. Thus, according to these authors,11 and contrary to a few
12 .
claims in the literature, buprenorphine induced dependence like other
opiates. The authors argue that the intensity of withdrawal is less
severe due to slow dissociation of the drug from the receptors.11
The neurochemical effects of buprenorphine were compared to those
of morphine and haloperidol in rats.^ The effect of a wide range of
doses of buprenorphine (0.001 10 mg/kg, subcutaneous administration)
was studied a) with normal concentrations of dopamine, noradrenaline,


4
5-hydroxytryptamine etc. and b) with lower concentrations of dopamine
and noradrenaline in rat brain following the treatment with alpha-methyl
para-tyrosine (alpha-MpT), which is a inhibitor of catecholamine
synthesis. Morphine and haloperidol were used as reference agents.
Buprenorphine increased the alpha-MpT induced rate of dopamine depletion
but did not deplete norepinephrine. Similar results were obtained with
a higher dose (30 mg/kg) of morphine but it increased the alpha-MpT
induced depletion of norepinephrine. Apparently similar effects of
buprenorphine and haloperidol on dopaminergic neurotransmission were
distinguished by pretreating the rats with naloxone (which antagonized
the effect of buprenorphine, and prevented dopamine depletion). These
neurochemical results were claimed to support the view that one site of
action of buprenorphine is on opiate receptors located on the
dopaminergic neurons.^
In a double-blind comparison between fentanyl and buprenorphine in
supplemented nitrous oxide analgesia, buprenorphine or fentanyl (0.3 and
0.125 mg respectively administered IV) were used as supplements in 40
14
patients undergoing major abdominal surgery. Initially both narcotics
appeared to suppress tachycardia and increase arterial pressure in
response to surgery but 80% of the patients who received fentanyl
eventually reguired a further supplement of halothane (0.5%), but no
patient who received buprenorphine required halothane. Recovery from
analgesia was similar in both groups, but the duration of analgesia
after the operation was significantly greater for buprenorphine (12 h)
than fentanyl (3 h).1^
In a double-blind randomized non-crossover trial, 47 patients
received either morphine (10 mg) or buprenorphine (0.3 mg) by regular IM


5
injection for 24 h after abdominal surgery.15 In this study, the two
drugs were equally effective at the dose ratio 1:33, buprenorphine to
7 9
morphine which is comparable to the results reported elsewhere.
One hundred twenty-six patients undergoing upper and lower
abdominal surgery were studied post-operatively to compare the analgesic
effect of IM morphine, sublingual buprenorphine and self administered IV
pethidine.15 There were no significant differences among analgesic
regimens in respect to subjective pain scores or static and dynamic lung
volumes assessed at 24 h, 48 h and 5 days after operation. Sublingual
buprenorphine produced more nausea and sedation than the other regimens,
but the results were not clinically important. These authors16 report
that buprenorphine offered considerable advantages in terms of ease of
administration.
When diamorphine and buprenorphine were compared in the relief of
chest pain in man, sublingual administration appeared to be as effective
17
as the IV route, but the onset of action was slow. There were no
significant changes in the systemic or pulmonary arterial blood pressure
17
or heart rate after IV buprenorphine. A randomized double-blind
controlled trial of equivalent doses of buprenorphine and diamorphine
showed no significant differences between the drugs in terms of pain
17 .
relief and duration of action. The occurence of nausea, vomiting and
other side effects was similar in the two groups. The onset of action of
buprenorhine was slightly but significantly slower than that of
diamorphine.1^
Buprenorphine and pethidine were compared in a double-blind study
of on-demand IV analgesia. Buprenorphine was about 600 times as potent
18
as pethidine. The incidence of side effects was similar with both


6
drugs. The quality of analgesia subjectively assessed was the same with
18
both drugs using this method of administration. These authors claim
that buprenorphine is a powerful analgesic agent that may be given
intravenously provided that its low potential for abuse is
substantiated.
In a smaller number of patients with chronic pain, usually due to
cancer, sublingually given buprenorphine (up to 0.8 mg 4 hourly)
provided adequate pain relief for periods up to several months, but side
effects (usually nausea and vomiting) required discontinuation of
19
treatment in about 1/3 to 1/2 of the ambulatory patients.
Following anesthesia with fentanyl in 180 patients, buprenorphine
(usually 0.4 to 0.8 mg TV) reversed some of the anesthetic effects while
producing continued analgesia that lasted about 8-12 h after a
20
single-dose. The antagonistic activity however, was frequently
short-lived, declining rapidly after 90 to 120 min and a second dose of
buprenorphine was often required to prevent the re-emergence of
20
anesthetic effects.
The efficacy of buprenorphine has been compared to lofentanil and
to saline placebo by extradural administration in the management of
21
post-operative pain in sixty patients. In a double-blind study, these
orthopedic patients were randomly assigned to three equal groups to
determine the analgesic effects, duration of action and side effects of
the extradural administration of lofentanil (5 ug) buprenorphine (0.3
21
mg) or physiological saline. No systemic analgesics were given
before, during or after surgery, and all the patients had operations on
the lower extremities under extradural analgesia (lignocaine or
bupivacaine). Upon administration of the test drug as soon as pain


7
occured in the post-operative period, a long duration of action and a
marked analgesic effect was observed with lofentanil. A shorter duration
of action and less pain suppression occured with buprenorphine and a
rather marked placebo effect was seen with saline. The only side effect
noticed was drowsiness in 3 patients in the lofentanil group and in 2
21
patients in the buprenorphine group.
22
In a randomized double-blind trial comparing analgesia produced
by combinations of droperidol with either buprenorphine or morphine,
buprenorphine was claimed to be as satisfactory as morphine to produce
analgesia during major surgery in 60 patients, with no difference in the
incidence of untoward side effects.
Epidural buprenorphine was investigated as a post-operative
analgesic in a randomized double-blind study of 158 patients given
intraoperative epidural analgesia with 2% mepivacaine or 0.5%
23
bupivacaine for orthopedic surgery of the lower extremity. At the end
of the surgery, the patients were given epidurally in 15 ml saline,
either 0.15 mg of buprenorphine (n=38) or 0.3 mg (n=37). A control group
received no epidural injection (n=47). The above 3 groups received 2%
mepivacaine as intraoperative anesthetic. A fourth group (n=36) received
0.3 mg buprenorphine in 15 ml saline, after intraoperative use of 0.5%
bupivacaine. The patients rated post-operative pain. Analgesia after
0.15 mg of buprenorphine was superior to that after saline injection,
and 0.3 mg buprenorphine was superior to both saline injection and to
23
0.15 mg of buprenorphine until 12th hour. Analgesia after bupivacaine
followed by 0.3 mg of buprenorphine was not significantly different than
analgesia seen after mepivacaine followed by 0.3 mg of buprenorphine.
21
These results are comparable to those reported elsewhere.


8
Respiratory effects. The respiratory depressant activity (such as
decreased respiratory rate, increased arterial P CCL and decreased
cl Z
arterial P 0) of single equianalgesic doses of buprenorphine and
cl Z
1 24 25
morphine appear to be similar in rats and rabbits. ' The extent of
buprenorphine-induced respiratory depression against dose plateaued in
26
animals, whereas such an effect was not clearly demonstrated in man,
which showed dose-related respiratory depression within the therapeutic
dose range (0.3 mg to 0.6 mg). The time to reach peak respiratory
depression in man was slower after intramuscular buprenorphine than
after morphine (3 h vs 1 h) and the duration of such an effect was
26
longer. There appears to be no completely reliable specific
antagonist for buprenorphine-induced respiratory depression since even
26
high doses of naloxone produced only partial reversal. Hcwever, the
respiratory stimulant drug doxapram has reversed respiratory depression
due to buprenorphine in a few healthy volunteers and in a few
. . 26
patients.
Cardiovascular effects. Hemodynamic changes in healthy volunteers
after IM (0.15 to 0.6 mg), sublingual (0.4 to 0.8 mg) or oral (1 to 4
ng) doses of buprenorphine include dose related reductions in heart rate
(up to 25%) and small decreases in systolic blood pressure (about
26
10%). These results are comparable to the cardiovascular effects of
26
morphine. Similar effects occured in anesthetized patients undergoing
surgery and in a few patients with myocardial infarctions. However, in
the latter group the heart rate was found to be relatively
27
unperturbed.
Addiction potential of buprenorphine. Buprenorphine appeared to
have a lower addiction potential than the opioid agonist pentazocine in


9
animals. However the extent to which such results can be extrapolated to
1 28
man was uncertain. In a single-dose addiction study in 5
volunteers, high (8 mg daily) intramuscular doses of buprenorphine,
administered up to 1 to 2 months produced a slowly emerging withdrawal
5 6
syndrome on abstinence from the drug. Though the results were
indicative of lesser addiction potential compared to morphine,
definitive statements about addiction cannot be made until it has been
more widely used in patients with chronic pain with repeated doses over
an extended period of time.^
Receptor binding studies. Receptor binding studies were undertaken
to elucidate the opioid binding characteristics of fentanyl and
29
buprenorphine, and to investigate differences between them.
Buprenorphine showed slow receptor equilibration (30 min) but with high
affinity to multiple sites. The dissociation was claimed to be slow
(half-life = 166 min) and incomplete (50% binding after 1 h). This
contrasted with the receptor binding of fentanyl, which achieved rapid
equilibrium (within 10 min) and dissociated equally rapidly (half-life =
6.8 min) and completely (100% by 1 h). Using competitive displacement
studies, it was claimed that buprenorphine displacement of fentanyl was
concentration and time dependent over the ranges (equimolar
buprenorphine and fentanyl concentrations, 2 nmol/liter) encountered in
clinical use. However, buprenorphine binding was displaced with only
. 29
high concentrations of other opioids.
Binding of buprenorphine to the rat forebrain (telencephelon,
diencephelon and mesencephelon) was claimed to be stereospecific,
30
saturable and had high affinity. Maximum binding (Bmax) was reached
by 30 min and dissociation from the receptor was slow. The regional


10
distribution of buprenorphine binding sites in the rat brain was claimed
to be qualitatively similar to the distribution of naloxone and
dihydromorphine binding sites. The Bmax for this receptor binding of
buprenorphdne was about 2 times that for the mu-opiate receptor drugs
and three times the for the delta-opiate receptor ligands (such as
enkephalins). Buprenorphine was also found to be very potent in
displacing naloxone, dihydromorphine and met-enkephalin. Since mu-
receptors bind with exogenous opioids (such as morphine), and delta-
receptors bind with endogenous opioids (such as enkephalins), the above
findings suggest that buprenorphine binds to both mu- and
delta-receptors.^
Side effects.
Moderate to marked drowsiness has been reported in about 40-50% of
the patients (up to 75% in some studies), but all such patients were
1 31 32
found to be easily arousable upon stimulation. Nausea and/or
vomiting occurred in 15% of the patients. Other minor side effects (e.g.
dizziness, sweating, headache or confusion), typical of strong
analgesics, have been reported with a widely varying incidence.
Respiratory depression, as determined by laboratory measurements of
respiratory functions, does occur with buprenorphine. The extent of such
depression was similar to other opioid drugs administered in usual
clinical doses.1 However, this was not a problem in clinical studies
7-9
which were usually conducted in fit patients. The effect of
buprenorphine on respiration in "poor risk" patients, such as those with
respiratory diseases or congestive heart failure, has not been
determined. However, it appears that buprenorphine would have the same
potential problems as morphine in this patient group.1


11
Dosage and Administration
Buprenorphine is presently available in Europe for parenteral
use.1 The recommended dose is 0.3 to 0.6 mg by IM or slow IV injection,
repeated every 6-8 h as needed. Administration of buprenorphine to
patients already receiving large doses of narcotic drugs should be
undertaken with caution until the response is established, since its
antagonistic activity could conceivably cause withdrawal symptoms.1
Pharmacokinetic Studies
There is limited information available on the pharmacokinetic
properties of buprenorphine in man.1 It was stated without
documentation or citation of references that rapid absorption and peak
plasma concentrations were seen in rats on oral and IM dosings where the
oral dose was 4 times the IM dose.1 It was claimed that in primates and
in human volunteers, peak plasma concentrations were reached more slowly
after oral administration (2 h) than by IM injection (7 min).1 Drug
concentrations were stated to be detectable in blood for longer times
after oral (24 h) than IM (7 h) administration of equivalent doses. In
man buprenorphine was claimed to be excreted unchanged in the feces, and
as glucuronide and N-dealkylated buprenorphine in urine.1 References of
studies supporting these data were not given.1
In a 3 h study, peak plasma buprenorphine concentration did not yet
.33
occur in some patients after sublingual administration. In a
subsequent 10 h study with 15 post-operative patients, 5 patients
received a sublingual dose 0.4 mg of buprenorphine, five 0.8 mg and 5
received placebo at 3 h after a 0.3 mg IV dose of buprenorphine. The
plasma buprenorphine concentration was measured by a specific
34
radioimmunoassay. The plasma concentration reached a peak level in an


12
average time of about 200 min in both the 0.4 mg and 0.8 mg groups
34
(range 90-360 min after the initial 3 h period). The plasma drug
concentration in the 0.8 mg group were approximately twice that in the
0.4 mg group. The absolute bioavailability was estimated to be about 55%
of the IV route for both groups by the ratio of the area under the
plasma concentration versus time (AUC) for sublingual and TV
administration. Uptake of buprenorphine from the sublingual site was
34
claimed to be complete by 5 h after the dose was given. In this
study, cross-reactivity between buprenorphine and its metabolites was
not ruled out. Two modes of administration (TV followed by subcutaneous)
were carried out in each study which complicated the pharmacokinetic
analysis.
Buprenorphine kinetics were studied in surgical patients using
35
radioimmunoassay. Buprenorphine was measured in the plasma of 21
patients who received 0.3 mg IV. After 3 h, ten of these patients
received further dose of 0.3 mg TV, and 11 patients were given 0.3 mg
IM. Plasma drug concentrations were measured up to 3 h after the second
dosing. Comparison of the pharmacokinetics in the same patient, awake
and anesthetized by general anesthesia, showed that the clearance was
significantly lower (900 ml/min) in the anesthetized state compared to
the unanesthetized state (1225 ml/min). Bioavailability was claimed to
be the same for both TV and IM administered drug. The peak plasma levels
were seen at 2-5 min and in 10 min respectively for IV and IM dosing
35
after the second dosing. Cross reactivity among buprenorphine and its
metabolites was not ruled out in this study. The sensitivity and limits
of detection for buprenorphine were not given. Thus the terminal plasma
buprenorphine concentrations at less than 1 ng/ml are questionable.


13
Procedures for obtaining various pharmacokinetic parameters were not
given.
Plasma concentrations were correlated with clinical effects after a
single IV dose of buprenorphine (0.3 or 0.6 mg) in patients recovering
36
from surgery. Analgesia was greater at the high dose without any
apparent parallel increase in respiratory depression. Better analgesia
was reported if the first required post-operative dose of 0.3 mg has
been preceded by a similar loading dose or by the use of a larger dose
36
during surgery. This study was largely descriptive without rigorous
pharmacokinetic analysis. The plasma concentrations obtained from a
number of patients were averaged to obtain a mean concentration. This is
not a valid pharmacokinetic technique.
Metabolism and Excretion
Higher amounts of polar metabolites were seen in plasma after oral
administration than after IM in rats.'*' The premise of drug conjugation
37 38
in the gut wall was supported by studies with rat gut preparations. '
Buprenorphine has been found conjugated or N-dealkylated in bile or
tissues of animals, but unchanged in the brain. This is possibly
indicative of the fact that buprenorphine and not a derivative is
responsible for the narcotic activity.1
In a study of pharmacokinetics of buprenorphine after IM
administration to rats, dogs, rhesus monkeys and one human volunteer,
most of the dosed radioactive drug was excreted in the feces, indicating
39
biliary excretion with possible enterohepatic recirculation. After IV
administration of the tritiated buprenorphine (100 p g/kg) to the bile
duct cannulated rats, over 90% of the administered drug was excreted in
the bile within 48 h after dosing. The major metabolite in the bile was


14
buprenorphine glucuronide. N-dealkylated buprenorphine was also present.
Intraduodenal infusion of rats with bile obtained from other rats dosed
with radiolabelled drug produced a slow but extensive excretion drug
. 39
related metabolites in the bile of the recipient animal. The plasma
concentrations were not measured in this study. The assay techniques
were not specific for the parent drug or its metabolites. Dose
dependency was not studied.
40 .
In a chronically cannulated cow, it was shown that the hepatic
extraction ratio for IV boluses of morphine, diamorphine, fentanyl,
methadone and buprenorphine increased towards a plateau value as the
portal vein drug concentration increased. The extraction ratio was
claimed to be independent of hepatic blood flow, but dependent on
concentration.
Disposition of radiolabelled buprenorphine in the rat after a
single 0.2 mg/kg IV bolus dose and continuous administration via a
41 ...
subcutaneous delivery system were carried out. After IV injection,
tri-exponential decay of the drug from brain was seen with half-lives of
0.6, 2.3 and 7.2 h, respectively. Plasma half-lives were 0.5 and 1.4 h
(the third phase was not estimated). Decay half-life of the drug from
its high affinity binding sites in brain were 1.1 and 68.7 h
respectively. Fat and lung had higher concentrations than other tissues
41
or plasma. No metbolites of the drug were detected in brain.
Unmetabolized drug excreted in the urine and feces one week after TV
injection were 1.9 and 22.4% of the dose, respectively, and 92% of the
dose was accounted for in 1 week. Urinary metabolites (%) were
conjugated buprenorphine 0.9; norbuprenorphine (free 9.4, conjugated


15
5.2); tentative 6-0-desmethyl norbuprenorphine (free 5.4, conjugated
15.9).41
Peak plasma concentration of buprenorphine occured in 4 weeks after
s.c. implantation of a long-acting radiolabelled buprenorphine (10 mg)
pellet. The apparent dissociation half-lives of the drug from the lcw-
and high-affinity binding sites in the brain were 4.6 and 6.8 weeks,
respectively. Fat, spleen and skeletal muscle had higher radioactivity
41
than other tissues and plasma. These authors state that high-affinity
binding of buprenorphine in brain and subsequent slow dissociation are
the factors responsible for its prolonged agonist and antagonist effects
and higher potency than other narcotic agonists.
Absorption and bioavailability. There are no published studies on
the oral absorption of this drug in man. It was claimed on the basis of
unpublished data that the peak plasma concentration of orally
administered radiolabelled buprenorphine in the rat was reached in 10
min with another peak in plasma appearing in about 5-8 h.1 This delayed
peak could be due to the late appearance of radiolabelled metabolites
(e.g., N-dealkylated buprenorphine and conjugates) in plasma.^ An
intramuscular dose of 20 y g/kg gave blood peak concentration similar to
that of a 100 yg/kg oral dose. In monkeys, unpublished data were cited
to support the statements that peak blood concentrations of
radiolabelled drug were reached at 2 min, 2 h and between 2-4 h
respectively for IM, oral and sublingual administration.'1' Also, it was
stated that in two healthy volunteers, peak blood concentrations were
reached rapidly after IM dosing (2 yg/kg) of radiolabelled
buprenorphine followed by a rapid decline. Peak concentrations were
reached slowly at 2 h after the oral administration of 15 yg/kg of the


16
drug, followed by a biexponential decline of concentration.
Concentrations as low as 0.5 to 3.5 ng/ml were claimed to be detected by
a specific radioimmunoassay technique after IV and IM administrations
1
(0.3 mg). In human volunteers a dose of 0.4 mg produced peak
concentrations of 1-2 ng/ml at about 2 h after oral administration.
References of studies supporting these data were not cited.1
Systemic bioavailability of buprenorphine was studied in female
rats following single-doses (200 jag/kg) administered by six different
42
routes. Relative to the 100% bioavailability from the intra-arterial
route, the mean bioavailabilities were, IV 98%, intrarectal 54%,
intrahepatoporta1 49%, sublingual 13% and intraduodenal 9.7%. AUC
analysis of buprenorphine concentrations in blood showed the relative
fractions of the drug excreted (first pass) by gut, liver and lung to be
0.8, 0.5 and 0.02 respectively. In vitro absorption studies showed that
poor bioavailability of intraduodenally administered buprenorphine was
not due to slow or incomplete absorption, but due to first-pass
42
metabolism. In this study, the authors computed AUC only up to 4 h
for the plasma data. The data showed two compartment model type
disposition for the drug in plasma. AUC would be different if calculated
up to time infinity.
In the above pharmacokinetic studies, low doses and subsequent low
terminal plasma concentrations have essentially limited the estimates of
terminal rate constants and half-lives of elimination. Sensitive and
selective assay techniques for buprenorphine and its metabolites in
biological fluids, and administration of large doses to a higher animal
such as dog could give acceptable pharmacokinetic parameters.


17
Protein binding. It was reported without documentation'1' that
buprenorphine was highly bound (96%) to alpha- and beta-globulin
fractions of human plasma proteins in the concentration range 0-9 ng/ml.
The fraction of drug bound to dog plasma protein was determined by
measuring the drug concentration in plasma water after
43
ultracentrifugation. The fraction bound was estimated to be 0.945.
Binding of buprenorphine to dog plasma proteins was also determined by
partitioning the drug into red blood cells. The estimation is based upon
the presumption of established equilibria between drug in plasma water,
44
red blood cells and plasma proteins. By this technique, the fraction
43
of buprenorhine bound to plasma proteins was estimated as 0.983. This
relatively high plasma protein binding for the lipophilic buprenorphine
45
contrasts to the 26-36% plasma protein binding of morphine, naloxone,
and naltrexone.46
RBC Partition. Partition studies have shown that red blood
43
cell-plasma water partition coefficient of buprenorphine was 6-11.
45
This is in contrast to 1.11 for morphine, 1.83 for naltrexone, and
1.49 for naloxone.46
Physical properties. Fluorescence (excitation 285 nm, emission 350
nm) of buprenorphine provided excellent detection for HPLC assay in
43
biological fluids with a 5 ng/ml sensitivity. Buprenorphine
solvolysis was specific-acid and specific-base catalysed. It yielded a
stoichiometric final acid degradation product (3), a fluorescent
detectable, rearranged demethoxy analogue of buprenorphine. Alkaline
43
hydrolysis produced no fluorescence products. Acid hydrolysis also
produced a fluorescent-detectable, transient dehydro intermediate (2)
that was also completely transformed into the demethoxy analogue (Scheme


18
Methyl migration
^ch2 -<]

' f
/CHj -<]
/

Scheme I
Acid Hydrolysis of Buprenorphine


19
I). Compound 2 was an excellent bioassay internal standard. Buprenorhine
was shown to be highly stable at neutral pH values, even at elevated
43
temperatures. Estimated buprenorphine pKa' values were 8.24 and 10
for the ammonium and phenolic groups respectively. The intrinsic aqueous
43
solubility of buprenorhine was 12.7 +_ 1.2 ;ug/ml at 23C.
Assay methods. Few assay methods of buprenorhine in biological
47
fluids have been reported in the literature. A radioimmunoassay has
been used to determine plasma levels of parenterally administered
34 35
buprenorphine in dogs and humans. A selective ion monitoring
method (SIM) of the silylated buprenorphine in GC-MS has been used to
determine the plasma levels of buprenorphine over a 20-3000 ng/ml
48
concentration range. A GC assay with flame-ionization detection of
silyl derivatives of buprenorhine was used in stability studies at 5-10
49
;ig/ml of aqueous solutions. An HPLC assay with fluorescence detection
43
of buprenorhine in biological fluids has been reported and its
modification and improvement is presented in this dissertation.


EXPERIMENTAL
Materials. Analytical grade solvents and reagents were used.
Buprenorphine hydrochloride, 21-cyclopropy1-7-alpha-[(s)-1-hydroxy-1, 2,
2-trimethylpropyl]-6,14 endo ethanotetrahydro-oripavine, 1, (National
48
Institute for Drug Abuse, Rockville, MD) and the demethoxy analog, 3,
49
of buprenorphine (Addiction Research Center, Lexington, KY) were used
as received. A standard sample of 21-cyclopropyl-7-alpha-[2-(3,
3-dimethyl-l-butenyl)] 6,14 endo ethanotetrahydro-oripavine, 2, was
obtained from Dr.G. Lloyd Jones of Rickett & Colman, Pharmaceutical
Division, Kingston-upon-Hull, England.
Apparatus. An HPLC (model M6000A pump, Waters Associates, Milford,
MA), equipped with a variable-wavelength fluorescence detector (model
600S Fluorescence Detector, Perkin-Elmer, Norwalk, CT), was used.
Injections were carried out with an auto sampler (WISP Autosampler,
Waters Associates), and the data were analysed by a microcomputer (Sigma
15, Data Station, Perkin Elmer). A separate HPLC pump (series 3B, Perkin
Elmer) equipped with a variable wavelength UV detector (model LC 75,
Perkin Elmer) was used in some studies. A laboratory centrifuge was used
in the separation of organic extract from biological fluids (Lab
Centrifuge, International Centrifuge Equipment Co., Needham Heights,
MA).50
Liquid Chromatographic Procedures. Aliquots (50-100 yL) of the
solutions to be analyzed were injected into the HPLC system equipped
with a packed [packing material was C^g 5- ym Bondapak-reversed phase
20


21
(ODS-Hypersil), Shannon Southern Products Ltd., Cheshire, U.K.] 120 mm
i.d. stainless steel column [Knauer HPLC analytical column (unpacked),
Knauer A.G. Berlin, F.R.G.] which was maintained at 40 C. The usual
mobile phase flow rate was 1.5 mL/min of a 40:60 acetonitrile:acetate
buffer (pH 3.75, 0.05M) containing 0.0004M tetrabutylammonium phosphate.
Fluorescence was effected at 285 nm excitation (slit 20 nm) and 350 nm
43
emission (slit 15 mm) and was used unless stated otherwise.
Calibration Curves in Biological Fluids
Buprenorphine. Aliquots (1 mL) of plasma, urine or bile in each of
ten 15mL centrifuge tubes were spiked with 100 p L of 100-1000 ng/mL of
buprenorphine (1). Each solution contained 50 ng/mL of the acid
degradation intermediate of buprenorphine, compound 2, as the internal
standard. The final sample contained no drug. Sodium borate-boric acid
buffer (1 mL at pH 9.1, 1 M) and 4.2 mL of benzene were added to each
tube. The tubes were shaken for 20 min, centrifuged at 3000 rpm for 10
min, and 4 mL of each benzene extract was transferred to another set of
ten 15miL centrifuge tubes. Hydrochloric acid (1 irL, 1 M) was added to
each tube and the tubes were shaken for 10 min and then centrifuged at
3000 rpm for 10 min. After removal of benzene layer by aspiration, 1 mL
of both 1 M NaOH and pH 9.1 borate buffer (1 M) were added to each of
the remaining aqueous phases. The pH values were confirmed or adjusted
to be between 9.05 to 9.15. Benzene (4.5 mL) was added to each tube
which was shaken for 10 min and centrifuged at 3000 rpm for 10 min. The
benzene extract (4.00 mL) was transferred to a 5miL vial (Reacti-vial,
Supelco, Inc. Bellefonte, Pa.) and the benzene was evaporated under a
stream of nitrogen at 55C. Sodium acetate-acetic acid buffer (pH 3.75,
0.05 M, 100 yL) was added to each of the Reacti-Vials and they were


22
vortexed for 30 s, and then 75 pL of the solution was analyzed by HPLC.
Buprenorphine conjugates. Aliquots (1 mL) of plamsa, urine or bile
in each of ten 15-mL centrifuge tubes were spiked with 100 y L of
100-1000 ng/mL of buprenorphine. The first sample contained no drug. To
each centrifuge tube, 1 mL of 6 N HC1 was added, and autoclaved at 15
lbs/sq.in pressure for 10 min. The tubes were allowed to equilibrate to
room temperature. To each tube containing the acid-transformed demethoxy
buprenorphine, 50 y L of unconverted buprenorphine (1 y g/mL) was added
as internal standard. Excess acid was neutralized with soduim carbonate.
The pH was adjusted to 9.1 with sodium borate-boric acid buffer (1 mL, 1
M) and 4.2 mL of benzene was added to each tube. The tubes were shaken
for 20 min, centrifuged at 3000 rpm for 10 min, and 4 mL of each benzene
extract was transferred to fresh 15-mL centrifuge tubes. Hydrochloric
acid (1 mL, 1 M) was added to each tube and the tubes were shaken for 10
min and centrifuged at 3000 rpm for 10 min. After removal of the benzene
by aspiration, 1 rriL of both 1.00 M NaOH and pH 9.1 borate buffer (1.00
M) were added to each reamining aqueous phases. The pH values were
confirmed or adjusted to be between 9.05 to 9.15. Benzene (4.5 mL) was
added to each tube which was shaken for 10 min and centrifuged for 10
min at 3000 rpm. The benzene extract, (4.00 mL) was transferred to a 5
rriL vial (Reacti-Vial) and the benzene was evaporated under a stream of
nitrogen at 55'C. Sodium acetate-acetic acid buffer (100 y L, pH 3.75,
0.05 M) was added to each vial (Reacti-Vial), vortexed for 30 s, and 75
yL of the solution was analyzed by HPLC.
Pharmacokinetic studies in dogs. Healthy mongrel male dogs (8) were
used for the pharmacokinetic investigations. Their blood analysis showed
no pathogenic abnormality or presence of microfilaria. The dogs were


23
fasted for at least 17-24 h before each study and were given water ad
libitum. The animals were supported by a dog sling in a frame placed on
a laboratory table. The dogs were infused with intravenous saline (35
drops per min) for at least 3 h until drug adminstration, when the
intravenous drip was reduced to 20 drops per min. The animals were
catheterized 3 h before the study with a 30.5-cm standard catheter
(Intracath, 16 GA size, Deseret Medical Inc., Sandy, Utah) in the
jugular vein after local anesthesia with mepivacaine hydrochloride
(Carbocaine hydrochloride; Winthrop Laboratories, New York, NY). Second
catheter was also implanted in a foreleg vein (vena brachialis) in most
IV infusion studies. The drug was injected directly into the jugular
catheter, followed by flushing of the catheter with 25 mL of normal
saline. The catheter was connected via a three-way stopcock (Pharmacea,
Toa Alta, PR) to the saline infusion bottle (McGaw Laboratories, Irvine,
CA). Blood samples (1-6 mL) were collected in heparinized Vacutainer
tubes (Becton Dickinson Vacutainers, Rutherford, NJ) after the dead
volume of the catheter was filled with 5 mL of blood by aspiration with
an extra syringe. These aspirations were carefully aseptically
reinjected into the jugular vein. The heparinized blood samples were
immediately centrifuged at 3000 rpm for 10 min. The plasmas were removed
with sterile glass pipets and were frozen until analysed.
Urine was collected from the dogs through a urinary catheter
(Polyurethane whistle tip units, 6 FR size, McGaw Laboratories) at
intervals of 15-60 min for up to 24 h and at longer intervals for up to
1 week. Withdrawal times, volumes and urinary pH values were recorded
and portions of each sample were frozen until analyzed.
Infusion studies were carried out using Harvard Infusion pump


24
(Harvard Apparatus Co., Dover, MA). Buprenorphine-HC1 was dissolved in
normal saline (150 mL, concentration^.73-78 mg/mL), ultrasnicated for
30 min and infused into the jugular vein at the rate of 0.7026 mL/min
for 162-175 min (studies 7-11). During infusion, blood samples were
collected from the brachialis vein. Post-infusion blood samples were
collected from both jugular and brachialis veins. In dog study 12, the
drug solution was infused into the brachialis vein (using the same drug
concentration and flow rate as above).
Dogs E, F and G underwent surgery.^ A 2% solution of thymalol
sodium was administered IV (6 mL/kg) to each dog and anesthesia was
maintained by halothane. After removal of the gallbladder, a screw-cap
was placed on the opposite side of the sphincter of Oddi and the
intestine was sewn to the abdominal wall (Fig 1). At least 1 month was
allowed for recovery from the surgery before the pharmacokinetic study
of buprenorphine in the bile-cannulated dogs. These dogs could be
repetitively used for bile cannulation studies by opening the screw-cap
and inserting a catheter (Fast Right Heart Cardiovascular catheter, 5 F
size, C.R. Bard Inc., Billerica, MA) into the bile duct. The balloon at
the tip of the above catheter was inflated with 0.8-1.0 mL of air,
pulled back until the catheter was securely positioned at the inside
wall of the spincter of Oddi. Complete bile collection was effected in
such studies at intervals of 15-120 min for up to 26 h.
Isolation of buprenorphine conjugate from bile. Two liquid
chromatographic glass columns (40 X 2.5 cm) were packed with nonionic
Amberlite XAD-4 beads (Sigma Chemical Co., St. Louis, Mo.) by passing a
slurry of the packing material in distilled water through the column.
The perforated disk at the bottom end of the column retained the


Figure 1. Schematic of the performed surgery. After gallbladder removal, screwcap
was placed on the opposite side of the sphincter of Oddi and the intestine was
sewn to the abdominal wall. During the bile cannulation, the screwcap was replaced
by a sealed perforated rubber stopper through which a bile catheter was positioned
into the bile duct. At the end of the study, the catheter was removed and the
screwcap was replaced (See also reference 51).


gall bladder-7
(removed) /-
duodenum
abdominal
wall


27
Amberlite beads. Each column was washed with 500 mL of water followed by
250 mL of methanol. The columns were closed at the bottom and soaked
with distilled water overnight. Pooled bile samples (150 mL) collected
from dog studies 9 and 10 were diluted to 500 mL with distilled water.
Aliquots (250 mL) were passed through each column and washed with 300 mL
of water until the eluent was colorless. Then, 300 mL of methanol was
passed through each column. These methanolic eluates were combined and
completely evaporated to dryness under reduced pressure. The residue was
dissolved in sterile normal saline (120 mL) and the solution was
filtered through a 0.22 pm Millipore filter aided under reduced
pressure and strictly aseptic conditions. The final sterile solution was
infused into dog F (Study #13) at the rate of 14 mL/min for 8.5 min. The
pooled bile samples collected from dog study #11 were similarly except
that chromatographic separation was achieved with only one Amberlite
XAD-4 column. The final sterile solution was infused into dog G (Study
#14) at the rate of 14 ml/min for 7 min.
Analysis of the conjugate by enzymatic hydrolysis. The enzyme
8-glucuronidase ( 8-glucuronide glucuronosohydrolase, 0.76 mg = 660,000
Fishman Units, Lot. #51F-9013, Sigma Chemical Co.) was dissolved (50 mg)
in 20 mL acetate buffer (pH 3.8, 0.05 M). Aliquots (500 pL) of the
enzyme preparation and the internal standard (100 pL of compound 2 1
ptg/mL) were added to 500 y L of diluted bile sample (1:10,000 dilution
made with distilled water) and the total volume was adjusted to 1.6 mL
with pH 3.8 acetate buffer. The samples were incubated at 37'C for 24 h.
Diluted bile (1:10,000 dilution) samples containing no drug were spiked
with buprenorphine and treated in the same manner to establish an
appropriate calibration curve. The generated aglycone buprenorphine was


28
assayed by HPLC separation and fluorimetric detection.
Catheter binding of buprenorphine. Buprenorphine-HCl was dissolved
in normal saline (150 mL, concentration = 0.7576 mg/mL of base). The
solution was passed through the plastic catheter (Intracath) without
back pressure at the rate of 0.7026 mL/min for 1 h (1 study) and 3 h (2
studies). The internal surface of the catheter was washed with 25 mL of
normal saline and dried under a stream of air. Then benzene (250 ml) was
pumped through the plastic catheter (Intracath) at the rate of 14
ml/min, evaporated in a collecting flask at 70*C under reduced pressure.
The residue was reconstituted in acetate buffer (pH 3.75, 0.05 M) and
aliquots were assayed by HPLC separation and fluorimetric detection.
Buprenorphine-HCl was dissolved in normal saline (0.7567 mg/mL of
base) and passed through the plastic catheter (Intracath) at the rate of
0.7026 mL/min for 3 h. The interior surface of the catheter was washed
with 25 mL of normal saline. The saline was allowed to flow from an
infusion bag under the gravitational force at the rate of 45 drops/min
for 2 h and was collected (300 mL). The pH was adjusted to 9.1 and the
saline solution was extracted twice with 250 mL portions of benzene. The
combined benzene layer was evaporated under reduced pressure at 70C.
The residue was reconsituted in acetate buffer (pH 3.75, 0.05 M) and
aliquots were assayed by HPLC separation and fluorimetric detection.
Buprenorphine (0.7567 mg/nL) in normal saline was passed through
the plastic catheter (Intracath) for 1 h at the flow rate of 0.7026
mL/min. At the end of 1 h, the catheter was washed with 25 mL of normal
saline, and saline drip (45 drops/min) was continued. Fresh blank dog
blood (1-3 mL) was drawn through the catheter at 1, 2, 5, 10, 15, 20,
30, 45, 60, 120 min. The blood samples were centrifuged at 3000 rpm for


29
10 min and the supernatent plasma was analysed for buprenorphine by HPLC
separation and fluorimetric detection. The experiment was repeated
following the pumping of buprenorphine solution (using the same
concentration and flow rate as above) through the catheter for 3 h.
In-vivo study. In dog study #12, buprenorphine was infused (0.5236
mg/min for 177 min) into the left brachialis vein through the indwelling
plastic catheter (Intracath). Blood samples during infusion were
collected from the jugular vein and the contralateral brachialis vein.
Upon cessation of infusion, the catheter through which the drug was
infused into the left brachialis vein was washed with 25 mL of normal
saline. Post-infusion blood samples were collected from the left
brachialis vein (site of infusion) through the plastic catheter, as well
as from the jugular and contralateral brachialis veins.


IV BOLUS STUDIES
Chromatographic assays of Buprenorphine and its conjugate. The HPLC
43
assay methods developed for buprenorphine have been published.
Chromatograms of the HPLC-assayed buprenorphine are given in Fig. 2. The
acid hydrolyzable conjugate (M) assay (Fig. 3) by fluorimetric detection
(285 nm excitation, slit width 15 nm and 350 nm emission, slit width 10
nm) was equally sensitive, Table 1 shows the relevant statistics of
calibration curves. The standard errors of estimates of the
concentration about its regression on peak height ratio ranged iron +
0.5 to +_ 3 ng/ml.
Some additional linear regressions of concentrations (C, ng/ml) of
buprenorphine in plasma with their standard errors of the parameter
estimates in accordance with
C +_ SER = ( m + sm ) PHR + b + s^ Eq. 1
in the range 5-50 ng/ml were, C _+ 1.52 ng/ml = (61.19 _+ 1.84) PHR 1.11
+ 0.808, r = 0.9968; C + 1.52 ng/ml = (76.64 + 2.518) PHR 3.04 +
1.068, r = 0.9962; C + 1.3 ng/ml = (54.34 + 2.6) PHR 5.01 + 1.42, r =
0.9943; C + 0.38 ng/ml = (72.21 + 1.8) PHR 12.3 + 0.98, r = 0.9991. In
the buprenorphine concentration range of 50-100 ng/ml, C +_ 0.97 ng/ml =
(75.49 + 1.76) PHR 13.45 + 2.1, r = 0.999; C + 2.42 ng/ml = (75.48 +
2.43) PHR 21.6 + 2.71, r = 0.9959; C + 1.78 ng/ml = (67.96 + 2.9) PHR
+ 6.02 + 3.026, r = 0.9964; C + 0.64 ng/ml = (27.94 + 0.4) PHR + 17.1 +
0.85, r = 0.9995.
30


31
Figure 2. Representative chromatograms after assay of buprenorphine (1,
60 ng/ml) with internal standard (2, 100 ng/ml) from plasma (a) and
urine (b). (The blank plasma and urine chromatograms without drug are
given underneath). Chromatogram of mixture of 25 ,-yg/ml of
buprenorphine, 1, with its products 2 and 3 after acid degradation in 1
M HC1 for 3 min (c). (See also reference 43).


Figure 3. Representative chromatograms after HPLC separation followed by
fluorimetric detection of buprenorphine conjugate in plasma, urine and bile. Blank
chromatograms of biological fluids without the drug and the internal standard are
given underneath. In the chromatograms (a, b, and c) peak 3 corresponds to the
demethoxy analog of buprenorphine obtained after acid hydrolysis of buprenorphine
conjugate M. Buprenorphine conjugate produces the aglycone on acid hydrolysis
which further quantitatively rearranges into demethoxy analog (peak 3; See also
reference 43). The HPLC retention time for compound (peak) 3 is different from
buprenorphine. (See figure lc). Thus buprenorphine (peak 1) could be used as
internal standard for the conjugate assay, a) Demethoxy analog (3, 90 ng/ml) of
buprenorphine conjugate and internal standard (1, 100 ng/ml) from plasma obtained
after acid hydrolysis of plasma followed by HPLC separation, b) Demethoxy analog
(3, 80 ng/ml) of buprenorphine conjugate and internal standard (1, 100 ng/ml) from
urine obtained after acid hydrolysis, c) Demethoxy analog (3, 60 ng/ml) of
buprenorphine conjugate and internal standard (1, 100 ng/ml) from bile obtained
after acid hydrolysis and HPLC separation. In obtaining chromatograms a, b and c,
the mobile phase was 25:75 acetonitrile:acetate buffer (pH 3.75, 0.05M) plus
0.0004M tetrabutyl ammonium phosphate; flow rate 1.2 ml/min. All other
chromatographic conditions were the same as described under the subheading 'Liquid
Chromatographic procedures' in experimental section.


mm
u>
UJ
J1
~iii*iiiir
0 2 4 6 8
min
10


Table 1 Typical statistics of plasma, and urine calibration curves for Buprenorphine (1) and
conjugate (M)
Biological
Fluid
Range
ng/ml
a
sy,x
b
m
c
s
m
bd
e
%
f
n
r9
Plasma (1)
20-100
1.38
58.96
1.19
-18.18
2.69
7
0.999
20-90
2.83
49.13
2.16
1.21
2.57
8
0.994
20-70
0.83
74.48
1.22
-5.9
0.84
5
0.999
Urine (1)
20-90
1.71
53.65
1.56
-4.10
1.74
7
0.998
20-90
2.07
52.05
1.88
-1.80
2.21
5
0.998
30-100
1.84
63.51
1.19
6.21
1.92
7
0.998
Plasma (M)
5-50
0.65
82.07
1.78
2.94
0.5
6
0.999
50-100
1.36
54.57
1.55
15.0
1.71
6
0.998
10-100
2.7
58.65
1.50
1.54
1.38
13
0.996
Urine (M)
10-80
1.98
117.2
3.3
-2.2
1.3
9
0.997
10-40
1.51
62.37
3.5
-10.8
2.00
7
0.992
40-100
2.73
91.29
4.73
-32.61
5.42
7
0.993
a Standard error of estimate about regression of concentration (ng/ml) on peak height ratio,
k Slope. c Standard error of slope. d Intercept. e Standard error of intecept. ^ Number of
points. ^ Correlation coefficient. In buprenorphine calibration curves, demethoxy analog of
buprenorphine (compound 2, Scheme I) was used as internal standard. Buprenorphine was used as
internal standard in the assay of conjugate (M). Some additional calibration curve statistics
are given in the text.


35
In urine, examples of regression equations for buprenorphine in the
range 5-100 ng/ml were, C _+ 1.59 ng/ml = (68.9 +_ 1.11) PHR 13.93 +_
1.12, r = 0.9991; C + 0.89 ng/ml = (113 + 1.89) PHR 6.8 + 0.851, r =
0.9993; C + 2.02 ng/ml = (66.5 + 1.26) PHR 7.31 + 1.17, r = 0.9977.
Examples of regression equations for buprenorphine conjugate (M) in
plasma in the range 10-50 ng/ml were, C + 2 ng/ml = (57.02 _+ 2.13) PHR +
4.9 _+ 1.211, r = 0.9958; range 60-100 ng/ml; C +_ 1.12 ng/ml = (39.57 +_
1.247) PHR + 22.2 +_ 1.83, r = 0.9985; range 5-100 ng/ml, C +_ 1.4 ng/ml =
(73.8 j+ 0.99) PHR 2.46 +_ 0.8, r = 0.9991; range 10-90 ng/ml; C +_ 1.3
ng/ml = (50.14 + 0.8) PHR 1.51 + 0.92, r = 0.9991.
Examples of regression equations for buprenorphine conjugate (M) in
urine in the range 10-200 ng/ml were, C +_ 1.8 ng/ml = (82 _+ 0.621) PHR +
0.72 +_ 0.82, r = 0.9997; range 10-120 ng/ml, C + 2.6 ng/ml = (92.99 +_
2.4) PHR 27 + 2.5, r = 0.998; C + 1.81 ng/ml = (162 + 2.9) PAR 13.19
+_ 1.5, r = 0.9991, where PAR = peak area ratio; range 10-100 ng/ml, C +_
2 ng/ml = (66.5 _+ 1.26) PHR 7.31 +_ 1.17, r = 0.9977. An example of
regression equation for buprenorphine conjugate (M) in bile in the range
10-200 ng/ml was: C _+ 6 ng/ml = (102 _+ 2.7) PHR 0.53 +_ 2.63, r =
0.9956.
Twice the standard error of estimate of buprenorphine and the
metabolite concentrations (ng/ml) on peak height ratio ranged from 1-5
ng/ml (Table 1), indicative of the sensitivity of the fluorimetric assay
of buprenorphine and its metabolite in biological fluids.
Plasma Pharmacokinetics and Volumes of Distribution. The plasma
concentration-time profile of buprenorphine could be fitted to a sum of
three exponentials (Eq. 2, Figs. 4-9). There may not be an unique linear
sum of three exponentials Cp^ (estimated plasm concentration) that


Figure 4. Semilogarithmic plots of concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.4171 mg/kg dose in 22.85 kg dog A (Study #1, Table 2). In the bottom and middle
figures, the solid line represents the curve obtained by fitting the plasma data
to a sum of three exponentials in accordance with the equation (2):
Cp(ng/ml) = 986.3 e-0'6823 t + 491.5 e-0'02627 t
39.8 e'0-'00076 1
The middle inset is the continuation of the data and fitted curve for an extended
time scale up to 2000 min. The top inset represents the data fitted to a
4-compartment model in accordance with the equation:
Cp (ng/ml) = 1066 e
-0.77
t joo -0.0304
+ 488 e
t ^ .c -0.00426
+ 45.4 e
t
L -0.0003434 t
+ 22 e
Refer to the section "Validity of the terminal rate constant" for a discussion of
fitting of the data to 4-comartment model.


CGNC. NG/ML


Figure 5. Samilogarithmic plots of concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.6369 mg/kg dose in 17.6 kg dog B (Study #2, Table 2). The solid line represents
the curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
010 -0.2632 t i.r -7 -0.01731 t
818.1 e + 435.7 e
-0.000904 t
+ 54.33 e
The inset is a representation of the data and fitted curve for the initial period
of 800 min.


NI W
m
iiE nm*
I 1 i
nua i unz\ ud9
TJ/SN 'GNOO


Figure 6. Semilogarithmic plots of concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.2023 mg/kg dose 22.5 kg dog C (Study #4, Table 2). The solid line represents the
curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
= 2459 e
-0.1173
+ 259 e *0145 t + 31.37 e0-00103
t
The inset is the continuation of data for an extended time scale up to 1500 min.


3RD 5^in 3211 9D
MIN
CONO. NG/ML
i_j
~ n c: a
a a
Vf
mnrirj


Figure 7. Semilogarithmic plot of the concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
2.5632 mg/kg dose in 19.0 kg dog B (Study #3, Table 2). The solid line represents
the curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
= 3508 e
-0.4295 t
+ 1142 e
-0.0217
t
+ 31.2
-0.000463 t


\]ril¡Z U\)ZZ !Jfj91
co
NiW
un 11 uss
^ 1 1 h-
m
UUl
uun i
uuun i
CCNC NG/ML


Figure 8. Semilogarithmic plots of the concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.439 mg/kg dose in 24.2 kg dog C (Study #5, Table 2). The solid line represents
the curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
-me -0.562 t ^ _1Q -0.0114 t .c -0.00093 t
4075 e + 318 e + 45 e
The insets are the continuation of the data and the fitted curve for the extended
time scale up tp 3000 min.


280 <120 bBO nO
CCNC NG/ML
C3
o
g
£
s*


Figure 9. Semilogarithmic plots of the concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma ( O > Fluorescence
detection; Q Electrochemical detection) against time (min) for the 0.7766 mg/kg
dose in dog D (Study #6, Table 2). The solid line represents the curve obtained by
fitting the plasma data to a sum of three exponentials in accordance with the
equation (2):
Cp (ng/ml) = 2519 e
-0.2473
t A -0.012 t ^ OD -0.00158 t
+ 204 e + 38.6 e
The middle inset is the representation of the data and the fitted curve for the
initial 200 min. The top inset is the plot of the weighted residuals calculated in
accordance with the equation (3) against log fitted concentrations. See fig. 10
for details on the residual plots.


.yi-r
'I [ID 6DD 8[][]
2D
MIN
IDD


48
best fits the actual data Cp ; instead there may be several
exp
solutions with similar minimum sum of squares. A unique solution can be
obtained only if the drug transferred into other compartments or
transformed into metabolites were analysed in their respective
52 ...
compartments. The plasma data of buprenorphine administered
intravenously to 6 dogs were fitted by nonlinear regression to a sum of
three exponentials (In study #1, Dog A, the data were also fitted to a
53
4-compartment model; Fig. 4, top inset). The fitting was effected
54
with the computer program of Yamaoka et al. (See also appendix I),
where 1/Cp, the inverse of the plasma concentration was the weighting
factor (See appendix II for a discussion of different weighting
techniques). The validity of the triexponential equation,
QPcaic = P e1T + A e~a t + B e" 31 Eq. 2
was confirmed by demonstration that regressions of the various studies
of the weighted residuals
( ^exp ^calc ) / ^calc
Eq. 3
against log Cpca^c gave mean residuals £ slopes and intercepts,
55
which were not significantly different from zero (Fig. 10, Table 2).
The residuals were randomly distributed above and below the regression
line, indicating no bias in the fitting of the chosen model. (Fig. 10)
Outliers were defined as those experimental concentrations which had
residual values, 6, greater than 2 (Eq. 3) which corresponds to a
greater than 200% deviation from the presumed best fitted value. One
such outlier in dog B at 2.5632 mg/kg (Study #3) dose of buprenorphine
was not included in the nonlinear least square curve fitting technique


Figure 10. Representative examples of the plots of the weighted residuals against
log Cpcalc values. These weighted residuals were obtained from the equation (3):
6 ( ^exp ^calc ] 1 ^calc
The calculated plasma values were obtained from the triexponential equation 2
fitted to the plasma data of buprenorphine: a) 1.4171 mg/kg dose study in dog A,
Study #1; b) 1.6369 mg/kg dose study in dog B, Study #2; c) the plasma metabolite
(M) residuals obtained after IV administration of buprenorphine for the 1.2023
mg/kg dose study in dog C, Study #4; d) the plasma metabolite residuals obtained
after IV administration of buprenorphine for the 1.439 mg/kg dose study in dog C,
Study #5.
The observed means, slopes and intercepts of these weighted residuals are
given in Table 2. These parameters were not statistically significantly different
from zero as confirmed by t-test. The random distribution of the residuals above
and below the regression line indicated no bias in the fitting of the chosen
model. The validity of the triexponential curve fitting to the plasma data of the
metabolite is discussed in the text.


RESIDUALS RESIDUA:
RESIDUALS RESIDUALS


Table 2. Pharmacokinetics of intravenously administered bolus Buprenorphine (1) in dogs.
Parameter
Dog A
Dog B
Dog B
Dog C
Dog C
Dog D
Mean 1 SEM
Study No.
1
2
3
4
5
6
Dog No.
B364
B344
B344
W444
W444
W4123
Dosed mg
32.38
28.81
48.7
27.051
34.824
20.502
Weight, Kg.
22.85
17.6
19.0
22.5
24.2
26.4
Dose mg/kg
1.4171
1.6369
2.5632
1.2023
1.4390
0.7766
Parameters from plasma data
for 1
lO^Pf b
0.3046
0.2835
0.7204
0.9089
1.1700
1.2290
0.77 1 0.17
10 Af
1.5179
1.5123
2.345
0.959
0.9132
0.9972
1.37 1 0.22
106 Bf
1.2292
1.886
0.6402
1.16
1.2922
1.8827
1.35 1 0.19
10 TT C
6.823
2.362
4.295
1.173
5.616
2.473
3.79 1 0.88
9
(1.02)
(2.93)
(1.614)
(5.91)
(1.23)
(2.8)
(2.58 1 0.74)
10 a
2.627
1.731
2.166
1.45
1.14
1.19
1.72 1 0.24
A
(26.4)
(40)
(32)
(47.8)
(60.8)
(58.2)
(44.2 1 5.7)
104 0
7.565
9.041
4.627
10.3
9.248
15.81
9.43 1 1.51
(916)
(767)
(1498)
(673)
(749)
(440)
(841 1 146)
Residual plots
io2 d
1.33
1.49
3.6
6.1
2.38
2.88
Slope6 ^
-0.01510.04
0.00510.04
-0.01510.05
0.00410.05
-0.02410.05
0.03110.036
Intercept
0.04110.08
0.00510.09
0.06610.106
0.05310.11
0.07310.1
-0.02510.068
Clearances
Cl 9
tot
470
324
380
391
416
396
396 1 19
Cl- h
ren
2.69(5.1)
5.24(-8.2)
0.053(-1.6)
0.13(1.23)
1.453(-12.6)
1.91 1 0.96
Cl- 1
met
467.3
318.76
379.95
390.87
415.5
394.5 1 24
2.72
2.06
1.27
3.47
2.38 1 0.47
464.6
316.7
378.7
387.4
387 1 30
ciM 1
ren
1.94(11.8)
3.6(-18.5)
0.93(-9.0)
4.4(-30)
0.98(-9.2)
2.36 1 0.7


Table 2. Continued
Parameter Dog A Dog B Dog B Dog C Dog C Dog D Mean 1 SEM
% Recoveries of buprenorphine and M in urine
Uoo'*' /dosem 0.23
0.52
0.065
UooM /dosem 0.66
0.44
0.33
Volumes of
distribution of buprenorphine
(L)
v n
c
21.2
22
10.1
558
326
637
V P
0.705
0.166
0.339
m
Parameters
iron plasma data for conjugate
(M)
104 P b
0.1071
q
105 A
1.0232
0.9295
r
106 Bf
1.043
1.172
0.888
10 tt C
1.91
o
(3.63)
HT a
2.4
1.69

(29)
(41)

104 6
2.41
3.44
6.31
(2871)
(2016)
(1098)
Residual plots.
102 d
2.2
1.32
Slope6 £
0.000310.07
-0.01310.05

Intercept^
0.02U0.123
0.03810.09

0.09
0.13
0.21 1 0.08
0.79
0.13
0.47 1 0.12
9.84
7.85
7.42
13.1 1 2.73
379
450
251
434 1 59
2.054
0.816 1 0.4
0.6613
0.2087

0.3257 1 0.17
1.3486
0.9620

1.07 1 0.10
1.70
1.344

1.23 1 0.14
6.13
(1.13)
3.66
(19)
22.75
(305)
1.06
(6.5)
0.68
(104)
4.95
(1400)

3.03 1 1.57
(3.76 1 1.56)
2.1 1 0.63
(48 1 19)
4.3 1 0.9
(1846 1 391)r
3.58
-0.0410.05
0.110.09
2.9
0.00710.064
0.014310.144



a
Values correspond to buprenorphine base. Administered as HC1 salt, dissolved in 30 ml normal saline.
kpf, Af and values equal to P, A and B values expressed in fractions
A and B values were obtained from the nonlinear least square fitting of
of dose per ml of plasma. The P,
54
plasma data with 1/Cp weighting.
C 1
Unit for tt a and 3 values is min Parenthetical values correspond to
cVfean of the weighted residuals. (C = (Q?exp C-Pcapc )/ Q?cagc ). None
statistically significantly different from zero.
half-lives in min.
of the mean residuals were
0 f
' These are the slopes and intercepts of plots of 6 against log fitted cPca]c The parenthetical values
correspond to standard errors. Both slope and intercept were also not significantly different from zero,
indicating that the sum of three exponentials best fits the plasma data of buprenorphine and the conjugate.
^Ratio of the dose to the total area under the plasma concentration-time curve of buprenorphine, where the
calculated AUC = (P/tr ) + (A/a ) + (B/ 0 ) and that calculated from the trapezoidal rule (plus the quotient of
the last observed plasma level Cp(n) and 3) viere within 5-7% in all cases except in dog C at 1.439 mg/kg dose
level where the difference was 10%. Unit, ml/min.
^Estimates from the slopes of cumulative amounts of buprenorphine excreted ( zU ugs) renally against the area
under the plasma concentration time curve (AUC^) at that time in accordance with z U = Cl^^ AUC^
These values were calculated from the initial slopes observed (Figs. 26-28), and these ratios changed as pH of
the urine changed (Fig. 26). The values in parenthesis are ^U at AUC=0 from the best linear plots of data as
shown in Figs. 26-28. The plots of Au/At vs Cp^-md. (Plasma concentration at the mid point of urine
collection interval) were highly scattered in most studies (Fig. 37, see also text).
1C1 was calculated from the difference between total clearance Cl. and renal clearance, Cl of
met tot ren
buprenorphine.
^Cl^et Clg >M was calculated using equation 35.
k 1 1>M
Biliary clearance of M was calculated from the knowledge of Clme^ and (Cl t C1B ) values.
1 M
Renal clearance of metabolite, Clrgn was estimated in accordance with equation 30 (Figs. 32-34).


^Percent recoveries of buprenorphine and M in urine obtained from the quotient of the amount recovered in
urine and the total IV bolus dose of buprenorphine.
Volume of distribution of the central compartment (V ) was obtained using equation 10; P, A, and B are the
parameters from the plasma data for buprenorphine.
V, was calculated from Cl, / r .
d tot p
^Estimated using equation 35.
^Plasma conjugate profile could not be fitted to a sum of 3 exponentials, see Fig. 17. However, the terminal
rate constant was estimated frcm the semilogarithmic plots of the terminal plasma data against time. See also
text.
rOutlier dog C at 1.2023 mg/kq dose was not included in the calculation of average and SEM.
U1
.t.


55
54
(Appendix I). The outlier was included in all other pertinent
pharmacokinetic analyses and plots, such as excretion rate, sigma minus,
and clearance plots. There were no outliers in the other studies.
Since the triexponential equation 1 adequately described the
post-intravenous bolus injection data (Figs. 4-9), a 3-compartment body
model was the simplest pharmacokinetic model for the disposition of
buprenorphine in dogs. The elimination of buprenorphine could occur from
a central compartment (C), reversibly connected with shallow (S) and
53
deep (D) peripheral compartments (scheme II):
The equation which describes the time course of the IV bolus
administered drug in the central compartment Cp as a function of time t
53
as per scheme 2 is given by
cp = (X0/Vc) [ [ (k21 tt ) (k31 -TT )/(TT a ) (TT B) ] e-7r +
[ (k21 a ) ( a -k31 )/(ir-a)(a-g)] e at +
[(k21 B) (k31 -B )/(a-e ) ( TT B ) ] e"et ] Eq. 4
where Xq (k21 -tt ) (k^^ tt )/Vc(tt a) ( tt -B ) = P Eq. 5
X0 (k21 a ) (a -k31 ) /Vc ( tt a ) ( a -B ) = A Eq. 6
and
XQ (k21 B ) (k31 B ) /Vc (a -B ) ( ir -B ) = B Eq. 7


56
where X = dose, V = volume of distribution of the central
0 c
compartment.
Validity of the terminal rate constant. Proper estimation (Appendix
II) of the terminal rate constant (and half-life) depends upon a)
analytical sensitivity; b) number of terminal plasma concentration
values, the time interval between these values, and the number of
terminal half-lives over which the samples were collected; c) selection
of the compartment model; and d) proper weighting of the data. Upon
acute IV bolus administration of buprenorphine in dogs at the 0.7-2.6
mg/kg doses used, the plasma concentrations of buprenorphine were below
20 ng/ml at 1000 min (See Figs. 4-9). Thus the available analytical
sensitivity of 5 ng/ml did not permit accurate estimation of the
terminal half-life. For example, at the 2.5632 mg/kg (Study #3) IV bolus
dose of buprenorphine in dog C, the estimated terminal rate constant
obtained from a semilogarithmic plot of the terminal phase plasma data
against time (n=12) was 1.7 X 10 4 (half-life = 4040 min) +_ 0.70 X
-4 -1
10 (SE) min Thus the range that would include the 95% confidence
limits for this rate constant would be 1.48 X 10 ^ (half-life = 47000
min) to 3.3 X 10 4 (half-life = 2111 min) min 1 (See Table 3).
The terminal half-life significantly depends upon the number of
compartments assumed. Consider dog A (Study #1). Fitting of the data
weighted by the inverse of the concentration to a 3-compartment model
-4 -1
gave a terminal rate constant of 7.6 X 10 min (half-life = 916
min). When the same data were fitted to a 4-compartment model, the
terminal rate constant estimated by using the computer program (Appendix
I) was 3.78 X 10-4 +0.984 X 104 (SE) min1 (half-life = 1840 min,
n=3; The 95% confidence limits; + smt, where t=12.71; 433 min to time


Table 3. Statistics of the calculated terminal rate constants.
Parameter
Dog A
Dog B
Dog B
Dog C
Dog C
Dog D
Study No.
1
2
3
4
5
6
Dog No.
B364
B344
B344
W444
W444
W4123
a
n
10
10
12
13
10
10
Intercept (ng/ml)b 39.8
54.3
31.2
31.0
45.6
34.3
104 8 min 1 C
5.504
8.36
1.715
9.965
8.77
14.2
tl/2 111111
1259
829
4040
695
791
489
104 s of 8 ^
m
0.526
0.965
0.704
1.76
1.0
1.81
95% Confidence
limits for
the terminal
half-life.6
Upper limit
1615
1129
47000
1136
1074
693
Lower limit
1032
654
2111
501
623
378
95% Confidence
limits for total body clearance
(ml/min)
Lower limit
287
247
22
301
329
334
Upper limit
408
362
313
442
457
446
Number of plasma points.
K Q
' Terminal phase intercepts and rate constants were calculated from the regressions of
the logarithm of plasma concentrations against time.
d Standard errors, s values of the terminal rate constants,e were calculated from the
m # j a
statistics of the regressions of the logarithm of the terminal plasma concentrations
against time (also see reference 59).
0 f
' 95% confidence intervals for the terminal rate constants were calculated from t-table
at a =0.05 level of significance for (n-2) degrees of freedom (see also reference 59).
Cl. was estimated using equations 8 and 9.


58
infinity? Fig. 4, top inset). This large range for the confidence limits
is attributable to the estimation of a terminal rate constant from few
(n=3) plasma values. The estimated terminal rate constants from the
semilogarithmic plots of the terminal plasma cocentrations against time,
their respective standard errors, and 95% confidence limits are given in
Table 3.
The terminal half-life estimated for studies 1,2,4,5 and 6 have
relatively less error compared to study 3 (Table 3). Yet, estimation of
the true terminal half-life depends on the number of terminal plasma
values, the time interval between these values and the number of
terminal half-lives over which the samples were collected. The terminal
plasma data in studies 1,2,4,5, and 6 were not representative of the
true terminal phase since the plasma data needed to accurately estimate
the terminal half-life were below the analytical sensitivity and were
not available.
Total body clearance. The total body clearance Cl^t of a dose,
53
XQ, can be calculated from
Cl
tot
- VAUCoo
Eq. 8
where AUC^ = area under the plasma concentration-time curve up to time
infinity. AUCt up to the last observed plasma point, Cp^ can be
calculated by the trapezoidal rule. The area from the last plasma
sampling time to infinity can be estimated from Cpn / 8 where g is the
terminal rate constant. Also, AUC^ can be explicitly calculated by
integrating equation 2 between time 0 to oo, i.e.,
AUC^ = (P/tt ) + (A/a ) + (B/0 )
Eq. 9


59
The parameters of the above equation were obtained by fitting the
buprenorphine plasma data of dogs 1-6 to equation 2 using the computer
54
program of Yamaoka et. al. (Appendix I). The values of the parameters
of equation 9 are given in the legends of Figs. 4-9 or can be calculated
from the normalized values given in Table 2. The calculated percent
contribution of the term B/3 of the terminal area to the total area in
studies 1-6 were 72, 68, 53, 44, 58 and 47 respectively. This
demonstrates the significance of 3 in the estimation of AUC^ and
consequently the total body clearance derived from this value (Equation
8). Thus, uncertainties in the estimates of 6 can lead to uncertainties
in the estimates of AUC and total body clearance. In the IV bolus
oo
studies (#1-6), the contributions of the terms P/ir and A/a were only
about half of the total area under the plasma concentration time curve.
When equation 2 was used to fit the plasma data of buprenorphine
54
(Yamaoka et. al., Appendix I), the P, ir A, anda parameters were
estimated from the data in high range (50-5000 ng/ml) of plasma
concentrations. These data are held in greater confidence than the
estimates obtained from the low values of the terminal phase. Thus, if
the error in AUC estimation is primarily due to the error in the
oo
estimation of 6 the 95% confidence limits for AUC and the derived
oo
total body clearance (Equation 8) can be estimated from the terminal
rate constant, 3 and its standard error.
To estimate the error in AUCqq (Equation 9), the parameters P, tt ,
A, anda were obtained by fitting the complete plasma data of
buprenorphine to the tri-exponential equation 2 (using the computer
54
program of Yamaoka et. al. Appendix I). However, the parameters B
and 3 were obtained from the regressions of the semilogarithmic plots of


60
the terminal phase plasma data against time. The standard error value,
sm, of the terminal slope was multiplied by the t-value (obtained from
t table for a=0.025 level of significance, two tailed for (n-2) degree
of freedom; where n is the number of terminal plasma points). The
resulting g+_ t.sm permitted the estimation of the the upper and lower
95% confidence limits for AUC calculated in accordance with equation
oo
9. The upper and lower limits for the CltQt were derived from the upper
and lower limits of AUC in accordance with equation 8. These calculated
total body clearances and the respective 95% confidence limits are
reported in Table 3 for the 6 TV bolus studies in the dogs.
Volumes of distribution of buprenorphine. The plasma concentration
53
of a drug in the central compartment at time zero is given by
CpQ = P+A+B = XQ / V, Eq. 10
when an IV bolus is administered into a 3-compartment body model. Vc is
the apparent volume of distribution of the central compartment. The
average Vc was 13.1 +_ 2.73 (SEM) L (Table 2). This value exceeds the
56 57
volume of blood (1.8 L) and the extracellular water (4.8-6.6 L) in
dogs. This indicates rapid sequestration of the drug in the
extracellular space upon bolus administration.
If the clearing organ is in the central compartment (Scheme II),
53
then the clearance from the central compartment, Clc, is given by
Cl = V k.n Eq. 11
c c 10 ^
If the drug is solely eliminated from the body through the central
compartment, the Clc is the total body clearance Cltot at any time
53
during the post-distributive phase in accordance with the equation,


61
Eq. 12
where is the overall apparent volume of distribution of the
equilibrated fluids of the body.
Thus,
Eq. 13
and
Eq. 14
If 3 or AUC have large errors, then the estimates of have large
errors. Thus the calculated distribution volumes in accordance with
equation 13 based on the best computer fit (Appendix I) of the plasma
data to tri-exponential equation are suspect. However, the calculated
Vj values in accordance with equation 13 (reported in Table 2) averaged
57
434 L, in excess of total body water in dogs (11-15 L) and does
indicate a high degree of sequestration by body tissues.
Dose-independent pharmacokinetics of buprenorphine. The
pharmacokinetic parameters of a drug are dose-independent when all
distribution and elimination processes are first order with respect to
compartmental concentrations. The rate constants must be invariant at
highly varying administered doses and there must be no saturable first
pass metabolism. To establish whether or not there is dose-independency,
the drug is administered to the same animal at different doses. If the
plasma levels divided by the respective doses are superimposable, then
dose independency can be postulated.


62
Unfortunately dose independent pharmacokinetics of buprenorphine in
dogs could not be studied at highly varying intravenous bolus (1-100
fold) dose levels. The lower limit of detecton (5 ng/ml) of
buprenorphine in plasma necessitated a certain minimal IV bolus dose to
adequately quantify terminal plasma concentrations. The fact that the
doses of buprenorphine in excess of 1.2-2.6 mg/kg would exhibit
significant side effects demanded an upper limit to the TV bolus dose
that could be administered.
At least two or more of the following toxic effects were observed
during a pharmacokinetic study: Defecation and muscle relaxation,
labored and forceful breathing for about 1 h after bolus dose, profuse
salivation continuing up to 4 h. The side effects observed following
rapid IV bolus injection of buprenorphine could be attributed to the
peak plasma levels (2000-5000 ng/ml, Figs. 4-9) reached immediately. All
five dogs exhibited drowsiness throughout the experiment, and the state
of general depression (characterized by lack of food intake, minimal
physical motion, lack of response to stimulus such as clapping of hands
and prolonged sleeping up to 12 h at a stretch) continued up to 1-5 days
depending upon the dose of buprenorphine. Higher doses produced longer
duration of these side effects.
To minimize the peak plasma concentrations of buprenorphine and the
associated side effects encountered upon TV bolus administration, and
yet to obtain adequate plasma concentration values in the terminal
phase, the higher doses of buprenorphine, 4.69, 3.85 and 3.741 mg/kg
dose in dog B, D and F (Study #7, 8 and 11), respectively, were
administered by constant rate infusion over a period of 3 h. However,
superimposition to validate dose independency is inoperative if the drug


63
is administered by two different modes (such as IV bolus and infusion).
If a relationship can be established between the plasma levels of a drug
administered by IV bolus and by IV infusion, super imposition can be
challenged by the use of the transformed IV infusion data.
Superimposition of this transformed high dose IV infusion data on low
58
dose IV bolus data was effected by the outlined procedure that
follows.
Analysis and transformation of IV infusion data. The post-infusion
data were fitted to a sum of either two (Study #7 and 8) or three (Study
53
#11) exponentials in accordance with the equation,
P' e Tr *t-T^ + A' e-a *t-T* + B' e- ^ *t-T) Eq. 15
where T is the time at which infusion was stopped and t is the time
after initiating the infusion. The first term in the above expression is
set equal to zero when the post-infusion data are fitted to a
2-compartment body model. The relationship between P and P' of equations
. 53
2 and 15 respectively is
P = P'T tt / (l-e-7T T ) Eq. 16
Similarly, the relationships between A, A' and B, B' are
A = A'T a/(l-e-a T ) Eq. 17
B = B'TS / (l-e~ BT ) Eq. 18
The calculated P, A, and B values were used to generate the Q? .
values of equation 2. These could be the calculated plasma
concentrations if the same dose was administered by IV bolus. These
estimated Cpca^c concentrations obtained from the infusion studies were


64
divided by the total infused dose (mg/kg) and superimposed on the
experimental values of buprenorphine (divided by the IV bolus dose in
mg/kg) obtained after low dose bolus injection in the same dog. In dog B
at three dose levels (1.64, 2.56, 4.69 mg/kg, Study #2,3 and 7), dog C
at two dose levels (1.2, 1.44 mg/kg, Study #4 and 5), dog D at two dose
levels (0.78 and 3.85 mg/kg, Study #6 and 8) and dog F at two dose
levels (0.754 and 3.741 mg/kg, Study #17 and 11) there were no apparent
dose dependencies as demonstrated by the tests of superimposition
59
(statistically confirmed by nonparametric Kruskal-Wallis test applied
to the dose-normalised plasma concentration data. See Figs. 11-14 and
the legends, also refer to Appendix III). The parameters of equations
15-18 for TV infusion studies in dogs B, D and F are given in Table 5.
Plasma pharmacokinetics of the derived metabolite. The metabolite
(M) assayed in plasma was the acid hydrolyzable conjugate of
43
buprenorphine (1). This buprenophine conjugate (M) upon acid
hydrolysis presumably generated the aglycone which quantitatively
rearranged to demethoxybuprenorphine (3). Rather than assaying the
buprenorphine conjugate or the aglycone directly, this rearranged
product was assayed by HPLC separation and florimetric detection. Other
metabolites such as norbuprenorphine or its conjugates observed in
38 39
man were not detectable in dog plasma with the assay sensitivity
of 5 ng/ml. The conjugate concentration in plasma was highest at the
initial sampling time, and decreased at a rate similar to that of the
parent compound (Fig. 15). The metabolite profile in 4 IV bolus studies
could be fitted by a triexponential equation (Eq. 2). The fitting was
effected by nonlinear least square regression by using the computer
54
program (Appendix I) where the metabolite concentrations in plasma


Figure 11. Semilogarithmic plots of the concentrations of buprenorphine (1) in
plasma divided by the dose in mg/kg (cone./dose) plotted against time (min) for
the 1.6369 mg/kg (Study #2, O )> 2.5632 mg/kg (Study #3, ), and 4.69 mg/kg
(Study #7, on the presumption of IV bolus administration) doses of
buprenorphine in dog B. The middle inset is the plot of the data for the first 200
min after administration, and the top inset is the continuation of the data on an
extended time scale. The data for the highest dose, 4.69 mg/kg (Study #7, (\>) was
derived from the IV infusion study in which buprenorphine was infused at the rate
of 0.5058 mg/min for 165 min. The superimposition of the infusion data on the IV
bolus data was effected by the procedure described in this chapter under the
subheading "Dose-independent pharmacokinetics of buprenorphine". The points ((\,)
for the infusion study were calculated on the premise of IV bolus administration
of 4.69 mg/kg dose of buprenorphine in accordance with the equation 2. The
parameters of equation 2 were obtained through equations 15-18. The nonparametric
rank sum test (Kruskal-Wallis test, Appendix III; see also reference 59) was used
to test the hypothesis (H') that the dose-normalised plasma concentrations at the
above three dose levels were drawn from identical distributions. The critical
value of chi-square with a =0.05 and df=2 is 5.99. The observed H' (-7) is less
than 5.99. Therefore it can be concluded that there is no difference among the
three groups.


2nn ma 6un snn mm
MIN
CONC./DOSE
ng/ml (mg/kg)~^
cz
a
O
99


Figure 12. Semilogarithmic plots of the concentrations (ng/ml) of buprenorphine in
plasma plotted against time (min) for the 0.7766 mg/kg (Study #6 O) dose in dog
D. The 3.847 mg/kg dose (Study #8 Q) was administered by IV infusion over a
period of 171 min. Infusion rate of buprenorphine as base = 0.5084 mg/min. The
superimposition of infusion data on IV bolus data was effected by the procedure
described in this chapter under the subheading "Dose-independent pharmacokinetics
of buprenorphine". The points () represent quotient of concentrations divided by
dose that were calculated on the premise of IV bolus administration of 3.847 mg/kg
dose of buprenorphine in accordance with equation 2. The parameters of equation 2
were obtained through equations 15-18. These calculated points were multiplited by
0.2019 = 0.7766/3.847 to challenge superimposition. The nonparametric rank sum
test (Kruskal-Wallis test, Appendix III; see also reference 59) was used to test
the hypothesis (H') that the dose-normalised plasma concentrations at the above
two dose levels were drawn from identical distributions. The critical value of
chi-square with a =0.05 and df=l is 3.84. The observed H' (=0.37) is less than
3.84. Therefore it can be concluded that there is no difference among the two
groups.


CONG/.DOSE
ng/ml (mgAg)_'1'
CD CD
CD ZD CD
89
I


Figure 13. Semilogarithmic plots of the concentrations of buprenorphine (1) in
plasma divided by the dose (mg/kg) plotted against time (min) for the 1.2023 mg/kg
(Study #4, O) and 1.439 mg/kg (Study #5,0) dose of buprenorphine dog C. The
inset is the continuation of data on an extended time scale up to 1500 min. The
nonparametric rank sum test (Kruskal-Wallis test, Appendix III; see also reference
59) was used to test the hypothesis (H') that the dose-normalised plasma
concentrations at the above two dose levels were drawn from identical
distributions. The critical value of chi-square with a =0.05 and df=l is 3.84. The
observed H' (=0.78) is less than 3.84. Therefore it can be concluded that there is
no difference among these two groups.


NI W
D8 Ut>9 U8l> U38 U9I
CONC./DOSE


Figure 14. Semilogarithmic plots of the concentrations (ng/ml) of buprenorphine
(1) in plasma plotted against time (min) for the 0.7542 mg/kg
(O) IV bolus dose of buprenorphine in the bile cannulated dog F (morphine-
buprenorphine interaction study, #17). The 3.7408 mg/kg dose (Study #11, ) was
administered by IV infusion over a period of 162 min. Infusion rate of
buprenorphine as base = 0.5588 mg/min. The superimposition of infusion data on IV
bolus data was effected by the prodedure described in this chapter under the
subheading "Dose-independent pharmacokinetics of buprenorphine". The points ()
represent quotient of the concentrations divided by dose that were calculated on
the premise of IV bolus administration of 3.7408 mg/kg dose of buprenorphine in
accordance with the equation 2. The parameters of the equation 2 were obtained
through equations 15-18. These calculated points were multiplied by 0.2016 =
0.7542/3.7408 to challenge superimposition. The nonparametric rank sum test
(Kruskal-Wallis test, Appendix III; see also reference 59) was used to test the
hypothesis (H') that the dose-normalised plasma concentrations at the above two
dose levels were drawn from identical distributions. The critical value of
chi-square with a =0.05 and df=l is 3.84. The observed H' (=0.053) is less than
3.84. Therefore it can be concluded that there is no difference among the two
groups.


n^/mi uu^/kg) J
MIN
2I6
288G
38D


Figure 15. Semilogarithmic plots of the concentrations of buprenorphine, 1,
(O) and metabolite, M, () in plasma plotted against tme for a) 1.4171 mg/kg
dose of buprenorphine in dog A, Study #1; b) 1.6369 mg/kg dose of buprenorphine in
dog B, Study #2; c) 1.2023 mg/kg dose of buprenorphine in dog C, Study #4; d)
1.439 mg/kg dose of buprenorphine in dog C, Study #5. The solid lines represent
curves fitted to the plasma data of buprenorphine and M in accordance with
equation 2.


nun i
CONC. NS'tlL CONC. KG/ML
NIK
tJDLi 1195 IJZt' 1)02 DM


75
were weighted by their inverse. The validity of triexponential equation
2 was confirmed by demonstration that the regressions in various studies
(Fig. 10) of the weighted residuals (Eq. 3) against log Mpca^c
(estimated metabolite concentations) gave mean residuals slopes
and intercepts, all of which were not statistically significantly
different from zero (Table 2). The plasma concentration-time profiles of
metabolite in the IV bolus studies (1-5) are given in Figs. 16-20.
Maximum plasma concentration of the metabolite was observed at the
initial sampling time (about 1 min). Continued sampling gave
monotonically declining metabolite concentrations similar to the decay
of the parent compound. The parallel decays of buprenorphine and its
conjugate concentrations (Fig. 15) in plasma during the initial
distributive phase indicate that the rate determining step in the plasma
decay of the conjugate was its formation. During the terminal
elimination phase, the rate determining step in the plasma decay of
buprenorphine and its conjugate was the slow return of buprenorphine
from deep tissues to the central compartment where it could be
metabolized. This is the classical 'flip-flop' pharmacokinetics for the
. 53
conjugate.


Figure 16. Semilogarithmic plots of the plasm concentrations of metabolite (M)
against time (min) for the 1.4171 mg/kg IV bolus dose of buprenorphine in 22.85 kg
dog A, Study #1. The solid line represents the curve obtained by fitting the
plasm data to a sum of two exponentials in accordance with the equation:
Cp(ng/ml) = 331 e-0*024 + 33.8 e_0*000241 t
The inset is the continuation of the data for the extended time scale up to 3000
min.


MIN


Figure 17. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) against time (min) for the 1.6369 mg/kg IV bolus dose of
buprenorphine in 17.6 kg dog B, Study #2. The solid line represents the curve
obtained by fitting the plasma data of M to a sum of three exponentials in
accordance with equation (2):
Cp (ng/ml) = 308 e '191 t + 267.7 e_0'0169 t
+ 33.8 e
-0.000344 t
The inset is the representation of the data and the fitted curve for the initial
period of 750 min.


NI W
IJJI1C HU^ JI19I JJ9
1U/SN '9N03


Figure 18. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) against time (min) for the 1.2023 mg/kg IV bolus dose of
buprenorphine (1) in 22.5 kg dog C, Study #4. The solid line represents the curve
obtained by fitting the plasma data of M to a sum of three exponentials in
accordance with the equation (2):
~ -0.602 t _C1 -0.0346 t Q -0.00191 t
Cp (ng/ml) = 1781 e + 361 e + 40.8 e
The inset is a continuation of the data and the fitted curve for an extended time
scale up tp 1500 min. The terminal half-life was estimated to be 363 min. This
value had much error due to limited analytical sensitivity, low dose and lack of
sufficient number of terminal phase plasma points.


cosa. NG'Hi


Figure 19. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) in against time (min) for the 2.5623 mg/kg IV bolus dose of
buprenorphine (1) in the 19.0 kg dog B, Study #3. The inset represents data and
the straight line fitted to the terminal phase in accordance with the
monoexponential equation,
Cp (ng/ml) = 43.25 e
-0.000631
t


CCNC-, NG'ML
MTN


Figure 20. Semi logarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) against time (min) for the 1.439 mg/kg dose of buprenorphine in
24.2 kg dog C, Study #5. The solid line represents the curve obtained by fitting
the plasma data of M to a sum of three exponentials in accordance with the
equation (2):
_ -0.106 t A -,oc -0.0068 t Mr q -0.000495 t
Cp (ng/ml) = 727 e + 335 e + 46.8 e
The inset is a continuation of the data and the fitted curve on an extended time
scale up tp 2750 min.


N1W
Li 095 WZV D9£ UN
1W/SN CNOCJ


URINARY EXCRETION OF BUPRENORPHINE
Sigma minus plots. If it can assumed that buprenorphine is solely
eliminated from the central compartment, the urinary excretion rate of
intact drug can be defined as
dU/dt = ku Xc Eq. 19
where is the urinary excretion rate constant, and Xc is the amount
of drug in the central compartment at time t. Integrating equation 19
. 53
between 0 to U (time; 0 to t) results in
I U -E U = P"e~ 1711 + A"e-at + B"e Eq. 20
oo
vhere
= P k V / ir
Eq.
21
u c
= A k V / a
Eq.
22
u c
= B k V / 6
u c
Eq.
23
The values of P, A and B are same as in Eqs. 5,6 and 7, respectively if
constant renal clearance is presumed. Thus a plot of the logarithm of
the amount of unchanged drug remaining to be excreted versus time (sigma
minus plot) gives a straight line with a terminal slope equal to
- g/2.303, i.e., the same terminal slope obtained from a semilogarithmic
plot of plasma concentration (Cp) versus time.
Representative examples of the sigma minus plots for the urinary
excretion of buprenorphine are given in Fig. 21. For dog A (Study #1,
86


Figure 21. Sard logarithmic plots of the amounts of the unchanged buprenorpine (1)
remaining to be excreted in urine versus time (sigma minus plot) in accordance
with equation 20. a) Semilogarithmic fitting of the initial urine data up to 100
min for the 1.4171 mg/kg IV bolus dose of buprenorphine in dog A, Study #1. An
apparent rate constant of 0.0176/min (half-life = 39 min) was obtained, b) Fitting
of the sigma minus plot of buprenorphine in urine of dog B, Study #2 at 1.6369
mg/kg dose of buprenorphine to a sum of two exponentials. The estimated hybrid
rate constants were 0.026/min (half-life = 27 min) and 0.00176/min (half-life =
390 min), c) Sigma minus plot of urinary excretion of buprenorphine for the 1.2023
mg/kg dose of buprenorphine in dog C, Study #4. The apparent terminal phase rate
constant for the monoexponential fitting was 0.0017/min (half-life = 400 min), d)
The fitted sigma minus plot of buprenorphine in urine of dog C at 1.439 mg/kg IV
bolus dose of buprenorphine, Study #5, to a sum of two exponentials. The estimated
apparent rate constants were 0.00695/min (half-life = 100 min) and 0.000287/min
(half-life = 2412 min) respectively.


GUI* GUI! I Win '1(1(1 QUO 12(111 IGlill 21111(1
MIH mu
88
on i


89
Fig. 21a), semilogarithmic fitting of the initial data was linear only
up to 100 min. The estimated apparent rate constant was 0.0176 min ^
(half-life = 39 min). This corresponded to the second distributional
half-life (26 min) obtained for buprenorphine from the plasma data
(Table 2). The sigma minus plot of buprenorphine in urine of dog B (Fig.
21b) at 1.6369 mg/kg (Study #2) dose showed curvature, and could be
fitted to a sum of two exponentials. The resulting hybrid rate constants
were 0.026 (half-life = 27 min) and 0.00176 (half-life = 390 min) min
The first half-life corresponded to the second distributional half-life
of buprenorphine (39 min, Table 2) for this dog. For dog C (Fig. 21c) at
1.2023 mg/kg dose (Study #4, Table 2), the sigma minus plot of urinary
data gave an apparent terminal phase rate constant of 0.0017 min ^
(half-life = 400 min). This corresponded with the terminal half-life of
buprenorphine (673 min) obtained from the plasma data. For the same dog
at 1.439 mg/kg dose (Study #5), sigma minus plot (Fig. 21d) showed
curvature, and could be fitted to a sum of two exponentials, and the
respective apparent rate constants were 0.00695 (half-life = 100 min)
and 0.000287 (half-life = 2412 min) min The first half-life obtained
from the urine data corresponded with the second distributional
half-life (61 min, Table 2) obtained for buprenorphine from plasma data.
The sigma minus plots for the urinary excretion of buprenorphine in
other dogs showed great scattering and reasonable estimates of the
apparent rate constants were not possible.
The half-lives obtained from the various sigma minus plots shown in
Fig. 21 for the urinary excretion of buprenorphine reasonably
approximated the first and second distributional half-lives of
buprenorphine in plasma. Since a minor fraction of the the dose was


90
excreted unchanged in urine (<1%) and the limit of detection of
buprenorphine was 5 ng/ml, the terminal half-life of buprenorphine in
dogs could not be readily estimated from the urinary data.
Sigma minus plots for the conjugates (M) are given in Figs. 22,23.
For dog A (Study #1), the curve could be unexpectedly and for no obvious
reason, fitted best by a simple linear equation to indicate a constant
rate of renal elimination even with decreasing plasma concentrations of
the conjugate. The excretion rate was approximately 330 ng/min,
independent of concentration of metabolite in the central compartment
(Fig. 22a). For dog B at 1.6369 mg/kg dose (Study #2) of buprenorphine
(Table 2), the sigma minus plot gave an apparent rate constant of 0.0032
min ^ (half-life = 215 min, Fig. 22b). For dog C at 1.2023 mg/kg dose
(Study #4), (Fig. 22c) an apparent rate constant of 0.0022 min 1
(half-life = 312 min) was obtained, which corresponded well with the
terminal phase half-life obtained for M from plasma data (305 min, Table
2). For dog B at 2.5632 mg/kg dose (Study #3), the sigma minus plot
(Fig. 22d) showed curvature and could be fitted to a sum of two
exponentials, and the apparent rate constants were 0.023 min ^
(half-life = 30 min) and 0.000567 min ^ (half-life = 1220 min)
respectively, where the second half-life corresponded with the terminal
half-life obtained from the plasma data of M in this dog (Table 2,
half-life = 1098 min). The sigma minus plot for M in dog C at 1.439
mg/kg dose (Study #5) showed curvature (Fig. 23) and could be fitted to
a sum of two exponentials, the apparent rate constants being 0.018 min
1 (half-life = 39 min) and 0.000812 min 1 (half-life = 853 min).
In dog C at 1.2023 mg/kg (Study #4) IV bolus dose of buprenorphine,
the terminal half-life of buprenorphine was estimated as 673 min (Table


Figure 22. Semi1ogarithmic plots of the amounts of metabolite (M) remaining to be
excreted in urine versus time (sigma minus plot) following IV bolus administration
of buprenorphine (1) in accordance with equation 20. a) The excretion data of M in
urine up to 700 min could be fitted to a simple linear equation in dog A, Study #1
at 1.4171 mg/kg dose of buprenorphine. The excretion rate was estimated to be 330
ng/min. b) Sigma minus plot of M in urine of dog B, Study #2 following 1.6369
mg/kg dose of buprenorphine, resulting in a estimated apparent rate constant
0.0032/min (half-life = 215 min), c) Sigma minus plot of M in urine for the 1.2023
mg/kg dose of buprenorphine in dog C, Study #4. The apparent rate constant was
estimated tas 0.0022/min (half-life = 312 min), d) Sigma minus plot of the urinary
excretion of M for the 2.5632 mg/kg IV bolus dose of buprenorphine in dog B, Study
#3. The da tata were fitted to a sum of two exponentials in accordance with
equation 20. The estimate apparent rate constants were 0.023/min (half-lige = 30
min) and 0.000567/min (half-life = 1220 min) respectively.


NII4
Ultfl Il'ltE \)Zr,Z 11891 IH9
cm N1W
cri ntra uw not u?c ii9i
at ,92 -*92 SSlf 92 *92
o
-
O'-.
o-.
o-.
o
o
O,
q3b-
--um
1 DUD I
HIM
ssrf 92 -*92 nz nz


Figure 23. Semi 1 ogarithmic plot of the amount of the metabolite (M) remaining to
be excreted versus time (sigma minus plot) following 1.439 mg/kg dose of
buprenorphine (1) in dog C, Study #5. The data was fitted to a sum of two
exponentials. The estimated apparent rate constants were 0.0018/min (half-life =
39 min) and 0.000812/min (half-life = 853 min) respectively.


94
SGf ni -nz
4Il 6[IL¡ 2f¡[i Gtil 21¡[ii
MTH


Full Text

PAGE 1

3+$50$&2.,1(7,&6 2) %835(1253+,1( ,1 '2*6 %\ 9 5$9, &+$1'5$1 $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

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

PAGE 3

7$%/( 2) &217(176 $&.12:/('*(0(176 $%675$&7 LY ,1752'8&7,21 (;3(5,0(17$/ ,9 %2/86 678',(6 85,1$5< (;&5(7,21 2) %835(1253+,1( ,9 ,1)86,21 678',(6 3+$50$&2.,1(7,&6 2) 7+( ,9 $'0,1,67(5(' 0(7$%2/,7( 6800$5< $1' &21&/86,216 $33(1',; 352*5$0 08/7, $33(1',; ,, ),77,1* 2) '$7$ 72 (48$7,216 $33(1',; ,,, .586.$/:$//,6 7(67 $33(1',; ,9 7$%/(6 2) 5$: '$7$ */266$5< 2) 7(506 5()(5(1&(6 %,2*5$3+,&$/ 6.(7&+ LLL

PAGE 4

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

PAGE 5

FRQVWDQWV RI WKH ,9 LQIXVLRQ VWXGLHV DYHUDJHG B K ZLWK DQ DYHUDJHG WRWDO ERG\ FOHDUDQFH RI B POPLQ 7KH DSSUHQW YROXPHV RI GLVWULEXWLRQ RI EXSUHQRUSKLQH UHIHUHQFHG WR WKH WRWDO SODVPD FRQFHQWUDWLRQ ZHUH / 9 FHQWUDO FRPSDUWPHQW YROXPHf DQG / 9M WRWDO ERG\ YROXPHf LQGLFDWLYH RI D KLJKO\ ERXQG VHTXHVWHUHG RU OLSRSKLOLF GUXJ 8QFKDQJHG EXSUHQRUSKLQH LV LQVLJQLILFDQWO\ UHQDOO\ b RI WKH GRVHf DQG ELOLDU\ bf H[FUHWHG 7KH PDMRU URXWH RI EXSUHQRUSKLQH GLVSRVLWLRQ LV E\ KHSDWLF FRQMXJDWLRQ WR JOXFXURQLGH ZKLFK LV HOLPLQDWHG LQWR WKH ELOH DERXW bf ZLWK RQO\ VPDOO DPRXQWV DSSHDULQJ LQ XULQH b DV PHWDEROLWHf 0LQRU PHWDEROLWHV H[FUHWHG LQ WKH ELOH DFFRXQWHG IRU DERXW b RI WKH DGPLQLVWHUHG GRVH 'LUHFW ,9 DGPLQLVWUDWLRQ RI WKH PHWDEROLWH JDYH D WHUPLQDO KDOIOLIH RI K 8QOLNH LQWUDYHQRXVO\ DGPLQLVWHUHG PRUSKLQH JOXFXURQLGH ZKLFK ZDV QRW H[FUHWHG LQ WKH ELOH PRUH WKDQ b RI WKH V\VWHPLFDOO\ FLUFXODWLQJ PHWDEROLWH ZDV H[FUHWHG LQ ELOH DQG RQO\ b LQ XULQH 7KH RUDO ELRDYDLODELOLW\ HVWLPDWHG IURP WKH DUHDV XQGHU WKH EXSUHQRUSKLQH SODVPD FRQFHQWUDWLRQWLPH FXUYH IROORZLQJ 79 DQG RUDO DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH LQ WKH GRJV ZDV b ,Q D ELOH FDQQXODWHG GRJ LQWUDGXRGHQDOO\ DGPLQLVWHUHG PHWDEROLWH GHPRQVWUDWHG b HQWHURKHSDWLF UHFLUFXODWLRQ RI WKH FRQMXJDWH 7KHUH ZHUH QR DSSDUHQW FRUUHODWLRQV RI WKH EXSUHQRUSKLQH WLPH FRXUVH ZLWK FDUGLRYDVFXODU SDUDPHWHUV VXFK DV KHDUW UDWH (&* DQG EORRG SUHVVXUH 0LRWLF HIIHFW ZDV VLJQLILFDQW 5HVSLUDWRU\ GHSUHVVLRQ ZDV REVHUYHG GXULQJ WKH ILUVW K DIWHU ,9 EROXV LQMHFWLRQ EXW QRW GXULQJ WKH LQIXVLRQ VWXGLHV Y

PAGE 6

,1752'8&7,21 %XSUHQRUSKLQH f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f LQ PDQ ZDV VORZHU WKDQ ZLWK PRUSKLQH EXW WKH GXUDWLRQ RI VXFK HIIHFWV ZDV ORQJHU DERXW KRXUVf WKDQ ZLWK PRUSKLQH $OVR WKH DQDOJHVLF SRWHQF\ RI EXSUHQRUSKLQH ZDV DERXW WLPHV WKDW RI PRUSKLQH RQ D SHU XQLW ZHLJKW EDVLVf 7KHUDSHXWLF 7ULDOV ,Q D FRPSDUDWLYH VWXG\ RI WKH WUHDWPHQW RI FKURQLF SDLQ RI PDOLJQDQW RULJLQ E\ LQWUDPXVFXODUO\ DGPLQLVWHUHG EXSUHQRUSKLQH DQG PRUSKLQH SDWLHQWV UHFHLYHG EXSUHQRUSKLQH PJf DQG PRUSKLQH PJf LQ D GRXEOHEOLQG VLQJOHGRVH ZLWKLQSDWLHQW VWXG\ 7KHUH ZHUH QR

PAGE 7

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f RI EXSUHQRUSKLQH DQG PRUSKLQH JLYHQ LQWUDWKHFDOO\ J LQ FRQVFLRXV UDWV ZHUH FRPSDUHG $IWHU LQWUDWKHFDO LQMHFWLRQ WKH SHDN PLQf DQWLQRFLFHSWLYH SRWHQFLHV RI EXSUHQRUSKLQH RU PRUSKLQH ZHUH J VLPLODU 7KH DQDOJHVLF SURILOHV RI EXSUHQRUSKLQH DQG PRUSKLQH PJ DQG PJ UHVSHFWLYHO\f ZHUH FRPSDUHG LQ D GRXEOHEOLQG QRQFURVVRYHU PXOWLSOH GRVH VWXG\ ,0 DGPLQLVWUDWLRQf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

PAGE 8

WZHQW\ SDWLHQWV XQGHUJRLQJ RUWKRSHGLF RSHUDWLRQV ZHUH GLYLGHG LQWR IRXU JURXSV RI SDWLHQWV HDFK 7KH IRXU WUHDWPHQWV ZHUH RU PJ RI EXSUHQRUSKLQH FRPELQHG ZLWK SDUDFHWDPRO PJ RU SDUDFHWDPRO PJf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f ZDV VWXGLHG Df ZLWK QRUPDO FRQFHQWUDWLRQV RI GRSDPLQH QRUDGUHQDOLQH

PAGE 9

K\GUR[\WU\SWDPLQH HWF DQG Ef ZLWK ORZHU FRQFHQWUDWLRQV RI GRSDPLQH DQG QRUDGUHQDOLQH LQ UDW EUDLQ IROORZLQJ WKH WUHDWPHQW ZLWK DOSKDPHWK\O SDUDW\URVLQH DOSKD0S7f ZKLFK LV D LQKLELWRU RI FDWHFKRODPLQH V\QWKHVLV 0RUSKLQH DQG KDORSHULGRO ZHUH XVHG DV UHIHUHQFH DJHQWV %XSUHQRUSKLQH LQFUHDVHG WKH DOSKD0S7 LQGXFHG UDWH RI GRSDPLQH GHSOHWLRQ EXW GLG QRW GHSOHWH QRUHSLQHSKULQH 6LPLODU UHVXOWV ZHUH REWDLQHG ZLWK D KLJKHU GRVH PJNJf RI PRUSKLQH EXW LW LQFUHDVHG WKH DOSKD0S7 LQGXFHG GHSOHWLRQ RI QRUHSLQHSKULQH $SSDUHQWO\ VLPLODU HIIHFWV RI EXSUHQRUSKLQH DQG KDORSHULGRO RQ GRSDPLQHUJLF QHXURWUDQVPLVVLRQ ZHUH GLVWLQJXLVKHG E\ SUHWUHDWLQJ WKH UDWV ZLWK QDOR[RQH ZKLFK DQWDJRQL]HG WKH HIIHFW RI EXSUHQRUSKLQH DQG SUHYHQWHG GRSDPLQH GHSOHWLRQf 7KHVH QHXURFKHPLFDO UHVXOWV ZHUH FODLPHG WR VXSSRUW WKH YLHZ WKDW RQH VLWH RI DFWLRQ RI EXSUHQRUSKLQH LV RQ RSLDWH UHFHSWRUV ORFDWHG RQ WKH GRSDPLQHUJLF QHXURQVA ,Q D GRXEOHEOLQG FRPSDULVRQ EHWZHHQ IHQWDQ\O DQG EXSUHQRUSKLQH LQ VXSSOHPHQWHG QLWURXV R[LGH DQDOJHVLD EXSUHQRUSKLQH RU IHQWDQ\O DQG PJ UHVSHFWLYHO\ DGPLQLVWHUHG ,9f ZHUH XVHG DV VXSSOHPHQWV LQ SDWLHQWV XQGHUJRLQJ PDMRU DEGRPLQDO VXUJHU\ ,QLWLDOO\ ERWK QDUFRWLFV DSSHDUHG WR VXSSUHVV WDFK\FDUGLD DQG LQFUHDVH DUWHULDO SUHVVXUH LQ UHVSRQVH WR VXUJHU\ EXW b RI WKH SDWLHQWV ZKR UHFHLYHG IHQWDQ\O HYHQWXDOO\ UHJXLUHG D IXUWKHU VXSSOHPHQW RI KDORWKDQH bf EXW QR SDWLHQW ZKR UHFHLYHG EXSUHQRUSKLQH UHTXLUHG KDORWKDQH 5HFRYHU\ IURP DQDOJHVLD ZDV VLPLODU LQ ERWK JURXSV EXW WKH GXUDWLRQ RI DQDOJHVLD DIWHU WKH RSHUDWLRQ ZDV VLJQLILFDQWO\ JUHDWHU IRU EXSUHQRUSKLQH Kf WKDQ IHQWDQ\O KfA ,Q D GRXEOHEOLQG UDQGRPL]HG QRQFURVVRYHU WULDO SDWLHQWV UHFHLYHG HLWKHU PRUSKLQH PJf RU EXSUHQRUSKLQH PJf E\ UHJXODU ,0

PAGE 10

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

PAGE 11

GUXJV 7KH TXDOLW\ RI DQDOJHVLD VXEMHFWLYHO\ DVVHVVHG ZDV WKH VDPH ZLWK ERWK GUXJV XVLQJ WKLV PHWKRG RI DGPLQLVWUDWLRQ 7KHVH DXWKRUV FODLP WKDW EXSUHQRUSKLQH LV D SRZHUIXO DQDOJHVLF DJHQW WKDW PD\ EH JLYHQ LQWUDYHQRXVO\ SURYLGHG WKDW LWV ORZ SRWHQWLDO IRU DEXVH LV VXEVWDQWLDWHG ,Q D VPDOOHU QXPEHU RI SDWLHQWV ZLWK FKURQLF SDLQ XVXDOO\ GXH WR FDQFHU VXEOLQJXDOO\ JLYHQ EXSUHQRUSKLQH XS WR PJ KRXUO\f SURYLGHG DGHTXDWH SDLQ UHOLHI IRU SHULRGV XS WR VHYHUDO PRQWKV EXW VLGH HIIHFWV XVXDOO\ QDXVHD DQG YRPLWLQJf UHTXLUHG GLVFRQWLQXDWLRQ RI WUHDWPHQW LQ DERXW WR RI WKH DPEXODWRU\ SDWLHQWV )ROORZLQJ DQHVWKHVLD ZLWK IHQWDQ\O LQ SDWLHQWV EXSUHQRUSKLQH XVXDOO\ WR PJ 79f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f EXSUHQRUSKLQH PJf RU SK\VLRORJLFDO VDOLQH 1R V\VWHPLF DQDOJHVLFV ZHUH JLYHQ EHIRUH GXULQJ RU DIWHU VXUJHU\ DQG DOO WKH SDWLHQWV KDG RSHUDWLRQV RQ WKH ORZHU H[WUHPLWLHV XQGHU H[WUDGXUDO DQDOJHVLD OLJQRFDLQH RU EXSLYDFDLQHf 8SRQ DGPLQLVWUDWLRQ RI WKH WHVW GUXJ DV VRRQ DV SDLQ

PAGE 12

RFFXUHG LQ WKH SRVWRSHUDWLYH SHULRG D ORQJ GXUDWLRQ RI DFWLRQ DQG D PDUNHG DQDOJHVLF HIIHFW ZDV REVHUYHG ZLWK ORIHQWDQLO $ VKRUWHU GXUDWLRQ RI DFWLRQ DQG OHVV SDLQ VXSSUHVVLRQ RFFXUHG ZLWK EXSUHQRUSKLQH DQG D UDWKHU PDUNHG SODFHER HIIHFW ZDV VHHQ ZLWK VDOLQH 7KH RQO\ VLGH HIIHFW QRWLFHG ZDV GURZVLQHVV LQ SDWLHQWV LQ WKH ORIHQWDQLO JURXS DQG LQ SDWLHQWV LQ WKH EXSUHQRUSKLQH JURXS ,Q D UDQGRPL]HG GRXEOHEOLQG WULDO FRPSDULQJ DQDOJHVLD SURGXFHG E\ FRPELQDWLRQV RI GURSHULGRO ZLWK HLWKHU EXSUHQRUSKLQH RU PRUSKLQH EXSUHQRUSKLQH ZDV FODLPHG WR EH DV VDWLVIDFWRU\ DV PRUSKLQH WR SURGXFH DQDOJHVLD GXULQJ PDMRU VXUJHU\ LQ SDWLHQWV ZLWK QR GLIIHUHQFH LQ WKH LQFLGHQFH RI XQWRZDUG VLGH HIIHFWV (SLGXUDO EXSUHQRUSKLQH ZDV LQYHVWLJDWHG DV D SRVWRSHUDWLYH DQDOJHVLF LQ D UDQGRPL]HG GRXEOHEOLQG VWXG\ RI SDWLHQWV JLYHQ LQWUDRSHUDWLYH HSLGXUDO DQDOJHVLD ZLWK b PHSLYDFDLQH RU b EXSLYDFDLQH IRU RUWKRSHGLF VXUJHU\ RI WKH ORZHU H[WUHPLW\ $W WKH HQG RI WKH VXUJHU\ WKH SDWLHQWV ZHUH JLYHQ HSLGXUDOO\ LQ PO VDOLQH HLWKHU PJ RI EXSUHQRUSKLQH Q f RU PJ Q f $ FRQWURO JURXS UHFHLYHG QR HSLGXUDO LQMHFWLRQ Q f 7KH DERYH JURXSV UHFHLYHG b PHSLYDFDLQH DV LQWUDRSHUDWLYH DQHVWKHWLF $ IRXUWK JURXS Q f UHFHLYHG PJ EXSUHQRUSKLQH LQ PO VDOLQH DIWHU LQWUDRSHUDWLYH XVH RI b EXSLYDFDLQH 7KH SDWLHQWV UDWHG SRVWRSHUDWLYH SDLQ $QDOJHVLD DIWHU PJ RI EXSUHQRUSKLQH ZDV VXSHULRU WR WKDW DIWHU VDOLQH LQMHFWLRQ DQG PJ EXSUHQRUSKLQH ZDV VXSHULRU WR ERWK VDOLQH LQMHFWLRQ DQG WR PJ RI EXSUHQRUSKLQH XQWLO WK KRXU $QDOJHVLD DIWHU EXSLYDFDLQH IROORZHG E\ PJ RI EXSUHQRUSKLQH ZDV QRW VLJQLILFDQWO\ GLIIHUHQW WKDQ DQDOJHVLD VHHQ DIWHU PHSLYDFDLQH IROORZHG E\ PJ RI EXSUHQRUSKLQH 7KHVH UHVXOWV DUH FRPSDUDEOH WR WKRVH UHSRUWHG HOVHZKHUH

PAGE 13

5HVSLUDWRU\ HIIHFWV 7KH UHVSLUDWRU\ GHSUHVVDQW DFWLYLW\ VXFK DV GHFUHDVHG UHVSLUDWRU\ UDWH LQFUHDVHG DUWHULDO 3 &&/ DQG GHFUHDVHG FO = DUWHULDO 3 ff RI VLQJOH HTXLDQDOJHVLF GRVHV RI EXSUHQRUSKLQH DQG FO = PRUSKLQH DSSHDU WR EH VLPLODU LQ UDWV DQG UDEELWV n n 7KH H[WHQW RI EXSUHQRUSKLQHLQGXFHG UHVSLUDWRU\ GHSUHVVLRQ DJDLQVW GRVH SODWHDXHG LQ DQLPDOV ZKHUHDV VXFK DQ HIIHFW ZDV QRW FOHDUO\ GHPRQVWUDWHG LQ PDQ ZKLFK VKRZHG GRVHUHODWHG UHVSLUDWRU\ GHSUHVVLRQ ZLWKLQ WKH WKHUDSHXWLF GRVH UDQJH PJ WR PJf 7KH WLPH WR UHDFK SHDN UHVSLUDWRU\ GHSUHVVLRQ LQ PDQ ZDV VORZHU DIWHU LQWUDPXVFXODU EXSUHQRUSKLQH WKDQ DIWHU PRUSKLQH K YV Kf DQG WKH GXUDWLRQ RI VXFK DQ HIIHFW ZDV ORQJHU 7KHUH DSSHDUV WR EH QR FRPSOHWHO\ UHOLDEOH VSHFLILF DQWDJRQLVW IRU EXSUHQRUSKLQHLQGXFHG UHVSLUDWRU\ GHSUHVVLRQ VLQFH HYHQ KLJK GRVHV RI QDOR[RQH SURGXFHG RQO\ SDUWLDO UHYHUVDO +FZHYHU WKH UHVSLUDWRU\ VWLPXODQW GUXJ GR[DSUDP KDV UHYHUVHG UHVSLUDWRU\ GHSUHVVLRQ GXH WR EXSUHQRUSKLQH LQ D IHZ KHDOWK\ YROXQWHHUV DQG LQ D IHZ SDWLHQWV &DUGLRYDVFXODU HIIHFWV +HPRG\QDPLF FKDQJHV LQ KHDOWK\ YROXQWHHUV DIWHU ,0 WR PJf VXEOLQJXDO WR PJf RU RUDO WR QJf GRVHV RI EXSUHQRUSKLQH LQFOXGH GRVH UHODWHG UHGXFWLRQV LQ KHDUW UDWH XS WR bf DQG VPDOO GHFUHDVHV LQ V\VWROLF EORRG SUHVVXUH DERXW bf 7KHVH UHVXOWV DUH FRPSDUDEOH WR WKH FDUGLRYDVFXODU HIIHFWV RI PRUSKLQH 6LPLODU HIIHFWV RFFXUHG LQ DQHVWKHWL]HG SDWLHQWV XQGHUJRLQJ VXUJHU\ DQG LQ D IHZ SDWLHQWV ZLWK P\RFDUGLDO LQIDUFWLRQV +RZHYHU LQ WKH ODWWHU JURXS WKH KHDUW UDWH ZDV IRXQG WR EH UHODWLYHO\ XQSHUWXUEHG $GGLFWLRQ SRWHQWLDO RI EXSUHQRUSKLQH %XSUHQRUSKLQH DSSHDUHG WR KDYH D ORZHU DGGLFWLRQ SRWHQWLDO WKDQ WKH RSLRLG DJRQLVW SHQWD]RFLQH LQ

PAGE 14

DQLPDOV +RZHYHU WKH H[WHQW WR ZKLFK VXFK UHVXOWV FDQ EH H[WUDSRODWHG WR PDQ ZDV XQFHUWDLQ n ,Q D VLQJOHGRVH DGGLFWLRQ VWXG\ LQ YROXQWHHUV KLJK PJ GDLO\f LQWUDPXVFXODU GRVHV RI EXSUHQRUSKLQH DGPLQLVWHUHG XS WR WR PRQWKV SURGXFHG D VORZO\ HPHUJLQJ ZLWKGUDZDO V\QGURPH RQ DEVWLQHQFH IURP WKH GUXJ n 7KRXJK WKH UHVXOWV ZHUH LQGLFDWLYH RI OHVVHU DGGLFWLRQ SRWHQWLDO FRPSDUHG WR PRUSKLQH GHILQLWLYH VWDWHPHQWV DERXW DGGLFWLRQ FDQQRW EH PDGH XQWLO LW KDV EHHQ PRUH ZLGHO\ XVHG LQ SDWLHQWV ZLWK FKURQLF SDLQ ZLWK UHSHDWHG GRVHV RYHU DQ H[WHQGHG SHULRG RI WLPHA 5HFHSWRU ELQGLQJ VWXGLHV 5HFHSWRU ELQGLQJ VWXGLHV ZHUH XQGHUWDNHQ WR HOXFLGDWH WKH RSLRLG ELQGLQJ FKDUDFWHULVWLFV RI IHQWDQ\O DQG EXSUHQRUSKLQH DQG WR LQYHVWLJDWH GLIIHUHQFHV EHWZHHQ WKHP %XSUHQRUSKLQH VKRZHG VORZ UHFHSWRU HTXLOLEUDWLRQ PLQf EXW ZLWK KLJK DIILQLW\ WR PXOWLSOH VLWHV 7KH GLVVRFLDWLRQ ZDV FODLPHG WR EH VORZ KDOIOLIH PLQf DQG LQFRPSOHWH b ELQGLQJ DIWHU Kf 7KLV FRQWUDVWHG ZLWK WKH UHFHSWRU ELQGLQJ RI IHQWDQ\O ZKLFK DFKLHYHG UDSLG HTXLOLEULXP ZLWKLQ PLQf DQG GLVVRFLDWHG HTXDOO\ UDSLGO\ KDOIOLIH PLQf DQG FRPSOHWHO\ b E\ Kf 8VLQJ FRPSHWLWLYH GLVSODFHPHQW VWXGLHV LW ZDV FODLPHG WKDW EXSUHQRUSKLQH GLVSODFHPHQW RI IHQWDQ\O ZDV FRQFHQWUDWLRQ DQG WLPH GHSHQGHQW RYHU WKH UDQJHV HTXLPRODU EXSUHQRUSKLQH DQG IHQWDQ\O FRQFHQWUDWLRQV QPROOLWHUf HQFRXQWHUHG LQ FOLQLFDO XVH +RZHYHU EXSUHQRUSKLQH ELQGLQJ ZDV GLVSODFHG ZLWK RQO\ KLJK FRQFHQWUDWLRQV RI RWKHU RSLRLGV %LQGLQJ RI EXSUHQRUSKLQH WR WKH UDW IRUHEUDLQ WHOHQFHSKHORQ GLHQFHSKHORQ DQG PHVHQFHSKHORQf ZDV FODLPHG WR EH VWHUHRVSHFLILF VDWXUDEOH DQG KDG KLJK DIILQLW\ 0D[LPXP ELQGLQJ %PD[f ZDV UHDFKHG E\ PLQ DQG GLVVRFLDWLRQ IURP WKH UHFHSWRU ZDV VORZ 7KH UHJLRQDO

PAGE 15

GLVWULEXWLRQ RI EXSUHQRUSKLQH ELQGLQJ VLWHV LQ WKH UDW EUDLQ ZDV FODLPHG WR EH TXDOLWDWLYHO\ VLPLODU WR WKH GLVWULEXWLRQ RI QDOR[RQH DQG GLK\GURPRUSKLQH ELQGLQJ VLWHV 7KH %PD[ IRU WKLV UHFHSWRU ELQGLQJ RI EXSUHQRUSKGQH ZDV DERXW WLPHV WKDW IRU WKH PXRSLDWH UHFHSWRU GUXJV DQG WKUHH WLPHV WKH IRU WKH GHOWDRSLDWH UHFHSWRU OLJDQGV VXFK DV HQNHSKDOLQVf %XSUHQRUSKLQH ZDV DOVR IRXQG WR EH YHU\ SRWHQW LQ GLVSODFLQJ QDOR[RQH GLK\GURPRUSKLQH DQG PHWHQNHSKDOLQ 6LQFH PX UHFHSWRUV ELQG ZLWK H[RJHQRXV RSLRLGV VXFK DV PRUSKLQHf DQG GHOWD UHFHSWRUV ELQG ZLWK HQGRJHQRXV RSLRLGV VXFK DV HQNHSKDOLQVf WKH DERYH ILQGLQJV VXJJHVW WKDW EXSUHQRUSKLQH ELQGV WR ERWK PX DQG GHOWDUHFHSWRUVA 6LGH HIIHFWV 0RGHUDWH WR PDUNHG GURZVLQHVV KDV EHHQ UHSRUWHG LQ DERXW b RI WKH SDWLHQWV XS WR b LQ VRPH VWXGLHVf EXW DOO VXFK SDWLHQWV ZHUH IRXQG WR EH HDVLO\ DURXVDEOH XSRQ VWLPXODWLRQ n f 1DXVHD DQGRU YRPLWLQJ RFFXUUHG LQ b RI WKH SDWLHQWV 2WKHU PLQRU VLGH HIIHFWV HJ GL]]LQHVV VZHDWLQJ KHDGDFKH RU FRQIXVLRQf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

PAGE 16

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f WKDQ E\ ,0 LQMHFWLRQ PLQf 'UXJ FRQFHQWUDWLRQV ZHUH VWDWHG WR EH GHWHFWDEOH LQ EORRG IRU ORQJHU WLPHV DIWHU RUDO Kf WKDQ ,0 Kf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

PAGE 17

DYHUDJH WLPH RI DERXW PLQ LQ ERWK WKH PJ DQG PJ JURXSV UDQJH PLQ DIWHU WKH LQLWLDO K SHULRGf 7KH SODVPD GUXJ FRQFHQWUDWLRQ LQ WKH PJ JURXS ZHUH DSSUR[LPDWHO\ WZLFH WKDW LQ WKH PJ JURXS 7KH DEVROXWH ELRDYDLODELOLW\ ZDV HVWLPDWHG WR EH DERXW b RI WKH ,9 URXWH IRU ERWK JURXSV E\ WKH UDWLR RI WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ YHUVXV WLPH $8&f IRU VXEOLQJXDO DQG 79 DGPLQLVWUDWLRQ 8SWDNH RI EXSUHQRUSKLQH IURP WKH VXEOLQJXDO VLWH ZDV FODLPHG WR EH FRPSOHWH E\ K DIWHU WKH GRVH ZDV JLYHQ ,Q WKLV VWXG\ FURVVUHDFWLYLW\ EHWZHHQ EXSUHQRUSKLQH DQG LWV PHWDEROLWHV ZDV QRW UXOHG RXW 7ZR PRGHV RI DGPLQLVWUDWLRQ 79 IROORZHG E\ VXEFXWDQHRXVf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f LQ WKH DQHVWKHWL]HG VWDWH FRPSDUHG WR WKH XQDQHVWKHWL]HG VWDWH POPLQf %LRDYDLODELOLW\ ZDV FODLPHG WR EH WKH VDPH IRU ERWK 79 DQG ,0 DGPLQLVWHUHG GUXJ 7KH SHDN SODVPD OHYHOV ZHUH VHHQ DW PLQ DQG LQ PLQ UHVSHFWLYHO\ IRU ,9 DQG ,0 GRVLQJ DIWHU WKH VHFRQG GRVLQJ &URVV UHDFWLYLW\ DPRQJ EXSUHQRUSKLQH DQG LWV PHWDEROLWHV ZDV QRW UXOHG RXW LQ WKLV VWXG\ 7KH VHQVLWLYLW\ DQG OLPLWV RI GHWHFWLRQ IRU EXSUHQRUSKLQH ZHUH QRW JLYHQ 7KXV WKH WHUPLQDO SODVPD EXSUHQRUSKLQH FRQFHQWUDWLRQV DW OHVV WKDQ QJPO DUH TXHVWLRQDEOH

PAGE 18

3URFHGXUHV IRU REWDLQLQJ YDULRXV SKDUPDFRNLQHWLF SDUDPHWHUV ZHUH QRW JLYHQ 3ODVPD FRQFHQWUDWLRQV ZHUH FRUUHODWHG ZLWK FOLQLFDO HIIHFWV DIWHU D VLQJOH ,9 GRVH RI EXSUHQRUSKLQH RU PJf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nrn 7KH SUHPLVH RI GUXJ FRQMXJDWLRQ LQ WKH JXW ZDOO ZDV VXSSRUWHG E\ VWXGLHV ZLWK UDW JXW SUHSDUDWLRQV n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f WR WKH ELOH GXFW FDQQXODWHG UDWV RYHU b RI WKH DGPLQLVWHUHG GUXJ ZDV H[FUHWHG LQ WKH ELOH ZLWKLQ K DIWHU GRVLQJ 7KH PDMRU PHWDEROLWH LQ WKH ELOH ZDV

PAGE 19

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f 'HFD\ KDOIOLIH RI WKH GUXJ IURP LWV KLJK DIILQLW\ ELQGLQJ VLWHV LQ EUDLQ ZHUH DQG K UHVSHFWLYHO\ )DW DQG OXQJ KDG KLJKHU FRQFHQWUDWLRQV WKDQ RWKHU WLVVXHV RU SODVPD 1R PHWEROLWHV RI WKH GUXJ ZHUH GHWHFWHG LQ EUDLQ 8QPHWDEROL]HG GUXJ H[FUHWHG LQ WKH XULQH DQG IHFHV RQH ZHHN DIWHU 79 LQMHFWLRQ ZHUH DQG b RI WKH GRVH UHVSHFWLYHO\ DQG b RI WKH GRVH ZDV DFFRXQWHG IRU LQ ZHHN 8ULQDU\ PHWDEROLWHV bf ZHUH FRQMXJDWHG EXSUHQRUSKLQH QRUEXSUHQRUSKLQH IUHH FRQMXJDWHG

PAGE 20

f WHQWDWLYH GHVPHWK\O QRUEXSUHQRUSKLQH IUHH FRQMXJDWHG f 3HDN SODVPD FRQFHQWUDWLRQ RI EXSUHQRUSKLQH RFFXUHG LQ ZHHNV DIWHU VF LPSODQWDWLRQ RI D ORQJDFWLQJ UDGLRODEHOOHG EXSUHQRUSKLQH PJf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f LQ SODVPDA $Q LQWUDPXVFXODU GRVH RI \ JNJ JDYH EORRG SHDN FRQFHQWUDWLRQ VLPLODU WR WKDW RI D \JNJ RUDO GRVH ,Q PRQNH\V XQSXEOLVKHG GDWD ZHUH FLWHG WR VXSSRUW WKH VWDWHPHQWV WKDW SHDN EORRG FRQFHQWUDWLRQV RI UDGLRODEHOOHG GUXJ ZHUH UHDFKHG DW PLQ K DQG EHWZHHQ K UHVSHFWLYHO\ IRU ,0 RUDO DQG VXEOLQJXDO DGPLQLVWUDWLRQnn $OVR LW ZDV VWDWHG WKDW LQ WZR KHDOWK\ YROXQWHHUV SHDN EORRG FRQFHQWUDWLRQV ZHUH UHDFKHG UDSLGO\ DIWHU ,0 GRVLQJ \JNJf RI UDGLRODEHOOHG EXSUHQRUSKLQH IROORZHG E\ D UDSLG GHFOLQH 3HDN FRQFHQWUDWLRQV ZHUH UHDFKHG VORZO\ DW K DIWHU WKH RUDO DGPLQLVWUDWLRQ RI \JNJ RI WKH

PAGE 21

GUXJ IROORZHG E\ D ELH[SRQHQWLDO GHFOLQH RI FRQFHQWUDWLRQ &RQFHQWUDWLRQV DV ORZ DV WR QJPO ZHUH FODLPHG WR EH GHWHFWHG E\ D VSHFLILF UDGLRLPPXQRDVVD\ WHFKQLTXH DIWHU ,9 DQG ,0 DGPLQLVWUDWLRQV PJf ,Q KXPDQ YROXQWHHUV D GRVH RI PJ SURGXFHG SHDN FRQFHQWUDWLRQV RI QJPO DW DERXW K DIWHU RUDO DGPLQLVWUDWLRQ 5HIHUHQFHV RI VWXGLHV VXSSRUWLQJ WKHVH GDWD ZHUH QRW FLWHG 6\VWHPLF ELRDYDLODELOLW\ RI EXSUHQRUSKLQH ZDV VWXGLHG LQ IHPDOH UDWV IROORZLQJ VLQJOHGRVHV MDJNJf DGPLQLVWHUHG E\ VL[ GLIIHUHQW URXWHV 5HODWLYH WR WKH b ELRDYDLODELOLW\ IURP WKH LQWUDDUWHULDO URXWH WKH PHDQ ELRDYDLODELOLWLHV ZHUH ,9 b LQWUDUHFWDO b LQWUDKHSDWRSRUWD b VXEOLQJXDO b DQG LQWUDGXRGHQDO b $8& DQDO\VLV RI EXSUHQRUSKLQH FRQFHQWUDWLRQV LQ EORRG VKRZHG WKH UHODWLYH IUDFWLRQV RI WKH GUXJ H[FUHWHG ILUVW SDVVf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

PAGE 22

3URWHLQ ELQGLQJ ,W ZDV UHSRUWHG ZLWKRXW GRFXPHQWDWLRQnn WKDW EXSUHQRUSKLQH ZDV KLJKO\ ERXQG bf WR DOSKD DQG EHWDJOREXOLQ IUDFWLRQV RI KXPDQ SODVPD SURWHLQV LQ WKH FRQFHQWUDWLRQ UDQJH QJPO 7KH IUDFWLRQ RI GUXJ ERXQG WR GRJ SODVPD SURWHLQ ZDV GHWHUPLQHG E\ PHDVXULQJ WKH GUXJ FRQFHQWUDWLRQ LQ SODVPD ZDWHU DIWHU XOWUDFHQWULIXJDWLRQ 7KH IUDFWLRQ ERXQG ZDV HVWLPDWHG WR EH %LQGLQJ RI EXSUHQRUSKLQH WR GRJ SODVPD SURWHLQV ZDV DOVR GHWHUPLQHG E\ SDUWLWLRQLQJ WKH GUXJ LQWR UHG EORRG FHOOV 7KH HVWLPDWLRQ LV EDVHG XSRQ WKH SUHVXPSWLRQ RI HVWDEOLVKHG HTXLOLEULD EHWZHHQ GUXJ LQ SODVPD ZDWHU UHG EORRG FHOOV DQG SODVPD SURWHLQV %\ WKLV WHFKQLTXH WKH IUDFWLRQ RI EXSUHQRUKLQH ERXQG WR SODVPD SURWHLQV ZDV HVWLPDWHG DV 7KLV UHODWLYHO\ KLJK SODVPD SURWHLQ ELQGLQJ IRU WKH OLSRSKLOLF EXSUHQRUSKLQH FRQWUDVWV WR WKH b SODVPD SURWHLQ ELQGLQJ RI PRUSKLQH QDOR[RQH DQG QDOWUH[RQH 5%& 3DUWLWLRQ 3DUWLWLRQ VWXGLHV KDYH VKRZQ WKDW UHG EORRG FHOOSODVPD ZDWHU SDUWLWLRQ FRHIILFLHQW RI EXSUHQRUSKLQH ZDV 7KLV LV LQ FRQWUDVW WR IRU PRUSKLQH IRU QDOWUH[RQH DQG IRU QDOR[RQH 3K\VLFDO SURSHUWLHV )OXRUHVFHQFH H[FLWDWLRQ QP HPLVVLRQ QPf RI EXSUHQRUSKLQH SURYLGHG H[FHOOHQW GHWHFWLRQ IRU +3/& DVVD\ LQ ELRORJLFDO IOXLGV ZLWK D QJPO VHQVLWLYLW\ %XSUHQRUSKLQH VROYRO\VLV ZDV VSHFLILFDFLG DQG VSHFLILFEDVH FDWDO\VHG ,W \LHOGHG D VWRLFKLRPHWULF ILQDO DFLG GHJUDGDWLRQ SURGXFW f D IOXRUHVFHQW GHWHFWDEOH UHDUUDQJHG GHPHWKR[\ DQDORJXH RI EXSUHQRUSKLQH $ONDOLQH K\GURO\VLV SURGXFHG QR IOXRUHVFHQFH SURGXFWV $FLG K\GURO\VLV DOVR SURGXFHG D IOXRUHVFHQWGHWHFWDEOH WUDQVLHQW GHK\GUR LQWHUPHGLDWH f WKDW ZDV DOVR FRPSOHWHO\ WUDQVIRUPHG LQWR WKH GHPHWKR[\ DQDORJXH 6FKHPH

PAGE 23

0HWK\O PLJUDWLRQ AFK @  n I &+M @  6FKHPH $FLG +\GURO\VLV RI %XSUHQRUSKLQH

PAGE 24

,f &RPSRXQG ZDV DQ H[FHOOHQW ELRDVVD\ LQWHUQDO VWDQGDUG %XSUHQRUKLQH ZDV VKRZQ WR EH KLJKO\ VWDEOH DW QHXWUDO S+ YDOXHV HYHQ DW HOHYDWHG WHPSHUDWXUHV (VWLPDWHG EXSUHQRUSKLQH S.Dn YDOXHV ZHUH DQG IRU WKH DPPRQLXP DQG SKHQROLF JURXSV UHVSHFWLYHO\ 7KH LQWULQVLF DTXHRXV VROXELOLW\ RI EXSUHQRUKLQH ZDV B XJPO DW & $VVD\ PHWKRGV )HZ DVVD\ PHWKRGV RI EXSUHQRUKLQH LQ ELRORJLFDO IOXLGV KDYH EHHQ UHSRUWHG LQ WKH OLWHUDWXUH $ UDGLRLPPXQRDVVD\ KDV EHHQ XVHG WR GHWHUPLQH SODVPD OHYHOV RI SDUHQWHUDOO\ DGPLQLVWHUHG EXSUHQRUSKLQH LQ GRJV DQG KXPDQV n $ VHOHFWLYH LRQ PRQLWRULQJ PHWKRG 6,0f RI WKH VLO\ODWHG EXSUHQRUSKLQH LQ *&06 KDV EHHQ XVHG WR GHWHUPLQH WKH SODVPD OHYHOV RI EXSUHQRUSKLQH RYHU D QJPO FRQFHQWUDWLRQ UDQJH $ *& DVVD\ ZLWK IODPHLRQL]DWLRQ GHWHFWLRQ RI VLO\O GHULYDWLYHV RI EXSUHQRUKLQH ZDV XVHG LQ VWDELOLW\ VWXGLHV DW LJPO RI DTXHRXV VROXWLRQV $Q +3/& DVVD\ ZLWK IOXRUHVFHQFH GHWHFWLRQ RI EXSUHQRUKLQH LQ ELRORJLFDO IOXLGV KDV EHHQ UHSRUWHG DQG LWV PRGLILFDWLRQ DQG LPSURYHPHQW LV SUHVHQWHG LQ WKLV GLVVHUWDWLRQ

PAGE 25

(;3(5,0(17$/ 0DWHULDOV $QDO\WLFDO JUDGH VROYHQWV DQG UHDJHQWV ZHUH XVHG %XSUHQRUSKLQH K\GURFKORULGH F\FORSURS\DOSKD>VfK\GUR[\ WULPHWK\OSURS\O@ HQGR HWKDQRWHWUDK\GURRULSDYLQH 1DWLRQDO ,QVWLWXWH IRU 'UXJ $EXVH 5RFNYLOOH 0'f DQG WKH GHPHWKR[\ DQDORJ RI EXSUHQRUSKLQH $GGLFWLRQ 5HVHDUFK &HQWHU /H[LQJWRQ . GLPHWK\OOEXWHQ\Of@ HQGR HWKDQRWHWUDK\GURRULSDYLQH ZDV REWDLQHG IURP 'U* /OR\G -RQHV RI 5LFNHWW t &ROPDQ 3KDUPDFHXWLFDO 'LYLVLRQ .LQJVWRQXSRQ+XOO (QJODQG $SSDUDWXV $Q +3/& PRGHO 0$ SXPS :DWHUV $VVRFLDWHV 0LOIRUG 0$f HTXLSSHG ZLWK D YDULDEOHZDYHOHQJWK IOXRUHVFHQFH GHWHFWRU PRGHO 6 )OXRUHVFHQFH 'HWHFWRU 3HUNLQ(OPHU 1RUZDON &7f ZDV XVHG ,QMHFWLRQV ZHUH FDUULHG RXW ZLWK DQ DXWR VDPSOHU :,63 $XWRVDPSOHU :DWHUV $VVRFLDWHVf DQG WKH GDWD ZHUH DQDO\VHG E\ D PLFURFRPSXWHU 6LJPD 'DWD 6WDWLRQ 3HUNLQ (OPHUf $ VHSDUDWH +3/& SXPS VHULHV % 3HUNLQ (OPHUf HTXLSSHG ZLWK D YDULDEOH ZDYHOHQJWK 89 GHWHFWRU PRGHO /& 3HUNLQ (OPHUf ZDV XVHG LQ VRPH VWXGLHV $ ODERUDWRU\ FHQWULIXJH ZDV XVHG LQ WKH VHSDUDWLRQ RI RUJDQLF H[WUDFW IURP ELRORJLFDO IOXLGV /DE &HQWULIXJH ,QWHUQDWLRQDO &HQWULIXJH (TXLSPHQW &R 1HHGKDP +HLJKWV 0$f /LTXLG &KURPDWRJUDSKLF 3URFHGXUHV $OLTXRWV \/f RI WKH VROXWLRQV WR EH DQDO\]HG ZHUH LQMHFWHG LQWR WKH +3/& V\VWHP HTXLSSHG ZLWK D SDFNHG >SDFNLQJ PDWHULDO ZDV &AJ \P %RQGDSDNUHYHUVHG SKDVH

PAGE 26

2'6+\SHUVLOf 6KDQQRQ 6RXWKHUQ 3URGXFWV /WG &KHVKLUH 8.@ PP LG VWDLQOHVV VWHHO FROXPQ >.QDXHU +3/& DQDO\WLFDO FROXPQ XQSDFNHGf .QDXHU $* %HUOLQ )5*@ ZKLFK ZDV PDLQWDLQHG DW & 7KH XVXDO PRELOH SKDVH IORZ UDWH ZDV P/PLQ RI D DFHWRQLWULOHDFHWDWH EXIIHU S+ 0f FRQWDLQLQJ 0 WHWUDEXW\ODPPRQLXP SKRVSKDWH )OXRUHVFHQFH ZDV HIIHFWHG DW QP H[FLWDWLRQ VOLW QPf DQG QP HPLVVLRQ VOLW PPf DQG ZDV XVHG XQOHVV VWDWHG RWKHUZLVH &DOLEUDWLRQ &XUYHV LQ %LRORJLFDO )OXLGV %XSUHQRUSKLQH $OLTXRWV P/f RI SODVPD XULQH RU ELOH LQ HDFK RI WHQ f§P/ FHQWULIXJH WXEHV ZHUH VSLNHG ZLWK S / RI QJP/ RI EXSUHQRUSKLQH f (DFK VROXWLRQ FRQWDLQHG QJP/ RI WKH DFLG GHJUDGDWLRQ LQWHUPHGLDWH RI EXSUHQRUSKLQH FRPSRXQG DV WKH LQWHUQDO VWDQGDUG 7KH ILQDO VDPSOH FRQWDLQHG QR GUXJ 6RGLXP ERUDWHERULF DFLG EXIIHU P/ DW S+ 0f DQG P/ RI EHQ]HQH ZHUH DGGHG WR HDFK WXEH 7KH WXEHV ZHUH VKDNHQ IRU PLQ FHQWULIXJHG DW USP IRU PLQ DQG P/ RI HDFK EHQ]HQH H[WUDFW ZDV WUDQVIHUUHG WR DQRWKHU VHW RI WHQ f§PL/ FHQWULIXJH WXEHV +\GURFKORULF DFLG LU/ 0f ZDV DGGHG WR HDFK WXEH DQG WKH WXEHV ZHUH VKDNHQ IRU PLQ DQG WKHQ FHQWULIXJHG DW USP IRU PLQ $IWHU UHPRYDO RI EHQ]HQH OD\HU E\ DVSLUDWLRQ P/ RI ERWK 0 1D2+ DQG S+ ERUDWH EXIIHU 0f ZHUH DGGHG WR HDFK RI WKH UHPDLQLQJ DTXHRXV SKDVHV 7KH S+ YDOXHV ZHUH FRQILUPHG RU DGMXVWHG WR EH EHWZHHQ WR %HQ]HQH P/f ZDV DGGHG WR HDFK WXEH ZKLFK ZDV VKDNHQ IRU PLQ DQG FHQWULIXJHG DW USP IRU PLQ 7KH EHQ]HQH H[WUDFW P/f ZDV WUDQVIHUUHG WR D f§PL/ YLDO 5HDFWLYLDO 6XSHOFR ,QF %HOOHIRQWH 3Df DQG WKH EHQ]HQH ZDV HYDSRUDWHG XQGHU D VWUHDP RI QLWURJHQ DW f& 6RGLXP DFHWDWHDFHWLF DFLG EXIIHU S+ 0 \/f ZDV DGGHG WR HDFK RI WKH 5HDFWL9LDOV DQG WKH\ ZHUH

PAGE 27

YRUWH[HG IRU V DQG WKHQ S/ RI WKH VROXWLRQ ZDV DQDO\]HG E\ +3/& %XSUHQRUSKLQH FRQMXJDWHV $OLTXRWV P/f RI SODPVD XULQH RU ELOH LQ HDFK RI WHQ P/ FHQWULIXJH WXEHV ZHUH VSLNHG ZLWK \ / RI QJP/ RI EXSUHQRUSKLQH 7KH ILUVW VDPSOH FRQWDLQHG QR GUXJ 7R HDFK FHQWULIXJH WXEH P/ RI 1 +& ZDV DGGHG DQG DXWRFODYHG DW OEVVTLQ SUHVVXUH IRU PLQ 7KH WXEHV ZHUH DOORZHG WR HTXLOLEUDWH WR URRP WHPSHUDWXUH 7R HDFK WXEH FRQWDLQLQJ WKH DFLGWUDQVIRUPHG GHPHWKR[\ EXSUHQRUSKLQH \ / RI XQFRQYHUWHG EXSUHQRUSKLQH \ JP/f ZDV DGGHG DV LQWHUQDO VWDQGDUG ([FHVV DFLG ZDV QHXWUDOL]HG ZLWK VRGXLP FDUERQDWH 7KH S+ ZDV DGMXVWHG WR ZLWK VRGLXP ERUDWHERULF DFLG EXIIHU P/ 0f DQG P/ RI EHQ]HQH ZDV DGGHG WR HDFK WXEH 7KH WXEHV ZHUH VKDNHQ IRU PLQ FHQWULIXJHG DW USP IRU PLQ DQG P/ RI HDFK EHQ]HQH H[WUDFW ZDV WUDQVIHUUHG WR IUHVK P/ FHQWULIXJH WXEHV +\GURFKORULF DFLG P/ 0f ZDV DGGHG WR HDFK WXEH DQG WKH WXEHV ZHUH VKDNHQ IRU PLQ DQG FHQWULIXJHG DW USP IRU PLQ $IWHU UHPRYDO RI WKH EHQ]HQH E\ DVSLUDWLRQ UUL/ RI ERWK 0 1D2+ DQG S+ ERUDWH EXIIHU 0f ZHUH DGGHG WR HDFK UHDPLQLQJ DTXHRXV SKDVHV 7KH S+ YDOXHV ZHUH FRQILUPHG RU DGMXVWHG WR EH EHWZHHQ WR %HQ]HQH P/f ZDV DGGHG WR HDFK WXEH ZKLFK ZDV VKDNHQ IRU PLQ DQG FHQWULIXJHG IRU PLQ DW USP 7KH EHQ]HQH H[WUDFW P/f ZDV WUDQVIHUUHG WR D UUL/ YLDO 5HDFWL9LDOf DQG WKH EHQ]HQH ZDV HYDSRUDWHG XQGHU D VWUHDP RI QLWURJHQ DW n& 6RGLXP DFHWDWHDFHWLF DFLG EXIIHU \ / S+ 0f ZDV DGGHG WR HDFK YLDO 5HDFWL9LDOf YRUWH[HG IRU V DQG \/ RI WKH VROXWLRQ ZDV DQDO\]HG E\ +3/& 3KDUPDFRNLQHWLF VWXGLHV LQ GRJV +HDOWK\ PRQJUHO PDOH GRJV f ZHUH XVHG IRU WKH SKDUPDFRNLQHWLF LQYHVWLJDWLRQV 7KHLU EORRG DQDO\VLV VKRZHG QR SDWKRJHQLF DEQRUPDOLW\ RU SUHVHQFH RI PLFURILODULD 7KH GRJV ZHUH

PAGE 28

IDVWHG IRU DW OHDVW K EHIRUH HDFK VWXG\ DQG ZHUH JLYHQ ZDWHU DG OLELWXP 7KH DQLPDOV ZHUH VXSSRUWHG E\ D GRJ VOLQJ LQ D IUDPH SODFHG RQ D ODERUDWRU\ WDEOH 7KH GRJV ZHUH LQIXVHG ZLWK LQWUDYHQRXV VDOLQH GURSV SHU PLQf IRU DW OHDVW K XQWLO GUXJ DGPLQVWUDWLRQ ZKHQ WKH LQWUDYHQRXV GULS ZDV UHGXFHG WR GURSV SHU PLQ 7KH DQLPDOV ZHUH FDWKHWHUL]HG K EHIRUH WKH VWXG\ ZLWK D FP VWDQGDUG FDWKHWHU ,QWUDFDWK *$ VL]H 'HVHUHW 0HGLFDO ,QF 6DQG\ 8WDKf LQ WKH MXJXODU YHLQ DIWHU ORFDO DQHVWKHVLD ZLWK PHSLYDFDLQH K\GURFKORULGH &DUERFDLQH K\GURFKORULGH :LQWKURS /DERUDWRULHV 1HZ
PAGE 29

+DUYDUG $SSDUDWXV &R 'RYHU 0$f %XSUHQRUSKLQH+& ZDV GLVVROYHG LQ QRUPDO VDOLQH P/ FRQFHQWUDWLRQA PJP/f XOWUDVQLFDWHG IRU PLQ DQG LQIXVHG LQWR WKH MXJXODU YHLQ DW WKH UDWH RI P/PLQ IRU PLQ VWXGLHV f 'XULQJ LQIXVLRQ EORRG VDPSOHV ZHUH FROOHFWHG IURP WKH EUDFKLDOLV YHLQ 3RVWLQIXVLRQ EORRG VDPSOHV ZHUH FROOHFWHG IURP ERWK MXJXODU DQG EUDFKLDOLV YHLQV ,Q GRJ VWXG\ WKH GUXJ VROXWLRQ ZDV LQIXVHG LQWR WKH EUDFKLDOLV YHLQ XVLQJ WKH VDPH GUXJ FRQFHQWUDWLRQ DQG IORZ UDWH DV DERYHf 'RJV ( ) DQG XQGHUZHQW VXUJHU\A $ b VROXWLRQ RI WK\PDORO VRGLXP ZDV DGPLQLVWHUHG ,9 P/NJf WR HDFK GRJ DQG DQHVWKHVLD ZDV PDLQWDLQHG E\ KDORWKDQH $IWHU UHPRYDO RI WKH JDOOEODGGHU D VFUHZFDS ZDV SODFHG RQ WKH RSSRVLWH VLGH RI WKH VSKLQFWHU RI 2GGL DQG WKH LQWHVWLQH ZDV VHZQ WR WKH DEGRPLQDO ZDOO )LJ f $W OHDVW PRQWK ZDV DOORZHG IRU UHFRYHU\ IURP WKH VXUJHU\ EHIRUH WKH SKDUPDFRNLQHWLF VWXG\ RI EXSUHQRUSKLQH LQ WKH ELOHFDQQXODWHG GRJV 7KHVH GRJV FRXOG EH UHSHWLWLYHO\ XVHG IRU ELOH FDQQXODWLRQ VWXGLHV E\ RSHQLQJ WKH VFUHZFDS DQG LQVHUWLQJ D FDWKHWHU )DVW 5LJKW +HDUW &DUGLRYDVFXODU FDWKHWHU ) VL]H &5 %DUG ,QF %LOOHULFD 0$f LQWR WKH ELOH GXFW 7KH EDOORRQ DW WKH WLS RI WKH DERYH FDWKHWHU ZDV LQIODWHG ZLWK P/ RI DLU SXOOHG EDFN XQWLO WKH FDWKHWHU ZDV VHFXUHO\ SRVLWLRQHG DW WKH LQVLGH ZDOO RI WKH VSLQFWHU RI 2GGL &RPSOHWH ELOH FROOHFWLRQ ZDV HIIHFWHG LQ VXFK VWXGLHV DW LQWHUYDOV RI PLQ IRU XS WR K ,VRODWLRQ RI EXSUHQRUSKLQH FRQMXJDWH IURP ELOH 7ZR OLTXLG FKURPDWRJUDSKLF JODVV FROXPQV ; FPf ZHUH SDFNHG ZLWK QRQLRQLF $PEHUOLWH ;$' EHDGV 6LJPD &KHPLFDO &R 6W /RXLV 0Rf E\ SDVVLQJ D VOXUU\ RI WKH SDFNLQJ PDWHULDO LQ GLVWLOOHG ZDWHU WKURXJK WKH FROXPQ 7KH SHUIRUDWHG GLVN DW WKH ERWWRP HQG RI WKH FROXPQ UHWDLQHG WKH

PAGE 30

)LJXUH 6FKHPDWLF RI WKH SHUIRUPHG VXUJHU\ $IWHU JDOOEODGGHU UHPRYDO VFUHZFDS ZDV SODFHG RQ WKH RSSRVLWH VLGH RI WKH VSKLQFWHU RI 2GGL DQG WKH LQWHVWLQH ZDV VHZQ WR WKH DEGRPLQDO ZDOO 'XULQJ WKH ELOH FDQQXODWLRQ WKH VFUHZFDS ZDV UHSODFHG E\ D VHDOHG SHUIRUDWHG UXEEHU VWRSSHU WKURXJK ZKLFK D ELOH FDWKHWHU ZDV SRVLWLRQHG LQWR WKH ELOH GXFW $W WKH HQG RI WKH VWXG\ WKH FDWKHWHU ZDV UHPRYHG DQG WKH VFUHZFDS ZDV UHSODFHG 6HH DOVR UHIHUHQFH f

PAGE 31

JDOO EODGGHU UHPRYHGf GXRGHQXP DEGRPLQDO ZDOO

PAGE 32

$PEHUOLWH EHDGV (DFK FROXPQ ZDV ZDVKHG ZLWK P/ RI ZDWHU IROORZHG E\ P/ RI PHWKDQRO 7KH FROXPQV ZHUH FORVHG DW WKH ERWWRP DQG VRDNHG ZLWK GLVWLOOHG ZDWHU RYHUQLJKW 3RROHG ELOH VDPSOHV P/f FROOHFWHG IURP GRJ VWXGLHV DQG ZHUH GLOXWHG WR P/ ZLWK GLVWLOOHG ZDWHU $OLTXRWV P/f ZHUH SDVVHG WKURXJK HDFK FROXPQ DQG ZDVKHG ZLWK P/ RI ZDWHU XQWLO WKH HOXHQW ZDV FRORUOHVV 7KHQ P/ RI PHWKDQRO ZDV SDVVHG WKURXJK HDFK FROXPQ 7KHVH PHWKDQROLF HOXDWHV ZHUH FRPELQHG DQG FRPSOHWHO\ HYDSRUDWHG WR GU\QHVV XQGHU UHGXFHG SUHVVXUH 7KH UHVLGXH ZDV GLVVROYHG LQ VWHULOH QRUPDO VDOLQH P/f DQG WKH VROXWLRQ ZDV ILOWHUHG WKURXJK D SP 0LOOLSRUH ILOWHU DLGHG XQGHU UHGXFHG SUHVVXUH DQG VWULFWO\ DVHSWLF FRQGLWLRQV 7KH ILQDO VWHULOH VROXWLRQ ZDV LQIXVHG LQWR GRJ ) 6WXG\ f DW WKH UDWH RI P/PLQ IRU PLQ 7KH SRROHG ELOH VDPSOHV FROOHFWHG IURP GRJ VWXG\ ZHUH VLPLODUO\ H[FHSW WKDW FKURPDWRJUDSKLF VHSDUDWLRQ ZDV DFKLHYHG ZLWK RQO\ RQH $PEHUOLWH ;$' FROXPQ 7KH ILQDO VWHULOH VROXWLRQ ZDV LQIXVHG LQWR GRJ 6WXG\ f DW WKH UDWH RI POPLQ IRU PLQ $QDO\VLV RI WKH FRQMXJDWH E\ HQ]\PDWLF K\GURO\VLV 7KH HQ]\PH JOXFXURQLGDVH JOXFXURQLGH JOXFXURQRVRK\GURODVH PJ )LVKPDQ 8QLWV /RW ) 6LJPD &KHPLFDO &Rf ZDV GLVVROYHG PJf LQ P/ DFHWDWH EXIIHU S+ 0f $OLTXRWV S/f RI WKH HQ]\PH SUHSDUDWLRQ DQG WKH LQWHUQDO VWDQGDUG S/ RI FRPSRXQG SWJP/f ZHUH DGGHG WR \ / RI GLOXWHG ELOH VDPSOH GLOXWLRQ PDGH ZLWK GLVWLOOHG ZDWHUf DQG WKH WRWDO YROXPH ZDV DGMXVWHG WR P/ ZLWK S+ DFHWDWH EXIIHU 7KH VDPSOHV ZHUH LQFXEDWHG DW n& IRU K 'LOXWHG ELOH GLOXWLRQf VDPSOHV FRQWDLQLQJ QR GUXJ ZHUH VSLNHG ZLWK EXSUHQRUSKLQH DQG WUHDWHG LQ WKH VDPH PDQQHU WR HVWDEOLVK DQ DSSURSULDWH FDOLEUDWLRQ FXUYH 7KH JHQHUDWHG DJO\FRQH EXSUHQRUSKLQH ZDV

PAGE 33

DVVD\HG E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ &DWKHWHU ELQGLQJ RI EXSUHQRUSKLQH %XSUHQRUSKLQH+&O ZDV GLVVROYHG LQ QRUPDO VDOLQH P/ FRQFHQWUDWLRQ PJP/ RI EDVHf 7KH VROXWLRQ ZDV SDVVHG WKURXJK WKH SODVWLF FDWKHWHU ,QWUDFDWKf ZLWKRXW EDFN SUHVVXUH DW WKH UDWH RI P/PLQ IRU K VWXG\f DQG K VWXGLHVf 7KH LQWHUQDO VXUIDFH RI WKH FDWKHWHU ZDV ZDVKHG ZLWK P/ RI QRUPDO VDOLQH DQG GULHG XQGHU D VWUHDP RI DLU 7KHQ EHQ]HQH POf ZDV SXPSHG WKURXJK WKH SODVWLF FDWKHWHU ,QWUDFDWKf DW WKH UDWH RI POPLQ HYDSRUDWHG LQ D FROOHFWLQJ IODVN DW r& XQGHU UHGXFHG SUHVVXUH 7KH UHVLGXH ZDV UHFRQVWLWXWHG LQ DFHWDWH EXIIHU S+ 0f DQG DOLTXRWV ZHUH DVVD\HG E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ %XSUHQRUSKLQH+&O ZDV GLVVROYHG LQ QRUPDO VDOLQH PJP/ RI EDVHf DQG SDVVHG WKURXJK WKH SODVWLF FDWKHWHU ,QWUDFDWKf DW WKH UDWH RI P/PLQ IRU K 7KH LQWHULRU VXUIDFH RI WKH FDWKHWHU ZDV ZDVKHG ZLWK P/ RI QRUPDO VDOLQH 7KH VDOLQH ZDV DOORZHG WR IORZ IURP DQ LQIXVLRQ EDJ XQGHU WKH JUDYLWDWLRQDO IRUFH DW WKH UDWH RI GURSVPLQ IRU K DQG ZDV FROOHFWHG P/f 7KH S+ ZDV DGMXVWHG WR DQG WKH VDOLQH VROXWLRQ ZDV H[WUDFWHG WZLFH ZLWK P/ SRUWLRQV RI EHQ]HQH 7KH FRPELQHG EHQ]HQH OD\HU ZDV HYDSRUDWHG XQGHU UHGXFHG SUHVVXUH DW f& 7KH UHVLGXH ZDV UHFRQVLWXWHG LQ DFHWDWH EXIIHU S+ 0f DQG DOLTXRWV ZHUH DVVD\HG E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ %XSUHQRUSKLQH PJQ/f LQ QRUPDO VDOLQH ZDV SDVVHG WKURXJK WKH SODVWLF FDWKHWHU ,QWUDFDWKf IRU K DW WKH IORZ UDWH RI P/PLQ $W WKH HQG RI K WKH FDWKHWHU ZDV ZDVKHG ZLWK P/ RI QRUPDO VDOLQH DQG VDOLQH GULS GURSVPLQf ZDV FRQWLQXHG )UHVK EODQN GRJ EORRG P/f ZDV GUDZQ WKURXJK WKH FDWKHWHU DW PLQ 7KH EORRG VDPSOHV ZHUH FHQWULIXJHG DW USP IRU

PAGE 34

PLQ DQG WKH VXSHUQDWHQW SODVPD ZDV DQDO\VHG IRU EXSUHQRUSKLQH E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ 7KH H[SHULPHQW ZDV UHSHDWHG IROORZLQJ WKH SXPSLQJ RI EXSUHQRUSKLQH VROXWLRQ XVLQJ WKH VDPH FRQFHQWUDWLRQ DQG IORZ UDWH DV DERYHf WKURXJK WKH FDWKHWHU IRU K ,QYLYR VWXG\ ,Q GRJ VWXG\ EXSUHQRUSKLQH ZDV LQIXVHG PJPLQ IRU PLQf LQWR WKH OHIW EUDFKLDOLV YHLQ WKURXJK WKH LQGZHOOLQJ SODVWLF FDWKHWHU ,QWUDFDWKf %ORRG VDPSOHV GXULQJ LQIXVLRQ ZHUH FROOHFWHG IURP WKH MXJXODU YHLQ DQG WKH FRQWUDODWHUDO EUDFKLDOLV YHLQ 8SRQ FHVVDWLRQ RI LQIXVLRQ WKH FDWKHWHU WKURXJK ZKLFK WKH GUXJ ZDV LQIXVHG LQWR WKH OHIW EUDFKLDOLV YHLQ ZDV ZDVKHG ZLWK P/ RI QRUPDO VDOLQH 3RVWLQIXVLRQ EORRG VDPSOHV ZHUH FROOHFWHG IURP WKH OHIW EUDFKLDOLV YHLQ VLWH RI LQIXVLRQf WKURXJK WKH SODVWLF FDWKHWHU DV ZHOO DV IURP WKH MXJXODU DQG FRQWUDODWHUDO EUDFKLDOLV YHLQV

PAGE 35

,9 %2/86 678',(6 &KURPDWRJUDSKLF DVVD\V RI %XSUHQRUSKLQH DQG LWV FRQMXJDWH 7KH +3/& DVVD\ PHWKRGV GHYHORSHG IRU EXSUHQRUSKLQH KDYH EHHQ SXEOLVKHG &KURPDWRJUDPV RI WKH +3/&DVVD\HG EXSUHQRUSKLQH DUH JLYHQ LQ )LJ 7KH DFLG K\GURO\]DEOH FRQMXJDWH 0f DVVD\ )LJ f E\ IOXRULPHWULF GHWHFWLRQ QP H[FLWDWLRQ VOLW ZLGWK QP DQG QP HPLVVLRQ VOLW ZLGWK QPf ZDV HTXDOO\ VHQVLWLYH 7DEOH VKRZV WKH UHOHYDQW VWDWLVWLFV RI FDOLEUDWLRQ FXUYHV 7KH VWDQGDUG HUURUV RI HVWLPDWHV RI WKH FRQFHQWUDWLRQ DERXW LWV UHJUHVVLRQ RQ SHDN KHLJKW UDWLR UDQJHG LURQ WR B QJPO 6RPH DGGLWLRQDO OLQHDU UHJUHVVLRQV RI FRQFHQWUDWLRQV & QJPOf RI EXSUHQRUSKLQH LQ SODVPD ZLWK WKHLU VWDQGDUG HUURUV RI WKH SDUDPHWHU HVWLPDWHV LQ DFFRUGDQFH ZLWK & B 6(5 P VP f 3+5 E VA (T LQ WKH UDQJH QJPO ZHUH & B QJPO B f 3+5 U & QJPO f 3+5 U & QJPO f 3+5 U & QJPO f 3+5 U ,Q WKH EXSUHQRUSKLQH FRQFHQWUDWLRQ UDQJH RI QJPO & B QJPO f 3+5 U & QJPO f 3+5 U & QJPO f 3+5 U & QJPO f 3+5 U

PAGE 36

)LJXUH 5HSUHVHQWDWLYH FKURPDWRJUDPV DIWHU DVVD\ RI EXSUHQRUSKLQH QJPOf ZLWK LQWHUQDO VWDQGDUG QJPOf IURP SODVPD Df DQG XULQH Ef 7KH EODQN SODVPD DQG XULQH FKURPDWRJUDPV ZLWKRXW GUXJ DUH JLYHQ XQGHUQHDWKf &KURPDWRJUDP RI PL[WXUH RI \JPO RI EXSUHQRUSKLQH ZLWK LWV SURGXFWV DQG DIWHU DFLG GHJUDGDWLRQ LQ 0 +& IRU PLQ Ff 6HH DOVR UHIHUHQFH f

PAGE 37

)LJXUH 5HSUHVHQWDWLYH FKURPDWRJUDPV DIWHU +3/& VHSDUDWLRQ IROORZHG E\ IOXRULPHWULF GHWHFWLRQ RI EXSUHQRUSKLQH FRQMXJDWH LQ SODVPD XULQH DQG ELOH %ODQN FKURPDWRJUDPV RI ELRORJLFDO IOXLGV ZLWKRXW WKH GUXJ DQG WKH LQWHUQDO VWDQGDUG DUH JLYHQ XQGHUQHDWK ,Q WKH FKURPDWRJUDPV D E DQG Ff SHDN FRUUHVSRQGV WR WKH GHPHWKR[\ DQDORJ RI EXSUHQRUSKLQH REWDLQHG DIWHU DFLG K\GURO\VLV RI EXSUHQRUSKLQH FRQMXJDWH 0 %XSUHQRUSKLQH FRQMXJDWH SURGXFHV WKH DJO\FRQH RQ DFLG K\GURO\VLV ZKLFK IXUWKHU TXDQWLWDWLYHO\ UHDUUDQJHV LQWR GHPHWKR[\ DQDORJ SHDN 6HH DOVR UHIHUHQFH f 7KH +3/& UHWHQWLRQ WLPH IRU FRPSRXQG SHDNf LV GLIIHUHQW IURP EXSUHQRUSKLQH 6HH ILJXUH OFf 7KXV EXSUHQRUSKLQH SHDN f FRXOG EH XVHG DV LQWHUQDO VWDQGDUG IRU WKH FRQMXJDWH DVVD\ Df 'HPHWKR[\ DQDORJ QJPOf RI EXSUHQRUSKLQH FRQMXJDWH DQG LQWHUQDO VWDQGDUG QJPOf IURP SODVPD REWDLQHG DIWHU DFLG K\GURO\VLV RI SODVPD IROORZHG E\ +3/& VHSDUDWLRQ Ef 'HPHWKR[\ DQDORJ QJPOf RI EXSUHQRUSKLQH FRQMXJDWH DQG LQWHUQDO VWDQGDUG QJPOf IURP XULQH REWDLQHG DIWHU DFLG K\GURO\VLV Ff 'HPHWKR[\ DQDORJ QJPOf RI EXSUHQRUSKLQH FRQMXJDWH DQG LQWHUQDO VWDQGDUG QJPOf IURP ELOH REWDLQHG DIWHU DFLG K\GURO\VLV DQG +3/& VHSDUDWLRQ ,Q REWDLQLQJ FKURPDWRJUDPV D E DQG F WKH PRELOH SKDVH ZDV DFHWRQLWULOHDFHWDWH EXIIHU S+ 0f SOXV 0 WHWUDEXW\O DPPRQLXP SKRVSKDWH IORZ UDWH POPLQ $OO RWKHU FKURPDWRJUDSKLF FRQGLWLRQV ZHUH WKH VDPH DV GHVFULEHG XQGHU WKH VXEKHDGLQJ n/LTXLG &KURPDWRJUDSKLF SURFHGXUHVn LQ H[SHULPHQWDO VHFWLRQ

PAGE 38

PP X! 8aLf§Lf§Lf§rf§Lf§Lf§Lf§Lf§U PLQ

PAGE 39

7DEOH 7\SLFDO VWDWLVWLFV RI SODVPD DQG XULQH FDOLEUDWLRQ FXUYHV IRU %XSUHQRUSKLQH f DQG FRQMXJDWH 0f %LRORJLFDO )OXLG 5DQJH QJPO D V\[ E P F V P EG H b I Q U 3ODVPD f 8ULQH f 3ODVPD 0f 8ULQH 0f D 6WDQGDUG HUURU RI HVWLPDWH DERXW UHJUHVVLRQ RI FRQFHQWUDWLRQ QJPOf RQ SHDN KHLJKW UDWLR N 6ORSH F 6WDQGDUG HUURU RI VORSH G ,QWHUFHSW H 6WDQGDUG HUURU RI LQWHFHSW A 1XPEHU RI SRLQWV A &RUUHODWLRQ FRHIILFLHQW ,Q EXSUHQRUSKLQH FDOLEUDWLRQ FXUYHV GHPHWKR[\ DQDORJ RI EXSUHQRUSKLQH FRPSRXQG 6FKHPH ,f ZDV XVHG DV LQWHUQDO VWDQGDUG %XSUHQRUSKLQH ZDV XVHG DV LQWHUQDO VWDQGDUG LQ WKH DVVD\ RI FRQMXJDWH 0f 6RPH DGGLWLRQDO FDOLEUDWLRQ FXUYH VWDWLVWLFV DUH JLYHQ LQ WKH WH[W

PAGE 40

,Q XULQH H[DPSOHV RI UHJUHVVLRQ HTXDWLRQV IRU EXSUHQRUSKLQH LQ WKH UDQJH QJPO ZHUH & B QJPO B f 3+5 B U & QJPO f 3+5 U & QJPO f 3+5 U ([DPSOHV RI UHJUHVVLRQ HTXDWLRQV IRU EXSUHQRUSKLQH FRQMXJDWH 0f LQ SODVPD LQ WKH UDQJH QJPO ZHUH & QJPO B f 3+5 B U UDQJH QJPO & B QJPO B f 3+5 B U UDQJH QJPO & B QJPO M f 3+5 B U UDQJH QJPO & B QJPO f 3+5 U ([DPSOHV RI UHJUHVVLRQ HTXDWLRQV IRU EXSUHQRUSKLQH FRQMXJDWH 0f LQ XULQH LQ WKH UDQJH QJPO ZHUH & B QJPO B f 3+5 B U UDQJH QJPO & QJPO B f 3+5 U & QJPO f 3$5 B U ZKHUH 3$5 SHDN DUHD UDWLR UDQJH QJPO & B QJPO B f 3+5 B U $Q H[DPSOH RI UHJUHVVLRQ HTXDWLRQ IRU EXSUHQRUSKLQH FRQMXJDWH 0f LQ ELOH LQ WKH UDQJH QJPO ZDV & B QJPO B f 3+5 B U 7ZLFH WKH VWDQGDUG HUURU RI HVWLPDWH RI EXSUHQRUSKLQH DQG WKH PHWDEROLWH FRQFHQWUDWLRQV QJPOf RQ SHDN KHLJKW UDWLR UDQJHG IURP QJPO 7DEOH f LQGLFDWLYH RI WKH VHQVLWLYLW\ RI WKH IOXRULPHWULF DVVD\ RI EXSUHQRUSKLQH DQG LWV PHWDEROLWH LQ ELRORJLFDO IOXLGV 3ODVPD 3KDUPDFRNLQHWLFV DQG 9ROXPHV RI 'LVWULEXWLRQ 7KH SODVPD FRQFHQWUDWLRQWLPH SURILOH RI EXSUHQRUSKLQH FRXOG EH ILWWHG WR D VXP RI WKUHH H[SRQHQWLDOV (T )LJV f 7KHUH PD\ QRW EH DQ XQLTXH OLQHDU VXP RI WKUHH H[SRQHQWLDOV &SA HVWLPDWHG SODVP FRQFHQWUDWLRQf WKDW

PAGE 41

)LJXUH 6HPLORJDULWKPLF SORWV RI FRQFHQWUDWLRQV DV QJPO RI EDVHf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODVPD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ $ 6WXG\ 7DEOH f ,Q WKH ERWWRP DQG PLGGOH ILJXUHV WKH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f &SQJPOf Hn W Hn W A Hnn 7KH PLGGOH LQVHW LV WKH FRQWLQXDWLRQ RI WKH GDWD DQG ILWWHG FXUYH IRU DQ H[WHQGHG WLPH VFDOH XS WR PLQ 7KH WRS LQVHW UHSUHVHQWV WKH GDWD ILWWHG WR D FRPSDUWPHQW PRGHO LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ &S QJPOf H W MRR H W A F H W / ff W H 5HIHU WR WKH VHFWLRQ 9DOLGLW\ RI WKH WHUPLQDO UDWH FRQVWDQW IRU D GLVFXVVLRQ RI ILWWLQJ RI WKH GDWD WR FRPDUWPHQW PRGHO

PAGE 42

&*1& 1*0/

PAGE 43

)LJXUH 6DPLORJDULWKPLF SORWV RI FRQFHQWUDWLRQV DV QJPO RI EDVHf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODVPD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ % 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f &SQJPOf W LU W H H W H 7KH LQVHW LV D UHSUHVHQWDWLRQ RI WKH GDWD DQG ILWWHG FXUYH IRU WKH LQLWLDO SHULRG RI PLQ

PAGE 44

1, : P LL( QPr Lf§ QXD L XQ]? XG 7-61 n*122

PAGE 45

)LJXUH 6HPLORJDULWKPLF SORWV RI FRQFHQWUDWLRQV DV QJPO RI EDVHf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODVPD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH NJ GRJ & 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f &SQJPOf H H rr W Hf W 7KH LQVHW LV WKH FRQWLQXDWLRQ RI GDWD IRU DQ H[WHQGHG WLPH VFDOH XS WR PLQ

PAGE 46

5' ALQ ' 0,1 &212 1*0/ f§ LBM a Q F D ’ D D ’ 9I PQULUM

PAGE 47

)LJXUH 6HPLORJDULWKPLF SORW RI WKH FRQFHQWUDWLRQV DV QJPO RI EDVHf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODVPD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ % 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f &SQJPOf H W H W W

PAGE 48

?@ULOc= 8?f== -IM FR 1L: XQ XVV A K P 88O XXQ L XXXQ L &&1&} 1*0/

PAGE 49

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV DV QJPO RI EDVHf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODVPD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ & 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f &SQJPOf PH W A B4 W F W H H H 7KH LQVHWV DUH WKH FRQWLQXDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH H[WHQGHG WLPH VFDOH XS WS PLQ

PAGE 50

E%2 Q2 &&1&} 1*0/ & R J e Vr

PAGE 51

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV DV QJPO RI EDVHf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODVPD 2 )OXRUHVFHQFH GHWHFWLRQ 4 (OHFWURFKHPLFDO GHWHFWLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ GRJ 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f &S QJPOf H W $ W A 2' W H H 7KH PLGGOH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ 7KH WRS LQVHW LV WKH SORW RI WKH ZHLJKWHG UHVLGXDOV FDOFXODWHG LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f DJDLQVW ORJ ILWWHG FRQFHQWUDWLRQV 6HH ILJ IRU GHWDLOV RQ WKH UHVLGXDO SORWV

PAGE 52

\LU n, >,' '' >@>@ ' 0,1 ,''

PAGE 53

EHVW ILWV WKH DFWXDO GDWD &S LQVWHDG WKHUH PD\ EH VHYHUDO H[S VROXWLRQV ZLWK VLPLODU PLQLPXP VXP RI VTXDUHV $ XQLTXH VROXWLRQ FDQ EH REWDLQHG RQO\ LI WKH GUXJ WUDQVIHUUHG LQWR RWKHU FRPSDUWPHQWV RU WUDQVIRUPHG LQWR PHWDEROLWHV ZHUH DQDO\VHG LQ WKHLU UHVSHFWLYH FRPSDUWPHQWV 7KH SODVPD GDWD RI EXSUHQRUSKLQH DGPLQLVWHUHG LQWUDYHQRXVO\ WR GRJV ZHUH ILWWHG E\ QRQOLQHDU UHJUHVVLRQ WR D VXP RI WKUHH H[SRQHQWLDOV ,Q VWXG\ 'RJ $ WKH GDWD ZHUH DOVR ILWWHG WR D FRPSDUWPHQW PRGHO )LJ WRS LQVHWf 7KH ILWWLQJ ZDV HIIHFWHG ZLWK WKH FRPSXWHU SURJUDP RI
PAGE 54

)LJXUH 5HSUHVHQWDWLYH H[DPSOHV RI WKH SORWV RI WKH ZHLJKWHG UHVLGXDOV DJDLQVW ORJ &SFDOF YDOXHV 7KHVH ZHLJKWHG UHVLGXDOV ZHUH REWDLQHG IURP WKH HTXDWLRQ f AH[S f AFDOF @ AFDOF 7KH FDOFXODWHG SODVPD YDOXHV ZHUH REWDLQHG IURP WKH WULH[SRQHQWLDO HTXDWLRQ ILWWHG WR WKH SODVPD GDWD RI EXSUHQRUSKLQH Df PJNJ GRVH VWXG\ LQ GRJ $ 6WXG\ Ef PJNJ GRVH VWXG\ LQ GRJ % 6WXG\ Ff WKH SODVPD PHWDEROLWH 0f UHVLGXDOV REWDLQHG DIWHU ,9 DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH IRU WKH PJNJ GRVH VWXG\ LQ GRJ & 6WXG\ Gf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

PAGE 55

5(6,'8$/6 5(6,'8$ 5(6,'8$/6 5(6,'8$/6

PAGE 56

7DEOH 3KDUPDFRNLQHWLFV RI LQWUDYHQRXVO\ DGPLQLVWHUHG EROXV %XSUHQRUSKLQH f LQ GRJV 3DUDPHWHU 'RJ $ 'RJ % 'RJ % 'RJ & 'RJ & 'RJ 0HDQ 6(0 6WXG\ 1R 'RJ 1R % % % : : : 'RVHG PJ :HLJKW .J 'RVH PJNJ 3DUDPHWHUV IURP SODVPD GDWD IRU O2A3I E $I %I 77 & f f f f f f f  D $ f f f f f f f f f f f f f f 5HVLGXDO SORWV LR G 6ORSH A ,QWHUFHSW &OHDUDQFHV &O WRW &O K UHQ f f f f f &O PHW FL0 UHQ f f f f f

PAGE 57

7DEOH &RQWLQXHG 3DUDPHWHU 'RJ $ 'RJ % 'RJ % 'RJ & 'RJ & 'RJ 0HDQ 6(0 b 5HFRYHULHV RI EXSUHQRUSKLQH DQG 0 LQ XULQH 8RRnrn GRVHP 8RR0 GRVHP 9ROXPHV RI GLVWULEXWLRQ RI EXSUHQRUSKLQH /f Y Q F 9 3 P 3DUDPHWHUV LURQ SODVPD GDWD IRU FRQMXJDWH 0f 3 E T $ U %I WW & R f +7 D f§ f§ f f f§ f§ f f f 5HVLGXDO SORWV G 6ORSH e f§ f§ ,QWHUFHSWA 8 f§ f§ f§ f§ f§ f§ f§ f§ f f f f f f f§ f§ f f fU f§ f§

PAGE 58

D 9DOXHV FRUUHVSRQG WR EXSUHQRUSKLQH EDVH $GPLQLVWHUHG DV +& VDOW GLVVROYHG LQ PO QRUPDO VDOLQH NSI $I DQG YDOXHV HTXDO WR 3 $ DQG % YDOXHV H[SUHVVHG LQ IUDFWLRQV $ DQG % YDOXHV ZHUH REWDLQHG IURP WKH QRQOLQHDU OHDVW VTXDUH ILWWLQJ RI RI GRVH SHU PO RI SODVPD 7KH 3 SODVPD GDWD ZLWK &S ZHLJKWLQJ & f 8QLW IRU WW D DQG YDOXHV LV PLQ 3DUHQWKHWLFDO YDOXHV FRUUHVSRQG WR F9IHDQ RI WKH ZHLJKWHG UHVLGXDOV & 4"H[S &3FDSF f 4"FDJF f 1RQH VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR KDOIOLYHV LQ PLQ RI WKH PHDQ UHVLGXDOV ZHUH I n 7KHVH DUH WKH VORSHV DQG LQWHUFHSWV RI SORWV RI DJDLQVW ORJ ILWWHG F3FD@F 7KH SDUHQWKHWLFDO YDOXHV FRUUHVSRQG WR VWDQGDUG HUURUV %RWK VORSH DQG LQWHUFHSW ZHUH DOVR QRW VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR LQGLFDWLQJ WKDW WKH VXP RI WKUHH H[SRQHQWLDOV EHVW ILWV WKH SODVPD GDWD RI EXSUHQRUSKLQH DQG WKH FRQMXJDWH A5DWLR RI WKH GRVH WR WKH WRWDO DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH ZKHUH WKH FDOFXODWHG $8& 3WU f $D f % f DQG WKDW FDOFXODWHG IURP WKH WUDSH]RLGDO UXOH SOXV WKH TXRWLHQW RI WKH ODVW REVHUYHG SODVPD OHYHO &SQf DQG f YLHUH ZLWKLQ b LQ DOO FDVHV H[FHSW LQ GRJ & DW PJNJ GRVH OHYHO ZKHUH WKH GLIIHUHQFH ZDV b 8QLW POPLQ A(VWLPDWHV IURP WKH VORSHV RI FXPXODWLYH DPRXQWV RI EXSUHQRUSKLQH H[FUHWHG ]8 XJVf UHQDOO\ DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ WLPH FXUYH $8&Af DW WKDW WLPH LQ DFFRUGDQFH ZLWK ] 8 &OAA $8&A 7KHVH YDOXHV ZHUH FDOFXODWHG IURP WKH LQLWLDO VORSHV REVHUYHG )LJV f DQG WKHVH UDWLRV FKDQJHG DV S+ RI WKH XULQH FKDQJHG )LJ f 7KH YDOXHV LQ SDUHQWKHVLV DUH A8 DW $8& IURP WKH EHVW OLQHDU SORWV RI GDWD DV VKRZQ LQ )LJV 7KH SORWV RI $X$W YV &SAPG 3ODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDOf ZHUH KLJKO\ VFDWWHUHG LQ PRVW VWXGLHV )LJ VHH DOVR WH[Wf & ZDV FDOFXODWHG IURP WKH GLIIHUHQFH EHWZHHQ WRWDO FOHDUDQFH &O DQG UHQDO FOHDUDQFH &O RI PHW WRW UHQ EXSUHQRUSKLQH A&OAHW B &OJ !0 ZDV FDOFXODWHG XVLQJ HTXDWLRQ N f§!0 %LOLDU\ FOHDUDQFH RI 0 ZDV FDOFXODWHG IURP WKH NQRZOHGJH RI &OPHA DQG &Of§ W &% f YDOXHV 0 5HQDO FOHDUDQFH RI PHWDEROLWH &OUJQ ZDV HVWLPDWHG LQ DFFRUGDQFH ZLWK HTXDWLRQ )LJV f

PAGE 59

A3HUFHQW UHFRYHULHV RI EXSUHQRUSKLQH DQG 0 LQ XULQH REWDLQHG IURP WKH TXRWLHQW RI WKH DPRXQW UHFRYHUHG LQ XULQH DQG WKH WRWDO ,9 EROXV GRVH RI EXSUHQRUSKLQH 9ROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO FRPSDUWPHQW 9 f ZDV REWDLQHG XVLQJ HTXDWLRQ 3 $ DQG % DUH WKH SDUDPHWHUV IURP WKH SODVPD GDWD IRU EXSUHQRUSKLQH 9 ZDV FDOFXODWHG IURP &O U G WRW S A(VWLPDWHG XVLQJ HTXDWLRQ A3ODVPD FRQMXJDWH SURILOH FRXOG QRW EH ILWWHG WR D VXP RI H[SRQHQWLDOV VHH )LJ +RZHYHU WKH WHUPLQDO UDWH FRQVWDQW ZDV HVWLPDWHG IUFP WKH VHPLORJDULWKPLF SORWV RI WKH WHUPLQDO SODVPD GDWD DJDLQVW WLPH 6HH DOVR WH[W U2XWOLHU GRJ & DW PJNT GRVH ZDV QRW LQFOXGHG LQ WKH FDOFXODWLRQ RI DYHUDJH DQG 6(0 8 W

PAGE 60

$SSHQGL[ ,f 7KH RXWOLHU ZDV LQFOXGHG LQ DOO RWKHU SHUWLQHQW SKDUPDFRNLQHWLF DQDO\VHV DQG SORWV VXFK DV H[FUHWLRQ UDWH VLJPD PLQXV DQG FOHDUDQFH SORWV 7KHUH ZHUH QR RXWOLHUV LQ WKH RWKHU VWXGLHV 6LQFH WKH WULH[SRQHQWLDO HTXDWLRQ DGHTXDWHO\ GHVFULEHG WKH SRVWLQWUDYHQRXV EROXV LQMHFWLRQ GDWD )LJV f D FRPSDUWPHQW ERG\ PRGHO ZDV WKH VLPSOHVW SKDUPDFRNLQHWLF PRGHO IRU WKH GLVSRVLWLRQ RI EXSUHQRUSKLQH LQ GRJV 7KH HOLPLQDWLRQ RI EXSUHQRUSKLQH FRXOG RFFXU IURP D FHQWUDO FRPSDUWPHQW &f UHYHUVLEO\ FRQQHFWHG ZLWK VKDOORZ 6f DQG GHHS 'f SHULSKHUDO FRPSDUWPHQWV VFKHPH ,,f 7KH HTXDWLRQ ZKLFK GHVFULEHV WKH WLPH FRXUVH RI WKH ,9 EROXV DGPLQLVWHUHG GUXJ LQ WKH FHQWUDO FRPSDUWPHQW &S DV D IXQFWLRQ RI WLPH W DV SHU VFKHPH LV JLYHQ E\ FS ;9Ff > > N f§WW f N 77 f77 D f 77 %f @ HU > N D f D N fLUDfDJf@ H DW >N %f N % fDH f 77 % f @ HHW @ (T ZKHUH ;T N WW f NAA WW f9FWW Df WW % f 3 (T ; N D f D N f 9F WW D f D % f $ (T DQG ;4 N % f N % f 9F D % f LU % f % (T

PAGE 61

ZKHUH ;f GRVH 9 YROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO F FRPSDUWPHQW 9DOLGLW\ RI WKH WHUPLQDO UDWH FRQVWDQW 3URSHU HVWLPDWLRQ $SSHQGL[ ,,f RI WKH WHUPLQDO UDWH FRQVWDQW DQG KDOIOLIHf GHSHQGV XSRQ Df DQDO\WLFDO VHQVLWLYLW\ Ef QXPEHU RI WHUPLQDO SODVPD FRQFHQWUDWLRQ YDOXHV WKH WLPH LQWHUYDO EHWZHHQ WKHVH YDOXHV DQG WKH QXPEHU RI WHUPLQDO KDOIOLYHV RYHU ZKLFK WKH VDPSOHV ZHUH FROOHFWHG Ff VHOHFWLRQ RI WKH FRPSDUWPHQW PRGHO DQG Gf SURSHU ZHLJKWLQJ RI WKH GDWD 8SRQ DFXWH ,9 EROXV DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH LQ GRJV DW WKH PJNJ GRVHV XVHG WKH SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH ZHUH EHORZ QJPO DW PLQ 6HH )LJV f 7KXV WKH DYDLODEOH DQDO\WLFDO VHQVLWLYLW\ RI QJPO GLG QRW SHUPLW DFFXUDWH HVWLPDWLRQ RI WKH WHUPLQDO KDOIOLIH )RU H[DPSOH DW WKH PJNJ 6WXG\ f ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & WKH HVWLPDWHG WHUPLQDO UDWH FRQVWDQW REWDLQHG IURP D VHPLORJDULWKPLF SORW RI WKH WHUPLQDO SKDVH SODVPD GDWD DJDLQVW WLPH Q f ZDV ; KDOIOLIH PLQf B ; 6(f PLQ 7KXV WKH UDQJH WKDW ZRXOG LQFOXGH WKH b FRQILGHQFH OLPLWV IRU WKLV UDWH FRQVWDQW ZRXOG EH ; A KDOIOLIH PLQf WR ; KDOIOLIH PLQf PLQ 6HH 7DEOH f 7KH WHUPLQDO KDOIOLIH VLJQLILFDQWO\ GHSHQGV XSRQ WKH QXPEHU RI FRPSDUWPHQWV DVVXPHG &RQVLGHU GRJ $ 6WXG\ f )LWWLQJ RI WKH GDWD ZHLJKWHG E\ WKH LQYHUVH RI WKH FRQFHQWUDWLRQ WR D FRPSDUWPHQW PRGHO JDYH D WHUPLQDO UDWH FRQVWDQW RI ; PLQ KDOIOLIH PLQf :KHQ WKH VDPH GDWD ZHUH ILWWHG WR D FRPSDUWPHQW PRGHO WKH WHUPLQDO UDWH FRQVWDQW HVWLPDWHG E\ XVLQJ WKH FRPSXWHU SURJUDP $SSHQGL[ ,f ZDV ; ; f 6(f PLQf KDOIOLIH PLQ Q 7KH b FRQILGHQFH OLPLWV VPW ZKHUH W PLQ WR WLPH

PAGE 62

7DEOH 6WDWLVWLFV RI WKH FDOFXODWHG WHUPLQDO UDWH FRQVWDQWV 3DUDPHWHU 'RJ $ 'RJ % 'RJ % 'RJ & 'RJ & 'RJ 6WXG\ 1R 'RJ 1R % % % : : : D Q ,QWHUFHSW QJPOfE PLQ & WO V RI A P b &RQILGHQFH OLPLWV IRU WKH WHUPLQDO KDOIOLIH 8SSHU OLPLW /RZHU OLPLW b &RQILGHQFH OLPLWV IRU WRWDO ERG\ FOHDUDQFH POPLQf /RZHU OLPLW 8SSHU OLPLW 1XPEHU RI SODVPD SRLQWV 4 n 7HUPLQDO SKDVH LQWHUFHSWV DQG UDWH FRQVWDQWV ZHUH FDOFXODWHG IURP WKH UHJUHVVLRQV RI WKH ORJDULWKP RI SODVPD FRQFHQWUDWLRQV DJDLQVW WLPH G 6WDQGDUG HUURUV V YDOXHV RI WKH WHUPLQDO UDWH FRQVWDQWVH ZHUH FDOFXODWHG IURP WKH P M D VWDWLVWLFV RI WKH UHJUHVVLRQV RI WKH ORJDULWKP RI WKH WHUPLQDO SODVPD FRQFHQWUDWLRQV DJDLQVW WLPH DOVR VHH UHIHUHQFH f I n b FRQILGHQFH LQWHUYDOV IRU WKH WHUPLQDO UDWH FRQVWDQWV ZHUH FDOFXODWHG IURP WWDEOH DW D OHYHO RI VLJQLILFDQFH IRU Qf GHJUHHV RI IUHHGRP VHH DOVR UHIHUHQFH f &O ZDV HVWLPDWHG XVLQJ HTXDWLRQV DQG

PAGE 63

LQILQLW\" )LJ WRS LQVHWf 7KLV ODUJH UDQJH IRU WKH FRQILGHQFH OLPLWV LV DWWULEXWDEOH WR WKH HVWLPDWLRQ RI D WHUPLQDO UDWH FRQVWDQW IURP IHZ Q f SODVPD YDOXHV 7KH HVWLPDWHG WHUPLQDO UDWH FRQVWDQWV IURP WKH VHPLORJDULWKPLF SORWV RI WKH WHUPLQDO SODVPD FRFHQWUDWLRQV DJDLQVW WLPH WKHLU UHVSHFWLYH VWDQGDUG HUURUV DQG b FRQILGHQFH OLPLWV DUH JLYHQ LQ 7DEOH 7KH WHUPLQDO KDOIOLIH HVWLPDWHG IRU VWXGLHV DQG KDYH UHODWLYHO\ OHVV HUURU FRPSDUHG WR VWXG\ 7DEOH f
PAGE 64

7KH SDUDPHWHUV RI WKH DERYH HTXDWLRQ ZHUH REWDLQHG E\ ILWWLQJ WKH EXSUHQRUSKLQH SODVPD GDWD RI GRJV WR HTXDWLRQ XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 65

WKH WHUPLQDO SKDVH SODVPD GDWD DJDLQVW WLPH 7KH VWDQGDUG HUURU YDOXH VP RI WKH WHUPLQDO VORSH ZDV PXOWLSOLHG E\ WKH WYDOXH REWDLQHG IURP W WDEOH IRU D OHYHO RI VLJQLILFDQFH WZR WDLOHG IRU Qf GHJUHH RI IUHHGRP ZKHUH Q LV WKH QXPEHU RI WHUPLQDO SODVPD SRLQWVf 7KH UHVXOWLQJ JB WVP SHUPLWWHG WKH HVWLPDWLRQ RI WKH WKH XSSHU DQG ORZHU b FRQILGHQFH OLPLWV IRU $8& FDOFXODWHG LQ DFFRUGDQFH ZLWK HTXDWLRQ RR 7KH XSSHU DQG ORZHU OLPLWV IRU WKH &OW4W ZHUH GHULYHG IURP WKH XSSHU DQG ORZHU OLPLWV RI $8& LQ DFFRUGDQFH ZLWK HTXDWLRQ 7KHVH FDOFXODWHG WRWDO ERG\ FOHDUDQFHV DQG WKH UHVSHFWLYH b FRQILGHQFH OLPLWV DUH UHSRUWHG LQ 7DEOH IRU WKH 79 EROXV VWXGLHV LQ WKH GRJV 9ROXPHV RI GLVWULEXWLRQ RI EXSUHQRUSKLQH 7KH SODVPD FRQFHQWUDWLRQ RI D GUXJ LQ WKH FHQWUDO FRPSDUWPHQW DW WLPH ]HUR LV JLYHQ E\ &S4 3$% ;4 9 (T ZKHQ DQ ,9 EROXV LV DGPLQLVWHUHG LQWR D FRPSDUWPHQW ERG\ PRGHO 9F LV WKH DSSDUHQW YROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO FRPSDUWPHQW 7KH DYHUDJH 9F ZDV B 6(0f / 7DEOH f 7KLV YDOXH H[FHHGV WKH YROXPH RI EORRG /f DQG WKH H[WUDFHOOXODU ZDWHU /f LQ GRJV 7KLV LQGLFDWHV UDSLG VHTXHVWUDWLRQ RI WKH GUXJ LQ WKH H[WUDFHOOXODU VSDFH XSRQ EROXV DGPLQLVWUDWLRQ ,I WKH FOHDULQJ RUJDQ LV LQ WKH FHQWUDO FRPSDUWPHQW 6FKHPH ,,f WKHQ WKH FOHDUDQFH IURP WKH FHQWUDO FRPSDUWPHQW &OF LV JLYHQ E\ &O 9 NQ (T F F A ,I WKH GUXJ LV VROHO\ HOLPLQDWHG IURP WKH ERG\ WKURXJK WKH FHQWUDO FRPSDUWPHQW WKH &OF LV WKH WRWDO ERG\ FOHDUDQFH &OWRW DW DQ\ WLPH GXULQJ WKH SRVWGLVWULEXWLYH SKDVH LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ

PAGE 66

(T ZKHUH LV WKH RYHUDOO DSSDUHQW YROXPH RI GLVWULEXWLRQ RI WKH HTXLOLEUDWHG IOXLGV RI WKH ERG\ 7KXV (T DQG (T ,I RU $8& KDYH ODUJH HUURUV WKHQ WKH HVWLPDWHV RI KDYH ODUJH HUURUV 7KXV WKH FDOFXODWHG GLVWULEXWLRQ YROXPHV LQ DFFRUGDQFH ZLWK HTXDWLRQ EDVHG RQ WKH EHVW FRPSXWHU ILW $SSHQGL[ ,f RI WKH SODVPD GDWD WR WULH[SRQHQWLDO HTXDWLRQ DUH VXVSHFW +RZHYHU WKH FDOFXODWHG 9M YDOXHV LQ DFFRUGDQFH ZLWK HTXDWLRQ UHSRUWHG LQ 7DEOH f DYHUDJHG / LQ H[FHVV RI WRWDO ERG\ ZDWHU LQ GRJV /f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

PAGE 67

8QIRUWXQDWHO\ GRVH LQGHSHQGHQW SKDUPDFRNLQHWLFV RI EXSUHQRUSKLQH LQ GRJV FRXOG QRW EH VWXGLHG DW KLJKO\ YDU\LQJ LQWUDYHQRXV EROXV IROGf GRVH OHYHOV 7KH ORZHU OLPLW RI GHWHFWRQ QJPOf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f UHDFKHG LPPHGLDWHO\ $OO ILYH GRJV H[KLELWHG GURZVLQHVV WKURXJKRXW WKH H[SHULPHQW DQG WKH VWDWH RI JHQHUDO GHSUHVVLRQ FKDUDFWHUL]HG E\ ODFN RI IRRG LQWDNH PLQLPDO SK\VLFDO PRWLRQ ODFN RI UHVSRQVH WR VWLPXOXV VXFK DV FODSSLQJ RI KDQGV DQG SURORQJHG VOHHSLQJ XS WR K DW D VWUHWFKf FRQWLQXHG XS WR GD\V GHSHQGLQJ XSRQ WKH GRVH RI EXSUHQRUSKLQH +LJKHU GRVHV SURGXFHG ORQJHU GXUDWLRQ RI WKHVH VLGH HIIHFWV 7R PLQLPL]H WKH SHDN SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DQG WKH DVVRFLDWHG VLGH HIIHFWV HQFRXQWHUHG XSRQ 79 EROXV DGPLQLVWUDWLRQ DQG \HW WR REWDLQ DGHTXDWH SODVPD FRQFHQWUDWLRQ YDOXHV LQ WKH WHUPLQDO SKDVH WKH KLJKHU GRVHV RI EXSUHQRUSKLQH DQG PJNJ GRVH LQ GRJ % DQG ) 6WXG\ DQG f UHVSHFWLYHO\ ZHUH DGPLQLVWHUHG E\ FRQVWDQW UDWH LQIXVLRQ RYHU D SHULRG RI K +RZHYHU VXSHULPSRVLWLRQ WR YDOLGDWH GRVH LQGHSHQGHQF\ LV LQRSHUDWLYH LI WKH GUXJ

PAGE 68

LV DGPLQLVWHUHG E\ WZR GLIIHUHQW PRGHV VXFK DV ,9 EROXV DQG LQIXVLRQf ,I D UHODWLRQVKLS FDQ EH HVWDEOLVKHG EHWZHHQ WKH SODVPD OHYHOV RI D GUXJ DGPLQLVWHUHG E\ ,9 EROXV DQG E\ ,9 LQIXVLRQ VXSHU LPSRVLWLRQ FDQ EH FKDOOHQJHG E\ WKH XVH RI WKH WUDQVIRUPHG ,9 LQIXVLRQ GDWD 6XSHULPSRVLWLRQ RI WKLV WUDQVIRUPHG KLJK GRVH ,9 LQIXVLRQ GDWD RQ ORZ GRVH ,9 EROXV GDWD ZDV HIIHFWHG E\ WKH RXWOLQHG SURFHGXUH WKDW IROORZV $QDO\VLV DQG WUDQVIRUPDWLRQ RI ,9 LQIXVLRQ GDWD 7KH SRVWLQIXVLRQ GDWD ZHUH ILWWHG WR D VXP RI HLWKHU WZR 6WXG\ DQG f RU WKUHH 6WXG\ f H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ 3n Hf 7U rW7A $n HD rW7r %n H A rW7f (T ZKHUH 7 LV WKH WLPH DW ZKLFK LQIXVLRQ ZDV VWRSSHG DQG W LV WKH WLPH DIWHU LQLWLDWLQJ WKH LQIXVLRQ 7KH ILUVW WHUP LQ WKH DERYH H[SUHVVLRQ LV VHW HTXDO WR ]HUR ZKHQ WKH SRVWLQIXVLRQ GDWD DUH ILWWHG WR D FRPSDUWPHQW ERG\ PRGHO 7KH UHODWLRQVKLS EHWZHHQ 3 DQG 3n RI HTXDWLRQV DQG UHVSHFWLYHO\ LV 3 3n7 WW OH7 7 f (T 6LPLODUO\ WKH UHODWLRQVKLSV EHWZHHQ $ $n DQG % %n DUH $ $n7 DOHD 7 f (T % %n76 OHa %7 f (T 7KH FDOFXODWHG 3 $ DQG % YDOXHV ZHUH XVHG WR JHQHUDWH WKH 4" YDOXHV RI HTXDWLRQ 7KHVH FRXOG EH WKH FDOFXODWHG SODVPD FRQFHQWUDWLRQV LI WKH VDPH GRVH ZDV DGPLQLVWHUHG E\ ,9 EROXV 7KHVH HVWLPDWHG &SFDAF FRQFHQWUDWLRQV REWDLQHG IURP WKH LQIXVLRQ VWXGLHV ZHUH

PAGE 69

GLYLGHG E\ WKH WRWDO LQIXVHG GRVH PJNJf DQG VXSHULPSRVHG RQ WKH H[SHULPHQWDO YDOXHV RI EXSUHQRUSKLQH GLYLGHG E\ WKH ,9 EROXV GRVH LQ PJNJf REWDLQHG DIWHU ORZ GRVH EROXV LQMHFWLRQ LQ WKH VDPH GRJ ,Q GRJ % DW WKUHH GRVH OHYHOV PJNJ 6WXG\ DQG f GRJ & DW WZR GRVH OHYHOV PJNJ 6WXG\ DQG f GRJ DW WZR GRVH OHYHOV DQG PJNJ 6WXG\ DQG f DQG GRJ ) DW WZR GRVH OHYHOV DQG PJNJ 6WXG\ DQG f WKHUH ZHUH QR DSSDUHQW GRVH GHSHQGHQFLHV DV GHPRQVWUDWHG E\ WKH WHVWV RI VXSHULPSRVLWLRQ VWDWLVWLFDOO\ FRQILUPHG E\ QRQSDUDPHWULF .UXVNDO:DOOLV WHVW DSSOLHG WR WKH GRVHQRUPDOLVHG SODVPD FRQFHQWUDWLRQ GDWD 6HH )LJV DQG WKH OHJHQGV DOVR UHIHU WR $SSHQGL[ ,,,f 7KH SDUDPHWHUV RI HTXDWLRQV IRU 79 LQIXVLRQ VWXGLHV LQ GRJV % DQG ) DUH JLYHQ LQ 7DEOH 3ODVPD SKDUPDFRNLQHWLFV RI WKH GHULYHG PHWDEROLWH 7KH PHWDEROLWH 0f DVVD\HG LQ SODVPD ZDV WKH DFLG K\GURO\]DEOH FRQMXJDWH RI EXSUHQRUSKLQH f 7KLV EXSUHQRSKLQH FRQMXJDWH 0f XSRQ DFLG K\GURO\VLV SUHVXPDEO\ JHQHUDWHG WKH DJO\FRQH ZKLFK TXDQWLWDWLYHO\ UHDUUDQJHG WR GHPHWKR[\EXSUHQRUSKLQH f 5DWKHU WKDQ DVVD\LQJ WKH EXSUHQRUSKLQH FRQMXJDWH RU WKH DJO\FRQH GLUHFWO\ WKLV UHDUUDQJHG SURGXFW ZDV DVVD\HG E\ +3/& VHSDUDWLRQ DQG IORULPHWULF GHWHFWLRQ 2WKHU PHWDEROLWHV VXFK DV QRUEXSUHQRUSKLQH RU LWV FRQMXJDWHV REVHUYHG LQ PDQ n ZHUH QRW GHWHFWDEOH LQ GRJ SODVPD ZLWK WKH DVVD\ VHQVLWLYLW\ RI QJPO 7KH FRQMXJDWH FRQFHQWUDWLRQ LQ SODVPD ZDV KLJKHVW DW WKH LQLWLDO VDPSOLQJ WLPH DQG GHFUHDVHG DW D UDWH VLPLODU WR WKDW RI WKH SDUHQW FRPSRXQG )LJ f 7KH PHWDEROLWH SURILOH LQ ,9 EROXV VWXGLHV FRXOG EH ILWWHG E\ D WULH[SRQHQWLDO HTXDWLRQ (T f 7KH ILWWLQJ ZDV HIIHFWHG E\ QRQOLQHDU OHDVW VTXDUH UHJUHVVLRQ E\ XVLQJ WKH FRPSXWHU SURJUDP $SSHQGL[ ,f ZKHUH WKH PHWDEROLWH FRQFHQWUDWLRQV LQ SODVPD

PAGE 70

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV RI EXSUHQRUSKLQH f LQ SODVPD GLYLGHG E\ WKH GRVH LQ PJNJ FRQHGRVHf SORWWHG DJDLQVW WLPH PLQf IRU WKH PJNJ 6WXG\ 2 f! PJNJ 6WXG\ Â’ f DQG PJNJ 6WXG\ RQ WKH SUHVXPSWLRQ RI ,9 EROXV DGPLQLVWUDWLRQf GRVHV RI EXSUHQRUSKLQH LQ GRJ % 7KH PLGGOH LQVHW LV WKH SORW RI WKH GDWD IRU WKH ILUVW PLQ DIWHU DGPLQLVWUDWLRQ DQG WKH WRS LQVHW LV WKH FRQWLQXDWLRQ RI WKH GDWD RQ DQ H[WHQGHG WLPH VFDOH 7KH GDWD IRU WKH KLJKHVW GRVH PJNJ 6WXG\ ?!f ZDV GHULYHG IURP WKH ,9 LQIXVLRQ VWXG\ LQ ZKLFK EXSUHQRUSKLQH ZDV LQIXVHG DW WKH UDWH RI PJPLQ IRU PLQ 7KH VXSHULPSRVLWLRQ RI WKH LQIXVLRQ GDWD RQ WKH ,9 EROXV GDWD ZDV HIIHFWHG E\ WKH SURFHGXUH GHVFULEHG LQ WKLV FKDSWHU XQGHU WKH VXEKHDGLQJ 'RVHLQGHSHQGHQW SKDUPDFRNLQHWLFV RI EXSUHQRUSKLQH 7KH SRLQWV ?f IRU WKH LQIXVLRQ VWXG\ ZHUH FDOFXODWHG RQ WKH SUHPLVH RI ,9 EROXV DGPLQLVWUDWLRQ RI PJNJ GRVH RI EXSUHQRUSKLQH LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ 7KH SDUDPHWHUV RI HTXDWLRQ ZHUH REWDLQHG WKURXJK HTXDWLRQV 7KH QRQSDUDPHWULF UDQN VXP WHVW .UXVNDO:DOOLV WHVW $SSHQGL[ ,,, VHH DOVR UHIHUHQFH f ZDV XVHG WR WHVW WKH K\SRWKHVLV +nf WKDW WKH GRVHQRUPDOLVHG SODVPD FRQFHQWUDWLRQV DW WKH DERYH WKUHH GRVH OHYHOV ZHUH GUDZQ IURP LGHQWLFDO GLVWULEXWLRQV 7KH FULWLFDO YDOXH RI FKLVTXDUH ZLWK D DQG GI LV 7KH REVHUYHG +n f LV OHVV WKDQ 7KHUHIRUH LW FDQ EH FRQFOXGHG WKDW WKHUH LV QR GLIIHUHQFH DPRQJ WKH WKUHH JURXSV

PAGE 71

QQ PD XQ VQQ PP 0,1 &21&'26( QJPO PJNJfaA f§ ’ F] f§ D ’ ’ ’ ’ 2

PAGE 72

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV QJPOf RI EXSUHQRUSKLQH LQ SODVPD SORWWHG DJDLQVW WLPH PLQf IRU WKH PJNJ 6WXG\ 2f GRVH LQ GRJ 7KH PJNJ GRVH 6WXG\ 4f ZDV DGPLQLVWHUHG E\ ,9 LQIXVLRQ RYHU D SHULRG RI PLQ ,QIXVLRQ UDWH RI EXSUHQRUSKLQH DV EDVH PJPLQ 7KH VXSHULPSRVLWLRQ RI LQIXVLRQ GDWD RQ ,9 EROXV GDWD ZDV HIIHFWHG E\ WKH SURFHGXUH GHVFULEHG LQ WKLV FKDSWHU XQGHU WKH VXEKHDGLQJ 'RVHLQGHSHQGHQW SKDUPDFRNLQHWLFV RI EXSUHQRUSKLQH 7KH SRLQWV Â’f UHSUHVHQW TXRWLHQW RI FRQFHQWUDWLRQV GLYLGHG E\ GRVH WKDW ZHUH FDOFXODWHG RQ WKH SUHPLVH RI ,9 EROXV DGPLQLVWUDWLRQ RI PJNJ GRVH RI EXSUHQRUSKLQH LQ DFFRUGDQFH ZLWK HTXDWLRQ 7KH SDUDPHWHUV RI HTXDWLRQ ZHUH REWDLQHG WKURXJK HTXDWLRQV 7KHVH FDOFXODWHG SRLQWV ZHUH PXOWLSOLWHG E\ WR FKDOOHQJH VXSHULPSRVLWLRQ 7KH QRQSDUDPHWULF UDQN VXP WHVW .UXVNDO:DOOLV WHVW $SSHQGL[ ,,, VHH DOVR UHIHUHQFH f ZDV XVHG WR WHVW WKH K\SRWKHVLV +nf WKDW WKH GRVHQRUPDOLVHG SODVPD FRQFHQWUDWLRQV DW WKH DERYH WZR GRVH OHYHOV ZHUH GUDZQ IURP LGHQWLFDO GLVWULEXWLRQV 7KH FULWLFDO YDOXH RI FKLVTXDUH ZLWK D DQG GI O LV 7KH REVHUYHG +n f LV OHVV WKDQ 7KHUHIRUH LW FDQ EH FRQFOXGHG WKDW WKHUH LV QR GLIIHUHQFH DPRQJ WKH WZR JURXSV

PAGE 73

&21*'26( QJPO PJ$JfBnn &' &' &' =' &' ‹’’’’,

PAGE 74

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV RI EXSUHQRUSKLQH f LQ SODVPD GLYLGHG E\ WKH GRVH PJNJf SORWWHG DJDLQVW WLPH PLQf IRU WKH PJNJ 6WXG\ 2f DQG PJNJ 6WXG\ f GRVH RI EXSUHQRUSKLQH GRJ & 7KH LQVHW LV WKH FRQWLQXDWLRQ RI GDWD RQ DQ H[WHQGHG WLPH VFDOH XS WR PLQ 7KH QRQSDUDPHWULF UDQN VXP WHVW .UXVNDO:DOOLV WHVW $SSHQGL[ ,,, VHH DOVR UHIHUHQFH f ZDV XVHG WR WHVW WKH K\SRWKHVLV +nf WKDW WKH GRVHQRUPDOLVHG SODVPD FRQFHQWUDWLRQV DW WKH DERYH WZR GRVH OHYHOV ZHUH GUDZQ IURP LGHQWLFDO GLVWULEXWLRQV 7KH FULWLFDO YDOXH RI FKLVTXDUH ZLWK D DQG GI O LV 7KH REVHUYHG +n f LV OHVV WKDQ 7KHUHIRUH LW FDQ EH FRQFOXGHG WKDW WKHUH LV QR GLIIHUHQFH DPRQJ WKHVH WZR JURXSV

PAGE 75

1, : ' 8W! 8O! 8 8, &21&'26(

PAGE 76

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV QJPOf RI EXSUHQRUSKLQH f LQ SODVPD SORWWHG DJDLQVW WLPH PLQf IRU WKH PJNJ 2f ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ WKH ELOH FDQQXODWHG GRJ ) PRUSKLQH EXSUHQRUSKLQH LQWHUDFWLRQ VWXG\ f 7KH PJNJ GRVH 6WXG\ Â’ f ZDV DGPLQLVWHUHG E\ ,9 LQIXVLRQ RYHU D SHULRG RI PLQ ,QIXVLRQ UDWH RI EXSUHQRUSKLQH DV EDVH PJPLQ 7KH VXSHULPSRVLWLRQ RI LQIXVLRQ GDWD RQ ,9 EROXV GDWD ZDV HIIHFWHG E\ WKH SURGHGXUH GHVFULEHG LQ WKLV FKDSWHU XQGHU WKH VXEKHDGLQJ 'RVHLQGHSHQGHQW SKDUPDFRNLQHWLFV RI EXSUHQRUSKLQH 7KH SRLQWV Â’f UHSUHVHQW TXRWLHQW RI WKH FRQFHQWUDWLRQV GLYLGHG E\ GRVH WKDW ZHUH FDOFXODWHG RQ WKH SUHPLVH RI ,9 EROXV DGPLQLVWUDWLRQ RI PJNJ GRVH RI EXSUHQRUSKLQH LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ 7KH SDUDPHWHUV RI WKH HTXDWLRQ ZHUH REWDLQHG WKURXJK HTXDWLRQV 7KHVH FDOFXODWHG SRLQWV ZHUH PXOWLSOLHG E\ WR FKDOOHQJH VXSHULPSRVLWLRQ 7KH QRQSDUDPHWULF UDQN VXP WHVW .UXVNDO:DOOLV WHVW $SSHQGL[ ,,, VHH DOVR UHIHUHQFH f ZDV XVHG WR WHVW WKH K\SRWKHVLV +nf WKDW WKH GRVHQRUPDOLVHG SODVPD FRQFHQWUDWLRQV DW WKH DERYH WZR GRVH OHYHOV ZHUH GUDZQ IURP LGHQWLFDO GLVWULEXWLRQV 7KH FULWLFDO YDOXH RI FKLVTXDUH ZLWK D DQG GI O LV 7KH REVHUYHG +n f LV OHVV WKDQ 7KHUHIRUH LW FDQ EH FRQFOXGHG WKDW WKHUH LV QR GLIIHUHQFH DPRQJ WKH WZR JURXSV

PAGE 77

QAPL XXANJf 0,1 , '

PAGE 78

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV RI EXSUHQRUSKLQH 2f DQG PHWDEROLWH 0 Â’f LQ SODVPD SORWWHG DJDLQVW WPH IRU Df PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ Ef PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ Ff PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ Gf PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 7KH VROLG OLQHV UHSUHVHQW FXUYHV ILWWHG WR WKH SODVPD GDWD RI EXSUHQRUSKLQH DQG 0 LQ DFFRUGDQFH ZLWK HTXDWLRQ

PAGE 79

QXQ L &21& 16nWO/ &21& .*0/ 1,. W-'/L ,-=Wn f '0

PAGE 80

ZHUH ZHLJKWHG E\ WKHLU LQYHUVH 7KH YDOLGLW\ RI WULH[SRQHQWLDO HTXDWLRQ ZDV FRQILUPHG E\ GHPRQVWUDWLRQ WKDW WKH UHJUHVVLRQV LQ YDULRXV VWXGLHV )LJ f RI WKH ZHLJKWHG UHVLGXDOV f (T f DJDLQVW ORJ 0SFDAF HVWLPDWHG PHWDEROLWH FRQFHQWDWLRQVf JDYH PHDQ UHVLGXDOV f VORSHV DQG LQWHUFHSWV DOO RI ZKLFK ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR 7DEOH f 7KH SODVPD FRQFHQWUDWLRQWLPH SURILOHV RI PHWDEROLWH LQ WKH ,9 EROXV VWXGLHV f DUH JLYHQ LQ )LJV 0D[LPXP SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH ZDV REVHUYHG DW WKH LQLWLDO VDPSOLQJ WLPH DERXW PLQf &RQWLQXHG VDPSOLQJ JDYH PRQRWRQLFDOO\ GHFOLQLQJ PHWDEROLWH FRQFHQWUDWLRQV VLPLODU WR WKH GHFD\ RI WKH SDUHQW FRPSRXQG 7KH SDUDOOHO GHFD\V RI EXSUHQRUSKLQH DQG LWV FRQMXJDWH FRQFHQWUDWLRQV )LJ f LQ SODVPD GXULQJ WKH LQLWLDO GLVWULEXWLYH SKDVH LQGLFDWH WKDW WKH UDWH GHWHUPLQLQJ VWHS LQ WKH SODVPD GHFD\ RI WKH FRQMXJDWH ZDV LWV IRUPDWLRQ 'XULQJ WKH WHUPLQDO HOLPLQDWLRQ SKDVH WKH UDWH GHWHUPLQLQJ VWHS LQ WKH SODVPD GHFD\ RI EXSUHQRUSKLQH DQG LWV FRQMXJDWH ZDV WKH VORZ UHWXUQ RI EXSUHQRUSKLQH IURP GHHS WLVVXHV WR WKH FHQWUDO FRPSDUWPHQW ZKHUH LW FRXOG EH PHWDEROL]HG 7KLV LV WKH FODVVLFDO nIOLSIORSn SKDUPDFRNLQHWLFV IRU WKH FRQMXJDWH

PAGE 81

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVP FRQFHQWUDWLRQV RI PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ NJ GRJ $ 6WXG\ 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVP GDWD WR D VXP RI WZR H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ &SQJPOf Hr HBr W 7KH LQVHW LV WKH FRQWLQXDWLRQ RI WKH GDWD IRU WKH H[WHQGHG WLPH VFDOH XS WR PLQ

PAGE 82

0,1

PAGE 83

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV QJPOf RI PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ NJ GRJ % 6WXG\ 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD RI 0 WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK HTXDWLRQ f &S QJPOf H rn W HBn W H W 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO SHULRG RI PLQ

PAGE 84

1, : ,--,& +8A -,, -861 n1

PAGE 85

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV QJPOf RI PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH f LQ NJ GRJ & 6WXG\ 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD RI 0 WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f a W B& W 4 W &S QJPOf H H H 7KH LQVHW LV D FRQWLQXDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU DQ H[WHQGHG WLPH VFDOH XS WS PLQ 7KH WHUPLQDO KDOIOLIH ZDV HVWLPDWHG WR EH PLQ 7KLV YDOXH KDG PXFK HUURU GXH WR OLPLWHG DQDO\WLFDO VHQVLWLYLW\ ORZ GRVH DQG ODFN RI VXIILFLHQW QXPEHU RI WHUPLQDO SKDVH SODVPD SRLQWV

PAGE 86

FRVD 1*n+L

PAGE 87

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV QJPOf RI PHWDEROLWH 0f LQ DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH f LQ WKH NJ GRJ % 6WXG\ 7KH LQVHW UHSUHVHQWV GDWD DQG WKH VWUDLJKW OLQH ILWWHG WR WKH WHUPLQDO SKDVH LQ DFFRUGDQFH ZLWK WKH PRQRH[SRQHQWLDO HTXDWLRQ &S QJPOf H W

PAGE 88

&&1& 1*n0/ 071

PAGE 89

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV QJPOf RI PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ NJ GRJ & 6WXG\ 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD RI 0 WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f B W $ RF W 0U T W &S QJPOf H H H 7KH LQVHW LV D FRQWLQXDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH RQ DQ H[WHQGHG WLPH VFDOH XS WS PLQ

PAGE 90

1: Â’Â’/L :=9 'e 81 :61 f&12&-

PAGE 91

85,1$5< (;&5(7,21 2) %835(1253+,1( 6LJPD PLQXV SORWV ,I LW FDQ DVVXPHG WKDW EXSUHQRUSKLQH LV VROHO\ HOLPLQDWHG IURP WKH FHQWUDO FRPSDUWPHQW WKH XULQDU\ H[FUHWLRQ UDWH RI LQWDFW GUXJ FDQ EH GHILQHG DV G8GW NX ;F (T ZKHUH LV WKH XULQDU\ H[FUHWLRQ UDWH FRQVWDQW DQG ;F LV WKH DPRXQW RI GUXJ LQ WKH FHQWUDO FRPSDUWPHQW DW WLPH W ,QWHJUDWLQJ HTXDWLRQ EHWZHHQ WR 8 WLPH WR Wf UHVXOWV LQ 8 ( 8 3Ha $HDW %Hf (T RR YKHUH 3 N 9 LU (T X F $ N 9 D (T X F % N 9 X F (T 7KH YDOXHV RI 3 $ DQG % DUH VDPH DV LQ (TV DQG UHVSHFWLYHO\ LI FRQVWDQW UHQDO FOHDUDQFH LV SUHVXPHG 7KXV D SORW RI WKH ORJDULWKP RI WKH DPRXQW RI XQFKDQJHG GUXJ UHPDLQLQJ WR EH H[FUHWHG YHUVXV WLPH VLJPD PLQXV SORWf JLYHV D VWUDLJKW OLQH ZLWK D WHUPLQDO VORSH HTXDO WR J LH WKH VDPH WHUPLQDO VORSH REWDLQHG IURP D VHPLORJDULWKPLF SORW RI SODVPD FRQFHQWUDWLRQ &Sf YHUVXV WLPH 5HSUHVHQWDWLYH H[DPSOHV RI WKH VLJPD PLQXV SORWV IRU WKH XULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH DUH JLYHQ LQ )LJ )RU GRJ $ 6WXG\

PAGE 92

)LJXUH 6DUG ORJDULWKPLF SORWV RI WKH DPRXQWV RI WKH XQFKDQJHG EXSUHQRUSLQH f UHPDLQLQJ WR EH H[FUHWHG LQ XULQH YHUVXV WLPH VLJPD PLQXV SORWf LQ DFFRUGDQFH ZLWK HTXDWLRQ Df 6HPLORJDULWKPLF ILWWLQJ RI WKH LQLWLDO XULQH GDWD XS WR PLQ IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ $Q DSSDUHQW UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf ZDV REWDLQHG Ef )LWWLQJ RI WKH VLJPD PLQXV SORW RI EXSUHQRUSKLQH LQ XULQH RI GRJ % 6WXG\ DW PJNJ GRVH RI EXSUHQRUSKLQH WR D VXP RI WZR H[SRQHQWLDOV 7KH HVWLPDWHG K\EULG UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf Ff 6LJPD PLQXV SORW RI XULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH IRU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 7KH DSSDUHQW WHUPLQDO SKDVH UDWH FRQVWDQW IRU WKH PRQRH[SRQHQWLDO ILWWLQJ ZDV PLQ KDOIOLIH PLQf Gf 7KH ILWWHG VLJPD PLQXV SORW RI EXSUHQRUSKLQH LQ XULQH RI GRJ & DW PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH 6WXG\ WR D VXP RI WZR H[SRQHQWLDOV 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf UHVSHFWLYHO\

PAGE 93

*8,r *8, :LQ n 482 ,*OLOO 0,+ PX RQ L

PAGE 94

)LJ Df VHPLORJDULWKPLF ILWWLQJ RI WKH LQLWLDO GDWD ZDV OLQHDU RQO\ XS WR PLQ 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQW ZDV PLQ A KDOIOLIH PLQf 7KLV FRUUHVSRQGHG WR WKH VHFRQG GLVWULEXWLRQDO KDOIOLIH PLQf REWDLQHG IRU EXSUHQRUSKLQH IURP WKH SODVPD GDWD 7DEOH f 7KH VLJPD PLQXV SORW RI EXSUHQRUSKLQH LQ XULQH RI GRJ % )LJ Ef DW PJNJ 6WXG\ f GRVH VKRZHG FXUYDWXUH DQG FRXOG EH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV 7KH UHVXOWLQJ K\EULG UDWH FRQVWDQWV ZHUH KDOIOLIH PLQf DQG KDOIOLIH PLQf PLQ 7KH ILUVW KDOIOLIH FRUUHVSRQGHG WR WKH VHFRQG GLVWULEXWLRQDO KDOIOLIH RI EXSUHQRUSKLQH PLQ 7DEOH f IRU WKLV GRJ )RU GRJ & )LJ Ff DW PJNJ GRVH 6WXG\ 7DEOH f WKH VLJPD PLQXV SORW RI XULQDU\ GDWD JDYH DQ DSSDUHQW WHUPLQDO SKDVH UDWH FRQVWDQW RI PLQ A KDOIOLIH PLQf 7KLV FRUUHVSRQGHG ZLWK WKH WHUPLQDO KDOIOLIH RI EXSUHQRUSKLQH PLQf REWDLQHG IURP WKH SODVPD GDWD )RU WKH VDPH GRJ DW PJNJ GRVH 6WXG\ f VLJPD PLQXV SORW )LJ Gf VKRZHG FXUYDWXUH DQG FRXOG EH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV DQG WKH UHVSHFWLYH DSSDUHQW UDWH FRQVWDQWV ZHUH KDOIOLIH PLQf DQG KDOIOLIH PLQf PLQ 7KH ILUVW KDOIOLIH REWDLQHG IURP WKH XULQH GDWD FRUUHVSRQGHG ZLWK WKH VHFRQG GLVWULEXWLRQDO KDOIOLIH PLQ 7DEOH f REWDLQHG IRU EXSUHQRUSKLQH IURP SODVPD GDWD 7KH VLJPD PLQXV SORWV IRU WKH XULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH LQ RWKHU GRJV VKRZHG JUHDW VFDWWHULQJ DQG UHDVRQDEOH HVWLPDWHV RI WKH DSSDUHQW UDWH FRQVWDQWV ZHUH QRW SRVVLEOH 7KH KDOIOLYHV REWDLQHG IURP WKH YDULRXV VLJPD PLQXV SORWV VKRZQ LQ )LJ IRU WKH XULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH UHDVRQDEO\ DSSUR[LPDWHG WKH ILUVW DQG VHFRQG GLVWULEXWLRQDO KDOIOLYHV RI EXSUHQRUSKLQH LQ SODVPD 6LQFH D PLQRU IUDFWLRQ RI WKH WKH GRVH ZDV

PAGE 95

H[FUHWHG XQFKDQJHG LQ XULQH bf DQG WKH OLPLW RI GHWHFWLRQ RI EXSUHQRUSKLQH ZDV QJPO WKH WHUPLQDO KDOIOLIH RI EXSUHQRUSKLQH LQ GRJV FRXOG QRW EH UHDGLO\ HVWLPDWHG IURP WKH XULQDU\ GDWD 6LJPD PLQXV SORWV IRU WKH FRQMXJDWHV 0f DUH JLYHQ LQ )LJV )RU GRJ $ 6WXG\ f WKH FXUYH FRXOG EH XQH[SHFWHGO\ DQG IRU QR REYLRXV UHDVRQ ILWWHG EHVW E\ D VLPSOH OLQHDU HTXDWLRQ WR LQGLFDWH D FRQVWDQW UDWH RI UHQDO HOLPLQDWLRQ HYHQ ZLWK GHFUHDVLQJ SODVPD FRQFHQWUDWLRQV RI WKH FRQMXJDWH 7KH H[FUHWLRQ UDWH ZDV DSSUR[LPDWHO\ QJPLQ LQGHSHQGHQW RI FRQFHQWUDWLRQ RI PHWDEROLWH LQ WKH FHQWUDO FRPSDUWPHQW )LJ Df )RU GRJ % DW PJNJ GRVH 6WXG\ f RI EXSUHQRUSKLQH 7DEOH f WKH VLJPD PLQXV SORW JDYH DQ DSSDUHQW UDWH FRQVWDQW RI PLQ A KDOIOLIH PLQ )LJ Ef )RU GRJ & DW PJNJ GRVH 6WXG\ f )LJ Ff DQ DSSDUHQW UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf ZDV REWDLQHG ZKLFK FRUUHVSRQGHG ZHOO ZLWK WKH WHUPLQDO SKDVH KDOIOLIH REWDLQHG IRU 0 IURP SODVPD GDWD PLQ 7DEOH f )RU GRJ % DW PJNJ GRVH 6WXG\ f WKH VLJPD PLQXV SORW )LJ Gf VKRZHG FXUYDWXUH DQG FRXOG EH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV DQG WKH DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ A KDOIOLIH PLQf DQG PLQ A KDOIOLIH PLQf UHVSHFWLYHO\ ZKHUH WKH VHFRQG KDOIOLIH FRUUHVSRQGHG ZLWK WKH WHUPLQDO KDOIOLIH REWDLQHG IURP WKH SODVPD GDWD RI 0 LQ WKLV GRJ 7DEOH KDOIOLIH PLQf 7KH VLJPD PLQXV SORW IRU 0 LQ GRJ & DW PJNJ GRVH 6WXG\ f VKRZHG FXUYDWXUH )LJ f DQG FRXOG EH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV WKH DSSDUHQW UDWH FRQVWDQWV EHLQJ PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf ,Q GRJ & DW PJNJ 6WXG\ f ,9 EROXV GRVH RI EXSUHQRUSKLQH WKH WHUPLQDO KDOIOLIH RI EXSUHQRUSKLQH ZDV HVWLPDWHG DV PLQ 7DEOH

PAGE 96

)LJXUH 6HPLRJDULWKPLF SORWV RI WKH DPRXQWV RI PHWDEROLWH 0f UHPDLQLQJ WR EH H[FUHWHG LQ XULQH YHUVXV WLPH VLJPD PLQXV SORWf IROORZLQJ ,9 EROXV DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH f LQ DFFRUGDQFH ZLWK HTXDWLRQ Df 7KH H[FUHWLRQ GDWD RI 0 LQ XULQH XS WR PLQ FRXOG EH ILWWHG WR D VLPSOH OLQHDU HTXDWLRQ LQ GRJ $ 6WXG\ DW PJNJ GRVH RI EXSUHQRUSKLQH 7KH H[FUHWLRQ UDWH ZDV HVWLPDWHG WR EH QJPLQ Ef 6LJPD PLQXV SORW RI 0 LQ XULQH RI GRJ % 6WXG\ IROORZLQJ PJNJ GRVH RI EXSUHQRUSKLQH UHVXOWLQJ LQ D HVWLPDWHG DSSDUHQW UDWH FRQVWDQW PLQ KDOIOLIH PLQf Ff 6LJPD PLQXV SORW RI 0 LQ XULQH IRU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 7KH DSSDUHQW UDWH FRQVWDQW ZDV HVWLPDWHG WDV PLQ KDOIOLIH PLQf Gf 6LJPD PLQXV SORW RI WKH XULQDU\ H[FUHWLRQ RI 0 IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ 7KH GD WDWD ZHUH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK HTXDWLRQ 7KH HVWLPDWH DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ KDOIOLJH PLQf DQG PLQ KDOIOLIH PLQf UHVSHFWLYHO\

PAGE 97

1,, 8OWIOf ,OnOW( ?f=U= ,+f FP 1: FUL QWUD XZ QRWf X"F LLL DW r 66OI r R fk 2n R R R Rk ‘2 TE XP '8' +,0 VVUI r Q] ‘rfQ]

PAGE 98

)LJXUH 6HPL RJDULWKPLF SORW RI WKH DPRXQW RI WKH PHWDEROLWH 0f UHPDLQLQJ WR EH H[FUHWHG YHUVXV WLPH VLJPD PLQXV SORWf IROORZLQJ PJNJ GRVH RI EXSUHQRUSKLQH f LQ GRJ & 6WXG\ 7KH GDWD ZDV ILWWHG WR D VXP RI WZR H[SRQHQWLDOV 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf UHVSHFWLYHO\

PAGE 99

6*I QL fQ] ,O >,/c Ic>L *WLO c>LL 07+

PAGE 100

f 7KH SODVP GDWD DQG VLJPD PLQXV SORW RI 0 LQ WKLV GRJ JDYH DQ DSSDUHQW WHUPLQDO KDOIOLYHV RI )LJ f DQG )LJ Ff UHVSHFWLYHO\ 7KLV PHWDEROLWH KDOIOLIH LV WKHUHIRUH DQ DSSDUHQW GLVWULEXWLRQDO KDOIOLIH DQG QRW WKH WHUPLQDO KDOIOLIH 8ULQDU\ H[FUHWLRQ UDWH SORWV 6LQFH [F YF &S LQ HTXDWLRQ VXEVWLWXWLQJ WKH YDOXH RI &S IURP HTXDWLRQ LQWR HTXDWLRQ 7YLLL f7W A LLL DW s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f ILQLWH DPRXQWV $ 8f RI HLWKHU RU 0 H[FUHWHG GXULQJ D ILQLWH WLPH LQWHUYDO D Wf DJDLQVW WPLG PLGSRLQW RI WKH FROOHFWLRQ LQWHUYDOf ZHUH KLJKO\ VFDWWHUHG LQ PRVW RI WKH VWXGLHV 7KXV RQO\ WKH GDWD IRU GRJ $ 6WXG\ f DQG % 6WXG\ f DUH UHSRUWHG KHUH ,Q GRJ $ 6WXG\ f XULQH GDWD RI EXSUHQRUSKLQH XS

PAGE 101

WR PLQ FRXOG EH ILWWHG WR ORJ $8 $W Nnf WPLG LQWHUFHSW DQG WKH DSSDUHQW UDWH FRQVWDQW Nf PLQ A KDOIOLIH PLQf FRUUHVSRQGHG ZLWK WKH SODVPD VHFRQG GLVWULEXWLRQDO KDOIOLIH RI PLQ 7DEOH )LJ Df ,Q GRJ % DW PJNJ GRVH 6WXG\ f WKH H[FUHWLRQ UDWH SORW IRU 0 )LJ Ef JDYH DQ DSSDUHQW UDWH FRQVWDQW PLQ KDOIOLIH PLQf ,Q WKH VDPH GRJ DW WKLV GRVH OHYHO WKH H[FUHWLRQ UDWH SORW RI EXSUHQRUSKLQH FRXOG EH ILWWHG LQWR WZR VHSDUDWH OLQHDU VHJPHQWV )LJ f IURP ZKLFK WKH WZR DSSDUHQW UDWH FRQVWDQWV REWDLQHG ZHUH PLQ A KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf %RWK WKHVH KDOIOLYHV FRUUHVSRQGHG ZLWK WKH KDOIOLYHV REWDLQHG IURP WKH SODVPD GDWD 7DEOH DQG PLQf &OHDUDQFHV RI %XSUHQRUSKLQH f DQG &RQMXJDWH 0f 5HQDO FOHDUDQFH RI EXSUHQRUSKLQH 8SRQ UHDUUDQJHPHQW RI HTXDWLRQ G8GW NX 9F &S (T ,QWHJUDWLQJ EHWZHHQ WR 8 WLPH WR Wf W e8 N9 I &S GW &O $8& (T X F TU UHQ W A ZKHUH $8&A LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH 7KH UHQDO FOHDUDQFH RI EXSUHQRUSKLQH &OAHQ f HVWLPDWHG IURP WKH VORSHV RI FXPXODWLYH DPRXQWV H[FUHWHG LQ XULQH (8 DJDLQVW $8&IF DYHUDJHG B 6(0f POPLQ 7DEOH f ZKLFK LQGLFDWH KLJK SURWHLQ ELQGLQJ LI XQERXQG GUXJ H[FUHWHG VROHO\ E\ JORPHUXODU ILOWUDWLRQ 7KHVH FOHDUDQFH SORWV )LJV f IUHTXHQWO\ GLG QRW JR WKURXJK WKH RULJLQ DQG FRXOG EH EHVW FKDUDFWHUL]HG E\ RQH RU PRUH VWUDLJKW OLQHV FRQIRUPLQJ WR WKH HTXDWLRQ

PAGE 102

2 f )LJXUH 6HU£ ORJDULWKPLF SORWV RI WKH DPRXQWV \ Jf RI Df EXSUHQRUSKLQH f DQG Ef PHWDEROLWH 0f H[FUHWHG LQ XULQH SHU PLQ \JPLQf SORWWHG DJDLQVW WPLG WKH PLG SRLQW RI WKH XULQH FROOHFWLRQ LQWHUYDO LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ ORJ $8 $W aNnf WPLG LQWHUFHSW )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ 7DEOH f WKH SORW LQ DFFRUGDQFH ZLWK WKH DERYH HTXDWLRQ IRU JDYH DQ DSSDUHQW UDWH FRQVWDQW PLQ KDOIOLIH PLQf )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ WKH SORW LQ DFFRUGDQFH ZLWK WKH DERYH HTXDWLRQ IRU 0 JDYH DQ DSSDUHQW UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf

PAGE 103

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH DPRXQWV \ Jf RI EXSUHQRUSKLQH f H[FUHWHG LQ XULQH SHU PLQ \JPLQf SORWWHG DJDLQVW WPLG WKH PLG SRLQW RI WKH XULQH FROOHFWLRQ LQWHUYDO IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ ORJ $8$ W Nnf WPLG LQWHUFHSW 7KH LQVHWV UHSUHVHQW WKH GDWD ILWWHG LQWR WZR VHSDUDWH OLQHDU VHJPHQWV DV SHU WKH DERYH HTXDWLRQ 7KH HVWLPDWHG UDWH FRQVWDQWV ZHUH PLQ D KDOIOLIH PLQf DQG PLQ E KDOIOLIH PLQf 1RWH WKH FRUUHVSRQGHQFH RI WKHVH UDWH FRQVWDQWV ZLWK WKRVH UHSRUWHG LQ ILJ IRU WKH SODVPD GDWD RI WKLV GRJ 6WXG\ 7DEOH f

PAGE 104

''7 S*0,1 O XP R F3 OR R 2 2 b OUS )RY 2 nnn2 O r R R2 R 2 2 D f§ R D f 2nn 2n R + K R , ,%2 7 0,' +,+f 2 R + + VWLQ OWO ,27 7 0,' &,1f >O QQ YR

PAGE 105

)LJXUH 3ORW RI WKH FXPXODWLYH DPRXQWV \Jf RI EXSUHQRUSKLQH f H[FUHWHG LQ XULQH DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH $8& \JPLQPOf LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f 8 &O $8& $8&Q f UHQ n W ZKHUH $8&A LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW ( 8 )RU WKH UUTNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ WKH FXUYH VKRZV WKUHH GLVWLQFWO\ OLQHDU VHJPHQWV DWWULEXWDWEOH WR WKH S+ HIIHFW RI XULQH 7KH VORSH &OUHQf RI WKH LQLWLDO OLQHDU VHJPHQW IRU WKH S+ UDQJH EHWZHHQ ZDV HVWLPDWHG WR EH POPLQ 6HH DOVR QH[W ILJXUH

PAGE 106

VVn QL L QQ E P Ic WL LUL IW8&7 M-* ; 0,1 0/ U->O

PAGE 107

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV ( 8 S Jf RI EXSUHQRUSKLQH f H[FUHWHG LQ XULQH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH WLPH RI XULQH FROOHFWLRQ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f = 8 &O > $8& $8&D @ UHQ W ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ WLPH FXUYH DW L 8 Df )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ WKH LQLWLDO VORSH ZDV HVWLPDWHG WR EH POPLQ Ef )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ WKH LQLWLDO VORSH &OUHQ f ZDV HVWLPDWHG DV POPLQ Ff )RU WKH ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ WKH HVWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ IRU WKH LQLWLDO WLPH SHULRG XS WR PLQ Gf ,Q WKH VDPH GRJ DW WKLV GRVH OHYHO HVWLPDWHG FOHDUDQFH ZDV POPLQ IRU WKH XULQH FROOHFWLRQ WLPH EHWZHHQ PLQ ,Q WKLV GRJ WKH S+ RI WKH XULQH UDQJHG EHWZHHQ GXULQJ WKH LQLWLDO PLQ WLPH SHULRG WKH S+ UDQJH ZDV IRU WKH WLPH SHULRG EHWZHHQ PLQ

PAGE 108

VUI Q] VVU7 UQ 06 WQnMLL &LG An D 2n R 6 A ? ? A V k ? ? 9 ? ? 0LO ,6 06,, f§ 6 ,4 ,6 6 Q8&7 -2 ; 0,1 0/ Wf§ 004 & r 0 2nn *5,, B nnnR Y! A Rnn R f 2n 0LO nn• 2nnn QXF -2 ; 0,1 0/ UX -8*6 2-*6

PAGE 109

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV e 8 \ Jf RI EXSUHQRUSKLQH f H[FUHWHG LQ XULQH DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH $8& W \JPLQPOf DW WKH WLPH RI XULQH FROOHFWLRQ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f e 8 &O UHQ > $8&W $8&T @ ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW [ 8 R Df )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ WKH HVWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ IRU WKH LQLWLDO WLPH SHULRG XS WR PLQ Ef 6DPH DV LQ Df H[FHSW WKH SRLQWV XS WR PLQ ZHUH QRW LQFOXGHG LQ WKH UHJUHVVLRQ WLPH PLQf (VWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ 7KLV ORZ UHQDO FOHDUDQFH FRXOG EH DWWULEXWDEOH WR WKH FHVVDWLRQ RI XULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH GXULQJ WKH WLPH LQWHUYDO EHWZHHQ PLQ Ff ,Q WKH VDPH GRJ WKH HVWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ IRU WKH ODWWHU WLPH SHULRG EHWZHHQ PLQ Gf )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ WKH HVWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ IRU WKH LQLWLDO WLPH SHULRG EHWZHHQ PLQ ,Q WKH VDPH GRJ UHJUHVVLRQ DFFRUGLQJ WR WKH DERYH HTXDWLRQ f JDYH WKH VORSH &OUHQ POPLQ IRU WKH LQLWLDO WLPH SHULRG XS WR PLQ ,QWHUFHSW U VHH DOVR 7DEOH f

PAGE 110

VVUU QL VVUU P 0 ,4 A : 0 0 A E %2 2 2n 2 2n22 2n 2n + t 6 IW8&7 --* ; 0,1 0/ 2E fn4 RR 2 IW8&7 -,* ; 0,1 0/ K E +

PAGE 111

= X &OUHQ $8&W $8&T f (T ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ WLPH FXUYH DW (8 DV HVWLPDWHG IURP WKH H[WUDSRODWLRQ RI WKH EHVW OLQHDU SORWV RI 8 YHUVXV $8& 7DEOH f 7KLV QRQ]HUR LQWHUFHSW FRXOG EH DWWULEXWHG WR RQH RI VHYHUDO IDFWRUV :KHQ WKH XULQDU\ FOHDUDQFH REWDLQHG IURP WKH TXRWLHQW RI $ 8 $W DJDLQVW &SAB A ZKHUH ODWWHU LV WKH SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI VXFFHVVLYH XULQH FROOHFWLRQVf ZDV OLQHDUO\ UHODWHG WR XULQDU\ S+ LQ GRJ $ 6WXG\ )LJ f 5HQDO FOHDUDQFH ZDV ORZ DW KLJK XULQH S+ ,I LW FDQ EH K\SRWKHVL]HG WKDW WKH XQFKDUJHG EXSUHQRUSKLQH LQ XULQH DW KLJK S+ YDOXHV S.Dn f FDQ XQGHUJR UHQDO WXEXODU UHDEVRUSWLRQ WKHQ ORZHU FOHDUDQFHV VKRXOG EH REVHUYHG DW KLJK XULQH S+ YDOXHV 7KH SRVVLEOH UHQDO PHFKQLVP FRXOG EH S+ GHSHQGHQW WXEXODU UHDEVRUSWLRQ RI QHXWDO VSHFLHV DQG LQFUHDVHG H[FUHWLRQ RI LRQL]HG VSHFLHV DW ORZHU S+ YDOXHV 7KLV LV VXSSRUWHG E\ WKH IDFW WKDW LQ GRJ % DW PJNJ 79 EROXV GRVH RI EXSUHQRUSKLQH 6WXG\ f QR GUXJ ZDV REVHUYHG LQ WKH XULQH IRU D S+ DERYH )LJ f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

PAGE 112

)LJXUH 3ORWV RI &OUHQ POPLQf DJDLQVW XULQDU\ S+ 7KH UHQDO FOHDUDQFH ZDV FDOFXODWHG IURP WKH TXRWLHQW RI WKH XULQDU\ H[FUHWLRQ UDWH D8D W \ JPLQ DQG WKH SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO &SA Df )RU WKH PJNJ 79 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ U f Ef )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ U f Ff )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % VWXG\ 1RWH WKH DEVHQFH RI UHQDO FOHDUDQFH DERYH S+ 6HH DOVR WH[W

PAGE 113

&/ .(1 0/0,1 1! ,6f

PAGE 114

)LJXUH 3ORWV RI XULQH IORZ POPLQf DJDLQVW WPLG WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH f LQ GRJ $ 6WXG\ Ef )RU WKH PJNJ 6WGX\ 2f DQG PJNJ 6WXG\ Â’f ,9 EROXV GRVHV UHVSHFWLYHO\ RI EXSUHQRUSKLQH LQ GRJ % 1RWH WKH GRVH GHSHQGHQW GHFUHDVH LQ XULQH IORZ UDWH Ff )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\

PAGE 115

r 4 7 0,' 0,1f 85,1( )/28 0O0,1 85,1( )/&8 00,1

PAGE 116

,OO ILUVW IHZ KRXUV DIWHU WKH DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH )LJ f ZKLFK DOVR LQGLFDWHG GRVHGHSHQGHQW UHQDO HOLPLQDWLRQ )LJ Ef 7KLV FRXOG SRVVLEO\ H[SODLQ WKH QHJDWLYH LQWHUFHSWV REVHUYHG LQ SORWV LQ DFFRUGDQFH ZLWK HTXDWLRQ +RZHYHU VXFK D VPDOO IUDFWLRQ b RI WKH GRVHf LV H[FUHWHG LQ XULQH WKLV ZRXOG KDYH QR SURQRXQFHG HIIHFW LQ WKH RYHUDOO GRVHLQGHSHQGHQW SKDUPDFRNLQHWLFV 1R GHSHQGHQFH RI FOHDUDQFH RQ XULQH IORZ UDWH ZDV REVHUYHG IRU EXSUHQRUSKLQH )LJ f 5HQDO FOHDUDQFH RI WKH PHWDEROLWH 5HQDO FOHDUDQFH RI WKH SODVPD PHWDEROLWH REWDLQHG IURP SORWV )LJV f LQ DFFRUGDQFH ZLWK HTXDWLRQ DYHUDJHG B 6(0f POPLQ 7DEOH f 7KLV ZDV KLJKHU WKDQ WKH UHQDO FOHDUDQFH RI EXSUHQRUSKLQH POPLQf 6LPLODU WR EXSUHQRUKLQH WKH SORWV )LJV f DFFRUGLQJ WR HTXDWLRQ VKRZHG ODUJH QHJDWLYH LQWHUFHSWV 7KLV FRXOG QRW EH H[SODLQHG DV WKHUH ZDV QR S+ RU XULQH IORZ GHSHQGHQW FOHDUDQFH )LJV f REVHUYHG IRU WKH PHWDEROLWH 5HQDO FOHDUDQFHV REWDLQHG IRU EXSUHQRUSKLQH DQG WKH PHWDEROLWH IURP WKH SORWV RI D8D W YHUVXV F3WBPMBG ZHUH KLJKO\ VFDWWHUHG 6RPH SORWV ZLWK PLQLPXP VFDWWHULQJf DUH VKRZQ LQ )LJ 0HWDEROLF FOHDUDQFH RI EXSUHQRUSKLQH 6LQFH GRVHLQGHSHQGHQW SKDUPDFRNLQHWLFV RI EXSUHQRUSKLQH LQ WKH GRVH UDQJH VWXGLHG FRXOG QRW EH GHQLHG LW FDQ EH SRVWXODWHG WKDW WKH PHWDEROLVP LV ILUVW RUGHU DQG WKDW WKH UDWHV DUH GHSHQGHQW RQO\ RQ WKH FRQFHQWUDWLRQV RI EXSUHQRUSKLQH LQ WKH FHQWUDO FRPSDUWPHQW 7KXV WKH UDWH RI IRUPDWLRQ RI WKH WRWDO PHWDEROLWH 0 G0GW N 9 &S (T W P F A A ZKHUH G0GW LV WKH UDWH RI IRUPDWLRQ RI WRWDO PHWDEROLWH N 9 LV W PH

PAGE 117

)LJXUH 3ORWV RI UHQDO FOHDUDQFH &O POPLQf DJDLQVW XULQH IORZ UDWH POPLQf 7KH UHQDO FOHDUDQFHV ZHUH FDOFXODWHG IURP WKH TXRWLHQW RI WKH XULQDU\ H[FUHWLRQ UDWH D8 $Wf DQG WKH SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO &SWBPAGf 7KH VORSHV DQG WKH UHVSHFWLYH VWDQGDUG HUURUV DUH DV IROORZV Df )RU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ 6ORSH B Ef )RU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ 6ORSH B Ff )RU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 6ORSH B Gf )RU WKH PJNJ GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 6ORSH B 7KHVH VORSHV ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR DV FRQILUPHG E\ WWHVW

PAGE 118

R r Vn 7 cW W 2 G 2 2 2 2 R r R Rf§Rn R R Rr r 4f§ / OLOL , 85,1( ), 28 0/,,1 U

PAGE 119

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV H 8 S Jf RI PHWDEROLWH 0f H[FUHWHG LQ XULQH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH $8&W \JPLQPOf DW WKH WLPH RI XULQH FROOHFWLRQ LQWHUYDO LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f (8 > $8&W $8&T @ ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ WLPH FXUYH DW e 8 Df )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ $ 6WXG\ WKH HVWLPDWHG UHQDO FOHDUDQFH IRU 0 ZDV POPLQ IRU WKH WLPH SHULRG EHWZHHQ PLQ 7KH HVWLPDWHG UHQDO FOHDUDQFH GXULQJ WKH ILUVW PLQ ZDV POPLQ VHH WDEOH f Ef )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ WKH HVWLPDWHG LQLWLDO UHQDO FOHDUDQFH RI 0 ZDV POPLQ Ff )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ WKH HVWLPDWHG UHQDO FOHDPDFH RI 0 ZDV POPLQ IRU WKH WLPH SHULRG PLQ +RZHYHU IRU WKH LQLWLDO PLQ WKH UHQDO FOHDUDQFH ZDV POPLQ ,QWHUFHSW f Gf )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ WKH HVWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ IRU WKH WLPH SHULRG PLQ ,Q WKH VDPH GRJ WKH HVWLPDWHG UHQDO FOHDUDQFH IRU WKH ILUVW PLQ YDV POPLQ LQWHUFHSW f

PAGE 120

X VVUI UV VVU QL

PAGE 121

)LJXUH 3ORW RI WKH FXPXODWLYH DPRXQW ]8 \ Jf RI WKH PHWDEROLWH 0f H[FUHWHG LQ XULQH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH $8&W \JPLQPOf DW WKH WLPH RI XULQH FROOHFWLRQ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f O 8 &O > $8& $8&Q @ UHQ W ZKHUH $8&A LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW ( 8 IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ 7KH GDWD ZHUH ILWWHG WR WKUHH OLQHDU VHJPHQWV 7KH UHJUHVVLRQV RQ WKHVH VHJPHQWV DUH JLYHQ LQ WKH OHJHQG RI )LJ

PAGE 122

IW8&7 -8* ; 0,1 0/ , -8*6 R & UVM D UR RQ ,, WO>M

PAGE 123

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV M 8 \ Jf RI WKH PHWDEROLWH 0f H[FUHWHG LQ XULQH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH $8&W \ JPLQPOf DW WKH WLPH RI XULQH FROOHFWLRQ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f = &O UHQ > $8&IF $8&T @ ZKHUH $8&Q LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW (8 IRU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ Df (VWLPDWHG UHQDO FOHDUDQFH IRU WKH WLPH SHULRG XS WR PLQ ZDV POPLQ Ef WKH UHQDO FOHDUDQFH IRU WKH WLPH SHULRG PLQ ZDV POPLQ Ff WKH FOHDUDQFH IRU WKH WLPH SHULRG PLQ ZDV POPLQ

PAGE 124

VRUW Q] VRUW Q] VRQI QL

PAGE 125

)LJXUH 3ORWV RI WKH UHQDO FOHDUDQFH &OUHQ POPLQf RI WKH PHWDEROLWH 0f DJDLQVW XULQDU\ S+ 7KH UHQDO FOHDUDQFH ZDV FDOFXODWHG IURP WKH TXRWLHQW RI WKH XULQDU\ H[FUHWLRQ UDWH $8 $Wf DQG SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO f 7KH VORSHV ZLWK WKH UHVSHFWLYH VWDQGDUG HUURUV IRU WKHVH SORWV DUH DV IROORZV Df )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH f LQ GRJ $ 6WXG\ 6ORSH B Ef )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ 6ORSH B Ff )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 6ORSH Gf )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 6ORSH B 7KHVH VORSHV ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR DV FRQILUPHG E\ WWHVW

PAGE 126

8U!r6 89/ / 8nMfJ D 5(1 0/0,1 &/ 5(1 0/0,1 &/ 5(1 0/0,1 /eB'(e_6M R R R TGn p!G 2 R 2 &/ $ R f§ f§ UYM Xf A f f f f f f 3 0 &' $ &' V f§ V V FX F F !

PAGE 127

)LJXUH 3ORWV RI WKH UHQDO FOHDUDQFH &OUHQ POPLQf RI WKH PHWDEROLWH 0f DJDLQVW WKH XULQH IORZ UDWH POPLQf 7KH UHQDO FOHDUDQFH ZDV FDOFXODWHG IURP WKH TXRWLHQW RI WKH XULQDU\ H[FUHWLRQ UDWH $X$Wf DQG WKH SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI WKH XULQH FROOHFWLRQ LQWHUYDO &SWBPAf 7KH VORSHV DQG WKH VWDQGDUG HUURUV DUH DV IROORZV Df )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH f LQ GRJ $ 6WXG\ 6ORSH B Ef )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 6ORSH B Ff )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ 6ORSH B Gf )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ & 6WXG\ 6ORSH B 7KHVH VORSHV ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR DV FRQILUPHG E\ WWHVW

PAGE 128

E EOO QELL  m = 8f f-,, f§% &,8 QELL EQ , a A [ 8O f G 2 E R R R -2 r R R R R rRn 2 R R R R EOO EOO 85,1( )8 0/0,1 2 f§, EOO 2 G R R R n!‘ R2 R R G 2LO 85,1( ),8 0/0,1 2 2 -O + L EQ

PAGE 129

)LJXUH 3ORWV RI WKH XULQDU\ H[FUHWLRQ UDWH JPLQf RI EXSUHQRUSKLQH f DQG PHWDEROLWH 0f DJDLQVW SODVPD FRQFHQWUDWLRQ RI HLWKHU RU + &S B QJPO f LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ Df )RU DW PJNJ6WXG\ f ,9 EROXV GRVH RI EXSUHQRUSKLQH (VWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ ZKLFK FRUUHVSRQGHG ZHOO ZLWK WKH UHQDO FOHDUDQFH POPLQf REWDLQHG XVLQJ HTXDWLRQ 6HH ILJ Ef Ef )RU DW PJNJ 6WXG\ f ,9 EROXV GRVH RI EXSUHQRUSKLQH (VWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ ZKLFK FRUUHVSRQGHG ZHOO ZLWK WKH UHQDO FOHDUDQFH REWDLQHG XVLQJ HTXDWLRQ POPLQ VHH 7DEOH f Ff )RU 0 DW PJNJ GRVH RI EXSUHQRUSKLQH 6WXG\ f (VWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ

PAGE 130

'/,'I --*0,1 2827 -*0,1 '8'7 -*0,1

PAGE 131

WKH PHWDEROLF FOHDUDQFH &OA f 7KH PHWDEROLF FOHDUDQFH RI WKH SDUHQW GUXJ &O Wf DQG WKH DSSDUHQW YROXPH RI GLVWULEXWLRQ 9Pf RI WKH PHWDEROLWH WKDW LV H[FUHWHG LQ WKH XULQH DQG WKH ELOH FDQ EH HVWLPDWHG E\ LQWHJUDWLQJ WKH DERYH HTXDWLRQ EHWZHHQ DQG W ZLWK UHVSHFW WR WLPH DQG FRQVLGHULQJ WKH VWRLFKLRPHWU\ RI WKH WRWDO PHWDEROLWH 0 N 9 &SGW &O A $8& W P F U PHW W 8 9 P % (T P P P ZKHUH $8&IF LV WKH DUHD XQGHU WKH SDUHQW GUXJ f FRQFHQWUDWLRQWLPH FXUYH 8 DQG % DUH WKH DPRXQWV RI PHWDEROLWH H[FUHWHG LQWR WKH XULQH P P DQG ELOH UHVSHFWLYHO\ XS WR WKDW WLPH DQG P LV WKH PHWDEROLWH FRQFHQWUDWLRQ LQ SODVPD ,I LW FDQ EH DVVXPHG WKDW D FRQVWDQW IUDFWLRQ RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH LV SDUWLWLRQHG LQWR WKH ELOH LH WKHUH LV D FRQVWDQW ELOLDU\ FOHDUDQFH WKHQ FRQVWDQW ELOLDU\ FOHDUDQFH WKHQ % &/ $8& P % W 6XEVWLWXWLQJ WKH YDOXH RI %A LQWR HTXDWLRQ &O &/ f $8& 8 9 P n PHW % W PP 7KH HTXDWLRQ FDQ EH UHDUUDQJHGA LQWR (T (T 8 P 9 &O &OQ f $8& P (T P P PHW % W A RU 8 $8& 9 P$8& &O &/ f (T P W P W n PHW % A ZKHUH &O &OB f DQG 9 FDQ EH REWDLQHG IURP WKH VORSHV DQG PHW % P LQWHUFHSWV RI WKH DSSURSULDWH SORWV RI WKH GHVLJQDWHG TXRWLHQWV RI $8&A

PAGE 132

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f B VWDQGDUG HUURU LQ POPLQ 7DEOH )LJ f 7KH DSSDUHQW YROXPHV RI GLVWULEXWLRQ 9 RI WKH PHWDEROLWH VWDQGDUG HUURU P f§ LQ PO B B B B 7KH ODWWHU WZR ZHUH PXFK VPDOOHU WKDQ WKH SUHVXPHG SODVPD YROXPH PO IRU DQ KHPDWRFULW RI f LQ GRJVA 7KLV UHVXOW LV QRW FRQVLVWHQW ZLWK WKH DVVXPSWLRQ WKDW WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH DSSHDULQJ LQ WKH V\VWHPLF FLUFXODWLRQ LV FRPSOHWHO\ H[FUHWHG LQ XULQH 7KXV XULQDU\ H[FUHWLRQ PD\ QRW EH WKH RQO\ URXWH RI HOLPLQDWLRQ RI WKH V\VWHPLF PHWDEROLWH ,Q IDFW DV LW ZLOO EH VKRZQ ODWHU D PDMRU IUDFWLRQ RI WKH V\VWHPLFDOO\ FLUFXODWLQJ PHWDEROLWH LV H[FUHWHG LQ ELOH 6LQFH DQ LQVLJQLILFDQW IUDFWLRQ b UHFRYHU\ B f RI XQFKDQJHG EXSUHQRUSKLQH LV H[FUHWHG LQ XULQH LW FDQ QRZ EH SRVWXODWHG WKDW IRU DOO SUDFWLFDO SXUSRVHV WKH HVWLPDWHG WRWDO FOHDUDQFH JLYHQ DV POPLQ LQ 7DEOH EDVHG RQ WKH XQZDUUHQWHG DVVXPSWLRQ RI WKH YDOLGLWLHV RI DQG $8&f LV HVVHQWLDOO\ HTXDO WR WKH PHWDEROLF

PAGE 133

)LJXUH 3ORWV RI WKH TXRWLHQW RI WKH FXPXODWLYH DPRXQWV RI WKH PHWDEROLWH DQG SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH DW WKH XULQH FROOHFWLRQ WLPH 8APf YHUVXV WKH TXRWLHQW RI WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH DQG WKH PHWDEROLWH OHYHO LQ SODVPD $8& Pf LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ Df )RU WKH PJNJ 79 EROXV GRVH RI EXSUHQRUKLQH 6WXG\ 7KH HVWLPDWHG FOHDUDQFH &OMMA &OA ZDV POPLQ Ef )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ HVWLPDWHG FOHDUDQFH POPLQ Ff )RU WKH PJNJ ,9 EROXV GRVH RI EXSUHQRUSKLQH LQ GRJ % VWXG\ HVWLPDWHG FOHDUDQFH POPLQ

PAGE 134

VU %H OH K O XHLRQX E X"fH XW!f X\ L RV 8 80 OfI ( f fe 8! 8I6 / K 2 mnLRQV 8Sn6 'fe f§, K f e E 6, e" 3 / '& XQQ XQ0

PAGE 135

FOHDUDQFH &OMAA POPLQ 7DEOH f 7KLV LQWHJUDO PHWKRG XVLQJ HTXDWLRQ JDYH WKH GLIIHUHQFH EHWZHHQ WKH PHWDEROLF DQG ELOLDU\ 0 FOHDUDQFHV &OAA &OJ f DV POPLQ 7DEOH f 7KXV ELOLDU\ FOHDUDQFH &OA POPLQ 7DEOH f YDOXH LQGLFDWHG HOLPLQDWLRQ RI EXSUHQRUSKLQH IURP WKH ERG\ YLUWXDOO\ E\ PHWDEROLVP 7KH 79 EROXV GRVHV XVHG LQ WKH VWXGLHV SURGXFHG WHUPLQDO SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH ZKLFK ZHUH EHORZ WKH DQDO\WLFDO VHQVLWLYLW\ QJPOf DQG GLG QRW SHUPLW DFFXUDWH HVWLPDWLRQ RI WKH WHUPLQDO KDOIOLIH 7KH IDFW WKDW WKH GRVHV RI EXSUHQRUSKLQH WR PJNJf XVHG LQ WKH ILUVW ,9 EROXV VWXGLHV 7DEOH f H[KLELWHG VLJQLILFDQW VLGH HIIHFWV JDYH D XSSHU OLPLW WR WKH 79 EROXV GRVH WKDW FRXOG EH DGPLQLVWHUHG 7R PLQLPL]H WKH SHDN SODVPD FRQFHQWUDWLRQV RI EXSUHQRUKLQH DQG WKH DVVRFLDWHG VLGH HIIHFWV HQFRXQWHUHG XSRQ ,9 EROXV DGPLQLVWUDWLRQ \HW WR JHW D JUHDWHU DPRXQW RI WKH GUXJ LQ WKH ERG\ WR SURYLGH DGHTXDWH QXPEHU RI TXDQWLILDEOH SODVPD FRQFHQWUDWLRQV LQ WKH WHUPLQDO SKDVH KLJKHU GRVHV RI WKH GUXJ ZHUH DGPLQLVWHUHG E\ VORZ ,9 LQIXVLRQ 7KHVH VWXGLHV DUH GHVFULEHG LQ WKH QH[W VHFWLRQ

PAGE 136

,9 ,1)86,21 678',(6 3ORWV RI SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH ZLWK WLPH IRU WKH PLQ FRQVWDQW UDWH LQIXVLRQ RI EXSUHQRUSKLQH 6WXGLHV f LQ GRJV %'()* DQG +f DUH VKRZQ LQ )LJXUHV ,Q VWXGLHV WKH GUXJ ZDV LQIXVHG LQWR WKH MXJXODU YHLQ ,Q WKHVH VWXGLHV GXULQJ LQIXVLRQ EORRG VDPSOHV ZHUH FROOHFWHG IURP WKH IRUHOHJnV EUDFKLDOLV YHLQ ,Q VWXG\ WKH GUXJ ZDV LQIXVHG WKURXJK WKH EUDFKLDOLV YHLQ DQG WKH EORRG VDPSOHV ZHUH FROOHFWHG GXULQJ LQIXVLRQ IURP FRQWUDODWHUDO EUDFKLDOLV DQG MXJXODU YHLQV ,Q VWXGLHV DQG SRVWLQIXVLRQ EORRG VDPSOHV ZHUH FROOHFWHG IURP ERWK EUDFKLDOLV DQG MXJXODU YHLQV 'RJV () DQG ZHUH DOVR ELOH FDQQXODWHG DQG WKH ELOH ZDV FROOHFWHG XS WR K LQ WKHVH GRJV 6WXGLHV DQG f &DWKHWHU ELQGLQJ RI EXSUHQRUSKLQH ,Q ,9 LQIXVLRQ VWXGLHV f EXSUHQRUSKLQH K\GURFKORULH ZDV GLVVROYHG LQ QRUPDO VDOLQH DV EDVH FRQFHQWUDWLRQ PJPO S+ LQIXVLRQ UDWH POPLQf DQG LQIXVHG LQWR WKH MXJXODU YHLQ VWXGLHV f RU EUDFKLDOLV YHLQ VWXG\ f XVLQJ DQ LQWUDYHQRXV FDWKHWHU SODFHPHQW XQLW VHH H[SHULPHQWDOf IRU D SHULRG RI XS WR K %XSUHQRUSKLQH VORZO\ SDUWLWLRQHG LQWR WKH SODVWLF FDWKHWHU GXULQJ SURORQJHG LQIXVLRQ $IWHU FHVVDWLRQ RI LQIXVLRQ ZKHQ EORRG ZDV GUDZQ IURP WKH GRJ WKURXJK WKH VDPH FDWKHWHU XVHG IRU LQIXVLRQ WKH GUXJ UHSDUWLWLRQHG LQWR WKH EORRG DQG JDYH DUWLIDFWXDOO\ KLJKHU SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH 7KH QRUPDO VDOLQH LQIXVLRQ GURSVPLQf LQWR WKH YHLQ WKURXJK WKH VDPH FDWKHWHU ZKLFK ZDV FRQGXFWHG EHWZHHQ EORRG VDPSOLQJV FRPSOHWHO\ UHPRYHG WKH GUXJ IURP WKH FDWKHWHU

PAGE 137

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD EXSUHQRUSKLQH FRQFHQWUDWLRQV DV QJPO RI EDVH XSRQ PJPLQ FRQVWDQW UDWH ,9 LQIXVLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ % 6WXG\ 7DEOH f 7KH SRLQWV 2f DQG f UHSUHVHQW WKH MXJXODU DQG EUDFKLDOLV YHLQ SODVPD FRQFHQWUDWLRQV UHVSHFWLYHO\ RI EXSUHQRUSKLQH 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH EUDFKLDOLV DQG MXJXODU YHLQ SODVPD GDWD WR HTXDWLRQ 7KH LQVHW LV WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 138

1*n0/

PAGE 139

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV DV QJPO RI EDVH XSRQ PJPLQ FRQVWDQW UDWH ,9 LQIXVLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ 6WXG\ 7DEOH f 7KH SRLQWV 2f DQG ff UHSUHVHQW WKH MXJXODU DQG EUDFKLDOLV YHLQ SODVPD FRQFHQWUDWLRQV UHVSHFWLYHO\ RI EXSUHQRUSKLQH 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH H[SHULPHQWDO MXJXODU DQG EUDFKLDOLV YHLQ SODVPD GDWD WR HTXDWLRQ 7KH LQVHW WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 140

MeO PW! 1*n0/ VHL PRD

PAGE 141

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DV QJPO RI EDVH XSRQ PJPLQ FRQVWDQW UDWH ,9 LQIXVLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ ELOH FDQQXODWHG GRJ ( 6WXG\ 7DEOH f 7KH SRLQWV 2f DQG ff UHSUHVHQW WKH H[SHULPHQWDO MXJXODU DQG EUDFKLDO LV YHLQ SODVPD FRQFHQWUDWLRQV UHVSHFWLYHO\ RI EXSUHQRUSKLQH 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH H[SHULPHQWDO H[SHULPHQWDO EUDFKLDOLV DQG MXJXODU YHLQ SODVPD GDWD RI EXSUHQRUSKLQH WR HTXDWLRQ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 142

1*n0/

PAGE 143

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH SODVPD EXSUHQRUSKLQH FRQFHQWUDWLRQV DV QJPO RI EDVH XSRQ PJPLQ FRQVWDQW UDWH ,9 LQIXVLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ ELOH FDQQXODWHG GRJ ) 6WXG\ 7DEOH f 7KH SRLQWV f DQG 2f UHSUHVHQW WKH H[SHULPHQWDO EUDFKLDOLV DQG MXJXODU YHLQ SODVPD FRQFHQWUDWLRQV UHVSHFWLYHO\ RI EXSUHQRUSKLQH 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH H[SHULPHQWDO EUDFKLDOLV DQG MXJXODU YHLQ SODVPD GDWD WR HTXDWLRQ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 144

1*nIO/

PAGE 145

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD EXSUHQRUSKLQH FRQFHQWUDWLRQV DV QJPO RI EDVH XSRQ PJPLQ FRQVWDQW UDWH ,9 LQIXVLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ ELOH FDQQXODWHG GRJ 6WXG\ 7DEOH f 7KH SRLQWV ff DQG 2f UHSUHVHQW WKH H[SHULPHQWDO EUDFKLDOLV DQG MXJXODU YHLQ SODVPD FRQFHQWUDWLRQV UHVSHFWLYHO\ RI EXSUHQRUSKLQH 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH H[SHULPHQWDO EUDFKLDOLV DQG MXJXODU YHLQ SODVPD GDWD WR HTXDWLRQ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 146

1*0/

PAGE 147

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD EXSUHQRUSKLQH FRQFHQWUDWLRQV DV QJPO RI EDVH XSRQ PJPLQ FRQVWDQW UDWH ,9 LQIXVLRQf DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ + 6WXG\ 7DEOH f 7KH GUXJ ZDV LQIXVHG LQWR WKH EUDFKLDOLV YHLQ WKURXJK WKH LQGZHOOLQJ FDWKHWHU ,QWUDFDWK VHH H[SHULPHQWDOf DQG SODVPD VDPSOHV ZHUH FROOHFWHG IURP WKH FRQWUDODWHUDO EUDFKLDOLV f DQG MXJXODU YHLQV 2f f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD WR HTXDWLRQ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 148

:1

PAGE 149

LQ DERXW PLQ 7KHVH ILQGLQJV DUH GHPRQVWUDWHG LQ WKH IROORZLQJ LQ YLWUR DQG LQ YLYR VWXGLHV ,Q YLWUR VWXGLHV :KHQ PJPO VROXWLRQ RI EXSUHQRUSKLQH LQ QRUPDO VDOLQH ZDV SXPSHG WKURXJK WKH FDWKHWHU DW WKH UDWH RI POPLQ IRU K PJ WRWDOf WKH WRWDO DPRXQW RI EXSUHQRUSKLQH UHFRYHUHG IURP WKH FDWKHWHU E\ EHQ]HQH H[WUDFWLRQ ZDV \ J :KHQ EXSUHQRUSKLQH VROXWLRQ VDPH UDWH DQG FRQFHQWUDWLRQ DV DERYHf ZDV SDVVHG WKRUXJK WKH FDWKHWHU IRU K PJ WRWDOf WKH WRWDO DPRXQWV RI EXSUHQRUSKLQH UHFRYHUHG IURP WKH FDWKHWHU E\ EHQ]HQH H[WUDFWLRQ LQ WZR VWXGLHV ZHUH KLJKHU LH DQG \J UHVSHFWLYHO\ :KHQ QRUPDO VDOLQH GURSVPLQf ZDV SDVVHG WKURXJK WKH FDWKHWHU IROORZLQJ K RI WKH GUXJ DW WKH VDPH FRQFHQWUDWLRQ DQG LQIXVLRQ UDWH \J bf RI WKH FDWKHUWHU ERXQG GUXJ ZDV UHFRYHUHG LQ WKH QRUPDO VDOLQH ZLWKLQ PLQ 7KH WRWDO DPRXQW RI EXUHQRUSKLQH UHFRYHUHG LQ WKH VDOLQH LQ PLQ ZDV \J DSSUR[LPDWHO\ WKH VDPH DV WKH DPRXQW UHFRYHUHG IURP WKH FDWKHWHU E\ EHQ]HQH H[WUDFWLRQ 7KHVH UHVXOWV GHPRQVWUDWHG WKDW WKH FDWKHWHUERXQG GUXJ UHGLVVROYHG LQ WKH LQIXVHG VDOLQH DQG ZDV UHPRYHG IURP WKH FDWKHWHU FRPSOHWHO\ LQ DERXW PLQ $IWHU SDVVLQJ D VROXWLRQ PJPOf RI EXSUHQRUSKLQH LQ QRUPDO VDOLQH WKURXJK WKH FDWKHWHU DW WKH UDWH RI PJPLQ IRU K WKH GUXJ DOVR UHSDUWLRQHG LQWR WKH IUHVK EORRG VXEVHTXHQWO\ GUDZQ WKURXJK LW 6HH )LJ f :KHQ EXSUHQRUSKLQH PJPO LQ QRUPDO VDOLQH POf VROXWLRQ ZDV SDVVHG LQ V WKURXJK WKH FDWKHWHU WR VLPXODWH DQ ,9 EROXV DGPLQLQVWUDWLRQ WKHUH ZDV QR ELQGLQJ RI WKH GUXJ WR WKH FDWKHWHU DV GHPRQVWUDWHG E\ WKH IDFW WKDW QR GUXJ ZDV UHFRYHUHG LQ VXEVHTXHQW EHQ]HQH H[WUDFWLRQ

PAGE 150

D R R r R R R ,' K $6 0,1 + )LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DV QJPO RI EDVHf DJDLQVW WLPH PLQf %XSUHQRUSKLQH GLVVROYHG LQ QRUPDO VDOLQH ZDV SDVVHG WKURXJK WKH FDWKHWHU ,QWUDFDWK VHH H[SHULPHQWDOf DW WKH UDWH RI PJPLQ IRU K )LJ Df DQG K )LJ Ef 7KH FDWKHWHU ZDV ZDVKHG ZLWK PO QRUPDO VDOLQH IUHVK EODQN EORRGV ZHUH GUDZQ WKURXJK WKH FDWKHWHU DQG WKH SODVPDV ZHUH DQDO\VHG

PAGE 151

0HWDEROLWH VROXWLRQ \ JPO LQ QRUPDO VDOLQHf SDVVHG WKURXJK WKH FDWKHWHU DW WKH UDWH RI POPLQ IRU PLQ GLG QRW VKRZ DQ\ ELQGLQJ WR WKH FDWKHWHU 7KLV ZDV GHPRQVWUDWHG E\ +3/& DQDO\VLV IROORZLQJ DFLG WUHDWPHQW RI WKH FDWKHWHU ,Q YLYR VWXGLHV :KHQ WKH GUXJ ZDV LQWUDYHQRXVO\ LQIXVHG IRU K LQWR WKH GRJ WKH QRUPDO VDOLQH GULS ZDV VXEVHTXHQWO\ PDLQWDLQHG IRU K 7KXV WKH PLQRU IUDFWLRQ b RI WKH GRVHf RI WKH GUXJ WKDW ZDV ERXQG WR WKH FDWKHWHU UHSDUWLWLRQHG LQWR VDOLQH DQG HYHQWXDOO\ JRW LQWR WKH DQLPDO 8QIRUWXQDWHO\ KRZHYHU ZKHQ EORRG ZDV GUDZQ WKURXJK WKH FDWKHWHU WKH GUXJ DOVR UHSDUWLWLRQHG LQWR WKH VDPSOHV RI VPDOO YROXPHV SURGXFLQJ DUWLIDFWXDOO\ KLJKHU FRQFHQWUDWLRQV VHH )LJV f :KHQ EORRG ZDV VDPSOHG IURP WKH EUDFKLDOLV YHLQ XSRQ LQIXVLRQ RI WKH GUXJ WKURXJK WKH SODVWLF FDWKHWHU LQWR WKH MXJXODU YHLQ WKH SRVWLQIXVLRQ MXJXODU YHLQ SODVPD FRQFHQWUDWLRQV )LJ 7DEOH f REVHUYHG GXULQJ WKH ILUVW PLQ RI WKH SRVWLQIXVLRQ GLVWULEXWLYH SKDVH ZHUH VLJQLILFDQWO\ KLJKHU WKDQ WKH KLJKHVW REVHUYHG EUDFKLDOLV YHLQ SODVPD FRQFHQWUDWLRQV DW WKH WLPH RI FHVVDWLRQ RI LQIXVLRQ 6LPLODUO\ XSRQ LQIXVLRQ RI WKH GUXJ WKURXJK WKH SODVWLF FDWKHWHU LQWR WKH OHIW EUDFKLDOLV YHLQ WKH VLWXDWLRQ ZDV UHYHUVHG LH WKH SRVWLQIXVLRQ OHIW EUDFKLDOLV YHLQ SODVPD FRQFHQWUDWLRQV GXULQJ WKH ILUVW PLQ RI WKH SRVWLQIXVLRQ GLVWULEXWLYH SKDVH ZHUH VLJQLILFDQWO\ KLJKHU WKDQ WKH KLJKHVW MXJXODU DQG FRQWUDODWHUDO ULJKWf EUDFKLDOLV YHLQ FRQFHQWUDWLRQV REVHUYHG MXVW EHIRUH WKH FHVVDWLRQ RI LQIXVLRQ )LJ f 7KHVH UHVXOWV GHPRQVWUDWHG WKDW WKH REVHUYHG GLIIHUHQFHV LQ SRVWLQIXVLRQ EXSUHQRUSKLQH FRQFHQWUDWLRQV LQ SODVPD REWDLQHG IURP GLIIHUHQW YHLQV ZHUH QRW GXH WR DQ\ GUXJLQGXFHG FKDQJHV LQ WKH FLUFXODWRU\ SK\VLRORJ\ RI WKH GRJ EXW ZHUH GXH WR WKH UHSDUWLWLRQLQJ RI WKH FDWKHWHUERXQG

PAGE 152

)LJXUH 6DLG ORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV DV QJPO RI EDVHf RI EXSUHQRUSKLQH SORWWHG DJDLQVW WLPH PLQf IROORZLQJ ,9 LQIXVLRQ RI WKH GUXJ LQWR WKH MXJXODU YHLQ 7KH SRLQWV f DQG f UHSUHVHQW WKH MXJXODU DQG EUDFKLDOLV YHLQ SODVPD FRQFHQWUDWLRQV UHVSHFWLYHO\ RI EXSUHQRUSKLQH Df PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ Ef PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ Ff PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ Gf PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ VWXG\ 7KH VROLG OLQHV UHSUHVHQW WKH MXJXODU YHLQ SODVPD GDWD ILWWHG WR HTXDWLRQ

PAGE 153

7:+ 81 81 81

PAGE 154

)LJXUH 6HPLRJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DV QJPO RI EDVHf DJDLQVW WLPH PLQf IROORZLQJ FRQVWDQW UDWH PJPLQf LQIXVLRQ LQWR WKH EUDFKLDOLV YHLQ RI GRJ + 6WXG\ 7KH SRLQWV Df DQG E ff UHSUHVHQW WKH FRQFHQWUDWLRQV RI EXSUHQRUSKLQH LQ SODVPD REWDLQHG IURP MXJXODU DQG FRQWUDODWHUDO EUDFKLDOLV YHLQV UHVSHFWLYHO\ 7KH SRLQWV Â’f UHSUHVHQW WKH SRVWLQIXVLRQ SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH REWDLQHG IURP EUDFKLDOLV ZKHUH WKH EORRG ZDV GUDZQ WKURXJK WKH LQGZHOOLQJ FDWKHWHU XVHG LQ WKH LQIXVLRQ RI WKH GUXJ

PAGE 155

7DEOH 3RVWLQIXVLRQ MXJXODU DQG EUDFKLDO YHLQ FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DQG 0 LQ GRJ %XSUHQRUSKLQH -XJXODU YHLQ 7LPH PLQ QJPO %UDFKLDO YHLQ 7LPH PLQ QJPO 3RVWLQIXVLRQ MXJXODU DQG EUDFKLDO YHLQ FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DQG PHWDEROLWH LQ GRJ 6WXG\ f IROORZHG E\ FRQVWDQW UDWH ,9 LQIXVLRQ RI EXSUHQRUSKLQH EDVH LQWR WKH MXJXODU YHLQ DW WKH UDWH RI PJPLQ

PAGE 156

GUXJ LQWR WKH EORRG WR SURGXFH DUWLIDFWXDOO\ KLJKHU OHYHOV RI EXSUHQRUSKLQH LQ WKH SODVPD VDPSOHV GUDZQ WKURXJK WKH FDWKHWHU XVHG LQ WKH LQIXVLRQ RI WKH GUXJf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f ZHUH UHDVRQDEO\ FRLQFLGHQW 6HH )LJ f ,Q VWXG\ ZKHUH WKH GUXJ ZDV LQIXVHG WKURXJK WKH FDWKHWHU LQWR WKH OHIW EUDFKLDOLV YHLQ WKH SODVPD FRQFHQWUDWLRQV RI WKH GUXJ PRQLWRUHG LQ WKH MXJXODU YHLQ DQG FRQWUDODWHUDO ULJKW EUDFKLDOLV YHLQf ZHUH SUDFWLFDOO\ FRLQFLGHQW DQG PD\ EH FRQVLGHUHG DV UHSUHVHQWDWLYH RI WKH EXSUHQRUSKLQH FRQFHQWUDWLRQV LQ WKH V\VWHPLF FLUFXODWLRQ )LJV f 7ZR FRPSDUWPHQW PRGHO ,Q VWXGLHV DQG 7DEOH f WKH SRVWLQIXVLRQ SODPVD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DV D IXQFWLRQ RI WLPH ZHUH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK &S $ H DW %H (J XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 157

7DEOH 3KDUPDFRNLQHWLFV RI EXSUHQRUSKLQH DQG 0 LQ GRJV XSRQ ,9 LQIXVLRQ 3DUDPHWHU 'RJ % 'RJ 'RJ ( 'RJ ) 'RJ 'RJ + 0HDQ s 6(0 6WXG\ 'RJ 1R % : 5 5% 5 %: NJ PJPLQfD 7 PLQfr 'RVH PJf :HLJKW .J 'RVH PJNJ 3DUDPHWHUV IURP SODVPD GDWD IRU EXSUHQRUSKLQH S n F s Y s %I s 7G s R f§ f§ f§ f§ f§ f§ f f f s f D s $ f f f f f f s f s H f f f f f f s f L2A 3 f§ f§ f§ f§ f§ s $I s %I s $8&f n $8&7RR LR $XHQ RR M 5HVLGXDO SORWV LR HN 6ORSH s s s s s ,QWHUFHSW s s s s s s

PAGE 158

7DEOH &RQWLQXHG 3DUDPHWHU 'RJ % 'RJ 'RJ ( 'RJ ) 'RJ 'RJ + 0HDQ s 6(0 6WXG\ &OHDUDQFHV POPLQf &/ Q WRW s &Of§ r UHQ f f f f f§ f§ s !0 S PHW f§ f§ f§ s &0 A UHQ f f f f f§ f§ s b 5HFRYHULHV RI EXSUHQRUSKLQH DQG 0 LQ XULQH 8RR9GRVHU f§ f§ s 8RR0GRVHV f§ f§ s %RRAGRVHA f§ f§ f§ f§ %RR0GRVHX f§ f§ f§ s 9ROXPHV RI GLVWULEXWLRQ RI EXSUHQRUSKLQH /f 9 9 F f f f f f f s 9 ; ; s D 'RVH LQ PJ FRUUHVSRQG WR EXSUHQRUSKLQH EDVH $GPLQLVWHUHG DV EXSUHQRUSKLQH +& VDOW GLVVROYHG LQ QRUPDO VDOLQH 7LPH RI LQIXVLRQ LQ PLQ F 3nI $nM DQG %n A DUH WKH LQWHUFHSWV DW W 7 REWDLQHG E\ ILWWLQJ WKH SRVWLQI XV LRQ SODVPD GDWD WR HTXDWLRQ E\ QRQOLQHDU OHDVW VTXDUH FXUYH ILWWLQJ XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 159

7KH PHDQ DQG VWDQGDUG HUURU RI PHDQ ZHUH FRPSXWHG IRU GRJV % ( DQG RQO\ 7KH PHDQ s 6(0 IRU GRJ ) DQG ZHUH VLJQLILFDQWO\ GLIIHUHQW IUDQ WKH RWKHU IRXU GRJV +RZHYHU WKH WHUPLQDO SODVPD GDWD RQ WKHVH WZR GRJV KDG JUHDWHU VFDWWHULQJ 6HH )LJV f WKHQ WKH GRJV % ( DQG A $I %A DQG YDOXHV ZHUH FDOFXODWHG IURP WKH $ % DQG & YDOXHV REWDLQHG IURP HTXDWLRQV DQG H[SUHVVHG DV IUDFWLRQV RI WKH WRWDO GRVH ;T SHU PO RI SODVPD A 7KH WKHRUHWLFDO DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH GXULQJ WKH LQIXVLRQ SKDVH ZDV FDOFXODWHG XVLQJ HTXDWLRQ LQ GRJV % DQG ( ,Q GRJV ) DQG + HTXDWLRQ ZDV XVHG 3RVWLQIXVLRQ DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH ZDV REWDLQHG E\ LQWHJUDWLQJ HTXDWLRQ EHWZHHQ 7 WR RR $8&AA 3n LUf $n f f %n f 7KH WRWDO DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH ZDV FDOFXODWHG XVLQJ WKH WUDSH]RLGDO UXOH 7KLV DUHD ZDV XVHG LQ WKH HVWLPDWLRQ RI WRWDO ERG\ FOHDUDQFH DQG DSSDUHQW YROXPH RI GLVWULEXWLRQ RI EXSUHQRUSKLQH 9f LQ GRJV r ,Q VWXG\ WKH FDOFXODWHG DUHD E\ WUDSH]RLGDO UXOH XS WR PLQ ZDV QJPLQPO 7KH TXRWLHQW RI WKH SODVPD FRQFHQWUDWLRQ RI EXSUHQRUSKLQH QJPOf DW DW PLQ DQG WKH DYHUDJH WHUPLQDO SKDVH UDWH FRQVWDQW PLQf ZDV QJPLQPO 7KXV WKH WRWDO DUHD ZDV HVWLPDWHG DV QJPLQPO 0HDQ RI WKH ZHLJKWHG UHVLGXDOV FDOFXODWHG LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ 1RQH RI WKH PHDQ UHVLGXDOV ZHUH VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW LURQ ]HUR P n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f POPLQ r (VWLPDWHV LURQ WKH VORSHV RI WKH FXPXODWLYH DPRXQWV RI EXSUHQRUSKLQH H[FUHWHG (8 SJf UHQDOO\ DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ 7KHVH UDWLRV FKDQJHG DV S+ RI WKH XULQH FKDQJHG 6HH )LJ f 9DOXHV JLYHQ LQ SDUHQWKHVLV FRUUHVSRQG WR (8 DW $8& IURP WKH EHVW OLQHDU SORWV RI WKH GDWD VKRZQ LQ )LJV A &OMAHA0 ZDV FDOFXODWHG XVLQJ HTXDWLRQ A &0 WKH UHQDO FOHDUDQFH RI WKH SODVPD PHWDEROLWH ZDV FDOFXODWHG LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ VHH DIVR )LJ

PAGE 160

UVWX SHUFHQ UHFRYHULHV RI EXSUHQRUSKLQH DQG 0 LQ XULQH DQG ELOH REWDLQHG LURQ WKH TXRWLHQW RI WKH DPRXQWV UHFRYHUHG LQ XULQH RU ELOH DQG WKH WRWDO LQIXVHG GRVH RI EXSUHQRUSKLQH Y $SSDUHQW YROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO FRPSDUWPHQW HVWLPDWHG E\ ILWWLQJ WKH SRVWLQIXVLRQ GDWD WR HLWKHU HTXDWLRQ FRPSDUWPHQW PRGHOf RU FRPSDUWPHQW PRGHOf E\ QRQOLQHDU OHDVW VTXDUH UHJUHVVLRQ $SSHQGL[ ,f 7KH YDOXHV LQ SDUHQWKHVLV ZHUH FDOFXODWHG IURP HTXDWLRQ ZKHUH WKH YDOXHV RI 3 $ DQG % ZHUH REWDLQHG WKURXJK HTXDWLRQV 7KH PHDQ DQG WKH VWDQGDUG HUURU UHSUHVHQWV WKH YROXPHV RI GLVWULEXWLRQ HVWLPDWHG WKURXJK HTXDWLRQ RU f Z 9M WKH DSSDUHQW YROXPH RI GLVWULEXWLRQ RI EXSUHQRUSKLQH LQ WKH ERG\ ZDV FDOFXODWHG IURP WKH UDWLR RI &: [ ,Q GRJV ) WKH DYHUDJH WHUPLQDO SKDVH UDWH FRQVWDQW PLQf UDWKHU WKDQ WKH HVWLPDWHG WHUPLQDO UDWH FRQVWDQW ZDV XVHG LQ WKH HVWLPDWLRQ RI DSSDUHQW YROXPH RI GLVWULEXWLRQ

PAGE 161

DFFRUGDQFH ZLWK WKH HTXDWLRQ f DJDLQVW ORJDULWKP RI WKH FDOFXODWHG SODVPD FRQFHQWUDWLRQV JDYH PHDQ UHVLGXDOV f VORSHV DQG LQWHUFHSWV ZKLFK ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR )LJ 7DEOH f 7KH SDUDPHWHUV RI WKH DERYH VXP RI ELH[SRQHQWLDO ILWV RI WKH SRVWLQIXVLRQ SODVPD GDWD RI EXSUHQRUSKLQH DUH OLVWHG LQ 7DEOH LQ DGGLWLRQ WR WKH FDOFXODWHG SDUDPHWHUV HTXDWLRQV f IRU DQ HTXLYDOHQW ,9 EROXV DGPLQLVWUDWLRQ 7KH HVWLPDWHG DYHUDJH WHUPLQDO KDOIOLYHV RI EXSUHQRUSKLQH ZHUH DQG PLQ LQ GRJV % DQG ( UHVSHFWLYHO\ 7KH HVWLPDWHG b FRQILGHQFH OLPLWV IRU WKH WHUPLQDO UDWH FRQVWDQWV DUH JLYHQ LQ 7DEOH 7KH YDOXH RI WKH H[LW UDWH FRQVWDQW IURP WKH GHHS FRPSDUWPHQW ZDV FDOFXODWHG IURP WKH H[SUHVVLRQ N $ %D f $%f (T ZKHUH $ DQG % ZHUH REWDLQHG IURP HTXDWLRQV )RU D GUXJ FRQIRUPLQJ WR D FRPSDUWPHQW ERG\ PRGHO WKH HTXDWLRQ WKDW GHVFULEHV WKH WLPH FRXUVH RI WKH GUXJ LQ WKH FHQWUDO FRPSDUWPHQW N9Ff > > N Df OHD7fDFWf@ HaDW >NfOH S7 f D f@ H W @ (T ZKHUH 7 LV WKH GXUDWLRQ RI LQIXVLRQ DQG W LV WKH WLPH DIWHU LQLWLDWLQJ LQIXVLRQ LQ PLQ 'XULQJ LQIXVLRQ 7 W DQG XSRQ FHVVDWLRQ RI LQIXVLRQ 7 EHFRPHV D FRQVWDQW HTXDO WR WKH WLPH RI LQIXVLRQ ,Q WKH DERYH H[SUHVVLRQ H[FHSW IRU 9F DOO WKH RWKHU FRQVWDQWV DUH NQRZQ 7KXV LW LV SRVVLEOH WR REWDLQ 9 WKH YROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO FRPSDUWPHQW E\ ILWWLQJ WKH SRVWLQIXVLRQ GDWD ZLWK WKH DERYH HTXDWLRQ

PAGE 162

)LJXUH 5HSUHVHQWDWLYH H[DPSOHV RI WKH SORWV RI WKH ZHLJKWHG UHVLGXDOV DJDLQVW WKH ORJDULWKP RI FDOFXODWHG SODVPD FRQFHQWDWLRQV 7KH ZHLJKWHG UHVLGXDOV ZHUH FDOFXODWHG LQ DFFRUGDQFH ZLWK HJXDWLRQ &SH[S f &SFDOFf AFDOF Df WKH SRVWLQIXVLRQ SODVPD GDWD RI EXSUHQRUSKLQH DGPLQLVWHUHG E\ FRQVWDQW UDWH PJPLQf ,9 LQIXVLRQ IRU WKH PJNJ GRVH VWXG\ LQ NJ GRJ % 6WXG\ Ef WKH SRVWLQIXVLRQ SODVPD GDWD RI EXSUHQRUSKLQH DGPLQLVWHUHG E\ FRQVWDQW UDWH PJPLQf ,9 LQIXVLRQ IRU WKH PJNJ GRVH VWXG\ LQ NJ GRJ 6WXG\ Ff WKH SRVWLQIXVLRQ SODVPD GDWD RI EXSUHQRUSKLQH DGPLQLVWHUHG E\ FRQVWDQW UDWH PJPLQf ,9 LQIXVLRQ IRU WKH PJNJ GRVH VWXG\ LQ NJ ELOH FDQQXODWHG GRJ ) 6WXG\ Gf WKH SRVWLQIXVLRQ SODVPD GDWD RI EXSUHQRUSKLQH DGPLQLVWHUHG E\ FRQVWDQW UDWH PJPLQf 79 LQIXVLRQ IRU WKH PJNJ GRVH VWXG\ LQ NJ ELOH FDQQXODWHG GRJ 6WXG\ 7KH REVHUYHG PHDQV VORSHV DQG WKH LQWHUFHSWV RI WKHVH ZHLJKWHG UHVLGXDOV DUH JLYHQ LQ WDEOH 7KHVH SDUDPHWHUV ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR DV FRQILUPHG E\ WWHVW 7KH UDQGRP GLVWULEXWLRQ RI WKH UHVLGXDOV DERYH DQG EHORZ WKH UHJUHVVLRQ OLQH LQGLFDWHG QR ELDV LQ WKH ILWWLQJ RI WKH FKRVHQ PRGHO

PAGE 163

5(6,'8$/6 5(6,'8$/6 5(6,'8$/6 5(6,'8$/6

PAGE 164

7DEOH 6WDWLVWLFV RI WRWDO DQG PHWDEROLF FOHDUDQFHV RI EXSUHQRUSKLQH 3DUDPHWHU 'RJ % 'RJ 'RJ ( 'RJ ) 'RJ 'RJ + 0HDQ s 6(0 6WXG\ 'RJ 1R % : 5 5% 5 %: 6WDWLVWLFV IRU WKH WHUPLQDO UDWH FRQVWDQW % QJPOf D E 6( RI % & G Q 8SSHU H /RZHU H EO PLQf 8SSHU /RZHU $8& WRW 8SSHU /RZHU &OAA POPLQ A s 8SSHU /RZHU &O K WRW s !0 M s PHW DnA7HUPLQDO SKDVH LQWHUFHSWV % QJPOf DQG UDWH FRQVWDQWV f ZHUH HVWLPDWHG LURQ WKH VHPLORJDULWKPLF SORWV RI WKH WHUPLQDO SODVPD GDWD RI EXSUHQRUSKLQH DJDLQVW WLPH 4 6WDQGDUG HUURU RI WKH HVWLPDWHG WHUPLQDO UDWH FRQVWDQW Jf U RI WHUPLQDO SKDVH SODVPD SRLQWV XVHG LQ WKH HVWLPDWLRQ RI WHUPLQDO UDWH FRQVWDQW 8 YR

PAGE 165

Hb &RQILGHQFH OLPLWV ZHUH FDOFXODWHG IURP WKH WWDEOH DW D OHYHO RI VLJQLILFDQFH IRU Qf GHJUHHV RI IUHHGRP I ,Q WKH HVWLPDWLRQ RI WRWDO DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ RI EXSUHQRUSKLQH DJDLQVW WLPH LQ DFFRUGDQFH ZLWK HTXDWLRQ WKH SDUDPHWHUV 3 DQG $ ZHUH REWDLQHG WKURXJK HTXDWLRQV DQG 7KH SDUDPHWHUV LW DQGD ZHUH REWDLQHG IURP WKH FRPSXWHU ILW RI WKH SRVWLQIXVLRQ GDWD WR HTXDWLRQ 7KH SDUDPHWHUV % DQG J ZHUH REWDLQHG IURP WKH VHPLORJDULWKPLF SORWV RI WKH WHUPLQDO SKDVH SODVPD GDWD DJDLQVW WLPH 7KH b FRQILGHQFH LQWHUYDOV IRU $8& ZHUH REWDLQHG IURP WKH FRQILGHQFH OLPLWV HVWLPDWHG IRU WKH WHUPLQDO UDWH FRQVWDQW DVVXPLQJ QR HUURU LQ WKH 3 $ LU DQGD YDOXHV 6HH DOVR GLVFXVVLRQ LQ WKH ODVW VHFWLRQ XQGHU WKH VXEKHDGLQJ 9DOLGLW\ RI WKH WHUPLQDO UDWH FRQVWDQW A7RWDO FOHDUDQFH ZDV HVWLPDWHG LURQ WKH TXRWLHQW RI 'RVH$8& ZKHUH $8& ZDV HVWLPDWHG IURP WKH RR RR SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH 7KH b FRQILGHQFH OLPLWV IRU WKH WRWDO FOHDUDQFHV ZHUH FDOFXODWHG IURP WKH b FRQILGHQFH OLPLWV RI WKH $8& YDOXHV A7KH WRWDO FOHDUDQFHV ZHUH FDOFXODWHG XVLQJ WUDSH]RLGDO UXOH OU7KH PHDQV DQG VWDQGDUG HUURU RI WKH PHDQV IRU WKH WRWDO FOHDUDQFHV ZHUH FDOFXODWHG IRU WKH ELOH FDQQXODWHG GRJV ( ) DQG RQO\ 7KH RWKHU GRJV ZHUH QRW ELOH FDQQXODWHGf r&T WKH ELOLDU\ FOHDUDQFHV RI EXSUHQRUSKLQH DV PHWDEROLWH ZHUH HVWLPDWHG IURP HTXDWLRQ %

PAGE 166

ZLWK RQH XQNQRZQ SDUDPHWHU &XUYH ILWWLQJV RI WKH LQIXVLRQ GDWD WR WKH DERYH HTXDWLRQ XVLQJ WKH FRPSXWHU SURJUDP RI ND f D D % f @ (T DQG 6 N9Ff > NH f f@ (T 7KH SRVWLQIXVLRQ DUHD $8&Af XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH ZDV REWDLQHG E\ LQWHJUDWLQJ WKH HTXDWLRQ EHWZHHQ W7f WKH WLPH ZKHQ LQIXVLRQ ZDV VWRSSHG WR WLPH LQILQLW\ RRf $8&R $nD f %9 f (T

PAGE 167

7KXV WKH WRWDO DUHD LV $8&A $8&TBW GXULQJ LQIXVLRQf $8&A SRVWLQIXVLRQf (T 7KHVH FDOFXODWHG DUHDV DUH JLYHQ LQ 7DEOH 7KH WRWDO FOHDUDQFHV &OW4A FDOFXODWHG IURP WKH HTXDWLRQ &OWRW 'RVH$8&A ZHUH HVWLPDWHG DV DQG POPLQ LQ GRJV % DQG ( UHVSHFWLYHO\ 7DEOH DQG f 7KH b FRQILGHQFH OLPLWV IRU WKHVH FOHDUDQFHV DUH UHSRUWHG LQ 7DEOH 7KH RYHUDOO YROXPHV RI GLVWULEXWLRQ HVWLPDWHG IURP WKH HTXDWLRQ ZHUH DQG / UHVSHFWLYHO\ LQ GRJV % DQG ( LQGLFDWLQJ KLJK GHJUHH RI VHTXHVWUDWLRQ RI EXSUHQRUSKLQH LQWR ERG\ WLVVXHV 7KUHH FRPSDUWPHQW PRGHO ,Q VORZ ,9 LQIXVLRQ VWXGLHV DQG WKH SRVWLQIXVLRQ SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DV D IXQFWLRQ RI WLPH ZHUH ILWWHG WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 168

SODVPD GDWD LQ VWXGLHV DQG ZHUH PRUH ZLGHO\ VFDWWHUHG )LJV f WKDQ LQ VWXGLHV DQG )LJV f 7KH WHUPLQDO KDOIOLYHV HVWLPDWHG IURP WKH VHPLORJDULWKPLF SORWV RI WKH WHUPLQDO SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DJDLQVW WLPH DQG WKHLU b FRQILGHQFH OLPLWV LQ SDUHQWKHVLVf ZHUH f DQG f PLQ UHVSHFWLYHO\ LQ GRJV ) DQG VHH DOVR 7DEOH f 7KH HVWLPDWHG DYHUDJHG ILUVW DQG VHFRQG GLVWULEXWLRQDO KDOIOLYHV ZHUH B 6(0f PLQ VWXGLHV DQG f DQG B 6(0f PLQ VWXGLHV VHH 7DEOH f 7KH YDOXHV RI N DQG NA WKH UHVSHFWLYH H[LW UDWH FRQVWDQWV IURP WKH VKDOORZ DQG GHHS FRPSDUWPHQWV ZHUH FDOFXODWHG IURP WKH H[SUHVVLRQVn N > N > E9E Ff@ E 9E Ff @ ZKHUH E WW % LU $ 3 $ D S D %f 3$%f DQG (T (T (T (T F RWLU EW $D 3f3$%f ZKHUH 3 $ DQG % YDOXHV ZHUH REWDLQHG IURP HTXDWLRQV )RU D GUXJ FRQIRUPLQJ WR D FRPSDUWPHQW ERG\ PRGHO WKH HTXDWLRQ WKDW GHVFULEHV WKH WLPH FRXUVH RI WKH GUXJ LQ WKH FHQWUDO FRPSDUWPHQW LV &3 FDOF N9Ff &> N f Z f NO U f OHr 7f D LW f WW f @ >N DfN DfOHD 7fDUDfDf@ HfDW >N f N f H 7 f %R%f LU f@ H W @ (T YKHUH 7 LV WKH GXUDWLRQ RI LQIXVLRQ DQG W LV WKH WLPH DIWHU LQLWLDWLQJ Z W

PAGE 169

LQIXVLRQ LQ PLQ 'XULQJ LQIXVLRQ 7 W DQG XSRQ FHVVDWLRQ RI LQIXVLRQ 7 EHFRPHV D FRQVWDQW HTXDO WR WKH WLPH RI LQIXVLRQ ,Q WKH DERYH H[SUHVVLRQ H[FHSW IRU 9 DOO WKH RWKHU FRQVWDQWV DUH NQRZQ 7KXV LW LV SRVVLEOH WR REWDLQ 9F WKH YROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO FRPSDUWPHQW E\ ILWWLQJ WKH SRVWLQIXVLRQ GDWD ZLWK WKH DERYH HTXDWLRQ ZLWK RQH XQNQRZQ SDUDPHWHU &XUYH ILWWLQJV RI WKH LQIXVLRQ GDWD WR WKH DERYH HTXDWLRQ XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 170

ZKHUH 4 N9> N77 f N 77 f ,7 D 77 fr" f@ 5 NYFf WNFW f ND f D LW Df D f @ (T (T DQG 6 N9Ff>NUfNUH f m f WW f @ (T 7KH SRVWLQIXVLRQ DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH ZDV REWDLQHG E\ LQWHJUDWLQJ WKH HTXDWLRQ EHWZHHQ W7f WKH WLPH ZKHQ LQIXVLRQ ZDV VWRSSHG WR WLPH LQILQLW\ RRf $8&RR 3n f $Df %nH f (T 7KXV $8& $8&IOA $8&n DQG WKH FDOFXODWHG DUHDV DUH JLYHQ 22 Y L RR LQ 7DEOH 7KH WRWDO FOHDUDQFHV &OWRW FDOFXODWHG IURP WKH HTXDWLRQ &OAA 'RVH$8&A ZHUH DQG POPLQ VHH DOVR 7DEOH f IRU GRJV ) DQG + UHVSHFWLYHO\ 7KH DYHUDJH WRWDO ERG\ FOHDUDQFH HVWLPDWHG IRU DOO GRJV ZDV B 6(0f POPLQ 7DEOH DQG f 7KH b FRQILGHQFH OLPLWV IRU WKHVH FOHDUDQFHV DUH UHSRUWHG LQ 7DEOH 7KLV YDOXH LV ORZHU WKDQ WKH WRWDO FOHDUDQFH REWDLQHG IURP ,9 EROXV VWXGLHV B 6(0f POPLQ 7DEOH f 7KXV RYHU HVWLPDWLRQ RI &OW W YDOXH LQ ,9 EROXV VWXGLHV FRXOG EH DWWULEXWHG WR WKH ODFN RI VXIILFLHQW QXPEHU RI TXDQWLILDEOH WHUPLQDO SODVPD SRLQWV WR REWDLQ UHDVRQDEOH HVWLPDWHV RI WHUPLQDO UDWH FRQVWDQW DQG WKH GHULYHG WRWDO ERG\ FOHDUDQFH 7KH RYHUDOO YROXPH RI GLVWULEXWLRQ 9A HVWLPDWHG IURP WKH HTXDWLRQ ZDV B 6(0 Q f / LQGLFDWLQJ KLJK GHJUHH RI VHTXHVWUDWLRQ LQWR ERG\ WLVVXHV FRQVLVWHQW ZLWK WKH REVHUYDWLRQV IURP ,9 EROXV VWXGLHV / 7DEOH f 3ODVPD SKDUPDFRNLQHWLFV RI WKH GHULYHG PHWDEROLWH 0f 7KH EUDFKLDOLV DQG MXJXODU YHLQ SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH

PAGE 171

FRQMXJDWH ZHUH DSSDUHQWO\ VDPH LQ WKH SRVWLQIXVLRQ SKDVH )LJV f 6LPLODU WR WKH FDVH RI ,9 EROXV DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH ZKHUH WKH KLJKHVW SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH RFFXUHG LPPHGLDWHO\ IROORZLQJ WKH EROXV GRVH WKH KLJKHVW SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH RFFXUHG LPPHGLDWHO\ DIWHU WKH FHVVDWLRQ RI LQIXVLRQ RI EXSUHQRUSKLQH )LJV f 7KLV LV SRVVLEOH RQO\ ZKHQ WKH KHSDWLFDOO\ GHULYHG PHWDEROLWH LV VR UDSLGO\ IRUPHG DV ZHOO DV HOLPLQDWHG IURP WKH V\VWHPLF FLUFXODWLRQ WR PLPLF WKH EXSUHQRUSKLQH FRQFHQWUDWLRQV LQ SODVPD ,Q DOO WKUHH ELOH FDQQXODWLRQ VWXGLHV f QR GHWHFWDEOH SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH ZDV REVHUYHG DIWHU K IROORZLQJ LQLWLDWLRQ RI LQIXVLRQ GXUDWLRQ RI LQIXVLRQ PLQ VHH )LJV f +RZHYHU ZKHQ WKH ELOH FDWKHWHU ZDV UHPRYHG DW K DQG WKH VFUHZFDS )LJ f ZDV UHSODFHG WKH ELOH WR IORZHG QRUPDOO\ LQWR WKH GXRGHQXP DQG PHWDEROLWH UHDSSHDUHG LQ WKH SODVPD VWXGLHV DQG )LJV f 7KLV VWURQJO\ LQGLFDWHV WKDW WKH HQWHURKHSDWLF UHFLUFXODWLRQ RI WKH PHWDEROLWH UHVXPHG ZKHQ WKH ELOH ZDV QR ORQJHU FROOHFWHG FRPSOHWHO\ ,Q GRJ EXSUHQRUSKLQH FRQMXJDWH PJf ZDV DGPLQLVWHUHG LQWUDGXRGHQDO\ DQG LW DSSHDUHG LQ SODVPD )LJ f 7KLV SURYLGHG DGGLWLRQDO HYLGHQFH IRU WKH HQWHURKHSDWLF UHFLUFXODWLRQ RI WKH PHWDEROLWH $ PLQRU IUDFWLRQ bf RI WKH LQWUDGXRGHQDOO\ DGPLQLVWHUHG PHWDEROLWH ZDV UHFRYHUHG LQ ELOH 1HLWKHU GUXJ QRU PHWDEROLWH ZHUH GHWHFWDEOH LQ XULQH 7KHVH UHVXOWV FRQILUPHG WKH IDFW WKDW WKH WHUPLQDO KDOIOLIH RI EXSUHQRUSKLQH LQ D JLYHQ GRJ ZRXOG QRW EH DIIHFWHG E\ ELOH FDQQXODWLRQ DQG FRPSOHWH ELOH FROOHFWLRQ

PAGE 172

)LJXUH 6DUG ORJDULWKPLF SORWV RI WKH H[SHULPHQWDO MXJXODU YHLQ 2f DQG EUDFKLDOLV YHLQ f SODVPD FRQFHQWUDWLRQV QJPOf RI WKH KHSDWLFDOO\ GHULYHG DFLGK\GURO\]DEOH PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH SODVPD FRQFHQWUDWLRQV RI WKH PHWDEROLWH XS WR PLQ

PAGE 173

,:n61 2 R R R R QQQ R R r Wf§ &84 2 OXQD 0,1 + $88 @ *+ EQQ4

PAGE 174

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH H[SHULPHQWDO MXJXODU YHLQ 2f DQG EUDFKLDOLV YHLQ ff SODVPD FRQFHQWUDWLRQV QJPOf RI WKH KHSDWLFDOO\ GHULYHG DFLGK\GURO\]DEOH PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH SODVPD FRQFHQWUDWLRQV RI WKH PHWDEROLWH XS WS PLQ

PAGE 175

1, : >@@I8E & 80= ,-=

PAGE 176

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH H[SHULPHQWDO MXJXODU 2f DQG EUDFKLDOLV f YHLQ SODVPD FRQFHQWUDWLRQV QJPOf RI WKH KHSDWLFDOO\ IRUPHG DFLGK\GURO\]DEOH PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SRVWLQIXVLRQ GDWD WR WKH HTXDWLRQ & &R H[SNWf ZKHUH &R FRQFHQWUDWLRQ DW WLPH ZKHQ LQIXVLRQ ZDV VWRSSHG DQG N LV WKH DSSDUHQW ILUVW RUGHU HOLPLQDWLRQ UDWH FRQVWDQW 7KH PLGGOH LQVHW UHSUHVHQWV WKH ILWWHG SRVWLQIXVLRQ SODVPD GDWD XS WR PLQ DQG WKH WRS LQVHW LV WKH EUDFKHDOLV f SODVPD FRQFHQWUDWLRQ RI PHWDEROLWH GXULQJ LQIXVLRQ DQG SRVWLQIXVLRQ MXJXODU YHLQ 2f SODVPD FRQFHQWUDWLRQV RI PHWDEROLWH 7KH H[SHULPHQWDO SODVPD SRLQWV f DURXQG PLQ FRUUHVSRQG WR EORRG WKDW ZHUH VDPSOHG EXW QR PHWDEROLWH ZDV GHWHFWDEOH LQ SODVPD DW WKH DQDO\WLFDO VHQVLWLYLW\ RI QJPO

PAGE 177

1,: *8 '*! ''( 8W! '=, :1

PAGE 178

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH H[SHULPHQWDO MXJXODU YHLQ 2f DQG EUDFKLDOLV YHLQ f SODVPD FRQFHQWUDWLRQV QJPOf RI WKH PHWDEROLWH 0f DJDLQVW WLPH PLQf IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ 7KH H[SHULPHQWDO SODVPD SRLQWV DURXQG PLQ f FRUUHVSRQG WR EORRG WKDW ZHUH VDPSOHG EXW QR PHWDEROLWH ZDV GHWHFWDEOH DW WKH DQDO\WLFDO VHQVLWLYLW\ RI QJPO

PAGE 179

0,1 Â’QXQ 8* *8, 8'8W! RQX" 1*n0O

PAGE 180

R R L 0,1 *22 )LJXUH 6HPLORJDULWKPLF SORW RI WKH SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH JOXFXURQLGH QJPOf SORWWHG DJDLQVW WLPH PLQf IROORZLQJ LQWUDGXRGHQDO DGPLQLVWUDWLRQ RI PJ RI WKH PHWDEROLWH WR GRJ *

PAGE 181

8ULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH DQG PHWDEROLWH 6RPH H[DPSOHV RI VLJPD PLQXV SORWV HTXDWLRQV f IRU EXSUHQRUSLQH DQG PHWDEROLWH DUH JLYHQ LQ )LJV 8ULQDU\ H[FUHWLRQ UDWH SORWV ORJ$8 $W YHUVXV WPLGf ZHUH VFDWWHUHG DQG RQO\ WKH H[DPSOHV ZKLFK IROORZHG WKH HTXDWLRQ DUH SUHVHQWHG LQ )LJ 7KH UDWH FRQVWDQWV REWDLQHG IURP WKH VORSHV RI WKHVH SORWV DUH JLYHQ LQ OHJHQGV RI ILJXUHV 7KH\ FRUUHVSRQGHG WR WKH ILUVW DQG VHFRQG GLVWULEXWLRQDO KDOIOLYHV REWDLQHG IURP WKH SODVPD GDWD 7DEOH f 5HQDO FOHDUDQFH RI EXSUHQRUSKLQH DQG PHWDEROLWH 7KH UHQDO FOHDUDQFH RI EXSUHQRUSKLQH LQ GRJ ( DW PJNJ GRVH VKRZHG D GUDPDWLF S+ GHSHQGHQF\ 6WXG\ )LJ f 7KH YDOXHV RI UHQDO FOHDUDQFH IRU EXSUHQRUSKLQH DQG PHWDEROLWH FDOFXODWHG IURP WKH VORSHV LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ DUH JLYHQ LQ 7DEOH 6HH DOVR )LJV f 7KH XULQH S+ UDQJHV ZHUH QDUURZHU LQ RWKHU VWXGLHV $SSHQGL[ 79 7DEOHV $,9EEEEEEf 7KXV DQ\ DSSDUHQW S+ HIIHFWV RQ UHQDO FOHDUDQFH RI EXSUHQRUSKLQH LQ PDQ\ FRXOG QRW EH GHWHFWHG GXH WR ODFN RI HQRXJK S+ YDULDELOLW\ 7KH PHWDEROLWH VKRZHG QHLWKHU S+ QRU XULQH IORZ GHSHQGHQW UHQDO FOHDUDQFH )LJ DEf %XSUHQRUSKLQH FOHDUDQFH ZDV QRW XULQH IORZ GHSHQGHQW )LJ Ff 7KHVH UHVXOWV ZHUH FRQVLVWHQW ZLWK WKRVH REWDLQHG IURP WKH ,9 EROXV VWXGLHV %LOLDU\ H[FUHWLRQ RI EXSUHQRUSKLQH DQG PHWDEROLWH $QDO\VLV RI EXSUHQSKLQH FRQMXJDWH H[FUHWHG LQ ELOH E\ +3/& IROORZLQJ DFLG K\GURO\VLV DQG JOXFXURQLGDVH K\GURO\VLV VHH H[SHULPHQWDOf JDYH LGHQWLFDO UHVXOWV )LJ f ,Q VWXG\ FXPXODWLYH DPRXQWV RI WKH FRQMXJDWH H[FUHWHG LQ ELOH DQDO\VHG E\ +3/& IROORZLQJ DFLG DQG JOXFXURQLGDVH K\GURO\VLV UHVSHFWLYHO\ ZHUH DQG PJ

PAGE 182

)LJXUH 6HPLORJDULWKQLLF SORWV RI WKH DPRXQWV RI WKH XQFKDQJHG EXSHQRUSKLQH f UHPDLQLQJ WR EH H[FUHWHG LQ XULQH YHUVXV WLPH VLJPD PLQXV SORWf LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ Df 6HPLORJDULWKPLF ILWWLQJ RI WKH SRVWLQIXVLRQ XULQH GDWD WR D VXP RI WZR H[SRQHQWLDOV IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH WR GRJ 6WXG\ 7DEOH f 7KH HVWLPDWHG K\EULG UDWH FRQVWDQWV ZHUH PLQ KDOI OLIH PLQf DQG PLQ KDOI OLIH PLQf Ef 6LJPD PLQXV SORW RI WKH SRVWLQIXVLRQ XULQDU\ H[FUHWLRQ RI EXSUHQRUSKLQH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ 7DEOH f 7KH DSSDUHQW UDWH FRQVWDQW IRU WKLV PRQRH[SRQHQWLDO ILWWLQJ ZDV PLQ KDOI OLIH PLQ f 7KHVH HVWLPDWHG UDWH FRQVWDQWV FRUUHVSRQG ZLWK WKH UDWH FRQVWDQWV REWDLQHG IURP WKH SODVPD GDWD 7DEOH f LQ WKHVH VWXGLHV

PAGE 183

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH DPRXQWV RI WKH PHWDEROLWH 0f UHPDLQLQJ WR EH H[FUHWHG LQ XULQH YHUVXV WLPH VLJPD PLQXV SORWf IROORZLQJ ,9 LQIXVLRQ RI EXSUHQRUSKLQH LQ DFFRUGDQFH ZLWK HTXDWLRQ Df 6LJPD PLQXV SORW RI PHWDEROLWH LQ XULQH RI GRJ % 6WXG\ f IROORZLQJ PJNJ ,9 LQIXVLRQ RI EXSUHQRUSKLQH UHVXOWLQJ LQ DQ HVWLPDWHG DSSDUHQW UDWH FRQVWDQW PLQ KDOIOLIH PLQf Ef 6LJPD PLQXV SORW RI PHWDEROLWH LQ XULQH RI GRJ 6WXG\ f IROORZLQJ PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQW ZDV PLQ KDOIOLIH PLQf Ff 6LJPD PLQXV SORW RI WKH XULQDU\ H[FUHWLRQ RI PHWDEROLWH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ f 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQW ZDV PLQ KDOIOLIH PLQf Gf 6LJPD PLQXV SORW RI WKH XULQDU\ H[FUHWLRQ RI PHWDEROLWH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ) 6WXG\ f 7KH GDWD ZHUH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK HTXDWLRQ 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf UHVSHFWLYHO\

PAGE 184

VVUW QfQ[ VVUI QL LELE XVH e8WX XHV ,2'2 + rf§, WP r 0,1

PAGE 185

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH DPRXQWV \ Jf EXSUHQRUSKLQH H[FUHWHG LQ XULQH D Ef DQG ELOH Ff SHU PLQXWH SORWWHG DJDLQVW WPLG WKH PLG SRLQW RI WKH ELRORJLFDO IOXLG FROOHFWLRQ LQWHUYDO LQ DFFRUGDQFH ZLWK WKH UHGXFHG IRUP RI WKH HTXDWLRQ f /RJ D8 $W Nnf WPLG LQWHUFHSW IRU Df PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ f UHVXOWLQJ LQ DQ HVWLPDWHG DSSDUHQW UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf Ef PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ f ZLWK DQ HVWLPDWHG DSSDUHQW UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf DQG Ff GRJ ( DW WKH VDPH DERYH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ f WKH ELOLDU\ H[FUHWLRQ UDWH XJPLQf RI EXSUHQRUSKLQH FRXOG EH ILWWHG WR D VXP RI WZR H[SRQHQWLDOV UHVXOWLQJ LQ DSSDUHQW UDWH FRQVWDQWV RI PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf UHVSHFWLYHO\

PAGE 186

'OY'7 -M*n01 28'7 M-*n1,1 '827 -*n0,1 *n WLQ XQ QFR LQX 70,' &0,K2 &,'

PAGE 187

)LJXUH 3ORWV RI FXPXODWLYH DPRXQWV ( 8 \ Jf RI EXSUHQRUSKLQH H[FUHWHG LQ XULQH DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQ WLPH FXUYH $8&W S JPLQPOf LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f = 8 &O $8& $8&Q f UHQ n W 2n ZKHUH $8&J LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW e 8 )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ f WKH SORW VKRZHG IRXU GLVWLQFWO\ OLQHDU VHJPHQWV DWWULEXWDEOH WR WKH S+ HIIHFW RQ UHQDO FOHDUDQFH RI EXSUHQRUSKLQH 7KH UHQDO FOHDUDQFH RI EXSUHQRUSKLQH HVWLPDWHG IURP WKH VORSH RI WKH OLQHDU VHJPHQW IRU WKH S+ UDQJH EHWZHHQ LQVHWf ZDV POPLQ

PAGE 188

, f,1 :7 --* ; 0,1 0/ LQQ 8 Q

PAGE 189

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV ,8 \Jf RI EXSUHQRUSKLQH H[FUHWHG LQ XULQH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH WLPH RI XULQH FROOHFWLRQ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f (8 &OUHQ $8&W $8& f ZKHUH $8&S LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW ( 8 Df )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ f WKH FOHDUDQFH HVWLPDWHG IURP WKH LQLWLDO VORSH ZDV POPLQ Ef )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ f WKH HVWLPDWHG UHQDO FOHDUDQFH ZDV POPLQ IRU WKH LQLWLDO SHULRG XS WR PLQ Ff )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI LQ GRJ ) 6WXG\ f WKH HVWLPDWHG FOHDUDQFH ZDV POPLQ IRU WKH XULQH FROOHFWLRQ WLPH EHWZHHQ PLQ

PAGE 190

VJUIP VVU QV VDUIQ[

PAGE 191

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV H8 \Jf RI PHWDEROLWH 0f H[FUHWHG LQ XULQH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH WLPH RI XULQH FROOHFWLRQ LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ f (8 &OUHQ $8&W $8& f ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW(8 Df )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ f WKH FOHDUDQFH HVWLPDWHG IRU WKH WLPH SHULRG PLQ ZDV POPLQ Ef IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ f WKH HVWLPDWHG UHQDO FOHDUDQFH IRU WKH LQLWLDO SHULRG XS WR PLQ ZDV POPLQ Ff )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI LQ GRJ ( 6WXG\ f WKH HVWLPDWHG UHQDO FOHDUDQFH IURP WKH LQLWLDO VORSH ZDV POPLQ Gf )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ) 6WXG\ f IRU WKH WLPH SHULRG EHWZHHQ PLQ WKH UHQDO FOHDUDQFH RI PHWDEROLWH HVWLPDWHG DV POPLQ DQG EHWZHHQ PLQ WKH FOHDUDQFH ZDV POPLQ

PAGE 192

VVUI UD VVUW Q] VDUI Q M VVUI +

PAGE 193

)LJXUH 3ORWV RI UHQDO FOHDUDQFH POPLQf RI EXSUHQRUSKLQH DQG PHWDEROLWH 0f DJDLQVW XULQH IORZ POPLQf DQG S+ 7KH UHQDO FOHDUDQFHV ZHUH FDOFXODWHG IURP WKH TXRWLHQW RI WKH XULQDU\ H[FUHWLRQ UDWH D8 $W S JPLQf DQG SODVPD FRQFHQWUDWLRQ RI EXSUHQRUSKLQH RU PHWDEROLWH QJPOf DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO 7KH VORSHV DQG WKH UHVSHFWLYH VWDQGDUG HUURUV DUH Df )RU WKH PJNJ 79 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ % 6WXG\ f WKH HVWLPDWHG VORSH RI WKH SORW RI UHQDO FOHDUDQFH RI PHWDEROLWH YHUVXV XULQH IORZ POPLQf ZDV B Ef )RU PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ f WKH VORSH RI WKH SORW RI UHQDO FOHDUDQFH RI PHWDEROLWH YHUVXV S+ ZDV B Ff ,Q GRJ ( 6WXG\ f DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH WKH VORSH RI WKH SORW RI WKH UHQDO FOHDUDQFH RI EXSUHQRUSKLQH YHUVXV XULQH IORZ ZDV B 7KHVH VORSHV ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR DV FRQILUPHG E\ WWHVW

PAGE 194

&O 5(1 0/nn0,1 2 2 ] &NU 2 RQ 7 IL 2 R R ‘ K R R R 2 2 R r 2 R R R R 84 + K 3+ 2 2

PAGE 195

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV ,%0 PJf RI EXSUHQRUSKLQH FRQMXJDWH H[FUHWHG LQ ELOH RI GRJ 6WXG\ f DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSLQH 7KH FRQMXJDWH DPRXQWV ZHUH HVWLPDWHG E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ RI GHPHWKR[\EXSUHQRUSKLQH f REWDLQHG DIWHU DFLG K\GURO\VLV 2f RI WKH EXSUHQRUSKLQH FRQMXJDWH DQG E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ RI EXSUHQRUSKLQH REWDLQHG DIWHU J JOXFXURQLGDVH K\GURO\VLV Â’f RI WKH EXSUHQRUSKLQH FRQMXJDWH 7KH FXPXODWLYH DPRXQWV RI WKH EXSUHQRUSKLQH FRQMXJDWH REWDLQHG E\ WKHVH WZR GLIIHUHQW K\GURO\VLV WHFKQLTXHV ZHUH 2f DQG Â’f PJV UHVSHFWLYHO\

PAGE 196

+ ,/, 0, OWO>0,1 =%0 0* F ,7

PAGE 197

6LJPD PLQXV SORWV RI WKH ELOLDU\ H[FUHWLRQ RI WKH XQFKDQJHG EXSUHQRUSKLQH 6WXGLHV )LJ f DQG KHSDWLFDOO\ IRUPHG PHWDEROLWH 6WXGLHV )LJ f DUH IURP WKH GDWD REWDLQHG GXULQJ WKH HQWLUH ELOH FROOHFWLRQ SHULRG Kf 7KHVH SORWV ZHUH DSSDUHQWO\ OLQHDU H[FHSW VWXG\ )LJ Ff 7KH HVWLPDWHG DSSDUHQW KDOIOLYHV DUH UHSRUWHG LQ WKH ILJXUH OHJHQGV 7KHVH KDOIOLYHV FRUUHVSRQGHG WR WKH QG GLVWULEXWLRQDO KDOIOLYHV RI EXSUHQRUSKLQH LQ SODVPD 7DEOH f %LOLDU\ FOHDUDQFH RI EXSUHQRUSKLQH DQG PHWDEROLWH ,Q ELOH FDQQXODWHG GRJV ( ) DQG WKH SHUFHQWDJHV RI WKH WRWDO GRVHV H[FUHWHG LQ ELOH DV XQFKDQJHG EXSUHQRUSKLQH ZHUH DQG UHVSHFWLYHO\ 7DEOH f 7KH ELOLDU\ FOHDUDQFHV RI EXSUHQRUSKLQH ZHUH HVWLPDWHG IURP WKH SORWV RI WKH FXPXODWLYH DPRXQWV RI WKH XQFKDQJHG EXSUHQRUSKLQH H[FUHWHG LQ ELOH DJDLQVW WKH DUHDV XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH RI EXSUHQRUSKLQH LQ SODVPD LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ ,% &OA >$8&W $8&T@ (T ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH ZKHQ ,% ,Q WKH ELOH FDQQXODWHG GRJV ( DQG ) )LJ 7DEOH f WKH HVWLPDWHG ELOLDU\ FOHDUDQFHV IRU XQFKDQJHG EXSUHQRUSKLQH ZHUH DQG POPLQ UHVSHFWLYHO\ ,Q WKH ELOH FDQQXODWHG GRJV ( ) DQG WKH DYHUDJH RI WKH WRWDO GRVH H[FUHWHG LQ ELOH DVVD\HG DV DFLG K\GURO\]DEOH FRQMXJDWH 0f RI EXSUHQRUSKLQH ZDV B b 6(0f 6HH 7DEOH f 7KLV LV LQ FRQWUDVW WR PRUSKLQH ZKHUH b RI WKH GRVH ZDV H[FUHWHG LQ WKH ELOH RI GRJV DV PRUSKLQH JOXFXURPGH 6LQFH D PLQRU IUDFWLRQ RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH ZDV H[FUHWHG LQ XULQH WKH WHUP LQ HTXDWLRQ FDQ EH QHJOHFWHG 7KXV

PAGE 198

+ 8 8 OnMWO 0,1 )LJXUH 6HPLORJDULWKPLF SORWV RI WKH DPRXQWV RI EXSUHQRUSKLQH UHPDLQLQJ WR EH H[FUHWHG LQ ELOH YHUVXV WLPH 6LJPD PLQXV SORWf IROORZLQJ ,9 LQIXVLRQ RI EXSUHQRUSKLQH LQ DFFRUGDFH ZLWK HTXDWLRQ Df 6LJPD PLQXV SORW RI EXSUHQRUSKLQH LQ ELOH RI GRJ ( 6WXG\ f IROORZLQJ PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 7KH HVWLPDWHG DSSDUHQW HOLPLQDWLRQ UDWH FRQVWDQW ZDV PLQ KDOIOLIH PLQf Ef 6LJPD PLQXV SORW RI EXSUHQRUSKLQH LQ ELOH RI GRJ ) 6WXG\ f IROORZLQJ PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 7KH HVWLPDWHG DSSDUHQW UDWH FRQVWDQW ZDV PLQ KDOIOLIH PLQf 6HH DOVR 7DEOH

PAGE 199

)LJXUH 6HPL ORJDULWKPLF SORWV RI WKH DPRXQWV RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH 0f UHPDLQLQJ WR EH H[FUHWHG LQ ELOH YHUVXV WLPH 6LJPD PLQXV SORWf IROORZLQJ ,9 LQIXVLRQ RI EXSUHQRUSKLQH LQ DFFRUGDFH ZLWK HTXDWLRQ Df 6LJPD PLQXV SORW RI PHWDEROLWH LQ ELOH RI GRJ ( 6WXG\ f IROORZLQJ PJNJ ,9 LQIXVLRQ RI EXSUHQRUSKLQH UHVXOWLQJ LQ DQ HVWLPDWHG DSSDUHQW HOLPLQDWLRQ UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf Ef 6LJPD PLQXV SORW IRU WKH ELOLDU\ H[FUHWLRQ RI PHWDEROLWH LQ GRJ ) 6WXG\ f IROORZLQJ PJNJ ,9 LQIXVLRQ RI EXSUHQRUSKLQH 7KH HVWLPDWHG DSSDUHQW HOLPLQDWLRQ UDWH FRQVWDQW ZDV PLQ KDOIOLIH PLQf Ff 6LJPD PLQXV SORW RI PHWDEROLWH LQ ELOH RI GRJ 6WXG\ f XSRQ ,9 LQIXVLRQ RI PJNJ GRVH RI EXSUHQRUSKLQH (VWLPDWHG DSSDUHQW H[FUHWLRQ UDWH FRQVWDQW ZDV PLQ KDOIOLIH PLQf

PAGE 201

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV ( % \ Jf RI EXSUHQRUSKLQH H[FUHWHG LQ ELOH DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH $8&W \JPLQPOf DW WKH WLPH RI XULQH FROOHFWLRQ LQWHUYDO LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ ( % &OJ >$8&W $8&T @ ZKHUH $8&T LV WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH DW ( % Df )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ f WKH HVWLPDWHG ELOLDU\ FOHDUDQFH RI EXSUHQRUSKLQH ZDV POPLQ Ef )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ) 6WXG\ f HVWLPDWHG ELOLDU\ FOHDUDQFH ZDV POPLQ

PAGE 202

HTXDWLRQ FDQ EH ZULWWHQ DV % P !0 &O n $8& 9 P PHW W P S (T ZKHUH % LV WKH FXPXODWLYH DPRXQW RI PHWDEROLWH 0f FROOHFWHG LQ ELOH &OAHW D33DUHQW PHWDEROLF FOHDUDQFH RI EXSUHQRUSKLQH DV 0 $8&IF DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH DW WLPH W 9P LV DSSDUHQW YROXPH RI GLVWULEXWLRQ RI WKH PHWDEROLWH DQG PA LV WKH PHWDEROLWH FRQFHQWUDWLRQ LQ SODVPD 7KXV WKH DSSDUHQW PHWDEROLF FOHDUDQFH &AA0 RI EXSUHQRUSKLQH DV 0 FDQ EH HVWLPDWHG E\ PXOWLSOH OLQHDU UHJUHVVLRQ RI WKH FXPXODWLYH DPRXQWV RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH 0f H[FUHWHG LQ ELOH DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI EXSUHQRUSKLQH DQG WKH FRUUHVSRQGLQJ PHWDEROLWH FRQFHQWUDWLRQ LQ SODVPD )RU GRJV ( ) DQG WKHVH DSSDUHQW PHWDEROLF FOHDUDQFHV REWDLQHG IURP WKH HTXDWLRQ ZHUH DQG POPLQ )LJ 7DEOH ZKHUH DUHDV ZHUH FDOFXODWHG XVLQJ WUDSH]RLGDO UXOHf DQG WKH DSSDUHQW YROXPHV RI GLVWULEXWLRQ RI WKH PHWDEROLWH ZHUH DQG / UHVSHFWLYHO\ 3ORWV RI $% $W DJDLQVW f WKH SODVPD FRQFHQWUDWLRQV RI HLWKHU EXSUHQRUSKLQH RU WKH PHWDEROLWH ZHUH XVXDOO\ VFDWWHUHG 6RPH H[DPSOHV DUH JLYHQ LQ )LJ 0LQRU PHWDEROLWHV LQ ELOH 7KUHH DGGLWLRQDO SHDNV WKDW FRXOG EH DVVLJQHG WR PLQRU PHWDEROLWHV LQ WKH ELOH ZHUH REVHUYHG LQ WKH FKURPDWRJUDPV RI WKH ELOH VDPSOHV IURP GRJV ( ) DQG VWXGLHV f 7\SLFDO FKURPDWRJUDPV REWDLQHG DIWHU DFLG DQG % JOXFXURQLGDVH HQ]\PH K\GURO\VLV RI ELOH DUH SUHVHQWHG LQ )LJ 1RUEXSUHQRUSKLQH UHDUUDQJHV LQ DFLG WR IRUP GHPHWKR[\QRUEXSUHQRUSKLQH :KHQ ELOH ZDV DQDO\VHG E\ +3/& IROORZLQJ DFLG K\GURO\VLV WKH SHDN ZLWK WKH ORZHVW UHWHQWLRQ WLPH KDG WKH VDPH

PAGE 203

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV ]%0 \ Jf RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH 0 H[FUHWHG LQ ELOH DJDLQVW WLPH PLQf 7KH VROLG OLQHV UHSUHVHQW WKH FXPXODWLYH DPRXQWV RI WKH PHWDEROLWH H[FUHWHG LQ ELOH FDOFXODWHG LQ DFFRUGDQFH ZLWK HTXDWLRQ ZKHUH WKH PHWDEROLF FOHDUDQFH RI WKH SDUHQW FRPSRXQG DQG WKH DSSDUHQW YROXPH RI WKH GLVWULEXWLRQ RI WKH PHWDEROLWH ZHUH HVWLPDWHG IURP WKH PXOWLSOH OLQHDU UHJUHVVLRQ RI WKH FXPXODWLYH DPRXQWV RI WKH FRQMXJDWH H[FUHWHG LQ ELOH DJDLQVW DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH RI WKH SDUHQW FRPSRXQG DQG WKH PHDWEROLWH FRQFHQWUDWLRQ LQ SODVPD Df 'RJ ( DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ Ef 'RJ ) DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ Ff 'RJ DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ 7KH HVWLPDWHG PHWDEROLF FOHDUDQFHV ZUH DQG POPLQ DQG WKH DSSDUHQW YROXPHV RI GLVWULEXWLRQ RI WKH PHWDEROLWH ZHUH DQG / UHVSHFWLYHO\

PAGE 204

;%IOM-*6 ,%0 8*6

PAGE 205

)LJXUH 3ORWV RI H[FUHWLRQ UDWH $X $W S JPLQf RI HLWKHU EXSUHQRUSKLQH RU PHWDEROLWH 0f H[FUHWHG LQ ELOH RU XULQH DJDLQVW WKH SODVPD FRQFHQWUDWLRQ RI EXSUHQRUSKLQH RU 0 QJPOf LQ DFFRUGDQFH ZLWK HTXDWLRQ Df )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ f WKH HVWLPDWHG UHQDO FOHDUDQFH RI EXSUHQRUSKLQH ZDV POPLQ Ef )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ 6WXG\ f ELOLDU\ FOHDUDQFH RI PHWDEROLWH ZDV HVWLPDWHG DV POPLQ Ff )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH LQ GRJ ( 6WXG\ f DSSDUHQW ELOLDU\ FOHDUDQFH RI EXSUHQRUSKLQH DV KHSDWLFDOO\ HOLPLQDWHG PHWEROLWH ZDV HVWLPDWHG DV POPLQ Gf ,Q WKH VDPH VWXG\ ELOLDU\ FOHDUDQFH RI EXSUHQRUSKLQH DV XQFKDQJHG GUXJ ZDV HVWLPDWHG DV POPLQ

PAGE 206

'%'7 -*0,1 2%0'7 --*n0,1 f .QB r e K \ 0 70,' 1*0/n2

PAGE 207

)LJXUH 7KH FKURPDWRJUDSKLF SHDNV FRUUHVSRQGLQJ WR DQG DUH WKH DJO\FRQHV JHQHUDWHG IURP WKH FRQMXJDWHG PHWDEROLWHV IROORZLQJ JOXFXURQLGDVH K\GURO\VLV O EXSUHQRUSKLQH QRUEXSUHQRUSKLQH XQNQRZQ PHWDEROLWHVf 7KH FKURPDWRJUDSKLF SHDNV DQG FRUUHVSRQG WR UHDUUDQJHG DJO\FRQHV JHQHUDWHG DIWHU DFLG K\GURO\VLV RI WKH FRQMXJDWHG PHWDEROLWHV GHPHWKR[\EXSUHQRUSKLQH GHPHWKR[\QRUEXSUHQRUSKLQH UHDUUDQJHG DJO\FRQH RI FRQMXJDWHG PHWDEROLWH DQG DUH WKH WZR UHDUUDQJHPHQW SURGXFWV SUHVXPDEO\ JHQHUDWHG IURP WKH DJO\FRQH f XSRQ DFLG K\GURO\VLV Df &KURPDWRJUDPV REWDLQHG DIWHU JOXFXURQLGDVH K\GURO\VLV RI EXSUHQRUSKLQH DQG RWKHU PLQRU PHWDEROLWH FRQMXJDWHV 7KH SHDNV DQG FRUUHVSRQG WR WKH DJO\FRQHV EXSUHQRUSKLQH DQG QRUEXSUHQRUSKLQH UHVSHFWLYHO\ 7KH SHDNV DQG FRUUHVSRQG WR DJO\FRQHV RI XQNQRZQ PLQRU PHWDEROLWHV Ef 7KH VWDQGDUG FKURPDWRJUDP RI ELOH VSLNHG ZLWK QRUEXSUHQRUSKLQH QJPOf DQG EXSUHQRUSKLQH QJPOf Ff &KURPDWRJUDPV REWDLQHG DIWHU DFLG K\GURO\VLV RI FRQMXJDWHV RI EXSUHQRUSKLQH DQG RWKHU PLQRU PHWDEROLWHV GHPHWKR[\EXSUHQRUSKLQH GHPHWKR[\QRUEXSUHQRUSKLQH DFLG UHDUUDQJHPHQW SURGXFWV RI WKH DJO\FRQHV DQG f JHQHUDWHG IURP WKH FRQMXJDWHV RI WKHVH PLQRU PHWDEROLWHVf Gf 7KH SHDNV DQG IURP WKH FKURPDWRJUDP Df ZHUH FROOHFWHG E\ +3/& VHSDUDWLRQ DQG VXEMHFWHG WR DFLG K\GURO\VLV 7KH UHVXOWLQJ K\GURO\VHG SURGXFWV ZHUH FKURPDWRJUDSKHG E\ +3/& VHSDUDWLRQ DQG IORULPHWULF GHWHFWLRQ GHPHWKR[\QRUEXSUHQRUSKLQH DFLG UHDUUDQJHG SURGXFW RI WKH PLQRU PHWDEROLWH JHQHUDWHG IURP WKH UHVSHFWLYH FRQMXJDWHf Hf 6WDQGDUG FKURPDWRJUDP RI GHPHWK[R\QRUEXSUHQRUSKLQH f REWDLQHG DIWHU DFLG K\GURO\VLV RI ELOH VSLNHG ZLWK QJPO RI QRUEXSUHQRUSKLQH f If 7KH SHDN IURP FKURPDWRJUDP Df ZDV FROOHFWHG E\ +3/& VHSDUDWLRQ DQG VXEMHFWHG WR DFLG K\GURO\VLV 7KH UHVXOWLQJ VROXWLRQ ZDV FKURPDWRJUDSKHG E\ +3/& VHSDUDWLRQ DQG IORULPHWULF GHWHFWLRQ 7KLV JDYH WZR SHDNV DQG

PAGE 209

UHWHQWLRQ WLPH DV D UHIHUHQFH VWDQGDUG RI GHPHWKR[\QRUEXSUHQRUSKLQH VHH )LJ DQG WKH OHJHQGf 1RUEXSUHQRUSKLQH ZDV QRW REVHUYHG LQ ELOH EHIRUH DFLG RU HQ]\PDWLF K\GURO\VLV 7KHVH UHVXOWV LQGLFDWH WKDW WKH DJO\FRQH QRUEXSUHQRUSKLQH JHQHUDWHG IROORZLQJ HQ]\PDWLF K\GURO\VLV RU WKH UHDUUDQJHG GHPHWKR[\QRUEXSUHQRUSKLQH JHQHUDWHG DIWHU DFLG K\GURO\VLV ZHUH SUHVXPDEO\ GHULYHG IURP WKH FRQMXJDWH RI QRUEXSUHQRUSKLQH 7KHVH ILQGLQJV ZHUH FRQILUPHG VHH )LJ f E\ DFLG DQG JOXFXURQLGDVH K\GURO\VLV XVLQJ D VWDQGDUG VDPSOH RI QRUEXSUHQRUSKLQH REWDLQHG IURP 5HFNLWW t &ROPDQ &R .LQJVWRQ8SRQ+XOO (QJODQGf 7KH RWKHU WZR XQLGHQWLILHG PLQRU PHWDEROLWHV ZHUH K\SRWKHVL]HG WR EH FRQMXJDWHV DV WKH\ ZHUH H[WUDFWDEOH IURP WKH ELOH RQO\ DIWHU DFLG K\GURO\VLV 1RQH RI WKH PLQRU PHWDEROLWHV ZHUH GHWHFWDEOH LQ SODVPD RU XULQH QRUEXSUHQRUSKLQH GHWHFWLRQ OLPLW QJPOf 3ORWV RI WKH FXPXODWLYH DPRXQWV RI WKH PLQRU PHWDEROLWHV FROOHFWHG LQ ELOH DUH VKRZQ LQ )LJV ,Q WKHVH SORWV WKH FXPXODWLYH DPRXQW WLO RI WKH PHWDEROLWH ZDV HVWLPDWHG IURP WKH H[SUHVVLRQ 1 M L 3+5L ; ') ; 9f (J ZKHUH 3IILW LV WKH SHDN KHLJKW UDWLR RI WKH LA PHWDEROLWH EXSUHQRUSKLQH ZDV WKH LQWHUQDO VWDQGDUGf ') LV WKH GLOXWLRQ IDFWRU 9 LV WKH YROXPH RI ELOH FROOHFWHG DW HDFK LQWHUYDO DQG 1 LV WKH QXPEHU RI ELOH VDPSOHV 7KH WRWDO DPRXQWV RI WKH QRUEXSUHQRUSKLQH FROOHFWHG LQ WKHVH VWXGLHV f ZHUH DQG PJ UHVSHFWLYHO\ 7KXV WKH SHUFHQWDJH RI WKH WRWDO GRVH H[FUHWHG LQ ELOH DV QRUEXSUHQRUSKLQH FRQMXJDWH ZHUH DQG UHVSHFWLYHO\

PAGE 210

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV RI WKH PLQRU DFLG K\GURO\]DEOH FRQMXJDWHV RI EXSUHQRUSKLQH QRUEXSUHQRUSKLQH FRQMXJDWH 2f FRQMXJDWHV RI XQNQRZQ PHWDEROLWHV Â’f DQG _?!f H[FUHWHG LQ ELOH DJDLQVW WLPH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ f LQ GRJ ( $LnV RI WKH OHIW RUGLQDWH UHSUHVHQW WKH VXPPDWLRQ RI 3+5 ; ') ; 9 ZKHUH 3+5 SHDN KHLJKW UDWLRV REWDLQHG E\ DFLG K\GURO\VLV +3/& VHSDUDWLRQ IROORZHG E\ IOXRULPHWULF GHWHFWLRQ RI WKHVH PLQRU PHWDEROLWHV XVLQJ EXSUHQRUSKLQH DV LQWHUQDO VWDQGDUG ') GLOXWLRQ IDFWRU 9 YROXPH RI ELOH H[FUHWHG GXULQJ D ELOH FROOHFWLRQ LQWHUYDO 6HH DOVR )LJ IRU WKHVH FKURPDWRJUDPVf &DOLEUDWLRQ FXUYH XVLQJ QRUEXSUHQRUSKLQH DV LQWHUQDO VWDQGDUG JDYH WKH DFWXDO DPRXQWV RI WKH DFLG K\GURO\]DEOH FRQMXJDWH RI QRUEXSUHQRUSKLQH f H[FUHWHG LQ ELOH 7KH ULJKW RUGLQDWH UHSUHVHQWV WKHVH FXPXODWLYH DPRXQWV RI WKH QRUEXSUHQRUSKLQH FRQMXJDWH 2f H[FUHWHG LQ ELOH LQ PJ

PAGE 211

**'B 2 2 H E + 2 2 2 2 J % % % , K ,* ,*4

PAGE 212

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV RI WKH PLQRU DFLG K\GURO\]DEOH FRQMXJDWHV RI EXSUHQRUSKLQH QRUEXSUHQRUSKLQH FRQMXJDWH 2f FRQMXJDWHV RI XQNQRZQ PHWDEROLWHV Â’f DQG >?H[FUHWHG LQ ELOH DJDLQVW WLPH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ f LQ GRJ ) $LnV RI WKH OHIW RUGLQDWH UHSUHVHQW WKH VXPPDWLRQ RI 3+5 ; ') ; 9 ZKHUH 3+5 SHDN KHLJKW UDWLRV REWDLQHG E\ DFLG K\GURO\VLV +3/& VHSDUDWLRQ IROORZHG E\ IOXRULPHWULF GHWHFWLRQ RI WKHVH PLQRU PHWDEROLWHV XVLQJ EXSUHQRUSKLQH DV LQWHUQDO VWDQGDUG ') GLOXWLRQ IDFWRU 9 YROXPH RI ELOH H[FUHWHG GXULQJ D ELOH FROOHFWLRQ LQWHUYDO 6HH DOVR )LJ IRU WKHVH FKURPDWRJUDPVf &DOLEUDWLRQ FXUYH XVLQJ QRUEXSUHQRUSKLQH DV LQWHUQDO VWDQGDUG JDYH WKH DFWXDO DPRXQWV RI WKH DFLG K\GURO\]DEOH FRQMXJDWH RI QRUEXSUHQRUSKLQH f H[FUHWHG LQ ELOH 7KH ULJKW RUGLQDWH UHSUHVHQWV WKHVH FXPXODWLYH DPRXQWV RI WKH QRUEXSUHQRUSKLQH FRQMXJDWH 2f H[FUHWHG LQ ELOH LQ PJ

PAGE 214

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV RI WKH PLQRU DFLG K\GURO\]DEOH FRQMXJDWHV RI EXSUHQRUSKLQH QRUEXSUHQRUSKLQH FRQMXJDWH 2fW FRQMXJDWHV RI XQNQRZQ PHWDEROLWHV Â’f DQG W?f H[FUHWHG LQ ELOH DJDLQVW WLPH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ f LQ GRJ $LnV RI WKH OHIW RUGLQDWH UHSUHVHQW WKH VXPPDWLRQ RI 3+5 ; ') ; 9 ZKHUH 3+5 SHDN KHLJKW UDWLRV REWDLQHG E\ DFLG K\GURO\VLV +3/& VHSDUDWLRQ IROORZHG E\ IOXRULPHWULF GHWHFWLRQ RI WKHVH PLQRU PHWDEROLWHV XVLQJ EXSUHQRUSKLQH DV LQWHUQDO VWDQGDUG ') GLOXWLRQ IDFWRU 9 YROXPH RI ELOH H[FUHWHG GXULQJ D ELOH FROOHFWLRQ LQWHUYDO 6HH DOVR )LJ IRU WKHVH FKURPDWRJUDPVf &DOLEUDWLRQ FXUYH XVLQJ QRUEXSUHQRUSKLQH DV LQWHUQDO VWDQGDUG JDYH WKH DFWXDO DPRXQWV RI WKH DFLG K\GURO\]DEOH FRQMXJDWH RI QRUEXSUHQRUSKLQH f H[FUHWHG LQ ELOH 7KH ULJKW RUGLQDWH UHSUHVHQWV WKHVH FXPXODWLYH DPRXQWV RI WKH QRUEXSUHQRUSKLQH FRQMXJDWH 2f H[FUHWHG LQ ELOH LQ PJ

PAGE 216

7KH VLJPD PLQXV SORWV IRU WKHVH PLQRU PHWDEROLWHV LQ WHUPV RI WKH DPRXQWV DUH VKRZQ LQ )LJ 7KHVH SORWV ZHUH DSSDUHQWO\ OLQHDU GXULQJ WKH ELOH FROOHFWLRQ SHULRG 7KH DSSDUHQW UDWH FRQVWDQWV HVWLPDWHG IURP WKHVH SORWV DUH JLYHQ LQ ILJXUH OHJHQGV 7KHVH UDWH FRQVWDQWV ZHUH VLPLODU DPRQJ WKH PLQRU PHWDEROLWHV DQG DOVR FRUUHVSRQGHG ZLWK WKH UDWH FRQVWDQW REWDLQHG IURP WKH VLJPD PLQXV SORW RI WKH PDMRU PHWDEROLWH VHH )LJ DQG WKH OHJHQGf 7KHVH UHVXOWV LQGLFDWH SDUDOOHO FRQMXJDWLRQ RI DOO WKH PHWDEROLWHV LQ WKH OLYHU

PAGE 217

)LJXUH 6DUG ORJDULWKPLF SORWV RI WKH WKHRUHWLFDO DPRXQWV RI WKH PLQRU PHWDEROLWHV QRUEXSUHQRUSKLQH 2 XQNQRZQ PHWDEROLWHV Â’ DQG E f DJDLQVW WLPH Df 7KH HVWLPDWHG DSSDUHQW UDWH DSSDUHQW UDWH FRQVWDQWV LQ DFFRUGDQFH ZLWK HTXDWLRQ ZHUH PLQ 2f PLQ Â’f DQG PLQ Vf LQ GRJ ( DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH 6WXG\ f Ef ,Q GRJ ) DW PJNJ ,9 LQIXVLQ GRVH RI EXSUHQRUSKLQH WKH HVWLPDWHG DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ 2f I PLQ Â’f DQG PLQ ?f Ff ,Q GRJ DW PJNJ ,9 LQIXVLRQ GRVH RI EXSUHQRUSKLQH WKH HVWLPDWHG DSSDUHQW UDWH FRQVWDQWV ZHUH PLQ 2f PLQ Â’f DQG PLQ EM 1RWH WKH FRUUHVSRQGHQFH RI WKHVH UDWH FRQVWDQWV ZLWK WKH UDWH FRQVWDQWV REWDLQHG IRU WKH PDMRU PHWDEROLWH 0 LQ UHVSHFWLYH VWXGLHV VHH OHJHQG IRU )LJ f

PAGE 219

3+$50$&2.,1(7,&6 2) 7+( ,9 $'0,1,67(5(' 0(7$%2/,7( 6HPLORJDULWKPLF SORWV RI SODVPD FRQFHQWUDWLRQV RI WKH PHWDEROLWH DJDLQVW WLPH DIWHU DQG PLQ FRQVWDQW UDWH LQIXVLRQ RI WKH PHWDEROLWH LQ VWXGLHV DQG LQ GRJV ) DQG UHVSHFWLYHO\ DUH VKRZQ LQ )LJXUHV 7DEOH f 'RJ ZDV ELOH FDQQXODWHG DQG WKH ELOH ZDV FROOHFWHG XS WR K LQ WKLV GRJ 6WXG\ f 7KH SRVWLQIXVLRQ SODVPD FRQFHQWUDWLRQV RI WKH PHWDEROLWH ZHUH ILWWHG WR D VXP RI WKUHH H[SRQHQWLDOV LQ DFFRUGDQFH ZLWK HTXDWLRQ XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 220

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV QJPOf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf LQ SODVPD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ WKH NJ QRQELOH FDQQXODWHG GRJ ) 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH H[SHULPHQWDO SODVPD GDWD WR HTXDWLRQ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 221

:61

PAGE 222

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV QJPOf RI WKH LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf LQ SODVPD XSRQ FRQVWDQW UDWH PJPLQf ,9 LQIXVLRQ RI WKH FRQMXJDWH SORWWHG DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ ELOHFDQQXODWHG GRJ 6WXG\ 7DEOH f 7KH VROLG OLQH UHSUHVHQWV WKH FXUYH REWDLQHG E\ ILWWLQJ WKH H[SHULPHQWDO MXJXODU YHLQ SODVPD GDWD WR HTXDWLRQ 7KH LQVHW LV WKH UHSUHVHQWDWLRQ RI WKH GDWD DQG WKH ILWWHG FXUYH IRU WKH LQLWLDO PLQ

PAGE 223

:61 0,1 8 , 08*

PAGE 224

7DEOH 3KDUPDFRNLQHWLFV RI 79 DGPLQLVWHUHG 0HWDEROLWH 3DUDPHWHU 'RJ ) 'RJ 6WXG\ 'RJ 1R 5% 5 N4 PJPLQfD 7 PLQfE 'RVH PJf :HLJKW .J 'RVH PJNJ 3DUDPHWHUV IURP SODVPD GDWD IRU WKH PHWDEROLWH 3nI F $n %nI f f 7 D f f r f f 3 H $ % $8& ,'f $8&, A 7RR 5HVLGXDO SORWV K 6ORSH ,QWHUFHSW &OHDUDQFHV POPLQf &O A WRW f f FL0 UHQ f f SL0 P % f§ Q b 5HFRYHULHV RI WKH PHWDEROLWH LQ XULQH DQG ELOH 8RR0GRVHr %RR0GRVHA f§ 9ROXPHV RI GLVWULEXWLRQ RI WKH PHWDEROLWH /f 9 r F f f 9

PAGE 225

7DEOH &RQWLQXHG D 'RVH LQ PJ FRUURVSRQG WR EXSUHQRUSKLQH FRQMXJDWH DVVD\HG E\ DFLG K\GURO\VLV IROORZHG E\ +3/& VHSDUDWLRQ DQG IOXRULPHWULF GHWHFWLRQ 7LPH RI LQIXVLRQ LQ PLQ 4 3nI $nA DQG %nA DUH WKH LQWHUFHSWV REWDLQHG E\ ILWWLQJ WKH SRVWLQIXVLRQ SODVPD GDWD WR HTXDWLRQ E\ QRQOLQHDU OHDVW VTXDUH FXUYH ILWWLQJ XVLQJ WKH FRPSXWHU SURJUDP RI
PAGE 226

7DEOH &RQWLQXHG 7KLV ELOLDU\ FOHDUDQFH ZDV FDOFXODWHG IURP WKH H[SUHVVLRQ I&O ZKHUH I LV WKH IUDFWLRQ RI WKH GRVH H[FUHWHG LQ ELOH 7KH ELOLDU\ FOHDUDQFH HVWLPDWHG IURP D SORW RI WKH FXPXODWLYH DPRXQWV RI WKH V\VWHPLF PHWDEROLWH H[FUHWHG LQ ELOH ZDV POPLQ VHH )LJ G 7KLV FOHDUDQFH HVWLPWHG IURP WKH LQLWLDO VORSH ZDV ELOH IORZ GHSHQGHQW )LJ Df rnS 3HUFHQW UHFRYHULHV RI WKH FRQMXJDWH LQ XULQH DQG ELOH REWDLQHG IURP WKH TXRWLHQW RI WKH DPRXQWV UHFRYHUHG LQ XULQH RU ELOH DQG WKH WRWDO LQIXVHG GRVH RI WKH FRQMXJDWH A $SSDUHQW YROXPH RI GLVWULEXWLRQ RI WKH FHQWUDO FRPSDUWPHQW HVWLPDWHG E\ ILWWLQJ WKH SRVWLQIXVLRQ GDWD WR HTXDWLRQ E\ QRQOLQHDU OHDVW VTXDUH UHJUHVVLRQ $SSHQGL[ ,f 7KH YDOXHV LQ SDUHQWKHVLV ZHUH FDOFXODWHG IURP HTXDWLRQ ZKHUH WKH YDOXHV RI 3 $ DQG % ZHUH REWDLQHG WKURXJK HTXDWLRQV U 9 ZDV FDOFXODWHG IURP WKH UDWLR RI &O U G WRW Y

PAGE 227

)LJXUH 3ORWV RI WKH ZHLJKWHG UHVLGXDOV DJDLQVW WKH ORJDULWKP RI WKH FDOFXODWHG SODVPD FRQFHQWUDWLRQV 7KH ZHLJKWHG UHVLGXDOV ZHUH FDOFXODWHG LQ DFFRUGDQFH ZLWK HTXDWLRQ AH[S f AFDOF AFDOF Df 7KH UHVLGXDOV FDOFXODWHG IRU WKH SRVWLQIXVLRQ MXJXODU YHLQ SODVPD GDWD RI EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf DGPLQLVWHUHG E\ FRQVWDQW UDWH PJPLQf ,9 LQIXVLRQ IRU WKH PJNJ GRVH VWXG\ LQ NJ QRQELOHFDQQXODWHG GRJ ) 6WXG\ 7DEOH f Ef 7KH UHVLGXDOV FDOFXODWHG IRU WKH SRVWLQIXVLRQ MXJXODU YHLQ SODVPD GDWD RI EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf DGPLQLVWHUHG E\ FRQVWDQW UDWH PJPLQf ,9 LQIXVLRQ IRU WKH PJNJ GRVH LQ NJ ELOHFDQQXODWHG GRJ 6WXG\ 7DEOH f 7KH REVHUYHG UHVLGXDO PHDQV VORSHV DQG LQWHUFHSWV ZHUH QRW VWDWLVWLFDOO\ VLJQLILFDQWO\ GLIIHUHQW IURP ]HUR DV FRQILUPHG E\ WWHVW 7KH UDQGRP GLVWULEXWLRQ RI WKH UHVLGXDOV DERYH DQG EHORZ WKH UHJUHVVLRQ OLQH LQGLFDWHG QR ELDV LQ WKH ILWWLQD RI WKH FKRVHQ PRGHO

PAGE 228

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
PAGE 229

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf UHPDLQLQJ WR EH H[FUHWHG LQ ELOHXULQH YHUVXV WLPH VLJPD PLQXV SORWf LQ DFFRUGDQFH ZLWK HTXDWLRQ Df 6HPLORJDULWKPLF ILWWLQJ RI WKH SRVWLQIXVLRQ XULQH GDWD WR D VXP RI WZR H[SRQHQWLDOV IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI WKH PHWDEROLWH LQ WKH QRQELOHFDQQXODWHG GRJ ) 6WXG\ 7DEOH f 7KH HVWLPDWHG K\EULG UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf Ef 6LJPD PLQXV SORW RI WKH SRVWLQIXVLRQ ELOLDU\ H[FUHWLRQ RI WKH PHWDEROLWH IRU WKH PJNJ ,9 LQIXVLRQ GRVH RI WKH PHWDEROLWH LQ WKH ELOHFDQQXODWHG GRJ 6WXG\ 7DEOH f 7KH DSSDUHQW UDWH FRQVWDQW IRU WKLV PRQRH[SRQHQWLDO ILW ZDV PLQ KDOIOLIH PLQf ,Q WKH VDPH GRJ WKH VLJPD PLQXV SORW RI WKH SRVWLQIXVLRQ XULQDU\ H[FUHWLRQ RI WKH PHWDEROLWH FRXOG EH ILWWHG WR D VXP RI H[SRQHQWLDOV 7KH HVWLPDWHG K\EULG UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf

PAGE 230

1,8 F U

PAGE 231

HVWLPDWHG DSSDUHQW UDWH FRQVWDQW RI PLQ KDOIOLIH PLQf DQ LQWHUPHGLDWH YDOXH EHWZHHQ VHFRQG GLVWULEXWLRQDO DQG WHUPLQDO KDOIOLYHV REWDLQHG IURP WKH SODVPD GDWD 6HH 7DEOH f 8ULQDU\ DQG ELOLDU\ H[FUHWLRQ UDWH SORWV ZHUH VFDWWHUHG WKH WZR H[DPSOHV ZKLFK IROORZHG HTXDWLRQ DUH JLYHQ LQ )LJ 7KH UDWH FRQVWDQWV REWDLQHG IURP WKHVH SORWV DUH UHSRUWHG LQ WKH OHJHQGV RI ILJXUHV DQG 7KH\ FRUUHVSRQGHG WR WKH VHFRQG GLVWULEXWLRQDO DQG WHUPLQDO KDOIOLYHV REWDLQHG IURP SODVPD GDWD 6HH DOVR 7DEOH f 5HQDO DQG ELOLDU\ FOHDUDQFHV RI WKH PHWDEROLWH 7KH SHUFHQWDJHV RI WKH WRWDO LQWUDYHQRXVO\ DGPLQLVWHUHG FRQMXJDWH GRVH H[FUHWHG LQ XULQH ZHUH DQG b UHVSHFWLYHO\ LQ GRJ ) 6WXG\ QRQELOH FDQQXODWHGf DQG GRJ 6WXG\ ELOH FDQQXODWHGf ,Q GRJ WKH SHUFHQWDJH RI WKH PHWDEROLWH H[FUHWHG LQ ELOH ZDV $ERXW b RI WKH DGPLQLVWHUHG PHWDEROLWH ZDV UHFRYHUHG LQ WKH ELOH RI GRJ 6WXG\ f ZLWKLQ WKH ILUVW K 7KLV LV LQ FRQVWUDVW WR WKH SKDUPDFRNLQHWLFV RI WKH LQWUDYHQRXVO\ DGPLQLVWHUHG PRUSKLQH JOXFXURQLGH ZKLFK ZDV VROHO\ HOLPLQDWHG LQ WKH XULQH %LOLDU\ DQG UHQDO FOHDUDQFH SORWV IRU WKH LQWUDYHQRXVO\ DGPLQLVWHUHG FRQMXJDWH LQ ELOH DQG XULQH DUH VKRZQ LQ )LJV DQG IRU GRJV ) DQG 6WXGLHV DQG f UHVSHFWLYHO\ 7KH SORWV IRU GRJ VKRZHG WZR GLVWLQFWO\ GLIIHUHQW OLQHDU VHJPHQWV )LJ FGf 7KH ELOLDU\ DQG XULQDU\ FOHDUDQFHV RI WKH PHWDEROLWH HVWLPDWHG IURP WKH LQLWLDO VORSHV ZHUH DQG POPLQ UHVSHFWLYHO\ +RZHYHU WKH FOHDUDQFHV HVWLPDWHG IURP WKH H[SUHVVLRQ I&OWRWf ZKHUH I LV WKH IUDFWLRQ RI WKH GRVH H[FUHWHG WKURXJK D JLYHQ HOLPLQDWLRQ URXWH WKH ELOLDU\ DQG XULQDU\ FOHDUDQFHV LQ GRJ ZHUH DQG POPLQ UHVSHFWLYHO\ 7KH KLJKHU ELOLDU\ DQG XULQDU\ FOHDUDQFHV RI WKH

PAGE 232

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH H[FUHWLRQ UDWH $ %0$ W RU $8 $Wf RI WKH EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf SORWWHG DJDLQVW WPLG WKH PLG SRLQW RI WKH ELRORJLFDO IOXLG FROOHFWLRQ LQWHUYDO LQ DFFRUGDQFH ZLWK HTXDWLRQ Df )RU PJNJ ,9 LQIXVLRQ GRVH RI WKH PHWDEROLWH LQ GRJ 6WXG\ 7DEOH f WKH ELOLDU\ H[FUHWLRQ GDWD ZDV ILWWHG WR D VXP RI WKUHH H[SRQHQWLDOV 7KH HVWLPDWHG K\EULG UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf 6HH DOVR 7DEOH IRU WKH FRUUHVSRQGHQFH RI WKHVH HVWLPDWHG UDWH FRQVWDQWV WR WKRVH REWDLQHG IURP SODVPD GDWD Ef ,Q WKH VDPH GRJ 6WXG\ f WKH XULQDU\ H[FUHWLRQ GDWD IRU WKH PHWDEROLWH ZDV ILWWHG WR D VXP RI WZR H[SRQHQWLDOV 7KH HVWLPDWHG K\EULG UDWH FRQVWDQWV ZHUH PLQ KDOIOLIH PLQf DQG PLQ KDOIOLIH PLQf

PAGE 233

)LJXUH 3ORWV RI WKH FXPXODWLYH DPRXQWV ] %0 ] 8 \ Jf RI WKH LQWUDYHQRXVO\ LQIXVHG EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf LQ DFFRUGDQFH ZLWK HTXDWLRQ Df )RU PJNJ ,9 LQIXVLRQ GRVH RI WKH PHWDEROLWH LQ WKH ELOHFDQQXODWHG GRJ 6WXG\ 7DEOH f WKH DSSUHQW XULQDU\ FOHDUDQFH RI WKH FRQMXJDWH HVWLPDWHG IURP WKH LQLWLDO VORSH ZDV POPLQ Ef ,Q WKH VDPH GRJ 6WXG\ f WKH ELOLDU\ FOHDUDQFH HVWLPDWHG IURP WKH LQLWLDO VORSH ZDV POPLQ F Gf &RPSOHWH SURILOHV RI WKH FOHDUDQFH SORWV IRU WKH PHWDEROLWH LQ XULQH DQG ELOH UHVSHFWLYHO\ LQ GRJ 6WXG\ f

PAGE 234

UXQ JV VJUI JJ] 6I Z

PAGE 235

)LJXUH 3ORW RI WKH FXPXODWLYH DPRXQW RI WKH LQWUDYHQRXVO\ LQIXVHG EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf H[FUHWHG LQ XULQH DJDLQVW WKH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH LQ DFFRUGDQFH ZLWK HTXDWLRQ )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI WKH FRQMXJDWH LQ WKH QRQELOHFDQQXODWHG GRJ ) 6WXG\ 7DEOH f WKH HVWLPDWHG XULQDU\ FOHDUDQFH RI WKH PHWDEROLWH ZDV POPLQ

PAGE 236

PHWDEROLWH GXULQJ WKH LQLWLDO SHULRG XSWR Kf ZDV DWWULEXWDEOH WR WKH ELOH DQG XULQH IORZ GHSHQGHQW ELOLDU\ DQG XULQDU\ FOHDUDQFHV RI WKH PHWDEROLWH VHH )LJ DEf +RZHYHU XULQDU\ FOHDUDQFH ZDV QRW S+ GHSHQGHQW )LJ Ff 7KH FOHDUDQFHV HVWLPDWHG IURP WKH SORWV RI WKH XULQDU\ RU ELOLDU\ H[FUHWLRQ UDWHV DJDLQVW WKH SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH DW WKH PLGSRLQW RI WKH ELRORJLFDO IOXLG FROOHFWLRQ LQWHUYDO )LJ f FRUUHVSRQGHG ZLWK WKH FOHDUDQDFHV HVWLPDWHG IURP WKH VLJPD PLQXV SORWV 6HH ILJXUH OHJHQGV DQG f 2UDO %LRDYDLODELOLW\ RI %XSUHQRUSKLQH LQ 'RJV %XSUHQRUSKLQH LV DOPRVW FRPSOHWHO\ KHSDWLFDOO\ PHWDEROL]HG LQ GRJV )LUVW SDVV PHWDEROLVP LV DQFL WLSD WHG XSRQ RUDO DGPLQLVWUDWLRQ 7KH DPRXQW $ RI WKH RUDOO\ DGPLQLVWHUHG GRVH ;J WKDW HYHQWXDOO\ UHDFKHV WKH V\VWHPLF FLUFXODWLRQ XQFKDQJHG LV $ I f SP I ; D I;f (J ZKHUH I LV IUDFWLRQ RI WKH GRVH HOLPLQDWHG E\ ILUVWSDVV PHWDEROLVP SP EHIRUH UHDFKLQJ WKH V\VWHPLF FLUFXODWLRQ I LV IUDFWLRQ RI WKH GRVH DGPLQLVWHUHG WKDW LV DEVRUEHG XQFKDQJHG DQG I LV WKH IUDFWLRQ RI WKH GRVH WKDW HYHQWXDOO\ UHDFKHV WKH V\VWHPLF FLUFXODWLRQ LQWDFW 7KH HTXDWLRQ LV YDOLG LI WKHUH LV QR VDWXUDEOH ILUVWSDVV OLYHU PHWDEROLVP DQG QR JXW ZDOO PHWDEROLVP 6LQFH EXSUHQRUSKLQH VKRZHG GRVHLQGHSHQGHQW SKDUPDFRNLQHWLFV LQ WKH GRVH UDQJH VWXGLHG WKH WRWDO ERG\ FOHDUDQFH RI WKH GUXJ DGPLQLVWHUHG ,9 LV &O ,9 WRW ; $8&,9 RR (T )RU WKH VDPH GUXJ DGPLQLVWHUHG RUDOO\ DVVXPLQJ WKDW WKHUH LV QRW JXW

PAGE 237

)LJXUH 3ORWV RI WKH DSSDUHQW ELOLDU\XULQDU\ FOHDUDQFHV RI WKH EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf DJDLQVW ELOHXULQH IORZ DQG XULQH S+ 7KH DSSDUHQW XULQDU\ELOLDU\ FOHDUDQFHV ZHUH FDOFXODWHG IURP WKH TXRWLHQW RI WKH H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH DW WKH PLG SRLQW RI WKH ELRORJLFDO IOXLG FROOHFWLRQ LQWHUYDO 7KH UHVSHFWLYH VORSHV DQG LQWHUFHSWV DUH Df )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI WKH FRQMXJDWH LQ WKH ELOHFDQQXODWHG GRJ 6WXG\ 7DEOH f WKH HVWLPDWHG VORSH RI WKH SORW RI WKH ELOLDU\ FOHDUDQFH DJDLQVW ELOH IORZ ZDV B 7KLV ZDV VWDWLVWLFDOO\ VLJQLILFDQW VORSH DV FRQILUPHG E\ WWHVW Ef ,Q WKH VDPH GRJ 6WXG\ f WKH HVWLPDWHG VORSH RI WKH SORW RI WKH XULQDU\ FOHDUDQFH DJDLQVW WKH XULQH IORZ ZDV B 7KLV VORSH ZDV DOVR VWDWLVWLFDOO\ VLJQLILFDQW DV FRQILUPHG E\ WWHVW Ff ,Q WKH VDPH GRJ 6WXG\ f WKH VORSH RI WKH SORW RI XULQDU\ FOHDUDQFH DJDLQVW S+ ZDV B ZKLFK ZDV QRW VWDWLVWLFDOO\ VLJQLILFDQW

PAGE 238

&/ 5(1 0/0,1 &/ 5(1 0/0,1 &/ ( 0/0,1 f§ f§ 0/8XMUBF/QDL RL1MF'QFLFQ0DR$2 N 2 R R V! R 2 n R R R ‘ m" R R f§ 0XXM$PP 27IRF'$]DFQUMFQ[ND f§ f§ 1 1f 1f 8 8 A D D!LYMPFDtD!eMDULQ FVRRRRRFLFDFLF@ &' &r IF FLn HQ &' &' Uar P R 8 B U UR ? X &7 &' &' + ? R $ •9 X} n ?R f 2 9 n3 UR OR 2

PAGE 239

)LJXUH &OHDUDQFH SORWV RI WKH DPRXQWV RI WKH EXSUHQRUSKLQH FRQMXJDWH 0 PHWDEROLWHf H[FUHWHG LQ XULQH RU ELOH SHU XQLW WLPH DJDLQVW WKH SODVPD FRQFHQWUDWLRQ RI WKH PHWDEROLWH DW WKH PLG SRLQW RI WKH FROOHFWLRQ LQWHUYDO Df )RU WKH PJNJ ,9 LQIXVLRQ GRVH RI WKH PHWDEROLWH LQ WKH QRQELOH FDQQXODWHG GRJ ) 6WXG\ 7DEOH f WKH HVWLPDWHG XULQDU\ FOHDUDQFH ZDV POPLQ Ef 7KH XULQDU\ FOHDUDQFH RI WKH PHWDEROLWH LQ GRJ 6WXG\ f ZDV HVWLPDWHG DV POPLQ Ff ,Q WKH VDPH GRJ WKH ELOLDU\ FOHDUDQFH SORW VKRZHG FXUYDWXUH 7KH YDOXHV RXWVLGH WKH SDUHQWKHVLV FRUUHVSRQG WR WKH LQVWDQWDQHRXV ELOLDU\ FOHDUDQFH DQG YDOXHV ZLWKLQ WKH SDUHQWKHVLV FRUUHVSRQG WR WKH PLG SRLQW RI WKH ELOH FROOHFWLRQ LQWHUYDO LQ PLQ

PAGE 240

1LXVUI MDQD 1LXARII LFYUD QLX*IOA$UDD r \ B ,' aFG 2 f§ '* L ,' ,* ,** 2 f ,&4 0 70,' 1*n0/ R + 5' +2' f 2 f§K ,&4 0 ‘n0,' 1*n0/ f§,f§ 5' f§, LKTJ

PAGE 241

ZDOO PHWDEROLVP DQG QR VDWXUDEOH ILUVWSDVV PHWDEROLVP (T 6LQFH WRWDO ERG\ FOHDUDQFH LV WKH VDPH LUUHVSHFWLYH RI WKH URXWH RI DGPLQLVWUDWLRQ HTXDWLRQV DQG FDQ EH HTXDWHG DQG RQ UHDUUDQJHPHQW WKH IUDFWLRQ RI WKH GRVH WKDW HYHQWXDOO\ UHDFKHV WKH V\VWHPLF FLUFXODWLRQ LV RUDO ;r1 $8&rUr RR I I f I f§f§7 OSP D
PAGE 242

)LJXUH 6HPLORJDULWKPLF SORWV RI WKH SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH D Ff DQG PHWDEROLWH E Gf DJDLQVW WLPH IROORZLQJ RUDO DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH Df %XSUHQRUSKLQH LQ SODVPD IROORZLQJ PJ RUDO GRVH RI EXSUHQRUSKLQH LQ LQ GRJ % VWXG\ Ef 0HWDEROLWH LQ SODVPD LQ WKH GRJ % LQ WKH VDPH VWXG\ f Ff %XSUHQRUSKLQH LQ SODVPD IROORZLQJ PJ RUDO GRVH EXSUHQRUSKLQH LQ GRJ VWXG\ Gf 0HWDEROLWH LQ SODVPD LQ GRJ LQ WKH VDPH VWXG\ f

PAGE 243

ILX n 6WLOO 5' PLQ 0,+ 1*n0W 1*n0O ’ 1*IO f§ R R D 1*n0/ ==

PAGE 244

7DEOH 2UDO ELRDYDLODELOLW\ RI EXSUHQRUSKLQH 3DUDPHWHU 'RJ % 'RJ 6WXG\ 'RJ 1R % : :HLJKW .J 79 'RVH PJf 2UDO 'RVH PJf $UHDV XQGHU WKH SODVPD FRQFHQWUDWLRQ WLPH FXUYH ,9 D $8& RR $8&UDO 22 $8&A ,9f $8&LRUDOf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f 7KH YDOXHV ZHUH HVWLPDWHG LQ DFFRUGDQFH ZLWK HTXDWLRQ )UDFWLRQ RI WKH DEVRUEHG GUXJ WKDW XQGHUJRHV ILUVW SDVV PHWDEROLVP (J f

PAGE 245

I D $GI RUDOf [I $8&A ,9f RUDO f2 (T 7KXV WKH FDOFXODWHG SHUFHQWDJHV RI WKH GRVH DEVRUEHG ZHUH DQG UHVSHFWLYHO\ LQ GRJV % DQG 6WXG\ 7DEOH f DQG WKH IUDFWLRQV RI WKH GRVHV FOHDUHG E\ ILUVWSDVV PHWDEROLVP EHIRUH UHDFKLQJ WKH V\VWHPLF FLUFXODWLRQ HVWLPDWHG LQ DFFRUGDQFH ZLWK WKH HTXDWLRQ I II f (T SP n Dn A ZHUH DQG b UHVSHFWLYHO\ LQ GRJ % DQG 6WXG\ f 7KH H[WHQW RI ILUVW SDVV PHWDEROLVP HVWLPDWHG IURP WKH UDWLRV RI WKH WRWDO ERG\ FOHDUDQFH DQG KHSDWLF EORRG IORZ POPLQ LQ D NJ GRJAf ZHUH DQG LQ GRJV % DQG 7KLV FRQWUDGLFWLRQ PD\ EH H[SODLQHG E\ RQH RU PRUH RI WKH DERYH DVVXPSWLRQV QRW EHLQJ YDOLG 6WXGLHV ZLWK UDW JXW SUHSDUDWLRQV n KDYH GHPRQVWUDWHG JXW ZDOO PHWDEROLVP RI EXSUHQRUSKLQH 7KXV DQ\ VLJQLILFDQW JXW ZDOO PHWDEROLVP ZRXOG RYHUHVWLPDWH WKH ILUVWSDVV PHWDEROLVP FDOFXODWHG LQ DFFRUGDQFH ZLWK HTXDWLRQ

PAGE 246

6800$5< $1' &21&/86,216 7KH SKDUPDFRNLQHWLF GLVSRVLWRQ RI EXSUHQRUSKLQH LQ GRJV FDQ EH DGHTXDWHO\ GHVFULEHG E\ D FRPSDUWPHQW ERG\ PRGHO )LJV f %XSUHQRUSKLQH UHDGLO\ GLVWULEXWHV LQWR VKDOORZ DQG GHHS FRPSDUWPHQWV IROORZLQJ UDSLG ,9 EROXV LQMHFWLRQ 7KH SURSHU HVWLPDWLRQV RI WKH WHUPLQDO UDWH FRQVWDQWV DQG WKH WRWDO ERG\ FOHDUDQFHV ZHUH QRW IHDVLEOH IROORZLQJ DFXWH ,9 EROXV PJNJ VWXGLHV f GRVHV RI EXSUHQRUSKLQH 7KLV ZDV DWWULEXWHG WR WKH DQDO\WLFDO VHQVLWLYLW\ ZKLFK GLG QRW SHUPLW HVWLPDWLRQV RI EXSUHQRUSKLQH SODVPD FRQFHQWUDWLRQV EHORZ QJPO 7KH IDFW WKDW GRVHV PJNJf RI EXSUHQRUSKLQH DGPLQLVWHUHG LQ WKH ILUVW ,9 EROXV VWXGLHV H[KLELWHG VLJQLILFDQW VLGH HIIHFWV JDYH DQ XSSHU OLPLW WR WKH PD[LPDO ,9 EROXV GRVH WKDW FRXOG EH DGPLQLVWHUHG 7R PLQLPL]H LQLWLDO SHDN SODVPD FRQFHQWUDWLRQV RI EXSUHQRUSKLQH DQG WKH DVVRFLDWHG VLGH HIIHFWV EXSUHQRUSKLQH ZDV DGPLQLVWHUHG WR VL[ GRJV VWXGLHV f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f IRU WKH WLPH LQWHUYDOV GXULQJLQIXVLRQ DV ZHOO DV SRVWLQIXVLRQ

PAGE 247

7KH HVWLPDWHG WHUPLQDO KDOIOLYHV DQG WKH GHULYHG WRWDO ERG\ FOHDUDQFHV IURP WKHVH ,9 LQIXVLRQ VWXGLHV DYHUDJHG B PLQ 6(0 Q f DQG B POPLQ 6(0 Q f UHVSHFWLYHO\ 2QO\ D PLQRU IUDFWLRQ bf RI WKH LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH ZDV HOLPLQDWHG XQFKDQJHG LQ WKH XULQH 7KHUH ZDV QR UHQDO FOHDUDQFH ZKHQ XULQH S+ ZDV DERYH )LJ f $VVXPLQJ WKDW RQO\ WKH XQLRQL]HG EXSUHQRUSKLQH S.Dn f FDQ XQGHUJR UHQDO WXEXODU UHDEVRUSWLRQ WKHQ ORZHU UHQDO FOHDUDQFH FDQ EH DQWLFLSDWHG DW KLJKHU S+ YDOXHV 7KLV LV VXSSRUWHG E\ WKH IDFW WKDW LQ GRJ % VWXG\ f DQG GRJ ( VWXG\ f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f GHPRQVWUDWLQJ GRVHLQGHSHQGHQF\ LQ WKH GRVH UDQJH VWXGLHG %XSUHQRUSKLQH FRQMXJDWH ZDV WKH RQO\ PHWDEROLWH GHWHFWDEOH LQ SODVPD 7KH SODVPD FRQFHQWUDWLRQWLPH GDWD RI WKLV PHWDEROLWH SDUDOOHOHG WKH WKH SODVPD FRQFHQWUDWLRQWLPH GDWD RI EXSUHQRUSKLQH )LJ f )ROORZLQJ ,9 EROXV DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH WKH KLJKHVW SODVPD FRQFHQWUDWLRQV RI WKH PHWDEROLWH RFFXUHG ZLWKLQ PLQ )LJ f ,Q 79 LQIXVLRQ VWXGLHV WKH KLJKHVW FRQFHQWUDWLRQV RI WKH PHWDEROLWH RFFXUUHG

PAGE 248

LPPHGLDWHO\ DIWHU WKH FHVVDWLRQ RI LQIXVLRQ RI EXSUHQRUSKLQH )LJV f DQG ZHUH FRLQFLGHQW ZLWK WKH PD[LPDO EXSUHQRUSKLQH FRQFHQWUDWLRQV LQ SODVPD 7KH SDUDOOHO GHFD\V RI EXSUHQRUSKLQH DQG WKH FRQMXJDWH LQ SODVPD )LJ f GXULQJ WKH GLVWULEXWLYH SKDVH LQGLFDWHG WKDW WKH UDWH GHWHUPLQLQJ VWHS LQ WKH SODVPD GHFD\ RI WKH FRQMXJDWH LV WKH UDWH RI UHWXUQ RI WKH GUXJ IURP WKH VKDOORZ FRPSDUWPHQW 6LPLODUO\ GXULQJ WKH WHUPLQDO HOLPLQDWLRQ SKDVH WKH UDWH GHWHUPLQLQJ VWHS LQ WKH SODVPD GHFD\ RI ERWK EXSUHQRUSKLQH DQG LWV PHWDEROLWH LV WKH VORZ UHWXUQ RI EXSUHQRUSKLQH IURP WKH GHHS FRPSDUWPHQW WR WKH FHQWUDO FRPSDUWPHQW ZKHUH LW FRXOG EH PHWDEROL]HG ,Q ELOH FDQQXODWHG GRJV VWXGLHV f QR GHWHFWDEOH SODVPD FRQFHQWUDWLRQV RI WKH PHWDEROLWH ZHUH REVHUYHG DIWHU K IROORZLQJ LQLWLDWLRQ RI LQIXVLRQ +RZHYHU ZKHQ WKH ELOH FDWKHWHU ZDV UHPRYHG DW K DQG WKH VFUHZFDS )LJ f ZDV UHSODFHG WKH ELOH IORZHG QRUPDOO\ LQWR WKH GXRGHQXP DQG WKH PHWDEROLWH UHDSSHDUHG LQ SODVPD 7KLV VWURQJO\ LQGLFDWHG HQWHURKHSDWLF UHFLUFXODWLRQ 8SRQ LQWUDGXRGHQD DGPLQLVWUDWLRQ RI WKH EXSUHQRUSKLQH FRQMXJDWH LW DSSHDUHG LQ SODVPD SURYLGLQJ IXUWKHU HYLGHQFH IRU WKH HQWHURKHSDWLF UHFLUFXODWLRQ RI WKH PHWDEROLWH ,Q WKH VDPH VWXG\ D PLQRU IUDFWLRQ bf RI WKH LQWUDGXRGHQDOO\ DGPLQLVWHUHG PHWDEROLWH ZDV UHFRYHUHG LQ ELOH DV FRQMXJDWH )UHH EXSUHQRUSKLQH ZDV QRW GHWHFWHG LQ SODVPD EXW REVHUYHG LQ VPDOO DPRXQWV LQ XULQH 7KHVH UHVXOWV FRQILUPHG WKDW WKH HQWHURKHSDWLF UHFLUFXODWLRQ RI EXSUHQRUSKLQH FRQMXJDWH ZRXOG KDYH QHJOLJLEOH HIIHFWV RQ WKH WHUPLQDO KDOIOLIH RI EXSUHQRUSKLQH 7KH IUDFWLRQ RI WKH ,9 DGPLQLVWHUHG EXSUHQRUSKLQH WKDW ZDV UHFRYHUHG DV FRQMXJDWH LQ WKH ELOH RI GRJV ( ) DQG *f DYHUDJHG B b 6(0f $ERXW b RI WKH ,9 DGPLQLVWHUHG EXSUHQRUSKLQH ZDV

PAGE 249

UHFRYHUHG LQ XULQH DV FRQMXJDWH $ PLQRU IUDFWLRQ bf RI WKH DGPLQLVWHUHG EXSUHQRUSKLQH ZDV UHFRYHUHG XQFKDQJHG LQ WKH ELOH RI GRJV ( DQG ) VWXGLHV f 7KLV PD\ EH GXH WR WKH HQ]\PDWLF K\GURO\VLV RI WKH FRQMXJDWH LQ ELOH 1R IUHH EXSUHQRUSKLQH ZDV GHWHFWHG LQ WKH ELOH RI WKH WKLUG GRJ VWXG\ f 7KUHH DGGLWLRQDO +3/& SHDNV WKDW FRXOG EH DVVLJQHG WR PLQRU PHWDEROLWHV ZHUH REVHUYHG LQ WKH FKURPDWRJUDPV RI WKH ELOH VDPSOHV 7KHVH ZHUH K\SRWKHVLVHG WR EH FRQMXJDWHV VLQFH WKH\ ZHUH H[WUDFWDEOH IURP WKH ELOH RQO\ DIWHU DFLG RU HQ]\PDWLF K\GURO\VLV :KHQ WKH ELOH ZDV DQDO\VHG E\ +3/& IROORZLQJ DFLG K\GURO\VLV WKH SHDN ZLWK WKH ORZHVW UHWHQWLRQ WLPH )LJ f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f 7KH WHUPLQDO SODVPD KDOIOLYHV HVWLPDWHG LQ WZR VWXGLHV ZHUH DQG K UHVSHFWLYHO\ LQ GRJV ) DQG VWXGLHV DQG f 7KH HVWLPDWHG DYHUDJH WHUPLQDO KDOIOLIH RI WKH FRQMXJDWH LQ SODVPD IROORZLQJ 79 EROXV DGPLQLVWUDWLRQ RI EXSUHQRUSKLQH ZDV K 7DEOH f 7KH IDFW WKDW WKH WHUPLQDO KDOIOLIH RI WKH ,9 DGPLQLVWHUHG PHWDEROLWH ZDV VKRUWHU WKDQ WKH KHS£WLFDOO\ IRUPHG PHWDEROLWH IROORZLQJ ,9 DGPLQLVWUDWLRQ RI EXSUHQRUSKLQHf FRQILUPHG WKH K\SRWKHVLV WKDW WKH VORZHVW SURFHVV WKH

PAGE 250

UDWH RI UHWXUQ RI EXSUHQRUSKLQH IURP WKH GHHS FRPSDUWPHQW PXVW EH WKH UDWH GHWHUPLQLQJ VWHS LQ WKH RYHUDOO GLVSRVLWLRQ RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH ,Q RQH VWXG\ GRJ VWXG\ f WKH SHUFHQWDJH RI WKH ,9 DGPLQLVWHUHG PHWDEROLWH H[FUHWHG LQ WKH ELOH ZDV b $ERXW b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f 7KH HVWLPDWHG ELOLDU\ FOHDUDQFHV RI WKH LQWUDYHQRXVO\ DGPLQLVWHUHG PHWDEROLWH LQ GRJV ) DQG ZHUH DQG POPLQ UHVSHFWLYHO\ 7DEOH f ,Q DOO VWXGLHV WKH SODVPD PHWDEROLWH GDWD IROORZLQJ WKH ,9 DGPLQLVWUDWLRQ RI WKH SDUHQW FRPSRXQG SDUDOOHOHG WKH EXSUHQRUSKLQH SODVPD GDWD )LJV f 7KHVH UHVXOWV OHG WR WKH K\SRWKHVLV WKDW ZKHQ EXSUHQRUSKLQH ZDV GHOLYHUHG WR WKH OLYHU KHSDWRF\WHV WKURXJK WKH KHSDWLF DUWHU\ RU SRUWDO YHLQ WKH FRQMXJDWH IRUPHG DW WKH LQLWLDO VWDJHV RI EXSUHQRUSKLQH WUDQVLW WKURXJK WKH OLYHU SUHVXPDEO\ UHDFKHV UDSLG HTXLOLEUDWLRQ ZLWK WKH V\VWHPLFDOO\ FLUFXODWLQJ PHWDEROLWH $V WKH GUXJ LV WUDQVSRUWHG GHHSHU LQWR WKH OLYHU WLVVXHV WKH IRUPHG PHWDEROLWH LV SUHVXPDEO\ WUDSSHG LQ WKHVH KHSDWRF\WHV 7KXV WKH PHWDEROLWH FDQ QR ORQJHU SDUWLWLRQ LQWR WKH V\VWHPLF FLUFXODWLRQ DQG FDQ EH FRQFHLYHG DV EHLQJ VXVFHSWLEOH WR GLUHFW ELOLDU\ H[FUHWLRQ 7KH IUDFWLRQ RI WKH

PAGE 251

KHSDWLFDOO\ IRUPHG PHWDEROLWH WKDW UHDFKHV WKH V\VWHPLF FLUFXODWLRQ ZDV HVWLPDWHG IURP WKH UDWLRV RI WKH DUHDV XQGHU WKH SODVPD PHWDEROLWH FRQFHQWUDWLRQWLPH FXUYH IROORZLQJ ,9 DGPLQLVWUDWLRQ RI WKH PHWDEROLWH DQG WKH SDUHQW FRPSRXQG 7KH HVWLPDWHG SHUFHQWDJHV RI WKH KHSDWLFDOO\ IRUPHG PHWDEROLWH UHDFKLQJ WKH V\VWHPLF FLUFXODWLRQ ZHUH DQG b UHVSHFWLYHO\ LQ GRJV ) DQG 7KLV LV LQ FRQWUDVW WR PRUSKLQH SKDUPDFRNLQHWLFV ZKHUH b RI WKH KHSDWLFDOO\ GHULYHG PHWDEROLWH UHDFKHV WKH V\VWHPLF FLUFXODWLRQ %XSUHQRUSKLQH LV DOPRVW FRPSOHWHO\ KHSDWLFDOO\ PHWDEROL]HG LQ GRJV )LUVW SDVV PHWDEROLVP LV DQWLFLSDWHG XSRQ RUDO DGPLQLVWUDWLRQ 7KH H[WHQW RI WKH ILUVWSDVV PHWDEROLVP HVWLPDWHG IURP WKH UDWLRV RI WRWDO ERG\ FOHDUDQFH DQG WKH KHSDWLF SODVPD IORZ POPLQ LQ D NJ GRJaAf DYHUDJHG B 6(0f LQ VWXGLHV 7KXV DERXW b RI WKH GUXJ ZDV FOHDUHG GXULQJ RQH SDVV WKURXJK WKH OLYHU 7KH DEVROXWH ELRDYDLODELOLW\ RI EXSUHQRUSKLQH HVWLPDWHG IURP WKH DUHDV XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH IROORZLQJ RUDO DQG ,9 DGPLQLVWUDWLRQV ZHUH DQG b UHVSHFWLYHO\ LQ GRJV % DQG VWXGLHV DQG f 7KLV ORZ ELRDYDLODELOLW\ ZDV DWWULEXWHG WR SRRU DEVRUSWLRQ UDWKHU WKDQ ILUVWSDVV PHWDEROLVP

PAGE 252

$33(1',; 352*5$0 08/7, ',0 78f&8f3+f92/f 35,17r 08/7,/,1(6 ),77,1*6 r 35,1735,17'(),1( (48$7,216 $7 35,17 35,17 &3 $1' 7 $5( '(3(1'(17 $1' ,1'(3(1'(17 9$5,$%/(6 35,1735,173f 3f $5( 3$5$0(7(56 72 ),7 35,1735,17 7$%f*&72 ,) ',9(5*(')3 ',00(f0(f *$8661(:7210(f '$03,1* *$8661(:721 0(f 0$548$5'70(f 6,03/(; 35,17)25, 72 35,17,f 0(,f 0(7+2'1(;7 35,17,1387:+,&+ $/*25,7+0 '2 <28 6(/(&7$/ 35,1735,17r %(/,(9( <28 +$9( '(),1(' (48$7,216 r ,138768%-(&7 1$0(1 35,17,1387 ),/( 1$0( ,1387 ) 23(1,O) ,1387180%(5 2) /,1(6 ,1',01/ ,1f ,1387:(,*+7 2) '$7$ f,:,1387180%(5 2) 3$5$0(7(560 325, O72/1 35,17 180%(5 2) 32,176 f ,1387 1/ ,f 1(;7 ,13871 1 )25, O72/11 11/,f 1(;7',07;1f &91f $00f 30f ;00f 1/f %6 )25O72,1%6 %61/-Of35,17 325 O721/-f35,177-,f &3-,f,1387 7;%6,f &9 %6,f 1(;7 ,-,) $/ 7+(1 325, O721,138778,f&8,f3+,f92/,f1(;7, 3& &) ,) )3 7+(1 ',0&610f)3 35,17,1387'7 )25 -$&2%,$1 f'735,17)25 O720 35,17,1,7,$/ 3,f ,1387 $,f3,f $,f1(;7&/26(*268% 6 66 35,17 ,1,7,$/ 66 66325. O72O22*268% *268% *268% ----,) --! 7+(1 )25 72 03,f $,f$,0f1(;7*268% '6 $%66O66f,) $/! 25 66 7+(1 ): )25 7203: 3:;,f r$,0f&)r$,1%f r$,0f 1(;7 ,) '6):! 7+(1 &) &) ,) '63: 7+(1 &) r&) ,) '6 3&r6O 7+(1 ,) $/ $1' 66!6O 7+(1 )25 72 0$,0f r$,0f1(;7*&72 )25 72 0$,f 3 ,f 1(;76O 6635,1735,17/223 ,) $/ 7+(1 35,17 '$03 -)25 72 035,173,f 3,f1(;735,1766 661(;7 5(0 &+$1*( 72 35,17(5 35,1735,17r1r %< 0($/f 0(7+2'35,17:(,*+7 &3m ,:f ,) $/! $1' 1!0 7+(1 *268% ,)66 7+(1 35,17$,& ,1),1,7(*272 35,17$,& 1r/2*66fr0 ,) $/ 7+(1 35,17$/3+$ $$ %(7$ %% *$00$ &&35,17 ,) $/! 7+(1 35,17'7 '7

PAGE 253

,) $/ 7+(1 35,17)$&725 &) )25, O72035,17),1$/ 3, 3,f ,) $/! $1' ;,f! $1' 1!0 7+(1 35,17 6' 645;,fr6610f f 35,171(;735,17),1$/ 66 66%6 )25O72 /1%6 %61/-Of 35,17)5, 71/-f7 7;%6,f21 *268% 35,1777 &3&3 &9%6,ff1(;7,35,1735,17:+,&+ $/*25,7+0 '2 <28 6(/(&7" ,1387 25 f$/,) $/ 7+(1 (1' ,) $/ 7+(1 *272 &3 3fr(;33fr7f3fr(;33fr7f3fr(;33fr7f5(7851 &3 3fr3f3f3fffr(;33fr7f(;33fr7ff5(7851 )25-6 O72037 3-6f3-6f )7'721 *268% '' &33-6f 37'721 *268% &6%6,-6f ''&3fr'7f3-6f 371(;75(7851 $$ %% && 6* (3& 35,17)25, O72035,17,1,7,$/ 3 f ,1387 $,f 1(;7 )25 72 03O325 72 0$,-f r51'fr$,fr51'Off1(;7 )25. O 72 0O)25, O7203,f $,.f1(;7*268% $.f 661(;7 35,17)25 72 035,1766, $,f 1(;7*&72 65 6/ ()25720,) 65$-f 7+(1 -+ -65 $-f ,) 6/!$-f 7+(1 -/ -6/ $-f 1(;765 )25 72 0,) -2-+ $1' 65$-f 7+(1 -6 -65 $-f 1(;7)25 720;,f )25 72 0,) -2-+ 7+(1 ;,f ;,f$,f 1(;7;,f ;,f01(;7325 72 0$,f $$f r;,f$$r$,-+f 3,f $,f1(;7*268% 65 66,) 65 $-6f 7+(1 ,) 65$-+f 7+(1 )25 72 0$,-+f $,f1(;7$-+f 65 )25 72 0$,f %%r$,-+f%%fr;,f 3,f $,f1(;7*268% 65 66 ,) 65$-+f 7+(1 )25 72 0$,-+f $,f 1(;7$-+f 65*2U2 )25 72 0O)25, O 72 0$,.f $,.f$,-/f f3,f $,.f 1(;7 *268% $.f 661(;7*272 ,) 65$-/f 7+(1 )25 72 0$,-+f $,f1(;7$-+f 65*&72 )25, 720;,f &&r$,f&&fr;,f3,f ;,f1(;7*268% 6, 6 6 ,) 6/65 7+(1 )25 72 0$,-+f ;,f1(;7$-+f 6/*&72 *272 66 %6 )25 72 /1%6 %61/-Of)25 72 1/-f7 7;%6,f 21 *268% 66 66&9%6,f&3f&9%6,fr,: 1(;7 ,-5(7851 65 )25 72 0O65 65$,f1(;7 ,) $%6656*f!3&r6* 7+(1 6* 65*272 )25 72 03,f $,-/f1(;766 $-/f*&72 ,) 13 7+(1 $f $f$f5(7851 50 $%6$ff)25 ,6 72 13)25 -6 72 13 ,) 50$%6$-6,6ff 7+(1 50 $%6$-6,6ff

PAGE 254

1(;7 -6,6)25 .6 72 13: 325 ,6 .6 72 13 ,) $%6 $,6.6ff: 7+(1 : $%6$,6.6ff-6 ,6 1(;7,) -6 .6 7+(1 )25 ,6 .6 72 13: $.6,6f$.6,6f $-6,6f$-6,6f :1(;7 3 $.6.6f)25 -6 .6 72 13$.6-6f $.6-6fr3: $.6-6f ,) : 7+(1 )25 ,6 .6 72 13$,6-6f $,6-6f$,6.6fr:1(;7 1(;71(;7$1313f $1313f$1313f)25 ,6 72 13 /6 13,6: $/613f325 -6 /6 72 13 : :$/6 -6f r$-613f 1(;7$/613f :1(;75(7851 1/f %6 )25O72/1%6 %61/-Of)25 72 1/-f7 7;%6,f 21 *268% &6%6f &9%6,f&3*268% 1(;7 ,-325 72 0)25 72 0$,-f 325 / 72 1 $,-f $,-f&6 /,f r&6 / -f&9/f f,:1(;7$-,f $, -f 1(;7 -,5(7851 )25 72 0$,0f 325 72 1 $,0)Of $,0IOf&6-,fr&6-f&9-f r,:1(;7-,13 0 ,) $/ 7+(1 )25 72 0$,,f $,,f&);,f $,0f1(;7 5(7851 *268% )25 72 0)25 72 0;,-f $,-f1(;7 -, )25 72 0)25 72 0325 72 0$,-f ;,-f1(;7 -,)25 72 0 $,0f 1(;7$.0f *268% ;.f $.0f1(;75(7851

PAGE 255

352*5$0 08/7, 287387 r%3+ 3/$60$r %< '$03,1* :(,*+7 &3} f ),1$/ 3 ),1$/ 3 ),1$/ 3 ),1$/ 3 ),1$/ 3 ),1$/ 3 ( ),1$/ 66 *$8661(:721 0(7+2' 6' 6' 6' 6' ( 6' L 6' ( 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 f 7 &3 L f 7 &3 f 7 &3 f 7 &3 f )LWWLQJ RI WKH SODVPD FRQFHQWUDWLRQV DV EDVH QJPOf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f DJDLQVW WLPH PLQf IRU WKH PJ$J GRVH LQ GRJ & 7DEOH f WR HTXDWLRQ 9DOXHV LQ SDUHQWKHVLV FRUUHVSRQG WR H[SHULPHQWDO SODVPD FRQFHQWUDWLRQV RI

PAGE 256

$33(1',; ,, ),77,1* 2) '$7$ 72 (48$7,216 7KH SXUSRVH RI ILWWLQJ HTXDWLRQV DUH VHYHUDO IROGA Df 7R VXPPDUL]H D PDVV RI GDWD LQ RUGHU WR REWDLQ SUHGLFWLYH HTXDWLRQV IRUPXODV DQG FDOLEUDWLRQ FXUYHV" Ef 7R FRQILUP RU UHIXWH DQ HVWDEOLVKHG WKHRU\ RU UHODWLRQVKLS E\ FRPSDULQJ DQG HYDOXDWLQJ VHYHUDO VHWV RI GDWD LQ WHUPV RI FHUWDLQ SDUDPHWHUV DQG Ff 7R GHYHORS D WKHRUHWLFDO PRGHO $ JRRG PHWKRG RI ILWWLQJ GDWD WR HTXDWLRQV VKRXOGA Df 8VH DOO UHOHYDQW GDWD Ef +DYH UHVRQDEOH HFRQRP\ LQ WKH QXPEHU RI SDUDPHWHUV FKRVHQ Ff 7DNH LQWR DFFRXQW WKH HUURU LQ WKH GDWD Gf )LQG RXWOLHUV LI DQ\ Hf 3URYLGH VRPH PHDVXUH KRZ ZHOO WKH HTXDWLRQ ZLOO SUHGLFW IXWXUH HYHQWV /HDVW VTXDUH /6f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

PAGE 257

1RQOLQHDU /6 HVWLPDWLRQ 7KH HTXDWLRQ LV QRQOLQHDU ZKHQ WKH YDOXHV RI RQH RU PRUH RI WKH FRQVWDQW FRHIILFLHQWV RI WKH HTXDWLRQ FDQ QRW EH GLUHFWO\ FDOFXODWHG IURP WKH YDOXHV RI WKH LQGHSHQGHQW DQG GHSHQGHQW YDULDEOHV LH (T $ ZKHUH D E D DQG J DUH WKH QRQOLQHDU FRHIILFLHQWV ZKLFK FDQ QRW EH GLUHFWO\ FDOFXODWHG IURP WKH YDOXHV RI WKH LQGHSHQGHQW YDULDEOH W DQG GHSHQGHQW YDULDEOH & 7R ILW GDWD WR HTXDWLRQ $ XVLQJ QRQOLQHDU OHDVW VTXDUH DQDO\VLV FRPSXWHU SURJUDPV IRU H[DPSOH VHH $SSHQGL[ ,f SUHOLPLQDU\ HVWLPDWHV RI DOO SDUDPHWHUV PXVW EH DYDLDEOH ,I WKHVH HVWLPDWHV DUH QRW FORVH HQRXJK WR WKH EHVW YDOXHV RI WKH SDUDPHWHUV FRPSXWHU FDOFXODWHG HVWLPDWHV RI WKH SDUDPHWHUV PD\ QRW FRQYHUJH RQ WKH EHVW YDOXHV 7KH WHUP nEHVWn UDWKHU WKDQ nDFWXDOn LV XVHG LQ WKH SUHYLRXV VWDWHPHQW DV WKHUH PD\ EH PRUH WKDQ RQH VHW RI nEHVWn YDOXHV RI WKH SDUDPHWHUV WKDW FDQ DGHTXDWHO\ GHVFULEH WKH GDWDA 7KH WUDGLWLRQDO PHWKRG RI OHDVW VTXDUHV HVWLPDWLRQ DVVXPHVDf WKH FRUUHFW IRUP RI HTXDWLRQ KDV EHHQ FKRVHQ Ef WKH GDWD UHVSUHVHQW WKH SRSXODWLRQ Ff HDFK GDWXP LV VWDWLVWLFDOO\ LQGHSHQGHQW Gf LQGHSHQGHQW YDULDEOH LV PHDVXUHG ZLWKRXW DQ\ HUURU Hf DOO GDWD KDYH WKH VDPH HYHQ WKRXJK XQNQRZQ YDULDQFH If XQFRQWUROOHG HUURU LQ WKH GDWD LV UDQGRPO\ GLVWULEXWHG :HLJKWLQJ RI GDWD ,Q D QRQZHLJKWHG OHDVW VTXDUH DQDO\VLV WKH IROORZLQJ IXQFWLRQ LV PLQLPL]HG 1 (T $ L O

PAGE 258

WLO ZKHUH
PAGE 259

)LJXUH $O 6HPLORJDULWKPLF SORWV RI WKH FRQFHQWUDWLRQV DV EDVH QJPOf RI LQWUDYHQRXVO\ DGPLQLVWHUHG EXSUHQRUSKLQH f LQ SODPVD DJDLQVW WLPH PLQf IRU WKH PJNJ GRVH LQ NJ GRJ & 7DEOH $Of 7KH VROLG OLQHV UHSUHVHQW WKH FXUYH REWDLQHG E\ ILWWLQJ WKH SODVPD GDWD E\ YDULRXV WHFKQLTXHV DQG ZHLJKWLQJ XVLQJ 0XOWL $SSHQGL[ ,f Df :HLJKW Ef :HLJKW Ff /RJ
PAGE 260

ZQ ,,8 , 8 6%, ,,,0,1 0,1 1*n0/ 1*WO/ GKRTL

PAGE 261

7DEOH $O )LWWLQJ RI SODVPD GDWD ZLWK YDULRXV ZHLJKWLQJ IDFWRUV :HLJKW )HDWKHULQJ /RJ
PAGE 262

ILWWLQJ RI WKH VDPH GDWD XVLQJ WKH 0XOWL SURJUDP $SSHQGL[ ,f RI
PAGE 263

$33(1',; ,,, .586.$/:$//,6 7(67 7KH .UXVNDO:DOOLV WHVW LV D QRQSDUDPHWULH UDQN VXP WHVW WKDW FDQ EH XVHG WR FRPSDUH WZR RU PRUH VDPSOHV RI SRSXODWLRQV ,Q SDUWLFXODU VXSSRVH WKDW QA REVHUYDWLRQV DUH GUDZQ DW UDQGRP IURP SRSXODWLRQ QA IURP SRSXODWLRQ DQG QA IURP SRSXODWLRQ N 7KH K\SRWKHVLV WKDW WKH N VDPSOHV DUH GUDZQ IURP LGHQWLFDO EXW QRW QHFHVVDULO\ QRUPDOf GLVWULEXWLRQV FDQ EH FKHFNHG E\ WKH .UXVNDO:DOOLV WHVW ,Q WKLV PHWKRG +T 7KH N GLVWULEXWLRQV DUH LGHQWLFDO + 1RW DOO WKH GLVWULEXWLRQV DUH WKH VDPH D 7HVW 6WDWLVWLF + > / WW @ f Qf QQOf WM Q L L ZKHUH + IROORZV FKLVTXDUH GLVWULEXWLRQ P LV WKH QXPEHU RI (T $ REVHUYDWLRQV IURP VDPSOH LL O Nf Q LV WKH FRPELQHG VDPSOH VL]H WKDW LV Q QA DQG 7A GHQRWHV WKH VXP RI WKH UDQNV IRU WKH PHDVXUHPHQWV LQ VDPSOH L DIWHU WKH FRPELQHG VDPSOH PHDVXUHPHQWV KDYH EHHQ UDQNHG 5HMHFWLRQ 5HJLRQ )RU D VSHFLILHG YDOXH RI D UHMHFW +4 LI + H[FHHGV WKH FULWLFDO YDOXH RI FKLVTXDUH IRU D D DQG GI N $V DQ H[DPSOH FRQVLGHU WKH ILJXUH 7KH QXOO DQG WKH UHVHDUFK K\SRWKHVHV IRU WKLV H[DPSOH FDQ EH VWDWHG DV IROORZV +T 7KHUH LV QR VLJQLILFDQW GLIIHUHQFH EHWZHHQ WKH WKUHH GRVH QRUPDOLVHG SODVPD FRQFHQWUDWLRQV LH WKH GRVH QRUPDOLVHG SODVPD

PAGE 264

FRQFHQWUDWLRQV LQ WKH WKUHH VWXGLHV DUH GUDZQ IURP LGHQWLFDO SRSXODWLRQV 7KXV GRVHLQGHSHQGHQW SKDUPDFRNLQHWLFV LV SRVWXODWHG +D $W OHDVW RQH RI WKH WKUHH GRVH QRUPDOL]HG SODVPD FRQFHQWUDWLRQ VLJQLILFDQWO\ GLIIHUV IURP WKH RWKHUV 7KXV GRVHGHSHQGHQW SKDUPDFRNLQHWLFV LV SRVWXODWHG 7KH GRVH QRUPDOL]HG SODVPD FRQFHQWUDWLRQV IURP VWXGLHV DQG DUH UDQNHG DV JLYHQ LQ 7DEOH $ EHORZ 7DEOH $ 6WXG\ f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f 6WXG\ f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f 6WXG\ f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f )URP WKH DERYH WDEOH WKH VXPV 7Af RI WKH UDQNV YDOXHV LQ SDUHQWKHVLVf IRU WKH WKUHH JURXSV DUH DQG 6XEVWLWXWLQJ

PAGE 265

WKHVH YDOXHV LQ HTXDWLRQ $ ZH REWDLQ + 7KH FULWLDO YDOXH RI FKLVTXDUH ZLWK D DQG GI N IURP WKH FKLVTXDUH WDEOH LV 6LQFH WKH REVHUYHG + LV VPDOOHU WKDQ ZH DFFHSW WKH QXOO K\SRWKHVLV DQG FRQFOXGH WKDW WKHUH LV QR VLJQLILFDQW GLIIHUHQFH DPRQJ WKH WKUHH JURXSV 7KXV GRVHLQGHSHQGHQW SKDUPDFRNLQHWLFV FDQ QRW EH GHQLHG DW WKH GRVH UDQJH VWXGLHG

PAGE 266

$33(1',; ,9 7$%/(6 2) 5$: '$7$ 7DEOH $,9OD 3ODVPD EXSUHQRUSKLQH 'RJ 6WXG\ 7LPH &S H[SW &S FDOF $8& $8& PLQ QJP/ QJUUL/ FDOF WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 267

7DEOH $,9OE %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV ,8 \ JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO

PAGE 268

7DEOH $,9OH %XSUHQRUSKLQH 8ULQH 'RJ 6WXG\ e \JV $9 $W P/PLQ $ 8 $W YJPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH ,

PAGE 269

7DEOH $,9,G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF QJP/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 270

7DEOH $,9OH 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ S+ 8 \JV e 8 S JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO =8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 271

7DEOH $,9OI 0HWDEROLWH LQ XULQH 'RJ 6WXG\ = \JV $9 $W P/PLQ $8 $W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 272

7DEOH $,9D 3ODVPD EXSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF QJP/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 273

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO

PAGE 274

7DEOH $,9F %XSUHQRUSKLQH 8ULQH 'RJ 6WXG\ ; $9 $W $8 $W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ SJPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 275

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH &S H[SW &S FDOF $8& $8& PLQ QJP/ QJP/ FDOF WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 276

7DEOH $79H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ S+ 8 \JV =8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 277

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ ] \JV $9 $W P/PLQ $8 $W SJPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ FOS UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 278

7DEOH $,9D 3ODVPD EXSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF QJP/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 279

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV ,8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO e8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 280

7DEOH $,9F %XSUHQRUSKLQH 8ULQH 'RJ 6WXG\ (f \JV $9 $W $8 $W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 281

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW $8& QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 282

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 SJV e8 SJV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW SJPLQPO

PAGE 283

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ ]a $9 $W $8 $W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 284

7DEOH $,9D 3ODVPD EXSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF QJP/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 285

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO e8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 286

7DEOH $,9F %XSUHQRUSKLQH 8ULQH 'RJ 6WXG\ ( \JV $9 $W P/PLQ $8 $W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 287

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF QJUUL/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 288

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV ]X XJV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 289

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ ] \JV $9 $W P/PLQ $8 $W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 290

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF $8& QJP/ FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 291

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH UUL/ 3+ 8 \JV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO e8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 292

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ ( \JV $9 $W UUL/PLQ $8 $W YJPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 293

7DEOH $,9D 3ODVPD EXSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ &S FDOF QJP/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 294

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 295

7DEOH $,9F %XSUHQRUSKLQH 8ULQH 'RJ 6WXG\ H a SJV $9 $W P/PLQ $8 $W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ QOLPLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 296

7DEOH $,9 3ODVPD EXSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJUUL/ &S FDOF QJP/ $8& FDOF $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV &S FDOF &DOFXODWHG SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ FDOFXODWHG FDOFf RU HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 297

7DEOH $,9D 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW $8& QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 298

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 299

7DEOH $,9F %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ Hf \JV $9 $W $8$W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 300

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH &S H[SW $8& PLQ QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 301

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 SJV ;8 \JV $8&W 8$PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO ( 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 302

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ ( \V $9 $W P/PLQ $8 $ W X JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 303

7DEOH $,9D 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW $8& QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 304

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 SJV =8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO ] 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 305

7DEOH $,9F %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ ( f 86 $9 $W $8 $ W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVP FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVP FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVP FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 306

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW $8& QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 307

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJUUL/ 9ROXPH P/ 3+ 8 \ JV (8 X JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO e 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 308

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ ]\JV $9 $W P/PLQ $ $W \ JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 309

7DEOH $,9D 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH &S H[SW $8& PLQ QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 310

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV (8 \ JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW SJPLQPO

PAGE 311

7DEOH $,9F %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ L \JV $9 $W P/PLQ $8 $ W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 312

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 313

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ S+ XJV (8 SJV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO ( 8 &XLQXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 314

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ U \V $9 $W P/PLQ $8 $W SJPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 315

7DEOH $,9J 0HWDEROLWH LQ %LOH 'RJ 6WXG\ 7LPH &RQH 9RO 8 \JV (8 \JV $8&W PLQ \ JP/ P/ 8 $PRXQW H[FUHWHG LQ ELOH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ ELOH $8&W 7KH DUHD XQGHU WKH EXSUHQRUSKLQH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO XQLW \ JPLQPO

PAGE 316

7DEOH $,9K 0HWDEROLWH LQ ELOH 'RJ 6WXG\ ]\JV $9 $W P/PLQ $8 $W SJPLQ WPLG PLQ &S WPLG QJP/ &%D P/PLQ &%E P/PLQ WPLG 0LGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ RI EXSUHQRUSKLQH DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO Df %LOLDU\ FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH ELOH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV ELOLDU\ FOHDUDQFH ZDV REWDLQHG IURP WKH UDWLR RI WKH ELOLDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO

PAGE 317

7DEOH $,9D 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW $8& QJUUL/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQUUL/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSfr

PAGE 318

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \JV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 319

7DEOH $,9F %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ $9 $W P/PLQ $8 $W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 320

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH &S H[SW $8& PLQ QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSfr

PAGE 321

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \ JV O 8 SJV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 322

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ U\JV $9 $W $8 $W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 323

7DEOH $,9O2J 0HWDEROLWH LQ %LOH 'RJ 6WXG\ 7LPH PLQ &RQH \ JP/ 9RO P/ 8 \JV e8 \ JV $8&W 8 $PRXQW H[FUHWHG LQ ELOH GXULQJ D FROOHFWLRQ LQWHUYDO e8 &XPXODWLYH DPRXQWV H[FUHWHG LQ ELOH $8&W 7KH DUHD XQGHU WKH EXSUHQRUSKLQH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 324

7DEOH $UYK 0HWDEROLWH LQ ELOH 'RJ 6WXG\ \JV D9 $W D8 $W WPLG &S WPLG &% D &% E P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ RI EXSUHQRUSKLQH DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO Df %LOLDU\ FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH ELOH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV ELOLDU\ FOHDUDQFH ZDV REWDLQHG IURP WKH UDWLR RI WKH ELOLDU\ H[FUHWLRQ UDWH DQG WKH SODVP" FRQFHQWDWLRQ DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO

PAGE 325

7DEOH $,9OOD 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW $8& QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf}

PAGE 326

7DEOH $,9OOE 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 327

7DEOH $,9OOF 0HWDEROLWH LQ %LOH 'RJ 6WXG\ 7LPH PLQ &RQH \ JP/ 9RO P/ 8 \JV e8 SJV $8&W 8 $PRXQW H[FUHWHG LQ ELOH GXULQJ D FROOHFWLRQ LQWHUYDO O 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ ELOH $8&W 7KH DUHD XQGHU WKH EXSUHQRUSKLQH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO XQLW \ JPLQPO

PAGE 328

7DEOH $,9OOG 0HWDEROLWH LQ ELOH 'RJ 6WXG\ ]\ JV $9 $W P/PLQ $8 $W X JPLQ WPLG PLQ &S WPLG QJP/ &O D P/PLQ &O E 8% P/PLQ WPLG 0LGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ RI EXSUHQRUSKLQH DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO Df %LOLDU\ FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH ELOH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV ELOLDU\ FOHDUDQFH ZDV REWDLQHG IURP WKH UDWLR RI WKH ELOLDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO

PAGE 329

7DEOH $,9 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH &S H[SW $8& PLQ QJP/ WUDS

PAGE 330

7DEOH $,9 &RQWLQXHG &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 331

7DEOH $,9D 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH &S H[SW $8& PLQ QJP/ WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 332

7DEOH $,9E 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ S+ 8 \JV =8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO = 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 333

7DEOH $,9& 0HWDEROLWH LQ XULQH 'RJ 6WXG\ V\JV $9 $W P/PLQ $8 $W S JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVP FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 334

7DEOH $,9D 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQUUL/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSfr

PAGE 335

7DEOH $ ,9E 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ S+ 8 \ JV = 8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO ,8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 336

7DEOH $,9F 0HWDEROLWH LQ XULQH 'RJ 6WXG\ U SV $9 $ W P/PLQ $8 $W \JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVP FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVP FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVP FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 337

7DEOH $,9G 0HWDEROLWH LQ %LOH 'RJ 6WXG\ 7LPH PLQ &RQH \JP/ 9RO P/ 8 \JV ,8 \JV $8&W 8 $PRXQW H[FUHWHG LQ ELOH GXULQJ D FROOHFWLRQ LQWHUYDO (8 &XPXODWLYH DPRXQWV H[FUHWHG LQ ELOH $8&W 7KH DUHD XQGHU WKH PHWDEROLWH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO XQLW\ JPLQPO

PAGE 338

7DEOH $,9H 0HWDEROLWH LQ ELOH 'RJ 6WXG\ $9$ W P/PLQ $8 $W 0 JPLQ WPLG PLQ &S WPLG QJP/ &O D % P/PLQ &O E 8% P/PLQ WPLG 0LGSRLQW RI ELOH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ RI WKH PHWDEROLWH DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO Df %LOLDU\ FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH ELOH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV ELOLDU\ FOHDUDQFH ZDV REWDLQHG IURP WKH UDWLR RI WKH ELOLDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI ELOH FROOHFWLRQ LQWHUYDO

PAGE 339

7DEOH $,9D 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 340

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJUUL/ 9ROXPH P/ S+ 8 \JV =8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO ]8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 341

7DEOH $,9F %XSUHQRUSKLQH LQ XULQH 'HJ 6WXG\ $9 $W $8 $ W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 342

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 343

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 \ JV =8 \ JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO = 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 344

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ USJV $9 $W P/PLQ $8 $W \ JPLQ WPLG PLQ &S WPLG QJP/ &O D UHQ P/PLQ &O E UHQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 345

7DEOH $,9D 3ODVPD %XSUHQRUSKLQH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf}

PAGE 346

7DEOH $,9E %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH P/ 3+ 8 SJV (8 \JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO ( 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW SJPLQPO

PAGE 347

7DEOH $,9F %XSUHQRUSKLQH LQ XULQH 'RJ 6WXG\ ] SJV $9 $W $8$W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ \JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 348

7DEOH $,9G 3ODVPD PHWDEROLWH 'RJ 6WXG\ 7LPH PLQ &S H[SW QJP/ $8& WUDS &S H[SW ([SHULPHQWDO SODVPD FRQFHQWUDWLRQV $8& $UHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH QJPLQP/ HVWLPDWHG E\ WUDSH]RLGDO UXOH WUDSf

PAGE 349

7DEOH $,9H 0HWDEROLWH LQ XULQH 'RJ 6WXG\ 7LPH PLQ &RQH QJP/ 9ROXPH UUL/ S+ 8 S JV 8S JV $8&W 8 $PRXQW H[FUHWHG LQ XULQH GXULQJ D FROOHFWLRQ LQWHUYDO 8 &XPXODWLYH DPRXQWV H[FUHWHG LQ XULQH $8&W 7KH DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH FXUYH DW WKH PLGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO XQLW \JPLQPO

PAGE 350

7DEOH $,9I 0HWDEROLWH LQ XULQH 'RJ 6WXG\ I\JV $9 $W $8 $W WPLG &S WPLG &O D UHQ &O E UHQ P/PLQ S JPLQ PLQ QJP/ P/PLQ P/PLQ WPLG 0LGSRLQW RI XULQH FROOHFWLRQ LQWHUYDO &S WPLG SODVPD FRQFHQWUDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ LQWHUYDO Df 5HQDO FOHDUDQFH FDOFXODWHG IURP WKH UDWLR RI WKH FXPXODWLYH DPRXQW H[FUHWHG LQ WKH XULQH YHUVXV DUHD XQGHU WKH SODVPD FRQFHQWUDWLRQWLPH SURILOH Ef ,QVWDQWDQHRXV UHQDO FOHDUDQFH REWDLQHG IURP WKH UDWLR RI WKH XULQDU\ H[FUHWLRQ UDWH DQG WKH SODVPD FRQFHQWDWLRQ DW WKH PLG SRLQW RI XULQH FROOHFWLRQ WLPH

PAGE 351

*/266$5< 2) 7(506 $8&W $UHD XQGHU WKH DSSDUHQW GUXJPHWDEROLWH FRQFHQWUDWLRQ LQ SODVPD YHUVXV WLPH FXUYH QJPLQPOf $SSDUHQW ILUVW RUGHU HOLPLQDWLRQ UDWH FRQVWDQW IRU D GUXJ WKDW GLVWULEXWHV LQ WKH ERG\ LQ DFFRUGDQFH ZLWK D PXOWLFRPSDUWPHQW ERG\ PRGHO REWDLQHG IURP WKH WHUPLQDO VORSH RI D VHPLORJDULWKPLF SORW RI WKH GUXJ FRQFHQWUDWLRQ LQ SODVPD YHUVXV WLPH PLQf % P $PRXQW RI WKH PHWDEROLWH H[FUHWHG LQ ELOH XS WR WLPH W \ Jf &O WRW 7RWDO ERG\ FOHDUDQFH POPLQf &Of§!0 % %LOLDU\ FOHDUDQFH RI GUXJ DV PHWDEROLWH POPLQf &Of§ 8% %LOLDU\ FOHDUDQFH RI WKH XQFKDQJHG GUXJ POPLQf &O UHQ 5HQDO FOHDUDQFH RI WKH XQFKDQJHG GUXJ POPLQf 0 &O UHQ 5HQDO FOHDUDQFH RI WKH PHWDEROLWH POPLQf &O PHW 0HWDEROLF FOHDUDQFH RI WKH GUXJ POPLQf &S 'UXJ FRQFHQWUDWLRQ LQ SODVPD DW WLPH W QJPOf b 'UXJ FRQFHQWUDWLRQ LQ SODVPD LPPHGLDWHO\ IROORZLQJ 79 EROXV LQMHFWLRQ QJPOf I )UDFWLRQ RI WKH RUDOO\ DGPLQLVWHUHG GRVH WKDW HYHQWXDOO\ UHDFKHV WKH V\WHPLF FLUFXDWLRQ XQFKDQJHG I D )UDFWLRQ RI WKH RUDOO\ DGPLQLVWHUHG GRVH WKDW UHDFKHV WKH OLYHU XQFKDQJHG I OSP )UDFWLRQ RI WKH DEVRUEHG GRVH WKDW XQGHUJRHV ILUVWSDVV PHWDEROLVP

PAGE 352

$SSDUHQW ILUVW RUGHU LQWHUFRPSDUWPHQWD WUDQVIHU UDWH FRQVWDQWV ZKHUH L O M O LAM OPLQf $SSDUHQW ILUVW RUGHU UDWH FRQVWDQW IRU WKH PHWDEROLWH IRUPDWLRQ LQ WKH FHQWUDO FRPSDUWPHQW IRU D GUXJ WKDW GLVWULEXWHV LQ WKH ERG\ LQ DFFRUGDQFH ZLWK D PXOWLFRPSDUWPHQW ERG\ PRGHO OPLQf =HUR RUGHU LQIXVLRQ UDWH FRQVWDQW PJPLQf $SSUHQW ILUVW RUGHU HOLPLQDWLRQ UDWH FRQVWDQW IRU WKH GUXJ IURP WKH FHQWDO FRPSDUWPHQW OPLQf 5DWH RI PHWDEROLWH IRUPDWLRQ LQ WKH FHQWUDO FRPSDUWPHQW 7LPH PLQf 7LPH DW ZKLFK ]HUR RUGHU LQIXVLQ LV WHUPLQDWHG PLQf $PRXQW RI WKH PHWDEROLWH H[FUHWHG LQ XULQH WR WLPH W Jf $SSDUHQW YROXPH RI GLVWULEXWLRQ RI WKH GUXJ LQ WKH FHQWUDO FRPSDUWPHQW /f $ SURSRUWLQDOLW\ FRQVWDQW UHODWLQJ WKH DPRXQW RI WKH GUXJ LQ WKH ERG\ WR WKH GUXJ FRQFHQWUDWLRQ LQ SODVPD DW SVHXGRVWHDG\ VWDWH /f $ SURSRUWLRQDOLW\ FRQVWDQW UHODWLQJ WKH DPRXQW RI WKH PHWDEROLWH LQ WKH ERG\ WR WKH PHWDEROLWH FRQFHQWUDWLRQV LQ SODVPD RQ WKH SUHVXPSWLRQ WKDW SODVPD PHWDEROLWH FRQFHQWUDWLRQV DUH UHSUHVHQWDWLYH RI WKH PHWDEROLWH FRQFHQWUDWLRQV LQ WKH HTXLOLEUDWHG IOXLGV RI WKH ERG\ /f

PAGE 353

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

PAGE 354

(OOLV 5 +DLQHV 6KDK 5 &RWWRQ %5 6PLWK %U $QDHVWK +D\HV 0)UDVHU $5 +DPSWRQ -5 %U 0HG &KDNUDYDUW\ 7XFNHU : 5RVHQ 0 9LFNHUV 0' %U 0HG 5REELH '6 8QSXEOLVKHG GDWD IURP 5HFNLWW t &ROPDQ &R 6DPD\RD 'H /HRQ 5 &OLQLFDO XVH RI IHQWDQ\O LQ VHTXHQWLDO DQDOJHVLF DQHVWKHVLD 6RFLHWH Gn$QHVWKHVLH GH &KDUOHURL %HOJLXP S WKURXJK UHIHUHQFH %LOVEDFN 3 5RLO\ 7DPSXERORQ %U $QDHVWK *UHHQ ': 6LQFODLU -5 0LNKDHO 06 $QDHVWKHVLD /DQ] ( 6LPNR 7KHLVV *ORFNH 0+ $QHVWK $QDOJ &FZDQ $ 'R[H\ -& +DUU\ (-5 %U 3KDUPDFRO 6WHSKHQ *: &RRSHU /HVOH\ 9 $QDHVWKHVLD 2UZLQ -0 3DLQ1HZ SHUVSHFWLYHV LQ 0HDVXUHPHQW DQG 0DQDJHPHQW &KXUFKLOO /LYLQJVWRQH (GLQEXUJK :XVW -+ 8QSXEOLVKHG GDWD IURP 5HFNLWW t &ROPDQ &R &FZDQ $ODQ $GY %LRFKHP 3V\FRSKDUPFRO e %RDV 5$ 9LOOLJHU -: %U $QDHVWK 9LOOLJHU -: 7D\ORU .0 /LIH 6FL +RYHOO %& %U $QDHVWK .D\ % %U $QDHVWK %XOOLQJKDP 5(6 0F4XD\ +'Z\HU $OOHQ 0& 0RRUH 5$ %U &OLQ 3KDUPDFRO %XOOLQJKDP 5(6 0F4XD\ +3RUWHU (-% $OOHQ 0& 0RRUH 5$ %U &OLQ 3KDUPDFRO %XOOLQJKDP 5(6 0F4XD\ +0RRUH $ %HQQHWW 05' &OLQ 3KDUPDFRO 7KHU

PAGE 355

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
PAGE 356


PAGE 357

%,2*5$3+,&$/ 6.(7&+ 9 5DYL &KDQGUDQ ZDV ERUQ 0D\ LQ ,QGLD +H UHFHLYHG %3KDUP +RQRUVf GHJUHH LQ DQG 03KDUP LQ IURP -DGDYSXU 8QLYHUVLW\ &DOFXWWD +H ZDV WKHQ HPSOR\HG DV D UHVHDUFK SKDUPDFLVW LQ /LVWHU /DERUDWRULHV %RPED\ +H FDPH WR 8QLYHUVLW\ RI )ORULGD LQ DQG REWDLQHG D PDVWHUV GHJUHH LQ SKDUPDFHXWLFDO VFLHQFHV LQ $IWHU FRPSOHWLRQ RI WKH 3K' KH ZLOO EH HPSOR\HG DV 6HQLRU 5HVHDUFK 3KDUPDFLVW DW 6WHUOLQJ:LQWKURS 5HVHDUFK ,QVWLWXWH $OEDQ\ 1HZ
PAGE 358

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ (GZDUG 5 HWW &KDLUPDQ *UDGXDWH 5HVHDUFK 3URIHVVRU f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

PAGE 359

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ U .DWRYLFK $VVRFLDWH 3URIHVVRU RI 3KDUPDFRG\QDPLFV FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ +DUWPXW & 'HUHQGRUI } $VVLVWDQW 3URIHVVRU RI 3KDUPDFHXWLFV 7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH &ROOHJH RI 3KDUPDF\ DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVSK\ 'HFHPEHU 'HDQ &ROOHJH RI 3KDUPDF\ 'HDQ *UDGXDWH 6FKRRO

PAGE 360

81,9(56,7< 2) )/25,'$


PHARMACOKINETICS OF BUPRENORPHINE IN DOGS
By
V. RAVI CHANDRAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986

ACKNOWLEDGEMENT
I gratefully acknowledge Dr. Edward R. Garrett for his numerous and
varied contributions. I also thank him for his guidance, training,
support and facilities during my graduate career, which made this
dissertation possible.
My special thanks are extended to Dr. Jurgen Venitz for his time,
fruitful discussions and helpful suggestions, and to Dr. Larry J. Peters
and Dr. August H. Battles for animal preparations.
I wish to thank the current and past members of the "Beehive" for
their help, support, advice and friendship.
I acknowledge the members of my supervisory committee,
Dr. John H. Perrin, Dr. Hartmut C. Derendorf, Dr. James W. Simpkins,
Dr. Michael J. Katovich, Dr. C. Lindsay Devane, Dr. John A. Zoltewicz
for their contributions.
I take this opportunity to express my sincere appreciation to
Dr. Bernard Desoize, Dr. Peter Langguth, Mrs. Marjorie Rigby, Mrs. Kathy
Eberst, Mr. George Perry and Mr. Thomas Miller for their valuble help.
li

TABLE OF CONTENTS
ACKNOWLEDGEMENTS Ü
ABSTRACT iv
INTRODUCTION 1
EXPERIMENTAL 20
IV BOLUS STUDIES 30
URINARY EXCRETION OF BUPRENORPHINE 86
IV INFUSION STUDIES 131
PHARMACOKINETICS OF THE IV ADMINISTERED METABOLITE 214
SUMMARY AND CONCLUSIONS 241
APPENDIX I - PROGRAM "MULTI" 247
APPENDIX II - FITTING OF DATA TO EQUATIONS 251
APPENDIX III - KRUSKAL-WALLIS TEST 258
APPENDIX IV - TABLES OF RAW DATA 261
GLOSSARY OF TERMS 346
REFERENCES 348
BIOGRAPHICAL SKETCH 352
iii

Abstract of Dissertation presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PHARMACOKINETICS OF BUPRENORPHINE IN DOGS
By
V. Ravi Chandran
December 1986
Chairman: Dr. Edward R. Garrett
Cochairman: Dr. John H. Perrin
Major Department: Pharmaceutical Sciences
Specific and sensitive reverse-phase HPLC assays of buprenorphine
and its metabolite in biological fluids were developed with
sensitivities of 2-6 ng/ml using fluorimetric detection. Upon acute
bolus administration of buprenorphine in six dogs within the 0.7-2.6
mg/kg dose range, accurate estimation of the terminal rate constant and
the derived total body clearance were not feasible due to the lack of
sufficient quantifiable terminal plasma points at less than 5 ng/ml
sensitivity. The terminal plasma concentrations could not be increased
by increasing the bolus dose since such high doses would have
significant toxicity. This toxicity was circumvented and the terminal
plasma concentrations were increased by infusing 3.7-4.8 mg/kg doses of
buprenorphine over 3 h in six studies in six dogs. The terminal rate
IV

constants of the IV infusion studies averaged 34 +_ 3.7 h with an
averaged total body clearance of 212 _+ 35 ml/min. The apprent volumes of
distribution of buprenorphine referenced to the total plasma
concentration were 35 L (V , central compartment volume) and 617 L
(Vj, total body volume), indicative of a highly bound, sequestered or
lipophilic drug.
Unchanged buprenorphine is insignificantly renally (<0.5% of the
dose) and biliary (<0.5%) excreted. The major route of buprenorphine
disposition is by hepatic conjugation to glucuronide which is eliminated
into the bile (about 95%) with only small amounts appearing in urine
(<1% as metabolite). Minor metabolites excreted in the bile accounted
for about 3% of the administered dose.
Direct IV administration of the metabolite gave a terminal
half-life of 6 h. Unlike intravenously administered morphine glucuronide
which was not excreted in the bile, more than 90% of the systemically
circulating metabolite was excreted in bile and only 10% in urine.
The oral bioavailability estimated from the areas under the
buprenorphine plasma concentration-time curve following TV and oral
administration of buprenorphine in the dogs was 3-6%. In a bile
cannulated dog, intraduodenally administered metabolite demonstrated 6%
enterohepatic recirculation of the conjugate.
There were no apparent correlations of the buprenorphine time
course with cardiovascular parameters such as heart rate, ECG and blood
pressure. Miotic effect was significant. Respiratory depression was
observed during the first 4 h after IV bolus injection, but not during
the infusion studies.
v

INTRODUCTION
Buprenorphine (1) is a derivative of the morphine alkaloid
thebaine. It is a strong analgesic with marked narcotic activity. Since
the mid-sixties, its therapeutic potential as a morphine-type analgesic
at low doses and antagonistic activity at high doses, has been well
documented.^ Buprenorphine has been claimed to have an advantage over
morphine in that the dose does not need to be increased during several
2
weeks of chronic administration.
Pharmacodynamic and Therapeutic Studies
Buprenorphine has displayed narcotic agonist and antagonist
properties in animals and man. Agonistic effects often exhibited a bell
3
shaped dose-response curve, as occurs with pentazocine, and subjective
opiate-like effects reached a maximum at a dose of about 0.2 to 0.8 mg
4
subcutaneously in man. The onset of agonistic effects (peak effects
about 6 h after subcutaneous or IM injection) in man was slower than
with morphine but the duration of such effects was longer (about 72
5
hours) than with morphine. Also, the analgesic potency of
buprenorphine was about 25 times that of morphine (on a per unit weight
basis)
Therapeutic Trials
In a comparative study of the treatment of chronic pain of
malignant origin by intramuscularly administered buprenorphine and
morphine, 27 patients received buprenorphine (0.3 mg) and morphine (10
7
mg) in a double-blind, single-dose within-patient study. There were no
1

2
significant differences in the intensity of analgesic effect or the time
7
to reach it. However, buprenorphine had a significantly longer
duration of action than morphine. Sedation was the most frequent side
7
effect but dizziness, nausea and vomiting were also seen. Compared to
morphine, buprenorphine showed significantly higher incidences of side
7
effects, greater severity and earlier onset, and longer duration.
Following both treatments there were small but significant decreases in
7
pulse rate, blood pressure and respiratory rate.
Antinociceptive actions (blockade of impulses at the peripheral
pain sensitive nerves) of buprenorphine and morphine given intrathecally
g
in conscious rats were compared. After intrathecal injection the peak
(30 min) antinociceptive potencies of buprenorphine or morphine were
g
similar. The analgesic profiles of buprenorphine and morphine (0.3 mg
and 10 mg respectively) were compared in a double-blind non-crossover
9
multiple dose study (IM administration) in man. When the patient
complained of moderate to severe post-operative pain after upper
abdominal surgery, the first test dose of either drug was given. The
drugs gave an equal decrease in pain intensity, suggesting a relative
9
potency of 33:1. An average of 0.51 mg of buprenorphine or 16 mg of
morphine had to be administered for satisfactory initial analgesia. A
faster decrease in the rate of respiration was observed after
buprenorphine than after morphine, but ultimately both the drugs gave
9
the same minimum rate of respiration. These results were comparable to
7
those reported elsewhere.
An oral combination of buprenorphine and paracetamol was compared
to paracetamol in a single-dose double-blind study in man for the
initial acute treatment of post-operative pain.^ One hundred and

3
twenty patients undergoing orthopedic operations were divided into four
groups of 30 patients each. The four treatments were 1, 1.5 or 2 mg of
buprenorphine combined with paracetamol 1000 mg or paracetamol (1000 mg)
alone. There were no significant differences among the groups in
analgesia measured by the observer and by the pain intensity scoring by
the patients over the first six hour. The oral combinations of
buprenorphine and paracetamol produced a significant increase in
duration of analgesia beyond 6 hours over that of paracetamol alone at
all three dose concentrations. A significant increase in side effects
was seen only at the highest dose of buprenorphine-paracetamol
combination compared with paracetamol alone.^
In a study designed to assess the development of drug dependence,
rats were chronically treated subcutaneously for 4 days with
buprenorphine.11 These rats showed only weak signs of withdrawal upon
cessation of a treatment or upon challenge with naloxone.11 More
intense withdrawal symptoms were induced when morphine was substituted
for buprenorphine. Even one injection of morphine, given 12 h after the
last buprenorphine treatment, led to withdrawal symptoms with naloxone.
Naloxone did not cause withdrawal in naive rats treated with this dose
of morphine. Thus, according to these authors,11 and contrary to a few
12 .
claims in the literature, buprenorphine induced dependence like other
opiates. The authors argue that the intensity of withdrawal is less
severe due to slow dissociation of the drug from the receptors.11
The neurochemical effects of buprenorphine were compared to those
of morphine and haloperidol in rats.^ The effect of a wide range of
doses of buprenorphine (0.001 - 10 mg/kg, subcutaneous administration)
was studied a) with normal concentrations of dopamine, noradrenaline,

4
5-hydroxytryptamine etc. and b) with lower concentrations of dopamine
and noradrenaline in rat brain following the treatment with alpha-methyl
para-tyrosine (alpha-MpT), which is a inhibitor of catecholamine
synthesis. Morphine and haloperidol were used as reference agents.
Buprenorphine increased the alpha-MpT induced rate of dopamine depletion
but did not deplete norepinephrine. Similar results were obtained with
a higher dose (30 mg/kg) of morphine but it increased the alpha-MpT
induced depletion of norepinephrine. Apparently similar effects of
buprenorphine and haloperidol on dopaminergic neurotransmission were
distinguished by pretreating the rats with naloxone (which antagonized
the effect of buprenorphine, and prevented dopamine depletion). These
neurochemical results were claimed to support the view that one site of
action of buprenorphine is on opiate receptors located on the
dopaminergic neurons.^
In a double-blind comparison between fentanyl and buprenorphine in
supplemented nitrous oxide analgesia, buprenorphine or fentanyl (0.3 and
0.125 mg respectively administered IV) were used as supplements in 40
14
patients undergoing major abdominal surgery. Initially both narcotics
appeared to suppress tachycardia and increase arterial pressure in
response to surgery but 80% of the patients who received fentanyl
eventually reguired a further supplement of halothane (0.5%), but no
patient who received buprenorphine required halothane. Recovery from
analgesia was similar in both groups, but the duration of analgesia
after the operation was significantly greater for buprenorphine (12 h)
than fentanyl (3 h).1^
In a double-blind randomized non-crossover trial, 47 patients
received either morphine (10 mg) or buprenorphine (0.3 mg) by regular IM

5
injection for 24 h after abdominal surgery.15 In this study, the two
drugs were equally effective at the dose ratio 1:33, buprenorphine to
7 9
morphine which is comparable to the results reported elsewhere.
One hundred twenty-six patients undergoing upper and lower
abdominal surgery were studied post-operatively to compare the analgesic
effect of IM morphine, sublingual buprenorphine and self administered IV
pethidine.15 There were no significant differences among analgesic
regimens in respect to subjective pain scores or static and dynamic lung
volumes assessed at 24 h, 48 h and 5 days after operation. Sublingual
buprenorphine produced more nausea and sedation than the other regimens,
but the results were not clinically important. These authors15 report
that buprenorphine offered considerable advantages in terms of ease of
administration.
When diamorphine and buprenorphine were compared in the relief of
chest pain in man, sublingual administration appeared to be as effective
17
as the IV route, but the onset of action was slow. There were no
significant changes in the systemic or pulmonary arterial blood pressure
17
or heart rate after IV buprenorphine. A randomized double-blind
controlled trial of equivalent doses of buprenorphine and diamorphine
showed no significant differences between the drugs in terms of pain
17 . .
relief and duration of action. The occurence of nausea, vomiting and
other side effects was similar in the two groups. The onset of action of
buprenorhine was slightly but significantly slower than that of
diamorphine.1^
Buprenorphine and pethidine were compared in a double-blind study
of on-demand IV analgesia. Buprenorphine was about 600 times as potent
18
as pethidine. The incidence of side effects was similar with both

6
drugs. The quality of analgesia subjectively assessed was the same with
18
both drugs using this method of administration. These authors claim
that buprenorphine is a powerful analgesic agent that may be given
intravenously provided that its low potential for abuse is
substantiated.
In a smaller number of patients with chronic pain, usually due to
cancer, sublingually given buprenorphine (up to 0.8 mg 4 hourly)
provided adequate pain relief for periods up to several months, but side
effects (usually nausea and vomiting) required discontinuation of
19
treatment in about 1/3 to 1/2 of the ambulatory patients.
Following anesthesia with fentanyl in 180 patients, buprenorphine
(usually 0.4 to 0.8 mg IV) reversed some of the anesthetic effects while
producing continued analgesia that lasted about 8-12 h after a
20
single-dose. The antagonistic activity however, was frequently
short-lived, declining rapidly after 90 to 120 min and a second dose of
buprenorphine was often required to prevent the re-emergence of
20
anesthetic effects.
The efficacy of buprenorphine has been compared to lofentanil and
to saline placebo by extradural administration in the management of
21
post-operative pain in sixty patients. In a double-blind study, these
orthopedic patients were randomly assigned to three equal groups to
determine the analgesic effects, duration of action and side effects of
the extradural administration of lofentanil (5 ug) buprenorphine (0.3
21
mg) or physiological saline. No systemic analgesics were given
before, during or after surgery, and all the patients had operations on
the lower extremities under extradural analgesia (lignocaine or
bupivacaine). Upon administration of the test drug as soon as pain

7
occured in the post-operative period, a long duration of action and a
marked analgesic effect was observed with lofentanil. A shorter duration
of action and less pain suppression occured with buprenorphine and a
rather marked placebo effect was seen with saline. The only side effect
noticed was drowsiness in 3 patients in the lofentanil group and in 2
21
patients in the buprenorphine group.
22
In a randomized double-blind trial comparing analgesia produced
by combinations of droperidol with either buprenorphine or morphine,
buprenorphine was claimed to be as satisfactory as morphine to produce
analgesia during major surgery in 60 patients, with no difference in the
incidence of untoward side effects.
Epidural buprenorphine was investigated as a post-operative
analgesic in a randomized double-blind study of 158 patients given
intraoperative epidural analgesia with 2% mepivacaine or 0.5%
23
bupivacaine for orthopedic surgery of the lower extremity. At the end
of the surgery, the patients were given epidurally in 15 ml saline,
either 0.15 mg of buprenorphine (n=38) or 0.3 mg (n=37). A control group
received no epidural injection (n=47). The above 3 groups received 2%
mepivacaine as intraoperative anesthetic. A fourth group (n=36) received
0.3 mg buprenorphine in 15 ml saline, after intraoperative use of 0.5%
bupivacaine. The patients rated post-operative pain. Analgesia after
0.15 mg of buprenorphine was superior to that after saline injection,
and 0.3 mg buprenorphine was superior to both saline injection and to
23
0.15 mg of buprenorphine until 12th hour. Analgesia after bupivacaine
followed by 0.3 mg of buprenorphine was not significantly different than
analgesia seen after mepivacaine followed by 0.3 mg of buprenorphine.
21
These results are comparable to those reported elsewhere.

8
Respiratory effects. The respiratory depressant activity (such as
decreased respiratory rate, increased arterial P CCL and decreased
cl Z
arterial P 0„) of single equianalgesic doses of buprenorphine and
cl Z
1 24 25
morphine appear to be similar in rats and rabbits. ' ' The extent of
buprenorphine-induced respiratory depression against dose plateaued in
26
animals, whereas such an effect was not clearly demonstrated in man,
which showed dose-related respiratory depression within the therapeutic
dose range (0.3 mg to 0.6 mg). The time to reach peak respiratory
depression in man was slower after intramuscular buprenorphine than
after morphine (3 h vs 1 h) and the duration of such an effect was
26
longer. There appears to be no completely reliable specific
antagonist for buprenorphine-induced respiratory depression since even
26
high doses of naloxone produced only partial reversal. Hcwever, the
respiratory stimulant drug doxapram has reversed respiratory depression
due to buprenorphine in a few healthy volunteers and in a few
. . . 26
patients.
Cardiovascular effects. Hemodynamic changes in healthy volunteers
after IM (0.15 to 0.6 mg), sublingual (0.4 to 0.8 mg) or oral (1 to 4
ng) doses of buprenorphine include dose related reductions in heart rate
(up to 25%) and small decreases in systolic blood pressure (about
26
10%). These results are comparable to the cardiovascular effects of
26
morphine. Similar effects occured in anesthetized patients undergoing
surgery and in a few patients with myocardial infarctions. However, in
the latter group the heart rate was found to be relatively
27
unperturbed.
Addiction potential of buprenorphine. Buprenorphine appeared to
have a lower addiction potential than the opioid agonist pentazocine in

9
animals. However the extent to which such results can be extrapolated to
1 28
man was uncertain. ' In a single-dose addiction study in 5
volunteers, high (8 mg daily) intramuscular doses of buprenorphine,
administered up to 1 to 2 months produced a slowly emerging withdrawal
5 6
syndrome on abstinence from the drug. ' Though the results were
indicative of lesser addiction potential compared to morphine,
definitive statements about addiction cannot be made until it has been
more widely used in patients with chronic pain with repeated doses over
an extended period of time.^
Receptor binding studies. Receptor binding studies were undertaken
to elucidate the opioid binding characteristics of fentanyl and
29
buprenorphine, and to investigate differences between them.
Buprenorphine showed slow receptor equilibration (30 min) but with high
affinity to multiple sites. The dissociation was claimed to be slow
(half-life = 166 min) and incomplete (50% binding after 1 h). This
contrasted with the receptor binding of fentanyl, which achieved rapid
equilibrium (within 10 min) and dissociated equally rapidly (half-life =
6.8 min) and completely (100% by 1 h). Using competitive displacement
studies, it was claimed that buprenorphine displacement of fentanyl was
concentration and time dependent over the ranges (equimolar
buprenorphine and fentanyl concentrations, 2 nmol/liter) encountered in
clinical use. However, buprenorphine binding was displaced with only
. . 29
high concentrations of other opioids.
Binding of buprenorphine to the rat forebrain (telencephelon,
diencephelon and mesencephelon) was claimed to be stereospecific,
30
saturable and had high affinity. Maximum binding (Bmax) was reached
by 30 min and dissociation from the receptor was slow. The regional

10
distribution of buprenorphine binding sites in the rat brain was claimed
to be qualitatively similar to the distribution of naloxone and
dihydromorphine binding sites. The Bmax for this receptor binding of
buprenorphdne was about 2 times that for the mu-opiate receptor drugs
and three times the for the delta-opiate receptor ligands (such as
enkephalins). Buprenorphine was also found to be very potent in
displacing naloxone, dihydromorphine and met-enkephalin. Since mu-
receptors bind with exogenous opioids (such as morphine), and delta-
receptors bind with endogenous opioids (such as enkephalins), the above
findings suggest that buprenorphine binds to both mu- and
delta-receptors.^
Side effects.
Moderate to marked drowsiness has been reported in about 40-50% of
the patients (up to 75% in some studies), but all such patients were
1 31 32
found to be easily arousable upon stimulation. ' ’ Nausea and/or
vomiting occurred in 15% of the patients. Other minor side effects (e.g.
dizziness, sweating, headache or confusion), typical of strong
analgesics, have been reported with a widely varying incidence.
Respiratory depression, as determined by laboratory measurements of
respiratory functions, does occur with buprenorphine. The extent of such
depression was similar to other opioid drugs administered in usual
clinical doses.1 However, this was not a problem in clinical studies
7-9
which were usually conducted in fit patients. The effect of
buprenorphine on respiration in "poor risk" patients, such as those with
respiratory diseases or congestive heart failure, has not been
determined. However, it appears that buprenorphine would have the same
potential problems as morphine in this patient group.1

11
Dosage and Administration
Buprenorphine is presently available in Europe for parenteral
use.1 The recommended dose is 0.3 to 0.6 mg by IM or slow IV injection,
repeated every 6-8 h as needed. Administration of buprenorphine to
patients already receiving large doses of narcotic drugs should be
undertaken with caution until the response is established, since its
antagonistic activity could conceivably cause withdrawal symptoms.1
Pharmacokinetic Studies
There is limited information available on the pharmacokinetic
properties of buprenorphine in man.1 It was stated without
documentation or citation of references that rapid absorption and peak
plasma concentrations were seen in rats on oral and IM dosings where the
oral dose was 4 times the IM dose.1 It was claimed that in primates and
in human volunteers, peak plasma concentrations were reached more slowly
after oral administration (2 h) than by IM injection (7 min).1 Drug
concentrations were stated to be detectable in blood for longer times
after oral (24 h) than IM (7 h) administration of equivalent doses. In
man buprenorphine was claimed to be excreted unchanged in the feces, and
as glucuronide and N-dealkylated buprenorphine in urine.1 References of
studies supporting these data were not given.1
In a 3 h study, peak plasma buprenorphine concentration did not yet
.33
occur in some patients after sublingual administration. In a
subsequent 10 h study with 15 post-operative patients, 5 patients
received a sublingual dose 0.4 mg of buprenorphine, five 0.8 mg and 5
received placebo at 3 h after a 0.3 mg IV dose of buprenorphine. The
plasma buprenorphine concentration was measured by a specific
34
radioimmunoassay. The plasma concentration reached a peak level in an

12
average time of about 200 min in both the 0.4 mg and 0.8 mg groups
34
(range 90-360 min after the initial 3 h period). The plasma drug
concentration in the 0.8 mg group were approximately twice that in the
0.4 mg group. The absolute bioavailability was estimated to be about 55%
of the IV route for both groups by the ratio of the area under the
plasma concentration versus time (AUC) for sublingual and TV
administration. Uptake of buprenorphine from the sublingual site was
34
claimed to be complete by 5 h after the dose was given. In this
study, cross-reactivity between buprenorphine and its metabolites was
not ruled out. Two modes of administration (TV followed by subcutaneous)
were carried out in each study which complicated the pharmacokinetic
analysis.
Buprenorphine kinetics were studied in surgical patients using
35
radioimmunoassay. Buprenorphine was measured in the plasma of 21
patients who received 0.3 mg IV. After 3 h, ten of these patients
received further dose of 0.3 mg TV, and 11 patients were given 0.3 mg
IM. Plasma drug concentrations were measured up to 3 h after the second
dosing. Comparison of the pharmacokinetics in the same patient, awake
and anesthetized by general anesthesia, showed that the clearance was
significantly lower (900 ml/min) in the anesthetized state compared to
the unanesthetized state (1225 ml/min). Bioavailability was claimed to
be the same for both TV and IM administered drug. The peak plasma levels
were seen at 2-5 min and in 10 min respectively for IV and IM dosing
35
after the second dosing. Cross reactivity among buprenorphine and its
metabolites was not ruled out in this study. The sensitivity and limits
of detection for buprenorphine were not given. Thus the terminal plasma
buprenorphine concentrations at less than 1 ng/ml are questionable.

13
Procedures for obtaining various pharmacokinetic parameters were not
given.
Plasma concentrations were correlated with clinical effects after a
single IV dose of buprenorphine (0.3 or 0.6 mg) in patients recovering
36
from surgery. Analgesia was greater at the high dose without any
apparent parallel increase in respiratory depression. Better analgesia
was reported if the first required post-operative dose of 0.3 mg has
been preceded by a similar loading dose or by the use of a larger dose
36
during surgery. This study was largely descriptive without rigorous
pharmacokinetic analysis. The plasma concentrations obtained from a
number of patients were averaged to obtain a mean concentration. This is
not a valid pharmacokinetic technique.
Metabolism and Excretion
Higher amounts of polar metabolites were seen in plasma after oral
administration than after IM in rats.'*' The premise of drug conjugation
37 38
in the gut wall was supported by studies with rat gut preparations. '
Buprenorphine has been found conjugated or N-dealkylated in bile or
tissues of animals, but unchanged in the brain. This is possibly
indicative of the fact that buprenorphine and not a derivative is
responsible for the narcotic activity.1
In a study of pharmacokinetics of buprenorphine after IM
administration to rats, dogs, rhesus monkeys and one human volunteer,
most of the dosed radioactive drug was excreted in the feces, indicating
39
biliary excretion with possible enterohepatic recirculation. After IV
administration of the tritiated buprenorphine (100 p g/kg) to the bile
duct cannulated rats, over 90% of the administered drug was excreted in
the bile within 48 h after dosing. The major metabolite in the bile was

14
buprenorphine glucuronide. N-dealkylated buprenorphine was also present.
Intraduodenal infusion of rats with bile obtained from other rats dosed
with radiolabelled drug produced a slow but extensive excretion drug
. . 39
related metabolites in the bile of the recipient animal. The plasma
concentrations were not measured in this study. The assay techniques
were not specific for the parent drug or its metabolites. Dose
dependency was not studied.
40 .
In a chronically cannulated cow, it was shown that the hepatic
extraction ratio for IV boluses of morphine, diamorphine, fentanyl,
methadone and buprenorphine increased towards a plateau value as the
portal vein drug concentration increased. The extraction ratio was
claimed to be independent of hepatic blood flow, but dependent on
concentration.
Disposition of radiolabelled buprenorphine in the rat after a
single 0.2 mg/kg IV bolus dose and continuous administration via a
41 ...
subcutaneous delivery system were carried out. After IV injection,
tri-exponential decay of the drug from brain was seen with half-lives of
0.6, 2.3 and 7.2 h, respectively. Plasma half-lives were 0.5 and 1.4 h
(the third phase was not estimated). Decay half-life of the drug from
its high affinity binding sites in brain were 1.1 and 68.7 h
respectively. Fat and lung had higher concentrations than other tissues
41
or plasma. No metbolites of the drug were detected in brain.
Unmetabolized drug excreted in the urine and feces one week after TV
injection were 1.9 and 22.4% of the dose, respectively, and 92% of the
dose was accounted for in 1 week. Urinary metabolites (%) were
conjugated buprenorphine 0.9; norbuprenorphine (free 9.4, conjugated

15
5.2); tentative 6-0-desmethyl norbuprenorphine (free 5.4, conjugated
15.9).41
Peak plasma concentration of buprenorphine occured in 4 weeks after
s.c. implantation of a long-acting radiolabelled buprenorphine (10 mg)
pellet. The apparent dissociation half-lives of the drug from the lcw-
and high-affinity binding sites in the brain were 4.6 and 6.8 weeks,
respectively. Fat, spleen and skeletal muscle had higher radioactivity
41
than other tissues and plasma. These authors state that high-affinity
binding of buprenorphine in brain and subsequent slow dissociation are
the factors responsible for its prolonged agonist and antagonist effects
and higher potency than other narcotic agonists.
Absorption and bioavailability. There are no published studies on
the oral absorption of this drug in man. It was claimed on the basis of
unpublished data that the peak plasma concentration of orally
administered radiolabelled buprenorphine in the rat was reached in 10
min with another peak in plasma appearing in about 5-8 h.1 This delayed
peak could be due to the late appearance of radiolabelled metabolites
(e.g., N-dealkylated buprenorphine and conjugates) in plasma.''' An
intramuscular dose of 20 y g/kg gave blood peak concentration similar to
that of a 100 yg/kg oral dose. In monkeys, unpublished data were cited
to support the statements that peak blood concentrations of
radiolabelled drug were reached at 2 min, 2 h and between 2-4 h
respectively for IM, oral and sublingual administration.'1' Also, it was
stated that in two healthy volunteers, peak blood concentrations were
reached rapidly after IM dosing (2 yg/kg) of radiolabelled
buprenorphine followed by a rapid decline. Peak concentrations were
reached slowly at 2 h after the oral administration of 15 yg/kg of the

16
drug, followed by a biexponential decline of concentration.
Concentrations as low as 0.5 to 3.5 ng/ml were claimed to be detected by
a specific radioimmunoassay technique after IV and IM administrations
1
(0.3 mg). In human volunteers a dose of 0.4 mg produced peak
concentrations of 1-2 ng/ml at about 2 h after oral administration.
References of studies supporting these data were not cited.1
Systemic bioavailability of buprenorphine was studied in female
rats following single-doses (200 jag/kg) administered by six different
42
routes. Relative to the 100% bioavailability from the intra-arterial
route, the mean bioavailabilities were, IV 98%, intrarectal 54%,
intrahepatoporta1 49%, sublingual 13% and intraduodenal 9.7%. AUC
analysis of buprenorphine concentrations in blood showed the relative
fractions of the drug excreted (first pass) by gut, liver and lung to be
0.8, 0.5 and 0.02 respectively. In vitro absorption studies showed that
poor bioavailability of intraduodenally administered buprenorphine was
not due to slow or incomplete absorption, but due to first-pass
42
metabolism. In this study, the authors computed AUC only up to 4 h
for the plasma data. The data showed two compartment model type
disposition for the drug in plasma. AUC would be different if calculated
up to time infinity.
In the above pharmacokinetic studies, low doses and subsequent low
terminal plasma concentrations have essentially limited the estimates of
terminal rate constants and half-lives of elimination. Sensitive and
selective assay techniques for buprenorphine and its metabolites in
biological fluids, and administration of large doses to a higher animal
such as dog could give acceptable pharmacokinetic parameters.

17
Protein binding. It was reported without documentation'1' that
buprenorphine was highly bound (96%) to alpha- and beta-globulin
fractions of human plasma proteins in the concentration range 0-9 ng/ml.
The fraction of drug bound to dog plasma protein was determined by
measuring the drug concentration in plasma water after
43
ultracentrifugation. The fraction bound was estimated to be 0.945.
Binding of buprenorphine to dog plasma proteins was also determined by
partitioning the drug into red blood cells. The estimation is based upon
the presumption of established equilibria between drug in plasma water,
44
red blood cells and plasma proteins. By this technique, the fraction
43
of buprenorhine bound to plasma proteins was estimated as 0.983. This
relatively high plasma protein binding for the lipophilic buprenorphine
45
contrasts to the 26-36% plasma protein binding of morphine, naloxone,
and naltrexone.46
RBC Partition. Partition studies have shown that red blood
43
cell-plasma water partition coefficient of buprenorphine was 6-11.
45
This is in contrast to 1.11 for morphine, 1.83 for naltrexone, and
1.49 for naloxone.46
Physical properties. Fluorescence (excitation 285 nm, emission 350
nm) of buprenorphine provided excellent detection for HPLC assay in
43
biological fluids with a 5 ng/ml sensitivity. Buprenorphine
solvolysis was specific-acid and specific-base catalysed. It yielded a
stoichiometric final acid degradation product (3), a fluorescent
detectable, rearranged demethoxy analogue of buprenorphine. Alkaline
43
hydrolysis produced no fluorescence products. Acid hydrolysis also
produced a fluorescent-detectable, transient dehydro intermediate (2)
that was also completely transformed into the demethoxy analogue (Scheme

18
Methyl migration
^ch2 -<]
¿
' f
/CHj -<]
/
¿
Scheme I
Acid Hydrolysis of Buprenorphine

19
I). Compound 2 was an excellent bioassay internal standard. Buprenorhine
was shown to be highly stable at neutral pH values, even at elevated
43
temperatures. Estimated buprenorphine pKa1 values were 8.24 and 10
for the ammonium and phenolic groups respectively. The intrinsic aqueous
43
solubility of buprenorhine was 12.7 +_ 1.2 ;ug/ml at 23C.
Assay methods. Few assay methods of buprenorhine in biological
47
fluids have been reported in the literature. A radioimmunoassay has
been used to determine plasma levels of parenterally administered
34 35
buprenorphine in dogs and humans. ' A selective ion monitoring
method (SIM) of the silylated buprenorphine in GC-MS has been used to
determine the plasma levels of buprenorphine over a 20-3000 ng/ml
48
concentration range. A GC assay with flame-ionization detection of
silyl derivatives of buprenorhine was used in stability studies at 5-10
49
;ig/ml of aqueous solutions. An HPLC assay with fluorescence detection
43
of buprenorhine in biological fluids has been reported and its
modification and improvement is presented in this dissertation.

EXPERIMENTAL
Materials. Analytical grade solvents and reagents were used.
Buprenorphine hydrochloride, 21-cyclopropy1-7-alpha-[(s)-1-hydroxy-1, 2,
2-trimethylpropyl]-6,14 endo ethanotetrahydro-oripavine, 1, (National
48
Institute for Drug Abuse, Rockville, MD) and the demethoxy analog, 3,
49
of buprenorphine (Addiction Research Center, Lexington, KY) were used
as received. A standard sample of 21-cyclopropyl-7-alpha-[2-(3,
3-dimethyl-l-butenyl)] 6,14 endo ethanotetrahydro-oripavine, 2, was
obtained from Dr.G. Lloyd Jones of Rickett & Colman, Pharmaceutical
Division, Kingston-upon-Hull, England.
Apparatus. An HPLC (model M6000A pump, Waters Associates, Milford,
MA), equipped with a variable-wavelength fluorescence detector (model
600S Fluorescence Detector, Perkin-Elmer, Norwalk, CT), was used.
Injections were carried out with an auto sampler (WISP Autosampler,
Waters Associates), and the data were analysed by a microcomputer (Sigma
15, Data Station, Perkin Elmer). A separate HPLC pump (series 3B, Perkin
Elmer) equipped with a variable wavelength UV detector (model LC 75,
Perkin Elmer) was used in some studies. A laboratory centrifuge was used
in the separation of organic extract from biological fluids (Lab
Centrifuge, International Centrifuge Equipment Co., Needham Heights,
MA).50
Liquid Chromatographic Procedures. Aliquots (50-100 yL) of the
solutions to be analyzed were injected into the HPLC system equipped
with a packed [packing material was C^g 5- ym Bondapak-reversed phase
20

21
(ODS-Hypersil), Shannon Southern Products Ltd., Cheshire, U.K.] 120 mm
i.d. stainless steel column [Knauer HPLC analytical column (unpacked),
Knauer A.G. Berlin, F.R.G.] which was maintained at 40 C. The usual
mobile phase flow rate was 1.5 mL/min of a 40:60 acetonitrile:acetate
buffer (pH 3.75, 0.05M) containing 0.0004M tetrabutylammonium phosphate.
Fluorescence was effected at 285 nm excitation (slit 20 nm) and 350 nm
43
emission (slit 15 mm) and was used unless stated otherwise.
Calibration Curves in Biological Fluids
Buprenorphine. Aliquots (1 mL) of plasma, urine or bile in each of
ten 15—mL centrifuge tubes were spiked with 100 pL of 100-1000 ng/mL of
buprenorphine (1). Each solution contained 50 ng/mL of the acid
degradation intermediate of buprenorphine, compound 2, as the internal
standard. The final sample contained no drug. Sodium borate-boric acid
buffer (1 mL at pH 9.1, 1 M) and 4.2 mL of benzene were added to each
tube. The tubes were shaken for 20 min, centrifuged at 3000 rpm for 10
min, and 4 mL of each benzene extract was transferred to another set of
ten 15—miL centrifuge tubes. Hydrochloric acid (1 iríL, 1 M) was added to
each tube and the tubes were shaken for 10 min and then centrifuged at
3000 rpm for 10 min. After removal of benzene layer by aspiration, 1 mL
of both 1 M NaOH and pH 9.1 borate buffer (1 M) were added to each of
the remaining aqueous phases. The pH values were confirmed or adjusted
to be between 9.05 to 9.15. Benzene (4.5 mL) was added to each tube
which was shaken for 10 min and centrifuged at 3000 rpm for 10 min. The
benzene extract (4.00 mL) was transferred to a 5—miL vial (Reacti-vial,
Supelco, Inc. Bellefonte, Pa.) and the benzene was evaporated under a
stream of nitrogen at 55‘C. Sodium acetate-acetic acid buffer (pH 3.75,
0.05 M, 100 yL) was added to each of the Reacti-Vials and they were

22
vortexed for 30 s, and then 75 y L of the solution was analyzed by HPLC.
Buprenorphine conjugates. Aliquots (1 mL) of plamsa, urine or bile
in each of ten 15-mL centrifuge tubes were spiked with 100 y L of
100-1000 ng/mL of buprenorphine. The first sample contained no drug. To
each centrifuge tube, 1 mL of 6 N HC1 was added, and autoclaved at 15
lbs/sq.in pressure for 10 min. The tubes were allowed to equilibrate to
room temperature. To each tube containing the acid-transformed demethoxy
buprenorphine, 50 y L of unconverted buprenorphine (1 y g/mL) was added
as internal standard. Excess acid was neutralized with soduim carbonate.
The pH was adjusted to 9.1 with sodium borate-boric acid buffer (1 mL, 1
M) and 4.2 mL of benzene was added to each tube. The tubes were shaken
for 20 min, centrifuged at 3000 rpm for 10 min, and 4 mL of each benzene
extract was transferred to fresh 15-mL centrifuge tubes. Hydrochloric
acid (1 mL, 1 M) was added to each tube and the tubes were shaken for 10
min and centrifuged at 3000 rpm for 10 min. After removal of the benzene
by aspiration, 1 rriL of both 1.00 M NaOH and pH 9.1 borate buffer (1.00
M) were added to each reamining aqueous phases. The pH values were
confirmed or adjusted to be between 9.05 to 9.15. Benzene (4.5 mL) was
added to each tube which was shaken for 10 min and centrifuged for 10
min at 3000 rpm. The benzene extract, (4.00 mL) was transferred to a 5
rriL vial (Reacti-Vial) and the benzene was evaporated under a stream of
nitrogen at 55'C. Sodium acetate-acetic acid buffer (100 y L, pH 3.75,
0.05 M) was added to each vial (Reacti-Vial), vortexed for 30 s, and 75
yL of the solution was analyzed by HPLC.
Pharmacokinetic studies in dogs. Healthy mongrel male dogs (8) were
used for the pharmacokinetic investigations. Their blood analysis showed
no pathogenic abnormality or presence of microfilaria. The dogs were

23
fasted for at least 17-24 h before each study and were given water ad
libitum. The animals were supported by a dog sling in a frame placed on
a laboratory table. The dogs were infused with intravenous saline (35
drops per min) for at least 3 h until drug adminstration, when the
intravenous drip was reduced to 20 drops per min. The animals were
catheterized 3 h before the study with a 30.5-cm standard catheter
(Intracath, 16 GA size, Deseret Medical Inc., Sandy, Utah) in the
jugular vein after local anesthesia with mepivacaine hydrochloride
(Carbocaine hydrochloride; Winthrop Laboratories, New York, NY). Second
catheter was also implanted in a foreleg vein (vena brachialis) in most
IV infusion studies. The drug was injected directly into the jugular
catheter, followed by flushing of the catheter with 25 mL of normal
saline. The catheter was connected via a three-way stopcock (Pharmacea,
Toa Alta, PR) to the saline infusion bottle (McGaw Laboratories, Irvine,
CA). Blood samples (1-6 mL) were collected in heparinized Vacutainer
tubes (Becton Dickinson Vacutainers, Rutherford, NJ) after the dead
volume of the catheter was filled with 5 mL of blood by aspiration with
an extra syringe. These aspirations were carefully aseptically
reinjected into the jugular vein. The heparinized blood samples were
immediately centrifuged at 3000 rpm for 10 min. The plasmas were removed
with sterile glass pipets and were frozen until analysed.
Urine was collected from the dogs through a urinary catheter
(Polyurethane whistle tip units, 6 FR size, McGaw Laboratories) at
intervals of 15-60 min for up to 24 h and at longer intervals for up to
1 week. Withdrawal times, volumes and urinary pH values were recorded
and portions of each sample were frozen until analyzed.
Infusion studies were carried out using Harvard Infusion pump

24
(Harvard Apparatus Co., Dover, MA). Buprenorphine-HC1 was dissolved in
normal saline (150 mL, concentration^.73-78 mg/mL), ultrasónicated for
30 min and infused into the jugular vein at the rate of 0.7026 mL/min
for 162-175 min (studies 7-11). During infusion, blood samples were
collected from the brachialis vein. Post-infusion blood samples were
collected from both jugular and brachialis veins. In dog study 12, the
drug solution was infused into the brachialis vein (using the same drug
concentration and flow rate as above).
Dogs E, F and G underwent surgery.^ A 2% solution of thymalol
sodium was administered IV (6 mL/kg) to each dog and anesthesia was
maintained by halothane. After removal of the gallbladder, a screw-cap
was placed on the opposite side of the sphincter of Oddi and the
intestine was sewn to the abdominal wall (Fig 1). At least 1 month was
allowed for recovery from the surgery before the pharmacokinetic study
of buprenorphine in the bile-cannulated dogs. These dogs could be
repetitively used for bile cannulation studies by opening the screw-cap
and inserting a catheter (Fast Right Heart Cardiovascular catheter, 5 F
size, C.R. Bard Inc., Billerica, MA) into the bile duct. The balloon at
the tip of the above catheter was inflated with 0.8-1.0 mL of air,
pulled back until the catheter was securely positioned at the inside
wall of the spincter of Oddi. Complete bile collection was effected in
such studies at intervals of 15-120 min for up to 26 h.
Isolation of buprenorphine conjugate from bile. Two liquid
chromatographic glass columns (40 X 2.5 cm) were packed with nonionic
Amberlite XAD-4 beads (Sigma Chemical Co., St. Louis, Mo.) by passing a
slurry of the packing material in distilled water through the column.
The perforated disk at the bottom end of the column retained the

Figure 1. Schematic of the performed surgery. After gallbladder removal, screwcap
was placed on the opposite side of the sphincter of Oddi and the intestine was
sewn to the abdominal wall. During the bile cannulation, the screwcap was replaced
by a sealed perforated rubber stopper through which a bile catheter was positioned
into the bile duct. At the end of the study, the catheter was removed and the
screwcap was replaced (See also reference 51).

gall bladder-^
(removed) f-
duodenum
abdominal
wall

27
Amber lite beads. Each column was washed with 500 mL of water followed by
250 mL of methanol. The columns were closed at the bottom and soaked
with distilled water overnight. Pooled bile samples (150 mL) collected
from dog studies 9 and 10 were diluted to 500 mL with distilled water.
Aliquots (250 mL) were passed through each column and washed with 300 mL
of water until the eluent was colorless. Then, 300 mL of methanol was
passed through each column. These methanolic eluates were combined and
completely evaporated to dryness under reduced pressure. The residue was
dissolved in sterile normal saline (120 mL) and the solution was
filtered through a 0.22 pm Millipore filter aided under reduced
pressure and strictly aseptic conditions. The final sterile solution was
infused into dog F (Study #13) at the rate of 14 mL/min for 8.5 min. The
pooled bile samples collected from dog study #11 were similarly except
that chromatographic separation was achieved with only one Amberlite
XAD-4 column. The final sterile solution was infused into dog G (Study
#14) at the rate of 14 ml/min for 7 min.
Analysis of the conjugate by enzymatic hydrolysis. The enzyme
8-glucuronidase ( 8-glucuronide glucuronosohydrolase, 0.76 mg = 660,000
Fishman Units, Lot. #51F-9013, Sigma Chemical Co.) was dissolved (50 mg)
in 20 mL acetate buffer (pH 3.8, 0.05 M). Aliquots (500 pL) of the
enzyme preparation and the internal standard (100 pL of compound 2 , 1
ptg/mL) were added to 500 y L of diluted bile sample (1:10,000 dilution
made with distilled water) and the total volume was adjusted to 1.6 mL
with pH 3.8 acetate buffer. The samples were incubated at 37'C for 24 h.
Diluted bile (1:10,000 dilution) samples containing no drug were spiked
with buprenorphine and treated in the same manner to establish an
appropriate calibration curve. The generated aglycone buprenorphine was

28
assayed by HPLC separation and fluorimetric detection.
Catheter binding of buprenorphine. Buprenorphine-HCl was dissolved
in normal saline (150 mL, concentration = 0.7576 mg/mL of base). The
solution was passed through the plastic catheter (Intracath) without
back pressure at the rate of 0.7026 mL/min for 1 h (1 study) and 3 h (2
studies). The internal surface of the catheter was washed with 25 mL of
normal saline and dried under a stream of air. Then benzene (250 ml) was
pumped through the plastic catheter (Intracath) at the rate of 14
ml/min, evaporated in a collecting flask at 70*C under reduced pressure.
The residue was reconstituted in acetate buffer (pH 3.75, 0.05 M) and
aliquots were assayed by HPLC separation and fluorimetric detection.
Buprenorphine-HCl was dissolved in normal saline (0.7567 mg/mL of
base) and passed through the plastic catheter (Intracath) at the rate of
0.7026 mL/min for 3 h. The interior surface of the catheter was washed
with 25 ni/ of normal saline. The saline was allowed to flow from an
infusion bag under the gravitational force at the rate of 45 drops/min
for 2 h and was collected (300 mL). The pH was adjusted to 9.1 and the
saline solution was extracted twice with 250 mL portions of benzene. The
combined benzene layer was evaporated under reduced pressure at 70‘C.
The residue was reconsituted in acetate buffer (pH 3.75, 0.05 M) and
aliquots were assayed by HPLC separation and fluorimetric detection.
Buprenorphine (0.7567 mg/nL) in normal saline was passed through
the plastic catheter (Intracath) for 1 h at the flow rate of 0.7026
mL/min. At the end of 1 h, the catheter was washed with 25 mL of normal
saline, and saline drip (45 drops/min) was continued. Fresh blank dog
blood (1-3 mL) was drawn through the catheter at 1, 2, 5, 10, 15, 20,
30, 45, 60, 120 min. The blood samples were centrifuged at 3000 rpm for

29
10 min and the supernatent plasma was analysed for buprenorphine by HPLC
separation and fluorimetric detection. The experiment was repeated
following the pumping of buprenorphine solution (using the same
concentration and flow rate as above) through the catheter for 3 h.
In-vivo study. In dog study #12, buprenorphine was infused (0.5236
mg/min for 177 min) into the left brachialis vein through the indwelling
plastic catheter (Intracath). Blood samples during infusion were
collected from the jugular vein and the contralateral brachialis vein.
Upon cessation of infusion, the catheter through which the drug was
infused into the left brachialis vein was washed with 25 mL of normal
saline. Post-infusion blood samples were collected from the left
brachialis vein (site of infusion) through the plastic catheter, as well
as from the jugular and contralateral brachialis veins.

IV BOLUS STUDIES
Chromatographic assays of Buprenorphine and its conjugate. The HPLC
43
assay methods developed for buprenorphine have been published.
Chromatograms of the HPLC-assayed buprenorphine are given in Fig. 2. The
acid hydrolyzable conjugate (M) assay (Fig. 3) by fluorimetric detection
(285 nm excitation, slit width 15 nm and 350 nm emission, slit width 10
nm) was equally sensitive, Table 1 shows the relevant statistics of
calibration curves. The standard errors of estimates of the
concentration about its regression on peak height ratio ranged iron +
0.5 to +_ 3 ng/ml.
Some additional linear regressions of concentrations (C, ng/ml) of
buprenorphine in plasma with their standard errors of the parameter
estimates in accordance with
C +_ SER = ( m + sm ) PHR + b + s^ Eq. 1
in the range 5-50 ng/ml were, C _+ 1.52 ng/ml = (61.19 _+ 1.84) PHR - 1.11
+ 0.808, r = 0.9968; C + 1.52 ng/ml = (76.64 + 2.518) PHR - 3.04 +
1.068, r = 0.9962; C + 1.3 ng/ml = (54.34 + 2.6) PHR - 5.01 + 1.42, r =
0.9943; C + 0.38 ng/ml = (72.21 + 1.8) PHR - 12.3 + 0.98, r = 0.9991. In
the buprenorphine concentration range of 50-100 ng/ml, C +_ 0.97 ng/ml =
(75.49 + 1.76) PHR - 13.45 + 2.1, r = 0.999; C + 2.42 ng/ml = (75.48 +
2.43) PHR - 21.6 + 2.71, r = 0.9959; C + 1.78 ng/ml = (67.96 + 2.9) PHR
+ 6.02 + 3.026, r = 0.9964; C + 0.64 ng/ml = (27.94 + 0.4) PHR + 17.1 +
0.85, r = 0.9995.
30

31
Figure 2. Representative chromatograins after assay of buprenorphine (1,
60 ng/ml) with internal standard (2, 100 ng/ml) from plasma (a) and
urine (b). (The blank plasma and urine chromatograms without drug are
given underneath). Chromatogram of mixture of 25 ,-yg/ml of
buprenorphine, 1, with its products 2 and 3 after acid degradation in 1
M HC1 for 3 min (c). (See also reference 43).

Figure 3. Representative chromatograms after HPLC separation followed by
fluorimetric detection of buprenorphine conjugate in plasma, urine and bile. Blank
chromatograms of biological fluids without the drug and the internal standard are
given underneath. In the chromatograms (a, b, and c) peak 3 corresponds to the
demethoxy analog of buprenorphine obtained after acid hydrolysis of buprenorphine
conjugate M. Buprenorphine conjugate produces the aglycone on acid hydrolysis
which further quantitatively rearranges into demethoxy analog (peak 3; See also
reference 43). The HPLC retention time for compound (peak) 3 is different from
buprenorphine. (See figure lc). Thus buprenorphine (peak 1) could be used as
internal standard for the conjugate assay, a) Demethoxy analog (3, 90 ng/ml) of
buprenorphine conjugate and internal standard (1, 100 ng/ml) from plasma obtained
after acid hydrolysis of plasma followed by HPLC separation, b) Demethoxy analog
(3, 80 ng/ml) of buprenorphine conjugate and internal standard (1, 100 ng/ml) from
urine obtained after acid hydrolysis, c) Demethoxy analog (3, 60 ng/ml) of
buprenorphine conjugate and internal standard (1, 100 ng/ml) from bile obtained
after acid hydrolysis and HPLC separation. In obtaining chromatograms a, b and c,
the mobile phase was 25:75 acetonitrile:acetate buffer (pH 3.75, 0.05M) plus
0.0004M tetrabutyl ammonium phosphate; flow rate 1.2 ml/min. All other
chromatographic conditions were the same as described under the subheading 'Liquid
Chromatographic procedures' in experimental section.

a
b
min
UJ
Lb
«M
il
i—•—i—i—*—•—i—i—i—r
0 2 4 6 0
min
10

Table 1 - Typical statistics of plasma, and urine calibration curves for Buprenorphine (1) and
conjugate (M)
Biological
Fluid
Range
ng/ml
a
sy,x
b
m
c
s
m
bd
(D
i
f
n
r9
Plasma (1)
20-100
1.38
58.96
1.19
-18.18
2.69
7
0.999
20-90
2.83
49.13
2.16
1.21
2.57
8
0.994
20-70
0.83
74.48
1.22
-5.9
0.84
5
0.999
Urine (1)
20-90
1.71
53.65
1.56
-4.10
1.74
7
0.998
20-90
2.07
52.05
1.88
-1.80
2.21
5
0.998
30-100
1.84
63.51
1.19
6.21
1.92
7
0.998
Plasma (M)
5-50
0.65
82.07
1.78
2.94
0.5
6
0.999
50-100
1.36
54.57
1.55
15.0
1.71
6
0.998
10-100
2.7
58.65
1.50
1.54
1.38
13
0.996
Urine (M)
10-80
1.98
117.2
3.3
-2.2
1.3
9
0.997
10-40
1.51
62.37
3.5
-10.8
2.00
7
0.992
40-100
2.73
91.29
4.73
-32.61
5.42
7
0.993
a Standard error of estimate about regression of concentration (ng/ml) on peak height ratio,
k Slope. c Standard error of slope. d Intercept. e Standard error of intecept. ^ Number of
points. ^ Correlation coefficient. In buprenorphine calibration curves, demethoxy analog of
buprenorphine (compound 2, Scheme I) was used as internal standard. Buprenorphine was used as
internal standard in the assay of conjugate (M). Some additional calibration curve statistics
are given in the text.

35
In urine, examples of regression equations for buprenorphine in the
range 5-100 ng/ml were, C _+ 1.59 ng/ml = (68.9 +_ 1.11) PHR - 13.93 +_
1.12, r = 0.9991; C + 0.89 ng/ml = (113 + 1.89) PHR - 6.8 + 0.851, r =
0.9993; C + 2.02 ng/ml = (66.5 + 1.26) PHR - 7.31 + 1.17, r = 0.9977.
Examples of regression equations for buprenorphine conjugate (M) in
plasma in the range 10-50 ng/ml were, C + 2 ng/ml = (57.02 _+ 2.13) PHR +
4.9 _+ 1.211, r = 0.9958; range 60-100 ng/ml; C +_ 1.12 ng/ml = (39.57 _+
1.247) PHR + 22.2 +_ 1.83, r = 0.9985; range 5-100 ng/ml, C +_ 1.4 ng/ml =
(73.8 j+ 0.99) PHR - 2.46 +_ 0.8, r = 0.9991; range 10-90 ng/ml; C +_ 1.3
ng/ml = (50.14 + 0.8) PHR - 1.51 + 0.92, r = 0.9991.
Examples of regression equations for buprenorphine conjugate (M) in
urine in the range 10-200 ng/ml were, C +_ 1.8 ng/ml = (82 _+ 0.621) PHR +
0.72 +_ 0.82, r = 0.9997; range 10-120 ng/ml, C + 2.6 ng/ml = (92.99 +_
2.4) PHR - 27 + 2.5, r = 0.998; C + 1.81 ng/ml = (162 + 2.9) PAR - 13.19
+_ 1.5, r = 0.9991, where PAR = peak area ratio; range 10-100 ng/ml, C +_
2 ng/ml = (66.5 _+ 1.26) PHR - 7.31 +_ 1.17, r = 0.9977. An example of
regression equation for buprenorphine conjugate (M) in bile in the range
10-200 ng/ml was: C +_ 6 ng/ml = (102 2.7) PHR - 0.53 +_ 2.63, r =
0.9956.
Twice the standard error of estimate of buprenorphine and the
metabolite concentrations (ng/ml) on peak height ratio ranged from 1-5
ng/ml (Table 1), indicative of the sensitivity of the fluorimetric assay
of buprenorphine and its metabolite in biological fluids.
Plasma Pharmacokinetics and Volumes of Distribution. The plasma
concentration-time profile of buprenorphine could be fitted to a sum of
three exponentials (Eq. 2, Figs. 4-9). There may not be an unique linear
sum of three exponentials Cp^ (estimated plasm concentration! that

Figure 4. Semilogarithmic plots of concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.4171 mg/kg dose in 22.85 kg dog A (Study #1, Table 2). In the bottom and middle
figures, the solid line represents the curve obtained by fitting the plasma data
to a sum of three exponentials in accordance with the equation (2):
Cp(ng/ml) = 986.3 e-0'6823 t + 491.5 e~°'02627 t
♦ 39.8 e'0-100076 1
The middle inset is the continuation of the data and fitted curve for an extended
time scale up to 2000 min. The top inset represents the data fitted to a
4-compartment model in accordance with the equation:
Cp (ng/ml) = 1066 e
-0.77
t . joo -0.0304
+ 488 e
t ^ .c . -0.00426
+ 45.4 e
t
L „„ -0.0003434 t
+ 22 e
Refer to the section "Validity of the terminal rate constant" for a discussion of
fitting of the data to 4-comartment model.

CGNC* NG/ML

Figure 5. Samilogarithmic plots of concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.6369 mg/kg dose in 17.6 kg dog B (Study #2, Table 2). The solid line represents
the curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
= 818.1 e
-0.2632 t
435.7 e 0*01731 t
c. -0.000904 t
+ 54.33 e
The inset is a representation of the data and fitted curve for the initial period
of 800 min.

CGNC* NG^ni
m
C3
ro
E
c:
c:
6e
tjnnm

Figure 6. Semi1ogarithmic plots of concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.2023 mg/kg dose 22.5 kg dog C (Study #4, Table 2). The solid line represents the
curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
= 2459 e
-0.1173
+ 259 e °*0145 t + 31.37 e“0-00103
t
The inset is the continuation of data for an extended time scale up to 1500 min.

3RD 5^in 3211 9ÃœD
MIN
CONO. NG/ML
— 1 J ¡ :
— □ CD C3
â–¡ â–¡ cd a
Tfr
lunno

Figure 7. Semilogarithmic plot of the concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
2.5632 mg/kg dose in 19.0 kg dog B (Study #3, Table 2). The solid line represents
the curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
= 3508 e
-0.4295 t
+ 1142 e
-0.0217
t
+ 31.2
-0.000463 t

\]ril¡Z [)\)ZZ IJU91
co
NiW
un 11 uss
^ 1 1 h-
m
UUl
UUÍJI
uuun i
CCNC» NG/ML

Figure 8. Semilogarithmic plots of the concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma against time (min) for the
1.439 mg/kg dose in 24.2 kg dog C (Study #5, Table 2). The solid line represents
the curve obtained by fitting the plasma data to a sum of three exponentials in
accordance with the equation (2):
Cp(ng/ml)
-0.562 t ^ -,10 -0.0114 t ^ .c -0.00093 t
4075 e + 318 e + 45 e
The insets are the continuation of the data and the fitted curve for the extended
time scale up tp 3000 min.

280 *120 SGO nOÜ
CGNC» NG/ML
C3
o
g
£
s*

Figure 9. Semilogarithmic plots of the concentrations (as ng/ml of base) of
intravenously administered buprenorphine (1) in plasma ( O > Fluorescence
detection; Q , Electrochemical detection) against time (min) for the 0.7766 mg/kg
dose in dog D (Study #6, Table 2). The solid line represents the curve obtained by
fitting the plasma data to a sum of three exponentials in accordance with the
equation (2):
Cp (ng/ml) = 2519 e
-0.2473
t A -0.012 t ^ OD , -0.00158 t
+ 204 e + 38.6 e
The middle inset is the representation of the data and the fitted curve for the
initial 200 min. The top inset is the plot of the weighted residuals calculated in
accordance with the equation (3) against log fitted concentrations. See fig. 10
for details on the residual plots.

.yi-r
'I [ID 6DD 8[][]
2ÃœD
MIN
I â–¡â–¡â–¡

48
best fits the actual data Cp ; instead there may be several
exp
solutions with similar minimum sum of squares. A unique solution can be
obtained only if the drug transferred into other compartments or
transformed into metabolites were analysed in their respective
52 ...
compartments. The plasma data of buprenorphine administered
intravenously to 6 dogs were fitted by nonlinear regression to a sum of
three exponentials (In study #1, Dog A, the data were also fitted to a
53
4-compartment model; Fig. 4, top inset). The fitting was effected
54
with the computer program of Yamaoka et al. (See also appendix I),
where 1/Cp, the inverse of the plasma concentration was the weighting
factor (See appendix II for a discussion of different weighting
techniques). The validity of the triexponential equation,
QPcaic = P e“1T + A e~a t + B e" 31 Eq. 2
was confirmed by demonstration that regressions of the various studies
of the weighted residuals
€ ( ^exp ^calc ) / ^calc
Eq. 3
against log Cpca^c gave mean residuals £ , slopes and intercepts,
55
which were not significantly different from zero (Fig. 10, Table 2).
The residuals were randomly distributed above and below the regression
line, indicating no bias in the fitting of the chosen model. (Fig. 10)
Outliers were defined as those experimental concentrations which had
residual values, 6, greater than 2 (Eq. 3) which corresponds to a
greater than 200% deviation from the presumed best fitted value. One
such outlier in dog B at 2.5632 mg/kg (Study #3) dose of buprenorphine
was not included in the nonlinear least square curve fitting technique

Figure 10. Representative examples of the plots of the weighted residuals against
log Cpcalc values. These weighted residuals were obtained from the equation (3):
6 ( ^exp “ ^calc ] 1 ^calc
The calculated plasma values were obtained from the triexponential equation 2
fitted to the plasma data of buprenorphine: a) 1.4171 mg/kg dose study in dog A,
Study #1; b) 1.6369 mg/kg dose study in dog B, Study #2; c) the plasma metabolite
(M) residuals obtained after IV administration of buprenorphine for the 1.2023
mg/kg dose study in dog C, Study #4; d) the plasma metabolite residuals obtained
after IV administration of buprenorphine for the 1.439 mg/kg dose study in dog C,
Study #5.
The observed means, slopes and intercepts of these weighted residuals are
given in Table 2. These parameters were not statistically significantly different
from zero as confirmed by t-test. The random distribution of the residuals above
and below the regression line indicated no bias in the fitting of the chosen
model. The validity of the triexponential curve fitting to the plasma data of the
metabolite is discussed in the text.

¡JESIDUALS RESIDIA
RESIDUALS RESIDUALS

Table 2. Pharmacokinetics of intravenously administered bolus Buprenorphine (1) in dogs.
Parameter
Dog A
Dog B
Dog B
Dog C
Dog C
Dog D
Mean 1 SEM
Study No.
1
2
3
4
5
6
Dog No.
B364
B344
B344
W444
W444
W4123
Dosed , mg
32.38
28.81
48.7
27.051
34.824
20.502
Weight, Kg.
22.85
17.6
19.0
22.5
24.2
26.4
Dose mg/kg
1.4171
1.6369
2.5632
1.2023
1.4390
0.7766
Parameters from plasma data
for 1
lO^Pf b
0.3046
0.2835
0.7204
0.9089
1.1700
1.2290
0.77 1 0.17
10 Af
1.5179
1.5123
2.345
0.959
0.9132
0.9972
1.37 1 0.22
106 Bf
1.2292
1.886
0.6402
1.16
1.2922
1.8827
1.35 1 0.19
10 TT C
6.823
2.362
4.295
1.173
5.616
2.473
3.79 1 0.88
9
(1.02)
(2.93)
(1.614)
(5.91)
(1.23)
(2.8)
(2.58 1 0.74)
10¿ a
2.627
1.731
2.166
1.45
1.14
1.19
1.72 1 0.24
A
(26.4)
(40)
(32)
(47.8)
(60.8)
(58.2)
(44.2 1 5.7)
104 0
7.565
9.041
4.627
10.3
9.248
15.81
9.43 1 1.51
(916)
(767)
(1498)
(673)
(749)
(440)
(841 1 146)
Residual plots
io2 é d
1.33
1.49
3.6
6.1
2.38
2.88
Slope6 ^
-0.01510.04
0.00510.04
-0.01510.05
0.00410.05
-0.02410.05
0.03110.036
Intercept
0.04110.08
0.00510.09
0.06610.106
0.05310.11
0.07310.1
-0.02510.068
Clearances
Cl 9
tot
470
324
380
391
416
396
396 1 19
Cl- h
ren
2.69(5.1)
5.24(-8.2)
0.053(-1.6)
0.13(1.23)
1.453(-12.6)
1.91 1 0.96
Cl- 1
met
467.3
318.76
379.95
390.87
415.5
394.5 1 24
2.72
2.06
1.27
3.47
2.38 1 0.47
464.6
316.7
378.7
387.4
387 1 30
ciM 1
ren
1.94(11.8)
3.6(-18.5)
0.93(-9.0)
4.4(-30)
0.98(-9.2)
2.36 1 0.7

Table 2. Continued
Parameter Dog A Dog B Dog B Dog C Dog C Dog D Mean 1 SEM
% Recoveries of buprenorphine and M in urine
Uoo'*' /dosem 0.23
0.52
0.065
UooM /dosem 0.66
0.44
0.33
Volumes of
distribution of buprenorphine
(L)
v n
c
21.2
22
10.1
558
326
637
V P
0.705
0.166
0.339
m
Parameters
iron plasma data for conjugate
(M)
104 P b
0.1071
q
105 A
1.0232
0.9295
r
106 Bf
1.043
1.172
0.888
10 tt C
1.91
o
(3.63)
HT a
2.4
1.69
— —
A
(29)
(41)
— —
104 6
2.41
3.44
6.31
(2871)
(2016)
(1098)
Residual plots.
102 é d
2.2
1.32
Slope6 ^
0.000310.07
-0.01310.05
— —
Intercept^
0.02U0.123
0.03810.09
— —
0.09
0.13
0.21 1 0.08
0.79
0.13
0.47 1 0.12
9.84
7.85
7.42
13.1 1 2.73
379
450
251
434 1 59
2.054
0.816 1 0.4
0.6613
0.2087
— —
0.3257 1 0.17
1.3486
0.9620
— —
1.07 1 0.10
1.70
1.344
— —
1.23 1 0.14
6.13
(1.13)
3.66
(19)
22.75
(305)
1.06
(6.5)
0.68
(104)
4.95
(1400)
— —
3.03 1 1.57
(3.76 1 1.56)
2.1 1 0.63
(48 1 19)
4.3 1 0.9
(1846 1 391)r
3.58
-0.0410.05
0.110.09
2.9
0.00710.064
0.014310.144
— —

a
Values correspond to buprenorphine base. Administered as HC1 salt, dissolved in 30 ml normal saline.
kpf' Af and values equal to P, A and B values expressed in fractions
A and B values were obtained from the nonlinear least square fitting of
of dose per ml of plasma. The P,
54
plasma data with 1/Cp weighting.
C —1
Unit for tt , a and 3 values is min . Parenthetical values correspond to
cVfean of the weighted residuals. (6 = (Q?eXp - ^Pcapc ) / Cpca ^ ). None
statistically significantly different from zero.
half-lives in min.
of the mean residuals were
0 f
' These are the slopes and intercepts of plots of 6 against log fitted cPca]c The parenthetical values
correspond to standard errors. Both slope and intercept were also not significantly different from zero,
indicating that the sum of three exponentials best fits the plasma data of buprenorphine and the conjugate.
^Ratio of the dose to the total area under the plasma concentration-time curve of buprenorphine, where the
calculated AUC = (P/^ ) + (A/a ) + (B/ 0 ) and that calculated from the trapezoidal rule (plus the quotient of
the last observed plasma level Cp(n) and 3) viere within 5-7% in all cases except in dog C at 1.439 mg/kg dose
level where the difference was 10%. Unit, ml/min.
^Estimates from the slopes of cumulative amounts of buprenorphine excreted ( zU ugs) renally against the area
under the plasma concentration time curve (AUC ) at that time in accordance with z U = Cl^^ AUC^
These values were calculated from the initial slopes observed (Figs. 26-28), and these ratios changed as pH of
the urine changed (Fig. 26). The values in parenthesis are ^U at AUC=0 from the best linear plots of data as
shown in Figs. 26-28. The plots of Au/At vs Cpt_m^ (plasma concentration at the mid point of urine
collection interval) were highly scattered in most studies (Fig. 37, see also text).
1C1 , was calculated from the difference between total clearance Cl. , and renal clearance, Cl of
met tot ren
buprenorphine.
^Cl^et ~ Clg >M was calculated using equation 35.
k 1 1—>M
Biliary clearance of M was calculated from the knowledge of Clmgt and (Cl—et - C1B ) values.
1 . M
Renal clearance of metabolite, Clrgn was estimated in accordance with equation 30 (Figs. 32-34).

^Percent recoveries of buprenorphine and M in urine obtained from the quotient of the amount recovered in
urine and the total IV bolus dose of buprenorphine.
Volume of distribution of the central compartment (V ) was obtained using equation 10; P, A, and B are the
parameters from the plasma data for buprenorphine.
V, was calculated from Cl, , / r •
d tot p
^Estimated using equation 35.
^Plasma conjugate profile could not be fitted to a sum of 3 exponentials, see Fig. 17. However, the terminal
rate constant was estimated frcm the semilogarithmic plots of the terminal plasma data against time. See also
text.
rOutlier dog C at 1.2023 mg/kg dose was not included in the calculation of average and SEM.
U1
.t.

55
54
(Appendix I). The outlier was included in all other pertinent
pharmacokinetic analyses and plots, such as excretion rate, sigma minus,
and clearance plots. There were no outliers in the other studies.
Since the triexponential equation 1 adequately described the
post-intravenous bolus injection data (Figs. 4-9), a 3-compartment body
model was the simplest pharmacokinetic model for the disposition of
buprenorphine in dogs. The elimination of buprenorphine could occur from
a central compartment (C), reversibly connected with shallow (S) and
53
deep (D) peripheral compartments (scheme II):
The equation which describes the time course of the IV bolus
administered drug in the central compartment Cp as a function of time t
53
as per scheme 2 is given by
cp = (X0/Vc) [ [ (k21 —ir ) (k31 -TT )/(TT - a ) (TT - B) ] e-7r +
[ (k21 - a ) ( a -k31 ) / (-rr — ot ) ( a — 3 ) ] e at +
[(k21 - 3) (k31 -3)/(a-3)(TT-3)]e_et] Eq. 4
where Xq (k21 -ir ) (k31 - ir )/Vc(tt - a) ( tt - 3 ) = P Eq. 5
X0 (k21 - a ) (a -k31 ) /Vc ( tt - a ) ( a -3 ) =A Eq. 6
and
XQ (k21 - 3 ) (k31 — 3 ) /Vc (a —3 ) ( ir — 3 ) = B Eq. 7

56
where X„ = dose, V = volume of distribution of the central
0 c
compartment.
Validity of the terminal rate constant. Proper estimation (Appendix
II) of the terminal rate constant (and half-life) depends upon a)
analytical sensitivity; b) number of terminal plasma concentration
values, the time interval between these values, and the number of
terminal half-lives over which the samples were collected; c) selection
of the compartment model; and d) proper weighting of the data. Upon
acute IV bolus administration of buprenorphine in dogs at the 0.7-2.6
mg/kg doses used, the plasma concentrations of buprenorphine were below
20 ng/ml at 1000 min (See Figs. 4-9). Thus the available analytical
sensitivity of 5 ng/ml did not permit accurate estimation of the
terminal half-life. For example, at the 2.5632 mg/kg (Study #3) IV bolus
dose of buprenorphine in dog C, the estimated terminal rate constant
obtained from a semilogarithmic plot of the terminal phase plasma data
against time (n=12) was 1.7 X 10 4 (half-life = 4040 min) +_ 0.70 X
-4 -1
10 (SE) min Thus the range that would include the 95% confidence
limits for this rate constant would be 1.48 X 10 ^ (half-life = 47000
min) to 3.3 X 10 4 (half-life = 2111 min) min 1 (See Table 3).
The terminal half-life significantly depends upon the number of
compartments assumed. Consider dog A (Study #1). Fitting of the data
weighted by the inverse of the concentration to a 3-compartment model
-4 -1
gave a terminal rate constant of 7.6 X 10 min (half-life = 916
min). When the same data were fitted to a 4-compartment model, the
terminal rate constant estimated by using the computer program (Appendix
I) was 3.78 X 10-4 +0.984 X 10“4 (SE) min”1 (half-life = 1840 min,
n=3; The 95% confidence limits; + smt, where t=12.71; 433 min to time

Table 3. Statistics of the calculated terminal rate constants.
Parameter
Dog A
Dog B
Dog B
Dog C
Dog C
Dog D
Study No.
1
2
3
4
5
6
Dog No.
B364
B344
B344
W444
W444
W4123
a
n
10
10
12
13
10
10
Intercept (ng/ml)b 39.8
54.3
31.2
31.0
45.6
34.3
104 8 min 1 C
5.504
8.36
1.715
9.965
8.77
14.2
tl/2 111111
1259
829
4040
695
791
489
104 s of 8 ^
m
0.526
0.965
0.704
1.76
1.0
1.81
95% Confidence
limits for
the terminal
half-life.e
Upper limit
1615
1129
47000
1136
1074
693
Lower limit
1032
654
2111
501
623
378
95% Confidence
limits for total body clearance
(ml/min)
Lower limit
287
247
22
301
329
334
Upper limit
408
362
313
442
457
446
Number of plasma points.
K Q
' Terminal phase intercepts and rate constants were calculated from the regressions of
the logarithm of plasma concentrations against time.
d Standard errors, s values of the terminal rate constants,g , were calculated from the
m # j a
statistics of the regressions of the logarithm of the terminal plasma concentrations
against time (also see reference 59).
0 f
' 95% confidence intervals for the terminal rate constants were calculated from t-table
at a =0.05 level of significance for (n-2) degrees of freedom (see also reference 59).
Cl. . was estimated using equations 8 and 9.

58
infinity; Fig. 4, top inset). This large range for the confidence limits
is attributable to the estimation of a terminal rate constant from few
(n=3) plasma values. The estimated terminal rate constants from the
semilogarithmic plots of the terminal plasma cocentrations against time,
their respective standard errors, and 95% confidence limits are given in
Table 3.
The terminal half-life estimated for studies 1,2,4,5 and 6 have
relatively less error compared to study 3 (Table 3). Yet, estimation of
the true terminal half-life depends on the number of terminal plasma
values, the time interval between these values and the number of
terminal half-lives over which the samples were collected. The terminal
plasma data in studies 1,2,4,5, and 6 were not representative of the
true terminal phase since the plasma data needed to accurately estimate
the terminal half-life were below the analytical sensitivity and were
not available.
Total body clearance. The total body clearance Cl^t of a dose,
53
XQ, can be calculated from
Cl
tot
- VAUCoo
Eq. 8
where AUC^ = area under the plasma concentration-time curve up to time
infinity. AUCt up to the last observed plasma point, Cp^ can be
calculated by the trapezoidal rule. The area from the last plasma
sampling time to infinity can be estimated from Cpn / 8 where g is the
terminal rate constant. Also, AUC^ can be explicitly calculated by
integrating equation 2 between time 0 to oo, i.e.,
AUC^ = (P/tt ) + (A/a ) + (B/0 )
Eq. 9

59
The parameters of the above equation were obtained by fitting the
buprenorphine plasma data of dogs 1-6 to equation 2 using the computer
54
program of Yamaoka et. al. (Appendix I). The values of the parameters
of equation 9 are given in the legends of Figs. 4-9 or can be calculated
from the normalized values given in Table 2. The calculated percent
contribution of the term B/6 of the terminal area to the total area in
studies 1-6 were 72, 68, 53, 44, 58 and 47 respectively. This
demonstrates the significance of 6 in the estimation of AUC^ and
consequently the total body clearance derived from this value (Equation
8). Thus, uncertainties in the estimates of 6 can lead to uncertainties
in the estimates of AUC and total body clearance. In the IV bolus
oo
studies (#1-6), the contributions of the terms P/ir and A/a were only
about half of the total area under the plasma concentration time curve.
When equation 2 was used to fit the plasma data of buprenorphine
54
(Yamaoka et. al., Appendix I), the P, ir , A, anda parameters were
estimated from the data in high range (50-5000 ng/ml) of plasma
concentrations. These data are held in greater confidence than the
estimates obtained from the low values of the terminal phase. Thus, if
the error in AUC estimation is primarily due to the error in the
oo
estimation of 8 , the 95% confidence limits for AUC and the derived
oo
total body clearance (Equation 8) can be estimated from the terminal
rate constant, 6 , and its standard error.
To estimate the error in AUCqq (Equation 9), the parameters P, it ,
A, anda were obtained by fitting the complete plasma data of
buprenorphine to the tri-exponential equation 2 (using the computer
54
program of Yamaoka et. al. , Appendix I). However, the parameters B
and 6 were obtained from the regressions of the semilogarithmic plots of

60
the terminal phase plasma data against time. The standard error value,
sm, of the terminal slope was multiplied by the t-value (obtained from
t table for a=0.025 level of significance, two tailed for (n-2) degree
of freedom; where n is the number of terminal plasma points). The
resulting g+_ t.sm permitted the estimation of the the upper and lower
95% confidence limits for AUC calculated in accordance with equation
oo
9. The upper and lower limits for the CltQt were derived from the upper
and lower limits of AUC in accordance with equation 8. These calculated
total body clearances and the respective 95% confidence limits are
reported in Table 3 for the 6 TV bolus studies in the dogs.
Volumes of distribution of buprenorphine. The plasma concentration
53
of a drug in the central compartment at time zero is given by
CpQ = P+A+B = XQ / V, Eq. 10
when an IV bolus is administered into a 3-compartment body model. Vc is
the apparent volume of distribution of the central compartment. The
average Vc was 13.1 +_ 2.73 (SEM) L (Table 2). This value exceeds the
56 57
volume of blood (1.8 L) and the extracellular water (4.8-6.6 L) in
dogs. This indicates rapid sequestration of the drug in the
extracellular space upon bolus administration.
If the clearing organ is in the central compartment (Scheme II),
53
then the clearance from the central compartment, Clc, is given by
Cl = V k.n Eq. 11
c c 10 ^
If the drug is solely eliminated from the body through the central
compartment, the Clc is the total body clearance Cltot at any time
53
during the post-distributive phase in accordance with the equation,

61
Eq. 12
where is the overall apparent volume of distribution of the
equilibrated fluids of the body.
Thus,
Eq. 13
and
Eq. 14
If 3 or AUC have large errors, then the estimates of have large
errors. Thus the calculated distribution volumes in accordance with
equation 13 based on the best computer fit (Appendix I) of the plasma
data to tri-exponential equation are suspect. However, the calculated
Vj values in accordance with equation 13 (reported in Table 2) averaged
57
434 L, in excess of total body water in dogs (11-15 L) and does
indicate a high degree of sequestration by body tissues.
Dose-independent pharmacokinetics of buprenorphine. The
pharmacokinetic parameters of a drug are dose-independent when all
distribution and elimination processes are first order with respect to
compartmental concentrations. The rate constants must be invariant at
highly varying administered doses and there must be no saturable first
pass metabolism. To establish whether or not there is dose-independency,
the drug is administered to the same animal at different doses. If the
plasma levels divided by the respective doses are superimposable, then
dose independency can be postulated.

62
Unfortunately dose independent pharmacokinetics of buprenorphine in
dogs could not be studied at highly varying intravenous bolus (1-100
fold) dose levels. The lower limit of detecton (5 ng/ml) of
buprenorphine in plasma necessitated a certain minimal IV bolus dose to
adequately quantify terminal plasma concentrations. The fact that the
doses of buprenorphine in excess of 1.2-2.6 mg/kg would exhibit
significant side effects demanded an upper limit to the TV bolus dose
that could be administered.
At least two or more of the following toxic effects were observed
during a pharmacokinetic study: Defecation and muscle relaxation,
labored and forceful breathing for about 1 h after bolus dose, profuse
salivation continuing up to 4 h. The side effects observed following
rapid IV bolus injection of buprenorphine could be attributed to the
peak plasma levels (2000-5000 ng/ml, Figs. 4-9) reached immediately. All
five dogs exhibited drowsiness throughout the experiment, and the state
of general depression (characterized by lack of food intake, minimal
physical motion, lack of response to stimulus such as clapping of hands
and prolonged sleeping up to 12 h at a stretch) continued up to 1-5 days
depending upon the dose of buprenorphine. Higher doses produced longer
duration of these side effects.
To minimize the peak plasma concentrations of buprenorphine and the
associated side effects encountered upon TV bolus administration, and
yet to obtain adequate plasma concentration values in the terminal
phase, the higher doses of buprenorphine, 4.69, 3.85 and 3.741 mg/kg
dose in dog B, D and F (Study #7, 8 and 11), respectively, were
administered by constant rate infusion over a period of 3 h. However,
superimposition to validate dose independency is inoperative if the drug

63
is administered by two different modes (such as IV bolus and infusion).
If a relationship can be established between the plasma levels of a drug
administered by IV bolus and by IV infusion, superimposition can be
challenged by the use of the transformed IV infusion data.
Superimposition of this transformed high dose IV infusion data on low
58
dose IV bolus data was effected by the outlined procedure that
follows.
Analysis and transformation of IV infusion data. The post-infusion
data were fitted to a sum of either two (Study #7 and 8) or three (Study
53
#11) exponentials in accordance with the equation,
P' e“ Tr *t-T^ + A' e-a *t-T* + B' e- ^ *t-T) Eq. 15
where T is the time at which infusion was stopped and t is the time
after initiating the infusion. The first term in the above expression is
set equal to zero when the post-infusion data are fitted to a
2-compartment body model. The relationship between P and P' of equations
. 53
2 and 15 respectively is
P = P'T Tr/(l-e_7T T ) Eq. 16
Similarly, the relationships between A, A' and B, B' are
A = A'T a/(l-e-a T ) Eq. 17
B = B'TS / (l-e~ BT ) Eq. 18
The calculated P, A, and B values were used to generate the Cp .
values of equation 2. These could be the calculated plasma
concentrations if the same dose was administered by IV bolus. These
estimated Cpca^c concentrations obtained from the infusion studies were

64
divided by the total infused dose (mg/kg) and superimposed on the
experimental values of buprenorphine (divided by the IV bolus dose in
mg/kg) obtained after low dose bolus injection in the same dog. In dog B
at three dose levels (1.64, 2.56, 4.69 mg/kg, Study #2,3 and 7), dog C
at two dose levels (1.2, 1.44 mg/kg, Study #4 and 5), dog D at two dose
levels (0.78 and 3.85 mg/kg, Study #6 and 8) and dog F at two dose
levels (0.754 and 3.741 mg/kg, Study #17 and 11) there were no apparent
dose dependencies as demonstrated by the tests of superimposition
59
(statistically confirmed by nonparametric Kruskal-Wallis test applied
to the dose-normalised plasma concentration data. See Figs. 11-14 and
the legends, also refer to Appendix III). The parameters of equations
15-18 for TV infusion studies in dogs B, D and F are given in Table 5.
Plasma pharmacokinetics of the derived metabolite. The metabolite
(M) assayed in plasma was the acid hydrolyzable conjugate of
43
buprenorphine (1). This buprenophine conjugate (M) upon acid
hydrolysis presumably generated the aglycone which quantitatively
rearranged to demethoxybuprenorphine (3). Rather than assaying the
buprenorphine conjugate or the aglycone directly, this rearranged
product was assayed by HPLC separation and flúorimetric detection. Other
metabolites such as norbuprenorphine or its conjugates observed in
38 39
man ' were not detectable in dog plasma with the assay sensitivity
of 5 ng/ml. The conjugate concentration in plasma was highest at the
initial sampling time, and decreased at a rate similar to that of the
parent compound (Fig. 15). The metabolite profile in 4 IV bolus studies
could be fitted by a triexponential equation (Eq. 2). The fitting was
effected by nonlinear least square regression by using the computer
54
program (Appendix I) where the metabolite concentrations in plasma

Figure 11. Semilogarithmic plots of the concentrations of buprenorphine (1) in
plasma divided by the dose in mg/kg (cone./dose) plotted against time (min) for
the 1.6369 mg/kg (Study #2, O )> 2.5632 mg/kg (Study #3, â–¡ ), and 4.69 mg/kg
(Study #7, , on the presumption of IV bolus administration) doses of
buprenorphine in dog B. The middle inset is the plot of the data for the first 200
min after administration, and the top inset is the continuation of the data on an
extended time scale. The data for the highest dose, 4.69 mg/kg (Study #7, (\>) was
derived from the IV infusion study in which buprenorphine was infused at the rate
of 0.5058 mg/min for 165 min. The superimposition of the infusion data on the IV
bolus data was effected by the procedure described in this chapter under the
subheading "Dose-independent pharmacokinetics of buprenorphine". The points ((\,)
for the infusion study were calculated on the premise of IV bolus administration
of 4.69 mg/kg dose of buprenorphine in accordance with the equation 2. The
parameters of equation 2 were obtained through equations 15-18. The nonparametric
rank sum test (Kruskal-Wallis test, Appendix III; see also reference 59) was used
to test the hypothesis (H') that the dose-normalised plasma concentrations at the
above three dose levels were drawn from identical distributions. The critical
value of chi-square with a =0.05 and df=2 is 5.99. The observed H' (-7) is less
than 5.99. Therefore it can be concluded that there is no difference among the
three groups.

2nn 'ina 6Uti 8ua man
MIN
CONC./DOSE
ng/ml (mg/kg)~^
— □ cz
— a □ □
o â–¡ o a
99

Figure 12. Sard logarithmic plots of the concentrations (ng/ml) of buprenorphine in
plasma plotted against time (min) for the 0.7766 mg/kg (Study #6 O) dose in dog
D. The 3.847 mg/kg dose (Study #8 Q) was administered by IV infusion over a
period of 171 min. Infusion rate of buprenorphine as base = 0.5084 mg/min. The
superimposition of infusion data on IV bolus data was effected by the procedure
described in this chapter under the subheading "Dose-independent pharmacokinetics
of buprenorphine". The points (â–¡) represent quotient of concentrations divided by
dose that were calculated on the premise of IV bolus administration of 3.847 mg/kg
dose of buprenorphine in accordance with equation 2. The parameters of equation 2
were obtained through equations 15-18. These calculated points were multiplited by
0.2019 = 0.7766/3.847 to challenge superimposition. The nonparametric rank sum
test (Kruskal-Wallis test, Appendix III; see also reference 59) was used to test
the hypothesis (H') that the dose-normalised plasma concentrations at the above
two dose levels were drawn from identical distributions. The critical value of
chi-square with a =0.05 and df=l is 3.84. The observed H' (=0.37) is less than
3.84. Therefore it can be concluded that there is no difference among the two
groups.

I fj[jf][] Í
68
â–¡ o
â–¡ o
â–¡ o
â–¡o
â–¡ o
â–¡0
â–¡o
â–¡ o
â–¡ o
â–¡o
â–¡ o
CD
CD
CD
â–¡O
â–¡o
CO
CD
CD
O
co
rsi

Figure 13. Semilogarithmic plots of the concentrations of buprenorphine (1) in
plasma divided by the dose (mg/kg) plotted against time (min) for the 1.2023 mg/kg
(Study #4, O) and 1.439 mg/kg (Study #5,0) dose of buprenorphine dog C. The
inset is the continuation of data on an extended time scale up to 1500 min. The
nonparametric rank sum test (Kruskal-Wallis test, Appendix III; see also reference
59) was used to test the hypothesis (H') that the dose-normalised plasma
concentrations at the above two dose levels were drawn from identical
distributions. The critical value of chi-square with a =0.05 and df=l is 3.84. The
observed H' (=0.78) is less than 3.84. Therefore it can be concluded that there is
no difference among these two groups.

NI W
ÃœD8 Ut>9 U8l> UZZ U9I
CONC./DOSE

Figure 14. Semilogarithmic plots of the concentrations (ng/ml) of buprenorphine
(1) in plasma plotted against time (min) for the 0.7542 mg/kg
(O) IV bolus dose of buprenorphine in the bile cannulated dog F (morphine-
buprenorphine interaction study, #17). The 3.7408 mg/kg dose (Study #11, â–¡ ) was
administered by IV infusion over a period of 162 min. Infusion rate of
buprenorphine as base = 0.5588 mg/min. The superimposition of infusion data on IV
bolus data was effected by the prodedure described in this chapter under the
subheading "Dose-independent pharmacokinetics of buprenorphine". The points (â–¡)
represent quotient of the concentrations divided by dose that were calculated on
the premise of IV bolus administration of 3.7408 mg/kg dose of buprenorphine in
accordance with the equation 2. The parameters of the equation 2 were obtained
through equations 15-18. These calculated points were multiplied by 0.2016 =
0.7542/3.7408 to challenge superimposition. The nonparametric rank sum test
(Kruskal-Wallis test, Appendix III; see also reference 59) was used to test the
hypothesis (H') that the dose-normalised plasma concentrations at the above two
dose levels were drawn from identical distributions. The critical value of
chi-square with a =0.05 and df=l is 3.84. The observed H' (=0.053) is less than
3.84. Therefore it can be concluded that there is no difference among the two
groups.

n^/mi uu^/kg) J
MIN
2I6Ü
288G
3GGD

Figure 15. Semilogarithmic plots of the concentrations of buprenorphine, 1,
(O) and metabolite, M, (â–¡) in plasma plotted against tme for a) 1.4171 mg/kg
dose of buprenorphine in dog A, Study #1; b) 1.6369 mg/kg dose of buprenorphine in
dog B, Study #2; c) 1.2023 mg/kg dose of buprenorphine in dog C, Study #4; d)
1.439 mg/kg dose of buprenorphine in dog C, Study #5. The solid lines represent
curves fitted to the plasma data of buprenorphine and M in accordance with
equation 2.

nun i
CONC. NS'ttL CONC. KG/ML
NJW
OI J6 n^L. IJl-5 [J9E 1)91
8
y;
o
£
\
NIM
ODLi 095 OZt' 092 OH

75
were weighted by their inverse. The validity of triexponential equation
2 was confirmed by demonstration that the regressions in various studies
(Fig. 10) of the weighted residuals € (Eq. 3) against log Mp^^
(estimated metabolite concentations) gave mean residuals £ , slopes
and intercepts, all of which were not statistically significantly
different from zero (Table 2). The plasma concentration-time profiles of
metabolite in the IV bolus studies (1-5) are given in Figs. 16-20.
Maximum plasma concentration of the metabolite was observed at the
initial sampling time (about 1 min). Continued sampling gave
monotonically declining metabolite concentrations similar to the decay
of the parent compound. The parallel decays of buprenorphine and its
conjugate concentrations (Fig. 15) in plasma during the initial
distributive phase indicate that the rate determining step in the plasma
decay of the conjugate was its formation. During the terminal
elimination phase, the rate determining step in the plasma decay of
buprenorphine and its conjugate was the slow return of buprenorphine
from deep tissues to the central compartment where it could be
metabolized. This is the classical 'flip-flop' pharmacokinetics for the
. 53
conjugate.

Figure 16. Semilogarithmic plots of the plasma concentrations of metabolite (M)
against time (min) for the 1.4171 mg/kg IV bolus dose of buprenorphine in 22.85 kg
dog A, Study #1. The solid line represents the curve obtained by fitting the
plasma data to a sum of two exponentials in accordance with the equation:
Cp(ng/ml) = 331 e-0*024 + 33.8 e_0*000241 t
The inset is the continuation of the data for the extended time scale up to 3000
min.

MIN

Figure 17. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) against time (min) for the 1.6369 mg/kg IV bolus dose of
buprenorphine in 17.6 kg dog B, Study #2. The solid line represents the curve
obtained by fitting the plasma data of M to a sum of three exponentials in
accordance with equation (2):
Cp (ng/ml) = 308 e 0,191 t + 267.7 e_0,0169 t
+ 33.8 e
-0.000344 t
The inset is the representation of the data and the fitted curve for the initial
period of 750 min.

NI W
ÍJfJ'JC UUP? ÍJU9I !J!J? I ÍJÍJ9
1U/SN '9N03

Figure 18. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) against time (min) for the 1.2023 mg/kg IV bolus dose of
buprenorphine (1) in 22.5 kg dog C, Study #4. The solid line represents the curve
obtained by fitting the plasma data of M to a sum of three exponentials in
accordance with the equation (2):
~ nQ1 -0.602 t -0.0346 t Q -0.00191 t
Cp (ng/ml) = 1781 e + 361 e + 40.8 e
The inset is a continuation of the data and the fitted curve for an extended time
scale up tp 1500 min. The terminal half-life was estimated to be 363 min. This
value had much error due to limited analytical sensitivity, low dose and lack of
sufficient number of terminal phase plasma points.

cosía. NG'Hi

Figure 19. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) in against time (min) for the 2.5623 mg/kg IV bolus dose of
buprenorphine (1) in the 19.0 kg dog B, Study #3. The inset represents data and
the straight line fitted to the terminal phase in accordance with the
monoexponential equation,
Cp (ng/ml) = 43.25 e
-0.000631
t

CCNC-, NG'ML
MIN

Figure 20. Semilogarithmic plots of the plasma concentrations (ng/ml) of
metabolite (M) against time (min) for the 1.439 mg/kg dose of buprenorphine in
24.2 kg dog C, Study #5. The solid line represents the curve obtained by fitting
the plasma data of M to a sum of three exponentials in accordance with the
equation (2):
_ , . -0.106 t A -,oc -0.0068 t Mr q -0.000495 t
Cp (ng/ml) = 727 e + 335 e + 46.8 e
The inset is a continuation of the data and the fitted curve on an extended time
scale up tp 2750 min.

1W/SN 'ONOO
MIN

URINARY EXCRETION OF BUPRENORPHINE
Sigma minus plots. If it can assumed that buprenorphine is solely
eliminated from the central compartment, the urinary excretion rate of
intact drug can be defined as
dU/dt = ku Xc Eq. 19
where is the urinary excretion rate constant, and Xc is the amount
of drug in the central compartment at time t. Integrating equation 19
. 53
between 0 to U (time; 0 to t) results in
I U -E U = P"e~ 1Tt + A"e-at + B"e“ Eq. 20
oo
vhere
= P k V / ir
Eq.
21
u c
= A k V / a
Eq.
22
u c
= B k V / 6
u c
Eq.
23
The values of P, A and B are same as in Eqs. 5,6 and 7, respectively if
constant renal clearance is presumed. Thus a plot of the logarithm of
the amount of unchanged drug remaining to be excreted versus time (sigma
minus plot) gives a straight line with a terminal slope equal to
- g/2.303, i.e., the same terminal slope obtained from a semilogarithmic
plot of plasma concentration (Cp) versus time.
Representative examples of the sigma minus plots for the urinary
excretion of buprenorphine are given in Fig. 21. For dog A (Study #1,
86

Figure 21. Sard logarithmic plots of the amounts of the unchanged buprenorpine (1)
remaining to be excreted in urine versus time (sigma minus plot) in accordance
with equation 20. a) Semilogarithmic fitting of the initial urine data up to 100
min for the 1.4171 mg/kg IV bolus dose of buprenorphine in dog A, Study #1. An
apparent rate constant of 0.0176/min (half-life = 39 min) was obtained, b) Fitting
of the sigma minus plot of buprenorphine in urine of dog B, Study #2 at 1.6369
mg/kg dose of buprenorphine to a sum of two exponentials. The estimated hybrid
rate constants were 0.026/min (half-life = 27 min) and 0.00176/min (half-life =
390 min), c) Sigma minus plot of urinary excretion of buprenorphine for the 1.2023
mg/kg dose of buprenorphine in dog C, Study #4. The apparent terminal phase rate
constant for the monoexponential fitting was 0.0017/min (half-life = 400 min), d)
The fitted sigma minus plot of buprenorphine in urine of dog C at 1.439 mg/kg IV
bolus dose of buprenorphine, Study #5, to a sum of two exponentials. The estimated
apparent rate constants were 0.00695/min (half-life = 100 min) and 0.000287/min
(half-life = 2412 min) respectively.

Gm* Gun i win 'inn non 121111 igihi 2111111
mih mu
88
tim

89
Fig. 21a), semi logarithmic fitting of the initial data was linear only
up to 100 min. The estimated apparent rate constant was 0.0176 min ^
(half-life = 39 min). This corresponded to the second distributional
half-life (26 min) obtained for buprenorphine from the plasma data
(Table 2). The sigma minus plot of buprenorphine in urine of dog B (Fig.
21b) at 1.6369 mg/kg (Study #2) dose showed curvature, and could be
fitted to a sum of two exponentials. The resulting hybrid rate constants
were 0.026 (half-life = 27 min) and 0.00176 (half-life = 390 min) min 1
The first half-life corresponded to the second distributional half-life
of buprenorphine (39 min, Table 2) for this dog. For dog C (Fig. 21c) at
1.2023 mg/kg dose (Study #4, Table 2), the sigma minus plot of urinary
data gave an apparent terminal phase rate constant of 0.0017 min ^
(half-life = 400 min). This corresponded with the terminal half-life of
buprenorphine (673 min) obtained from the plasma data. For the same dog
at 1.439 mg/kg dose (Study #5), sigma minus plot (Fig. 21d) showed
curvature, and could be fitted to a sum of two exponentials, and the
respective apparent rate constants were 0.00695 (half-life = 100 min)
and 0.000287 (half-life = 2412 min) min The first half-life obtained
from the urine data corresponded with the second distributional
half-life (61 min, Table 2) obtained for buprenorphine from plasma data.
The sigma minus plots for the urinary excretion of buprenorphine in
other dogs showed great scattering and reasonable estimates of the
apparent rate constants were not possible.
The half-lives obtained from the various sigma minus plots shown in
Fig. 21 for the urinary excretion of buprenorphine reasonably
approximated the first and second distributional half-lives of
buprenorphine in plasma. Since a minor fraction of the the dose was

90
excreted unchanged in urine (<1%) and the limit of detection of
buprenorphine was 5 ng/ml, the terminal half-life of buprenorphine in
dogs could not be readily estimated from the urinary data.
Sigma minus plots for the conjugates (M) are given in Figs. 22,23.
For dog A (Study #1), the curve could be unexpectedly and for no obvious
reason, fitted best by a simple linear equation to indicate a constant
rate of renal elimination even with decreasing plasma concentrations of
the conjugate. The excretion rate was approximately 330 ng/min,
independent of concentration of metabolite in the central compartment
(Fig. 22a). For dog B at 1.6369 mg/kg dose (Study #2) of buprenorphine
(Table 2), the sigma minus plot gave an apparent rate constant of 0.0032
min ^ (half-life = 215 min, Fig. 22b). For dog C at 1.2023 mg/kg dose
(Study #4), (Fig. 22c) an apparent rate constant of 0.0022 min 1
(half-life = 312 min) was obtained, which corresponded well with the
terminal phase half-life obtained for M from plasma data (305 min, Table
2). For dog B at 2.5632 mg/kg dose (Study #3), the sigma minus plot
(Fig. 22d) showed curvature and could be fitted to a sum of two
exponentials, and the apparent rate constants were 0.023 min ^
(half-life = 30 min) and 0.000567 min ^ (half-life = 1220 min)
respectively, where the second half-life corresponded with the terminal
half-life obtained from the plasma data of M in this dog (Table 2,
half-life = 1098 min). The sigma minus plot for M in dog C at 1.439
mg/kg dose (Study #5) showed curvature (Fig. 23) and could be fitted to
a sum of two exponentials, the apparent rate constants being 0.018 min
1 (half-life = 39 min) and 0.000812 min 1 (half-life = 853 min).
In dog C at 1.2023 mg/kg (Study #4) IV bolus dose of buprenorphine,
the terminal half-life of buprenorphine was estimated as 673 min (Table

Figure 22. Semi1ogarithmic plots of the amounts of metabolite (M) remaining to be
excreted in urine versus time (sigma minus plot) following IV bolus administration
of buprenorphine (1) in accordance with equation 20. a) The excretion data of M in
urine up to 700 min could be fitted to a simple linear equation in dog A, Study #1
at 1.4171 mg/kg dose of buprenorphine. The excretion rate was estimated to be 330
ng/min. b) Sigma minus plot of M in urine of dog B, Study #2 following 1.6369
mg/kg dose of buprenorphine, resulting in a estimated apparent rate constant
0.0032/min (half-life = 215 min), c) Sigma minus plot of M in urine for the 1.2023
mg/kg dose of buprenorphine in dog C, Study #4. The apparent rate constant was
estimated tas 0.0022/min (half-life = 312 min), d) Sigma minus plot of the urinary
excretion of M for the 2.5632 mg/kg IV bolus dose of buprenorphine in dog B, Study
#3. The datata were fitted to a sum of two exponentials in accordance with
equation 20. The estimate apparent rate constants were 0.023/min (half-lige = 30
min) and 0.000567/min (half-life = 1220 min) respectively.

HIM
UII2I- Il'lie \)Zr,Z 11091 1)1-9
cm N1W
cri niia tii-9 iioi- u?c 1191
¡at ,92 -*92 ssrf 92 *92
o
•©-
O'-.
o''O'.
o-.
o-.
o
o©
"o,
Q3]o-
--00I
1 uno i
HIM
ssrf 92 -*92 ssrt" '"nZ

Figure 23. Semi 1 ogarithmic plot of the amount of the metabolite (M) remaining to
be excreted versus time (sigma minus plot) following 1.439 mg/kg dose of
buprenorphine (1) in dog C, Study #5. The data was fitted to a sum of two
exponentials. The estimated apparent rate constants were 0.0018/min (half-life =
39 min) and 0.000812/min (half-life = 853 min) respectively.

94
SSff HI -°°r\2
4l\[\ 6[IL¡ ! 2f¡fi * Gtiíl 2[¡fiti
MTN

95
2). The plasm data and sigma minus plot of M in this dog gave an
apparent terminal half-lives of 305 (Fig. 18) and 312 (Fig 22c)
respectively. This metabolite half-life is therefore, an apparent
distributional half-life and not the terminal half-life.
Urinary excretion rate plots. Since xc = vc Cp in equation 19,
substituting the value of Cp from equation 2 into equation 19,
Tvi-ii -ift ^ ,iii -at ± niii -8 t
dU/dt =P e + A e +B e
where P111 = P k V
u c
-in , , T7
A = A k V
u c
B111 = B k V
u c
Eq. 24
Eq. 25
Eq. 26
Eq. 27
A semilogarithmic plot of excretion rate of unmetabolized drug
versus time according to equation 24 would yield a triexponential curve.
As with the semilogarithmic plasm concentration-time plot, the terminal
exponential phase rate constant can be obtained from the terminal slope,
- 3/2.303, and B111 is the extrapolated intercept of the terminal
linear phase to time zero. Similar to the treatment of the plasm data
with multicompartment characteristics, the method of residuals could be
used to obtain the parameters of the distributional phases of equation
24.
Semilogarithmic plots of A U/ At (approximations of the
instantaneous excretory rate, dU/dt), finite amounts (A U) of either 1
or M excreted during a finite time interval ( a t) against t-mid
(mid-point of the collection interval) were highly scattered in most of
the studies. Thus only the data for dog A (Study #1) and B (Study #2)
are reported here. In dog A (Study #1), urine data of buprenorphine up

96
to 200 min could be fitted to log A U/ At = (—k.' /2.303) t-mid +
intercept, and the apparent rate constant (k1) 0.0394 min ^ (half-life
= 18 min) corresponded with the plasma second distributional half-life
of 26 min (Table 2, Fig. 24a). In dog B at 1.6369 mg/kg dose (Study #2),
the excretion rate plot for M (Fig. 24b) gave an apparent rate constant
0.0046 min 1 (half-life = 150 min). In the same dog at this dose level,
the excretion rate plot of buprenorphine could be fitted into two
separate linear segments (Fig. 25), from which the two apparent rate
constants obtained were, 0.019 min ^ (half-life = 37 min), and 0.0011
min 1 (half-life = 622 min). Both these half-lives corresponded with
the half-lives obtained from the plasma data (Table 2, 39 and 654 min).
Clearances of Buprenorphine (1) and Conjugate (M)
Renal clearance of buprenorphine. Upon rearrangement of equation
19,
dU/dt = ku Vc Cp Eq. 28
Integrating between 0 to U (time; 0 to t),
t
£U = kV f Cp dt = Cl AUC. Eq. 29
u c qJ r ren t ^
where AUC^ is the area under the plasma concentration-time curve. The
renal clearance of buprenorphine (Cl^en ) estimated from the slopes
1 1
of cumulative amounts excreted in urine EU against AUCfc averaged
1.91 _+ 0.96 (SEM) ml/min (Table 2), which indicate high protein binding
if unbound drug excreted solely by glomerular filtration.
These clearance plots (Figs. 26-28) frequently did not go through
the origin and could be best characterized by one or more straight lines
conforming to the equation,

97
O
•-3
Figure 24. Será logarithmic plots of the amounts (y g) of a)
buprenorphine (1) and b) metabolite (M) excreted in urine per min
( yg/min) plotted against t-mid, the mid point of the urine collection
interval in accordance with the equation:
log AU/ At = (~k'/2.303) t-mid + intercept
For the 1.4171 mg/kg IV bolus dose of buprenorphine in dog A (Study #1,
Table 2), the plot in accordance with the above equation for 1 gave an
apparent rate constant 0.0394/min (half-life = 18 min). For the 1.6369
mg/kg IV bolus dose of buprenorphine in dog B, Study #2, the plot in
accordance with the above equation for M gave an apparent rate constant
of 0.0046/min (half-life = 150 min).

Figure 25. Semi logarithmic plots of the amounts ( y g) of buprenorphine (1)
excreted in urine per min ( yg/min) plotted against t-mid, the mid point of the
urine collection interval for the 1.6369 mg/kg IV bolus dose of buprenorphine in
dog B, Study #2, in accordance with the equation:
log AU/A t = -(k'/2.303) t-mid + intercept
The insets represent the data fitted into two separate linear segments as per the
above equation. The estimated rate constants were 0.019/min (a, half-life = 37
min) and 0.0011/min (b, half-life = 622 min). Note the correspondence of these
rate constants with those reported in fig. 5 for the plasma data of this dog
(Study #2, Table 2).

Dü/DT pG/MIN
lü
O
::<£>
lo o
j
,um
o
o
%
lürp
Fov O
'''-O
I = :
.ül 1 ° o oO o
O O
.01
a
►—
o
u
a •
O''.
O
43
H 1 1 1 1 1 h
o
I I
0(1
120 IBO
T MID (MIN)
240
300
O
o
H 1 1 1 1 1 1 H 1 1
stin
! üütl lrof|[]
T MID CÍ1IN)
2[lüü
2bN[]

Figure 26. Plot of the cumulative amounts ( yg) of buprenorphine (1) excreted in
urine against the area under the plasma concentration-time curve (AUC ,
yg.min/ml) in accordance with the equation (30):
E U = Cl ( AUC. - AUCn )
ren ' t 0
where AUC^ is the area under the plasma concentration-time curve at E U = 0. For
the 1.4171 rrq/kg IV bolus dose of buprenorphine in dog A, Study #1, the curve
shows three distinctly linear segments attributatble to the pH effect of urine.
The slope (Clren) of the initial linear segment for the pH range between 5.2-5.8
was estimated to be 2.69 ml/min. See also next figure.

ru juGS
i rjfi -r-
4
4
4l\
Gfl
IÜ
3ti
ftUCT JJG X MIN / ML
101

Figure 27. Plots of the cumulative amounts (E U, p g) of buprenorphine (1)
excreted in urine against area under the plasma concentration-time curve at the
time of urine collection in accordance with the equation (30):
Z U = Cl [ AUC - AUCa ]
ren t 0
where AUCq is the area under the plasma concentration time curve at i U = 0. a)
For the 1.4171 mg/kg IV bolus dose of buprenorphine in dog A, Study #1, the
initial slope was estimated to be 2.69 ml/min. b) For the 1.6369 mg/kg IV bolus
dose of buprenorphine in dog B, Study #2, the initial slope ( Clren ) was
estimated as 5.24 ml/min. c) For the 1.2023 IV bolus dose of buprenorphine in dog
C, Study #4, the estimated renal clearance was 0.13 ml/min for the initial time
period up to 243 min. d) In the same dog at this dose level, estimated clearance
was 1.0 ml/min for the urine collection time between 243-1270 min. In this dog,
the pH of the urine ranged between 6-6.5 during the initial 243 min time period;
the pH range was 5.4-5.7 for the time period between 243-881 min.

¡rf n2 ssrr ro
35 -
63.50 .
/ "
r,n
,,'Ó
52.50..
a O''
o , -
<15
o>
33.50
V
\
\
^ 30 -
22. MI
Ib
3. MI
1 1— 1 1 f——1 1 1 1 1
5 IQ 15 211 25
DUCT JUG X MIN / ML
o r
3.MI .
x *
3.-1(1 _
c °
3.10
O''
6.00 .
.''O
Kfi
^ 6/jU
^cr' °
w 6,20-
5.MI -
,''ó
5.60
O
5.30
1 1 1 1 1 1 1 1 1 1
3<1 30 <12 -16 50
0UC1 ¿JG X MIN /- ML
ru jugs ¿igs
103

Figure 28. Plots of the cumulative amounts ( x U, p g) of buprenorphine (1)
excreted in urine against the area under the plasma concentration-time curve (AUC
t, pg.min/ml) at the time of urine collection in accordance with the equation
(30):
X U = Cl
ren
[ AUCt - AUCq ]
where AUCq is the area under the plasma concentration-time curve at x U = o. a)
For the 2.5632 mg/kg IV bolus dose of buprenorphine in dog B, Study #3, the
estimated renal clearance was 0.053 ml/min for the initial time period up to 271
min. b) Same as in (a), except the points up to 60 min were not included in the
regression (time; 90-363 min). Estimated renal clearance was 0.03 ml/min. This low
renal clearance could be attributable to the cessation of urinary excretion of
buprenorphine during the time interval between 180-240 min. c) In the same dog,
the estimated renal clearance was 0.86 ml/min for the latter time period between
1219-5650 min. d) For the 1.439 mg/kg IV bolus dose of buprenorphine in dog C,
Study #5, the estimated renal clearance was 0.51 ml/min for the initial time
period between 75-1164 min. In the same dog, regression according to the above
equation (30) gave the slope = Clren = 1.453 ml/min for the initial time period
up to 75 min. (Intercept = -12.6, r=0.997, see also Table 2).

ssrr ni ssrr m
2.20
2.14 .
2.080 .
2.020
1.96
^ 1.90
W 1.09
1.98
1.92
1.86
38
39.211
32.9(1
30.6(1
28.8(1

29
^ 28.2(1
23.9(1
21.60
19.BO
O
O'
O
O'OO
O,'
O'
H 1 1 1 1-
60 68 90
ftUCT JJG X MIN / ML
98
)'Q
oo.
J3
,o
O
,'o
*
O
o
o'
9 1 h
28
H 1 1 1 h-
36 49 82
ftUCT JIG X MIN / Ml.
6(1
105

106
Z u = Clren ( AUCt - AUCq ) Eq. 30
where AUCg is the area under the plasma concentration time curve at
EU=0 as estimated from the extrapolation of the best linear plots of U
versus AUC (Table 2). This non-zero intercept could be attributed to one
of several factors. When the urinary clearance (obtained from the
quotient of A U/ At against Cp^. where latter is the plasma
concentration at the mid point of successive urine collections) was
linearly related to urinary pH in dog A (Study #1, Fig. 29). Renal
clearance was low at high urine pH. If it can be hypothesized that the
43
uncharged buprenorphine in urine at high pH values (pKa' = 8.24) can
undergo renal tubular reabsorption, then lower clearances should be
observed at high urine pH values. The possible renal mechnism could be
pH dependent tubular reabsorption of neutal species and increased
excretion of ionized species at lower pH values. This is supported by
the fact that in dog B at 2.56 mg/kg TV bolus dose of buprenorphine
(Study #3), no drug was observed in the urine for a pH above 7.5 (Fig.
29) to indicate complete reabsorption of buprenorphine at these higher
pH values. However, since such a small fraction of unchanged
buprenorphine was excreted in urine, metabolic acidification of urine is
not a valid measure of counteracting narcotic toxicity due to accidental
overdosage.
45
It has been previously shown that morphine exhibits
dose-dependent pharmacodynamic effects on renal processes. Decreased
renal excretory rates and reductions in urinary flow rate were observed
at high morphine doses. The urine flow was considerably less during the

Figure 29. Plots of Clren (ml/min) against urinary pH. The renal clearance was
calculated from the quotient of the urinary excretion rate ( aU/a t,
y g/min and the plasma concentration at the mid point of urine collection interval
(Cpj. . a) For the 1.4171 mg/kg TV bolus dose of buprenorphine in dog A,
Study #1, (r=0.971). b) For the 1.6369 mg/kg IV bolus dose of buprenorphine in dog
B, Study #2 (r=0.873). c) For the 2.5632 mg/kg IV bolus dose of buprenorphine in
dog B, study #3. Note the absence of renal clearance above pH 7.5. See also text.

CL KEN ML/MIN
N> IS)
801

Figure 30. Plots of urine flow (ml/min) against t-mid, the mid point of
urine collection interval, a) For the 1.4171 mg/kg IV bolus dose of
buprenorphine (1) in dog A, Study #1. b) For the 1.6369 mg/kg, Stduy #2,
(O) and 2.5632 mg/kg, Study #3, (â–¡) IV bolus doses respectively of
buprenorphine in dog B. Note the dose dependent decrease in urine flow
rate, c) For the 1.2023 mg/kg IV bolus dose of buprenorphine in dog C,
Study #4.

<*80 64Q
T MID (MIN)
URINE FLOU Ml/MIN
URINE FLCU M/MIN
2.52

Ill
first few hours after the administration of buprenorphine (Fig. 30),
which also indicated dose-dependent renal elimination (Fig. 30b). This
could possibly explain the negative intercepts observed in plots in
accordance with equation 30. However, such a small fraction (<1% of the
dose) is excreted in urine, this would have no pronounced effect in the
overall dose-independent pharmacokinetics. No dependence of clearance on
urine flow rate was observed for buprenorphine (Fig. 31).
Renal clearance of the metabolite. Renal clearance of the plasma
metabolite obtained from plots (Figs. 32-34) in accordance with equation
30 averaged 9.2 _+ 2.7 (SEM) ml/min (Table 2). This was higher than the
renal clearance of buprenorphine (1.72 ml/min).
Similar to buprenorhine, the plots (Figs. 32-34) according to
equation 30 showed large negative intercepts. This could not be
explained as there was no pH or urine flow dependent clearance (Figs.
35,36) observed for the metabolite.
Renal clearances obtained for buprenorphine and the metabolite from
the plots of aU/a t versus cPt_mj_d were highly scattered. Some plots
(with minimum scattering) are shown in Fig. 37.
Metabolic clearance of buprenorphine. Since dose-independent
pharmacokinetics of buprenorphine in the dose range studied could not be
denied, it can be postulated that the metabolism is first order and that
the rates are dependent only on the concentrations of buprenorphine in
the central compartment. Thus the rate of formation of the total
metabolite M
dM./dt = k V Cp Eq. 31
t m c ^ ^
where dM,/dt is the rate of formation of total metabolite, k V is
t. me

Figure 31. Plots of renal clearance (Clren/ ml/min) against urine flow rate
(ml/min). The renal clearances were calculated from the quotient of the urinary
excretion rate ( aU/ At) and the plasma concentration at the mid point of urine
collection interval (Cpt_m^d). The slopes and the respective standard errors are
as follows: a) For the 1.4171 mg/kg dose of buprenorphine in dog A, Study #1,
Slope = -0.19 _+ 0.32; b) For the 1.6369 mg/kg dose of buprenorphine in dog B,
Study #2; Slope = -0.6 +_ 0.8; c) For the 1.2023 mg/kg dose of buprenorphine in dog
C, Study #4; Slope = 0.42 +_ 0.22; d) For the 1.439 mg/kg dose of buprenorphine in
dog C, Study #5; Slope = 0.24 +_ 0.3. These slopes were not statistically
significantly different from zero as confirmed by t-test.

o
*
sá
z
¡tí
.811 .
O
.6(1
d
.4(1
-
O
.211.
O
O
1
O
.8(1.
o °
o
.611.
-o-'ó'
.<111 -
o
o
.2(1
o° °<9
Q— L
1 1
lili
.3(1
1 I I 1
.6n .on
URINE FI OU ML/I1IN
1 t
1.2(1
113

Figure 32. Plots of the cumulative amounts (e U, p g) of metabolite (M) excreted
in urine against area under the plasma concentration-time curve
(AUCt, yg.min/ml) at the time of urine collection interval in accordance with
the equation (30):
EU = [ AUCt - AUCq ]
where AUCq is the area under the plasma concentration time curve at E U=0. a) For
the 1.4171 mg/kg IV bolus dose of buprenorphine in dog A, Study #1, the estimated
renal clearance for M was 11.79 ml/min for the time period between 153-700 min.
The estimated renal clearance during the first 153 min was 1.94 ml/min (see table
2). b) For the 1.6369 mg/kg IV bolus dose of buprenorphine in dog B, Study #2, the
estimated initial renal clearance of M was 3.6 ml/min. c) For the 1.2023 mg/kg IV
bolus dose of buprenorphine in dog C, Study #4, the estimated renal cleamace of M
was 11 ml/min for the time period 158-1270 min. However, for the initial 158 min,
the renal clearance was 4.4 ml/min (Intercept = -30.4). d) For the 1.439 mg/kg IV
bolus dose of buprenorphine in dog C, Study #5, the estimated renal clearance was
0.26 ml/min for the time period 75-2630 min. In the same dog, the estimated renal
clearance for the first 75 min vías 0.98 ml/min (intercept=-9.2).

¿u
ru jjgs JJSS
115

Figure 33. Plot of the cumulative amount ( zU, y g) of the metabolite (M) excreted
in urine against area under the plasma concentration-time curve
(AUCt, yg.min/ml) at the time of urine collection in accordance with the
equation (30):
l U = Cl [ AUC. - AUCn ]
ren t 0 J
where AUC^ is the area under the plasma concentration-time curve at E U=0, for the
2.5632 mg/kg IV bolus dose of buprenorphine in dog B, Study #3. The data were
fitted to three linear segments. The regressions on these segments are given in
the legend of Fig. 34.

117
Lf>
cm
â–¡
c:
CM
LO
â–¡
a
¡-T5
ssrf ni
AUCT jJG X MIN / ML

Figure 34. Plots of the cumulative amounts (j; U, y g) of the metabolite
(M) excreted in urine against area under the plasma concentration-time
curve (AUCt , y g.min/ml) at the time of urine collection in accordance
with the equation (30):
ZU = Cl
ren
[ AUCfc - AUCq ]
where AUCn is the area under the plasma concentration-time curve at
EU=0 for the 2.5632 mg/kg IV bolus dose of buprenorphine in dog B, Study
#3. a) Estimated renal clearance for the time period up to 90 min was
0.93 ml/min. b) the renal clearance for the time period 90-442 min was
0.24 ml/min. c) the clearance for the time period 541-5650 min was 1.8
ml/min.

sort nz sort nz - sonf ni
119

Figure 35. Plots of the renal clearance (Clren , ml/min) of the metabolite (M)
against urinary pH. The renal clearance was calculated from the quotient of the
urinary excretion rate ( AU/ At) and plasma concentration at the mid point of
urine collection interval ). The slopes with the respective standard
errors for these plots are as follows: a) For the 1.4171 mg/kg IV bolus dose of
buprenorphine (1) in dog A, Study #1; Slope = 3.42 +_ 1.59; b) For the 1.6369 mg/kg
IV bolus dose of buprenorphine in dog B, Study #2; Slope = -1.48 +_ 0.73; c) For
the 1.2023 mg/kg IV bolus dose of buprenorphine in dog C, Study #4; Slope = -3.9 +
2.51; d) For the 1.439 mg/kg IV bolus dose of buprenorphine in dog C, Study #5;
Slope = 0.067 +_ 0.18. These slopes were not statistically significantly different
from zero as confirmed by t-test.

. UVL. L
a REN ML/MIN
CL REN ML/MIN
CL REN ML/MIN
L¿ü2£2_D¿¿íE£|Sj
O ,
O !
o Qd!
®>$d,
O o !
O
CL
A
o
— — rvj u) -£t
• • • • • •
P m cd a an
= =2 s S O) E2 c
131
119 >

Figure 36. Plots of the renal clearance (Clren , ml/min) of the metabolite (M)
against the urine flow rate (ml/min). The renal clearance was calculated from the
quotient of the urinary excretion rate ( Au/At) and the plasma concentration at
the mid point of the urine collection interval (Cpt_m^). The slopes and the
standard errors are as follows: a) For the 1.6369 mg/kg IV bolus dose of
buprenorphine (1) in dog A, Study #2; Slope = -0.42 +_ 0.59; b) For the 1.2023
mg/kg IV bolus dose of buprenorphine in dog C, Study #4; Slope = 3.6 _+ 2.13; c)
For the 2.5632 mg/kg IV bolus dose of buprenorphine in dog B, Study #3; Slope =
-1.4 +_ 1.5; d) For the 1.439 mg/kg IV bolus dose of buprenorphine in dog C, Study
#5; Slope = 0.24 +_ 0.24. These slopes were not statistically significantly
different from zero as confirmed by t-test.

2b
22.bll
211
n.bii
a «
z
UJ
“ 12,‘JII
—B
CJ
IU
n.bii
5
2.bN
2
I.8Ü
1.6(1
~ 1.411
^ 1.211
x
Ul
“ I
d
.6(1
.6(1
.411
.2(1
O
b
o
o
o
jQ - "
" ° o
o
o o
°-o'
O o
o
o
o
.bfl
I .«ill
URINE E10U ML/MIN
O
—I
2. Ml
O
d
o
o
o
oO
E
+
o
o
4 E 1 1
.6(1 .Ml
URINE FIOU ML/MIN
O
O
I-
J(l
-4 I
1.2(1
H
I .Ml
123

Figure 37. Plots of the urinary excretion rate ( g/min) of
buprenorphine (1) and metabolite (M) against plasma concentration of
either 1 or H ( Cp, _ ., ng/ml ) in accordance with the equation 26. a)
For 1 at 1.6369 mg/kg1(Study #2) IV bolus dose of buprenorphine.
Estimated renal clearance was 4.7 ml/min which corresponded well with
the renal clearance (5.24 ml/min) obtained using equation 30 (See fig.
27b). b) For 1 at 1.439 mg/kg (Study #5) IV bolus dose of buprenorphine;
Estimated renal clearance was 1.38 ml/min, which corresponded well with
the renal clearance obtained using equation 30 (1.453 ml/min, see Table
2). c) For M at 1.6369 mg/kg dose of buprenorphine (Study #2). Estimated
renal clearance was 6.6 ml/min.

DLI/Df JJG/MIN OU/OT ¿JG/MIN DU/DT ¿JG/MIN
125
.40 —
.3G -_
.32--
.28-,
.24 -.
.20--
. 16 --
.12--
.080--
.040--
■Ó
o.
,0
cb 9''
o'
H &
O '
.0
o
Q
H h
H 1
IG
48
B TMIO HG^ML
32
G4
8D

126
the metabolic clearance (Cl^ ). The metabolic clearance of the parent
drug (Cl t) and the apparent volume of distribution (Vm) of the
metabolite that is excreted in the urine and the bile can be estimated
by integrating the above equation between 0 and t with respect to time
and considering the stoichiometry of the total metabolite
M, = k V J Cpdt=Cl ^ AUC.
t m c 0 r met t
= U + V m + B Eq. 32
m m m
where AUCfc is the area under the parent drug (1) concentration-time
curve, U and B are the amounts of metabolite excreted into the urine
m m
and bile respectively up to that time and m is the metabolite
concentration in plasma. If it can be assumed that a constant fraction
of the hepatically formed metabolite is partitioned into the bile, i.e.,
there is a constant biliary clearance, then constant biliary clearance,
then
B = C1D AUC.
m B t
Substituting the value of B^ into equation 32,
(Cl - C1D ) AUC. = U + V m
' met B t mm
The equation can be rearranged^ into
Eq. 33
Eq. 34
U /m = -V + (Cl - Cln ) AUC. /m Eq. 35
m m met B t
or U /AUC. = -V m/AUC, + (Cl - C1D ) Eq. 36
m t m t ' met B ^
where ( Cl . - Cl_. ) and V can be obtained from the slopes and
met B m
intercepts of the appropriate plots of the designated quotients of AUC^

127
of the drug and cumulative amounts of M excreted in urine against the
concentration of the metabolite m, at the same time. Such plots
according to the equation 35 are given in Fig. 38. Although this method
does not require any explicit knowledge of the dose or the fraction of
the drug transformed into metabolite, it requires that all of the
metabolite be excreted in the urine, and a constant biliary clearance of
the formed metabolite prior to any possible return to the systemic
circulation. Even though an insignificant fraction of the metabolite
appears in plasma, if all of this plasma metabolite is excreted into the
urine, this method could be applied to to the urinary data to obtain the
above parameters. Regressions according to equation 35 gave the
following clearances ( Cl ^ - Clg ) _+ standard error in ml/min (Table
2, Fig. 38); 2.72 + 0.5; 2.06 + 0.029; 3.47 + 0.11; 1.27 + 0.009. The
apparent volumes of distribution V of the metabolite + standard error
m —
in ml; 2054 _+ 403; 339 +_ 128; 705 _+ 498; 166 _+ 35. The latter two were
much smaller than the presumed plasma volume (1080 ml, for an hematocrit
of 0.4) in dogs.^ This result is not consistent with the assumption
that the hepatically formed metabolite appearing in the systemic
circulation is completely excreted in urine. Thus urinary excretion may
not be the only route of elimination of the systemic metabolite. In
fact, as it will be shown later, a major fraction of the systemically
circulating metabolite is excreted in bile.
Since an insignificant fraction (% recovery 0.2 _+ 0.08) of
unchanged buprenorphine is excreted in urine, it can now be postulated
that for all practical purposes, the estimated total clearance given as
396 ml/min in Table 2 (based on the unwarrented assumption of the
validities of $ and AUC) is essentially equal to the metabolic

Figure 38. Plots of the quotient of the cumulative amounts of the
metabolite and plasma concentration of the metabolite at the urine
collection time (U^/m) versus the quotient of the area under the
plasma concentration-time curve of buprenorphine and the metabolite
level in plasma (AUC, /m) in accordance with the equation 33. a) For
the 1.2023 mg/kg IV bolus dose of buprenorhine, Study #4. The estimated
clearance, Cljj^ - Cl^ was 3.47 ml/min. b) For the 1.6369 mg/kg IV
bolus dose of buprenorphine in dog B, Study #2; estimated clearance =
2.06 ml/min. c) For the 2.5632 mg/kg IV bolus dose of buprenorphine in
dog B, study #3; estimated clearance = 1.27 ml/min.

sr Be le h l
ueionu
b u?‘e ut>’2 uy i os-
U9-
U2M
08-1
dp-2
E
i)9-e
U2>
08>
UfS
9
6 02"L
I 1 h-
o
W'iarw
Up'S D9‘E
—I 1 h
08 ‘ I
E
9
b
21
SI
E?
81
12
P2
L2
DC
621
un/n üh/m

130
clearance, Clj^^ (395 ml/min, Table 2). This integral method using
equation 35 gave the difference between the metabolic and biliary
1 M
clearances ( Cl^^. - Clg ) as 2.38 ml/min (Table 2). Thus biliary
clearance, Cl^, 387 ml/min (Table 2) value indicated elimination of
D
buprenorphine from the body virtually by metabolism.
The TV bolus doses used in the studies 1-6 produced terminal plasma
concentrations of buprenorphine which were below the analytical
sensitivity (5 ng/ml) and did not permit accurate estimation of the
terminal half-life. The fact that the doses of buprenorphine (1.2 to 2.6
mg/kg) used in the first 5 IV bolus studies (Table 2) exhibited
significant side effects gave a upper limit to the TV bolus dose that
could be administered. To minimize the peak plasma concentrations of
buprenorhine and the associated side effects encountered upon IV bolus
administration, yet to get a greater amount of the drug in the body to
provide adequate number of quantifiable plasma concentrations in the
terminal phase, higher doses of the drug were administered by slow IV
infusion. These studies are described in the next section.

IV INFUSION STUDIES
Plots of plasma concentrations of buprenorphine with time for the
162-177 min constant rate infusion of buprenorphine (Studies 7-12) in 6
dogs (B,D,E,F,G and H) are shown in Figures 39-44. In studies 7-11, the
drug was infused into the jugular vein. In these studies, during
infusion, blood samples were collected from the foreleg's brachialis
vein. In study #12, the drug was infused through the brachialis vein and
the blood samples were collected during infusion from contralateral
brachialis and jugular veins. In studies 7-9,11, and 12, post-infusion
blood samples were collected from both brachialis and jugular veins.
Dogs E,F and G were also bile cannulated, and the bile was collected up
to 24-26 h in these dogs (Studies 9, 10 and 11).
Catheter binding of buprenorphine.
In IV infusion studies (7-12), buprenorphine hydrochlorie was
dissolved in normal saline (as base, concentration = 0.74-0.76 mg/ml, pH
= 5.25-5.5, infusion rate = 0.7026 ml/min) and infused into the jugular
vein (studies 7-11) or brachialis vein (study #12) using an intravenous
catheter placement unit (see experimental) for a period of up to 3 h.
Buprenorphine slowly partitioned into the plastic catheter during
prolonged infusion. After cessation of infusion, when blood was drawn
from the dog through the same catheter used for infusion, the drug
repartitioned into the blood and gave artifactually higher plasma
concentrations of buprenorphine. The normal saline infusion (45
drops/min) into the vein through the same catheter, which was conducted
between blood samplings, completely removed the drug from the catheter
131

Figure 39. Semilogarithmic plots of the plasma buprenorphine concentrations as
ng/ml of base (upon 0.5058 mg/min constant rate IV infusion) against time (min)
for the 4.6885 mg/kg dose in 17.8 kg dog B (Study #7, Table 5). The points (O)
and (#) represent the jugular and brachialis vein plasma concentrations
respectively of buprenorphine. The solid line represents the curve obtained by
fitting the brachialis and jugular vein plasma data to equation 39. The inset is
the data and the fitted curve for the initial 1000 min.

133
NIN
anus
â–¡nuu
nunc
nnsj?
nnn i
m
nnn ¡
NG'ML

Figure 40. Semi logarithmic plots of the plasma concentrations as ng/ml of base
(upon 0.548 mg/min constant rate IV infusion) against time (min) for the 3.847
mg/kg dose in 22.6 kg dog D (Study #8, Table 5). The points (O) and (•)
represent the jugular and brachialis vein plasma concentrations respectively of
buprenorphine. The solid line represents the curve obtained by fitting the
experimental jugular and brachialis vein plasma data to equation 39. The inset
the data and the fitted curve for the initial 360 min.

135

Figure 41. Semilogarithmic plots of the plasma concentrations of buprenorphine as
ng/ml of base (upon 0.5101 mg/min constant rate IV infusion) against time (min)
for the 4.80 mg/kg dose in 18.6 kg bile cannulated dog E (Study #9, Table 5). The
points (O) and (#) represent the experimental jugular and brachialis vein plasma
concentrations respectively of buprenorphine. The solid line represents the curve
obtained by fitting the experimental experimental brachialis and jugular vein
plasma data of buprenorphine to equation 39. The inset is the representation of
the data and the fitted curve for the initial 1000 min.

NG'ML
137

Figure 42. Semi logarithmic plots of the plasma buprenorphine concentrations as
ng/ml of base (upon 0.5288 mg/min constant rate IV infusion) against time (min)
for the 4.0864 mg/kg dose in 22.0 kg bile cannulated dog F (Study #10, Table 5).
The points (#) and (O) represent the experimental brachialis and jugular vein
plasma concentrations respectively of buprenorphine. The solid line represents the
curve obtained by fitting the experimental brachialis and jugular vein plasma data
to equation 50. The inset is the representation of the data and the fitted curve
for the initial 1000 min.

NG'flL
139

Figure 43. Semilogarithmic plots of the plasma buprenorphine concentrations as
ng/ml of base (upon 0.5588 mg/min constant rate IV infusion) against time (min)
for the 3.7408 mg/kg dose in 24.2 kg bile cannulated dog G (Study #11, Table 5).
The points (•) and (O) represent the experimental brachialis and jugular vein
plasma concentrations respectively of buprenorphine. The solid line represents the
curve obtained by fitting the experimental brachialis and jugular vein plasma data
to equation 50. The inset is the representation of the data and the fitted curve
for the initial 1000 min.

NG/ML
141

Figure 44. Semilogarithmic plots of the plasma buprenorphine concentrations as
ng/ml of base (upon 0.5236 mg/min constant rate IV infusion) against time (min)
for the 3.83 mg/kg dose in 24.2 kg dog H (Study #12, Table 5). The drug was
infused into the brachialis vein through the indwelling catheter (Intracath, see
experimental) and plasma samples were collected from the contralateral brachialis
(#) and jugular veins (O) • The solid line represents the curve obtained by
fitting the plasma data to equation 50. The inset is the representation of the
data and the fitted curve for the initial 1200 min.

1W/5N
143

144
in about 60 min. These findings are demonstrated in the following in
vitro and in vivo studies.
In vitro studies. When 0.7562 mg/ml solution of buprenorphine in
normal saline was pumped through the catheter at the rate of 0.7026
ml/min for 1 h (31.88 mg total), the total amount of buprenorphine
recovered from the catheter by benzene extraction was 283 y g. When
buprenorphine solution (same rate and concentration as above) was passed
thorugh the catheter for 3 h (95.64 mg total), the total amounts of
buprenorphine recovered from the catheter by benzene extraction in two
studies were higher, i.e., 392 and 435 yg respectively. When normal
saline (45 drops/min) was passed through the catheter following 3 h of
the drug at the same concentration and infusion rate, 59 yg (15%) of
the catherter bound drug was recovered in the normal saline within 1
min. The total amount of burenorphine recovered in the saline in 60 min
was 394 yg, approximately the same as the amount recovered from the
catheter by benzene extraction. These results demonstrated that the
catheter-bound drug redissolved in the infused saline and was removed
from the catheter completely in about 60 min.
After passing a solution (0.7562 mg/ml) of buprenorphine in normal
saline through the catheter at the rate of 0.52 mg/min for 3 h, the drug
also repartioned into the fresh blood subsequently drawn through it (See
Fig. 45).
When buprenorphine (1 mg/ml in normal saline, 30 ml) solution was
passed in 30 s through the catheter to simulate an IV bolus
admininstration, there was no binding of the drug to the catheter as
demonstrated by the fact that no drug was recovered in subsequent
benzene extraction.

145
\
CD
2
Figure 45. Semilogarithmic plots of the plasma concentrations of
buprenorphine (as ng/ml of base) against time (min). Buprenorphine
dissolved in normal saline was passed through the catheter (Intracath,
see experimental) at the rate of 0.52 mg/min for 1 h (Fig. a) and 3 h
(Fig. b). The catheter was washed with 25 ml normal saline, fresh blank
bloods were drawn through the catheter and the plasmas were analysed.

146
Metabolite solution (100 y g/ml in normal saline), passed through
the catheter at the rate of 14 ml/min for 15 min did not show any
binding to the catheter. This was demonstrated by HPLC analysis
following acid treatment of the catheter.
In vivo studies. When the drug was intravenously infused for 3 h
into the dog, the normal saline drip was subsequently maintained for 24
h. Thus the minor fraction (0.4% of the dose) of the drug that was bound
to the catheter repartitioned into saline and eventually got into the
animal. Unfortunately however, when blood was drawn through the
catheter, the drug also repartitioned into the samples of small volumes
producing artifactually higher concentrations (see Figs. 45-47).
When blood was sampled from the brachialis vein upon infusion of
the drug through the plastic catheter into the jugular vein, the
post-infusion jugular vein plasma concentrations (Fig. 46, Table 4)
observed during the first 15 min of the post-infusion distributive phase
were significantly higher than the highest observed brachialis vein
plasma concentrations at the time of cessation of infusion. Similarly,
upon infusion of the drug through the plastic catheter into the left
brachialis vein, the situation was reversed, i.e., the post-infusion
left brachialis vein plasma concentrations during the first 15 min of
the post-infusion distributive phase were significantly higher than the
highest jugular and contralateral (right) brachialis vein concentrations
observed just before the cessation of infusion (Fig. 47). These results
demonstrated that the observed differences in post-infusion
buprenorphine concentrations in plasma obtained from different veins
were not due to any drug-induced changes in the circulatory physiology
of the dog, but were due to the repartitioning of the catheter-bound

Figure 46. Said logarithmic plots of the plasma concentrations (as ng/ml of base)
of buprenorphine plotted against time (min) following IV infusion of the drug into
the jugular vein. The points (O) and (#) represent the jugular and brachialis
vein plasma concentrations respectively of buprenorphine. a) 4.6885 mg/kg IV
infusion dose of buprenorphine in dog B, Study #7; b) 3.847 mg/kg IV infusion dose
of buprenorphine in dog D, Study #8; c) 4.8 mg/kg IV infusion dose of
buprenorphine in dog E, Study #9; d) 3.7408 mg/kg IV infusion dose of
buprenorphine in dog G, study #11. The solid lines represent the jugular vein
plasma data fitted to equation 50.

TW/9H 1U/3N
1U/3N 1U/9N
148

149
Figure 47. Semi1ogarithmic plots of the plasma concentrations of
buprenorphine (as ng/ml of base) against time (min) following constant
rate (0.5236 mg/min) infusion into the brachialis vein of dog H, Study
#12. The points (a,0) and (b, •) represent the concentrations of
buprenorphine in plasma obtained from jugular and contralateral
brachialis veins respectively. The points (â–¡) represent the
post-infusion plasma concentrations of buprenorphine obtained from
brachialis where the blood was drawn through the indwelling catheter
used in the infusion of the drug.

150
Table 4. Post-infusion jugular and brachial
vein concentrations of buprenorphine and M in
dog D.
Buprenorphine
Jugular
vein
Time
min
ng/ml
Brachial
vein
Time
min
ng/ml
1.21
5823
2.11
771
5.67
1871
5.44
595
19.6
836
21.24
383
46.2
483
48.2
282
75.28
649
77.3
232
120.8
317
123.3
214.3
182.7
346
184.7
160.8
298.5
251.3
302
107
Post-infusion jugular and brachial vein
concentrations of buprenorphine and
metabolite in dog D (Study #8) followed by
constant rate IV infusion of buprenorphine
base into the jugular vein at the rate of
0.5084 mg/min.

151
drug into the blood to produce artifactually higher levels of
buprenorphine in the plasma samples (drawn through the catheter used in
the infusion of the drug) during the first few minutes following
cessation of infusion.
Plasma pharmacokinetics of buprenorphine.
In studies 7-11, the brachialis plasma concentrations of
buprenorphine during and immediately after cessation of infusion were
considered as representative of the concentrations of buprenorphine in
the systemic circulation and were used in the fitting of buprenorphine
plasma data. The post infusion plasma concentrations from brachialis and
jugular veins (except for the first 4-5 jugular vein plasma
concentrations immediately following cessation of infusion) were
reasonably coincident (See Fig. 46). In study 12, where the drug was
infused through the catheter into the left brachialis vein, the plasma
concentrations of the drug monitored in the jugular vein (and
contralateral right brachialis vein) were practically coincident and may
be considered as representative of the buprenorphine concentrations in
the systemic circulation (Figs. 44,47).
Two compartment model. In studies 7,8, and 9 (Table 5), the
post-infusion plamsa concentrations of buprenorphine as a function of
53
time were fitted to a sum of two exponentials in accordance with
Cp = A e at + Be
Eg. 37
54
using the computer program of Yamaoka et. al., (Appendix I). The
plasma concentrations were weighted by their inverse values in the
fittings. The validity of the biexponential equation 37 was confirmed by
demonstration that regressions of the weighted residuals (calculated in

Table 5. Pharmacokinetics of buprenorphine and M in dogs upon IV infusion.
Parameter
Dog B
Dog D
Dog E
Dog F
Dog G
Dog H
Mean ± SEM
Study #
7
8
9
10
11
12
Dog No.
B344
W4123
R5108
RB535
R5107
BW485
kg (mg/min)a
0.5058
0.5084
0.5101
0.5288
0.5588
0.5236
T (min)*3
165
171
175
170
162
177
Dose (mg)
83.46
86.94
89.274
89.9
90.53
92.68
Weight, Kg.
17.8
22.6
18.6
22.0
24.2
24.2
Dose mg/kg
4.6885
3.847
4.80
4.0864
3.7408
3.83
Parameters from plasma data for buprenorphine.
104 p ' c
0.04
0.0491
0.039
0.0427 ± 0.003
10, v
0.901
0.65
1.104
0.335
0.301
0.4115
0.62 ± 0.13
106 Bf1
1.172
2.23
0.883
0.609
0.37
0.512
1.04 ± 0.28
10 7Td
0.345
0.107
2.667
1.04 ± 0.82
o
— —
— —
— —
(20)
(64.8)
(2.6)
(29 ± 19)
10 «
2.00
4.4
0.796
0.3426
0.294
0.3523
1.36 ± 0.66
A
(35)
(15.8)
(87)
(202)
(236)
(197)
(129 ± 39)
104 3
3.583
3.433
3.8
1.334
1.319
2.965
3.45 ± 0.18e
(1934)
(2019)
(1824)
(5195)
(5254)
(2337)
(2028 ± 110)8
103 P
—
— —
— —
0.0233
0.0103
0.1837
0.072 ± 0.06
f—J
O
1 ^
>
-h \
0.3086
0.49
0.2045
0.0442
0.038
0.0553
0.19 ± 0.075
105 Bf
0.1207
0.23
0.0913
0.0615
0.0371
0.0526
0.1 ± 0.03
10-5 AUC„ 9
1.00
1.00
1.11
0.83
0.72
1.1
10' AUCT-oo .
3.106
5.779
2.8605
5.08
3.95
2.7
10"5 AUCn 1
O-oo
3.912
5.72
4.19
3.66j
4.50
3.878
Residual plots
io2 e.k
1.1
-15
5.5
1.32
2.4
0.72
Slope
0.015±0.055
-0.03±0.09
0.14±0.13
0.019±0.083
0.025±0.1
0.01710.032
Intercept
-0.018±0.11
-0.09±0.17
-0.22±0.26
0.048±0.16
-0.025±0.2
0.024±0.06
152

Table 5. Continued. . .
Parameter
Dog B
Dog D
Dog E
Dog F
Dog G
Dog H
Mean ± SEM
Study #
7
8
9
10
11
12
Clearances
(ml/min)
CL . n
tot
213
152
213
246
201
239
211 ± 13.7
Cl— °
ren
0.40(9.5)
0.89(45)
0.13(-24)
1.0(-80)
—
—
0.61 ± 0.21
1->M p
met
—
—
182
261
220
—
221 ± 23
C1M ^
ren
1.6(11.5)
0.15(24)
2.3(1.04)
4.7(9.8)
—
—
3.5 ± 0.9
% Recoveries of buprenorphine and M in urine
UooVdoser
0.33
0.247
0.037
0.24
—
—
0.21 ± 0.06
UooM/doses
0.4733
0.7442
0.865
0.623
—
—
0.68 ± 0.08
Boo^/dose^
—
—
0.112
0.92
0.00
—
—
BooM/doseu
—
—
89.61
95.7
92.51
—
92.6 ± 1.76
Volumes of
distribution of buprenorphine
(L)
V V
c
31.1(31.2)
19.6(19.5)
47.1(47.1)
35.4(35.3)
69.6(69.1)
5.3(5.3)
34.7 ± 9.1
V
595
443
561
710X
580X
806
616 ± 52
a Dose in mg correspond to buprenorphine base. Administered as buprenorphine HC1 salt, dissolved in normal
saline.
Time of infusion in min.
c P'f, A'j and B' ^ are the intercepts at t=T obtained by fitting the post-inf us ion plasma data to equation
54
15 by nonlinear least square curve fitting using the computer program of Yamaoka et al. where plasma
concentrations were weighted by their inverse values. The intercepts are expressed as fractions of the total
dose per ml of plasma.
ci 1
Units for ir , a and 3 values are in min . Parenthetical values correspond to half-lives in min.
153

0
The mean and standard error of mean were computed for dogs B, D, E and G only. The mean ± SEM for dog F and G
were significantly different from the other four dogs. However, the terminal plasma data on these two dogs had
greater scattering (See Figs. 42,43) then the dogs B, D, E and G.
^ Af, Bf and values were calculated from the A, B and C values obtained from equations 16-18 and
expressed as fractions of the total dose Xq per ml of plasma.
^ The theoretical area under the plasma concentration-time curve of buprenorphine during the infusion phase
was calculated using equation 41 in dogs B, D and E. In dogs F, G and H, equation 52 was used.
Post-infusion area under the plasma concentration-time curve was obtained by integrating equation 15 between
T to oo, AUC^,^ = (P'/ ir) + (A'/ “ ) + (B'/ 8 ) .
1 The total area under the plasma concentration-time curve was calculated using the trapezoidal rule. This
area was used in the estimation of total body clearance and apparent volume of distribution of buprenorphine
(V.) in dogs.
-* In study #10, the calculated area by trapezoidal rule up to 1616 min was 260508 ng.min/ml. The quotient of
the plasma concentration of buprenorphine (38.2 ng/ml) at at 1616 min and the average terminal phase rate
constant (0.000345/min) was 105234 ng.min/ml. Thus the total area was estimated as 371233 ng.min/ml.
Mean of the weighted residuals calculated in accordance with the equation 3. None of the mean residuals were
statistically significantly different from zero.
1 m
' Slopes and intercepts of the plots of C against log fitted post-infusion data. The parenthetical values
correspond to standard errors. Both slopes and intercepts were not statistically significantly different from
zero, indicative of the fact that in dogs B, D and E, the sum of two exponentials and in dogs F and G, the sum
of three exponentials best fit the post-infusion plasma data of buprenorphine.
n Ratio of the infused total dose to the total area under the plasma concentration-time carve of
buprenorphine. The AUC^ was calculated using trapeziodal rule. The calculated total clearances in studies
7-12 were 203, 128, 225, 152, 194, 244 ml/min respectively which averaged 191 + 18 (SEM) ml/min.
° Estimates iron the slopes of the cumulative amounts of buprenorphine excreted ( EU, pg) renally against the
area under the plasma concentration-time curve of buprenorphine in accordance with the equation 30. These
ratios changed as pH of the urine changed. (See Fig. 57). Values given in parenthesis correspond to EU at
AUC=0 from the best linear plots of the data shown in Figs. 57,58.
^ Cl^e^M was calculated using equation 58.
^ C1M , the renal clearance of the plasma metabolite was calculated in accordance with the equation 30,
see afso Fig. 59.
154

r,s,t,u percen1- recoveries of buprenorphine and M in urine and bile obtained iron the quotient of the amounts
recovered in urine or bile and the total infused dose of buprenorphine.
v Apparent volume of distribution of the central compartment estimated by fitting the post-infusion data to
either equation 39 (2-compartment model) or 50 (3-compartment model) by nonlinear least square regression
(Appendix I). The values in parenthesis were calculated from equation 10, where the values of P, A and B were
obtained through equations 16-18. The mean and the standard error represents the volumes of distribution
estimated through equation 39 (or 50).
w Vj, the apparent volume of distribution of buprenorphine in the body was calculated from the ratio of
CW 6
x In dogs F, the average terminal phase rate constant (0.000345/min) rather than the estimated terminal rate
constant was used in the estimation of apparent volume of distribution.
155

156
accordance with the equation 3) against logarithm of the calculated
plasma concentrations gave mean residuals €, slopes and intercepts which
were not statistically significantly different from zero (Fig. 48, Table
5).
The parameters of the above sum of biexponential fits of the
post-infusion plasma data of buprenorphine are listed in Table 5 in
addition to the calculated parameters (equations 17,18) for an
equivalent IV bolus administration. The estimated average terminal
half-lives of buprenorphine were 1934, 2019, and 1824 min in dogs B, D
and E respectively. The estimated 95% confidence limits for the terminal
rate constants are given in Table 6.
The value of , the exit rate constant from the deep
. 53
compartment was calculated from the expression
k21 = (A 6 +Ba )/(A+B) Eq. 38
where A and B were obtained from equations 17,18.
For a drug conforming to a 2-compartment body model, the equation
that describes the time course of the drug in the central compartment
(k0/Vc) [ [ (k21 -a) (l-eaT)/a(ct-8)] e~at
+ [ ( 3 ~k21) (1-e PT )/ 8 (a -8 )] e" 3t ] Eq. 39
where T is the duration of infusion and t is the time after initiating
infusion in min. During infusion, T=t and upon cessation of infusion, T
becomes a constant equal to the time of infusion. In the above
expression, except for Vc, all the other constants are known. Thus it
is possible to obtain V , the volume of distribution of the central
compartment by fitting the post-infusion data with the above equation

Figure 48. Representative examples of the plots of the weighted residuals against
the logarithm of calculated plasma concentations. The weighted residuals were
calculated in accordance with eguation 3:
G = (Cpexp ~ ^calc* / ^calc
a) the post-infusion plasma data of buprenorphine administered by constant rate
(0.5058 mg/min) IV infusion for the 4.6885 mg/kg dose study in 17.8 kg dog B,
Study #7; b) the post-infusion plasma data of buprenorphine administered by
constant rate (0.5084 mg/min) IV infusion for the 3.847 mg/kg dose study in 22.6
kg dog D, Study #8; c) the post-infusion plasma data of buprenorphine administered
by constant rate (0.5288 mg/min) IV infusion for the 4.0864 mg/kg dose study in
22.0 kg bile cannulated dog F, Study #10; d) the post-infusion plasma data of
buprenorphine administered by constant rate (0.5588 mg/min) TV infusion for the
3.7408 mg/kg dose study in 24.2 kg bile cannulated dog G, Study #11. The observed
means, slopes and the intercepts of these weighted residuals are given in table 4.
These parameters were not statistically significantly different from zero as
confirmed by t-test. The random distribution of the residuals above and below the
regression line indicated no bias in the fitting of the chosen model.

RESIDUALS RESIDUALS
RESIDUALS RESIDUALS
158

Table 6. Statistics of total and metabolic clearances of buprenorphine.
Parameter
Dog B
Dog D
Dog E
Dog F
Dog G
Dog H
Mean ± SEM
Study #
7
8
9
10
11
12
Dog No.
B344
W4123
R5108
RB535
R5107
BW485
Statistics for
the terminal
rate constant.
B (ng/ml) a
103.4
117.3
58.88
71.86
55.76
51.62
104 3 b
3.529
2.9078
3.177
1.76
2.0644
3.0706
104 SE of B C
0.303
0.191
0.347
0.2524
0.410
0.10
d
n
11
11
11
14
16
14
104 Upper 3 e
4.21
3.34
3.96
2.31
2.946
3.289
104 Lower 3 e
2.84
2.476
2.393
1.21
1.183
2.853
bl/2 (min)
1964
2383
2181
3938
3357
2257
Upper
2437
2800
2896
5727
5860
2429
Lower
1646
2075
1750
3000
2352
2107
10-5 AUC, J
tot
Upper
5.01
5.869
4.70
7.75
6.774
4.01
Lower
3.83
4.644
3.735
4.913
3.953
3.766
Cl^^ ml/min ^
203
128
225
152
194
244
191 ± 18
Upper
218
187.2
239
183
229
246
Lower
167
148
190
116
134
231
Cl h
tot
213
153
213
246
201
239
211 ± 141
1->M j
182
261
220
221 ± 23
met
a'^Terminal phase intercepts (B, ng/ml) and rate constants (3 ) were estimated iron the semilogarithmic plots
of the terminal plasma data of buprenorphine against time.
Q
Standard error of the estimated terminal rate constant ( g).
:r of terminal phase plasma points used in the estimation of terminal rate constant.
U1
vo

e95% Confidence limits were calculated from the t-table at a=0.025 level of significance for (n-2) degrees
of freedom.
f In the estimation of total area under the plasma concentration of buprenorphine against time in accordance
with equation 10, the parameters P and A were obtained through equations 16 and 17. The parameters u anda
were obtained from the computer fit of the post-infusion data to equation 15. The parameters B and g were
obtained from the semilogarithmic plots of the terminal phase plasma data against time. The 95% confidence
intervals for AUC were obtained from the confidence limits estimated for the terminal rate constant assuming
no error in the P, A, ir anda values. See also discussion in the last section under the subheading "Validity
of the terminal rate constant".
^Total clearance was estimated iron the quotient of Dose/AUC where AUC was estimated from the
oo oo
plasma concentrations of buprenorphine. The 95% confidence limits for the total clearances were calculated
from the 95% confidence limits of the AUC values.
^The total clearances were calculated using trapezoidal rule.
xThe means and standard error of the means for the total clearances were calculated for the bile cannulated
dogs E, F and G only (The other dogs were not bile cannulated).
-*C1q , the biliary clearances of buprenorphine as metabolite were estimated from equation 58.
B
160

161
with one unknown parameter. Curve fittings of the infusion data to the
54
above equation using the computer program of Yamaoka et al. (Appendix
I) are given in Figs. 39-41 (See also Table 5). The apparent volumes of
distribution of the central compartment (V ) estimated by this
procedure were 31, 19.6, and 47.1 L respectively (Table 5). Vc was also
calculated from equation 10 where the values of the parameters A and B
(dose-normalized, shown in Table 5) were obtained through equations
17,18. The estimated apparent volumes of distribution of the central
compartment by this procedure were 31, 19.5, and 47.1 L respectively
which agreed with the above Vc values estimated by the computer fitting
of the post-infusion plasma data to equation 39.
Estimation of AUC. When the constants in equation 39 are simplified
into single constants, the following equation results during infusion:
Cp = R (e_ott -1) + S (e-Bt -1) Eq. 40
Integrating the above expression between 0 to T, the time infusion was
ended, gives:
AUC0_t = (R/d ) (l-e"at - t) + (S/e ) (1-e" 3t - t) Eq. 41
where
R = (k0/VJ [ (k21-a ) / a (a - B ) ] Eq. 42
and
S = (k0/Vc) [ (k21-e )/ 3(3-a)] Eq. 43
The post-infusion area (AUC^) under the plasma
concentration-time curve was obtained by integrating the equation 15
between (t-T)=0, the time when infusion was stopped, to time infinity
(oo),
AUC¿o = (A'/a ) + (BV 3)
Eq. 44

162
Thus, the total area is
AUC^ = AUCq_t (during infusion) + AUC^ (post-infusion) Eq. 45
These calculated areas are given in Table 5.
The total clearances, Cltot, calculated from the equation
Cltot = Dose/AUC^ were estimated as 213, 152 and 213 ml/min in dogs
B, D and E respectively (Table 5 and 6). The 95% confidence limits for
these clearances are reported in Table 6. The overall volumes of
distribution estimated from the equation 13 were 595, 443 and 561 L
respectively in dogs B, D and E, indicating high degree of sequestration
of buprenorphine into body tissues.
Three compartment model. In slow IV infusion studies 10, 11 and 12,
the post-infusion plasma concentrations of buprenorphine as a function
of time were fitted to a sum of three exponentials in accordance with
54
the equation 15 using the computer program of Yamaoka et. al.
(Appendix I, Figs. 42-44). The plasma concentrations were weighted by
their inverse values. The validity of the triexponential equation 15 was
confirmed by demonstration that regressions of the weighted residuals
(calculated in accordance with the equation 3) against logarithm of the
calculated buprenorphine plasma concentrations gave mean residuals £,
slopes and intercepts which were not statistically significantly
different from zero (Fig. 48, Table 5).
The parameters of the above sum of three exponential fits of the
post-infusion plasma data of buprenorphine are listed in Table 5 in
addition to the calculated parameters (equations 15-18) for an
equivalent IV bolus administration. The estimated terminal half-lives of
buprenorphine in the body were 5195, 5254 and 2337 min respectively in
dogs F, G and H (studies 10, 11 and 12 respectively). The terminal

163
plasma data in studies 10 and 11 were more widely scattered (Figs. 42,
43) than in studies 7, 8, 9 and 12 (Figs. 39-41,44). The terminal
half-lives estimated from the semilogarithmic plots of the terminal
plasma concentrations of buprenorphine against time (and their 95%
confidence limits in parenthesis) were 3938 (3000-5727) and 3357
(2352-5860) min respectively in dogs F and G (see also Table 6). The
estimated averaged first and second distributional half-lives were 29 +_
19 (SEM) min (studies 10, 11 and 12) and 129 _+ 39 (SEM) min (studies
7-12, see Table 5).
The values of k21 and k^, the respective exit rate constants
from the shallow and deep compartments were calculated from the
expressions'
53
k31 = 0.5 [
k21 = 0.5 [
-b-V(b2 - 4c)]
-b+ V(b2 - 4c) ]
where
b = - ( tt B+ tt A+ 3 P+8 A+ a p+ a B) / (P+A+B)
and
Eq. 46
Eq. 47
Eq. 48
Eq. 49
c = (ctiT b+t: 8 A+a 8 P)/(P+A+B)
where P, A and B values were obtained from equations 16-18.
For a drug conforming to a 3-compartment body model, the equation
that describes the time course of the drug in the central compartment
. 53
is
CP,
calc
(k0/Vc) C[ (k21 “ w ) (k3l _7r ) (l-e* T) /" ( a - it ) ( tt - 8 ) ]
[(k21 -a)(k31 -a)(l-ea T)/a(7r-a)(a-8)] e“at +
[(k21 - 8) (k31 -6 ) (1-e BT )/ 8 (a-8 ) (8 -tt )] e~6 t ] Eq. 50
where T is the duration of infusion and t is the time after initiating
-tt t

164
infusion in min. During infusion, T=t and upon cessation of infusion, T
becomes a constant equal to the time of infusion. In the above
expression, except for V , all the other constants are known. Thus it
is possible to obtain Vc , the volume of distribution of the central
compartment by fitting the post-infusion data with the above equation
with one unknown parameter. Curve fittings of the infusion data to the
54
above equation using the computer program of Yamaoka et al. (Appendix
I) are given in Figs. 41-43 (See also Table 5). The apparent volumes of
distribution of the central compartment (VJ estimated by this
procedure were 35.4, 69.6 and 5.3 L respectively for dogs F, G and H.
Vc was also calculated from equation 10 where the values of the
parameters P, A and B (Table 5) were obtained through equation 16-18.
The estimated apparent volumes of distribution of the central
compartment by this procedure were 35.3, 69.1 and 5.3 L respectively in
dogs F, G and H, which are in agreement with the above Vc values
calculated by the computer fitting of the post-infusion data to equation
50.
Estimation of AUC for plasma buprenorphine. When the constants in
equation 41 are simplified into single constants, the following equation
results during infusion:
Cp = Q (e“ 7Tt -1) + R (e_a 1 -1) + S (e“3 1 -1) Eq. 51
Integrating the above expression between 0 to T, the time infusion was
ended, gives:
AUCq_t = (Q / 7T ) (1-e" " 1 - t) + (R / a ) (l-e"a - t) +
- Bt
(S / 6) (1-e
t)
Eq. 52

165
where
Q = (k0/VJ [ (k21-TT ) (k31- TT ) / IT ( a -TT )(*-(? )]
R = (k0/vc) [(k21-a ) (k31-a ) / a (ir- a) (a - 3)]
Eq. 53
Eq. 54
and
S = (k0/Vc)[(k2l"3)(k3re ) / 3 («-3 ) ( 3-tt ) ]
Eq. 55
The post-infusion area under the plasma concentration-time curve
was obtained by integrating the equation 15 between (t-T)=0, the time
when infusion was stopped, to time infinity (oo),
AUCóo = (P'/17 ) + (A'/a ) + (B'/P )
Eq. 56
Thus, AUC = AUCfl^ + AUC' , and the calculated areas are given
in Table 5.
The total clearances, Cltot, calculated from the equation Cl^^
= Dose/AUC^ were 246, 201 and 239 ml/min (see also Table 5) for dogs
F, G and H respectively. The average total body clearance estimated for
all 6 dogs was 211 +_ 13.7 (SEM) ml/min (Table 5 and 6). The 95%
confidence limits for these clearances are reported in Table 6. This
value is lower than the total clearance obtained from IV bolus studies
(396 _+ 19 (SEM) ml/min, Table 2). Thus over estimation of Clt t value
in IV bolus studies could be attributed to the lack of sufficient number
of quantifiable terminal plasma points to obtain reasonable estimates of
terminal rate constant, and the derived total body clearance. The
overall volume of distribution V^ estimated from the equation 13 was
616 +_ 52 (SEM, n=6) L, indicating high degree of sequestration into body
tissues, consistent with the observations from IV bolus studies (434 L,
Table 2).
Plasma pharmacokinetics of the derived metabolite (M). The
brachialis and jugular vein plasma concentrations of buprenorphine

166
conjugate were apparently same in the post-infusion phase (Figs. 49-52).
Similar to the case of IV bolus administration of buprenorphine, where
the highest plasma concentration of the metabolite occured immediately
following the bolus dose, the highest plasma concentration of the
metabolite occured immediately after the cessation of infusion of
buprenorphine (Figs. 49-52). This is possible only when the hepatically
derived metabolite is so rapidly formed as well as eliminated from the
systemic circulation to mimic the buprenorphine concentrations in
plasma.
In all three bile cannulation studies (9-11), no detectable plasma
concentration of the metabolite was observed after 12 h following
initiation of infusion (duration of infusion = 165-175 min; see Figs.
51,52). However, when the bile catheter was removed at 26 h and the
screwcap (Fig. 1) was replaced, the bile to flowed normally into the
duodenum, and metabolite reappeared in the plasma (studies 9 and 11,
Figs. 51,52). This strongly indicates that the entero-hepatic
recirculation of the metabolite resumed when the bile was no longer
collected completely.
In dog G, buprenorphine conjugate (9.08 mg) was administered
intraduodenally and it appeared in plasma (Fig. 53). This provided
additional evidence for the enterohepatic recirculation of the
metabolite.
A minor fraction (6.2%) of the intraduodenally administered
metabolite was recovered in bile. Neither drug nor metabolite were
detectable in urine. These results confirmed the fact that the terminal
half-life of buprenorphine in a given dog would not be affected by bile
cannulation and complete bile collection.

Figure 49. Sard logarithmic plots of the experimental jugular vein (O) and
brachialis vein (#) plasma concentrations (ng/ml) of the hepatically derived
acid-hydrolyzable metabolite (M) against time (min) for the 4.6885 mg/kg IV
infusion dose of buprenorphine in dog B, Study #7. The inset is the representation
of the plasma concentrations of the metabolite up to 500 min.

IW-'SN
O
o
o
o
o
2nnn
o
o
, °
-f-
3Í1ÜG
O
luna
MIN
I
H-
‘inuu
]—gh
bnnü
168

Figure 50. Semi logarithmic plots of the experimental jugular vein (O) and
brachialis vein (•) plasma concentrations (ng/ml) of the hepatically derived
acid-hydrolyzable metabolite (M) against time (min) for the 3.847 mg/kg IV
infusion dose of buprenorphine in dog D, Study #8. The inset is the representation
of the plasma concentrations of the metabolite up tp 700 min.

170
HI W
[](]fJ9 UU8l> ÜÜ9C DIM DUG!

Figure 51. Semilogarithmic plots of the experimental jugular (O) and brachialis
(#) vein plasma concentrations (ng/ml) of the hepatically formed
acid-hydrolyzable metabolite (M) against time (min) for the 4.80 mg/kg IV infusion
dose of buprenorphine in dog E, Study #9. The solid line represents the curve
obtained by fitting the post-infusion data to the equation: C = Co exp(-kt) where
Co = concentration at time when infusion was stopped and k is the apparent first
order elimination rate constant. The middle inset represents the fitted
post-infusion plasma data up to 600 min, and the top inset is the brachealis (#)
plasma concentration of metabolite during infusion and post-infusion jugular vein
(O) plasma concentrations of metabolite. The experimental plasma points (0)
around 1200 min correspond to blood that were sampled but no metabolite was
detectable in plasma at the analytical sensitivity of 5 ng/ml.

IW'SN
MIN
172

Figure 52. Semi logarithmic plots of the experimental jugular vein (O) and
brachialis vein (0) plasma concentrations (ng/ml) of the metabolite (M) against
time (min) for the 3.7408 mg/kg IV infusion dose of buprenorphine in dog G, Study
#11. The experimental plasma points around 1200 min (0) correspond to blood that
were sampled, but no metabolite was detectable at the analytical sensitivity of 5
ng/ml.

174
MIN
□num nuns auns UDUt» muz
NG/tll

175
o
o
i
240 360
MIN
480 GOO
Figure 53. Semilogarithmic plot of the plasma concentrations of
buprenorphine glucuronide (ng/ml) plotted against time (min) following
intraduodenal administration of 9.08 mg of the metabolite to dog G.

176
Urinary excretion of buprenorphine and metabolite. Some examples of
sigma minus plots (equations 20-24) for buprenorpine and metabolite are
given in Figs. 54,55. Urinary excretion rate plots (logAU/ At versus
t-mid) were scattered, and only the examples which followed the equation
24 are presented in Fig. 56. The rate constants obtained from the slopes
of these plots are given in legends of figures 54-56. They corresponded
to the first and second distributional half-lives obtained from the
plasma data (Table 5).
Renal clearance of buprenorphine and metabolite. The renal
clearance of buprenorphine in dog E at 4.8 mg/kg dose showed a dramatic
pH dependency (Study #9, Fig. 57). The values of renal clearance for
buprenorphine and metabolite calculated from the slopes in accordance
with the equation 30 are given in Table 5 (See also Figs. 58,59). The
urine pH ranges were narrower in other studies (Appendix IV, Tables
A-TV-2b,4b,5b,7b,8b,10b). Thus any apparent pH effects on renal
clearance of buprenorphine in many could not be detected due to lack of
enough pH variability. The metabolite showed neither pH nor urine flow
dependent renal clearance (Fig. 60a,b). Buprenorphine clearance was not
urine flow dependent (Fig. 60c). These results were consistent with
those obtained from the IV bolus studies.
Biliary excretion of buprenorphine and metabolite. Analysis of
buprenphine conjugate excreted in bile by HPLC following acid hydrolysis
and g-glucuronidase hydrolysis (see experimental) gave identical
results (Fig. 61). In study #11, cumulative amounts of the conjugate
excreted in bile analysed by HPLC following acid and 3 -glucuronidase
hydrolysis respectively were 83.75 and 83.1 mg.

177
Figure 54. Semilogarithniic plots of the amounts of the unchanged
bupenorphine (1) remaining to be excreted in urine versus time (sigma
minus plot) in accordance with the equation 20. a) Semilogarithmic
fitting of the post-infusion urine data to a sum of two exponentials for
the 3.847 mg/kg IV infusion dose of buprenorphine to dog D (Study #8,
Table 5). The estimated hybrid rate constants were 0.0072/min (half life
= 96 min) and 0.000276/min (half life = 2507 min), b) Sigma minus plot
of the post-infusion urinary excretion of buprenorphine for the 4.8
mg/kg IV infusion dose of buprenorphine in dog E (Study #9, Table 5).
The apparent rate constant for this monoexponential fitting was
0.00036/min (half life = 1931 min ). These estimated rate constants
correspond with the rate constants obtained from the plasma data (Table
5) in these studies.

Figure 55. Semilogarithmic plots of the amounts of the metabolite (M) remaining to
be excreted in urine versus time (sigma minus plot) following IV infusion of
buprenorphine in accordance with equation 20. a) Sigma minus plot of metabolite in
urine of dog B (Study #7) following 4.6885 mg/kg IV infusion of buprenorphine,
resulting in an estimated apparent rate constant 0.0013/min (half-life = 553 min),
b) Sigma minus plot of metabolite in urine of dog D (Study #8) following 3.847
mg/kg IV infusion dose of buprenorphine. The estimated apparent rate constant was
0.00037/min (half-life = 1877 min), c) Sigma minus plot of the urinary excretion
of metabolite for the 4.8 mg/kg IV infusion dose of buprenorphine in dog E (Study
#9). The estimated apparent rate constant was 0.0034/min (half-life = 203 min), d)
Sigma minus plot of the urinary excretion of metabolite for the 4.0864 mg/kg IV
infusion dose of buprenorphine in dog F (Study #10). The data were fitted to a sum
of two exponentials in accordance with equation 20. The estimated apparent rate
constants were 0.00567/min (half-life = 122 min) and 0.00009/min (half-life = 7700
min) respectively.

$sr1 nx-*ni ssrf ni-
ib-ib jjss tu¿tu ues
IODO
H 1 1 1 1 1 1 1 *—I 1
6tm I2QQ I8ÃœQ 2*1(10 3000
MIN
179

Figure 56. Semilogarithmic plots of the amounts ( y g) buprenorphine
excreted in urine (a, b) and bile (c) per minute plotted against t-mid,
the mid point of the biological fluid collection interval, in accordance
with the reduced form of the equation (22):
Log aU/ At = (k'/2.303) t-mid + intercept
for a) 4.8 mg/kg IV infusion dose of buprenorphine in dog E (Study #9)
resulting in an estimated apparent rate constant of 0.0031/min
(half-life = 225 min); b) 4.6885 mg/kg IV infusion dose of buprenorphine
in dog B (Study #7) with an estimated apparent rate constant of
0.0157/min (half-life = 44.3 min); and c) dog E at the same above 4.8
mg/kg IV infusion dose of buprenorphine (Study #9), the biliary
excretion rate (ug/min) of buprenorphine could be fitted to a sum of two
exponentials resulting in apparent rate constants of 0.031/min
(half-life = 22.2 min) and 0.0028/min (half-life = 251 min)
respectively.

DlvDT JjG'MN OU/DT JJG'MIN DU/OT pG'MIN
181

Figure 57. Plots of cumulative amounts ( E U, y g) of buprenorphine excreted in
urine against the area under the plasma concentration time curve (AUCt,
y g.min/ml) in accordance with the equation (28):
Z U = Cl (AUC AUCn )
ren ' t O'
where AUCg is the area under the plasma concentration-time curve at £ U=0. For the
4.8 mg/kg IV infusion dose of buprenorphine in dog E (Study #9), the plot showed
four distinctly linear segments attributable to the pH effect on renal clearance
of buprenorphine. The renal clearance of buprenorphine estimated from the slope of
the linear segment for the pH range between 6.14-6.39 (inset) was 0.134 ml/min.

I6Ü 2‘IN
^UCT JJG X MIN / ML
-inn
8U
32n
183

Figure 58. Plots of the cumulative amounts ( IU, yg) of buprenorphine
excreted in urine against area under the plasma concentration-time curve
at the time of urine collection in accordance with the equation (28):
ZÜ = Clren (AUCt - AUC0 )
where AUCp is the area under the plasma concentration-time curve at E U
= 0. a) For the 4.6885 mg/kg IV infusion dose of buprenorphine in dog B
(Study #7), the clearance estimated from the initial slope was 0.37
ml/min; b) For the 3.847 mg/kg IV infusion dose of buprenorphine in dog
D (Study #8), the estimated renal clearance was 0.9 ml/min for the
initial period up to 600 min; c) For the 4.0864 mg/kg IV infusion dose
of 1 in dog F (Study #10), the estimated clearance was 1.0 ml/min for
the urine collection time between 200-800 min.

sgrfm . ssrí rn sarfnx
185

Figure 59. Plots of the cumulative amounts ( eU, yg) of metabolite (M) excreted in
urine against area under the plasma concentration-time curve at the time of urine
collection in accordance with the equation (28):
EU = Clren (AUCt - AUC0 )
where AUCq is the area under the plasma concentration-time curve atEU = 0. a)
For the 4.6885 mg/kg IV infusion dose of buprenorphine in dog B (Study #7), the
clearance estimated for the time period 100-1800 min was 5.36 ml/min; b) for the
3.847 mg/kg IV infusion dose of buprenorphine in dog D (Study #8), the estimated
renal clearance for the initial period up to 12000 min was 1.714 ml/min; c) For
the 4.8 mg/kg IV infusion dose of 1 in dog E (Study #9), the estimated renal
clearance from the initial slope was 2.33 ml/min; d) For the 4.0864 mg/kg IV
infusion dose of buprenorphine in dog F (Study #10), for the time period between
200-500 min the renal clearance of metabolite estimated as 21.2 ml/min, and
between 600-1400 min the clearance was 1.5 ml/min.

ssrf ra ssrt nz
sarf nz ssrf n3
187

Figure 60. Plots of renal clearance (ml/min) of buprenorphine and metabolite (M)
against urine flow (ml/min) and pH. The renal clearances were calculated from the
quotient of the urinary excretion rate ( aU/ At, p g/min) and plasma concentration
of buprenorphine or metabolite (ng/ml) at the mid-point of urine collection
interval. The slopes and the respective standard errors are: a) For the 4.6885
mg/kg TV infusion dose of buprenorphine in dog B (Study #7), the estimated slope
of the plot of renal clearance of metabolite versus urine flow (ml/min) was 0.064
+_ 0.3. b) For 3.847 mg/kg IV infusion dose of buprenorphine in dog D (Study #8),
the slope of the plot of renal clearance of metabolite versus pH was -0.25 +_ 1.2.
c) In dog E (Study #9), at 4.8 mg/kg IV infusion dose of buprenorphine, the slope
of the plot of the renal clearance of buprenorphine versus urine flow was -0.1 _+
0.1. These slopes were not statistically significantly different from zero as
confirmed by t-test.

ClREN «.✓MIN
O
O
z
Ckr
O
o.5n T
6.35
fi..
5.25--
4.50 ..
3.35..
3 --
2.25--
1.5(1 - -
.35 - -
8,
o o
â– 4 1 h
o
o
o
.. D.
O O
o °
O o
o o
o
6.U8Q
6.36
H 1 1 h
PH
6.64
6.32
--O.
O
1
3.20
189

Figure 61. Plots of the cumulative amounts (IBM, mg) of buprenorphine conjugate
excreted in bile of dog G (Study #11) at 3.7408 mg/kg IV infusion dose of
buprenorpine. The conjugate amounts were estimated by HPLC separation and
fluorimetric detection of demethoxybuprenorphine (3) obtained after acid
hydrolysis (O) of the buprenorphine conjugate and by HPLC separation and
fluorimetric detection of buprenorphine obtained after g -glucuronidase hydrolysis
(â–¡) of the buprenorphine conjugate. The cumulative amounts of the buprenorphine
conjugate obtained by these two different hydrolysis techniques were 83.75 (O)
and 83.05 (â–¡) mgs respectively.

12H IÜ8LI M4Í1 I Bill]
MIN
ZBM MG
c:
I6T

192
Sigma minus plots of the biliary excretion of the unchanged
buprenorphine (Studies 10,11, Fig. 62) and hepatically formed metabolite
(Studies 9,10,11, Fig. 63) are from the data obtained during the entire
bile collection period (26 h). These plots were apparently linear
(except study #11, Fig. 63c). The estimated apparent half-lives are
reported in the figure legends. These half-lives corresponded to the 2nd
distributional half-lives of buprenorphine in plasma (Table 5).
Biliary clearance of buprenorphine and metabolite. In bile
cannulated dogs E, F and G, the percentages of the total doses excreted
in bile as unchanged buprenorphine were 0.112, 0.92 and 0.00
respectively (Table 5). The biliary clearances of buprenorphine were
estimated from the plots of the cumulative amounts of the unchanged
buprenorphine excreted in bile against the areas under the plasma
concentration-time profile of buprenorphine in plasma in accordance with
the equation
IB = Cl^ [AUCt - AUCq] Eq. 57
where AUCq is the area under the plasma concentration-time curve of
buprenorphine when IB=0. In the bile cannulated dogs E and F (Fig. 64,
Table 5), the estimated biliary clearances for unchanged buprenorphine
were 0.16 and 3.2 ml/min respectively.
In the bile cannulated dogs E, F and G, the average of the total
dose excreted in bile, assayed as acid hydrolyzable conjugate (M) of
buprenorphine, was 92.6 +_ 1.8 % (SEM) (See Table 5). This is in contrast
to morphine, where 20% of the dose was excreted in the bile of dogs as
45
morphine glucuromde.
Since a minor fraction of the hepatically formed metabolite was
excreted in urine, the term in equation 32 can be neglected. Thus

193
IDO:
CT
=1
CCT
UJ
Figure 62. Semilogarithmic plots of the amounts of buprenorphine
remaining to be excreted in bile versus time (Sigma minus plot)
following IV infusion of buprenorphine in accordace with equation 20. a)
Sigma minus plot of buprenorphine in bile of dog E (Study #9) following
4.8 mg/kg IV infusion dose of buprenorphine. The estimated apparent
elimination rate constant was 0.0032/min (half-life = 220 min), b) Sigma
minus plot of buprenorphine in bile of dog F (Study #10) following
4.0864 mg/kg IV infusion dose of buprenorphine. The estimated apparent
rate constant was 0.002/min (half-life = 340 min). See also Table 5.

Figure 63. Semi logarithmic plots of the amounts of the hepatically
formed metabolite (M) remaining to be excreted in bile versus time
(Sigma minus plot) following IV infusion of buprenorphine in accordace
with equation 20. a) Sigma minus plot of metabolite in bile of dog E
(Study #9) following 4.8 mg/kg IV infusion of buprenorphine, resulting
in an estimated apparent elimination rate constant of 0.0038/min
(half-life = 181 min). b) Sigma minus plot for the biliary excretion of
metabolite in dog F (Study #10) following 4.0864 mg/kg IV infusion of
buprenorphine. The estimated apparent elimination rate constant was
0.0029/min (half-life = 241 min), c) Sigma minus plot of metabolite in
bile of dog G (Study #11) upon IV infusion of 3.7408 mg/kg dose of
buprenorphine. Estimated apparent excretion rate constant was 0.0026/min
(half-life = 268 min).

195

196
Figure 64. Plots of the cumulative amounts (E B, y g) of buprenorphine
excreted in bile against the area under the plasma concentration-time
curve (AUCt , yg.min/ml) at the time of urine collection interval in
accordance with the equation:
E B = Clg [AUCt - AUCq ]
where AUCq is the area under the plasma concentration-time curve of
buprenorphine at E B=0. a) For the 4.8 mg/kg IV infusion dose of
buprenorphine in dog E (Study #9), the estimated biliary clearance of
buprenorphine was 0.16 ml/min. b) For the 4.0864 mg/kg IV infusion dose
of buprenorphine in dog F (Study #10), estimated biliary clearance was
3.24 ml/min.

197
equation 32 can be written as
B
m
1->M
= Cl- ' AUC - V m
met t m p
Eq. 58
where B is the cumulative amount of metabolite (M) collected in bile,
Cl^e^M = apparent metabolic clearance of buprenorphine as M, AUCfc
= area under the plasma concentration-time curve of buprenorphine at
time t, Vm is apparent volume of distribution of the metabolite and m^
is the metabolite concentration in plasma. Thus the apparent metabolic
clearance, C1^^M of buprenorphine as M can be estimated by
multiple linear regression of the cumulative amounts of the hepatically
formed metabolite (M) excreted in bile against the area under the plasma
concentration-time curve of buprenorphine and the corresponding
metabolite concentration in plasma. For dogs E, F and G, these apparent
metabolic clearances obtained from the equation 58 were 182, 261 and 220
ml/min (Fig. 65, Table 5 where areas were calculated using trapezoidal
rule) and the apparent volumes of distribution of the metabolite were
13.6, 281 and 67.6 L respectively. Plots of A B/ At against •
the plasma concentrations of either buprenorphine or the metabolite were
usually scattered. Some examples are given in Fig. 66.
Minor metabolites in bile. Three additional peaks that could be
assigned to minor metabolites in the bile were observed in the
chromatograms of the bile samples from dogs E, F and G (studies 9-11).
Typical chromatograms obtained after acid and 3-glucuronidase enzyme
hydrolysis of bile are presented in Fig. 67.
Norbuprenorphine rearranges in acid to form
demethoxynorbuprenorphine. When bile was analysed by HPLC following acid
hydrolysis, the peak with the lowest retention time had the same

Figure 65. Plots of the cumulative amounts ( IBM, yg) of the
hepatically formed metabolite M excreted in bile against time (min). The
solid lines represent the cumulative amounts of the metabolite excreted
in bile calculated in accordance with equation 58 where the metabolic
clearance of the parent compound and the apparent volume of the
distribution of the metabolite were estimated from the multiple linear
regression of the cumulative amounts of the conjugate excreted in bile
against area under the plasma concentration-time curve of the parent
compound and the meatbolite concentration in plasma, a) Dog E at 4.0864
mg/kg IV infusion dose of buprenorphine, Study #9; b) Dog F at 4.0864
mg/kg IV infusion dose of buprenorphine, Study #10; c) Dog G at 3.7408
mg/kg IV infusion dose of buprenorphine, Study #11. The estimated
metabolic clearances wre 182, 261 and 220 ml/min and the apparent
volumes of distribution of the metabolite were 13.6, 281 and 67.6 L
respectively.

XBfljJGS IBM UGS
199

Figure 66. Plots of excretion rate ( Au/ At, p g/min) of either buprenorphine or
metabolite (M) excreted in bile or urine against the plasma concentration of
buprenorphine or M (ng/ml) in accordance with equation 26. a) For the 3.847 mg/kg
IV infusion dose of buprenorphine in dog D (Study #8), the estimated renal
clearance of buprenorphine was 0.8 ml/min. b) For the 3.7408 mg/kg IV infusion
dose of buprenorphine in dog G (Study #11), biliary clearance of metabolite was
estimated as 1146 ml/min. c) For the 4.8 mg/kg IV infusion dose of buprenorphine
in dog E (Study #9), apparent biliary clearance of buprenorphine as hepatically
eliminated metbolite was estimated as 184 ml/min. d) In the same study #9, biliary
clearance of buprenorphine as unchanged drug was estimated as 0.22 ml/min.

DB/DT (JG/P1IN OBM/OT jJG'MN
400
360 _.
32tl -.
280
2*10..
2110 - .
160 - -
120
80
40
4-0
£
h 1 1 1 1 y
60 120 180
M T-MID CNG/MLJ
'O
201

Figure 67. The chromatographic peaks corresponding to 1, 4, 5 and 6 are
the aglycones generated from the conjugated metabolites following
3-glucuronidase hydrolysis (l=buprenorphine; 4=norbuprenorphine;
5,6=unknown metabolites). The chromatographic peaks 3, 7, 8, 9 and 10
correspond to rearranged aglycones generated after acid hydrolysis of
the conjugated metabolites (3=demethoxybuprenorphine;
7=demethoxynorbuprenorphine; 8=rearranged aglycone of conjugated
metabolite 5; and 9,10 are the two rearrangement products presumably
generated from the aglycone (6) upon acid hydrolysis, a) Chromatograms
obtained after 8-glucuronidase hydrolysis of buprenorphine and other
minor metabolite conjugates. The peaks 1 and 4 correspond to the
aglycones buprenorphine and norbuprenorphine respectively. The peaks 5
and 6 correspond to aglycones of unknown minor metabolites, b) The
standard chromatogram of bile spiked with norbuprenorphine (4, 60 ng/ml)
and buprenorphine (1, 60 ng/ml). c) Chromatograms obtained after acid
hydrolysis of conjugates of buprenorphine and other minor metabolites
(3=demethoxybuprenorphine; 7=demethoxynorbuprenorphine; 8,9 =acid
rearrangement products of the aglycones (5 and 6) generated from the
conjugates of these minor metabolites). d) The peaks 4 and 5 from the
chromatogram (a) were collected by HPLC separation and subjected to acid
hydrolysis. The resulting hydrolysed products were chromatographed by
HPLC separation and flúorimetric detection (7=demethoxynorbuprenorphine;
8=acid rearranged product of the minor metabolite 5 generated from the
respective conjugate). e) Standard chromatogram of
demethxoynorbuprenorphine (7) obtained after acid hydrolysis of bile
spiked with 50 ng/ml of norbuprenorphine (4). f) The peak 6 from
chromatogram (a) was collected by HPLC separation and subjected to acid
hydrolysis. The resulting solution was chromatographed by HPLC
separation and flúorimetric detection. This gave two peaks 9 and 10.

203

204
retention time as a reference standard of demethoxynorbuprenorphine (see
Fig. 67 and the legend). Norbuprenorphine was not observed in bile
before acid or enzymatic hydrolysis. These results indicate that the
aglycone norbuprenorphine generated following enzymatic hydrolysis or
the rearranged demethoxynorbuprenorphine generated after acid hydrolysis
were presumably derived from the conjugate of norbuprenorphine. These
findings were confirmed (see Fig. 67) by acid and 3-glucuronidase
hydrolysis using a standard sample of norbuprenorphine (obtained front
Reckitt & Colman Co., Kingston-Upon-Hull, England). The other two
unidentified minor metabolites were hypothesized to be conjugates as
they were extractable from the bile only after acid hydrolysis. None of
the minor metabolites were detectable in plasma or urine
(norbuprenorphine detection limit, 5 ng/ml).
Plots of the cumulative amounts of the minor metabolites collected
in bile are shown in Figs. 68-70. In these plots, the cumulative amount
"til
of the 1 1 metabolite was estimated from the expression:
N
h-Z
j=i
(PHRi X DF X V)
Eg. 59
where Pffit is the peak height ratio of the i^ metabolite
(buprenorphine was the internal standard), DF is the dilution factor, V
is the volume of bile collected at each interval, and N is the number of
bile samples. The total amounts of the norbuprenorphine collected in
these studies (9-11) were 0.936, 0.744 and 1.07 mg respectively. Thus
the percentage of the total dose excreted in bile as norbuprenorphine
conjugate were 1, 0.83 and 1.2 respectively.

Figure 68. Plots of the cumulative amounts of the minor acid hydrolyzable
conjugates of buprenorphine, norbuprenorphine conjugate, 4, (O), conjugates of
unknown metabolites, 5, (â–¡) and 6 (|\>) excreted in bile against time for the 4.8
mg/kg IV infusion dose of buprenorphine (Study #9) in dog E. Ai's of the left
ordinate represent the summation of PHR X DF X V where PHR = peak height ratios
obtained by acid hydrolysis, HPLC separation followed by flúorimetric detection of
these minor metabolites using buprenorphine as internal standard; DF= dilution
factor; V = volume of bile excreted during a bile collection interval. (See also
Fig. 67 for these chromatograms). Calibration curve using norbuprenorphine as
internal standard gave the actual amounts of the acid hydrolyzable conjugate of
norbuprenorphine (4) excreted in bile. The right ordinate represents these
cumulative amounts of the norbuprenorphine conjugate, 4, (O) excreted in bile in
mg.

8GGD_
1.00
O O
e b
H-
960
O O O O
.. 0.75
g B B B
0.50
I 1 h
0.25
I28G I6GQ
206

Figure 69. Plots of the cumulative amounts of the minor acid hydrolyzable
conjugates of buprenorphine, norbuprenorphine conjugate, 4, (O)/ conjugates of
unknown metabolites, 5, (â–¡) and 6 ((\>) excreted in bile against time for the
4.0864 mg/kg IV infusion dose of buprenorphine (Study #10) in dog F. Ai's of the
left ordinate represent the summation of PHR X DF X V where PHR = peak height
ratios obtained by acid hydrolysis, HPLC separation followed by fluorimetric
detection of these minor metabolites using buprenorphine as internal standard; DF
dilution factor; V = volume of bile excreted during a bile collection interval.
(See also Fig. 67 for these chromatograms). Calibration curve using
norbuprenorphine as internal standard gave the actual amounts of the acid
hydrolyzable conjugate of norbuprenorphine (4) excreted in bile. The right
ordinate represents these cumulative amounts of the norbuprenorphine conjugate, 4
(O) excreted in bile in mg.

208

Figure 70. Plots of the cumulative amounts of the minor acid hydrolyzable
conjugates of buprenorphine, norbuprenorphine conjugate, 4, (O)t conjugates of
unknown metabolites, 5, (â–¡) and 6 (t\) excreted in bile against time for the
3.7408 mg/kg IV infusion dose of buprenorphine (Study #11) in dog G. Ai's of the
left ordinate represent the summation of PHR X DF X V where PHR = peak height
ratios obtained by acid hydrolysis, HPLC separation followed by fluorimetric
detection of these minor metabolites using buprenorphine as internal standard; DF
dilution factor; V = volume of bile excreted during a bile collection interval.
(See also Fig. 67 for these chromatograms). Calibration curve using
norbuprenorphine as internal standard gave the actual amounts of the acid
hydrolyzable conjugate of norbuprenorphine (4) excreted in bile. The right
ordinate represents these cumulative amounts of the norbuprenorphine conjugate, 4
(O) excreted in bile in mg.

210

211
The sigma minus plots for these minor metabolites in terms of the
amounts are shown in Fig. 71. These plots were apparently linear
during the bile collection period. The apparent rate constants estimated
from these plots are given in figure legends. These rate constants were
similar among the minor metabolites and also corresponded with the rate
constant obtained from the sigma minus plot of the major metabolite (see
Fig. 63 and the legend). These results indicate parallel conjugation of
all the metabolites in the liver.

Figure 71. Sard logarithmic plots of the theoretical amounts of the minor
metabolites (norbuprenorphine, O; unknown metabolites, â–¡ and tb )
against time, a) The estimated apparent rate apparent rate constants in
accordance with equation 20 were 0.0027/min (O)/ 0.0034/min (â–¡), and
0.0036/min (11s) in dog E at 4.8 mg/kg IV infusion dose of buprenorphine
(Study #9). b) In dog F at 4.0864 mg/kg IV infusin dose of
buprenorphine, the estimated apparent rate constants were 0.0023/min
(O) f 0.0025/min (â–¡) and 0.002/min ((\). c) In dog G at 3.7408 mg/kg IV
infusion dose of buprenorphine, the estimated apparent rate constants
were 0.0021/min (O)f 0.0019/min (â–¡), and 0.0021/min (bj . Note the
correspondence of these rate constants with the rate constants obtained
for the major metabolite M in respective studies (see legend for Fig.
63).

213
's.~
-O,
XD
ti.
â–¡
—I
I6QQ
1440

PHARMACOKINETICS OF THE IV ADMINISTERED METABOLITE
Semilogarithmic plots of plasma concentrations of the metabolite
against time after 7 and 8.5 min constant rate infusion of the
metabolite in studies 13 and 14 in dogs F and G respectively are shown
in Figures 72,73 (Table 7). Dog G was bile cannulated and the bile was
collected up to 22 h in this dog (Study #14).
The post-infusion plasma concentrations of the metabolite were
fitted to a sum of three exponentials in accordance with equation 15
54
using the computer program of Yamaoka et. al. (Appendix I). The
plasma concentrations were weighted by their inverse values. The
validity of the triexponential equation 15 was confirmed by
demonstration that regressions of the weighted residuals (calculated in
accordance with the equation 3) against the logarithm of the estimated
concentrations of the metabolite gave mean residuals C, slopes and
intercepts which were not statistically significantly different from
zero (Fig. 74, Table 7).
The parameters of the sum of three exponentials that best fit the
post-infusion plasma data of buprenorphine are listed in Table 7. In
addition, the calculated parameters (equations 15-18) for an equivalent
IV bolus administration are given. The terminal half-lives of the IV
administered metabolite were 392 and 319 min respectively in dogs F and
G (Studies 13,14). The estimated average terminal half-life of the
metabolite in plasma following IV administration of the parent drug was
1846 min (Table 2). The fact that terminal half-life of the IV
214

Figure 72. Semilogarithmic plots of the concentrations (ng/ml) of intravenously
administered buprenorphine conjugate (M, metabolite) in plasma against time (min)
for the 1.889 mg/kg dose in the 20.2 kg non-bile cannulated dog F (Study #13,
Table 7). The solid line represents the curve obtained by fitting the experimental
plasma data to equation 50. The inset is the representation of the data and the
fitted curve for the initial 650 min.

1W/SN
216

Figure 73. Semilogarithmic plots of the concentrations (ng/ml) of the
intravenously administered buprenorphine conjugate (M, metabolite) in plasma upon
constant rate (1.7738 mg/min) IV infusion of the conjugate plotted against time
(min) for the 0.5153 mg/kg dose in 24.2 kg bile-cannulated dog G (Study #14, Table
7). The solid line represents the curve obtained by fitting the experimental
jugular vein plasma data to equation 50. The inset is the representation of the
data and the fitted curve for the initial 500 min.

1W/SN
MIN
28Ü
I I2Ü
M[1U
218

219
Table 7. Pharmacokinetics of TV administered Metabolite.
Parameter
Dog F
Dog G
Study #
13
14
Dog No.
RB535
R5107
kQ (mg/min)a
T (min)b
4.4944
1.7738
8.49
7.03
Dose (mg)
38.16
12.47
Weight, Kg.
20.2
24.2
Dose mg/kg
1.889
0.5153
Parameters from plasma data for the metabolite.
104 P'£C
4.32
1.80
105 A'
106 B'f
8.12
3.00
4.80
5.00
10 2 ^
5.78
17.0
9
(4)
(12)
10z a
1.19
2.8
(25)
(58)
10° 6
1.77
2.2
(319)
(392)
104 P, e
105 A
106 B
5.47
8.53
3.01
3.06
5.27
5.04
10' AUC. 1
10-5 AUC° 9
8.22
1.17
6.1
0.632
T-oo
Residual plots
102 0. h
2.2
0.9
Slope1
0.00640.02
0.00150.03
Intercept-1
0.040.07
0.00630.06
Clearances (ml/min)
Cl ^
1-1 tot
55(54-55)
166(162-176)
ciM 1
ren
23(93)
31(18)
P1M m
U1B
—
151n
% Recoveries of the metabolite in urine and bile.
UooM/dose°
38 9.5
BooM/dose^
— 91.3
Volumes of
distribution of the metabolite (L).
V *
c
1.75(1.6) 2.75(2.75)
V
31 76.5

220
Table 7. Continued . . . .
a Dose in mg corrospond to buprenorphine conjugate assayed by acid
hydrolysis followed by HPLC separation and fluorimetric detection.
Time of infusion in min.
Q
P'f, A'f, and B'^ are the intercepts obtained by fitting the
post-infusion plasma data to equation 15 by nonlinear least square curve
fitting using the computer program of Yamaoka et al. (Appendix I) where
plasma concentrations were weighted by their inverse values. The
intercepts are expressed as fractions of the total dose per ml of
plasma.
^ Unit for it , a and 3 values is min . Parenthetical values corrospond
to half-lives in min.
Pft Aand values were calculated using equations 16-18 and
expressed as fractions of the total dose per ml of plasma.
The theoretical area under the plasma concentration-time curve of
buprenorphine during the infusion phase was calculated lasing equation
52.
^ Post-infusion area under the plasma concentration-time curve was
obtained by integrating equation 15 between T to oo, AUC- =
(P'/tt ) + (A1 / a ) + (B'/ 3). 1-00
Mean of the weighted residuals calculated in accordance with the
equation 3. None of the mean residuals were statistically significantly
different from zero.
1,-) Slopes and intercepts of the plots of 6 against log fitted
post-infusion data. The parenthetical values corrospond to standard
errors. Both slopes and intercepts were not statistically significantly
different from zero, indicating that the sum of three exponentials best
fits the post-infusion plasma data of buprenorphine conjugate.
Ratio of the infused total dose to the total area under the plasma
concentration-time curve of buprenorphine conjugate. The AUC was
calculated from equations 52 and 56. The values in parenthesis
correspond to 95% confidence limits.
1 Estimates from the initial slopes of the cumulative amounts of
buprenorphine conjugate excreted ( £U, yg) renally against the area
under the plasma concentration-time curve of the conjugate in accordance
with the equation 30. Values in parenthesis corrospond to EU at AUC=0
from the best linear plots of the data shown in Figs. 77,78.
m Clg was calculated from a plot of the cumulative amount of the
conjugate excreted in bile against the area under the plasma
concentration time profile of the conjugate.

221
Table 7. Continued . . . .
This biliary clearance was calculated from the expression, f.Cl ,
where f is the fraction of the dose excreted in bile. The biliary
clearance, estimated from a plot of the cumulative amounts of the
systemic metabolite excreted in bile was 300 ml/min, see Fig. 77d. This
clearance estimted from the initial slope was bile flow dependent (Fig.
79a).
°'p Percent recoveries of the conjugate in urine and bile obtained from
the quotient of the amounts recovered in urine or bile and the total
infused dose of the conjugate.
^ Apparent volume of distribution of the central compartment estimated
by fitting the post-infusion data to equation 50 by nonlinear least
square regression (Appendix I). The values in parenthesis were
calculated from equation 10, where the values of P, A and B were
obtained through equations 16-18.
r V. was calculated from the ratio of Cl. , / r
d tot v

222
Figure 74. Plots of the weighted residuals against the logarithm of the
calculated plasma concentrations. The weighted residuals were calculated
in accordance with equation 3:
6 = ( ^exp “ ^calc5 / ^calc
a) The residuals calculated for the post-infusion jugular vein plasma
data of buprenorphine conjugate (M, metabolite) administered by constant
rate (4.4944 mg/min) IV infusion for the 1.889 mg/kg dose study in 20.2
kg non-bile-cannulated dog F (Study #13, Table 7); b) The residuals
calculated for the post-infusion jugular vein plasma data of
buprenorphine conjugate (M, metabolite) administered by constant rate
(1.7738 mg/min) IV infusion for the 0.5153 mg/kg dose in 24.2 kg
bile-cannulated dog G (Study #14, Table 7). The observed residual means,
slopes and intercepts were not statistically significantly different
from zero as confirmed by t-test. The random distribution of the
residuals above and below the regression line indicated no bias in the
fittina of the chosen model.

223
administered metabolite was shorter than the hepatically derived
metabolite supports the hypothesis that the rate-determining step for
metabolite elimination on buprenorphine administration is not the
elimination of the metabolite. The slowest process, the rate of return
of the drug from the deepest tissues, must be the rate determining step
in overall disposition of the drug and the hepatically derived
metabolite.
The volumes of distribution of the central compartment V , were
obtained by fitting the post-infusion data to equation 50 using the
54
computer program of Yamaoka et.al. (Appendix I, see also Figs.
72,73). The values of Vc estimated by this procedure were 1.72 and 2.75
L in dog F and G (Studies 13, 14) respectively. The V was also
estimated from equation 10, where the values of the parameters P, A and
B were obtained through equations 16-18. The estimated apparent volumes
of distribution of the central compartment by this procedure were 1.6
and 2.75 L respectively in dogs F and G (Studies 13 and 14).
The estimated total clearances (Cltot =Dose/AUCoo, see equations
51-56 for AUC estimations) for the metabolite were 55 and 166 ml/min
respectively in dogs F and G (Studies 13 and 14). The 95% confidence
limits for these clearances are reported in Table 7. The overall
apparent volumes of distribution of the metabolite in the body estimated
in accordance with equation 13 were 31 and 76.5 L respectively in dogs F
and G (Studies 13 and 14).
Urinary and biliary excretion of the metabolite. The sigma minus
plots (equations 20-24) for the metabolite excretion in bile and urine
are given in Fig. 75 and the estimated apparent rate constants are
reported in the figure's legend. Metabolite excretion in bile had an

Figure 75. Semilogarithmic plots of the buprenorphine conjugate (M,
metabolite) remaining to be excreted in bile/urine versus time (sigma
minus plot) in accordance with equation 20. a) Semilogarithmic fitting
of the post-infusion urine data to a sum of two exponentials for the
1.889 mg/kg IV infusion dose of the metabolite in the
non-bile-cannulated dog F (Study #13, Table 7). The estimated hybrid
rate constants were 0.0229/min (half-life = 30 min) and 0.0012/min
(half-life = 578 min). b) Sigma minus plot of the post-infusion biliary
excretion of the metabolite for the 0.5153 mg/kg IV infusion dose of the
metabolite in the bile-cannulated dog G (Study #14, Table 7). The
apparent rate constant for this monoexponential fit was 0.0051/min
(half-life = 139 min). In the same dog G, the sigma minus plot of the
post-infusion urinary excretion of the metabolite could be fitted to a
sum of 2 exponentials. The estimated hybrid rate constants were
0.0216/min (half-life = 32 min) and 0.005/min (half-life = 141 min).

sari sari' wai-^ua 3 sari um-"Vinz
225

226
estimated apparent rate constant of 0.05 min 1 (half-life = 140 min),
an intermediate value between second distributional and terminal
half-lives obtained from the plasma data (See Table 7). Urinary and
biliary excretion rate plots were scattered; the two examples which
followed equation 24 are given in Fig. 76. The rate constants obtained
from these plots are reported in the legends of figures 75 and 76. They
corresponded to the second distributional and terminal half-lives
obtained from plasma data (See also Table 7).
Renal and biliary clearances of the metabolite. The percentages of
the total intravenously administered conjugate dose excreted in urine
were 38 and 9.5% respectively in dog F (Study #13, non-bile cannulated)
and dog G (Study #14, bile cannulated). In dog G, the percentage of the
metabolite excreted in bile was 91.3. About 80% of the administered
metabolite was recovered in the bile of dog G (Study #14) within the
first 2 h. This is in constrast to the pharmacokinetics of the
intravenously administered morphine glucuronide which was solely
. . 45
eliminated in the urine.
Biliary and renal clearance plots for the intravenously
administered conjugate in bile and urine are shown in Figs. 77 and 78
for dogs F and G (Studies 13 and 14) respectively. The plots for dog G
showed two distinctly different linear segments (Fig. 77 c,d). The
biliary and urinary clearances of the metabolite estimated from the
initial slopes were 300 and 31 ml/min respectively. However the
clearances estimated from the expression (f.Cltot) where f is the
fraction of the dose excreted through a given elimination route, the
biliary and urinary clearances in dog G were 151 and 16 ml/min
respectively. The higher biliary and urinary clearances of the

227
Figure 76. Semilogarithmic plots of the excretion rate (A BM/A t or
AU/ At) of the buprenorphine conjugate (M, metabolite) plotted against
t-mid, the mid point of the biological fluid collection interval in
accordance with equation 24. a) For 0.5153 mg/kg IV infusion dose of the
metabolite in dog G (Study #14, Table 7), the biliary excretion data was
fitted to a sum of three exponentials. The estimated hybrid rate
constants were 0.0213/min (half-life = 33 min), 0.0079/min (half-life =
88 min) and 0.0021/min (half-life = 330 min). See also Table 7 for the
correspondence of these estimated rate constants to those obtained from
plasma data, b) In the same dog G (Study #14), the urinary excretion
data for the metabolite was fitted to a sum of two exponentials. The
estimated hybrid rate constants were 0.0215/min (half-life = 32 min) and
0.004/min (half-life = 173 min).

Figure 77. Plots of the cumulative amounts (z BM, z U, y g) of the intravenously
infused buprenorphine conjugate (M, metabolite) in accordance with equation 30. a)
For 0.5153 mg/kg IV infusion dose of the metabolite in the bile-cannulated dog G
(Study #14, Table 7) the apprent urinary clearance of the conjugate estimated from
the initial slope was 31 ml/min. b) In the same dog G (Study #14), the biliary
clearance estimated from the initial slope was 300 ml/min. c, d) Complete profiles
of the clearance plots for the metabolite in urine and bile respectively in dog G
(Study #14).

sari uai sari uaz
229

230
Figure 78. Plot of the cumulative amount of the intravenously infused
buprenorphine conjugate (M, metabolite) excreted in urine against the
area under the plasma concentration-time curve in accordance with
equation 30. For the 1.889 mg/kg IV infusion dose of the conjugate in
the non-bile-cannulated dog F (Study #13, Table 7), the estimated
urinary clearance of the metabolite was 23 ml/min.

231
metabolite during the initial period (upto 4 h) was attributable to the
bile and urine flow dependent biliary and urinary clearances of the
metabolite (see Fig. 79a,b). However, urinary clearance was not pH
dependent (Fig. 79c).
The clearances estimated from the plots of the urinary or biliary
excretion rates against the plasma concentration of the metabolite at
the mid-point of the biological fluid collection interval (Fig. 80)
corresponded with the clearanaces estimated from the sigma minus plots
(See figure legends 77,78 and 80).
Oral Bioavailability of Buprenorphine in Dogs.
Buprenorphine is almost completely hepatically metabolized in dogs.
First pass metabolism is ancitipated upon oral administration. The
amount, A, of the orally administered dose Xg, that eventually reaches
the systemic circulation unchanged is:
A = (1-f. )
ípm
f X-
a 0
= f.X„
Eg. 60
where f. is fraction of the dose eliminated by first-pass metabolism
ípm
before reaching the systemic circulation, f is fraction of the dose
administered that is absorbed unchanged and f is the fraction of the
dose that eventually reaches the systemic circulation intact. The
equation 60 is valid if there is no saturable first-pass liver
metabolism and no gut wall metabolism. Since buprenorphine showed
dose-independent pharmacokinetics in the dose range studied, the total
body clearance of the drug administered IV is
Cl
IV
tot
= XÍ7 / AUCIV
0 oo
Eq. 61
For the same drug administered orally, assuming that there is not gut

Figure 79. Plots of the apparent biliary/urinary clearances of the
buprenorphine conjugate (M, metabolite) against bile/urine flow and
urine pH. The apparent urinary/biliary clearances were calculated from
the quotient of the excretion rate and the plasma concentration of the
metabolite at the mid point of the biological fluid collection interval.
The respective slopes and intercepts are: a) For the 0.5153 mg/kg IV
infusion dose of the conjugate in the bile-cannulated dog G (Study #14,
Table 7), the estimated slope of the plot of the biliary clearance
against bile flow was 5276 +_ 212. This was statistically significant
slope as confirmed by t-test. b) In the same dog G (Study #14), the
estimated slope of the plot of the urinary clearance against the urine
flow was 5.2 +_ 1.3. This slope was also statistically significant as
confirmed by t-test. c) In the same dog G (Study #14) the slope of the
plot of urinary clearance against pH was -15 +_ 5.5 which was not
statistically significant.

6.24 6.68 1.12 1.56
CL REN ML/MIN
CL REN ML/MIN
CL 811 E ML/MIN
— — bjLOLjtkXkincn
oiNjcD-HdcnMaoAO
-I 1 1 1 k 1 1 1 1 1
/ O
o
o

o
O '
o o
o
-3
0
6
\
4?
o
o
— - MuicjAAincn
tnpoco.azacnr'jcnxiO
— — N N) N) U U ^
a a>KjmcaAa>£jjr>:n
oaoociaocicia
CD
C*
-U
ci¬
en
CD
co
r -i
m
o
a. _i
r~ ro
\
u
CT.
CD
m
-4 1 1 1 1 1 1 1 1 1
\
o
A
Óv
U» '
\o
0)
O V
'P
ro
uj
oj
83.88

Figure 80. Clearance plots of the amounts of the buprenorphine conjugate
(M, metabolite) excreted in urine or bile per unit time against the
plasma concentration of the metabolite at the mid point of the
collection interval, a) For the 1.889 mg/kg IV infusion dose of the
metabolite in the non-bile cannulated dog F (Study #13, Table 7), the
estimated urinary clearance was 14.3 ml/min. b) The urinary clearance of
the metabolite in dog G (Study #14) was estimated as 36 ml/min. c) In
the same dog the biliary clearance plot showed curvature. The values
outside the parenthesis correspond to the instantaneous biliary
clearance and values within the parenthesis correspond to the mid point
of the bile collection interval in min.

Niw/3fí iQ/na n!u/3(1 iQ/na Niu/ort^Wraa
235
2D
16
18
M
12
ID
8
6
O /
/
/ O
/
/
/
“"(3
«£-
34 D
b
H 1 1
68Q ID2D
M T-HID NG^ML
—I—
13RD
O
—I
HDD
2CD T
16C - _
I6D..
140..
120..
IQ0--
80--
60--
40 - -
O 322.59(46.6)
O 396.8(83.9)
C
20-- 0 258.7(114.7)
<*£-
+
340
S8G
1020
M 7-M!0 NG'HL
105.8(12) O
—I 1 1
1360 1000

236
wall metabolism and no saturable first-pass metabolism
Eq. 62
Since total body clearance is the same irrespective of the route of
administration, equations 61 and 62 can be equated and on rearrangement,
the fraction of the dose that eventually reaches the systemic
circulation is
.oral
X™ AUC°r*
0 oo
f = (1-f. ) f = —-—T-
lpm a Yoral
0
Eq. 63
.IV
oo
Plots of the plasma concentration-time profile of buprenorphine and
conjugate are presented in Fig. 81 for dog B and D following 84.7 and
87.11 mg oral doses of buprenorphine respectively. In dogs B and D
(Study #15,16), the apparent bioavailability f of buprenorphine
estimated in accordance with equation 63 (Table 8) were 6 and 3.7%
respectively.
If the following assumptions are valid, i.e., a) the drug is
eliminated from the body virtually completely by hepatic metabolism, b)
there is no gut wall metabolism, c) there is no saturable first-pass
metabolism, d) when the drug is delivered to the liver through either
portal vein or hepatic artery, the extent of first-pass metabolism is
the same, and e) a constant fraction of the hepatically derived
metabolite reaches the systemic circulation, then the areas under the
plasma concentration-time curves of the metabolite obtained after oral,
AUC^(©ral)' 311(1 IV administration, AUC^, of the parent
compound can be compared to estimate the fraction of the dose absrobed
unchanged:

Figure 81. Semilogarithmic plots of the plasma concentrations of buprenorphine (a,
c) and metabolite (b, d) against time following oral administration of
buprenorphine. a) Buprenorphine in plasma following 84.7 mg oral dose of
buprenorphine in in dog B, study #15. b) Metabolite in plasma in the dog B in the
same study (#15). c) Buprenorphine in plasma following 87.11 mg oral dose
buprenorphine in dog D, study #16. d) Metabolite in plasma in dog D in the same
study (#16).

238
TU/9N
1U/3N
1U/3N
1U/9H

239
Table 8. Oral bioavailability of buprenorphine.
Parameter
Dog B
Dog D
Study #
15
16
Dog No.
B344
W4123
Weight, Kg.
17.8
22.6
TV Dose (mg)
83.46
86.94
Oral Dose (mg)
84.7
87.11
Areas under the plasma
concentration-
-time curve.
IV a
AUC
oo
391290
572107
AUC0ral
OO
23706
21207
AUC^
1(IV)
163454
370001
AUCi(oral)
16549
74289
f b
0.06
0.037
f C
a
0.1
0.2
f. d
ípm
0.40
0.82
The areas under the plasma concentration-time curve up to the last
observed plasma point were measured by the trapezoidal rule. The areas
from the last observed plasma sampling time to infinity were estimated
from the ratio of the last plasma concetration and g , where g was
estimated from the semilogarithmic plot of terminal plasma
concentrations against time following IV administration. Same g values
were used for the AUC estimations of the metabolite concentrations in
plasma. Unit for area: ng.min/ml.
Fraction of the absorbed dose that eventually reaches the systemic
circulation unchanged,
c
Fraction of the orally administered dose absorbed unchanged (that is
delivered to the liver intact). The values were estimated in accordance
with equation 64.
Fraction of the absorbed drug that undergoes first pass metabolism
(Eg. 65).

240
f
a
= Aüdf, ,,
1(oral)
xf /
AUC^
C1(IV)
.oral
‘O
Eq. 64
Thus the calculated percentages of the dose absorbed were 10 and 20
respectively in dogs B and D (Study #15,16, Table 8), and the fractions
of the doses cleared by first-pass metabolism before reaching the
systemic circulation, estimated in accordance with the equation
f. = 1 - (f/f ) Eq. 65
lpm v a' ^
were 40 and 82% respectively in dog B and D (Study #15,16). The extent
of first pass metabolism estimated from the ratios of the total body
clearance and hepatic blood flow (360-400 ml/min in a 20-kg dog^)
were 0.6 and 0.43 in dogs B and D. This contradiction may be explained
by one or more of the above assumptions not being valid. Studies with
37 38
rat gut preparations ' have demonstrated gut wall metabolism of
buprenorphine. Thus any significant gut wall metabolism would
overestimate the first-pass metabolism calculated in accordance with
equation 65.

SUMMARY AND CONCLUSIONS
The pharmacokinetic dispositon of buprenorphine in dogs can be
adequately described by a 3-compartment body model (Figs. 4-9).
Buprenorphine readily distributes into shallow and deep compartments
following rapid IV bolus injection. The proper estimations of the
terminal rate constants and the total body clearances were not feasible
following acute IV bolus (0.7-2.6 mg/kg, studies 1-6) doses of
buprenorphine. This was attributed to the analytical sensitivity which
did not permit estimations of buprenorphine plasma concentrations below
5 ng/ml. The fact that doses (1.2-2.6 mg/kg) of buprenorphine
administered in the first 5 IV bolus studies exhibited significant side
effects gave an upper limit to the maximal IV bolus dose that could be
administered. To minimize initial peak plasma concentrations of
buprenorphine and the associated side effects, buprenorphine was
administered to six dogs (studies 7-12) by slow IV infusion which
delivered larger amounts of the drug to the animal and provided adequate
number of quantifiable terminal plasma concentrations.
Buprenorphine was shown to bind to the plastic material of the
indwelling catheter used in the slow infusion of buprenorphine into the
veins of dogs. This resulted in artifactually higher levels of
buprenorphine in blood samples drawn through the same catheter
immediately following cessation of infusion. This necessitated drawings
of blood from a different vein (vena brachialis or jugularis) for the
time intervals during-infusion as well as post-infusion.
241

242
The estimated terminal half-lives and the derived total body
clearances from these IV infusion studies averaged 2080 _+ 110 min (SEM,
n=4) and 212 +_ 10 ml/min (SEM, n=6) respectively.
Only a minor fraction (<0.5%) of the intravenously administered
buprenorphine was eliminated unchanged in the urine. There was no renal
clearance when urine pH was above 7.2 (Fig. 57). Assuming that only the
unionized buprenorphine (pKa' = 8.24) can undergo renal tubular
reabsorption, then lower renal clearance can be anticipated at higher pH
values. This is supported by the fact that in dog B (study #3) and dog E
(study #9), no drug was observed in the urine at pH values above 7.3,
indicating complete tubular reabsorption of buprenorphine at these
higher pH values. However, since such small fractions of buprenorphine
are excreted in urine, therapeutic acidification of urine is not a valid
measure of counteracting narcotic toxicity due to accidental overdosage.
Also, changes in the renal clearance due to pH variability would not
have significant effects on the dose-independent pharmacokinetics of
buprenorphine. The renal clearance of buprenorphine was not urine flow
dependent.
The dose-normalized plasma concentrations were superimposable
(0.7-4.8 mg/kg IV bolus and infusion doses, Figs. 11-14), demonstrating
dose-independency in the dose range studied.
Buprenorphine conjugate was the only metabolite detectable in
plasma. The plasma concentration-time data of this metabolite paralleled
the the plasma concentration-time data of buprenorphine (Fig. 15).
Following IV bolus administration of buprenorphine, the highest plasma
concentrations of the metabolite occured within 2 min (Fig. 15). In TV
infusion studies, the highest concentrations of the metabolite occurred

243
immediately after the cessation of infusion of buprenorphine (Figs.
49-52) and were coincident with the maximal buprenorphine concentrations
in plasma. The parallel decays of buprenorphine and the conjugate in
plasma (Fig. 15) during the distributive phase indicated that the rate
determining step in the plasma decay of the conjugate is the rate of
return of the drug from the shallow compartment. Similarly during the
terminal elimination phase, the rate determining step in the plasma
decay of both buprenorphine and its metabolite is the slow return of
buprenorphine from the deep compartment to the central compartment where
it could be metabolized.
In bile cannulated dogs (studies 9-11), no detectable plasma
concentrations of the metabolite were observed after 16 h following
initiation of infusion. However, when the bile catheter was removed at
26 h and the screwcap (Fig. 1) was replaced, the bile flowed normally
into the duodenum and the metabolite reappeared in plasma. This strongly
indicated entero-hepatic recirculation. Upon intraduodena1
administration of the buprenorphine conjugate, it appeared in plasma,
providing further evidence for the entero-hepatic recirculation of the
metabolite. In the same study, a minor fraction (6.2%) of the
intraduodenally administered metabolite was recovered in bile as
conjugate. Free buprenorphine was not detected in plasma, but observed
in small amounts in urine. These results confirmed that the
entero-hepatic recirculation of buprenorphine conjugate would have
negligible effects on the terminal half-life of buprenorphine.
The fraction of the IV administered buprenorphine that was
recovered as conjugate in the bile of dogs (E, F and G) averaged 92.6 +_
1.8 % (SEM). About 0.7% of the IV administered buprenorphine was

244
recovered in urine as conjugate. A minor fraction (<0.5%) of the
administered buprenorphine was recovered unchanged in the bile of dogs E
and F (studies 9, 10). This may be due to the enzymatic hydrolysis of
the conjugate in bile. No free buprenorphine was detected in the bile of
the third dog (study #11).
Three additional HPLC peaks that could be assigned to minor
metabolites were observed in the chromatograms of the bile samples.
These were hypothesised to be conjugates since they were extractable
from the bile only after acid or enzymatic hydrolysis. When the bile was
analysed by HPLC following acid hydrolysis, the peak with the lowest
retention time (Fig. 67) had the same retention time as a reference
standard of demethoxynorbuprenorphine. Norbuprenorphine rearranges in
acid to form demethxoynorbuprenorphine. Norbuprenorphine was not
observed in bile before acid or enzymatic hydrolysis. These results
indicated that the aglycone generated following enzymatic hydrolysis, or
in fact, the rearranged demethoxybuprenorphine generated after acid
hydrolysis were presumably derived from the conjugate of
norbuprenorphine.
Pharmacokinetics of intravenously administered buprenorphine
conjugate conformed to a 3-compartment body model (Scheme II). The
terminal plasma half-lives estimated in two studies were 5.25 and 6.5 h
respectively (in dogs F and G, studies 13 and 14). The estimated average
terminal half-life of the conjugate in plasma following TV bolus
administration of buprenorphine was 31 h (Table 2). The fact that the
terminal half-life of the IV administered metabolite was shorter than
the hepátically formed metabolite (following IV administration of
buprenorphine) confirmed the hypothesis that the slowest process, the

245
rate of return of buprenorphine from the deep compartment, must be the
rate determining step in the overall disposition of the hepatically
formed metabolite.
In one study (dog G, study #14), the percentage of the IV
administered metabolite excreted in the bile was 91.3%. About 80% of the
IV administered metabolite was recovered in bile within the first two
hours. These results are in contrast to the pharmacokinetics of
intravenously administered morphine glucuronide which was solely
. . 45
eliminated in the urine.
The total body clearances estimated from the ratios of the doses of
the drug to the total areas under the plasma concentration-time curve of
buprenorphine averaged 220 ml/min in the bile cannulated dogs E, F and
G. The metabolic clearances of buprenorphine estimated in accordance
with equation 58 averaged 220 ml/min in these three dogs (Table 5). The
estimated biliary clearances of the intravenously administered
metabolite in dogs F and G were 32 and 151 ml/min respectively (Table
7). In all studies, the plasma metabolite data following the IV
administration of the parent compound paralleled the buprenorphine
plasma data (Figs. 39-44, 49-52). These results led to the hypothesis
that when buprenorphine was delivered to the liver hepatocytes through
the hepatic artery or portal vein, the conjugate formed at the initial
stages of buprenorphine transit through the liver presumably reaches
rapid equilibration with the systemically circulating metabolite. As the
drug is transported deeper into the liver tissues, the formed metabolite
is presumably "trapped" in these hepatocytes. Thus the metabolite can no
longer partition into the systemic circulation and can be conceived as
being susceptible to direct biliary excretion. The fraction of the

246
hepatically formed metabolite that reaches the systemic circulation was
estimated from the ratios of the areas under the plasma metabolite
concentration-time curve following IV administration of the metabolite
and the parent compound. The estimated percentages of the hepatically
formed metabolite reaching the systemic circulation were 6 and 12%
respectively in dogs F and G. This is in contrast to morphine
45 ...
pharmacokinetics where 30-70% of the hepatically derived metabolite
reaches the systemic circulation.
Buprenorphine is almost completely hepatically metabolized in dogs.
First pass metabolism is anticipated upon oral administration. The
extent of the first-pass metabolism estimated from the ratios of total
body clearance and the hepatic plasma flow (360-400 ml/min in a 20-kg
dog~^) averaged 0.59 +_ 0.09 (SEM) in studies 7-12. Thus about 60% of
the drug was cleared during one pass through the liver. The absolute
bioavailability of buprenorphine estimated from the areas under the
plasma concentration-time curve following oral and IV administrations
were 6 and 3.7% respectively in dogs B and D (studies 15 and 16). This
low bioavailability was attributed to poor absorption rather than
first-pass metabolism.

APPENDIX I
PROGRAM "MULTI"
1 DIM TU(50),CU(50),PH(50),VOL(50)
10 PRINT"* MULTI-LINES FITTINGS *"
20 PRINT:PRINT"DEFINE EQUATIONS AT 1000,1100,1200,1300,1400":PRINT
30 PRINT "CP AND T ARE DEPENDENT AND INDEPENDENT VARIABLES."
35 PRINT:PRINT"P(1), P(2),.... ARE PARAMETERS TO FIT."
36 PRINT:PRINT TAB(8);"GCTO 840 IF DIVERGED.":FP=0
37 DIMME$(3):ME$(0)="GAUSS-NEWTON":ME$(1)="DAMPING GAUSS-NEWTON"
38 ME$ (2) ="MARQUARDT" :ME$ (3) ="SIMPLEX"
40 PRINT:FORI=0 TO 3:PRINT"(";I;") ";ME$(I);" METHOD":NEXT
45 PRINT:INPUT"WHICH ALGORITHM DO YOU SELECT";AL
49 PRINT:PRINT"* I BELIEVE YOU HAVE DEFINED EQUATIONS *"
50 INPUT"SUBJECT NAME";N$
51 PRINT"INPUT FILE NAME";: INPUT F$
52 OPEN"I",#l,F$
54 INPUT"NUMBER OF LINES" ;IN:DIMNL (IN)
55 INPUT"WEIGHT OF DATA (0,1,2)";IW:INPUT"NUMBER OF PARAMETERS";M
56 PORI=lTOLN: PRINT "NUMBER OF POINTS ("; I; ") ";: INPUT#1, NL (I) : NEXT
57 INPUT#1,N2
60 N=0:FORI=lTOLN:N=N+NL(I) :NEXT:DIMTX(N) ,CV(N) ,A(M,M+1) ,P(M) ,X(M,M)
65 NL(0)=0:BS=0:FORJ=lTOIN:BS=BS+NL(J-l):PRINT
70 POR I=lTONL(J):PRINT"T";J;"(";I;"), CP";J;"(";I;")";:INPUT#1, TX(BS+I), CV(
BS+I)
75 NEXT I,J:IF AL=3 THEN 3000
76 FORI=lTCN2:INPUT#l,TU(I),CU(I),PH(I),VOL(I):NEXTI
77 PC=.0001:CF=100:IF FP=0 THEN DIMCS(N,M):FP=1
78 PRINT:INPUT"DT FOR JACOBIAN (0.1-0.0001)";DT:PRINT:FOR I=lTOM
80 PRINT"INITIAL P(";I;")=";:INPUT#1, A(I,0):P(I)=A(I,0):NEXT:CLOSE#1:GOSUB 40
00:S1=SS
140 PRINT "INITIAL SS=";SS:PORK=lTOlOO:GOSUB 7000:GOSUB 7400:GOSUB 6000:JJ=0
490 JJ=JJ+1:IF JJ>25 THEN 730
500 FOR 1=1 TO M:P(I)=A(I,0)+A(I,M+1):NEXT:GOSUB 4000
510 DS=ABS(Sl-SS):IF AL<>2 OR SS=0 THEN 590
520 FW=0:FOR I=1TOM:PW=PW4X(I,0) *A(I,M+1) 4CF*A(I,NB-1) *A(I,M+1) :NEXT
530 IF DS/PW>.75 THEN CF=CF/2
540 IF DS/PW<.25 THEN CF=5*CF
590 IF DS<=PC*Sl THEN 730
600 IF AL=1 AND SS>Sl THEN FOR 1=1 TO M:A(I,M+1)=.5*A(I,M+1):NEXT:GCTO 490
630 FOR 1=1 TO M:A(I,0)=P(I):NEXT:Sl=SS:PRINT:PRINT"LOOP=";K
640 IF AL=1 THEN PRINT "DAMP=";JJ
660 FOR 1=1 TO M:PRINT"P(";I;")=";P(I):NEXT:PRINT"SS=";SS:NEXT
730 REM CHANGE TO PRINTER
731 PRINT#-2:PRINT#-2,"*";N$;"* BY ";ME$(AL);" METHOD":PRINT#-2,"WEIGHT=1/CP«(
";IW;")"
733 IF AL<>3 AND N>M THEN GOSUB 8000
734 IFSS=0 THEN PRINT"AIC=-INFINITE":GOTO 740
735 PRINT"AIC=";N*LOG(SS)+2*M
740 IF AL=3 THEN PRINT"ALPHA=";AA;" BETA=";BB;" GAMMA=";CC:PRINT
742 IF AL<>3 THEN PRINT"DT=";DT
247

248
745 IF AL=2 THEN PRINT"FACTOR=";CF
750 FORI=lTOM:PRINT#-2,"FINAL P";I;"=";P(I);
760 IF AL<>3 AND X(I,0)>0 AND N>M THEN PRINT#-2," S.D.=";SQR(X(I,0)*SS/(N-M)
);
810 PRINT#-2:NEXT:PRINT#-2,"FINAL SS=";SS:BS=0:PORJ=lTO LN:BS=BS+NL(J-l)
820 PRINT#-2:F0RI=1T0NL(J):T=TX(BS+I):ON J GOSUB 1000,1100,1200,1300,1400
830 PRINT#-2,"T";J;"=";T;" CP";J;"=";CP;" (";CV(BS+I);")":NEXTI,J
840 PRINT:PRINT"WHICH ALGORITHM DO YOU SELECT?"
850 INPUT"(0,1,2,3 OR -1)";AL:IF AL<0 THEN END
860 IF AL=3 THEN 3000
870 GOTO 77
1000 CP=P(1)*EXP(-P(2)*T)+P(3)*EXP(-P(4)*T)+P(5)*EXP(-P(6)*T):RETURN
1100 CP=(P(1)*P(2)/(P(2)-P(3)))*(EXP(-P(3)*T)-EXP(-P(2)*T)):RETURN
2000 FORJS=lTOM:PT=P(JS) :P(JS)=FT+DT:ON J GOSUB 1000,1100,1200,1300,1400
2020 DD=CP:P(JS)=PT-DT:ON J GOSUB 1000,1100,1200,1300,1400
2030 CS(BS+I,JS)=(DD-CP)/(2*DT):P(JS)=PT:NEXT:RETURN
3000 AA=1:BB=.5:CC=2:SG=1E10:PC=.00001
3025 PRINT:FORI=lTOM:PRINT"INITIAL P (";I; ") ";:INPUT A(I,1) :NEXT
3030 FOR J=2 TO MPl:POR 1=1 TO M:A(I,J)=2*RND(1)*A(I,1)+.01*(RND(l)-.5):NEXT I
,J
3040 FORK=l TO M+l:FORI=lTOM:P(I)=A(I,K):NEXT:GOSUB 4000:A(0,K)=SS:NEXT
3070 PRINT:FOR 1=1 TO M+-1:PRINT"SS";I; "=";A(0,I) :NEXT:GCTO 5000
3080 SR=0:SL=1E10:FORJ=lTOM+l:IF SR 3090 IF SL>A(0,J) THEN JL=J:SL=A(0,J)
3100 NEXT:SR=0:FOR J=1 TO M+1:IF JOJH AND SR 3110 NEXT:FOR I=1TOM:X(0,I)=0:FOR J=1 TO M+1:IF JOJH THEN X(0,I)=X(0,I)+A(I, J
)
3120 NEXT:X(0,I)=X(0,I)/M:NEXT:POR 1=1 TO M:A(I,0) = (1+AA) *X(0,I)-AA*A(I,JH)
3130 P(I)=A(I,0):NEXT:GOSUB 4000:SR=SS:IF SR<=A(0,JS) THEN 3300
3160 IF SR 3170 FOR 1=1 TO M:A(I,0)=BB*A(I,JH)+(1-BB)*X(0,I)
3180 P(I)=A(I,0):NEXT:GOSUB 4000:SR=SS
3190 IF SR 3200 FOR K=1 TO M+l:FORI=l TO M:A(I,K) = (A(I,K)+A(I,JL) )/2:P(I)=A(I,K) :NEXT
3210 GOSUB 4000:A(0,K)=SS:NEXT:GOTO 3070
3300 IF SR 3320 FOR 1=1 TO M:A(I,JH)=A(I,0):NEXT:A(0,JH)=SR:GCTO 3070
3500 FORI=1TOM:X(1,I)=CC*A(I,0)+(1-CC)*X(0,I):P(I)=X(1,I):NEXT:GOSUB 4000:SI/=S
S
3510 IF SL 3520 GOTO 3320
4000 SS=0:BS=0:FOR J=1 TO LN:BS=BS+NL(J-l):FOR 1=1 TO NL(J):T=TX(BS+I)
4020 ON J GOSUB 1000,1100,1200,1300,1400:SS=SS+(CV(BS+I)-CP)-2/CV(BS+I)*IW
4030 NEXT I,J:RETURN
5000 SR=0:FOR 1=1 TO M+l:SR=SR+A(0,I):NEXT
5030 IF ABS(SR-SG)>PC*SG THEN SG=SR:GOTO 3080
5040 FOR 1=1 TO M:P(I)=A(I,JL):NEXT:SS=A(0,JL):GCTO 730
6000 IF NP=1 THEN A(1,2)=A(1,2)/A(1,1):RETURN
6020 RM=ABS(A(1,1)):FOR IS=1 TO NP:FOR JS=1 TO NP
6050 IF RM
249
6060 NEXT JS,IS:FOR KS=1 TO NP-1:W=0:FOR IS=KS TO NP
6100 IF ABS (A(IS,KS)) 6110 W=ABS(A(IS,KS)):JS=IS
6130 NEXT:IF JS=KS THEN 6200
6150 FOR IS=KS TO NP+1:W=A(KS,IS):A(KS,IS)=A(JS,IS):A(JS,IS)=W:NEXT
6200 P=1/A(KS,KS):FOR JS=KS+1 TO NP+1:A(KS,JS)=A(KS,JS)*P:W=-A(KS,JS)
6250 IF W=0 THEN 6290
6260 FOR IS=KS+1 TO NP:A(IS,JS)=A(IS,JS)+A(IS,KS)*W:NEXT
6290 NEXT:NEXT:A(NP,NP+1)=A(NP,NP+1)/A(NP,NP):FOR IS=2 TO NP
6350 LS=NP-IS+1: W=-A(LS,NP+1):POR JS=LS+1 TO NP
6400 W=W+A(LS, JS)*A(JS,NP+1):NEXT:A(LS,NP+1)=-W:NEXT:RETURN
7000 NL(0) =0:BS=0:FORJ=lTOLN:BS=BS+NL(J-l) :FOR 1=1 TO NL(J):T=TX(BS+I)
7300 ON J GOSUB 1000,1100,1200,1300,1400:CS(BS+1,0)=CV(BS+I)-CP:GOSUB 2000
7310 NEXT I,J:POR 1=1 TO M:FOR J=1 TO M:A(I,J)=0:POR L=1 TO N
7390 A(I,J)=A(I,J) +CS(L,I)*CS(L,J)/CV(L)»IW:NEXT:A(J,I)=A(I,J):NEXT J,I:RETURN
7400 FOR 1=1 TO M:A(I,M+1)=0:FOR J=1 TO N
7440 A(I,Mfl)=A(I,Mfl)+CS(J,I)*CS(J,0)/CV(J) *IW:NEXTJ,I:NP=M
7460 IF AL=2 THEN FOR 1=1 TO M:A(I,I)=A(I,I)+CF:X(I,0)=A(I,M+1):NEXT
7470 RETURN
8000 GOSUB 7000:FOR 1=1 TO M:FOR J=1 TO M:X(I,J)=A(I,J):NEXT J,I
8010 FOR K=1 TO M:FOR 1=1 TO M:POR J=1 TO M:A(I,J)=X(I,J):NEXT J,I:FOR 1=1 TO
M
8020 A(I,M+1)=0:NEXT:A(K,M+1)=1:GOSUB 6000:X(K,0)=A(K,M+1):NEXT:RETURN

250
PROGRAM "MULTI" OUTPUT
*BPH#5 PLASMA* BY DAMPING
WEIGHT=1/CP»( 1 )
FINAL P 1 = 4075.34321
FINAL P 2 = .561657421
FINAL P 3 = 317.905047
FINAL P 4 = .0114009374
FINAL P 5 = 45.0639877
FINAL P 6 = 9.28169819E-0
FINAL SS= 109.876828
GAUSS-NEWTON METHOD
S.D.= 298.701518
S.D.= .0398633637
S.D.= 24.0497307
S.D.= 1.63965625E-03
S.D.= 10.0166502
i S.D.= 1.78104752E-04
T
1
=
1
CP 1 =
2683.3413 ( 2707 )
T
1
=
2.2
CP 1
= 1539.48823
( 1534 )
T
1
=
3.3
CP 1
= 989.668886
( 950 )
T
1
=
5.06
CP 1 = 582.569414
( 598 )
T
1
=
10.19
CP
1 =
340.998713
( 501.4 )
T
1
=
14.98
CP
1 =
313.340327
( 393.11 )
T
1
=
20.16
CP
1 =
296.903799
( 248.71 )
T
1
=
25.16
CP
1 =
282.654619
( 250.6 )
T
1
=
30.79
CP
1 =
267.586674
( 234.72 )
T
1
=
45.54
CP
1 =
232.351473
( 209.2 )
T
1
=
49.79
CP
1 =
223.234706
( 196.1 )
T
1
=
75.16
CP
1 =
176.971203
( 152.5 )
T
1
=
91.93
CP
1 =
152.838173
( 159.6 )
T
1
=
105.3
CP
1 =
136.569498
( 149.7 )
T
1
=
120.8
CP
1 =
120.483927
( 140.9 )
T
1
=
149.2
CP
1 =
97.2530431
( 104.1 )
T
1
=
180.5
CP
1 =
78.7174354
( 96.1 )
T
1
=
209.6
CP
1 =
66.2372391
( 68.5 )
T
1
=
240.1
CP
1 =
56.6430443
( 56.4 )
T
1
=
274.5
CP
1 =
48.832682
( 47.9 )
T
1
=
303.2
CP
1 =
44.0343266
( 45.9 )
T
1
=
360.5
CP
1 =
37.4646319
( 36.75 )
T
1
=
422.5
CP
1 =
33.0177463
( 34.45 )
T
1
=
470.2
CP
1 =
30.6201437
( 32 )
T
1
=
550.1
CP
1 =
27.6454205
( 21.43 )
T
1
=
607.2
CP
1 =
25.9620548
( 25.2 )
T
1
=
675
CP 1
= 24
i.2290939
( 27 )
T
1
=
1164
CP 1
. = 15.2981146
( 13.83 )
T
1
=
1560
CP 1
. = 10.5924245
( 8.33 )
T
1
=
2631
CP 1
. = 3
1.91990977
( 5.85 )
Fitting of the plasma concentrations (as base, ng/ml) of intravenously
administered buprenorphine (1) against time (min) for the 1.439 mgAg dose
in dog C (Table 2) to equation 2. Values in parenthesis correspond to
experimental plasma concentrations of 1.

APPENDIX II - FITTING OF DATA TO EQUATIONS
The purpose of fitting equations are several fold.^ a) To
summarize a mass of data in order to obtain predictive equations,
formulas and calibration curves? b) To confirm or refute an established
theory or relationship by comparing and evaluating several sets of data
in terms of certain parameters and c) To develop a theoretical model.
A good method of fitting data to equations should^1
a) Use all relevant data.
b) Have resonable economy in the number of parameters chosen.
c) Take into account the error in the data.
d) Find outliers, if any.
e) Provide some measure how well the equation will predict future
events.
Least square (LS) estimation. The method of least square is used to
estimate the values of the parameters in an equation that will minimize
the sum of squared deviations of the observed values from those
predicted by the equation.
Linear LS estimation. By definition, the requirement for linear
least square estimation is that the equation chosen is linear in all its
coefficients, i.e.,
C=aX+bY+ . . . + c Eq. A1
where X, Y,. . . are the independent variables and a, b,. . . are the
constant coefficients. These coefficients are linear as they can be
calculated directly from the values of the independent and dependent
variables.
251

252
Nonlinear LS estimation. The equation is nonlinear when the values
of one or more of the constant coefficients of the equation can not be
directly calculated from the values of the independent and dependent
variables, i.e.,
C = a e + b e
Eq. A2
where a, b, a , and g are the nonlinear coefficients which can not be
directly calculated from the values of the independent variable t and
dependent variable C. To fit data to equation A2, using non-linear least
square analysis computer programs (for example see Appendix I)
preliminary estimates of all parameters must be avaiable. If these
estimates are not close enough to the best values of the parameters,
computer calculated estimates of the parameters may not converge on the
best values. The term 'best' rather than 'actual' is used in the
previous statement as there may be more than one set of 'best' values of
the parameters that can adequately describe the data.^
The traditional method of least squares estimation assumesa)
the correct form of equation has been chosen; b) the data respresent the
population; c) each datum is statistically independent; d) independent
variable is measured without any error; e) all data have the same, even
though unknown, variance; f) uncontrolled error in the data is randomly
distributed.
Weighting of data. In a non-weighted least square analysis, the
following function is minimized.
N
Eq. A3
i=l

253
til
where Yi , is the value of 1 measurement and Yi , is the
obs calc
estimated 1th measurement. The above method is valid only when all
observations in Y have the same, though unknown, variance.^ When the
observed values do not have the same variance, each point should be
weighted by the inverse of its variance.*^ If it can be assumed that
the variance in Y is proportional to Y, then appropriate weighting
factor is 1/Y2.
Fitting of plasma data of buprenorphine. In pharmacokinetics,
proper estimation of the parameters of the plasma concentration-time
profile is dependent upon:
a) Compartment model chosen.
b) Number of experimental points, the time interval between these values
and the number of half-lives over which the samples were collected.
c) Weighing of data.
d) Analytical sensitivity, especially at low plasma concentrations.
The classical method of estimating the parameters of an equation
describing the plasma concentration-time profile of a drug conforming to
2 or 3-compartment body model is by "stripping", the method of
53i
residuals. In this technique, least square estimates of the terminal
phase are calculated. For a 2-compartment body model, the parameters of
the initial phase are estimated from a plot of the difference between
the initial values and the extrapolated terminal phase.~^1
As an example, for dog C at 1.439 mg/kg IV bolus dose of 1 (Table
2), fitting of the plasma data by the method of residuals is given in
Fig. A-ld. The sum of squares calculated in accordance with equation A3
is 81170. These initial estimates of the parameters are given in Table
Al. These parameters were used as initial estimates for the computer

Figure Al. Semilogarithmic plots of the concentrations (as base, ng/ml) of
intravenously administered buprenorphine (1) in plamsa against time (min) for the
1.439 mg/kg dose in 24.2 kg dog C (Table 2, Al). The solid lines represent the
curve obtained by fitting the plasma data by various techniques and weighting
(using "Multi", Appendix I): a) Weight=2; b) Weight=0; c) Log Yi values were
fitted with weight=0; d) By classical method of resdiduals. See Table Al for the
estimates of all parameters.

WO II2Ü I68Ü 22-10 2800 SRO 112(1 IG811 22-1(1 28(10
MIN MIN
NG'ML
NG41L
552
100(10

Table Al. Fitting of plasma data with various weighting factors.
Weight
Feathering
Log Yi3
0C
ld
2e
Parameter^
P
3743
3341
4228
4075
3585
A
254.3
304
452
318
284
B
48.13
36.25
227
45.1
32.82
7T
0.4773
0.461
0.713
0.562
0.487
a
0.0093
0.0097
0.0744
0.0114
0.09
6
0.0009
0.00075
0.0048
0.0009
0.00074
ssg
81170
122719
17583
41853
90010
Fitting of the plasma data of 1 from dog C by the method of residuals.
Plasma concentrations of 1 were transformed into natural logarithms and fitted by
"Multi" (appendix I) using equal weight for all points.
Q
Plasma data fitted by "Multi" (appendix I) with equal weight for all points.
Plasma data fitted by "Multi" (appendix I) with weight=l, i.e., plasma points were
weighted by 1/Yi values.
e 2
Plasma data fitted by "Milti" (appendix I) with weight=2, i.e., weighted by 1/Yi
values.
^ Paremeters of the equation 2 for intravenously administered buprenorpine (1) in plasma
against time for the 1.439 mg/kg dose in 24.2 kg dog C.
g Unweighted sum of squares.
256

257
fitting of the same data using the "Multi" program (Appendix I) of
54 . .
Yamaoka et al. By giving weights of 0,1, and 2 for the experimental
Yi values, the estimated parameters of the plasma concentration time
profile of 1 in dog C at 1.439 mg/kg dose and their respective minimum
sum of squares are given in Table Al (Fig. Al, also Fig. 8 in main text
for weight=l). Notice that when the sum of squares is a minimum with
equal (or 0) weighting, the fit completely missed all the terminal
points (Fig. Al-d).
Figure Al represents a type of fit where plasma concentrations were
transformed to their respective natural logarithms and then fitted by
"Multi" (Appendix I) with equal (or 0) weighting.
Except for equal (or 0) weighting, all other methods of weighting
gave parameters that were reasonably similar (Table Al). The unweighted
sum of squares calculated for various weighting was a minimum (excluding
0 weight) for weight=l (See Fig. 8 in main text and also Table Al). Thus
inverse plasma concentrations were chosen as the appropriate weighting
factor in all fittings of the plasma concentation-time profile of 1 in
dogs.

APPENDIX III - KRUSKAL-WALLIS TEST
. 59
The Kruskal-Wallis test is a nonparametric rank sum test that
can be used to compare two or more samples of populations. In
particular, suppose that n^ observations are drawn at random from
population 1, n^ from population 2,. . . . , and n^ from population k.
The hypothesis that the k samples are drawn from identical (but not
necessarily normal) distributions can be checked by the Kruskal-Wallis
test. In this method,
Hq: The k distributions are identical.
H : Not all the distributions are the same,
a
Test Statistic:
12
H = [
L tt— ] - 3 (n+1)
n(n+l) i i
where H follows chi-square distribution, m is the number of
Eq. A3
observations from sample i(i=l,2,3, . . ,k), n is the combined sample
size, that is, n = n^ and T^ denotes the sum of the ranks for the
measurements in sample i after the combined sample measurements have
been ranked.
Rejection Region: For a specified value of a / reject HQ if H
exceeds the critical value of chi-square for a=a and df = k-1.
As an example, consider the figure 11. The null and the research
hypotheses for this example can be stated as follows:
Hq: There is no significant difference between the three dose
normalised plasma concentrations, i.e., the dose normalised plasma
258

259
concentrations in the three studies are drawn from identical
populations. Thus dose-independent pharmacokinetics is postulated.
Ha: At least one of the three dose normalized plasma
concentration significantly differs from the others. Thus dose-dependent
pharmacokinetics is postulated.
The 30 dose normalized plasma concentrations from studies 2, 3, and
7 are ranked as given in Table A3 below:
Table A3.
Study #2
694.67(86)
582.76(85)
447.19(76)
475.96(78)
331.72(71)
266.48(68)
169.28(60)
211.35(65)
211.07(64)
168.55(61)
152.12(59)
87.97(53.5)
87.97(53.5)
63.35(47)
56.45(45)
57.76(46)
43.31(42)
35.19(39.5)
35.19(39.5)
26.49(34)
21.63(29)
30.45(37)
22.98(31)
21.81(30)
23.95(32)
15.59(17)
18.57(23)
10.51(10)
4.28(3)
4.23(2)
Study #3
1177.9(89)
976.24(88)
827.91(87)
507.14(79)
530.39(81)
376.79(73)
305.01(69)
239.39(66)
200.91(63)
147.94(58)
120.47(56)
87.94(52)
87.00(51)
67.88(48)
51.38(44)
38.62(41)
29.88(35)
21.54(28)
20.56(26)
13.33(14)
13.03(13)
10.88(12)
10.81(11)
9.09(8)
9.36(9)
4.04(1)
8.45(7)
6.75(5.5)
6.75(5.5)
6.29(4)
Study #7
554.82(84)
547.24(83)
538.06(82)
517.11(80)
467.07(77)
427.29(75)
387.78(74)
352.31(72)
321.73(70)
244.09(67)
186.24(62)
138.60(57)
111.56(55)
86.58(50)
70.39(49)
47.69(43)
35.14(38)
30.05(36)
24.23(33)
21.98(30)
20.65(27)
19.29(25)
18.60(24)
18.12(22)
17.71(21)
17.33(20)
16.96(19)
16.72(18)
14.38(16)
13.97(15)
From the above table the sums (T^) of the ranks (values in
parenthesis) for the three groups are 1387, 1224, and 1424. Substituting

260
these values in equation A3, we obtain H=-7.19. The critial value of
chi-square with a =0.05 and df = k-1 = 2 from the chi-square table is
5.99. Since the observed H is smaller than 5.99, we accept the null
hypothesis and conclude that there is no significant difference among
the three groups. Thus dose-independent pharmacokinetics can not be
denied at the dose range studied.

APPENDIX IV - TABLES OF RAW DATA
Table A-IV-la. Plasma buprenorphine, Dog Study #1
Time Cp, expt. Cp, calc. AUC AUC
min ng/mL ng/rriL calc. trap.
1.57
3.08
5.88
9.95
14.92
19.81
28.21
30.24
44.93
60.00
74.71
89.31
104.47
118.05
150.00
182.50
210.33
239.52
270.00
300.75
360.33
419.23
481.80
561.90
599.58
689.56
1458.25
1765.05
2865.00
849.20
613.70
479.10
412.20
395.00
367.00
287.30
206.50
185.80
151.20
102.90
75.50
74.60
66.80
57.20
44.83
33.40
39.30
32.50
29.63
26.12
27.80
28.00
27.00
23.20
17.70
13.72
10.60
7.72
849.26
613.58
478.61
419.04
371.50
331.29
273.20
260.98
189.45
139.66
106.66
84.26
68.37
58.52
45.09
38.74
35.90
34.11
32.86
31.88
30.34
28.99
27.65
26.02
25.29
23.62
13.21
10.47
4.56
1768.67
2845.33
4330.60
6141.71
8102.44
9818.63
12348.57
12890.65
16165.55
18620.89
20417.19
21800.66
22949.83
23807.60
25434.85
26784.38
27819.44
28839.39
29858.97
30853.84
32706.17
34453.07
36224.59
38373.18
39339.73
41539.39
55309.17
58925.23
66744.28
1857.92
2962.41
4492.33
6306.12
8312.01
10175.10
12923.16
13424.37
16305.81
18845.11
20714.01
22016.33
23154.09
24114.20
26095.10
27753.09
28841.66
29902.71
30996.95
31952.19
33612.99
35200.93
36946.63
39149.38
40095.15
41935.24
54011.36
57742.05
67817.59
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).
261

262
Table A-IV-lb Buprenorphine in urine, Dog Study #1
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
IU y gs
AUCt
15.000
872.300
31.000
5.540
27.041
27.041
8.132
30.000
875.200
12.000
5.270
10.502
37.544
12.828
46.000
1337.200
11.000
5.390
14.709
52.253
16.366
60.000
411.260
10.000
5.700
4.113
56.366
18.621
91.500
312.220
20.000
5.720
6.244
62.610
21.982
121.000
93.600
18.000
6.190
1.685
64.295
23.978
153.000
19.810
22.000
6.840
0.436
64.731
25.569
183.000
7.740
9.500
7.250
0.074
64.804
26.804
210.000
4.740
26.000
7.230
0.123
64.927
27.808
240.000
3.330
43.000
7.060
0.143
65.070
28.856
271.000
4.220
42.000
7.030
0.177
65.248
29.892
302.000
4.000
70.000
6.960
0.280
65.528
30.894
361.000
4.420
125.000
7.300
0.553
66.080
32.726
421.000
2.880
130.000
7.140
0.374
66.455
34.504
483.000
5.550
259.000
6.130
1.437
67.892
36.258
548.500
13.590
190.000
5.780
2.582
70.474
38.023
601.000
1.060
130.000
6.430
0.138
70.612
39.376
700.000
42.100
120.000
5.380
5.052
75.664
41.785
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval.

263
Table A-IV-le. Buprenorphine: Urine, Dog Study #1
z - pgs
AV/ At
mL/min
A U/ At
vg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren .
mL/min
Cl b
ren
mL/min
48.623
2.067
1.803
7.500
449.072
3.325
4.014
38.120
0.800
0.700
22.500
311.280
2.927
2.249
23.411
0.688
0.919
38.000
219.798
3.193
4.183
19.298
0.714
0.294
53.000
160.374
3.027
1.832
13.054
0.635
0.198
75.750
104.774
2.848
1.892
11.369
0.610
0.057
106.250
66.881
2.681
0.854
10.933
0.688
0.014
137.000
49.326
2.532
0.276
10.860
0.317
0.002
168.000
41.005
2.418
0.060
10.737
0.963
0.005
196.500
37.120
2.335
0.123
10.593
1.433
0.005
225.000
34.904
2.255
0.137
10.416
1.355
0.006
255.500
33.404
2.183
0.171
10.136
2.258
0.009
286.500
32.310
2.121
0.280
9.584
2.119
0.009
331.500
31.054
2.019
0.302
9.209
2.167
0.006
391.000
29.627
1.926
0.211
7.772
4.177
0.023
452.000
28.278
1.872
0.820
5.190
2.901
0.039
515.750
26.944
1.853
1.463
5.052
2.476
0.003
574.750
25.767
1.793
0.102
0.000
1.212
0.051
650.500
24.332
1.811
2.097
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentration at the mid point of urine
collection time.
I

264
Table A-IV-Id. Plasma metabolite, Dog Study #1
Time
min
Cp, expt.
ng/mL
Cp, calc
ng/mL
. AUC
calc.
AUC
trap.
1.57
352.50
352.85
563.49
276.71
3.08
346.80
341.54
1087.70
804.68
5.88
249.90
321.62
2015.82
1640.06
9.95
327.20
294.94
3269.64
2814.46
14.92
309.90
265.68
4661.34
4397.66
19.81
249.40
240.08
5896.71
5765.14
28.21
218.30
202.50
7750.31
7729.48
30.24
218.00
194.50
8153.20
8172.33
44.93
153.61
146.77
10639.45
10901.80
74.71
61.10
88.86
14047.19
14098.84
89.31
64.14
72.36
15217.17
15013.09
104.47
71.90
60.30
16217.30
16044.27
118.05
61.30
52.62
16981.26
16948.70
150.00
41.50
41.80
18468.37
18590.93
182.50
45.30
36.56
19731.46
20001.43
210.33
26.92
34.28
20714.17
21006.37
270.00
34.30
32.16
22685.24
22832.87
300.75
32.61
31.66
23665.96
23861.61
360.33
26.65
31.02
25531.61
25626.97
419.23
25.19
30.53
27343.87
27153.65
481.80
32.76
30.06
29239.51
28966.62
561.90
31.14
29.49
31624.34
31525.81
599.58
36.20
29.22
32730.31
32794.50
689.56
33.40
28.59
35331.00
35925.80
1458.25
24.50
23.75
55389.72
58179.38
1765.05
22.60
22.05
62412.62
65404.52
2865.00
15.14
16.91
83717.60
86160.58
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

265
Table A-IV-le. Metabolite in urine, Dog Study #1
Time
min
Cone.
ng/mL
Volume
mL
pH
U ygs
£ U p gs
AUCt
15.000
24.900
31.000
5.540
0.772
0.772
4.683
30.000
187.400
12.000
5.270
2.249
3.021
8.106
46.000
311.500
11.000
5.390
3.427
6.447
10.795
60.000
199.800
10.000
5.700
1.998
8.445
12.577
91.500
526.100
20.000
5.720
10.522
18.967
15.373
121.000
333.800
18.000
6.190
6.008
24.976
17.134
153.000
297.300
22.000
6.840
6.541
31.516
18.593
183.000
362.300
9.500
7.250
3.442
34.958
19.750
210.000
303.800
26.000
7.230
7.899
42.857
20.703
240.000
264.400
43.000
7.060
11.369
54.226
21.710
271.000
278.800
42.000
7.030
11.710
65.936
22.717
302.000
201.900
70.000
6.960
14.133
80.069
23.706
361.000
240.100
125.000
7.300
30.013
110.081
25.552
421.000
140.700
130.000
7.140
18.291
128.372
27.398
483.000
85.400
259.000
6.130
22.119
150.491
29.276
548.500
148.700
190.000
5.780
28.253
178.744
31.229
601.000
33.600
130.000
6.430
4.368
183.112
32.772
700.000
262.100
120.000
5.380
31.452
214.564
35.629
U=Amount excreted in urine during a collection interval. ZU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit, yg.min/ml

266
Table A-IV-lf. Metabolite in urine, Dog Study #1
Z- ygs
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
213.792
2.067
0.051
7.500
310.691
0.165
0.166
211.543
0.800
0.150
22.500
227.219
0.373
0.660
208.117
0.688
0.214
38.000
167.220
0.597
1.281
206.119
0.714
0.143
53.000
126.848
0.671
1.125
195.597
0.635
0.334
75.750
87.488
1.234
3.818
189.588
0.610
0.204
106.250
59.151
1.458
3.443
183.048
0.688
0.204
137.000
45.265
1.695
4.516
179.606
0.317
0.115
168.000
38.436
1.770
2.985
171.707
0.963
0.293
196.500
35.248
2.070
8.300
160.338
1.433
0.379
225.000
33.525
2.498
11.304
148.628
1.355
0.378
255.500
32.493
2.902
11.625
134.495
2.258
0.456
286.500
31.867
3.378
14.307
104.483
2.119
0.509
331.500
31.292
4.308
16.256
86.192
2.167
0.305
391.000
30.756
4.685
9.912
64.073
4.177
0.357
452.000
30.284
5.140
11.780
35.820
2.901
0.431
515.750
29.817
5.724
14.467
31.452
2.476
0.083
574.750
29.394
5.587
2.831
0.000
1.212
0.318
650.500
28.861
6.022
11.008
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

267
Table A-IV-2a. Plasma buprenorphine, Dog Study #2
Time
min
Cp, expt.
ng/mL
Cp, calc,
ng/mL
AUC
calc.
AUC
trap.
1.27
1137.10
1086.54
1513.87
1552.72
2.38
953.92
938.59
2634.42
2713.23
3.23
732.00
847.62
3392.34
3429.75
4.76
779.10
721.08
4587.05
4585.74
10.13
543.00
494.21
7743.00
8135.58
15.41
436.20
408.76
10097.06
10720.67
20.30
277.10
366.73
11985.43
12464.68
26.79
345.96
328.54
14235.38
14486.51
30.53
345.50
310.33
15429.48
15779.54
44.66
275.90
253.34
19393.79
20169.74
59.76
249.00
206.35
22849.16
24132.73
75.43
144.00
168.83
25775.69
27211.89
90.15
144.00
141.60
28052.20
29331.57
105.84
103.70
119.13
30089.91
31274.77
121.06
92.40
102.30
31769.59
32767.09
150.05
94.54
79.89
34384.84
35476.79
179.83
70.90
65.56
36533.86
37940.19
210.00
57.60
56.43
38363.73
39878.61
240.72
57.60
50.46
39999.08
41648.08
270.06
43.36
46.63
41419.93
43129.17
303.58
35.41
43.57
42928.55
44449.35
360.28
49.85
40.08
45292.89
46866.47
422.51
37.62
37.37
47699.05
49588.10
480.96
35.70
35.28
49820.82
51730.88
539.31
39.21
33.40
51823.78
53916.38
607.22
25.52
31.39
54022.95
56114.29
715.50
30.39
28.45
57260.09
59141.25
1260.00
17.20
17.39
69494.57
72097.63
1880.00
7.01
9.93
77748.35
79602.73
2760.50
6.93
4.48
83775.97
85739.82
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

268
Table A-IV-2b. Buprenorphine in urine, Dog Study #2
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
EU ygs
AUCt
16.000
2590.000
16.000
6.730
41.440
41.440
10.336
31.270
3391.000
11.000
5.930
37.301
78.741
15.658
46.500
1840.000
13.000
5.020
23.920
102.661
19.854
61.200
760.000
4.500
5.490
3.420
106.081
23.144
90.740
740.000
13.000
5.810
9.620
115.701
28.135
122.000
742.000
15.000
5.490
11.130
126.831
31.865
150.500
437.000
13.000
5.840
5.681
132.512
34.421
180.500
200.000
15.000
5.830
3.000
135.512
36.578
210.100
116.000
14.000
5.970
1.624
137.136
38.369
242.300
51.600
19.000
6.000
0.980
138.116
40.079
272.500
36.600
20.000
6.010
0.732
138.848
41.533
304.500
16.500
29.500
6.220
0.487
139.335
42.969
356.500
16.530
65.000
6.260
1.074
140.410
45.141
444.000
10.140
100.000
6.210
1.014
141.424
48.493
482.000
8.010
102.000
6.370
0.817
142.241
49.857
540.800
7.020
98.000
6.330
0.688
142.929
51.874
612.000
13.300
70.000
6.230
0.931
143.860
54.173
730.700
6.200
202.000
6.250
1.252
145.112
57.690
1260.000
6.010
375.000
7.000
2.254
147.366
69.495
2845.000
11.100
325.000
6.010
3.608
150.973
84.140
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval.

269
Table A-IV-2c. Buprenorphine: Urine, Dog Study #2
I-
AV/ At
AU/ At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
pg/min
min
ng/mL
mL/min
mL/min
109.533
1.000
2.590
8.000
556.918
4.009
4.651
72.232
0.720
2.443
23.635
345.689
5.029
7.066
48.312
0.854
1.571
38.885
274.821
5.171
5.715
44.892
0.306
0.233
53.850
223.310
4.584
1.042
35.272
0.440
0.326
75.970
167.710
4.112
1.942
24.142
0.480
0.356
106.370
118.470
3.980
3.005
18.461
0.456
0.199
136.250
89.243
3.850
2.234
15.461
0.500
0.100
165.500
71.618
3.705
1.396
13.837
0.473
0.055
195.300
60.365
3.574
0.909
12.857
0.590
0.030
226.200
52.968
3.446
0.575
12.125
0.662
0.024
257.400
48.112
3.343
0.504
11.638
0.922
0.015
288.500
44.811
3.243
0.339
10.564
1.250
0.021
330.500
41.725
3.110
0.495
9.550
1.143
0.012
400.250
38.261
2.916
0.303
8.733
2.684
0.022
463.000
35.892
2.853
0.599
8.045
1.667
0.012
511.400
34.279
2.755
0.341
7.114
0.983
0.013
576.400
32.284
2.656
0.405
5.861
1.702
0.011
671.350
29.614
2.515
0.356
3.608
0.708
0.004
995.350
22.091
2.121
0.193
0.000
0.205
0.002
2052.500
8.495
1.794
0.268
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

270
Table A-IV-2d. Plasma metabolite, Dog Study #2
Time Cp, expt. Cp, calc. AUC AUC
min ng/mL ng/mL calc. trap.
1.27
2.38
3.23
4.76
10.13
15.41
20.30
26.79
30.53
44.66
59.76
75.43
90.15
105.84
121.06
150.05
179.83
210.00
240.72
270.06
303.58
360.28
422.51
480.96
539.31
607.22
715.50
1260.00
1880.00
2760.50
527.00
509.80
440.30
406.90
317.90
242.20
214.20
208.60
206.50
189.30
109.40
105.30
85.20
91.90
70.40
57.10
44.40
32.50
31.40
33.90
28.80
32.40
40.60
30.90
25.60
23.70
32.60
20.40
18.80
12.79
537.91
486.76
453.73
405.04
303.78
256.13
229.82
205.45
194.03
159.04
130.46
107.59
90.95
77.19
66.88
53.18
44.49
39.06
35.63
33.54
31.98
30.43
29.40
28.69
28.07
27.41
26.40
21.89
17.69
13.07
727.26
1295.03
1694.40
2349.77
4216.12
5681.18
6865.08
8273.38
9019.99
11502.47
13678.90
15536.10
16992.29
18306.64
19399.75
21124.32
22568.29
23822.20
24965.35
25977.82
27074.00
28838.95
30698.41
32395.57
34051.43
35935.11
38847.72
51956.28
64180.43
77620.41
334.65
910.07
1313.86
1961.97
3908.06
5386.72
6502.62
7874.61
8650.84
11447.17
13702.35
15384.53
16786.61
18175.96
19411.06
21259.17
22770.51
23930.55
24912.05
25870.00
26920.85
28655.87
30927.27
33016.86
34665.24
36339.22
39387.31
53816.56
65968.56
79876.05
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

271
Table A-TV-2e. Metabolite in urine, Dog Study #2
Time
min
Cone.
ng/mL
Volume
mL
pH
U ygs
ZU ygs
AUCt
16.000
335.700
16.000
6.730
5.371
5.371
5.831
31.270
765.000
11.000
5.930
8.415
13.786
9.163
46.500
550.000
13.000
5.020
7.150
20.936
11.792
61.200
1231.000
4.500
5.490
5.540
26.476
13.865
90.740
878.000
13.000
5.810
11.414
37.890
17.046
122.000
810.700
15.000
5.490
12.161
50.050
19.462
150.500
607.000
13.000
5.840
7.891
57.941
21.148
180.500
413.700
15.000
5.830
6.206
64.147
22.598
210.100
394.800
14.000
5.970
5.527
69.674
23.826
242.300
253.000
19.000
6.000
4.807
74.481
25.022
272.500
182.500
20.000
6.010
3.650
78.131
26.059
304.500
156.700
29.500
6.220
4.623
82.754
27.103
356.500
121.500
65.000
6.260
7.898
90.651
28.724
444.000
69.500
100.000
6.210
6.950
97.601
31.327
482.000
19.600
102.000
6.370
1.999
99.600
32.425
540.800
36.300
98.000
6.330
3.557
103.158
34.093
612.000
36.300
70.000
6.230
2.541
105.699
36.066
730.700
56.300
202.000
6.250
11.373
117.071
39.248
1260.000
23.300
375.000
7.000
8.738
125.809
51.956
2845.000
1.000
325.000
6.010
0.325
126.134
78.709
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

272
Table A-IV-2f. Metabolite in urine, Dog Study #2
z- ygs
AV/ At
mL/min
AU/ At
pg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
clp5
ren
mL/min
120.763
1.000
0.336
8.000
334.464
0.921
1.004
112.348
0.720
0.551
23.635
216.349
1.505
2.547
105.198
0.854
0.469
38.885
172.146
1.776
2.727
99.658
0.306
0.377
53.850
140.776
1.910
2.677
88.244
0.440
0.386
75.970
106.901
2.223
3.614
76.084
0.480
0.389
106.370
76.788
2.572
5.066
68.193
0.456
0.277
136.250
58.893
2.740
4.701
61.987
0.500
0.207
165.500
48.152
2.839
4.296
56.460
0.473
0.187
195.300
41.385
2.924
4.512
51.653
0.590
0.149
226.200
37.053
2.977
4.029
48.003
0.662
0.121
257.400
34.331
2.998
3.520
43.380
0.922
0.144
288.500
32.598
3.053
4.431
35.483
1.250
0.152
330.500
31.128
3.156
4.879
28.533
1.143
0.079
400.250
29.724
3.116
2.672
26.533
2.684
0.053
463.000
28.896
3.072
1.821
22.976
1.667
0.061
511.400
28.362
3.026
2.133
20.435
0.983
0.036
576.400
27.706
2.931
1.288
9.063
1.702
0.096
671.350
26.804
2.983
3.574
0.325
0.708
0.017
995.350
23.977
2.421
0.688
0.000
0.205
0.000
2052.500
16.672
1.603
0.012
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concentration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

273
Table A-IV-3a. Plasma buprenorphine, Dog Study #3
Time
min
Cp, expt.
ng/mL
Cp, calc
ng/mL
:. AUC
calc.
AUC
trap.
1.45
3019.30
3019.91
5461.80
5583.08
2.17
2502.30
2505.25
7427.94
7557.05
3.05
2122.10
2048.94
9419.71
9591.79
5.12
1299.90
1443.31
12949.24
13133.56
10.43
1359.50
981.90
19061.91
20200.91
15.10
965.80
859.77
23333.53
25630.49
20.22
781.80
768.58
27489.82
30099.98
25.30
613.60
691.11
31197.04
33647.78
30.14
514.96
625.27
34379.86
36378.89
45.06
379.20
460.88
42416.69
43049.33
60.05
308.80
341.40
48379.53
48204.17
76.95
225.40
245.79
53293.62
52719.49
90.05
223.00
192.34
56145.77
55655.39
105.55
174.00
145.79
58747.04
58733.14
119.93
131.70
114.52
60607.11
60931.12
150.37
99.00
73.06
63393.96
64442.37
179.66
76.60
52.01
65193.85
67014.03
209.90
55.20
40.41
66572.85
69006.85
239.92
52.70
34.23
67683.73
70626.43
270.85
34.18
30.74
68683.17
71970.03
300.80
33.40
28.82
69572.63
72982.04
361.60
27.90
26.83
71256.25
74845.56
421.68
27.70
25.78
72834.36
76515.78
492.92
23.30
24.85
74636.59
78332.40
540.01
24.00
24.30
75793.57
79446.08
601.10
10.35
23.61
77256.79
80495.30
663.10
21.65
22.94
78699.88
81487.30
721.70
17.29
22.33
80026.25
82628.24
780.00
17.29
21.73
81310.59
83636.25
839.15
16.12
21.15
82578.73
84624.35
1218.50
22.60
17.74
89936.37
91968.57
1430.00
22.60
16.09
93511.24
96748.47
1620.00
12.48
14.73
96437.62
100081.07
2684.00
7.32
9.01
108818.80
110613.34
4132.00
11.10
4.61
118323.02
123947.61
4450.00
10.41
3.98
119685.84
127367.70
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

274
Table A-IV-3b. Buprenorphine in urine, Dog Study #3
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
IU ygs
AUCt
15.000
18.560
7.000
7.910
0.130
0.130
23.247
30.000
36.560
4.000
7.830
0.146
0.276
34.292
45.000
22.000
8.000
7.500
0.176
0.452
42.389
59.900
48.000
10.000
7.070
0.480
0.932
48.330
90.230
75.410
9.000
6.930
0.679
1.611
56.181
120.000
17.480
8.500
7.160
0.149
1.759
60.615
149.750
9.344
10.000
7.630
0.093
1.853
63.348
180.000
8.703
7.000
7.920
0.061
1.914
65.212
214.000
0.000
11.500
8.040
0.000
1.914
66.736
240.600
0.000
8.500
8.100
0.000
1.914
67.707
271.000
3.757
11.500
8.150
0.043
1.957
68.688
301.000
5.620
14.000
8.110
0.079
2.036
69.578
363.000
2.200
31.500
7.950
0.069
2.105
71.294
422.000
0.000
34.000
7.810
0.000
2.105
72.843
541.000
0.000
46.000
7.840
0.000
2.105
75.818
664.000
0.000
25.000
7.650
0.000
2.105
78.721
1219.000
0.000
550.000
7.570
0.000
2.105
89.945
2660.000
24.440
670.000
6.700
16.375
18.480
108.601
4123.000
33.480
208.000
7.580
6.964
25.444
118.281
5650.000
39.620
156.000
7.000
6.181
31.624
123.349
U=Amount excreted in urine during a collection interval. £U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml.

275
Table A-IV-3c. Buprenorphine: Urine, Dog Study #3
r~ vqs
AV/ At
AU/ At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
yg/min
min
ng/mL
mL/min
mL/min
31.494
0.467
0.009
7.500
1141.867
0.006
0.008
31.348
0.267
0.010
22.500
732.583
0.008
0.013
31.172
0.533
0.012
37.500
537.555
0.011
0.022
30.692
0.671
0.032
52.450
397.127
0.019
0.081
30.013
0.297
0.022
75.065
254.802
0.029
0.088
29.865
0.286
0.005
105.115
146.895
0.029
0.034
29.771
0.336
0.003
134.875
90.807
0.029
0.035
29.711
0.231
0.002
164.875
61.010
0.029
0.033
29.711
0.338
0.000
197.000
44.481
0.029
0.000
29.711
0.320
0.000
227.300
36.377
0.028
0.000
29.667
0.378
0.001
255.800
32.182
0.028
0.044
29.589
0.467
0.003
286.000
29.646
0.029
0.088
29.519
0.508
0.001
332.000
27.601
0.030
0.040
29.519
0.576
0.000
392.500
26.234
0.029
0.000
29.519
0.387
0.000
481.500
24.987
0.028
0.000
29.519
0.203
0.000
602.500
23.597
0.027
0.000
29.519
0.991
0.000
941.500
20.169
0.023
0.000
13.145
0.465
0.011
1939.500
12.710
0.170
0.894
6.181
0.142
0.005
3391.500
6.492
0.215
0.733
0.000
0.102
0.004
4886.500
3.251
0.256
1.245
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

276
Table A-IV-3d. Plasma metabolite, Dog Study #3
Time
min
Cp, expt. AUC
ng/mL trap.
1.45
614.50
445.51
2.17
1352.50
1148.72
3.05
1495.00
2401.62
5.12
1382.00
5379.31
10.43
797.00
11170.00
15.10
578.00
14380.63
20.22
649.00
17518.68
25.30
828.00
21273.95
30.14
551.70
24612.83
45.06
610.50
33282.84
60.05
608.00
42412.45
76.95
649.00
53037.24
90.05
798.00
62511.47
105.55
511.00
72659.50
119.93
539.00
80206.37
150.37
537.00
96585.78
179.66
403.00
110352.08
209.90
388.00
122312.00
239.92
331.00
133104.19
270.85
185.00
141084.13
300.80
91.60
145226.22
361.60
72.70
150220.94
421.68
54.50
154042.03
492.92
79.00
158797.30
540.01
45.32
161724.41
601.10
34.52
164163.12
663.10
30.90
166191.14
721.70
20.70
167703.02
780.00
22.00
168947.73
839.00
29.00
170452.23
1218.50
23.96
180501.39
1430.00
15.80
184706.01
1620.00
14.50
187584.51
2684.00
7.71
199400.23
4132.00
3.10
207227.68
4450.00
2.75
208158.05
Cp, expt. = Experimental plasma concentrations; AUC = Area under the
plasma concentration-time curve, ng.min/mL, estimated by trapezoidal
rule (trap.)-

277
Table A-IV-3e. Metabolite in urine, Dog Study #3
Time
min
Cone.
ng/mL
Volume
mL
PH
U pgs
£U pgs
AUCt
15.000
720.890
7.000
7.910
5.046
5.046
14.323
30.000
1838.200
4.000
7.830
7.353
12.399
24.535
45.000
1307.120
8.000
7.500
10.457
22.856
33.246
59.900
760.300
10.000
7.070
7.603
30.459
42.324
90.230
757.340
9.000
6.930
6.816
37.275
62.659
120.000
401.610
8.500
7.160
3.414
40.689
80.247
149.750
655.600
10.000
7.630
6.556
47.245
96.253
180.000
329.700
7.000
7.920
2.308
49.553
110.489
214.000
255.700
11.500
8.040
2.941
52.493
123.887
240.600
155.900
8.500
8.100
1.325
53.818
133.328
271.000
89.000
11.500
8.150
1.024
54.842
141.112
301.000
138.300
14.000
8.110
1.936
56.778
145.245
363.000
65.360
31.500
7.950
2.059
58.837
150.322
422.000
80.100
34.000
7.810
2.723
61.560
154.059
541.000
130.800
46.000
7.840
6.017
67.577
161.769
664.000
317.100
25.000
7.650
7.928
75.505
166.219
1219.000
38.800
550.000
7.570
21.340
96.845
180.513
2660.000
55.900
670.000
6.700
37.453
134.298
199.213
4123.000
61.420
208.000
7.580
12.775
147.073
207.200
5650.000
78.000
156.000
7.000
12.168
159.241
211.903
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: pg.min/ml

278
Table A-IV-3f. Metabolite in urine, Dog Study #3
z~
AV/ At
AU/ At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
yg/min
min
ng/mL
mL/min
mL/min
154.195
0.467
0.336
7.500
1089.500
0.352
0.309
146.842
0.267
0.490
22.500
738.500
0.505
0.664
136.385
0.533
0.697
37.500
581.100
0.687
1.200
128.782
0.671
0.510
52.450
609.250
0.720
0.838
121.966
0.297
0.225
75.065
628.500
0.595
0.358
118.552
0.286
0.115
105.115
654.500
0.507
0.175
111.996
0.336
0.220
134.875
538.000
0.491
0.410
109.688
0.231
0.076
164.875
470.000
0.448
0.162
106.748
0.338
0.086
197.000
395.500
0.424
0.219
105.423
0.320
0.050
227.300
359.500
0.404
0.139
104.399
0.378
0.034
255.800
258.000
0.389
0.130
102.463
0.467
0.065
286.000
138.300
0.391
0.467
100.404
0.508
0.033
332.000
82.150
0.391
0.404
97.681
0.576
0.046
392.500
63.600
0.400
0.726
91.664
0.387
0.051
481.500
66.750
0.418
0.757
83.736
0.203
0.064
602.500
32.710
0.454
1.970
62.396
0.991
0.038
941.500
26.480
0.536
1.452
24.943
0.465
0.026
1939.500
11.105
0.674
2.340
12.168
0.142
0.009
3391.500
5.406
0.710
1.615
0.000
0.102
0.008
4886.500
1.375
0.751
5.795
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

279
Table A-IV-4a. Plasma buprenorphine, Dog Study #4
Time
min
Cp, expt.
ng/mL
Cp, calc
ng/mL
AUC
calc.
AUC
trap.
1.26
3149.00
2406.75
3243.12
3715.99
2.10
2212.83
2204.58
5178.51
5967.96
3.15
1352.76
1977.99
7371.95
7839.89
6.46
1710.00
1419.48
12936.18
12908.76
10.51
1072.00
970.10
17705.19
18542.31
15.02
778.00
661.52
21325.89
22714.06
20.16
410.65
455.28
24146.52
25768.89
24.93
309.84
343.25
26028.76
27487.26
30.15
230.92
269.51
27611.61
28898.64
44.77
218.22
178.43
30760.83
32181.86
59.95
147.62
140.50
33151.12
34958.58
75.82
200.38
115.83
35174.04
37719.96
90.04
76.78
99.04
36697.32
39690.57
105.50
57.91
84.41
38111.16
40731.72
119.92
71.92
73.38
39246.13
41667.80
149.85
83.71
56.48
41172.02
43996.80
180.05
42.08
45.17
42695.25
45896.23
209.56
41.71
37.74
43911.58
47132.55
240.40
39.55
32.47
44988.99
48385.58
270.72
37.16
28.88
45915.79
49548.50
300.06
16.36
26.40
46724.80
50333.64
360.30
24.70
23.06
48205.45
51570.37
420.23
28.68
20.95
49520.21
53169.90
484.21
19.20
19.30
50805.46
54701.58
543.70
12.90
18.03
51914.82
55656.40
600.41
19.41
16.96
52906.42
56572.55
661.20
19.14
15.91
53904.96
57744.27
721.08
13.20
14.95
54828.45
58712.53
789.55
14.90
13.93
55816.56
59674.54
842.45
12.00
13.19
56533.58
60386.04
882.00
13.90
12.66
57044.69
60898.21
1270.00
10.11
8.49
61095.18
65556.15
1490.00
6.11
6.77
62767.48
67340.35
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasm concentrations. AUC = Area under the plasm concentration-time
curve, ng.min/mL, calculated (calc.) or estimted by trapezoidal rule
(trap.).

280
Table A-IV-4b. Buprenorphine in urine, Dog Study #4
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
EU ygs
AUCt
15.000
13.710
37.000
6.600
0.507
0.507
21.313
30.300
16.950
12.000
6.480
0.203
0.711
27.652
46.000
298.550
12.000
5.990
3.583
4.293
30.978
62.700
205.800
7.000
6.030
1.441
5.734
33.531
90.130
25.900
6.500
6.150
0.168
5.902
36.706
120.000
36.410
12.000
6.130
0.437
6.339
39.252
158.000
20.510
14.000
6.310
0.287
6.626
41.618
189.500
5.240
10.000
6.550
0.052
6.679
43.109
213.000
10.040
19.000
6.000
0.191
6.869
44.040
243.000
14.520
24.000
5.710
0.348
7.218
45.073
272.000
18.100
17.000
5.640
0.308
7.526
45.953
301.000
14.870
48.000
5.570
0.714
8.239
46.750
362.000
13.810
57.000
5.610
0.787
9.027
48.245
422.000
35.380
70.000
5.410
2.477
11.503
49.557
488.000
26.340
55.000
5.470
1.449
12.952
50.878
545.000
13.430
30.000
5.530
0.403
13.355
51.938
601.000
10.530
89.000
5.540
0.937
14.292
52.916
662.000
22.960
109.000
5.400
2.503
16.795
53.918
700.000
7.600
54.000
5.820
0.410
17.205
54.510
881.000
7.820
265.000
5.740
2.072
19.277
57.032
1270.000
10.340
400.000
7.360
4.136
23.413
61.095
U=Amount excreted in urine during a collection interval. £U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml.

281
Table A-IV-4c. Buprenorphine: Urine, Dog Study #4
E- ygs
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
22.906
2.467
0.034
7.500
1283.561
0.024
0.026
22.703
0.784
0.013
22.650
389.850
0.026
0.034
19.120
0.764
0.228
38.150
207.386
0.139
1.100
17.679
0.419
0.086
54.350
151.879
0.171
0.568
17.511
0.237
0.006
76.415
115.051
0.161
0.053
17.074
0.402
0.015
105.065
84.778
0.161
0.173
16.787
0.368
0.008
139.000
61.814
0.159
0.122
16.735
0.317
0.002
173.750
47.163
0.155
0.035
16.544
0.809
0.008
201.250
39.554
0.156
0.205
16.195
0.800
0.012
228.000
34.348
0.160
0.338
15.888
0.586
0.011
257.500
30.289
0.164
0.350
15.174
1.655
0.025
286.500
27.448
0.176
0.897
14.387
0.934
0.013
331.500
24.435
0.187
0.528
11.910
1.167
0.041
392.000
21.846
0.232
1.889
10.461
0.833
0.022
455.000
20.000
0.255
1.097
10.059
0.526
0.007
516.500
18.586
0.257
0.380
9.121
1.589
0.017
573.000
17.463
0.270
0.958
6.619
1.787
0.041
631.500
16.410
0.311
2.500
6.208
1.421
0.011
681.000
15.583
0.316
0.693
4.136
1.464
0.011
790.500
13.914
0.338
0.823
0.000
1.028
0.011
1075.500
10.376
0.383
1.025
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

282
Table A-IV-4d. Plasma metabolite, Dog Study #4
Time
min
Cp, expt.
ng/mL
Cp, calc
ng/rriL
AUC
calc.
AUC
trap.
1.26
1219.90
1219.82
2068.34
768.54
2.10
864.90
878.89
2938.10
1644.15
3.15
658.80
631.22
3717.93
2444.10
6.46
332.30
365.17
5246.65
4084.37
10.51
352.00
293.92
6554.55
5470.07
15.02
220.00
254.41
7786.21
6759.93
20.16
251.20
218.90
8999.73
7970.92
24.93
201.30
191.23
9976.07
9050.13
30.15
176.20
165.69
10905.65
10035.41
44.77
75.10
114.18
12920.52
11872.41
59.95
90.00
81.78
14387.14
13125.52
75.82
77.30
61.53
15510.47
14453.04
90.04
66.40
50.40
16300.38
15474.75
105.50
40.20
42.76
17015.93
16298.77
119.20
46.40
38.35
17569.63
16891.98
149.85
40.10
32.68
18647.80
18217.59
180.05
33.13
29.65
19585.35
19323.36
209.56
25.51
27.61
20428.82
20188.60
204.40
25.43
27.93
20285.54
20057.17
270.72
21.33
24.37
22014.10
21607.73
300.60
24.20
23.00
22721.46
22287.95
360.30
16.28
20.51
24018.68
23496.28
420.23
15.87
18.29
25180.14
24459.65
484.21
14.21
16.19
26281.82
25421.91
543.70
9.80
14.45
27192.21
26136.09
600.41
12.10
12.97
27968.89
26757.06
661.20
14.00
11.55
28713.17
27550.37
721.08
10.00
10.30
29366.52
28268.93
789.55
8.85
9.04
30027.55
28914.26
842.45
7.71
8.17
30482.26
29352.28
882.00
8.10
7.57
30793.44
29664.92
1270.00
7.04
3.61
32869.42
32602.08
1490.00
7.34
2.37
33518.11
34183.88
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

283
Table A-IV-4e. Metabolite in urine, Dog Study #4
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
zu ugs
AUCt
15.000
199.740
37.000
6.600
7.390
7.390
7.781
30.300
339.000
12.000
6.480
4.068
11.458
10.930
46.000
1427.630
12.000
5.990
17.132
28.590
13.059
62.700
748.100
7.000
6.030
5.237
33.827
14.606
90.130
912.330
6.500
6.150
5.930
39.757
16.305
120.000
796.060
12.000
6.130
9.553
49.310
17.600
158.000
588.310
14.000
6.310
8.236
57.546
18.910
189.500
428.600
10.000
6.550
4.286
61.832
19.862
213.000
554.890
19.000
6.000
10.543
72.375
20.523
243.000
461.420
24.000
5.710
11.074
83.449
21.320
272.000
378.210
17.000
5.640
6.430
89.878
22.045
301.000
326.900
48.000
5.570
15.691
105.570
22.731
362.000
150.630
57.000
5.610
8.586
114.156
24.053
422.000
180.800
70.000
5.410
12.656
126.812
25.212
488.000
141.070
55.000
5.470
7.759
134.570
26.343
545.000
162.700
30.000
5.530
4.881
139.451
27.211
601.000
175.770
89.000
5.540
15.644
155.095
27.977
662.000
78.300
109.000
5.400
8.535
163.630
28.722
700.000
80.260
54.000
5.820
4.334
167.964
29.145
881.000
74.100
265.000
5.740
19.637
187.600
30.786
1270.000
66.850
400.000
7.360
26.740
214.340
32.869
U=Amount excreted in urine during a collection interval. ZU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

284
Table A-IV-4f. Metabolite in urine, Dog Study #4
z- ygs
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
206.950
2.467
0.493
7.500
337.951
0.950
1.458
202.882
0.784
0.266
22.650
203.888
1.048
1.304
185.750
0.764
1.091
38.150
134.382
2.189
8.120
180.513
0.419
0.314
54.350
91.872
2.316
3.413
174.583
0.237
0.216
76.415
60.957
2.438
3.547
165.031
0.402
0.320
105.065
42.931
2.802
7.449
156.794
0.368
0.217
139.000
34.246
3.043
6.329
152.508
0.317
0.136
173.750
30.173
3.113
4.509
141.965
0.809
0.449
201.250
28.130
3.526
15.948
130.891
0.800
0.369
228.000
26.540
3.914
13.909
124.462
0.586
0.222
257.500
25.006
4.077
8.866
108.771
1.655
0.541
286.500
23.631
4.644
22.897
100.185
0.934
0.141
331.500
21.673
4.746
6.494
87.529
1.167
0.211
392.000
19.306
5.030
10.926
79.770
0.833
0.118
455.000
17.117
5.108
6.868
74.889
0.526
0.086
516.500
15.221
5.125
5.626
59.245
1.589
0.279
573.000
13.664
5.544
20.444
50.711
1.787
0.140
631.500
12.220
5.697
11.449
46.377
1.421
0.114
681.000
11.118
5.763
10.258
26.740
1.464
0.108
790.500
9.021
6.094
12.027
0.000
1.028
0.069
1075.500
5.235
6.521
13.131
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concentration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

285
Table A-IV-5d. Plasma metabolite, Dog Study #5
Time
min
Cp, expt.
ng/mL
Cp, calc. AUC
ng/mL calc.
AUC
trap.
1.00
1235.00
1032.99
1070.11
617.50
2.20
1181.00
952.04
2260.12
2067.10
3.30
683.00
886.11
3270.42
3092.30
5.06
648.50
794.89
4747.30
4264.02
10.19
576.50
605.31
8297.26
7406.15
14.98
551.00
497.01
10917.32
10106.51
20.16
549.00
423.80
13287.25
12955.51
25.16
539.00
378.76
15285.76
15675.51
30.79
285.00
345.45
17317.92
17995.07
45.54
262.00
297.39
22015.25
22029.19
49.79
260.00
288.21
23259.23
23138.44
75.16
264.50
246.43
30009.88
29791.73
91.93
209.00
224.21
33952.31
33762.02
105.30
225.00
208.32
36842.17
36663.31
120.80
184.00
191.60
39939.33
39833.06
149.20
178.00
165.12
44993.00
44973.46
180.50
138.00
141.17
49773.46
49918.86
209.60
94.50
122.92
53607.44
53301.74
240.10
112.00
107.19
57108.64
56450.86
274.50
91.30
92.82
60539.56
59947.62
303.20
96.00
83.04
63058.80
62635.38
360.50
76.20
68.13
67364.13
67568.91
422.50
63.40
56.99
71220.95
71896.51
470.20
67.00
50.84
73785.67
75006.55
550.10
53.00
43.63
77538.61
79800.55
607.20
28.20
40.07
79923.40
82118.81
675.00
37.10
36.92
82527.84
84332.48
1164.00
24.97
26.41
97559.07
99508.59
1560.00
18.29
21.61
107028.31
108074.07
2631.00
14.63
12.71
124986.86
125702.73
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

286
Table A-IV-5e. Metabolite in urine, Dog Study #5
Time
min
Cone.
ng/mL
Volume
rriL
PH
U ygs
EU ygs
AUCt
16.500
162.500
20.000
5.810
3.250
3.250
11.653
33.000
854.500
5.000
5.660
4.273
7.523
18.070
50.000
722.800
6.000
5.730
4.337
11.859
23.320
60.000
990.300
5.000
5.840
4.952
16.811
26.103
75.000
201.200
21.000
6.120
4.225
21.036
29.970
106.000
271.740
7.000
6.060
1.902
22.938
36.988
122.000
148.000
7.000
5.690
1.036
23.974
40.169
152.000
82.900
12.000
5.620
0.995
24.969
45.452
180.000
68.400
19.000
5.660
1.300
26.269
49.703
210.000
27.730
26.000
5.630
0.721
26.990
53.657
241.000
28.500
30.000
5.340
0.855
27.845
57.205
277.000
23.170
23.000
5.560
0.533
28.377
60.770
307.000
33.200
28.000
5.550
0.930
29.307
63.372
364.500
26.900
48.000
5.540
1.291
30.598
67.635
438.000
27.200
43.000
5.430
1.170
31.768
72.087
475.000
25.600
16.000
5.630
0.410
32.177
74.028
552.000
29.500
51.000
5.650
1.505
33.682
77.621
616.000
36.190
27.000
5.780
0.977
34.659
80.274
687.000
32.300
85.000
5.750
2.746
37.405
82.968
1164.000
24.170
37.000
6.080
0.894
38.299
97.559
1994.000
16.000
200.000
7.000
3.200
41.499
115.467
2630.000
66.450
80.000
7.420
5.316
46.815
124.974
U=Amount excreted in urine during a collection interval. £U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

287
Table A-IV-5f. Metabolite in urine, Dog Study #5
E- ygs
AV/ At
rriL/min
AU/ At
vg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
43.565
1.212
0.197
8.250
665.839
0.279
0.296
39.292
0.303
0.259
24.750
381.790
0.416
0.678
34.956
0.353
0.255
41.500
307.403
0.509
0.830
30.004
0.500
0.495
55.000
278.232
0.644
1.780
25.779
1.400
0.282
67.500
257.644
0.702
1.093
23.877
0.226
0.061
90.500
226.004
0.620
0.272
22.841
0.438
0.065
114.000
198.724
0.597
0.326
21.846
0.400
0.033
137.000
175.888
0.549
0.189
20.546
0.679
0.046
166.000
151.649
0.529
0.306
19.825
0.867
0.024
195.000
131.638
0.503
0.183
18.970
0.968
0.028
225.500
114.329
0.487
0.241
18.437
0.639
0.015
259.000
98.898
0.467
0.150
17.508
0.933
0.031
292.000
86.643
0.462
0.358
16.217
0.835
0.022
335.750
73.916
0.452
0.304
15.047
0.585
0.016
401.250
60.342
0.441
0.264
14.637
0.432
0.011
456.500
52.430
0.435
0.211
13.133
0.662
0.020
513.500
46.543
0.434
0.420
12.156
0.422
0.015
584.000
41.394
0.432
0.369
9.410
1.197
0.039
651.500
37.905
0.451
1.020
8.516
0.078
0.002
925.500
30.209
0.393
0.062
5.316
0.241
0.004
1579.000
21.410
0.359
0.180
0.000
0.126
0.008
2312.000
14.887
0.375
0.561
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

288
Table A-IV-5a. Plasma buprenorphine, Dog Study #5
Time
min
Cp, expt.
ng/mL
Cp, calc
ng/mL
AUC
calc.
AUC
trap.
1.00
2707.00
2683.36
3479.27
3572.63
2.20
1534.00
1539.51
5936.77
6117.23
3.30
950.00
989.68
7297.10
7483.43
5.06
598.00
582.55
8623.43
8845.67
10.19
501.40
340.96
10747.44
11665.63
14.98
393.11
313.31
12302.11
13807.99
20.16
248.71
296.88
13881.15
15470.30
25.16
250.60
282.64
15329.56
16718.57
30.79
234.72
267.58
16877.97
18084.75
45.54
209.20
232.36
20557.87
21358.66
49.79
196.10
223.25
21525.88
22219.92
75.16
152.50
177.00
26575.32
26641.91
91.93
159.60
152.87
29334.94
29258.87
105.30
149.70
136.60
31267.32
31326.54
120.80
140.90
120.51
33256.35
33578.69
149.20
104.10
97.27
36331.80
37057.69
180.50
96.10
78.73
39069.92
40190.82
209.60
68.50
66.24
41169.89
42585.75
240.10
56.40
56.64
43036.13
44490.48
274.50
47.90
48.82
44842.41
46284.44
303.20
45.90
44.02
46171.57
47630.47
360.50
36.75
37.45
48490.18
49998.39
422.50
34.45
33.00
50663.85
52205.59
470.20
32.00
30.60
52178.22
53790.42
550.10
21.43
27.63
54498.44
55924.95
607.20
25.20
25.95
56027.17
57256.24
675.00
27.00
24.23
57727.05
59025.82
1164.00
13.83
15.32
67212.75
69008.75
1560.00
8.33
10.62
72292.95
73396.43
2631.00
5.85
3.95
79513.22
80989.82
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

289
Table A-IV-5b. Buprenorphine in urine, Dog Study #5
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
EU ygs
AUCt
16.500
261.640
20.000
5.810
5.233
5.233
12.774
33.000
1153.000
5.000
5.660
5.765
10.998
17.463
50.000
713.700
6.000
5.730
4.282
15.280
21.573
60.000
591.640
5.000
5.840
2.958
18.238
23.700
75.000
174.560
21.000
6.120
3.666
21.904
26.547
106.000
89.470
7.000
6.060
0.626
22.530
31.363
122.000
105.330
7.000
5.690
0.737
23.268
33.400
152.000
56.500
12.000
5.620
0.678
23.946
36.601
180.000
41.830
19.000
5.660
0.795
24.740
39.030
210.000
74.300
26.000
5.630
1.932
26.672
41.196
241.000
59.000
30.000
5.340
1.770
28.442
43.087
277.000
29.300
23.000
5.560
0.674
29.116
44.964
307.000
33.650
28.000
5.550
0.942
30.058
46.338
364.500
33.210
48.000
5.540
1.594
31.652
48.639
438.000
44.600
43.000
5.430
1.918
33.570
51.169
475.000
14.500
16.000
5.630
0.232
33.802
52.325
552.000
16.280
51.000
5.650
0.830
34.632
54.551
616.000
9.010
27.000
5.780
0.243
34.876
56.255
687.000
8.110
85.000
5.750
0.689
35.565
58.016
1164.000
8.100
37.000
6.080
0.300
35.865
67.213
1994.000
10.000
200.000
7.000
2.000
37.865
76.090
2630.000
78.450
80.000
7.420
6.276
44.141
79.509
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml.

290
Table A-IV-5c. Buprenorphine: Urine, Dog Study #5
e ~ pgs
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
nL/min
38.908
1.212
0.317
8.250
373.655
0.410
0.849
33.143
0.303
0.349
24.750
283.773
0.630
1.231
28.861
0.353
0.252
41.500
241.435
0.708
1.043
25.903
0.500
0.296
55.000
212.652
0.770
1.391
22.237
1.400
0.244
67.500
189.609
0.825
1.289
21.610
0.226
0.020
90.500
154.753
0.718
0.131
20.873
0.438
0.046
114.000
127.230
0.697
0.362
20.195
0.400
0.023
137.000
106.379
0.654
0.212
19.400
0.679
0.028
166.000
86.547
0.634
0.328
17.469
0.867
0.064
195.000
72.026
0.647
0.894
15.699
0.968
0.057
225.500
60.860
0.660
0.938
15.025
0.639
0.019
259.000
52.017
0.648
0.360
14.082
0.933
0.031
292.000
45.741
0.649
0.687
12.488
0.835
0.028
335.750
39.897
0.651
0.695
10.571
0.585
0.026
401.250
34.310
0.656
0.760
10.339
0.432
0.006
456.500
31.228
0.646
0.201
9.508
0.662
0.011
513.500
28.877
0.635
0.373
9.265
0.422
0.004
584.000
26.606
0.620
0.143
8.576
1.197
0.010
651.500
24.801
0.613
0.391
8.276
0.078
0.001
925.500
19.110
0.534
0.033
6.276
0.241
0.002
1579.000
10.438
0.498
0.231
0.000
0.126
0.010
2312.000
5.299
0.555
1.862
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concentration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

291
Table A-IV-6. Plasma buprenorphine, Dog Study #6
Time
min
Cp, expt.
ng/rriL
Cp, calc
ng/mL
AUC
calc.
AUC
trap.
0.88
3349.00
2270.44
2194.31
2673.91
1.96
1552.00
1790.24
4385.66
5332.71
4.90
910.00
981.42
8318.38
8951.85
10.12
419.10
425.63
11693.29
12420.80
15.11
295.40
268.59
13351.89
14203.47
19.81
258.35
217.72
14476.13
15504.79
30.28
204.90
180.80
16524.85
17929.90
39.94
174.00
163.48
18184.01
19759.99
49.66
135.30
148.92
19700.76
21263.19
59.61
124.90
135.71
21115.56
22557.68
91.60
90.90
102.14
24887.49
26009.40
120.07
72.10
80.91
27477.20
28329.71
148.90
64.40
65.26
29572.48
30297.35
181.02
52.80
52.71
31455.67
32179.59
210.57
46.30
44.35
32883.58
33643.79
241.23
39.54
37.94
34140.30
34959.72
275.00
39.70
32.74
35329.23
36297.68
307.35
34.04
29.01
36325.35
37490.43
359.80
27.70
24.68
37726.06
39109.56
421.47
19.38
21.18
39133.38
40561.27
481.10
18.36
18.70
40319.11
41686.49
539.32
15.11
16.78
41350.28
42660.80
599.65
12.85
15.12
42311.16
43504.21
661.60
13.80
13.64
43200.67
44329.70
719.20
13.91
12.42
43950.30
45127.75
783.30
11.10
11.20
44706.54
45929.32
838.20
12.13
10.26
45295.38
46566.98
898.70
8.75
9.32
45887.41
47198.60
962.40
8.14
8.43
46452.29
47736.55
1000.00
8.55
7.94
46759.92
48050.32
Cp, expt. = Experimental plasma concentrations; Cp, calc. = Calculated
plasma concentrations. AUC = Area under the plasma concentration-time
curve, ng.min/mL, calculated (calc.) or estimated by trapezoidal rule
(trap.).

292
Table A-IV-7a. Plasma Buprenorphine, Dog Study #7
Time
min
Cp, expt. AUC
ng/mL trap.
11.09
204.10
1131.73
26.50
298.10
5001.19
37.70
317.30
8447.43
60.90
369.60
16415.47
116.20
645.60
44485.75
164.90
822.80
80241.29
195.05
381.00
98388.57
225.47
337.20
109312.39
259.55
200.00
118466.28
285.00
178.00
123276.33
370.50
117.00
135887.58
405.29
107.00
139784.06
465.29
99.85
145989.56
526.00
100.63
152075.13
585.40
99.50
158018.99
646.50
76.62
163399.46
705.30
75.00
167857.09
766.60
72.77
172386.24
823.30
63.00
176235.32
864.50
60.00
178769.12
1288.00
66.38
205530.08
1373.00
63.10
211032.98
1528.00
57.90
220410.48
1745.00
59.60
233159.23
2050.00
49.70
249827.48
2744.00
43.50
282167.88
2821.00
40.30
285394.18
2931.00
33.30
289442.18
3040.00
30.01
292892.58
3715.00
30.00
313145.95
4845.00
18.21
340384.60
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

293
Table A-IV-7b. Buprenorphine in urine, Dog Study #7
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
EU ygs
AUCt
64.000
136.100
68.000
6.810
9.255
9.255
17.585
165.000
1292.000
22.000
6.240
28.424
37.679
80.323
191.000
1704.000
6.000
6.220
10.224
47.903
96.725
219.000
544.600
12.000
6.280
6.535
54.438
107.101
265.000
181.800
25.000
6.420
4.545
58.983
119.543
291.000
73.680
23.000
6.760
1.695
60.678
124.331
315.000
5.769
51.000
6.820
0.294
60.972
128.295
358.000
30.200
52.000
6.720
1.570
62.542
134.369
407.000
22.920
28.000
6.930
0.642
63.184
139.967
510.000
0.940
53.000
7.300
0.050
63.234
150.467
539.000
10.900
123.000
7.330
1.341
64.575
153.382
697.000
0.000
257.000
7.390
0.000
64.575
167.234
875.000
26.230
270.000
7.470
7.082
71.657
179.400
1435.000
290.500
600.000
6.670
174.300
245.957
214.881
1735.000
75.100
300.000
7.610
22.530
268.487
232.564
3040.000
28.600
100.000
7.600
2.860
271.347
292.893
3715.000
4.820
445.000
7.250
2.145
273.492
313.146
4845.000
3.550
210.000
7.100
0.746
274.237
340.385
U=Amount excreted in urine during a collection interval. £U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

294
Table A-IV-7c. Buprenorphine in urine, Dog Study #7
e“ ygs
AV/ At
AU/At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
yg/min
min
ng/mL
mL/min
mL/min
264.982
1.063
0.145
32.000
307.700
0.526
0.470
236.558
0.218
0.281
114.500
507.600
0.469
0.554
226.334
0.231
0.393
178.000
601.900
0.495
0.653
219.799
0.429
0.233
205.000
359.100
0.508
0.650
215.254
0.543
0.099
242.000
268.600
0.493
0.368
213.559
0.885
0.065
278.000
189.000
0.488
0.345
213.265
2.125
0.012
303.000
147.500
0.475
0.083
211.695
1.209
0.037
336.500
147.500
0.465
0.248
211.053
0.571
0.013
382.500
112.000
0.451
0.117
211.003
0.515
0.000
458.500
103.425
0.420
0.005
209.663
4.241
0.046
524.500
100.240
0.421
0.461
209.663
1.627
0.000
618.000
88.060
0.386
0.000
202.580
1.517
0.040
786.000
67.885
0.399
0.586
28.280
1.071
0.311
1155.000
63.190
1.145
4.926
5.750
1.000
0.075
1585.000
58.750
1.154
1.278
2.890
0.077
0.002
2387.500
46.600
0.926
0.047
0.745
0.659
0.003
3377.500
30.005
0.873
0.106
0.000
0.186
0.001
4280.000
24.105
0.806
0.027
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

295
Table A-IV-7d. Plasma metabolite, Dog Study #7
Time
min
Cp, expt
ng/rriL
. AUC
trap.
11.09
14.52
80.51
26.50
25.60
389.64
37.70
87.50
1023.00
60.90
136.00
3615.60
116.20
197.50
12836.87
164.90
226.10
23151.53
167.96
225.20
23842.02
169.99
212.00
24285.78
174.96
181.00
25262.39
179.90
129.80
26030.06
185.18
90.30
26611.13
195.18
95.00
27537.63
210.15
86.80
28898.40
225.47
76.10
30146.21
259.55
70.30
32640.87
285.00
60.60
34306.57
370.50
32.00
38265.22
405.29
37.30
39470.69
465.29
23.41
41291.99
526.00
20.10
42612.74
585.40
27.00
44011.61
646.50
18.40
45398.58
705.30
30.90
46848.00
766.60
33.00
48806.54
823.30
36.80
50785.37
864.50
36.80
52301.53
1288.00
30.80
66615.83
1373.00
25.10
68991.58
1528.00
20.90
72556.58
1745.00
22.30
77243.78
2050.00
35.30
86027.78
2744.00
30.40
108825.68
2821.00
12.40
110473.48
2931.00
17.30
112106.98
3040.00
14.00
113812.83
3715.00
12.10
122621.58
4845.00
10.13
135181.53
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

296
Table A-IV-7e. Metabolite in urine, Dog Study #7
Time
min
Cone.
ng/rnL
Volume
mL
PH
U ygs
XU ygs
AUCt
64.000
340.900
68.000
6.810
23.181
23.181
4.043
165.000
2344.200
22.000
6.240
51.572
74.754
23.174
191.000
3846.600
6.000
6.220
23.080
97.833
27.145
219.000
1316.000
12.000
6.280
15.792
113.625
29.639
265.000
461.000
25.000
6.420
11.525
125.150
33.018
291.000
563.000
23.000
6.760
12.949
138.099
34.664
315.000
202.000
51.000
6.820
10.302
148.401
35.974
358.000
74.700
52.000
6.720
3.884
152.286
37.839
407.000
273.400
28.000
6.930
7.655
159.941
39.534
510.000
90.000
53.000
7.300
4.770
164.711
42.284
539.000
103.000
123.000
7.330
12.669
177.380
42.884
697.000
240.000
257.000
7.390
61.680
239.060
46.599
875.000
137.000
270.000
7.470
36.990
276.050
52.687
1435.000
80.100
600.000
6.670
48.060
324.110
70.496
1735.000
98.000
300.000
7.610
29.400
353.510
77.021
3040.000
94.400
100.000
7.600
9.440
362.950
113.813
3715.000
50.200
445.000
7.250
22.339
385.289
122.622
4845.000
44.930
210.000
7.100
9.435
394.724
135.182
U-Amount excreted in urine during a collection interval. E U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

297
Table A-IV-7f. Metabolite in urine, Dog Study #7
E- y9s
AV/ At
mL/min
AU/ A t
u g/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
371.543
1.063
0.362
32.000
56.550
5.734
6.405
319.971
0.218
0.511
114.500
166.750
3.226
3.062
296.891
0.231
0.888
178.000
155.400
3.604
5.712
281.099
0.429
0.564
205.000
90.900
3.834
6.205
269.574
0.543
0.251
242.000
73.200
3.790
3.423
256.625
0.885
0.498
278.000
65.450
3.984
7.609
246.323
2.125
0.429
303.000
46.300
4.125
9.271
242.439
1.209
0.090
336.500
46.300
4.025
1.951
234.783
0.571
0.156
382.500
34.650
4.046
4.509
230.013
0.515
0.046
458.500
30.355
3.895
1.526
217.344
4.241
0.437
524.500
21.755
4.136
20.081
155.664
1.627
0.390
618.000
22.700
5.130
17.197
118.674
1.517
0.208
786.000
34.900
5.239
5.954
70.614
1.071
0.086
1155.000
33.800
4.598
2.539
41.214
1.000
0.098
1585.000
21.600
4.590
4.537
31.774
0.077
0.007
2387.500
32.850
3.189
0.220
9.435
0.659
0.033
3377.500
13.050
3.142
2.536
0.000
0.186
0.008
4280.000
11.115
2.920
0.751
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

298
Table A-IV-8a. Plasma Buprenorphine, Dog Study #8
Time
min
Cp, expt. AUC
ng/mL trap.
4.92
240.70
592.12
15.20
604.20
4934.91
25.90
635.80
11568.91
35.70
534.40
17302.89
64.80
565.30
33303.52
100.60
653.00
55111.09
144.00
780.90
86226.72
173.11
770.82
108812.01
176.44
594.50
111085.27
192.24
383.30
118809.89
219.20
282.00
127778.13
248.30
232.00
135256.83
294.30
214.30
145521.73
355.70
160.80
157037.30
472.90
106.90
172724.52
589.40
104.60
185044.39
707.00
56.35
194508.25
829.00
47.31
200831.51
1484.00
117.20
254708.54
1683.00
90.30
275354.79
1729.00
132.30
280474.59
2785.00
55.50
379632.99
2955.00
40.50
387792.99
3171.00
36.11
396066.33
4231.00
43.93
438484.88
4400.00
40.40
445610.76
4588.00
39.81
453150.50
5773.00
24.74
491396.38
8531.00
10.99
540668.05
8956.00
9.99
545126.30
9971.00
5.90
553190.98
11431.00
4.01
560426.01
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

299
Table A-IV-8b. Buprenorphine in urine, Dog Study #8
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
ZU ygs
AUCt
44.000
1855.000
21.000
6.240
38.955
38.955
21.775
145.000
1493.000
60.000
5.930
89.580
128.535
87.007
166.000
756.300
28.000
6.240
21.176
149.711
103.323
186.500
284.000
37.000
6.450
10.508
160.219
116.390
206.000
63.500
76.000
6.840
4.826
165.045
123.728
221.000
57.400
73.000
6.880
4.190
169.236
128.283
241.000
33.100
64.000
6.890
2.118
171.354
133.517
262.000
34.360
60.000
6.950
2.062
173.416
138.399
281.000
41.200
91.000
6.970
3.749
177.165
142.638
306.000
22.300
110.000
7.010
2.453
179.618
147.969
323.000
7.020
80.000
7.150
0.562
180.179
151.313
357.000
18.100
58.000
7.050
1.050
181.229
157.246
411.000
27.100
93.000
6.730
2.520
183.750
165.226
484.000
40.410
37.000
6.270
1.495
185.245
173.910
587.000
35.100
115.000
6.400
4.037
189.281
184.793
617.000
8.910
195.000
6.850
1.737
191.019
187.775
657.000
2.840
57.500
7.100
0.163
191.182
191.178
709.000
2.780
230.000
6.950
0.639
191.821
194.621
767.000
5.340
110.000
6.750
0.587
192.409
197.756
829.000
5.170
160.000
6.850
0.827
193.236
200.832
1484.000
11.810
300.000
7.010
3.543
196.779
254.709
1729.000
7.140
160.000
6.960
1.142
197.921
280.475
2785.000
10.620
398.000
6.850
4.227
202.148
379.633
8531.000
9.900
420.000
6.400
4.158
206.306
540.668
8956.000
3.743
470.000
6.390
1.759
208.065
545.126
11431.000
21.540
335.000
5.900
7.216
215.281
560.426
U=Amount excreted in urine during a collection interval, z U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

300
Table A-IV-8c. Buprenorphine in urine, Dog Study #8
E “ U9S
AV/ At
AU/ A t
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
yg/min
min
ng/mL
mL/min
mL/min
176.326
0.477
0.885
22.000
620.000
1.789
1.428
86.746
0.594
0.887
94.500
609.150
1.477
1.456
65.570
1.333
1.008
155.500
775.860
1.449
1.300
55.062
1.805
0.513
176.250
682.660
1.377
0.751
50.236
3.897
0.247
196.250
332.650
1.334
0.744
46.046
4.867
0.279
213.500
332.650
1.319
0.840
43.927
3.200
0.106
231.000
257.000
1.283
0.412
41.866
2.857
0.098
251.500
223.150
1.253
0.440
38.116
4.789
0.197
271.500
223.150
1.242
0.884
35.663
4.400
0.098
293.500
223.150
1.214
0.440
35.102
4.706
0.033
314.500
187.550
1.191
0.176
34.052
1.706
0.031
340.000
187.550
1.153
0.165
31.532
1.722
0.047
384.000
133.850
1.112
0.349
30.037
0.507
0.020
447.500
133.850
1.065
0.153
26.000
1.117
0.039
535.500
105.750
1.024
0.371
24.263
6.500
0.058
602.000
80.475
1.017
0.720
24.099
1.438
0.004
637.000
80.475
1.000
0.051
23.460
4.423
0.012
683.000
80.475
0.986
0.153
22.872
1.897
0.010
738.000
51.830
0.973
0.195
22.045
2.581
0.013
798.000
51.830
0.962
0.257
18.502
0.458
0.005
1156.500
82.255
0.773
0.066
17.360
0.653
0.005
1606.500
103.750
0.706
0.045
13.133
0.377
0.004
2257.000
93.900
0.532
0.043
8.975
0.073
0.001
5658.000
32.275
0.382
0.022
7.216
1.106
0.004
8743.500
10.490
0.382
0.395
0.000
0.135
0.003 ;
10193.500
4.956
0.384
0.588
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasm
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasm concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasm concentation at the mid point of urine
collection time.

301
Table A-IV-8d. Plasma metabolite, Dog Study #8
Time
min
Cp, expt. AUC
ng/mL trap.
4.92
24.37
59.95
15.20
44.60
414.46
25.90
101.74
1197.38
35.70
129.76
2331.73
64.80
222.00
7449.83
100.60
333.60
17395.07
143.40
546.00
36218.51
173.10
492.00
51632.81
176.40
476.40
53230.67
192.24
332.00
59633.20
219.20
157.00
66224.92
248.30
141.00
70560.82
294.30
90.10
75876.12
355.70
80.90
81125.82
472.90
74.00
90202.96
589.40
62.10
98130.79
707.00
74.70
106174.63
829.00
60.00
114391.33
1484.00
47.60
149630.33
1683.00
52.00
159540.53
1729.00
36.78
161582.47
2785.00
30.03
196858.15
2955.00
41.20
202912.70
3171.00
30.03
210605.54
4231.00
24.40
239453.44
4400.00
21.10
243298.19
4588.00
30.14
248114.75
5773.00
29.40
283392.20
8956.00
8.84
344251.16
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

302
Table A-IV-8e. Metabolite in urine, Dog Study #8
Time
min
Cone.
ng/rriL
Volume
mL
PH
U y gs
EU u gs
AUCt
44.000
1336.000
21.000
6.240
28.056
28.056
3.518
145.000
315.800
60.000
5.930
18.948
47.004
37.090
166.000
912.800
28.000
6.240
25.558
72.562
48.094
186.500
248.400
37.000
6.450
9.191
81.753
57.577
206.000
58.330
76.000
6.840
4.433
86.186
63.587
221.000
106.500
73.000
6.880
7.775
93.961
66.507
241.000
70.750
64.000
6.890
4.528
98.489
69.517
262.000
63.500
60.000
6.950
3.810
102.299
72.389
281.000
38.200
91.000
6.970
3.476
105.775
74.580
306.000
13.430
110.000
7.010
1.477
107.252
76.920
323.000
50.520
80.000
7.150
4.042
111.294
78.400
357.000
76.640
58.000
7.050
4.445
115.739
81.231
411.000
44.840
93.000
6.730
4.170
119.909
85.510
484.000
126.900
37.000
6.270
4.695
124.604
91.018
587.000
141.000
115.000
6.400
16.215
140.819
97.981
617.000
77.840
195.000
6.850
15.179
155.998
99.886
657.000
62.600
57.500
7.100
3.599
159.598
102.574
709.000
55.820
230.000
6.950
12.839
172.436
106.324
767.000
148.400
110.000
6.750
16.324
188.760
110.440
829.000
132.200
160.000
6.850
21.152
209.912
114.391
1484.000
357.000
300.000
7.010
107.100
317.012
149.630
1729.000
158.400
160.000
6.960
25.344
342.356
161.582
2785.000
182.300
398.000
6.850
72.555
414.912
196.858
8531.000
233.500
420.000
6.400
98.070
512.982
339.911
8956.000
125.200
470.000
6.390
58.844
571.826
344.251
11431.000
222.600
335.000
5.900
74.571
646.397
369.153
U=Amount excreted in urine during a collection interval. £ U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

303
Table A-IV-8f. Metabolite in urine, Dog Study #8
z-ygs
AV/ At
mL/min
AÜ/ At
y g/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
618.341
0.477
0.638
22.000
73.170
7.975
8.714
599.393
0.594
0.188
94.500
277.800
1.267
0.675
573.834
1.333
1.217
155.500
519.000
1.509
2.345
564.644
1.805
0.448
176.250
484.200
1.420
0.926
560.210
3.897
0.227
196.250
244.500
1.355
0.930
552.436
4.867
0.518
213.500
244.500
1.413
2.120
547.908
3.200
0.226
231.000
149.000
1.417
1.519
544.098
2.857
0.181
251.500
115.550
1.413
1.570
540.622
4.789
0.183
271.500
115.550
1.418
1.583
539.144
4.400
0.059
293.500
115.550
1.394
0.511
535.103
4.706
0.238
314.500
85.500
1.420
2.781
530.658
1.706
0.131
340.000
85.500
1.425
1.529
526.488
1.722
0.077
384.000
77.450
1.402
0.997
521.792
0.507
0.064
447.500
77.450
1.369
0.830
505.577
1.117
0.157
535.500
68.050
1.437
2.313
490.399
6.500
0.506
602.000
68.400
1.562
7.397
486.799
1.438
0.090
637.000
68.400
1.556
1.316
473.960
4.423
0.247
683.000
68.400
1.622
3.610
457.636
1.897
0.281
738.000
67.350
1.709
4.179
436.484
2.581
0.341
798.000
67.350
1.835
5.065
329.384
0.458
0.164
1156.500
53.800
2.119
3.039
304.040
0.653
0.103
1606.500
49.800
2.119
2.077
231.485
0.377
0.069
2257.000
33.405
2.108
2.057
133.415
0.073
0.017
5658.000
29.770
1.509
0.573
74.571
1.106
0.138
8743.500
19.120
1.661
7.241
0.000
0.135
0.030 10193.500
4.420
1.751
6.817
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

304
Table A-IV-9a. Plasma Buprenorphine, Dog Study #9
Time
min
Cp, expt. AUC
ng/iriL trap.
6.89
177.61
611.87
15.20
323.20
2692.73
29.20
516.78
8572.59
50.80
462.87
19152.81
63.70
616.40
26114.10
102.30
737.20
52238.58
124.14
700.70
67940.45
160.50
712.30
93628.79
221.40
848.10
141142.97
236.50
759.00
153276.58
266.70
492.20
172169.70
297.00
318.30
184448.77
324.80
329.60
193454.58
354.70
257.00
202224.25
414.80
335.00
220013.85
472.30
189.00
235078.85
533.40
128.66
244783.36
596.30
138.30
253179.26
660.10
109.10
261071.32
722.50
110.90
267935.32
776.70
99.97
273649.89
895.00
46.40
282307.68
1017.00
43.00
287761.08
1134.00
43.63
292828.93
1256.00
48.10
298424.46
1372.00
42.86
303700.14
1435.00
30.72
306017.91
1956.00
31.52
322231.43
2645.00
20.20
340048.97
3033.00
21.80
348196.97
4165.00
12.80
367780.57
5601.00
12.56
385989.05
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

305
Table A-IV-9b. Buprenorphine in urine, Dog Study #9
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
EU y gs
AUCt
70.000
0.000
35.000
7.590
0.000
0.000
30.060
138.000
0.000
25.000
7.120
0.000
0.000
77.683
190.000
0.000
11.000
7.030
0.000
0.000
115.612
303.000
133.100
23.000
6.570
3.061
3.061
186.366
357.000
10.700
59.500
6.240
0.637
3.698
202.819
422.000
35.800
60.000
5.910
2.148
5.846
222.360
475.000
15.500
84.000
6.100
1.302
7.148
235.586
533.700
9.000
110.000
6.250
0.990
8.138
244.822
599.000
4.800
102.000
6.250
0.490
8.628
253.551
656.500
3.030
44.000
5.980
0.133
8.761
260.676
724.000
3.530
70.000
5.840
0.247
9.008
268.101
780.000
0.000
54.000
6.760
0.000
9.008
273.977
895.000
0.000
160.000
7.090
0.000
9.008
282.308
1242.000
0.000
355.000
6.930
0.000
9.008
297.755
1375.000
0.000
210.000
7.090
0.000
9.008
303.828
1435.000
0.000
72.000
7.370
0.000
9.008
306.018
1531.000
0.000
160.000
7.880
0.000
9.008
308.974
1815.000
0.000
310.000
8.410
0.000
9.008
317.802
1934.000
4.800
70.000
7.040
0.336
9.344
321.538
2645.000
28.700
440.000
6.990
12.628
21.972
340.049
2895.000
9.100
72.000
6.420
0.655
22.627
345.228
3378.000
6.500
210.000
6.130
1.365
23.992
355.245
4165.000
3.200
405.000
6.140
1.296
25.288
367.781
5508.000
10.730
730.000
6.280
7.833
33.121
384.820
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: pg.min/ml

306
Table A-IV-9c. Buprenorphine in urine, Dog Study #9
i - ygs
AV/ At
mL/min
AU/ A t
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
33.121
0.500
0.000
35.000
489.825
0.000
0.000
33.121
0.368
0.000
104.000
718.950
0.000
0.000
33.121
0.212
0.000
164.000
780.200
0.000
0.000
30.060
0.204
0.027
246.500
625.600
0.016
0.043
29.423
1.102
0.012
330.000
293.300
0.018
0.040
27.275
0.923
0.033
389.500
296.000
0.026
0.112
25.973
1.585
0.025
448.500
262.000
0.030
0.094
24.983
1.874
0.017
504.350
158.830
0.033
0.106
24.494
1.562
0.007
566.350
133.480
0.034
0.056
24.360
0.765
0.002
627.750
123.700
0.034
0.019
24.113
1.037
0.004
690.250
110.000
0.034
0.033
24.113
0.964
0.000
752.000
105.435
0.033
0.000
24.113
1.391
0.000
837.500
73.185
0.032
0.000
24.113
1.023
0.000
1068.500
43.315
0.030
0.000
24.113
1.579
0.000
1308.500
45.480
0.030
0.000
24.113
1.200
0.000
1405.000
36.790
0.029
0.000
24.113
1.667
0.000
1483.000
31.120
0.029
0.000
24.113
1.092
0.000
1673.000
31.120
0.028
0.000
23.777
0.588
0.003
1874.500
31.120
0.029
0.091
11.149
0.619
0.018
2289.500
25.860
0.065
0.687
10.494
0.288
0.003
2770.000
21.000
0.066
0.125
9.129
0.435
0.003
3136.500
17.300
0.068
0.163
7.833
0.515
0.002
3771.500
17.300
0.069
0.095
0.000
0.544
0.006
4836.500
12.680
0.086
0.460
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

307
Table A-IV-9d. Plasma metabolite, Dog Study #9
Time
min
Cp, expt
ng/mL
. AUC
trap.
6.89
11.78
40.58
15.20
18.68
167.14
29.20
43.78
604.36
50.80
121.40
2388.31
63.70
204.70
4491.65
102.30
209.35
12482.82
124.14
233.90
17323.11
160.50
261.00
26320.39
184.80
316.18
33333.13
196.00
312.00
36850.93
221.40
270.00
44242.33
236.50
295.83
48514.35
266.70
197.00
55956.08
297.00
199.70
61966.09
324.80
117.80
66379.34
354.70
101.00
69650.40
414.80
89.43
75372.82
472.30
40.90
79119.81
533.40
34.03
81408.92
596.30
14.75
82943.05
660.10
10.83
83759.05
722.50
14.62
84553.09
776.70
12.19
85279.64
895.00
0.00
86000.68
1017.00
0.00
86000.68
1134.00
0.00
86000.68
1256.00
0.00
86000.68
1372.00
0.00
86000.68
1435.00
0.00
86000.68
1956.00
10.82
88819.29
2645.00
5.19
94334.74
3033.00
18.20
98872.40
4165.00
7.86
113622.36
5601.00
10.40
126733.04
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

308
Table A-IV-9e. Metabolite in urine, Dog Study #9
Time
min
Cone.
ng/mL
Volume
mL
pH
üugs
EU pgs
AUCt
70.000
359.800
35.000
7.590
12.593
12.593
5.784
138.000
1697.000
25.000
7.120
42.425
55.018
20.637
190.000
2239.000
11.000
7.030
24.629
79.647
34.972
303.000
3126.000
23.000
6.570
71.898
151.545
63.111
357.000
1775.000
59.500
6.240
105.613
257.158
69.882
422.000
1280.000
60.000
5.910
76.800
333.958
75.995
475.000
1430.000
84.000
6.100
120.120
454.078
79.230
533.700
559.000
110.000
6.250
61.490
515.568
81.419
599.000
493.000
102.000
6.250
50.286
565.854
82.983
656.500
388.000
44.000
5.980
17.072
582.926
83.720
724.000
433.000
70.000
5.840
30.310
613.236
84.575
780.000
639.000
54.000
6.760
34.506
647.742
85.319
895.000
357.000
160.000
7.090
57.120
704.862
86.001
1242.000
102.300
355.000
6.930
36.317
741.178
86.001
1375.000
71.200
210.000
7.090
14.952
756.130
86.001
1435.000
31.000
72.000
7.370
2.232
758.362
86.001
1531.000
26.400
160.000
7.880
4.224
762.586
86.096
1815.000
18.360
310.000
8.410
5.692
768.278
87.500
1934.000
10.610
70.000
7.040
0.743
769.020
88.586
2645.000
4.250
440.000
6.990
1.870
770.890
94.335
2895.000
7.900
72.000
6.420
0.569
771.459
96.680
U=Amount excreted in urine during a collection interval. E U=Cuinulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

309
Table A-IV-9f. Metabolite in urine, Dog Study #9
r y9s
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
758.866
0.500
0.180
35.000
82.590
2.177
2.178
716.441
0.368
0.624
104.000
221.625
2.666
2.815
691.812
0.212
0.474
164.000
288.590
2.277
1.641
619.914
0.204
0.636
246.500
246.415
2.401
2.582
514.302
1.102
1.956
330.000
109.400
3.680
17.877
437.502
0.923
1.182
389.500
95.215
4.394
12.409
317.382
1.585
2.266
448.500
65.165
5.731
34.780
255.892
1.874
1.048
504.350
37.465
6.332
27.960
205.606
1.562
0.770
566.350
24.390
6.819
31.573
188.534
0.765
0.297
627.750
12.790
6.963
23.214
158.224
1.037
0.449
690.250
12.725
7.251
35.288
123.718
0.964
0.616
752.000
13.405
7.592
45.966
66.598
1.391
0.497
837.500
6.095
8.196
81.492
30.281
1.023
0.105
1068.500
0.000
0.000
0.000
15.329
1.579
0.112
1308.500
0.000
0.000
0.000
13.097
1.200
0.037
1405.000
0.000
0.000
0.000
8.873
1.667
0.044
1483.000
5.410
8.857
8.133
3.181
1.092
0.020
1673.000
5.410
8.780
3.704
2.439
0.588
0.006
1874.500
5.410
8.681
1.154
0.569
0.619
0.003
2289.500
8.005
8.172
0.329
0.000
0.288
0.002
2770.000
11.695
7.980
0.195
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

310
Table
A-IV-9g.
Metabolite
! in Bile
, Dog Study #9
Time
Cone.
Vol.
U ygs
EU ygs
AUCt
min
y g/mL
mL
68.0
497.1
11.5
5716.7
5716.7
28.8
138.0
2098.0
8.5
17833.0
23549.7
77.7
206.0
2110.0
9.2
19412.0
42961.7
128.3
269.0
1247.2
7.8
9728.2
52689.8
173.3
358.0
590.0
11.0
6490.0
59179.8
203.1
419.0
437.1
8.0
3496.8
62676.6
221.4
474.0
330.4
6.6
2180.6
64857.3
235.4
535.0
429.1
6.8
2917.9
67775.1
245.0
599.0
328.5
6.5
2135.3
69910.4
253.6
656.0
236.8
8.5
2012.8
71923.2
260.6
779.0
173.7
8.8
1528.6
73451.7
273.9
900.0
171.3
7.0
1199.1
74650.8
282.5
1019.0
203.1
7.8
1584.2
76235.0
287.8
1135.0
184.7
8.3
1533.0
77768.0
292.9
1256.0
55.1
15.0
826.5
78594.5
298.4
1372.0
42.6
9.0
383.4
78977.9
303.7
1455.0
37.9
6.4
242.6
79220.5
306.6
U=Amount excreted in bile during a collection interval.
E U=Cumulative amounts excreted in bile. AUCt=The area under
the buprenorphine plasma concentration-time curve at the
mid-point of bile collection interval, unit: y g.min/ml

311
Table A-IV-9h. Metabolite in bile, Dog Study #9
z-,gs
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
C1Ba
mL/min
C1Bb
mL/min
73503.840
0.169
84.068
34.000
489.825
198.539
171.629
55670.840
0.121
254.757
103.000
718.950
303.151
354.346
36258.840
0.135
285.471
172.000
780.200
334.731
365.894
26530.680
0.124
154.415
237.500
625.600
304.062
246.827
20040.680
0.124
72.921
313.500
323.950
291.412
225.101
16543.880
0.131
57.325
388.500
296.000
283.094
193.664
14363.240
0.120
39.648
446.500
262.000
275.521
151.328
11445.360
0.111
47.834
504.500
158.830
276.645
301.165
9310.110
0.102
33.363
567.000
133.480
275.725
249.950
7297.310
0.149
35.312
627.500
123.700
275.969
285.467
5768.750
0.072
12.427
717.500
110.000
268.191
112.976
4569.650
0.058
9.910
839.500
73.185
264.214
135.409
2985.470
0.066
13.312
959.500
44.700
264.846
297.817
1452.460
0.072
13.216
1077.000
43.315
265.535
305.105
625.960
0.124
6.831
1195.500
45.841
263.368
149.008
242.560
0.078
3.305
1314.000
45.476
260.055
72.680
0.000
0.077
2.922
1413.500
36.810
258.358
79.392
t-mid = Mid-point of bile collection interval. Cp, t-mid = plasma
concenration of buprenorphine at the mid point of bile collection
interval, a) Biliary clearance calculated from the ratio of the
cumulative amount excreted in the bile versus area under the plasma
concentration-time profile, b) Instantaneous biliary clearance was
obtained from the ratio of the biliary excretion rate and the plasma
concentation at the mid point of bile collection interval.

312
Table A-IV-10a. Plasma Buprenorphine, Dog Study #10
Time
min
Cp, expt. AUC
ng/rriL trap.
7.34
254.50
934.01
15.69
283.80
3181.42
33.70
469.30
9963.08
49.50
459.50
17300.60
60.00
496.00
22316.98
111.00
553.90
49089.43
229.80
565.10
115558.03
259.33
301.80
128357.81
291.10
236.50
136908.70
320.59
250.30
144086.57
351.95
179.50
150825.83
409.10
208.10
161901.50
468.95
190.30
173823.62
529.25
144.70
183923.87
589.75
116.70
191831.22
649.75
120.70
198953.22
709.95
97.20
205512.01
771.85
88.00
211243.95
890.50
73.40
220819.01
1013.00
63.20
229185.76
1131.50
48.30
235792.13
1249.00
52.00
241684.76
1369.50
55.80
248179.71
1487.50
53.40
254622.51
1616.00
38.20
260507.81
2745.00
43.65
306712.13
3227.00
39.15
326666.93
5138.00
39.97
402266.09
5870.00
24.60
425898.71
6570.00
24.00
442908.71
6885.00
18.20
449555.21
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/rriL, estimated by trapezoidal rule (trap.)*

313
Table A-IV-10b. Buprenorphine in urine, Dog Study #10
Time
min
Cone.
ng/mL
Volume
mL
PH
U ygs
EU ygs
AUCt
80.000
410.200
17.000
5.910
6.973
6.973
32.464
213.000
610.700
48.000
5.940
29.314
36.287
106.078
233.000
379.000
21.000
6.350
7.959
44.246
117.321
260.700
206.000
34.000
6.150
7.004
51.250
128.769
295.000
128.000
35.000
6.030
4.480
55.730
137.835
322.000
163.000
32.000
5.580
5.216
60.946
144.437
354.000
227.000
64.000
5.800
14.528
75.474
151.195
411.000
148.400
148.000
6.010
21.963
97.437
162.296
470.000
116.200
76.000
6.050
8.831
106.268
174.023
530.500
68.400
102.000
6.040
6.977
113.245
184.104
591.500
66.600
176.000
6.110
11.722
124.967
192.036
650.000
19.000
156.000
6.510
2.964
127.931
198.983
711.000
24.900
106.000
6.440
2.639
130.570
205.614
773.000
44.300
124.000
5.780
5.493
136.063
211.345
893.000
25.000
105.000
6.410
2.625
138.688
221.002
1014.000
0.000
142.000
6.540
0.000
138.688
229.249
1132.000
6.780
100.000
6.950
0.678
139.366
235.816
1247.500
0.000
54.000
6.780
0.000
139.366
241.607
1370.000
0.000
86.000
6.620
0.000
139.366
248.208
1488.000
9.100
42.000
6.940
0.382
139.749
254.649
1612.000
9.800
42.000
6.740
0.412
140.160
260.354
2745.000
30.000
1150.000
8.930
34.500
174.660
306.712
3227.000
34.600
730.000
8.780
25.258
199.918
326.667
5138.000
14.300
600.000
7.660
8.580
208.498
402.266
6570.000
12.100
350.000
8.560
4.235
212.733
442.909
U=Amount excreted in urine during a collection interval. EU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

314
Table A-IV-10c. Buprenorphine in urine, Dog Study #10
AV/ At
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
205.760
0.213
0.087
40.000
464.400
0.215
0.188
176.446
0.361
0.220
146.500
559.500
0.342
0.394
168.487
1.050
0.398
223.000
559.500
0.377
0.711
161.483
1.227
0.253
246.850
433.450
0.398
0.583
157.003
1.020
0.131
277.850
269.150
0.404
0.485
151.787
1.185
0.193
308.500
243.400
0.422
0.794
137.259
2.000
0.454
338.000
214.900
0.499
2.113
115.296
2.596
0.385
382.500
193.800
0.600
1.988
106.465
1.288
0.150
440.500
199.200
0.611
0.751
99.488
1.686
0.115
500.250
167.500
0.615
0.688
87.766
2.885
0.192
561.000
130.700
0.651
1.470
84.802
2.667
0.051
620.750
118.700
0.643
0.427
82.163
1.738
0.043
680.500
108.950
0.635
0.397
76.670
2.000
0.089
742.000
92.600
0.644
0.957
74.045
0.875
0.022
833.000
80.700
0.628
0.271
74.045
1.174
0.000
953.500
68.300
0.605
0.000
73.367
0.847
0.006
1073.000
55.750
0.591
0.103
73.367
0.468
0.000
1189.750
50.150
0.577
0.000
73.367
0.702
0.000
1308.750
53.900
0.561
0.000
72.985
0.356
0.003
1429.000
54.600
0.549
0.059
72.573
0.339
0.003
1550.000
45.800
0.538
0.072
38.073
1.015
0.030
2178.500
40.925
0.569
0.744
12.815
1.515
0.052
2986.000
41.400
0.612
1.266
4.235
0.314
0.004
4182.500
39.560
0.518
0.113
0.000
0.244
0.003
5854.000
32.285
0.480
0.092
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

315
Table A-IV-10d. Plasma metabolite, Dog Study #10
Time
Cp, expt
. AUC
min
ng/mL
trap.
7.34
15.46
56.74
15.69
25.62
228.25
33.70
28.83
718.57
49.50
46.31
1312.18
60.00
53.93
1838.44
111.00
88.60
5472.95
171.06
234.00
15160.63
175.10
209.00
16055.49
184.60
128.70
17659.56
199.90
117.00
19539.17
215.24
110.10
21281.03
229.80
63.00
22541.19
259.33
38.20
24035.41
291.10
56.80
25544.49
320.59
47.20
27077.97
351.95
47.16
28557.53
409.10
43.51
31148.43
468.95
43.10
33740.23
529.25
47.80
36480.87
649.75
19.54
40538.10
710.00
17.68
41659.35
771.85
26.34
43020.67
890.50
15.46
45500.46
1013.00
20.30
47690.76
1131.50
18.80
50007.43
1249.00
15.93
52047.82
1369.50
12.93
53786.63
Cp, expt. =
Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.)*

316
Table A-IV-10e. Metabolite in urine, Dog Study #10
Time
min
Cone.
ng/mL
Volume
mL
PH
U y gs
E U pgs
AUCt
80.000
1772.000
17.000
5.910
30.124
30.124
3.053
213.000
2085.000
48.000
5.940
100.080
130.204
21.033
233.000
1254.000
21.000
6.350
26.334
156.538
22.738
260.700
663.000
34.000
6.150
22.542
179.080
24.088
295.000
644.000
35.000
6.030
22.540
201.620
25.764
322.000
717.000
32.000
5.580
22.944
224.564
27.145
354.000
646.000
64.000
5.800
41.344
265.908
28.654
411.000
619.000
148.000
6.010
91.612
357.520
31.231
470.000
377.000
76.000
6.050
28.652
386.172
33.786
530.500
243.000
102.000
6.040
24.786
410.958
36.540
591.500
36.700
176.000
6.110
6.459
417.417
39.002
650.000
58.000
156.000
6.510
9.048
426.465
40.543
711.000
52.400
106.000
6.440
5.554
432.020
41.677
773.000
30.970
124.000
5.780
3.840
435.860
43.051
893.000
44.900
105.000
6.410
4.715
440.574
45.539
1014.000
52.400
142.000
6.540
7.441
448.015
47.711
1132.000
40.800
100.000
6.950
4.080
452.095
50.017
1247.500
63.500
54.000
6.780
3.429
455.524
52.024
1370.000
52.400
86.000
6.620
4.506
460.031
53.793
1488.000
9.000
42.000
6.940
0.378
460.409
55.385
1612.000
111.000
42.000
6.740
4.662
465.071
57.200
2745.000
26.200
1150.000
8.930
30.130
495.201
80.503
3227.000
24.300
730.000
8.780
17.739
512.940
94.092
5138.000
9.200
600.000
7.660
5.520
518.460
169.555
6570.000
106.500
350.000
8.560
37.275
555.735
248.701
U=Amount excreted in urine during a collection interval. IU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

317
Table A-IV-10f. Metabolite in urine, Dog Study #10
rygs
AV/ At
AU/ At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
ug/min
min
ng/mL
mL/min
mL/min
525.611
0.213
0.377
40.000
37.570
9.867
10.023
425.531
0.361
0.752
146.500
161.300
6.190
4.665
399.197
1.050
1.317
223.000
86.550
6.884
15.213
376.655
1.227
0.814
246.850
50.600
7.434
16.083
354.115
1.020
0.657
277.850
47.500
7.826
13.835
331.171
1.185
0.850
308.500
52.000
8.273
16.342
289.827
2.000
1.292
338.000
47.180
9.280
27.384
198.215
2.596
1.607
382.500
45.335
11.448
35.452
169.563
1.288
0.486
440.500
43.305
11.430
11.214
144.777
1.686
0.410
500.250
45.450
11.247
9.014
138.317
2.885
0.106
561.000
33.670
10.702
3.145
129.269
2.667
0.155
620.750
33.670
10.519
4.594
123.715
1.738
0.091
680.500
18.610
10.366
4.893
119.875
2.000
0.062
742.000
22.010
10.124
2.814
115.160
0.875
0.039
833.000
20.900
9.675
1.880
107.719
1.174
0.061
953.500
17.880
9.390
3.439
103.639
0.847
0.035
1073.000
19.550
9.039
1.769
100.210
0.468
0.030
1189.750
17.365
8.756
1.710
95.704
0.702
0.037
1308.750
14.430
8.552
2.549
95.326
0.356
0.003
1429.000
6.465
8.313
0.495
90.664
0.339
0.038
1550.000
6.465
8.131
5.815
60.534
1.015
0.027
2178.500
6.465
6.151
4.113
42.795
1.515
0.037
2986.000
6.465
5.451
5.693
37.275
0.314
0.003
4182.500
6.465
3.058
0.447
0.000
0.244
0.026
5854.000
6.465
2.235
4.026
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

318
Table A-IV-lOg. Metabolite in Bile, Dog Study #10
Time
min
Cone,
y g/mL
Vol.
mL
U ygs
£U y gs
AUCt
120.0
1291.3
4.0
5165.2
5165.2
54.2
231.0
9391.4
2.5
23478.5
28643.7
127.6
293.9
10841.3
1.5
16262.0
44905.7
148.9
353.5
8952.4
1.0
8952.4
53858.1
162.4
590.0
5695.4
2.5
14238.5
68096.6
203.2
890.0
2426.1
4.0
9704.4
77801.0
232.1
1246.0
1003.6
4.0
4014.4
81815.4
252.9
1370.0
648.0
3.0
1944.0
83759.4
259.5
1633.0
279.1
6.0
1674.6
85434.0
272.5
U=Amount excreted in bile during a collection interval.
£U=Cumulative amounts excreted in bile. AUCt=The area under
the buprenorphine plasma concentration-time curve at the
mid-point of bile collection interval, unit: y g.min/ml

319
Table A-rv-10h. Metabolite in bile, Dog Study #10
ru9S
AV/ At
mL/min
AU/ At
pg/min
t-mid
min
Cp t-mid
ng/mL
C1Ba
mL/min
C1Bb
mL/min
80268.750
0.033
43.043
60.000
477.750
95.383
90.096
56790.250
0.023
211.518
175.500
654.200
224.548
323.323
40528.300
0.024
258.742
262.425
269.150
301.597
961.331
31575.900
0.017
150.082
323.675
214.900
331.564
698.381
17337.400
0.011
60.205
471.750
167.500
335.134
359.433
7633.000
0.013
32.348
740.000
92.600
335.184
349.330
3618.600
0.011
11.276
1068.000
55.750
323.559
202.267
1674.600
0.024
15.677
1308.000
53.900
322.723
290.861
0.000
0.023
6.367
1501.500
45.800
313.531
139.024
t-mid = Mid-point of bile collection interval. Cp, t-mid = plasma
concenration of buprenorphine at the mid point of bile collection
interval, a) Biliary clearance calculated from the ratio of the
cumulative amount excreted in the bile versus area under the plasma
concentration-time profile, b) Instantaneous biliary clearance was
obtained from the ratio of the biliary excretion rate and the plasm?
concentation at the mid point of bile collection interval.

320
Table A-IV-lla. Plasma Buprenorphine, Dog Study #11
Time
min
Cp, expt. AUC
ng/mL trap.
11.25
364.70
2051.44
46.59
421.70
15947.13
61.80
544.70
23296.60
121.25
700.46
60308.98
161.50
744.63
89391.41
162.50
750.00
90138.73
223.02
453.50
126556.64
252.74
433.70
139740.43
282.68
370.80
151783.80
283.93
310.40
152209.55
313.84
278.40
161015.05
319.15
363.50
162719.30
343.00
278.10
170370.38
372.70
251.90
178240.88
402.00
163.30
184323.56
463.70
140.70
193701.96
523.50
124.37
201627.55
522.05
109.20
201458.21
582.25
104.31
207884.86
643.27
112.51
214500.04
702.25
153.10
222332.88
762.60
84.20
229493.41
883.00
96.37
240363.72
1002.80
43.20
248723.96
1131.80
41.06
254158.73
1241.50
35.81
258375.05
1361.86
29.20
262287.35
1484.70
33.02
266108.91
1604.00
24.40
269534.01
1710.00
28.63
272344.60
2496.00
39.00
298923.19
2950.00
31.10
314835.89
4050.00
48.90
358835.89
4350.00
29.81
370642.39
5460.00
42.10
410552.44
6877.00
18.70
453629.24
8361.00
7.31
472926.51
9868.00
4.34
481704.18
Cp, expt. = Experimental plasma concentrations; AUC =
Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.)»

321
Table A-IV-llb. Plasma metabolite, Dog Study #11
Time
min
Cp, expt.
ng/mL
. AUC
trap.
11.25
30.39
170.94
46.59
38.34
1385.40
61.80
68.10
2194.88
121.25
140.10
8383.62
161.15
186.15
14892.31
164.86
240.20
15683.19
167.14
206.10
16191.97
181.67
245.70
19474.30
192.34
166.95
21675.79
202.32
118.20
23098.69
211.90
132.40
24299.06
223.02
70.00
25424.40
252.74
96.00
27891.16
282.68
35.20
29855.23
319.15
49.10
31392.44
343.00
28.40
32316.63
372.70
15.74
32972.11
402.00
17.70
33462.00
463.70
14.50
34455.37
522.05
7.59
35099.85
582.25
12.40
35701.55
643.27
9.60
36372.77
702.25
6.52
36848.14
762.60
7.09
37258.83
883.00
2.10
37812.06
1002.80
0.00
37937.85
1131.80
0.00
37937.85
1241.50
0.00
37937.85
1362.00
0.00
37937.85
1484.70
0.00
37937.85
1604.00
0.00
37937.85
1710.00
3.20
38107.45
2496.00
1.50
39954.55
2950.00
1.00
40522.05
4050.00
1.70
42007.05
4350.00
3.20
42742.05
5460.00
4.50
47015.55
6337.00
3.50
50523.55
8361.00
1.50
55583.55
9868.00
1.20
57618.00
Cp, expt. = Experimental plasma concentrations; AUC =
Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

322
Table A-IV-llc. Metabolite in Bile, Dog Study #11
Time
min
Cone,
y g/mL
Vol.
mL
U ygs
£U pgs
AUCt
90.0
1768.6
2.0
3537.2
3537.2
39.7
155.0
9187.6
2.4
22050.2
25587.4
84.6
195.0
8458.5
1.7
14379.5
39966.9
115.0
229.6
4629.8
1.3
6018.7
45985.6
137.2
346.4
5990.3
2.3
13777.7
59763.3
181.4
403.0
2380.5
1.5
3570.8
63334.1
194.6
471.8
1526.1
1.9
2899.6
66233.7
204.9
584.5
1644.7
2.3
3782.8
70016.5
217.7
641.0
898.1
2.2
1975.8
71992.3
223.9
765.0
586.1
1.6
937.8
72930.1
239.3
877.0
1234.3
2.4
2962.3
75892.4
249.4
1004.0
788.8
1.6
1262.1
77154.5
258.4
1244.0
1042.7
2.3
2398.2
79552.7
268.1
1485.0
840.7
3.0
2522.1
82074.8
275.7
1718.0
557.2
3.0
1671.6
83746.4
282.2
U=Amount excreted in bile during a collection interval,
l U=Cumulative amounts excreted in bile. AUCt=The area under
the buprenorphine plasma concentration-time curve at the
mid-point of bile collection interval, unit: y g.min/ml

323
Table A-IV-lld. Metabolite in bile, Dog Study #11
z-y gs
AV/ At
mL/min
AU/ At
y g/min
t-mid
min
Cp t-mid
ng/mL
Cl a
mL/min
Cl b
U1B
mL/min
80209.160
0.022
39.302
45.000
393.200
89.101
99.955
58158.920
0.037
339.234
122.500
722.545
302.524
469.499
43779.470
0.043
359.486
175.000
762.065
347.616
471.726
37760.730
0.038
173.952
212.300
585.900
335.260
296.897
23983.040
0.020
117.960
288.000
367.150
329.450
321.285
20412.290
0.027
63.087
374.700
207.600
325.493
303.889
17512.700
0.028
42.145
437.400
152.000
323.223
277.271
13729.890
0.020
33.565
528.150
106.755
321.550
314.414
11754.070
0.039
34.970
612.750
108.410
321.578
322.574
10816.310
0.013
7.563
703.000
118.650
304.735
63.739
7853.990
0.021
26.449
821.000
90.285
304.282
292.953
6591.910
0.013
9.938
940.500
69.785
298.582
142.404
4193.700
0.010
9.993
1124.000
42.130
296.737
237.184
1671.600
0.012
10.465
1364.500
31.110
297.647
336.392
0.000
0.013
7.174
1601.500
28.710
296.762
249.887
t-mid = Mid-point of bile collection interval. Cp, t-mid = plasma
concenration of buprenorphine at the mid point of bile collection
interval, a) Biliary clearance calculated from the ratio of the
cumulative amount excreted in the bile versus area under the plasma
concentration-time profile, b) Instantaneous biliary clearance was
obtained from the ratio of the biliary excretion rate and the plasma
concentation at the mid point of bile collection interval.

324
Table A-IV-12. Plasma Buprenorphine, Dog Study #12
Time Cp, expt. AUC
min ng/mL trap.
8.39
148.00
620.86
11.90
139.00
1124.55
20.53
389.00
3402.87
25.13
376.00
5162.37
38.05
499.00
10814.87
40.36
501.00
11969.87
59.91
659.60
23314.73
87.01
736.00
42225.11
96.52
670.00
48910.64
123.50
705.80
67470.18
149.80
836.30
87748.80
154.09
844.00
91353.04
168.70
974.00
104633.53
178.50
719.00
112929.23
178.97
589.50
113236.73
180.84
533.40
114286.64
182.11
565.60
114984.50
185.07
399.60
116413.00
186.84
531.70
117237.20
191.48
379.00
119350.03
196.68
473.00
121565.23
206.37
324.50
125429.11
220.79
333.70
130174.73
237.10
384.70
136033.29
266.05
457.00
148216.89
299.00
257.80
159993.22
323.11
351.00
167332.31
356.85
197.30
176582.13
417.50
188.00
188266.35
475.50
187.30
199150.05
539.00
151.00
209891.08
621.00
120.40
221018.48
688.00
136.20
229614.58
776.00
104.70
240214.18
905.00
69.30
251437.18
1030.00
48.00
258768.43
1139.00
52.50
264245.68
1257.00
30.00
269113.18
1389.00
23.00
272611.18
1500.00
39.50
276079.93
2605.00
22.65
310417.80
2860.00
24.37
316412.85
4042.00
12.10
337966.62
6945.00
7.46
366352.88
7063.00
6.32
367165.69
7183.00
5.92
367900.09

325
Table A-IV-12 Continued . . . .
7295.00
5.93
368563.69
8345.00
4.15
373855.69
8529.00
3.93
374599.05
8694.00
3.81
375237.60
8766.00
3.65
375506.17
9915.00
2.61
379102.54
10167.00
2.38
379731.27
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

326
Table A-IV-13a. Plasma metabolite, Dog Study #13
Time Cp, expt. AUC
min
ng/mL
trap.
11.28
16900.00
127355.25
14.02
14700.00
170726.25
18.17
12752.00
227620.52
23.25
10364.00
286392.95
28.92
7600.00
337275.98
39.09
4723.10
399969.75
49.16
3539.00
441569.42
68.25
2248.00
496806.34
100.15
1201.50
551825.86
128.82
1151.30
585553.25
162.99
556.00
614722.47
190.74
369.40
627562.40
217.89
300.10
636650.86
247.59
267.40
645078.24
279.49
210.70
652703.93
307.19
177.05
658074.27
365.99
127.67
667033.04
427.99
74.20
673291.01
491.59
52.05
677305.76
551.09
42.96
680132.30
615.29
43.80
682917.30
1309.49
12.41
702428.83
1601.49
7.96
705403.29
2038.49
2.89
707774.02
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

327
Table A-IV-13b. Metabolite in urine, Dog Study #13
Time
min
Cone.
ng/mL
Volume
mL
pH
U pgs
ZU ygs
AUCt
24.000
65772.000
82.000
6.480
5393.304
5393.304
294.029
40.190
60059.000
25.500
6.060
1531.505
6924.808
405.094
54.000
57370.000
14.000
6.240
803.180
7727.989
457.906
72.500
29160.000
27.500
6.580
801.900
8529.889
506.064
98.440
24721.000
64.000
6.040
1582.144
10112.033
549.723
129.500
11400.000
162.000
6.130
1846.800
11958.833
586.332
162.190
3072.000
126.000
6.440
387.072
12345.904
614.272
191.490
1732.000
92.000
6.710
159.344
12505.249
627.839
248.190
3594.000
70.000
6.630
251.580
12756.829
645.238
308.490
4203.000
42.000
6.800
176.526
12933.355
658.304
368.290
3128.000
34.000
6.940
106.352
13039.707
667.324
428.500
1881.000
20.000
7.120
37.620
13077.327
673.329
492.800
2912.000
46.000
7.090
133.952
13211.279
677.369
614.500
3424.000
44.000
6.850
150.656
13361.935
682.883
1294.500
1090.000
595.000
7.020
648.550
14010.485
702.238
2797.500
994.000
500.000
7.280
497.000
14507.485
710.376
U=Amount excreted in urine during a collection interval. Z U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

328
Table A-IV-13C. Metabolite in urine, Dog Study #13
s-ygs
AV/ At
mL/min
AU/ At
p g/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
rriL/min
Cl b
ren
rriL/min
9114.181
3.417
224.721
12.000
15800.000
18.343
14.223
7582.676
1.575
94.596
32.095
6161.550
17.094
15.353
6779.496
1.014
58.159
47.095
4131.050
16.877
14.079
5977.596
1.486
43.346
63.250
2893.500
16.855
14.980
4395.452
2.467
60.992
85.470
1724.750
18.395
35.363
2548.652
5.216
59.459
113.970
1176.400
20.396
50.543
2161.580
3.854
11.841
145.845
853.650
20.098
13.871
2002.236
3.140
5.438
176.840
462.700
19.918
11.754
1750.656
1.235
4.437
219.840
283.750
19.771
15.637
1574.130
0.697
2.927
278.340
239.050
19.646
12.246
1467.778
0.569
1.778
338.390
152.360
19.540
11.673
1430.158
0.332
0.625
398.395
100.935
19.422
6.190
1296.206
0.715
2.083
460.650
63.125
19.504
33.002
1145.550
0.362
1.238
553.650
43.380
19.567
28.537
497.000
0.875
0.954
954.500
28.107
19.951
33.933
0.000
0.333
0.331
2046.000
1.445
20.422
228.839
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasm
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

329
Table A-IV-14a. Plasma metabolite, Dog Study #14
Time
min
Cp, expt.
ng/mL
. AUC
trap.
2.00
1119.90
1119.90
4.00
1965.10
4204.90
6.00
2612.40
8782.40
9.45
2144.00
16987.19
13.58
1198.00
23888.42
17.06
966.00
27653.78
22.68
607.50
32075.32
27.49
507.60
34757.13
36.98
313.40
38652.78
48.63
213.70
41723.13
67.53
195.40
45589.13
96.33
102.10
49873.13
129.03
67.10
52639.55
156.23
53.80
54283.79
198.43
41.60
56296.73
244.73
34.50
58058.44
309.78
34.10
60289.66
391.03
28.50
62832.78
433.53
24.40
63956.91
488.03
30.80
65461.11
552.03
15.90
66955.51
610.03
17.30
67918.31
730.03
14.30
69814.31
849.03
9.20
71212.56
973.03
6.81
72205.18
1094.03
5.83
72969.90
1222.03
4.57
73635.50
1332.03
3.50
74079.35
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/rriL, estimated by trapezoidal rule (trap.)*

330
Table A-IV-14b. Metabolite in urine, Dog Study #14
Time
min
Cone.
ng/mL
Volume
mL
pH
U y gs
Z U ygs
AUCt
20.030
5179.500
67.000
6.740
347.027
347.027
30.241
40.130
4505.500
52.000
6.650
234.286
581.313
39.598
51.830
3957.100
45.000
6.730
178.070
759.382
42.402
66.030
1522.500
65.000
6.670
98.963
858.345
45.295
95.030
798.000
117.000
6.130
93.366
951.711
49.738
130.000
719.000
129.000
5.940
92.751
1044.462
52.704
158.630
450.000
112.000
6.780
50.400
1094.862
54.412
200.000
296.400
55.000
7.050
16.302
1111.164
56.362
295.000
137.100
200.000
6.590
27.420
1138.584
59.785
313.000
94.830
154.000
6.640
14.604
1153.187
60.399
382.000
77.500
114.000
6.630
8.835
1162.022
62.573
431.000
68.000
75.000
6.830
5.100
1167.122
63.895
494.000
130.800
44.000
6.840
5.755
1172.878
65.641
543.000
25.000
45.000
6.710
1.125
1174.003
66.802
613.000
21.800
34.000
7.120
0.741
1174.744
67.970
721.000
54.000
34.000
7.240
1.836
1176.580
69.684
842.000
56.500
52.000
7.780
2.938
1179.518
71.147
970.000
33.000
24.000
7.950
0.792
1180.310
72.184
1084.000
38.450
35.000
7.930
1.346
1181.655
72.911
1225.000
11.150
38.500
7.990
0.429
1182.085
73.649
U=Amount excreted in urine during a collection interval. IU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

331
Table A-IV-14c. Metabolite in urine, Dog Study #14
r p9s
AV/ A t
mL/min
AU/ At
yg/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
835.058
3.345
17.325
10.015
1671.000
11.475
10.368
600.772
2.587
11.656
30.080
410.500
14.681
28.395
422.703
3.846
15.220
45.980
263.550
17.909
57.748
323.740
4.577
6.969
58.930
204.550
18.950
34.071
230.374
4.034
3.220
80.530
148.750
19.135
21.644
137.623
3.689
2.652
112.515
84.600
19.817
31.351
87.223
3.912
1.760
144.315
60.450
20.122
29.121
70.921
1.329
0.394
179.315
47.700
19.715
8.261
43.501
2.105
0.289
247.500
34.300
19.045
8.415
28.897
8.556
0.811
304.000
34.300
19.093
23.654
20.062
1.652
0.128
347.500
31.300
18.571
4.091
14.962
1.531
0.104
406.500
26.450
18.266
3.935
9.207
0.698
0.091
462.500
27.600
17.868
3.310
8.082
0.918
0.023
518.500
23.350
17.574
0.983
7.341
0.486
0.011
578.000
16.600
17.283
0.638
5.505
0.315
0.017
667.000
15.800
16.884
1.076
2.567
0.430
0.024
781.500
11.750
16.579
2.066
1.775
0.188
0.006
906.000
8.005
16.351
0.773
0.429
0.307
0.012
1027.000
6.320
16.207
1.868
0.000
0.273
0.003
1154.500
5.200
16.050
0.585
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

332
Table A-IV-14d. Metabolite in Bile, Dog Study #14
Time
min
Cone.
yg/mL
Vol
mL
23.8
842.5
5.0
69.4
969.2
4.0
98.3
609.2
2.8
131.0
311.2
2.3
179.5
108.0
1.6
248.0
95.0
3.2
311.0
63.6
2.4
386.0
25.4
3.6
432.0
14.3
2.9
493.0
5.7
4.0
543.5
8.0
2.8
614.0
5.2
2.6
720.0
5.8
4.0
841.0
1.2
7.0
968.0
0.9
8.4
1083.5
0.7
6.9
1226.0
0.5
7.0
1332.0
0.5
6.2
U ygs IU ugs AUCt
4212.7
4212.7
32.8
3876.8
8089.5
46.0
1705.8
9795.3
50.1
715.8
10511.0
52.8
172.8
10683.8
55.5
304.0
10987.8
58.2
152.6
11140.4
60.3
91.4
11231.9
62.7
41.5
11273.4
63.9
22.9
11296.3
65.6
22.3
11318.6
66.8
13.6
11332.3
68.0
23.1
11355.4
69.7
8.5
11363.9
71.1
7.5
11371.4
72.2
4.8
11376.2
72.9
3.5
11379.7
73.7
3.2
11382.8
74.1
U=Amount excreted in bile during a collection interval.
EU=Cumulative amounts excreted in bile. AUCt=The area under
the metabolite plasma concentration-time curve at the
mid-point of bile collection interval, unit:y g.min/ml

333
Table A-IV-14e. Metabolite in bile, Dog Study #14
j.- y gs AV/ At AU/ At t-mid Cp t-mid Clg a Clg b
mL/min y g/min min ng/mL rriL/min mL/min
7170.194
0.210
176.779
3293.354
0.088
85.018
1587.594
0.097
59.023
871.834
0.070
21.889
699.034
0.033
3.563
395.034
0.047
4.438
242.394
0.038
2.424
150.954
0.048
1.219
109.484
0.063
0.902
86.548
0.066
0.376
64.211
0.055
0.442
50.574
0.037
0.194
27.446
0.038
0.218
18.927
0.058
0.070
11.456
0.066
0.059
6.648
0.060
0.042
3.176
0.049
0.024
0.000
0.058
0.030
11.915
1671.000
128.590
105.793
46.630
263.550
176.032
322.589
83.880
148.750
195.611
396.792
114.680
84.600
199.175
258.732
155.280
60.450
192.644
58.939
213.780
38.050
188.884
116.635
279.515
34.300
184.655
70.671
348.500
31.300
179.170
38.952
409.000
26.450
176.368
34.084
462.500
27.600
172.170
13.623
518.265
23.350
169.410
18.931
578.765
16.600
166.683
11.658
667.000
15.800
162.989
13.809
780.500
11.750
159.746
5.992
904.500
8.005
157.562
7.350
1025.765
6.320
156.034
6.585
1154.765
5.200
154.503
4.687
1279.000
4.035
153.658
7.425
t-mid = Mid-point of bile collection interval. Cp, t-mid = plasma
concenration of the metabolite at the mid point of bile collection
interval, a) Biliary clearance calculated from the ratio of the
cumulative amount excreted in the bile versus area under the plasma
concentration-time profile, b) Instantaneous biliary clearance was
obtained from the ratio of the biliary excretion rate and the plasma
concentation at the mid point of bile collection interval.

334
Table A-IV-15a. Plasma Buprenorphine, Dog Study #15
Time
min
Cp, expt.
ng/mL
AUC
trap.
5.20
37.95
98.67
10.80
65.13
387.29
17.30
56.40
782.27
19.40
60.33
904.84
25.00
60.78
1243.96
30.30
51.87
1542.48
40.70
42.79
2034.71
60.00
43.67
2869.05
90.10
34.00
4037.98
118.70
17.00
4767.28
147.90
14.42
5226.02
180.15
10.81
5632.85
257.30
11.00
6474.17
295.00
9.65
6863.33
359.00
7.75
7419.99
417.50
5.65
7812.08
479.50
5.57
8159.87
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.)-

335
Table A-IV-15b. Buprenorphine in urine, Dog Study #15
Time
min
Cone.
ng/rriL
Volume
mL
pH
U ygs
EU ygs
AUCt
34.000
6.590
35.000
7.020
0.231
0.231
1.728
62.400
3.766
75.000
7.280
0.282
0.513
2.973
88.200
28.000
160.000
7.190
4.480
4.993
3.973
119.500
0.000
100.000
7.160
0.000
4.993
4.781
181.500
10.677
50.000
6.920
0.534
5.527
5.647
258.000
1.729
92.000
6.630
0.159
5.686
6.482
302.000
0.000
38.000
6.660
0.000
5.686
6.930
360.000
0.000
195.000
6.960
0.000
5.686
7.428
418.000
24.290
108.000
7.010
2.623
8.309
7.815
480.000
66.450
152.000
6.940
10.100
18.410
8.163
1374.000
315.650
375.000
7.000
118.369
136.779
17.781
U=Amount excreted in urine during a collection interval. zU=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

336
Table A-IV-15c. Buprenorphine in urine, Deg Study #15
r wgs
AV/ At
AU/ A t
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
yg/min
min
ng/mL
mL/min
mL/min
136.548
1.029
0.007
17.000
60.765
0.133
0.112
136.265
2.641
0.010
48.200
43.230
0.173
0.230
131.785
6.202
0.174
75.300
38.835
1.257
4.471
131.785
3.195
0.000
103.850
25.500
1.044
0.000
131.252
0.806
0.009
150.500
12.615
0.979
0.683
131.092
1.203
0.002
219.750
10.905
0.877
0.191
131.092
0.864
0.000
280.000
10.323
0.820
0.000
131.092
3.362
0.000
331.000
8.698
0.766
0.000
128.469
1.862
0.045
389.000
6.702
1.063
6.748
118.369
2.452
0.163
449.000
5.610
2.255
29.042
0.000
0.419
0.132
927.000
2.783
7.692
47.584
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

337
Table A-IV-15d. Plasma metabolite, Dog Study #15
Time
min
Cp, expt.
ng/mL
AUC
trap.
5.20
43.19
112.29
10.80
48.10
367.91
17.30
53.10
696.81
19.40
49.40
804.43
25.00
45.62
1070.49
30.30
45.44
1311.80
40.70
39.00
1750.88
60.00
30.50
2421.56
90.10
16.82
3133.73
118.70
11.90
3544.42
147.90
10.20
3867.08
180.15
8.50
4168.62
257.30
8.00
4805.11
295.00
7.63
5099.73
359.00
4.32
5482.13
417.50
3.60
5713.79
479.50
3.80
5943.19
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.)-

338
Table A-IV-15e. Metabolite in urine, Dog Study #15
Time
min
Cone.
ng/mL
Volume
mL
PH
U y gs
ZU y gs
AUCt
34.000
370.250
35.000
7.020
12.959
12.959
1.476
62.400
635.050
75.000
7.280
47.629
60.588
2.493
88.200
272.150
160.000
7.190
43.544
104.132
3.101
119.500
170.450
100.000
7.160
17.045
121.177
3.554
181.500
362.500
50.000
6.920
18.125
139.302
4.180
258.000
108.500
92.000
6.630
9.982
149.284
4.811
302.000
60.900
38.000
6.660
2.314
151.598
5.152
360.000
99.910
195.000
6.960
19.482
171.080
5.486
418.000
54.410
108.000
7.010
5.876
176.956
5.716
480.000
98.300
152.000
6.940
14.942
191.898
5.945
1374.000
222.400
375.000
7.000
83.400
275.298
12.513
U=Amount excreted in urine during a collection interval. Z U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

339
Table A-IV-15f. Metabolite in urine, Dog Study #15
rpgs
AV/ At
mL/min
AU/ At
y g/min
t-mid
min
Cp t-mid
ng/mL
Cl a
ren
mL/min
Cl b
ren
mL/min
262.339
1.029
0.381
17.000
50.600
8.782
7.532
214.711
2.641
1.677
48.200
34.750
24.299
48.261
171.167
6.202
1.688
75.300
23.660
33.581
71.334
154.122
3.195
0.545
103.850
14.360
34.097
37.923
135.997
0.806
0.292
150.500
9.350
33.325
31.266
126.015
1.203
0.130
219.750
8.250
31.032
15.816
123.700
0.864
0.053
280.000
7.815
29.426
6.730
104.218
3.362
0.336
331.000
5.975
31.182
56.218
98.342
1.862
0.101
389.000
3.960
30.960
25.585
83.400
2.452
0.241
449.000
3.700
32.278
65.133
0.000
0.419
0.093
927.000
1.900
22.001
49.099
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

340
Table A-IV-16a. Plasma Buprenorphine, Dog Study #16
Time
min
Cp, expt.
ng/mL
AUC
trap.
2.07
3.14
3.25
4.60
3.45
11.59
9.70
14.23
56.69
15.55
27.71
179.36
21.15
44.83
382.47
25.15
40.35
552.83
31.25
38.66
793.81
40.60
36.82
1146.68
60.35
22.86
1736.02
91.65
19.87
2404.75
121.15
19.14
2980.14
151.55
9.05
3408.69
181.70
7.01
3650.86
211.20
5.86
3840.69
241.15
6.31
4022.94
300.60
5.56
4375.77
358.30
1.62
4582.91
422.30
3.44
4744.83
478.50
15.37
5273.40
538.00
13.00
6117.40
597.60
4.05
6625.49
1285.00
4.05
9409.46
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.)»

341
Table A-IV-16b. Buprenorphine in urine, Dog Study #16
Time
min
Cone.
ng/mL
Volume
mL
PH
U pgs
EU pgs
AUCt
18.200
16.200
40.000
7.200
0.648
0.648
0.264
33.500
16.690
28.000
7.050
0.467
1.115
0.880
46.000
10.180
24.000
6.900
0.244
1.360
1.335
62.950
21.240
47.000
6.420
0.998
2.358
1.795
93.500
13.550
46.000
6.190
0.623
2.981
2.441
152.000
26.030
20.000
6.270
0.521
3.502
3.413
213.750
20.960
28.000
5.990
0.587
4.089
3.856
303.000
27.900
42.000
5.320
1.172
5.261
4.389
371.000
14.480
68.000
5.600
0.985
6.245
4.606
424.000
44.930
66.000
5.990
2.965
9.211
4.751
480.500
16.720
92.000
5.830
1.538
10.749
5.304
539.000
8.113
68.000
5.720
0.552
11.300
6.130
602.000
12.620
90.000
5.340
1.136
12.436
6.643
1275.000
28.740
865.000
6.980
24.860
37.296
9.369
U=Amount excreted in urine during a collection interval. E U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: pg.min/ml

342
Table A-IV-16c. Buprenorphine in urine, Dog Study #16
z- pgs
AV/ At
AU/At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
yg/min
min
ng/mL
mL/min
mL/min
36.648
2.198
0.036
9.100
8.842
2.459
4.027
36.181
1.830
0.031
25.850
39.505
1.267
0.773
35.937
1.920
0.020
39.750
37.740
1.018
0.518
34.938
2.773
0.059
54.475
29.840
1.314
1.974
34.315
1.506
0.020
78.225
21.365
1.221
0.955
33.795
0.342
0.009
122.750
14.097
1.026
0.631
33.208
0.453
0.010
182.875
6.435
1.060
1.477
32.036
0.471
0.013
258.375
5.935
1.199
2.212
31.051
1.000
0.014
337.000
3.590
1.356
4.033
28.086
1.245
0.056
397.500
2.530
1.939
22.115
26.548
1.628
0.027
452.250
9.405
2.027
2.895
25.996
1.162
0.009
509.750
14.185
1.843
0.665
24.860
1.429
0.018
570.500
8.525
1.872
2.115
0.000
1.285
0.037
938.500
4.050
3.981
9.121
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concenration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

343
Table A-IV-16d. Plasma metabolite, Dog Study #16
Time
min
Cp, expt,
ng/mL
. AUC
trap.
2.07
17.63
18.25
4.60
16.94
61.98
9.70
17.15
148.93
15.55
29.83
286.35
21.15
64.30
549.92
25.15
76.49
831.50
31.25
78.13
1303.09
40.60
100.10
2136.33
60.35
103.30
4144.90
91.65
114.80
7558.17
121.15
58.80
10118.77
151.55
55.96
11863.12
181.70
57.52
13573.83
211.20
41.20
15029.95
241.15
41.76
16272.28
300.60
32.15
18469.25
358.30
25.00
20118.03
422.30
26.82
21776.27
478.50
20.85
23115.80
538.00
19.30
24310.26
597.60
15.96
25361.01
1285.00
13.34
35431.42
Cp, expt. = Experimental plasma concentrations; AUC
= Area under the plasma concentration-time curve,
ng.min/mL, estimated by trapezoidal rule (trap.).

344
Table A-IV-16e. Metabolite in urine, Dog Study #16
Time
min
Cone.
ng/mL
Volume
mL
pH
U p gs
I Up gs
AUCt
18.200
4.150
40.000
7.200
0.166
0.166
0.387
33.500
103.700
28.000
7.050
2.904
3.070
1.485
46.000
270.000
24.000
6.900
6.480
9.550
2.679
62.950
296.000
47.000
6.420
13.912
23.462
4.415
93.500
975.000
46.000
6.190
44.850
68.312
7.767
152.000
1262.000
20.000
6.270
25.240
93.552
11.888
213.750
668.000
28.000
5.990
18.704
112.256
15.135
303.000
672.000
42.000
5.320
28.224
140.480
18.546
371.000
778.000
68.000
5.600
52.904
193.384
20.438
424.000
277.500
66.000
5.990
18.315
211.699
21.822
480.500
155.600
92.000
5.830
14.315
226.014
23.157
539.000
82.600
68.000
5.720
5.617
231.631
24.330
602.000
92.000
90.000
5.340
8.280
239.911
25.431
1275.000
85.700
865.000
6.980
74.131
314.041
35.298
U=Amount excreted in urine during a collection interval. 1 U=Cumulative
amounts excreted in urine. AUCt=The area under the plasma
concentration-time curve at the mid-point of urine collection interval,
unit: yg.min/ml

345
Table A-IV-16f. Metabolite in urine, Dog Study #16
fygs
AV/ At
AU/ At
t-mid
Cp t-mid
Cl a
ren
Cl b
ren
mL/min
ug/min
min
ng/mL
mL/min
mL/min
313.875
2.198
0.009
9.100
17.048
0.429
0.535
310.972
1.830
0.190
25.850
77.311
2.067
2.455
304.492
1.920
0.518
39.750
89.116
3.564
5.817
290.580
2.773
0.821
54.475
101.700
5.314
8.070
245.730
1.506
1.468
78.225
109.050
8.795
13.462
220.490
0.342
0.431
122.750
57.380
7.869
7.519
201.786
0.453
0.303
182.875
49.360
7.417
6.137
173.562
0.471
0.316
258.375
36.955
7.575
8.557
120.658
1.000
0.778
337.000
28.575
9.462
27.227
102.343
1.245
0.346
397.500
25.910
9.701
13.337
88.027
1.628
0.253
452.250
23.835
9.760
10.630
82.411
1.162
0.096
509.750
20.075
9.521
4.783
74.130
1.429
0.131
570.500
17.630
9.434
7.455
0.000
1.285
0.110
938.500
14.650
8.897
7.519
t-mid = Mid-point of urine collection interval. Cp, t-mid = plasma
concentration at the mid point of urine collection interval, a) Renal
clearance calculated from the ratio of the cumulative amount excreted in
the urine versus area under the plasma concentration-time profile, b)
Instantaneous renal clearance obtained from the ratio of the urinary
excretion rate and the plasma concentation at the mid point of urine
collection time.

GLOSSARY OF TERMS
AUCt
Area under the apparent drug/metabolite concentration in
plasma versus time curve (ng.min/ml)
3
Apparent first order elimination rate constant for a drug that
distributes in the body in accordance with a multicompartment
body model, obtained from the terminal slope of a
semilogarithmic plot of the drug concentration in plasma
versus time (1/min).
B
m
Amount of the metabolite excreted in bile up to time t (y g)
Cl, .
tot
Total body clearance (ml/min)
Cl—->M
B
Biliary clearance of drug as metabolite (ml/min).
Cl—
U1B
Biliary clearance of the unchanged drug (ml/min).
Cl-
ren
Renal clearance of the unchanged drug (ml/min).
M
Cl
ren
Renal clearance of the metabolite (ml/min).
Cl-
met
Metabolic clearance of the drug (ml/min).
Cp
Drug concentration in plasma at time t (ng/ml).
%
Drug concentration in plasma immediately following IV bolus
injection (ng/ml).
f
Fraction of the orally administered dose that eventually
reaches the sytemic circuation unchanged.
f
a
Fraction of the orally administered dose that reaches the
liver unchanged.
f.
lpm
Fraction of the absorbed dose that undergoes first-pass
metabolism.
346

Apparent first order intercompartmenta1 transfer rate
constants, where i=l,2, . . . j=l,2, . . . i^j,
(l/min).
Apparent first order rate constant for the metabolite
formation in the central compartment for a drug that
distributes in the body in accordance with a multicompartment
body model (l/min).
Zero order infusion rate constant (mg/min).
Apprent first order elimination rate constant for the drug
from the cental compartment (l/min).
Rate of metabolite formation in the central compartment.
Time (min).
Time at which zero order infusin is terminated (min).
Amount of the metabolite excreted in urine to time t ( g).
Apparent volume of distribution of the drug in the central
compartment (L).
A proportinality constant relating the amount of the drug in
the body to the drug concentration in plasma at pseudo-steady
state (L).
A proportionality constant relating the amount of the
metabolite in the body to the metabolite concentrations in
plasma on the presumption that plasma metabolite
concentrations are representative of the metabolite
concentrations in the equilibrated fluids of the body (L).

REFERENCES
1. Heel, R.C.; Brogden, R.N.; Speight, T.M.; Avery, G.S. in "Focus on
Buprenorphine" Drugs; 1979 17, 81-111.
2. Adriaensen, H.; Van De Walle, Acta Anaeth. Bélgica. 1977, 27, 187.
3. Brogden, R.N.; Speight, T.M.; Avery, G.S. in "Pentazocine: A Review
of its Pharmacological Properties, Therapeutic efficacy and Dependence
Liability" Drugs; 1973, 5_, 6-91.
4. Jasinski, D.R.; Pevnick, J.S.; Griffith, J.D.; Gorodetzky, C.W.;
Cone, E.J. Progress report on the studies from the Clinical Pharmacology
section of the Addiction Research Center. Assessment of buprenorphine
for morphine-type effects in man and evaluation as a maintanence drug in
the treatment of narcotic addiction. Reported to the cormittee on
problems of drug dependence, Richmond, Virginia, 1976, p 131.
5. Jasinski, D.R.; Pevnick, J.S.; Griffith, J.D. Fed. Proc. Fed. Am.
Soc. Exp. Biol. 1977, 36, 1025.
6. Jasinski, D.R.; Pevnick, J.S.; Griffith, J.D. Arch. Gen. Psychiat.
1978, 35, 501-516.
7. Kjaer, M.; Henriksen, H.; Krudsen, J. Br. J. Clin. Pharmacol. 1982,
13, 487-492.
8. Bryant, R.M.; Tyers, M.B. Proc. B.P.S. 4-6 Apr, 1979, 472-473.
9. Tigerstedt, I.; Tammisto, T. Acta. Anaesth. Scand. 1980, 24,
462-468.
10. Bullingham, R.E.S.; McQuay, H.J.; Moore, R.A.; Weir, Lesley. Br. J.
Pharmacol. 1981, 12, 863-867.
11. Dum, J.; Blasig, J.? Herz, A. Eur. J. Pharmacol. 1981, 70,
293-300.
12.Cowan, A.; Lewis, J.W.; Macfarlane, I.R. Br. J. Pharmacol. 1977,
60, 537-545.
13. Dettmar, P.W.; Cowan, A.; Walter, D.S. Eur. J. Pharmacol. 1981,
69, 147-153.
14. Kay, B. Br. J. Anaesth. 1980, 52, 453-456.
15. Cook, P.J.; James, I.M.; Hobbs, K.E.F.; Browne, D.R.G. Br. J.
Anaesth. 1982, 54, 285-289.
348

349
16. Ellis, R.; Haines, D.; Shah, R.; Cotton, B.R.; Smith, G. Br. J.
Anaesth. 1982, 54, 421-428.
17. Hayes, M.J.; Fraser, A.R.; Hampton, J.R. Br. Med. J. 1979, 2,
300-302.
18. Chakravarty, K.; Tucker, W.; Rosen, M.; Vickers, M.D. Br. Med. J.
1979, 2, 895-897.
19. Robbie, D.S. Unpublished data from Reckitt & Colman Co.
20. Samayoa De Leon, R. Clinical use of fentanyl in sequential
analgesic anesthesia. Societe d'Anesthesie de Charleroi, Belgium, 1976,
p211, through reference 1.
21. Bilsback, P.; Roily, G.; Tampubolon, 0. Br. J. Anaesth. 1985, 57,
943-948.
22. Green, D.W.; Sinclair, J.R.; Mikhael, M.S. Anaesthesia 1985, 40,
371-375.
23. Lanz, E.; Simko, G.; Theiss, D.; Glocke, M.H. Anesth. Analg. 1984,
63, 593-598.
24. Ccwan, A.; Doxey, J.C.; Harry, E.J.R. Br. J. Pharmacol. 1977, 60,
547-554.
25. Stephen, G.W.; Cooper, Lesley V. Anaesthesia; 1977, 32, 324-327.
26. Orwin, J.M.; "Pain-New perspectives in Measurement and Management"
Churchill Livingstone: Edinburgh, 1977; 141-159.
27. Wust, J.H. Unpublished data from Reckitt & Colman Co.
28. Ccwan, Alan. Adv. Biochem. Psycopharmcol. 1974, £, 427-438.
29. Boas, R.A.; Villiger, J.W. Br. J. Anaesth. 1985, 57, 192-196.
30. Villiger, J.W.; Taylor, K.M. Life Sci. 1981, 29, 2699-2708.
31. Hovell, B.C. Br. J. Anaesth. 1977, 49, 913-916.
32. Kay, B. Br. J. Anaesth. 1978, 50, 605-609.
33. Bullingham, R.E.S.; McQuay, H.J.; Dwyer, D.; Allen, M.C.; Moore,
R.A. Br. J. Clin. Pharmacol. 1981, 12, 117-122.
34. Bullingham, R.E.S.; McQuay, H.J.; Porter, E.J.B.; Allen, M.C.;
Moore, R.A. Br. J. Clin. Pharmacol. 1982, 13, 665-673.
35.Bullingham, R.E.S.; McQuay, H.J.; Moore, A.; Bennett, M.R.D. Clin.
Pharmacol. Ther. 1980, 28, 667-672.

350
36. Watson, P.J.Q.; McQuay, H.J.; Bullingham, R.E.S.; Allen, M.C.;
Moore, R.A. Br. J. Anaesth. 1982, 54, 37-43.
37. Ranee, M.J.; Shillingford, J.S. Biochem. Pharmacol. 1976, 25,
735-741.
38. Ranee, M.J.; Shillingford, J.S. Xenobiotica 1977, 7, 529-536.
39. Brewster, D.; Humphrey, M.J.; McLeavy, M.A. Xenobiotica 1981, 11,
189-196.
40. Bullingham, R.E.S.; Moore, R.A.; Symonds, H.W.; Allen, M.C.;
Baldwin, D.; McQuay, H.J. Life Sci. 1984, 34, 2047-2056.
41. Pontani, R.B.; Vadlamani, N.L.; Misra, A.L. Xenobiotica 1985, 15,
287-297.
42. Brewster, D.; Humphrey, H.J.; McLeavy, M.A. J. Pharm. Pharmacol.
1981, 33, 500-506.
43. Garrett, Edward R.; Chandran, V. Ravi. J. Pharm. Sci. 1985, 74,
515-524.
44. Garrett, Edward R.; Lambert, Howard J. J. Pharm. Sci. 1973, 62,
550-572.
45. Garrett, Edward R.; Jackson, Andre, J. J. Pharm. Sci. 1979, 68,
753-771.
46. Derendorf, Hartmut; El-Koussi, Alaa El-Din; Garrett, Edward R. J.
Pharm. Sci. 1984, 73, 621-624.
47. Bartlett, A.J.; Lloyd-Jones, J.A.; Ranee, M.J.; Flockhart, I.R.;
Dockray, G.J.; Bennett, M.R.D.; Moore, R.A. Eur. J. Clin. Pharmacol.
1980, 18, 339-345.
48. Lloyd-Jones, J.G.; Robinson, P.; Henson, R.? Biggs, S.R.; Taylor,
T. Eur. J. Drug. Metab. Pharmacokinet. 1980, _5, 233-239.
49. Cone, E.J.; Gorodetzky, C.W.; Darwin, W.D.; Buchwald, W.F. J.
Pharm. Sci. 1984, 73, 243-246.
50. Roth, Willy; Beschke, Klaus; Jauch, Rolf; Zimmer, Amo; Koss, F.W.
J. Chromatog. Biomed. Appl. 1981, 222, 13-22.
51. Garrett, Edward R.; Derendorf, Hartmut; Mattha, Amir G. J. Pharm.
Sci. 1985, 74, 1203-1214.
52. Garrett, Edward R.; Hunt, C. Anthony. J. Pharm. Sci. 1977, 3,
395-407.
53.Gibaldi, Milo; Perrier, Donald. "Pharmacokinetics," 1st Ed.; Marcel
Dekker Inc.; New York, 1975.

351
54. Yamaoka, Kiyoshi; Tanigawara, Yusuke; Nakagawa, Terumichi; Uno,
Toyozo. J. Pham. Dyn. 1981, 4, 897-885.
55. Boxenbaum, Harold G.; Riegelman, Sidney; Elashoff, Robert M.; J.
Pharm. Biopharm. 1974, 2, 123-148.
56. Atlman, P.L.; Dittmer, D.S.; "Respiration and Circulation",
Biological Handbooks, Federation of American Societies for Experimental
Biology, Maryland, Md., 1971, p 429.
57. Elkinton, J.R.; and Danowski, T.S.; The Body Fluids, The Williams
and Wilkins Co., Baltimore, 1955, pp 3-34.
58. Garrett, Edward R.; Green, J. Russel; Bialer, Meir; Biopharm. and
Drug Disp. 1982 3_, 129-164
59. Lyman, Ott; "An Introduction to Statistical Methods and Data
Analysis", Prindle, Weber and Schmidt Publishers, Boston, 1984, pp
347-351.
60. Garrett, Edward R.; "Pharmacokinetics: A Modem View", Benet, Leslie
Z.; Levy, Gerhard; Ferraiolo, Bobbe, L.; Eds., Plenum Publishing
Corporation, New York, N.Y., 1984, 253-279.

BIOGRAPHICAL SKETCH
V. Ravi Chandran was born May 3, 1955 in India. He received B.Pharm
(Honors) degree in 1977 and M.Pharm in 1979 from Jadavpur University,
Calcutta. He was then employed as a research pharmacist in Lister
Laboratories, Bombay. He came to University of Florida in 1981 and
obtained a masters degree in pharmaceutical sciences in 1983. After
completion of the Ph.D. he will be employed as Senior Research
Pharmacist at Sterling-Winthrop Research Institute, Albany, New York.
352

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Edward R.
ett, Chairman
Graduate Research Professor
’harmacy
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
ames W. Simpkins
Professor of Pharmacodynamics
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
John A. Zoltewicz
Professor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
C. Lindsay (Devane
Associate Professor of
Pharmacy Practice

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
/?
Ú
Pharmacodynamics
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
J/ Ch ^ g- _/â– 
Hartmut C. Derendorf 7~~
Assistant Professor of
Pharmaceutics
This dissertation was submitted to the Graduate Faculty of the College
of Pharmacy and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosphy.
December 1986
Dean, College of Pharmacy
Dean, Graduate School

UNIVERSITY OF FLORIDA
3 1262 08554 3998



UNIVERSITY OF FLORIDA
3 1262 08554 3998


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID ES79KV2GS_NNJFCT INGEST_TIME 2012-04-06T14:33:13Z PACKAGE AA00010255_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES