Citation
Concepts for the determination of prostaglandins by tandem mass spectrometry

Material Information

Title:
Concepts for the determination of prostaglandins by tandem mass spectrometry
Creator:
Gillespie, Todd Allen, 1962-
Publication Date:
Language:
English
Physical Description:
viii, 176 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Anions ( jstor )
Chemicals ( jstor )
Gas pressure ( jstor )
Ionization ( jstor )
Ions ( jstor )
Mass spectroscopy ( jstor )
Prostaglandins ( jstor )
Purification ( jstor )
Sorbents ( jstor )
Urine ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Mass spectrometry ( lcsh )
Prostaglandins ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1989.
Bibliography:
Includes bibliographical references (leaves 169-175).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
Todd Allen Gillespie.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
030458597 ( ALEPH )
21049910 ( OCLC )
AGZ1586 ( NOTIS )
AA00004803_00001 ( sobekcm )

Downloads

This item has the following downloads:


Full Text















CONCEPTS FOR THE DETERMINATION OF PROSTAGLANDINS
BY TANDEM MASS SPECTROMETRY



By

TODD ALLEN GILLESPIE


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


1989




CONCEPTS FOR THE DETERMINATION OF PROSTAGLANDINS
BY TANDEM MASS SPECTROMETRY
By
TODD ALLEN GILLESPIE
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
1989


To my loving wife, Paula


ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to Dr. Richard A. Yost
for his guidance, direction, and friendship during this research. His
editorial assistance during the preparation of this dissertation and
various papers is very much appreciated.
I would like to express my gratitude to Dr. Joe Neu in the
Department of Neonatology at the University of Florida for his initiation
of this project and provision of supplies for the scintillation counting
work. Also I would like to express my sincere heartfelt thanks to Dr. Jim
Vrbanac, who, while at the Medical University of South Carolina in
Charleston, supplied samples, immunoaffinity gel, and expert advice as
well as a valued friendship during this collaborative research. In
addition, I thank Merrell Dow Research Institute for their support of this
work.
I acknowledge the members of my research committee, Drs. John G.
Dorsey, Anna Brajter-Toth, Samuel 0. Colgate and Joe Neu for their various
contributions to my thesis work and education at the University of
Florida.
This research would not have been possible or as much fun without
the support of and discussions with my friends and co-workers in the Yost
research group. I would especially like to thank Mark Hail, David
Berberich and Jodie Johnson for many helpful discussions about this work.
iii


In addition to the people mentioned above, I would like to thank Steve
Brooks, Mark Barnes and Jim Michels for their friendship.
I would particularly like to thank my parents, during all the years
of my education whether in or out of the classroom, for their endless
support. Most of all, I thank my wonderful, caring wife Paula, for her
constant love, understanding and patience throughout my years in graduate
school. She has made this work all possible and worthwhile.
iv


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
ABSTRACT vii
CHAPTERS
1 INTRODUCTION 1
Arachidonic Acid Metabolites
(Prostaglandins) 1
Recent Analytical Advances 13
Strategies for Mixture Analysis by MS/MS 15
Overview of Thesis Organization 20
2 SAMPLE PREPARATION STUDIES 22
Introduction 22
Concepts for Solid-Phase Extraction 23
Concepts for Derivatization 33
Experimental 35
Results and Discussion 43
Conclusions 52
3 OPTIMIZATION OF GC/MS AND GC/MS/MS CONDITIONS
FOR TRACE DETERMINATION OF PROSTAGLANDINS 54
Introduction 54
Experimental 54
Mass Spectrometry (GC/MS) 56
Tandem Mass Spectrometry (GC/MS/MS) 64
Conclusions 80
4 DIFFERENCES IN THE COLLISIONALLY ACTIVATED
DISSOCIATION OF STRUCTURALLY SIMILAR
PROSTAGLANDINS 83
Introduction 83
Experimental 85
Efficiency Calculations 88
Collision Energy Study of the [MO/TMS-PFB]"
Carboxylate Anions 89
v


CHAPTERS
Page
Collision Pressure Study of the
[MO/TMS-PFB]" Carboxylate Anions 93
Collision Pressure Study of the [M-PFB]"
Carboxylate Anions 95
Collision Pressure Study of the [M-H]'
Carboxylate Anions 98
Conclusions 100
5 EVALUATION OF SOLID-PHASE EXTRACTION GC/MS
AND GC/MS/MS FOR THE ANALYSIS OF ENDOGENOUS
PROSTAGLANDIN E2 IN URINE 101
Introduction 101
Experimental 103
Results from the Quantitation Study
of PGE2 in Urine 114
Trade-offs in the Steps of
the Analytical Procedure 121
Conclusions 138
6 EVALUATION OF SOLID-PHASE EXTRACTION
PROBE/MS/MS FOR THE ANALYSIS OF ENDOGENOUS
PROSTAGLANDIN E2 IN URINE 142
Introduction 142
Experimental 143
Solids Probe Analysis 145
Direct Chemical Ionization Analysis 153
Conclusions 164
7 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 165
Summary 165
Future Directions 167
LITERATURE CITED 169
BIOGRAPHICAL SKETCH 176
vi


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
CONCEPTS FOR THE DETERMINATION OF PROSTAGLANDINS
BY TANDEM MASS SPECTROMETRY
By
Todd Allen Gillespie
May, 1989
Chairman: Richard A. Yost
Major Department: Chemistry
An evaluation of the concepts for the trace determination of
prostaglandins (PGs) by tandem mass spectrometry (MS/MS) has been
achieved. Results from this work demonstrate the importance of the
optimization of various parameters in the collisionally-activated
dissociation (CAD) process before performing trace analysis. Dramatic
differences in the optimum collision gas pressure for selected-reaction
monitoring (SRM) with MS/MS for the determination of prostaglandins E2 and
F2a were observed. The differences in fragmentation behavior were examined
through the use of fragmentation, collection and overall CAD efficiency
studies. This work shows that the CAD efficiency for the derivatized and
underivatized carboxylate anions is significantly different for subtle
vii


structural changes in PGs. A possible explanation has been proposed to
explain these dramatic differences.
The advantages and limitations of immunoaffinity purification (IA) for
sample preparation of PGs in urine have been investigated. Results show
that IA purification coupled with a short 3 m GC capillary column
utilizing electron-capture negative chemical ionization (EC-NCI) SRM can
provide a selective, sensitive and rapid method of analysis for endogenous
levels of PGE2 in urine.
A systematic study was performed demonstrating the relative trade-offs
which exist throughout the entire analytical procedure. Eleven different
analytical schemes were systematically evaluated for the trade-offs in
sensitivity, selectivity, and total time of analysis. These trade-offs
are discussed in relation to how they affect the three basic steps (sample
preparation, sample introduction and mass spectrometric detection) of PG
analysis. This study indicates that the utilization of a more selective
sample preparation method (e.g., IA) with MS/MS can reduce the
chromatographic separation time required to achieve the necessary
selectivity and sensitivity for PG analysis in urine. However, results
show that MS/MS is not necessary if IA purification and a longer
chromatographic separation (more selective) technique are employed. This
systematic study should be applicable in the evaluation of any analytical
procedure for analysis of components in a biological sample. In addition,
future work is proposed which should further enhance PG analysis by MS/MS.
viii


CHAPTER 1
INTRODUCTION
Arachidonic Acid Metabolites (Prostaglandins)
The enzymatic oxidation of arachidonic acid (AA) leads to a
multitude of biochemically important products (1). Among these substances
are prostaglandins (PGs), thromboxanes (TXs) and leukotrienes (LTs).
Collectively, these compounds are referred to as eicosanoids and
constitute what is known as the arachidonic acid cascade (Figure 1-1).
Many of these oxygen-containing metabolites have interesting and diverse
pharmacological properties and significant medicinal potential (2).
Since, the initial description of PGs in 1935, a vast body of
knowledge has accumulated on their physiology and chemistry (1,2).
Recently, attention has been focused on PGs of certain series as antitumor
agents (3). Evidence indicates that PGs such as prostaglandin E2 (PGE2) ,
play an important role as local mediators and modulators of renal blood
flow and excretory functions (4). It has been suggested that most of the
primary PGs found in urine are derived from renal production (5); con
sequently, urinary levels of PGs have been applied as an index of renal
PG activity in numerous studies. Recently, PGE2 has seen application in
the induction of labor, softening of the cervix and prevention and
treatment of stress ulcers (1). While much has been learned about PGs
1


2
.-=
/= ^CCX
v>wn^v
11-wtnof immof
(11R)-11-Hvdrooaroy-6.M2. (llRM'-HfOrory-S 8.12.
acid 14-aico*atatraanoie acid
L
/^w^*^COOH
4
1S-M*7lor
|lSSV-lS-nri3roprory-S.l
11.13-*>eouiMrano tco
i*-+TEor
(iSSMS-hydroay-S.*.
11.15-a-coaaia on
/=>r5-<^^cOC
^
S-HTTlor
(SS)-S-nydroay-d .
11.1*-a>coaaialraaoic acid
*-Kato-ROF,, or
ft-kafooroaugiandin i,t
1
2SM 2-f>yarooarorv-S., 10. (12SH2-hydrory-5.#.10.
aaaiai/aanoc acj
wm
i SSl-S-nyOrooaroiY-d a.
M,1*-a.eoaiauaanoc ac
-coaaiatraanoic acid
/=v^=^^v^-cOH
OH
/ W'Vs^-'s^-
-Hydro iy-1
1.8.1 a-acoaa
hO Oh
)Cs^^COOH
TT
M.12-Tnhydrorr-.10. i11.12-Tnhydr*y-S.t.

OH
(T<^=^ooh
HO OH
Mnana
I acoaaiatraan
S^O.hydro **-7.8.11.14
COOM

(SS.12R and SS.12S1-5.12-
Oihydrory-d . IO-rrans-14-
LTV, or Kuiomm 8,
a 1
CO H-CH-CONhCH,COOH
.TC.or
NHj IWrantHouKoinanoCt
CO(CH,l,-H-COOH
M-CH-CONhCHjCOOH
r
:ooh
p-Vv~*ci
or Wu
LTC. or lauKoinana C.
HjH-CH-COHHCH.COOH
CH,
j^vV^COOM
LTD, or louaoUiaoa 0,
4-
H^a-CH-COOH
CH,
8
(^^I^COOH
'
LTV, or i*v*olfana E,
Figure 1-1: Arachidonic acid cascade


3
biological effects and how they relate to mammalian health, difficulty in
measuring low concentrations of PGs in biological systems has hindered
the progress of research.
The analysis of PGs and other AA metabolites can be divided into
three basic steps; sample preparation, sample introduction and measurement
by such techniques as bioassay, radioimmunoassay (RIA), high-performance
liquid chromatography (HPLC), gas chromatography (GC) and gas
chromatography/mass spectrometry (GC/MS). It has been shown that with
many of the analytical methods frequently used, PG concentrations are
often overestimated by as much as a factor of ten (6). This problem can
be traced to the lack of selectivity of the entire analytical scheme used
for analysis. Therefore, the development of an analytical scheme which
provides for accurate, sensitive and selective determination of PGs is
needed.
In this chapter, a brief review of the most frequently employed
techniques for sample preparation and measurement of PGs will be
discussed. More thorough reviews of sample preparation and measurement
techniques can be found in the literature (7,8). Recently, a review on
AA metabolism with examples of various analysis methods has been published
(9). Other, more specific reviews have been written by Traitler (10) and
Kelly (11) on mass spectrometric analysis methods of eicosanoids.
Sample Preparation Techniques for Prostaglandins
Sample preparation before the measurement step is extremely
important, with the extent of extraction and purification dramatically
affecting the validity of the data. In sample preparation of biological


4
fluids, a traditional technique that is commonly utilized is liquid-
liquid solvent extraction (7). This method is time-consuming and usually
yields only 80% to 90% recovery of most PGs (12). The degree of clean-up
provided by such extractions is limited; further purification is often
necessary for body fluids such as urine.
Another popular method for separating PGs from biological matrix
components is solid-phase extraction. Three types of solid-phase
extraction are commonly employed: (1) amberlite (XAD-2) column; (2)
octadecylsilyl (ODS) column (C18); and (3) selective packing materials,
such as immunoantibodies. Bradlow (13) described the use of an XAD-2
column that is advantageous when the biological matrix contains a large
concentration of proteins. Recoveries using this method have been
reported as about 90%. Both solvent extraction and XAD-2 resin extraction
procedures are time-consuming and require evaporation of relatively large
volumes of organic solvents. Moreover, they are not very selective and
give extractions containing extraneous material that must be removed
subsequently by various chromatographic purifications. A variety of
methods using a C18 column to extract PGs from biological samples have
been developed by Powell (8,14) and other researchers (15,16). The solid-
phase extraction using a C18 column is rapid, efficient and more selective
than solvent and XAD-2 extractions. Recovery with this method has been
reported to be greater than 90% in many cases.
Specialized packing materials can provide significantly more
selective extraction of specific targeted PGs. A phenylboronic acid
column has been used to selectively isolate thromboxane B2 (TXB2) and its
metabolites (17). The recovery of radio-labeled TXB2 after extraction was


5
reported at 90%. Potentially, an even more selective approach to sample
preparation is to combine the extraction and purification steps into one
procedure. This has been accomplished by using an antibody-mediated
extraction procedure developed by Krause et al. (18). Basically, the
prostaglandin-antibody was coupled to cyanogen bromide-activated Sepharose
4B and used as a stationary phase for the extraction of PG from the
samples. The antibody was coupled to Sepharose and packed into a Pasteur
pipette. The plasma samples were then applied to the gel in the column.
This one-step extraction-purification method has shown improved
specificity and sensitivity. Similar methods have also been employed by
Hubbard (19) and Vrbanac (20) for the analysis of TXB2 and 6-keto-PGF1a in
urine. Another approach to exploit the high selectivity of antibody-
antigen reactions for sample extraction is double-antibody precipitation.
This technique has been used for preparation of plasma samples before HPLC
analysis for (15R)-15 methyl-PGE2 (21).
In summary, the advantages of extraction (either solvent or solid-
phase) are: (1) it eliminates some extraneous material, thereby imparting
greater specificity to the assay; and (2) it improves sensitivity of the
analysis by concentrating the material. The disadvantages are: (1) it is
time-consuming; (2) a "carry-over" of non-eluted analyte may occur (if the
same column is reused) effecting the validity of subsequent assays: and
(3) the extraction efficiency of the procedure is variable. Simple
solvent or solid-phase extraction has been shown to yield samples that do
not permit accurate validity of PG quantitation. Improved validity of
subsequent quantitation has been observed after further purification


6
steps. A more detailed explanation of solid-phase extraction and
immunoaffinity (IA) purification can be found in Chapter 2.
Three types of chromatographic purification are described below: (1)
silica acid column chromatography; (2) thin-layer chromatography (TLC);
and (3) HPLC. Group separation of PGs and related compounds is
conveniently performed by silica acid column chromatography (22,23).
Recoveries were reported for this purification method of 85% to 90%. PGs
separated by silica acid chromatography usually require further
purification by TLC or HPLC prior to quantitation by RIA or GC/MS.
Separation of PGs by TLC was first investigated by Green and
Samuelsson (24). TLC is the most commonly used method for separation of
PGs because of its efficiency, simplicity and economy compared to other
chromatographic procedures. The major groups of PGs (A, B, D, E, F and
6-keto-PGF1a) were readily separated on a silica gel plate using various
solvent mixtures (25-27). The disadvantages of TLC are its low recovery
yields (typically 80%) and the lengthy procedures required for separation
of closely related compounds. Prostaglandin-related compounds with
similar behavior are often observed to migrate in a similar way even in
different solvent systems. Such problems can be avoided by using two-
dimensional TLC. A considerable improvement of resolution is achieved by
combining two solvent systems with different chromatographic properties.
Two-dimensional TLC analysis of PGs and related compounds has been
reported from a few laboratories (8,28-30).
The conventional techniques of column chromatography and TLC usually
suffer from poor chromatographic resolution and the need to use several
solvent systems to adequately separate arachidonate metabolites. HPLC has


7
been used successfully for the separation and purification of PGs from
biological sources since 1976 (31). This technique offers several
advantages: (1) there is high resolution of closely related compounds; (2)
good reproducibility is possible; and (3) fractions containing PG peaks
can be automatically collected and later quantitated by RIA, GC/MS or
scintillation counting of radio-labeled metabolites. Both normal-phase
HPLC on silica acid (32-34) and reverse-phase HPLC on octadecylsilyl
silica (35,36) have been used to separate the cyclooxygenase products of
arachidonic acid. However, HPLC can be an extremely lengthy technique for
purification and can yield low recoveries on the order of 60%.
Techniques for Determination and Measurement of Prostaglandins
A number of analytical methods have been developed for the detection
and measurement of PGs to study their physiological and pharmacological
effects. Among those, bioassay, RIA, HPLC and GC/MS are most widely used
for the quantitation of PGs in biological fluids.
Bioassav. Biological techniques and bioassay have contributed
greatly to the development of techniques for detecting and quantitating
AA metabolites (37,38). In general, bioassay has been highly beneficial
in establishing the biological significance of the unstable products of
AA metabolism. However, it provides only approximate quantitation and
relatively low selectivity.
Radioimmunoassay (RIA). RIA of PGs was introduced in 1970 by Levine
and Van Vunakis (39) with assays developed for PGE1 and PGF2a. The
literature has been expanding rapidly, and a large number of RIAs for PGs,
TXs and LTs have been reported. RIA is based on the competition between


8
radio-labeled and unlabeled molecules of a particular compound for binding
sites on an antibody directed against the same compound. The amount of
labeled compound is known and constant for all the tubes in an assay,
whereas the amount of unlabeled substance is either known and varied
(standard tubes) or unknown (sample tubes). A tube with no antibody
present is required as a "zero binding" tube. A tube containing no
unlabeled substance is also required as a "maximal binding" tube. When
larger amounts of unlabeled substance are present, the radioactive
molecules are displaced from the binding sites. The radioactivities of
the unbound fraction and antibody-bound fractions are usually separated
by dextran-coated charcoal or double-antibody methods, and the
radioactivity of either or both fractions is determined. The amount of
unlabeled compound in a sample tube is then obtained by comparison with
the standard tubes.
RIA has certain advantages over other quantitative methods, the most
important being its high sensitivity, with detection limits as low as a
picogram per sample. The precision and accuracy frequently compare
favorably with other methods. RIA is relatively rapid and also has high
sample capacity; for example, 100 samples can be analyzed within one or
two days, including radioactivity measurements and data processing.
RIA also has some drawbacks. First, the method is not entirely
specific under all circumstances. It is difficult to obtain a specific
antibody with a minimum of cross-reactivity and high affinity. Biological
samples, especially biological fluids (urine or plasma), usually need to
be purified through extraction, column chromatography, TLC, or even HPLC
before analysis by RIA. Appropriate purification steps are time-


9
consuming, but frequently necessary to remove most interfering compounds
and yield a specific assay with valid results. Other disadvantages of RIA
include the potential risk inherent in using radioactive materials and the
high cost of using disposable glassware, utensils, counting vials and
large volumes of scintillation fluid.
High-performance liquid chromatography (HPLO. HPLC has proven to
be useful for purification of PGs after an initial extraction procedure.
The HPLC technique is a good qualitative method; however, quantitation is
rather limited, especially for PGs. Terragno et al. (36) have found that
the highest molar extinction coefficient occurs around 192.5 nm for major
PGs, yielding detection limits in the nanogram range. Recently, a more
sensitive method using HPLC with a postcolumn derivatization and
fluorescence detection has been developed for eicosanoid quantitation.
Watkins and Peterson (41) developed a method to measure AA metabolites by
reverse-phase HPLC followed by formation of the ester derivative with P-
(9-anthroyloxy) phenacyl bromide. The disadvantages of HPLC are that this
technique can be lengthy and a relatively large volume of sample is
required for adequate detection of low levels of PGs in biological fluids.
Gas chromatography/mass spectrometry (GC/MS). GC/MS is the
analytical method of choice for the identification, characterization, and
quantitation of the products of the arachidonic acid cascade. Offering
both high sensitivity and selectivity, GC/MS has become the "gold
standard" for the analysis of PGs. Traditionally, GC/MS was used for
strictly qualitative analysis, with studies done on the determination of
the structures of several prostaglandins (42). Identification and


10
characterization of many prostaglandins and their metabolites were
performed by electron ionization/mass spectrometry through the early to
mid-1960's. In 1967, reports on eicosanoids first appeared, with limits
of detection in the low ng/mL range (42,43). The use of selected-ion
monitoring (SIM) with positive chemical ionization (PCI) and electron-
capture negative chemical ionization (EC-NCI) for quantitation
significantly improved the detection limits achieved by GC/MS.
The discussion that follows will focus on components of the
analytical technique of GC/MS for the analysis of PGs. In a typical
qualitative or quantitative analysis for PGs by GC/MS, the following steps
are performed: (1) sample preparation (extraction and purification); (2)
derivatization; (3) gas chromatographic separation; (4) ionization; and
(5) mass spectrometric detection. In the following pages, these
analytical steps will be discussed in reverse order, highlighting the mass
spectrometric component of the analysis, rather than sample preparation
which was discussed in detail earlier.
In mass spectrometric analysis, the quantitation of trace levels of
PGs is commonly performed by utilizing an isotope-labeled analog of the
compound of interest, with selective monitoring of the ions of each.
Since its introduction in 1967, stable isotope dilution (44) has been the
method of choice for quantitation. Many uses of stable isotope labeling
with SIM can be found in the prostaglandin literature (45-54). Both high
resolution mass spectrometry and low resolution mass spectrometry have
been employed for analysis of PGs. High resolution can reveal the
elemental composition of ions, which is helpful in identifying new
compounds. Low resolution is used for trace analysis despite its lower


11
selectivity. Examples of both techniques can be found in the literature
(55-59). A great deal of research has been devoted to trace analysis of
eicosanoids and their metabolites in all types of biological fluids, with
most determinations done in plasma and urine (48,49,60-63). The amounts
that have been analyzed are from the low ng to low pg/mL range, with
limits of detection as low as 50 fg reported in one study (64).
Three types of ionization are used today for most PGs analyses:
electron ionization (El), positive chemical ionization (PCI), and
electron-capture negative chemical ionization (EC-NCI). EI/MS, as
discussed earlier, is most often used for structural elucidation and
identification of new compounds. El mass spectra give structurally useful
fragmentation patterns, although the molecular ion may be weak or even
absent. For trace analysis, typical limits of detection with El are
approximately 100 pg/mL (57). PCI and EC-NCI are "gentler" ionization
techniques, generally producing less fragmentation, with a more prominent
(pseudo-) molecular ion. Thus, these techniques are useful for confirming
molecular weight, and for trace analysis by selected-ion monitoring. PCI
has been shown to be helpful in characterization of thromboxanes and
prostaglandins (65). Limits of detection vary for PCI and EC-NCI,
depending on both the compound and the reagent gas selected. Many types
of chemical ionization reagent gases have been used, but methane and
isobutane are the most common. Most trace analysis studies are now
performed with EC-NCI with methane as the reagent gas. Detection limits
are generally in the low pg/mL range, although limits as low as 50 fg/mL
have been reported (59). The three ionization techniques have been


12
compared for trace analysis of PGs, including limits of detection and
spectra obtained with each ionization technique (49,57).
Gas chromatography is generally used to separate the eicosanoids
from each other and from other potential interferents prior to their
identification or detection by mass spectrometry. The first GC/MS
analyses were accomplished with packed gas chromatography columns, which
were used extensively until the development of fused silica capillary
chromatographic columns. Until 1982, approximately equal use was made of
packed and capillary column techniques, but capillary chromatography has
led to better separation of closely related compounds. Coupled with
negative chemical ionization, it has allowed researchers to achieve limits
of detection in the low pg/mL range. These advantages have provided
higher sensitivity and selectivity in eicosanoids analysis. However,
packed column chromatography still has a role in prostaglandin analysis.
One recent study (66) showed the advantages of packed columns for highly
contaminated samples that exceeded the capacity of capillary columns.
Researchers have recently recognized the value of introducing the
capillary column directly into the ion source of the mass spectrometry
(67) This avoids problems with contamination, adsorption, and
decomposition of analytes (which can be severe with PGs) on active
surfaces in other GC/MS interfaces.
Derivatization of PGs has been important in their analysis, both to
increase their volatility for gas chromatography separation and to provide
for efficient EC-NCI to increase sensitivity of the GC/MS method. Today,
the methylester/methoxime/trimethylsilyl ether of PGs is the most
frequently cited derivative in GC/EI/MS analysis (63,64). However, it has


13
been shown that these derivatives are susceptible to hydrolysis, often
producing ions that are not optimal for selective-ion monitoring (68).
This is due to the low relative intensity of the high mass ions which are
optimal for quantitation.
The derivatization of PGs for GC/EC-NCI/MS seems to be standardizing
on the methoxime/trimethylsilyl ether/pentafluorobenzyl ester (MO/TMS/PFB)
mixed derivative (50,51,69-72). Derivatization with perfluorinated acid
anhydrides has been increasingly used for both qualitative and
quantitative work (69). These anhydrides usually incorporate a silylating
reagent such as N-(tetra-butyldimethylsilyl)/N-(methyltrifluoroacetamide).
This gives hydrolytic stability and increases high mass ion intensity for
optimal use of selective-ion monitoring. The use of such derivatives also
eliminates detection of many nonprostaglandin carboxylic acids, due to
their ability to derivatize with the carbonyl, rather than, or in addition
to, the carboxyl group. This makes these derivatives highly attractive
for detecting trace quantities of prostaglandins in biological matrices
(73).
Recent Analytical Advances
GC/MS remains the workhorse technique of PG research; however,
tandem mass spectrometry (MS/MS) and soft ionization techniques such as
fast atom bombardment (FAB) or liquid secondary ion mass spectrometry
(LSIMS) and liquid chromatography/mass spectrometry (LC/MS) are being
effectively employed. The sensitivity and selectivity of GC/MS/MS
compared to GC/MS has been studied in reports (74-76) utilizing both El
and EC-NCI. The advantages of GC/MS/MS have recently been exploited for


14
the trace analysis of PGs in biological samples (20,77,78). These studies
have been performed on both sector and quadrupole instruments. The high
selectivity of MS/MS makes it possible to perform analyses with minimal
sample preparation. MS/MS also minimizes or eliminates the need for
chromatographic separation in many cases, making the analysis extremely
rapid. MS/MS experiments have recently been reported in the literature
for analysis of underivatized prostaglandins (79,80).
In addition, with improved instrumentation has come the technique
of FAB or LSIMS (81-83). This method has aided structural elucidation,
as well as characterization of many PGs. LC/MS has become increasingly
popular in the analysis of PGs (84,85), as in all areas of chemistry.
LC/MS has the ability to analyze polar, thermally labile, and high
molecular weight eiconsanoids, and it saves time in sample preparation.
LC/MS with thermospray ionization (TSP-LC/MS) has been used by several
researchers to detect PGs and TXB2 at limits of detection as low as 10-
300 pg (on column), after derivatization with (diethylamino)ethyl chloride
(86). A series of PG standards were analyzed and investigated to show the
increase in sensitivity resulting from a post-column derivatization which
formed the methyl ester (87) The sensitivity is still not equal to the
GC/MS methods commonly employed. This is the limiting factor of LC/MS
for the analysis of PGs; however, there is reason to believe that the
necessary improvements in sensitivity can eventually be obtained. LC/MS
is a good qualitative technique which is still in its infancy. The
advantages to be gained in simplified sample preparation and the ability
to directly analyze the more polar eiconsanoids will stimulate further
improvements.


15
Another recent MS/MS technique which is promising is ion trap
(IT)MS/MS. The ITMS offers the potential for very selective and sensitive
GC/MS/MS analysis. In the ion trap, ion formation and mass analysis occur
in the same region (tandem-in-time), whereas, in tandem mass spectrometry
these two processes occur in different regions (tandem-in-space). The
analysis of PGs by this method has been reported by Strife (88,89). This
work shows the unique advantages of high sensitivity MS/MS,with nearly
100% conversion efficiencies of parent to daughter ion in MS/MS experi
ments .
This section of Chapter 1 has shown that much progress has been made
in the area of PG sample preparation and quantitation. Many limitations
remain, especially when the sample size is limited. In the chapters to
follow some of these limitations will be addressed and new analytical
schemes will be evaluated.
Strateeies for Mixture Analysis by MS/MS
Since the development of tandem mass spectrometry (MS/MS) in the
1970's, it has recently gained rapid acceptance as an exceptional
analytical tool for mixture analysis (90-93). MS/MS has the ability to
provide rapid, sensitive and selective analysis of complex biological
samples, often with minimal sample clean-up (94,95).
The MS/MS scan modes utilized in these studies are depicted in
Figure 1-2. In mixture analysis, chemical ionization of a mixture is
often utilized in the ion source of the mass spectrometer to produce ions
characteristic of the components in the mixture and to achieve a spectrum
with few fragments. Separation of the analyte from the matrix components


(a)
Q3 Full Scan
(c)
Selected-Ion
Monitoring (SIM)
Q2
Q
Q2
Q 3
QI
Q3
(b) Daughter Scan
Selected-Reaction
Monitoring (SRM)
Q2 Q3
Figure 1-2: Tandem mass spectrometry scan modes


17
is achieved by the mass selection of a characteristic ion of the analyte
by the first mass analyzer (Ql). The selected parent ion undergoes
collisionally activated dissociation (CAD) through collisions with neutral
gas molecules in the fragmentation region (Q2) to yield various fragment
or daughter ions. Subsequent mass analysis of the daughter ions by the
second mass analyzer (Q3) results in the analytical signal. This method
of MS/MS analysis corresponds to a daughter scan (Figure l-2b).
Although this operational mode is highly selective, this full-scan
daughter mass spectrum usually does not exhibit sufficient sensitivity for
trace analysis of an analyte in a complex matrix. Therefore, the scan
mode of selected-reaction monitoring (SRM) is commonly employed (Figure
l-2d). A characteristic daughter ion, typically the most abundant,
resulting from the fragmentation of the selected parent ion of the
analyte, is selected by the second mass analyzer for monitoring. SRM is
analogous to the selected-ion monitoring (SIM) (Figure l-2c) commonly used
to obtain maximum sensitivity in conventional GC/MS. Thus, an enhancement
in sensitivity is obtained at the expense of a gain in selectivity. In
addition to these MS/MS modes, the tandem mass spectrometer can be
operated as a normal MS by allowing all ions to pass through one mass
analyzer (Ql or Q3) and the collision cell (Q2), then scan the other mass
analyzer (Q3 or Ql) to produce a normal mass spectrum (Figure 2-la).
Optimization of many of these operational modes have been evaluated
throughout these studies and will be discussed in further detail as to
their significance in the trace determination of PGs.


18
Important Parameters for Trace Analysis
In order to perform trace analyses successfully, it is necessary to
think in terms of the four "S's" of analysis: (1) sensitivity; (2)
selectivity; (3) speed or analysis time; and (4) £ or cost. In the
determination of pure analytes, sensitivity can be a very useful
criterion; however, when required to determine an analyte in a complex
matrix, sensitivity alone may become meaningless. This is due to the fact
that chemical interferents in the matrix may themselves produce a response
or interfere with the signal of the analyte. Therefore, the factor which
may determine the smallest amount of analyte which can be determined
accurately is the second "S", selectivity. The selectivity can be
described as the ability of the method to distinguish the signal of the
analyte from that of the chemical interferents (so-called chemical noise).
The limit of detection (LOD), which depends upon both the selectivity and
sensitivity, is defined as the smallest amount of analyte which can be
detected.
The LOD required in trace analyses can be achieved by improving the
selectivity of the analytical scheme. Normally, this is accomplished
through the use of extensive sample clean-up and separation to enhance the
analyte signal with respect to the matrix components signal. These
extractions and purifications increase the possibility of sample
contamination and sample loss. Additionally, the methods necessary to
increase selectivity may become time-consuming and expensive, thus the
final two "S's", speed of the analysis and cost effectiveness may not be
optimum.


19
The Four Steps Involved in Trace Mixture Analysis
The analytical scheme for trace determination of an analyte in a
biological sample by MS/MS involves four basic steps: (1) sample
preparation; (2) sample separation/introduction; (3) ionization; and (4)
detection. When developing an accurate, reliable and specific method for
mixture analysis, a range of selectivity, sensitivity, time and cost are
observed for the four steps.
In sample preparation, a rapid, low cost and selective procedure is
desired. This can be achieved through the proper choice of extraction,
purification or derivatization methods which satisfy any or all of the
four "S's". The second step involves separation of the analyte of
interest from any matrix components which have not been eliminated by the
sample preparation methods. Typically, in MS/MS, gas chromatography is
employed for separation, if the analyte exhibits sufficient volatility.
Separation of components can be accomplished on short capillary GC columns
(3 m or less), when the sample has been adequately cleaned-up (96). Short
GC columns can only be utilized for separation of complex samples if the
sample preparation methods have the necessary selectivity. The choice of
an ionization method is based on the type of analysis required and the
analyte which is to be analyzed. In the low level trace determination of
analytes in biological samples, a "soft" ionization method (e.g., chemical
ionization) is usually selected which yields an intense molecular ion with
few fragments. Furthermore, for analytes which are highly electron
capturing (or can be derivatized), electron-capture negative chemical
ionization (EC-NCI) may be chosen in order to achieve the highest
sensitivity. Finally, the detection by MS/MS involves the optimization


20
of the parameters which constitute the operational modes which were
discussed above.
Overview of Thesis Organization
This thesis is divided into seven chapters. Chapter 2 describes
the sample preparation concepts and methods employed for this work.
Results from recovery studies on various types of extraction columns and
their characteristics are discussed in detail. The concept of
immunoaffinity purification is introduced and investigated.
The third chapter emphasizes the importance of optimizing MS/MS
parameters for trace determination of PGs. Optimization studies for
selected-ion monitoring (SIM) and selected-reaction monitoring (SRM) for
PGE2 and PGF2a are described and the results discussed.
Chapter 4 presents a study of the differences in the CAD efficiency
of two structurally similar PGs (PGE2 and PGF2q) Collision energy and
collision gas pressure studies of the carboxylate anions of four PGs are
evaluated and hypotheses for the differences noted are put forth.
The results of the quantitation study of endogenous PGE2 in urine can
be found in Chapter 5. The advantages and disadvantages of various
analytical schemes are pointed out. These schemes are systematically
evaluated for the trade-offs in sensitivity, selectivity and time of
analysis. The trade-offs are discussed in relation to how they are
affected by the three basic steps (sample preparation, sample introduction
and detection) of PG analysis.
Chapter 6 includes an evaluation of the rapid analysis techniques
of direct solids probe/MS/MS and direct chemical ionization (DCI)/MS/MS


21
utilizing an abbreviated derivatization procedure. The advantages and
limitations are discussed and the results of a quantitation study of
endogenous PGE2 in urine are presented.
The final chapter reviews the conclusions which were drawn from this
work. This chapter points out the potential of GC/MS/MS with selective
sample preparation and short GC capillary columns to determine endogenous
levels of PGE2 in urine. The importance of a systematic study of the
entire analytical scheme is finalized. In addition, future work is
proposed which should further enhance PG analysis by MS/MS.


CHAPTER 2
SAMPLE PREPARATION STUDIES
Introduction
Sample preparation is an important step in any analytical
methodology. This step prepares the sample for the detection method and
can dramatically affect the validity of the data obtained. The two main
parts of sample preparation for gas chromatography/mass spectrometry
(GC/MS) are sample purification and derivatization. When considering
sample purification, selectivity and speed of the method are of vital
importance. A method which is extremely selective can eliminate matrix
interferences and reduce the separation needed in GC. Sample throughput
is always an important factor in any analytical method. A rapid sample
purification step can greatly reduce the total time of analysis.
The other main part of sample preparation is derivatization. Many
compounds are not directly amenable to GC. The thermal lability of
prostaglandins (PGs) makes it impossible for them to pass through a GC
column intact without first undergoing derivatization. This
derivatization increases the volatility of the compound and reduces the
interaction of the polar substituents on the compound with the stationary
phase of the GC column. In addition, derivatization can add sensitivity
and/or selectivity for detection of a compound. Many organic
derivatization reactions with PGs enhance the efficiency of electron-
22


23
capture negative chemical ionization (EC-NCI) mass spectrometry (51,
70-72). Electron-capture NCI with derivatization produces much simpler
mass spectra and the major fragment ions occur at the high mass range
(50,69). Thus, these two features combined with the higher ionization
efficiency of EC-NCI provide added sensitivity and selectivity needed in
trace determination of PGs.
Concepts for Solid-Phase Extraction
Solid-phase extraction (SPE) has emerged, in the last ten years, as
the method of choice for isolation and purification of arachidonic acid
metabolites (8,14-16). SPE has the advantage of using low volumes of
solvents and high recoveries of 90% to 100% for most PGs. Rapid
extractions are usually possible with simple procedures. This results in
a rapid inexpensive extraction technique. The concept of SPE is based on
the selective retention of the analyte by a sorbent bed as a solvent in
which the analyte is dissolved is passed through the column. This idea
is displayed graphically in Figure 2-1. A sample containing analytes (A)
and interferences (I & M) is passed through the sorbent. The sorbent
selectively retains analytes (A) and some interferences (I). However, at
the same time, many interferences (M) pass unretained through the sorbent.
Appropriate solvents are then used to wash the sorbent, selectively
eluting previously retained interferences (I), while the analytes (A)
remain on the sorbent bed. Purified, concentrated analytes (A) are then
eluted from the sorbent.


24
Figure 2-1: Concept of solid-phase extraction:
A analyte; I & M interferences.


25
Sorbent/Analyte Interactions
Three types of chemical interactions are commonly employed in solid-
phase extractions (97). The first is the non-polar interaction which
occurs between the carbon-hydrogen bonds of the analyte and that of the
sorbent. Virtually all organic compounds have some non-polar character,
thus these types of interactions are the most commonly used to retain
analytes on sorbents. The forces which are involved in such non-polar
interactions are "van der Waals" or dispersion forces (97,98). The most
widely used sorbent in non-polar interactions is octadecyl silane bonded
to a silica substrate which is called C18. Many compounds can be retained
by a C18 sorbent, thus it is a very non-selective sorbent. In general,
non-polar solid-phase extraction is the least selective extraction
procedure. The concept of non-polar interaction is comparable to that of
reverse-phase chromatography. Retention of the analyte by non-polar
interaction is facilitated by a solvent more polar than that of the
non-polar sorbent. Elution is then accomplished by utilizing a solvent
with sufficient non-polar character to release the retained analyte from
its interaction with the sorbent.
Other interactions which are common for SPE are polar interactions.
These interactions are exhibited between many sorbents and functional
groups on analytes. All bonded silica exhibits polar interaction due to
the polar nature of the silica substrate to which the sorbent is bound
(97,98). Polar interactions include hydrogen bonding, dipole/dipole, pi
pi and many more interactions in which the distribution of electrons is
unequal in the atoms of the functional groups. This property of polar
sorbents allows an analyte which contains a polar functional group to


26
interact with a polar group on the sorbent. Groups that exhibit these
types of interactions include hydroxyls, amines, carbonyls and other
groups containing hetero-atoms such as oxygen, nitrogen, sulfur and
phosphorous. The most common polar sorbents are silica, diol, aminopropyl
and cyanopropyl. Polar sorbents function similarly to the interactions
found in normal-phase chromatography. Non-polar solvents are used to
promote retention of the analyte on the polar sorbent. Then a solvent,
more polar than the sorbent, is utilized to elute the analyte.
The third type of interaction is ionic. This occurs when an analyte
carrying a charge (either positive or negative) interacts with a sorbent
carrying a charge opposite to that of the analyte. Ionic interactions are
more selective than non-polar and polar interactions and can be controlled
by adjusting the pH of the sample solution. It is essential to know about
the functional groups on the sorbent and the analyte because both of these
need to be charged to facilitate ionic interaction. Two classes of ion-
exchange interaction exist, cationic (positively charged) and anionic
(negatively charged). Examples of cationic interactions include the
interaction of amines and certain inorganic cations with carboxymethyl,
sulfonylpropyl and benzenesulfonylpropyl sorbents. Anionic interactions
occur when sorbents containing primary, secondary, tertiary and quaternary
amines interact with carboxylic and sulfonic acids, phosphates and similar
groups on an analyte.
Recently, covalent interactions have been exploited for extraction
of specific types of compounds (99). Covalent chromatography is highly
chemically selective, involving an interaction of greater energy than is
employed in the other extraction methods. Retention of the analyte occurs


27
when a covalent bond can form between it and the sorbent. A change in the
solvent environment facilitates elution of the analyte. This is commonly
accomplished through the use of solvents with various pH's. One example
is phenyl boronic acid (PBA) which has been immobilized for the selective
retention of compounds with 1,2- or 1,3-diols such as catecholamines and
thromboxanes (17,100).
Many of the sorbents discussed above may exhibit more than one
interaction. Both polar and ionic interactions due to the silica
substrate used can occur in all sorbents. In the case of the PBA, non
polar, polar and ionic interactions can occur as secondary interactions
within the sorbent. The interactions which occur with a particular
sorbent are a function of the sample matrix and the solvent used for
washes and elution.
Sorbent Selection
The problem encountered in this analysis was to develop a solid-
phase extraction to selectively isolate PGs from interferences in urine.
Evaluation of different sorbents followed two fundamental steps. First,
sorbents were selected which in theory have the capability to retain PGs
from urine. Next, the different sorbents chosen were tested to evaluate
their actual ability to selectively retain the PGs of interest (97).
The sorbents which were chosen for the study were determined by
examining properties of the analyte (PGs) and the matrix (urine). First,
the determination of the interactions which PGs could undergo was
examined. Areas of carbon/hydrogen content with alkyl chains suggested
that non-polar retention was probable. The presence of such polar groups


28
as hydroxyls (OH) and carbonyls (=0) indicated a potential for retention
by polar interactions. Ionic interaction was indicated by the presence
of the carboxylic acid moiety. However, this method was not evaluated for
the analysis of PGs in urine due to the excessive quantities of compounds
in urine which would undergo anionic and cationic interactions.
Considering that PBA has been used for separation of the arachidonic acid
metabolite, thromboxane B2 (TXB2), covalent interaction with some PGs
appears possible due to the 1,3-diol present on the cyclopentane ring.
Next, the properties of the matrix and the potential interfering
components which are contained in urine were considered. Urine is an
aqueous media which contains many proteins, salts and solids. Components
with polar and non-polar functionalities can be found throughout urine
samples. This suggested that the interferences would undergo the same
interactions with the sorbents as the PGs. Therefore, to determine which
interactions would work most effectively, the sorbents required testing.
A sorbent testing scheme is shown in Figure 2-2 (97). First, each
sorbent needed to be prepared. This was accomplished by washing the
sorbent bed first and allowing the functional groups on the sorbent to
interact with the solvent. The next step was to remove the wash solvent
and create an environment that facilitated the analytes (PGs) retention.
After this process, the testing procedure began and involved five steps.
Standards were prepared identical to a "real" sample and applied to
the column (sorbent). The standards were then washed with the same
solvent in which they were dissolved, and the eluent collected. The
eluent was then checked for the presence of analyte, indicating sorbents
which did not provide adequate retention of the analyte. Next, strong


29
Optimize Retention of Standards
Optimize Elution of Standards
- Identify Wash Solvents
Test Blank Matrix
- Use Wash Solvents
Test Spiked Matrix
Troubleshoot if Necessary
Figure 2-2: Sorbent testing scheme.


30
elution solvents were chosen of which small volumes can be utilized to
completely elute the retained analyte. During this process, solvents
which would not elute the analyte were identified for use as wash
solvents. These were tested next with a blank matrix (urine) to determine
the solvent(s) which produced the cleanest extract. Clearly, this was far
more difficult to evaluate than the determination of analyte recovery.
After developing a procedure which provided sufficient analyte retention
and elution, as well as adequate clean-up of the matrix, the method was
tested with a sample (urine) spiked with analyte. Recoveries found in
this step were similar to those obtained with the standards. However, if
problems had been encountered, either the sorbent, wash solvents or
elution solvents may have been changed to provide for adequate retention
and elution of the analyte in the matrix.
Antibody Affinity Extraction
Extraction methods for PGs based on liquid-liquid or solid-phase
extraction are relatively nonselective and the final extracts are
frequently unsuitable for direct analysis, even by highly specific GC/MS
quantitation methods (7,101). The necessity of further purification of
the extracts before chromatographic analysis makes the analytical
procedures more complex, laborious and time-consuming to develop. This
problem has been avoided in many cases by taking advantage of immuno-
adsorption techniques to simplify extraction and clean-up procedures for
GC/MS analysis (18-21,102). Reports have shown that the selectivity of
the immunoadsorption procedures may permit the direct analysis of extracts
and eliminate the need for intermediate chromatographic clean-up.


31
Antibodies have been used for many years for the analysis of PGs by
radio-immunoassay (RIA). Unfortunately, the presence of substances within
the sample matrix which exhibit cross-reactivity with the polyclonal
antibody can be considerable (39,103). For example, antibodies for 20
carbon PGs and their metabolites may also bind the corresponding dinor
metabolites present in the matrix (19). Thus, HPLC is frequently employed
as a separation technique prior to RIA to avoid cross-reactivity. Reports
have shown that without separation of cross-reacting components by HPLC,
PG levels have been found 20 times higher than the actual levels present
(7,8). Immunoadsorption purification has been utilized as well prior to
PG analysis by RIA (104,105). However, this method has the disadvantage
of combining a purification procedure based on immunoaffinity with a
measurement procedure based upon the same principle. The advantage of
utilizing immunoadsorption for purification before GC/MS analysis is that
the highly specific antibody will enhance the selectivity by providing
discrimination which is unrelated and complements the characteristics of
GC/MS. This results in an analysis method for PGs which has a higher
degree of specificity than RIA.
These ideas have been incorporated in the sample preparation of PGs.
The inherent selectivity of the antibody-antigen interactions has been
exploited for PG analysis by Knapp and Vrbanac to obtain relatively pure
sample extracts (20,78). The basic principle of antibody affinity
extraction is displayed in Figure 2-3. In a typical affinity
chromatographic separation, the antibody is coupled to a stationary phase
(the most popular is agarose gel). The selectivity of affinity
separations is based on the principle of "lock and key" binding which


32
Adsorb
Regenerate
Wash
Figure 2-3: Basic principle of antibody affinity extraction
A analyte; I & M interferences.


33
occurs in biological systems. Extraction of the sample is accomplished
by passing the solution (containing analytes and interferences) through
the sorbent bed; the PGs which have affinity for the antibody are adsorbed
while other components pass through unretained. The retained or adsorbed
PGs are then eluted by changing the solvent.
Additional, secondary interactions are possible with immunoaffinity
chromatography. One important interaction discussed earlier is due to the
cross-reactivity of the polyclonal antibodies. Furthermore, non-specific
binding of interfering components may occur during the immunoadsorption
procedure. The bulk protein carrying the antibody has the potential for
interaction of components in the sample matrix. In addition, polar
interactions are possible between the silica stationary phase and any
polar functionalities found in the sample matrix.
In general, antibody affinity purification can decrease significant
loss of sample which can occur in TLC and HPLC. This method of sample
preparation is relatively rapid and requires no additional purification
of biological samples to obtain an adequate interference free GC trace.
The greatest advantage is the significant selectivity of the separation
process for antibody affinity purification compared to other conventional
chromatographic methods.
Concepts for Derivatization
Derivatization of PGs has been important in their analysis by GC/MS,
both to increase their volatility for GC separation and to provide for
efficient EC-NCI to increase sensitivity of the GC/MS method. Many
different derivatives have been used in the analysis for PGs (10,11). As
reported earlier in Chapter 1, the most commonly used derivative for


34
quantitative analysis by GC/MS is the methoxime/pentafluorobenzyl/tri-
methylsilyl (MO/PFB/TMS) derivative.
The keto group on PGE2 is converted to the methoxime derivative to
prevent silylation which can interfere with quantitation by producing
additional derivatives. Pentafluorobenzyl (PFB) esters are created to
enhance the efficiency of ionization by EC-NCI in order to achieve low
level determinations of PGs. These PFB esters have been found to give
about twice the sensitivity of the methyl ester derivative (106) Reaction
times are fast (-20 min) and quantitative (-100%) for this derivatization
procedure. The hydroxyl groups are converted to trimethylsilyl (TMS)
ethers using 0-bis(trimethylsilyl)-trifluoroacetamide (BSTFA). This TMS
donor has the additional advantage of creating extremely volatile reaction
by-products which usually elute with the solvent front in the GC trace.
Even though the derivatization for quantitative analysis of PGs by
GC/MS has been thoroughly documented, there are many variations in the
literature. It has been reported that by performing the methoximation
before the esterfication a fivefold increase in the derivative yield can
be obtained (47). However, many researchers still perform the ester-
fication step first in the derivatization procedure (10,11,74). Reaction
times for the methoximation step vary in the literature ranging from one
hour at 60 to 24 hours at room temperature. These differences, in
addition to the comparison of techniques for the removal of excess
derivative reagents by liquid-liquid extraction and nitrogen evaporation
were explored in this study.


35
Experimental
Prostaglandins and Reagents
All solvents were reagent or HPLC grade. Prostaglandin E2 (PGE2) was
purchased from Sigma Chemical Co. (St. Louis, MO). [5,6,8,11,12,14,15 -
3H2]-PGE2 and Riafluor liquid scintillator were from New England Nuclear
(Boston, MA) and were a gift from Dr. J. Neu of the Department of
Pediatrics, University of Florida (Gainesville, FL) The solid-phase
extraction columns were purchased from Analytichem International, Inc.
(Harbor City, CA) and Waters Assoc. (Sep-Pak columns; Milford, MA).
3,3',4,4'-(2H4) PGE2 and the antibody affinity sorbent were gifts from
Drs. J.J. Vrbanac and D.R. Knapp of the Department of Pharmacology,
Medical University of South Carolina (Charleston, SC) The derivatization
reagents and solvents pyridine, O-methylhydroxylamine hydrochloride,
acetonitrile, and N,N-diisopropylethyl amine for GC/MS percent recovery
studies were all purchased from Sigma Chemical Co.. Pentafluorobenzyl-
bromide (PFBBr) and bis(trimethylsilyl)-trifluoroacetamide (BSTFA) were
purchased from Pierce Chemical Co. (Rockford, IL). Urine was obtained
from the author. All glassware was silanized with a solution of 5%
dimethyldichlorosilane in toluene. These two chemicals were both
purchased from Sigma Chemical Co.. Helium used as GC carrier gas and
methane (>99%) used as the chemical ionization reagent gas were from
Matheson Gas Products, Inc. (Orlando, FL).
Sample Preparation
The sorbents for the percent recovery studies were chosen and tested
according to the procedures discussed earlier in this chapter. Extraction


36
procedures were determined for the non-polar, polar and phenyl boronic
acid columns by detection of the tritium-labeled PGE2 by scintillation
counting. The sorbents chosen are listed with the final extraction
procedure used for the percent recovery studies for both scintillation
counting and GC/MS.
Non-polar columns: octyl (C8), octadecyl (C18) and phenyl (PH)
(1) Conditioned the column with 10 mL of HPLC water and 10 mL of
methanol.
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Washed the column with 10 mL of HPLC water and 10 mL petroleum
ether.
(4) Eluted PGE2 with 10 mL of ethyl acetate.
Polar columns: silica (SI), cyanopropyl (CN), aminopropyl (NH2) and
diol (20H)
(1) Conditioned the column with 10 mL of benzene:ethyl acetate
(80:20 volume:volume).
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Washed the column with 10 mL benzene:ethyl acetate (60:40 v:v).
(4) Eluted PGE2 with 10 mL benzene:ethyl acetate:methanol
(60:40:30 v:v:v).
Phenyl boronic acid column (PBA)
(1) Conditioned the column with 5 mL of 0.1 M hydrochloric acid and
5 mL of 0.1 M sodium hydroxide.


37
(2) Passed sample of PGE2 (adjusted to pH 8.5 with 0.1 M phosphate
buffer (PBS)) through the column.
(3) Washed the column with 5 mL of methanol and 5 mL of HPLC water.
(4) Eluted PGE2 with 5 mL of 0.1 M PBS (pH 6.5).
The antibody affinity columns were tested and percent recovery data
calculated only with GC/MS.
Antibody affinity column [Immunoaffinity (IA)]
(1) Conditioned the column with 20 mL of PBS (pH 7.4).
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Allowed the sample to settle into the sorbent bed for 15 min at
room temperature.
(4) Washed the column with 25 mL of PBS (pH 7.4) and 10 mL HPLC
water. Removed all remaining water in the column.
(5) Eluted PGE2 with 15 mL of 95% acetonitrile solution (v:v).
(6) Washed column with an additional 10 mL of 95% acetonitrile to
assure removal of all the PGE2.
(7) Immediately rinsed the column with 10 mL of HPLC water and
15 mL of PBS (pH 7.4).
Scintillation Counting
A stock solution of 3H-PGE2 was used for the percent recovery
studies. This solution was 0.09375 microcuries (/iCi)/microliter (/jL) and
had a specific activity of 169.5 ^Ci/millimole. Six microliters of this
original solution was diluted with 100 /L of absolute ethyl alcohol
creating a solution of 5.625 x 10'3 /iCi//iL. Ten microliters of this


38
standard solution, corresponding to 3.319 x 10'4 mmoles or 0.1218 mg was
passed through each column tested. Following the extraction procedures
the eluent was collected and the solvent evaporated with nitrogen. The
3H-PGE2 was then diluted with 100 /tL of PBS (pH 7.4). Additionally, 3.5
mL of Riafluor liquid scintillator were added to the 9.375 x 103 /Ci
solution of 3H-PGE2 before the counting process. Each extraction was
performed three times with three individual columns.
A calibration curve was prepared in the same manner with the
exception of the actual extraction step (Figure 2-4a). Aliquots of 4,
5.5, 8, 10.5, 12 and 13.5 microliters of the 5.625 x 103 /iCi//iL solution
were added to separate vials and each diluted with 100 /iL of the PBS (pH
7.4). In addition, a blank containing only 100 /tL of the PBS (pH 7.4) was
prepared. The Riafluor liquid scintillator was added and the standards
counted and used to calculate the percent recovery values for the
different columns tested.
Gas Chromatography/Mass Spectrometry (GC/MS)
Ten nanograms (ng) of PGE2 were passed through each column for the
percent recovery studies of standards. Following the extraction procedure
for the columns tested, 10 ng of 2H4-PGE2 were added and the solutions were
evaporated to dryness with nitrogen. The same procedure was followed for
extraction of PGE2 in urine for percent recovery studies except that the
10 ng of PGE2 added to the urine is in addition to the endogenous levels
present.
Calibration curves for the GC/MS analysis were prepared by adding
a constant amount of 2H^-PGE2 (25 ng) and increasing amounts of PGE2 in the


39
Figure 2-4: Calibration curves: (a) Scintillation counting
(b) Gas chromatography/mass spectrometry (GC/MS)
with selected-ion monitoring (SIM).


Table 2-1: Calibration Curve Dilutions for GC/MS
h4-pge2
Added (ng)
pge2
Added (ng)
Volume of
Dilution (/L)
Concentration
of 2H4-PGE2 (pg//iL)
Concentration
of PGE2 (pg/AiL)
25.0
0.0
50.0
500.0
0.0
25.0
0.25
50.0
500.0
5.0
25.0
2.5
50.0
500.0
50.0
25.0
5.0
50.0
500.0
100.0
25.0
12.5
50.0
500.0
250.0
25.0
25.0
50.0
500.0
500.0
25.0
37.5
50.0
500.0
750.0
25.0
50.0
50.0
500.0
1000.0


41
solution (Figure 2-4b). Table 2-1 lists the amounts of 2H^-PGE2 and
standard PGE2 added to each vial and the final concentrations after
dilution with 50 /iL of silanizing reagent.
Derivatization for GC/MS
The methoxime/pentafluorobenzyl ester/trimethylsilyl (MO/PFB/TMS)
derivatives were formed for the GC/MS percent recovery and derivatization
studies. The method used was similar to the derivatization of H. L.
Hubbard et al. (19). The standards and samples of 2H4-PGE2 and PGE2 after
evaporation were treated with 100-200 /iL of methylhydroxylamine HC1 in dry
pyridine (4 mg/mL), allowed to stand overnight at room temperature, then
evaporated under nitrogen until dry. Each sample was acidified by adding
200 /iL of IN formic acid, extracted with two 1 mL aliquots of ethyl
acetate, and the extract dried under nitrogen. Then 50 /iL of
acetonitrile, 30 /iL of 30% PFBBr in acetonitrile, and 15 /iL of 10% N,N-
diisopropylethylamine in acetonitrile were added to the dried methoxime
derivative. Each solution was allowed to stand for 30 minutes at room
temperature before the reagents were evaporated with nitrogen. Excess
derivatizing reagent was removed by dissolving the sample in 200 /iL of
distilled water and extracting with two 1 mL aliquots of a methylene
chloride:hexane (50:50 v:v) solution; the extract was then dried under
nitrogen. The trimethylsilyl derivative then was formed by adding 50 /tL
of BSTFA to the standards for the calibration curve and 20 /iL to the
extraction samples and allowing the solutions to stand overnight at room
temperature. One-microliter injections containing 500 pg of 2H4-PGE2 were
made of each standard and sample.


42
Instrumentation
A Beckman LS 3800 liquid scintillation counter and a Finnigan MAT
triple stage quadrupole (TSQ45) gas chromatograph/mass spectrometer were
used in these studies. Gas chromatography was carried out on a
conventional J&W Scientific (Folsom, CA) DB-1 (30 m long, 0.25 mm i.d.,
0.25 /an film thickness) capillary column in the splitless mode with helium
carrier gas at a flow rate of 41 cm/s (inlet pressure 18-20 psi). The
initial temperature of 250C was held for 30 s, then increased at 20C/min
to 310C for the calibration curve and percent recovery studies of
standards. Urine percent recovery data were obtained with an initial
temperature of 100C held for 30 s, increased at 25C/min to 250C, then
increased again at 5C/min to 310C.
Mass spectrometry conditions were: interface and transfer line
temperature 300C, ionizer temperature 190C, electron energy 100 eV and
emission current 0.3 mA. Electron-capture negative chemical ionization
(EC-NCI) was carried out with methane at an ionizer pressure of 0.45 torr.
In the GC/MS percent recovery and derivatization studies, a specific
ion for PGE2 (524; [MO/TMS-PFB]) and for 2H4-PGE2 (528; [MO/TMS-PFB]')
were selected and monitored throughout these studies. The selected ion
monitoring mode (SIM) with quadrupole one was used on the mass
spectrometer. A baseline was chosen visually on the GC trace and the
areas for PGE2 and H^-PGE2 calculated by the INCOS computer system for the
calibration curve and percent recovery samples. The area of PGE2 divided
by the area of 2H^-PGE2 in the standards gives a ratio which is used in the
calibration curve. The amount of PGE2 recovered through each column was


43
calculated by comparing the ratio of these ions after the extraction
procedure to that of the calibration curve.
Results and Discussion
Percent Recovery Studies (Scintillation Counting)
Table 2-2 shows the percent recovery results for the different
sorbents tested. These recoveries were determined by scintillation
counting of 3H-PGE2 standards. Three samples were extracted for each
sorbent and the average and percent relative standard deviation (%RSD)
calculated. Examination of Table 2-2 indicates that a wide range of
recoveries was found for the different sorbents tested.
The non-polar sorbents investigated were octyl (C8), octadecyl (C18)
and phenyl (PH). The C18 columns had the highest percent recoveries
(97.2%) with the C8 (81.8%) and the PH (8.8%) columns having lower
recoveries. These low recovery values for the C8 and PH columns signify
either: (1) PGE2 was unretained as the initial standard solution was passed
through the column; (2) PGE2 was eluted during the wash procedure; or (3)
PGE2 was irreversibly bound to the column or not effectively eluted. The
reasons for poor recovery were investigated by examining all the eluents
which were passed through the respective columns to determine the presence
of PGE2. It was discovered that the C8 and PH columns did not initially
retain PGE2. Octadecyl columns exhibited the smallest variation from
column to column with a %RSD of 0.6.
Polar sorbents tested were silica (SI), cyanopropyl (CN) aminopropyl
(NH2) and diol (20H). As with the non-polar columns, a wide range of
recoveries were discovered for the different polar interactions tested.


Table 2-2: % Recovery of Standard PGE2 by Scintillation Counting
%
Recovery
Data
Column
Column 4
Average
% Recoverv
%RSD
1
2
3
C8 (Octyl)b
80.11
82.17
83.08
81.8
1.9
C18 (Octadecyl)
97.91
96.99
96.84
97.2
0.6
PH (Phenyl)
8.35
9.20
8.78
8.8
4.8
SI (Silica)
97.89
100.03
103.01
100.4
2.5
CN (Cyanopropyl)
24.02
27.92
22.82
24.9
10.7
NH2 (Aminopropyl)
12.75
13.96
11.12
12.6
11.3
2OH (Diol)
89.19
93.44
98.55
93.7
5.0
PBA (Phenyl
40.72
38.23
41.08
40.0
3.9
Boronic Acid)
a % Relative Standard
Deviation
b All columns were purchased from Analytichem.


45
The two sorbents that exhibited greater than 90% recovery were the SI
(100.4%) and 20H (93.7%). The recoveries for these columns were found to
be much higher than those found for CN (24.9%) and NH2 (12.6%) columns.
This difference in recoveries may be attributed to the interaction of the
polar groups on PGE2 (particularly the hydroxyls) with the hydroxyl groups
on the SI and 20H, rather than with the carbon/nitrogen interaction with
CN or the amine group with the NH2. Investigation of the eluents showed
that PGE2 was not effectively retained initially for the CN and NH2
columns. The variation from column to column (%RSD) for the SI (2.5%) and
20H (5.0%) were less than that found for CN (10.7%) and NH2 (11.3%).
In addition, phenyl boronic acid columns were tested. The percent
recovery found using this type of interaction was 40.0%, well below the
recovery values found for C18, SI and 20H columns. This extraction
technique is based on the premise that the tetrahedral anionic form of
boronates condense with 1,2- or 1,3-diols to form five- or six- membered
covalent complexes (107). The low recovery of PGE2 observed for the PBA
column can possibly be explained by the inability of the boronate to
condense with the diols on the cyclopentane ring of PGE2 to form a stable
complex. An explanation for the inability of PGs to condense with the PBA
column was reported by Lawson et al. (17). They believe that the tendency
of the planar phenyl groups to orient so that their pi (jt) orbitals align
or are stacked, thereby forcing the boronic acid groups to be too close
together, not allowing the sterically fixed cyclic 1,3-diols on PGs free
access.
Data obtained from testing these sorbents suggests that PGE2 has
preference for retention on specific non-polar (C18) and polar (SI and


46
20H) sorbents. Even sorbents with the same type of interactions
demonstrate varied retention for PGE2. Recoveries for the C18, SI and 20H
columns are similar and demonstrate adequate retention (>90%) of PGE2 to
justify further investigation.
Percent Recovery Studies (GC/MS)
Percent recovery data for standard PGE2 by GC/MS is listed in Table
2-3. The columns tested in this study were those that had been found to
provide adequate retention (>90%) for PGE2 in the previous scintillation
counting experiments. In addition, this study shows recovery data for
another brand of octadecyl sorbent (Sep-Pak) and a very selective sorbent
using antibody-antigen interaction (immunoaffinity). As in the initial
recovery study (Table 2-2), three individual columns were each used to
extract three samples of standard PGE2. Three injections of each sample
were made into the GC/MS. The average of the three injections and the
three samples, in addition to the %RSD is listed in Table 2-3.
Comparing the recovery data in Table 2-2 to the data in Table 2-3,
the average recovery values for the C18, SI and 20H are similar. The
values determined by GC/MS are consistently 3-10% lower than those
determined by scintillation counting. However, this slight difference
could be attributed to the basic difference in calculating counting data
and areas of GC/MS. The variation between columns is again small (<5.0%)
for all sorbents tested. The immunoaffinity column demonstrated a percent
recovery (93.1%) quite adequate for retention of PGE2. Octadecyl columns
from two different suppliers were compared to examine differences in
retention and selectivity. The recovery data for the Sep-Pak (Waters)


Table 2-3: % Recovery of Standard PGE2 by Gas Chromatography/Mass spectrometry
Average
% Recovery Data Average % Recovery %RSDa
Column
Column M
GC
Iniection
A
% Recoverv
%RSDa
of 3
of 3
1
1
91.85
2
91.72
3
91.15
91.6
0.4
Columns
Columns
{
Sep-Pak
2
86.30
84.60
84.12
85.0
1.4
89.11
4.0
(Octadecyl)
3
89.01
92.63
90.09
90.6
2.1
1
89.43
89.59
92.67
90.6
2.0
C18
2
95.63
94.98
95.06
95.2
0.4
92.8
2.5
(Octadecyl)
3
92.51
91.82
93.17
92.5
0.7
1
96.52
93.02
96.09
95.2
1.9
P*
SI
2
82.04
94.11
92.21
89.5
7.3
90.8
4.3
(Silica)
3
86.29
86.79
90.49
87.9
2.6
1
92.35
91.76
92.07
92.1
0.3
2 OH
2
90.44
88.69
91.13
90.1
1.4
90.0
2.4
(Diol)
3
88.58
86.90
87.88
87.8
1.0
1
88.50
98.18
102.02
96.2
7.2
IA
2
91.11
87.88
88.34
89.1
2.0
93.1
3.9
(Immununoaffinity)
3
90.67
89.55
101.60
93.9
7.1
a % Relative Standard Deviation


48
columns were slightly lower than that found for the C18 (Analytichem)
columns. This may be attributed to experimental error in the extraction
procedure; however, reports suggest that Sep-Paks have considerable faults
compared to octadecyl sorbents from other manufacturers (108).
Table 2-4 contains the percent recovery results of standard PGE2
spiked into urine by GC/MS analysis. The columns tested in this study
were C18, SI, 20H and a combination of C18 plus immunoaffinity (IA).
Biological samples can be directly applied to the IA column; however, for
PG analysis Knapp and Vrbanac (78) have found an advantage in preceeding
the IA purification procedure with a C18 column extraction. The advantage
is that employing the C18 extraction first removes large concentrations
of extremely polar impurities found in urine which can non-specifically
bind to the IA column. Averages and %RSD are listed in the table for
three injections of each sample and the three extractions which were
performed on individual columns. The data indicate that the columns (SI
and 20H) which utilize polar interactions are not effective for retention
of PGE2 in urine, even though they were successful for PGE2 standards.
This is presumably due to competition for binding sites on the sorbent
between matrix components in the urine and PGE2. The non-polar C18 column
and the C18 column coupled with the IA column provided similar recoveries
for PGE2 in urine as in standards. The variation from column to column is
low for all cases (<7%) including the C18 and IA samples. In the case of
the IA column data, the same sorbent bed (or column) was used for all
three samples. The %RSD for the three samples, in addition to the three
average recovery values, demonstrate the reusability of the IA sorbent.
The slight decrease in the recovery values between samples 1-3 indicates


Table 2-4:
% Recovery of
Standard PGE2 in
Urine by Gas
Chromatography/Mass
Spectrometry
Column(s)
Column 4
%
Recovery Data
GC Iniection 4 %
Average
Recoverv
%RSDa
% Recovery
of 3
%RSDa
of 3
1
2
3
Columns
Columns
1
89.95
84.13
88.66
87.9
3.5
C18
2
96.88
99.66
99.16
98.6
1.5
92.1
6.3
(Octadecyl)
3
90.74
90.33
89.20
90.1
0.9
1
9.58
10.22
10.88
10.2
6.4
SI
2
10.35
10.81
10.51
10.6
2.2
10.6
4.0
(Silica)
3
10.67
10.91
11.62
11.1
4.5
P'
VO
1
23.27
18.61
26.82
22.9
18.0
2 OH
2
21.29
24.48
23.82
23.2
7.3
22.2
6.8
(Diol)
3
21.09
20.46
19.81
20.5
3.1
1
81.25
93.65
102.7
92.5
11.6
C18 + IAb
2
87.15
92.08
87.46
88.9
3.1
89.7
2.8
3
87.50
88.65
86.97
87.7
1.0
a % Relative Standard Deviation
b Three different C18 columns, but the only one IA column.


50
that no carry-over of PGE2 occurred from sample to sample. Thus, the IA
sorbent can be reused for many urine samples in combination with a C18
column without loss of affinity for PGE2. The ability of IA to effectively
separate urine matrix components from PGE2 will be discussed in a later
chapter.
Derivatization Studies
Table 2-5 lists the results of the study of different derivatization
procedures. The GC/MS peak areas for three samples are listed along with
their average and %RSD. Each sample injected onto the GC column contained
500 pg of PGE2. Comparing the different results, the most effective method
of derivatization can be determined.
The first method listed followed the derivatization procedure
discussed in the experimental section. Comparing that method to a second
method, in which a more rapid methoximation at an elevated temperature (1
hr at 60C) was used, the peak area of method one was 1.4 times greater
when the 24 hour methoximation was employed. This suggests that at longer
reaction times more complete methoximation occurs. Recently, a study of
the methoximation of various PGs was reported in the literature (109).
These results showed that efficient methoximation of PGE2 by a procedure
similar to method one was 1.1 times greater than method two with a %RSD
of 11.8%. This corresponds to the values which were obtained in this
study. Another question addressed by this study is whether to perform the
methoximation step before or after the PFB esterification. Examining the
peak areas obtained for method three and comparing them to method one,
similar areas were calculated for 500 pg. The data suggest that either


Table 2-5: Study of Different Derivatization Procedures for PGE2
by GC/MS with SIM for the [M-PFB] ion
Peak
Area of PGE,
(counts)
Method
Sample 1
Samle 2
Sample
3
Average
%RSD'
lb
1.64
x 106
2.21 x 106
2.01
X
106
1.95
X
106
14.8
2C
1.29
x 106
1.58 x 106
1.44
X
106
1.44
X
106
10.1
3d
2.16
x 106
1.74 x 106
2.00
X
106
1.97
X
106
10.8
4e
1.14
x 106
1.14 x 106
1.16
X
106
1.15
X
106
1.0
5f
1.21
x 106
1.14 x 106
1.12
X
106
1.15
X
106
4.1
a % Relative Standard Deviation
b Procedure described on page 41
c Methoximation for 1 hr at 60C
d Esterification performed before methoximation
e Nitrogen evaporation only after the methoximation step
f Nitrogen evaporation performed after all steps
(no liquid-liquid extraction was performed)


52
step (methoximation or the PFB esterification) can be performed first.
The other question proposed in this study was the use of liquid-liquid
extraction to remove excess derivatizing reagents or the simpler, more
rapid method of only nitrogen evaporation. Two methods were studied, one
in which only nitrogen evaporation was performed after the methoximation
step, then liquid-liquid extraction after the esterification (method 4)
and the other in which only nitrogen evaporation was performed after all
derivatization steps (method 5). Comparing these two methods with method
one, the areas for 500 pg for both method four and five were approximately
40% less than method one. This suggests that removal of the excess
derivatizing reagents by liquid-liquid extraction is essential prior to
GC/MS, despite the increase in sample preparation time. The concentration
of PGE2 in urine is 100 to 400 pg/mL, thus having an effective
derivatization procedure which enhances the sensitivity of PGE2 is vital,
even at the expense of additional analysis time.
Conclusions
The optimum sample preparation for PGE2 in urine has been determined
in this chapter. Extraction and purification procedures as well as
derivatization steps have been investigated. The results from recovery
studies show that the use of either a C18 column or a combination of C18
and IA columns achieve adequate quantitative recoveries for PGE2 in urine.
Derivatization study results indicate that the time and temperature of the
methoximation reaction are important and appears to be optimum at longer
reaction times with lower temperatures. Performing either methoximation
or PFB esterification first in the derivatization procedure has little


53
effect on the area calculated for PGE2- Results from this study
demonstrate the advantage of using liquid-liquid extraction methods to
remove the excess derivatization reagents after each step in the
derivatization procedure.


CHAPTER 3
OPTIMIZATION OF GC/MS AND GC/MS/MS CONDITIONS
FOR TRACE DETERMINATION OF PROSTAGLANDINS
Introduction
Many reports of GC/MS analysis of prostaglandins (PGs) can be found
in the literature (2,17,48,62,101). The conditions employed in each case
vary depending on the type of analysis (qualitative or quantitative),
sample matrix (urine, serum, etc.), and targeted concentration. In the
trace determination of PGs, optimization of conditions is critical.
Detection of low levels of PGs (100-400 pg/mL) in urine requires a
technique that is both sensitive and selective. The many parameters which
exist in GC/MS and GC/MS/MS can be varied according to the analysis to
enhance either sensitivity or selectivity. Thus, to achieve the proper
conditions for trace determination of PGs the various parameters must be
characterized and optimized.
Experimental
Prostaglandins and Reagents
All solvents were reagent or HPLC grade. Prostaglandin E2 (PGE2) and
prostaglandin F2a (PGF2a) was purchased from Sigma Chemical Co. (St. Louis,
MO). The derivatization reagents pyridine, O-methylhydroxylamine
hydrochloride, acetonitrile and N,N-diisopropylethyl amine were all
54


55
purchased from Sigma Chemical Co. Pentafluorobenzylbromide (PFBBr) and
bis(trimethylsilyl)trifluoroacetamide (BSTFA) were purchased from Pierce
Chemical Co. (Rockford, IL). All glassware was silanized with a solution
of 5% dimethyldichlorosilane in toluene. These two chemicals were both
purchased from Sigma Chemical Co. Helium used as GC carrier gas, methane
(>99%) as chemical ionization reagent gas and nitrogen, argon and xenon
used as collision gases were from Matheson Gas Products, Inc. (Orlando,
FL).
Derivatization
The MO/PFB/TMS derivative of PGE2 and the PFB/TMS derivative of PGF2(J
were prepared by the same procedure as in Chapter 2.
Instrumental Conditions
A Finnigan MAT triple stage quadrupole (TSQ45) gas chromatograph/
mass spectrometer was employed. Mass spectrometry conditions were:
interface and transfer line temperature 300C, ionizer temperature 190C,
electron energy 100 eV and emission current 0.3 mA. GC was carried out
on a short J&W Scientific (Folsom, CA) DB-1 (3 m long, 0.25 mm i.d., 0.25
/im film thickness) capillary column in the splitless mode with helium
carrier gas at an inlet pressure of 4-6 psi. The initial temperature of
200C was held for 30 s, then increased at 20C/min to 260C. The
injector temperature was 300C.
Both full scan mass spectra and selected-ion monitoring (SIM) were
used in the GC/MS studies. An electron multiplier (EM) setting of 900 V
was used for the full scan spectra and a preamp gain of 10'8 A/V. A
baseline was chosen visually on the GC trace and the area for PGE2 (524*)


56
and PGF2a (569) calculated by the INCOS computer system in the SIM mode
of operation. In GC/MS/MS optimization studies full daughter spectra and
selected-reaction monitoring (SRM) were employed and areas calculated by
the same method as described for GC/MS. The EM was set at 1500 V for the
full daughter spectra obtained and a preamp gain of 108 V/A. In the
GC/MS/MS optimization the [M-PFB]' carboxylate anions of PGE2 and PGF2a
were selected in the first quadrupole (Ql) region and passed into the
collision cell (Q2) In this region these ions underwent CAD to form
characteristic fragments which were then mass analyzed in the third
quadrupole (Q3). A full daughter spectrum was acquired over the mass
range of 100-600 amu.
Calibration curves were prepared for both GC/MS and GC/MS/MS after
optimization of the various parameters. Selected-ion monitoring and
selected-reaction monitoring were used to determine linearity, precision
and limits of detection for standard PGE2 utilizing GC/MS and GC/MS/MS.
The EM was set at 1700 V for both the SIM and SRM calibration curve data
Q
with a preamp gain of 10 V/A.
Mass Spectrometry (GC/MS)
Choice of the appropriate ionization method is essential for trace
determination of PGs by GC/MS. Electron ionization (El) has been reported
in the determination and identification of various PGs (42,43,57).
Structural information is obtained by this technique due to the abundance
of fragment ions which are produced. However, in trace analysis of PGs
the creation of a single ion with a maximized intensity is preferred.


57
Chemical ionization (Cl) has the advantage of usually producing few
fragment ions and a very intense molecular ion. Many reports of chemical
ionization GC/MS for PG analysis appear in the literature (65-72). Both
positive and negative Cl have been incorporated for PG analysis. The
literature reports that appropriate derivatization of PGs coupled with
electron-capture negative chemical ionization (EC-NCI) results in the
detection of low levels of PGs (69-72). These reports generally employ
methane (CH^) as a reagent gas for its ability to thermalize electrons.
Thus, both the GC/MS and GC/MS/MS optimization studies have utilized EC-
NCI with methane as the reagent gas.
Ionizer Pressure Study
Although the literature includes numerous examples of methane as a
reagent gas for EC-NCI, many dramatically different ion source pressures
have been employed. This study was performed to determine the optimum
ionizer pressure at which the [M-PFB]' ions of PGE2 and PGF2a are produced
in the ion source. Figure 3-1 shows the average areas determined at
different ionizer pressures of methane for the 524' ion (PGE2) and 569" ion
(PGF2a) The average of three one-microliter injections of a 100 pg//L
solution of both PGE2 and PGF2a have been plotted on the graph. The
optimum ion source pressure for PGE2 and PGF2a occurs at 0.50 Torr of
methane.
At ionizer pressures lower than 0.50 Torr the [M-PFB]' ion has a
lower percent relative intensity compared to the reconstructed ion current
(RIC) for both PGE2 and PGF2a. As the ion source pressure is gradually
increased above 0.50 Torr, fragment ions begin to increase in relative


Average Area 10 (counts)
2.00 q
uso r
i.6o
1.40 ~
1.20 ~
1.00
0.80 t
0.60 1 l i i i i i i i i ; i i i i it~rt-1 ; 1 i t~f l l'iT't [ I I i i i i I i | i i i i i i ; l |
0:00 0.20 0.40 0.00 0.80 1:00
Ion Source Pressure (Torr)
figure 3-1 i Ion source pressure study of the [M-PfB]' Ion of PGfc2 and POF^.


59
intensity and contribute more to the RIC, thus decreasing the relative
intensity of the [M-PFB] ion compared to the RIC.
Ionizer Temperature Study
Reports in the literature have cited ion source temperatures for
EC-NCI/GC/MS and EC-NCI/GC/MS/MS in the range of 110C to 200C (69-78).
Figure 3-2 indicates the optimum ion source temperature observed in this
study for the analysis of PGE2 and PGF2a< Selected-ion monitoring (SIM)
of the 524' (PGE2) and 569" ion (PGF2a) was used over a range of ion source
temperatures from 100C to 190C. Three one-microliter injections of a
500 pg//iL solution of PGE2 and PGF2a were performed at ten different ion
source temperatures. The average of the three injections is plotted on
the graph. Both PGE2 and PGF2a have an optimum ion source temperature at
190C. Thus, the [M-PFB]carboxylate anion of PGE2 and PGF2a optimize at
the maximum ion source temperature of the instrument.
The percent relative intensity of the [M-PFB]' ion compared to the
RIC increases with an increase in the ion source temperature and reaches
a maximum at 190C. In addition fragment ions increase, as the
temperature is elevated to about 140C to 150C, then these fragments
gradually decrease as the ion source temperature is raised above 150C.
These two observations lead to the optimum ion source temperature of 190C
for the [M-PFB]' ion.
Electron-Capture Negative Chemical Ionization Mass Spectra
The mass spectra of standard PGE2 and PGF2a, obtained at the optimum
ion source pressure and temperature, are shown in Figure 3-3a and Figure
3-3b. Both spectra demonstrate the advantage of employing EC-NCI for


Average Area 10 (counts)
Ion Source Temperature (C)
Figure 3-2: Ion source temperature study of the [M-PFB]" ion of PGE2
ON
o
and PGF.


% Relative Abundance
Figure 3-3: Electron-capture negative chemical ionization mass spectra of:
(a) PGE2 MO/PFB/TMS derivative
(b) PGF^ PFB/TMS derivative


62
prostaglandin analysis. One intense peak, the [M-PFB]' ion, dominates
each mass spectrum. This ion, PGE2 (524) and PGF2a (569*), can be utilized
for SIM. Other low intensity fragment ions can be seen in the mass
spectrum of PGE2, corresponding to the loss of derivatives attached to
PGE2. In addition, no fragments of greater than 1% relative abundance are
observed in the mass spectrum of PGF2(t.
The M ion for both PGE2 (m/z 705) and PGF2a (m/z 750) is rarely
present in the EC-NCI mass spectra, thus it must be less than 0.1%
relative abundance. In addition, the PFB* ion (m/z 181) occurs in the EC-
NCI mass spectra of both PGs at less than 0.5% abundance.
Selected-Ion Monitoring Calibration Curve
A calibration curve for PGE2 (524) is shown in Figure 3-4. This
curve indicates the linearity and limit of detection for PGE2 with SIM.
Three one-microliter injections at nine different concentrations were
performed. The limit of detection was calculated from the calibration
data and corresponded to the amount of PGE2 which could give a GC peak area
three times greater than the average area obtained with a derivatized
blank. The use of SIM with standard PGE2 produced a limit of detection of
approximately 94 fg (femtograms) and is indicated on the curve. The
calibration curve showed good linearity above the limit of detection in
the range of concentrations expected for endogenous PGE2 in urine (100 to
400 pg/mL) (71,78). The linear dynamic range of the curve is from 500 fg
to 1 ng (solid line) and the slope of the linear regression best fit line
is 1.266 with a correlation coefficient of 0.9925. The non-linearity at
the low end of the calibration curve may be due to adsorption on the


10
10
o
o
CD
<
PGE2 Concentration (g)
as
u>
Figure 3-4:
Selected-ion monitoring calibration curve for the
[M-PFB] ion of the MO/PFB/TMS derivative of PGE2.


64
column, septum or injection port and subsequent adsorption by the next
injection. Precision of the GC/MS method utilizing SIM was determined by
performing ten one-microliter injections of a 50 pg//iL solution of PGE2.
The percent relative standard deviation (%RSD) of the ten injections was
5.5%. Calibration curves for PGF2a, PGD2 and DHKF2a were similar, with
varying limits of detection, in the range of 50 to 200 fg.
The results for this study agree well with the literature. Reports
have shown LODs using EI/MS at about 20 pg for the M+ (6,17,48,62,101) and
utilizing EC-NCI/MS about 100 fg (19,20,76,77) for the [M-PFB]' ion.
Tandem Mass Spectrometry (GC/MS/MS')
Monitoring the efficiencies of the collisionally activated
dissociation processes can help in determining optimum MS/MS conditions
for trace determination of PGs. These efficiencies are affected by
collision energy and collision gas pressure. Either parameter can be
varied to maximize the CAD efficiency for a particular parent ion.
Increasing the collision energy allows for more energetic collisions,
while increasing the collision gas pressure increases the number of
collisions each ion experiences.
Collision Gas Pressure Studies
The collision gas pressure for three different gases (N2, Ar, and Xe)
was optimized to determine which collision gas and pressure were the most
efficient for selected-reaction monitoring at the maximum available
collision energy of 30 eV. Pressure-resolved breakdown curves for
selected ions of the MO/PFB/TMS derivative of PGE2 are shown in Figures


(a)
Collision Gas
Collision Energy 30 eV
oooQo 524
SP 524"
la 524'
'AJ> 524'
434'
344
313'
268
0.0 1.0 2.0 3.0
Collision Gas Pressure (rnTorr)
(b)
CL
+
Cl
w
20-
-ai
/
lOptimum
Ar Collision Gas
1 /
Collision Energy 30 e
: / \
s" ;
- / / /\
OOOOQ 52.4"- 454"
o o o 524"-* 344"
A&AAA 524"- 313
00000 524 - 268
0.0 1.6 2.0
Collision Gas Pressure (rnTorr Ar)
(c)
ee
CL
t a
Q
W
1 Optimum
I
Xe
Collision Gas
: /
\ Collision Energy 30 eV
: /
QQ-QQQ 524 -> 434
i /
aoa 524 -> 344
- /
A A A A A 524-* 313"
1 X
O.0J2 0 0 524 268
¡ i
0.0 1.0 2.0 J.O
Collision Gas Pressure (rnTorr)
Figure 3-5: Pressure-resolved breakdown curve of the carboxylate
anion of the MO/PFB/TMS derivative of PGE2 with
collision gas: (a) Nitrogen (b) Argon (c) Xenon


(a)
(b)
Ar Collision Gas
Collision Energy 30 eV
ooooo 569 -
339'
569 -*
317'
A6AAA 569
299'
40000 569-+
273"
Collision Gas Pressure (mTorr)
(c)
Optimum
Xe Collision Gas
Collision Energy 30 eV
ooooo 569'-
389'
ODDD AO--
317"
299'
00000 569'-
273'
Collision Gas Pressure (mTorr)
Figure 3-6: Pressure-resolved breakdown curve of the carboxylate
anion of the PFB/TMS derivative of PGF^ with
collision gas: (a) Nitrogen (b) Argon (c) Xenon


67
3-5a, 3-5b and 3-5c and for the PFB/TMS derivative of PGF2a in Figures 3-
6a, 3-6b and 3-6c. The optimum collision gas pressure is indicated on
each curve. This type of curve can be calculated by dividing the area of
a selected daughter ion by the area of all the ions in the daughter
spectrum (DyfDj + P]) at each pressure. The point which is chosen as the
optimum is the pressure where one can obtain a qualitative daughter
spectrum which is "rich" in structural information with a number of
reasonably abundant daughter ions.
The optima indicated on Figures 3-5a, 3-5b and 3-5c occur at a
collision pressure of 0.5, 1.0 and 0.5 mTorr for N2, Ar, and Xe
respectively. However, in the case of PGF2a, the optima occur at
significantly higher pressures, 2.5, 1.5, and 1.0 mTorr for N2, Ar, and Xe
(Figures 3-6a, 3-6b and 3-6c). Comparing Figure 3-5a to 3-6a, the optimal
use of nitrogen as a collision gas requires a pressure five times higher
for PGF2a than for PGE2. This dramatic difference in optimum collision
pressure exists between two structurally similar PGs.
The relative differences in the optimum collision gas pressure for
PGF2a with the various collision gases can be explained by the relative
mass of the three different collision gases. The greater size of the
argon and xenon gas molecules increases the energy deposited into the
parent ion, therefore increasing the fragmentation efficiency. Therefore,
the optimum collision pressure decreases with an increase in the mass of
the gas molecules, because the abundance of the most prominent fragment
ions occur at lower pressures.
Notice the significant differences in the maximum relative intensity
of the daughter ions for the three collision gases. The curves with


68
nitrogen (Figures 3-5a and 3-6a) show a higher maximum relative intensity
for the selected reactions listed. Figure 3-6c for PGF2(J, utilizing xenon
as the collision gas, is particularly interesting. The relative intensity
of the daughter ions selected are 12 times lower than the intensity of the
same daughter ions displayed in Figure 3-6a for nitrogen. In addition,
the relative intensity of the daughter ions approach zero at higher
collision gas pressures (> 1.0 mTorr). Thus, either the parent ion
(carboxylate anion) is increasing at higher pressures or other daughter
ions are more abundant with argon and xenon at these collision gas
pressures. Clearly, for the CAD process, the parent ion decreases as the
collision gas pressure is increased. Therefore, various daughter ions not
listed in these figures must be prominent with argon and xenon at higher
collision gas pressures.
This is apparent from examining Figure 3-7, which shows the
pressure-resolved breakdown curves for different selected ions with the
PFB/TMS derivative of PGF2a with argon and xenon as collision gases.
Comparing Figure 3-7a and Figure 3-7b to Figure 3-6a the relative
intensity of the daughter ions for argon and xenon in this case are
similar to that found for nitrogen. The most intense reaction in both
cases in Figure 3-7 is the selected-reaction of 569 -* 89', corresponding
to a back-bone fragmentation.
A general trend appears in all the figures for both PGE2 and PGF2(J.
The loss of one and two HOTMS groups from the [M-PFB] ion tend to maximize
together at low collision gas pressures for the three collision gases.
Subsequently, these selected-reactions gradually decrease towards zero at
higher collision gas pressures. The four selected-reactions for PGE2 in


69
(a)
(b)
o.o
Optimum
Xe Collision Gas
Collision Energy 30 eV
ooooo 569 -
255'
569
215
A A A A A 569
161"
00000 569
89'
t r t t rm i i i i i m i n i rp t
1.0 2.0 3.0
T|
4.0
Collision Gas Pressure (mTorr)
Figure 3-7: Pressure-resolved breakdown curve of the carboxylate
anion of the PFB/TMS derivative of PGF^ with
collision gas: (a) Nitrogen (b) Argon


70
Figure 3-5 all increase at low collision gas pressures and then gradually
decrease as higher collision gas pressures are employed. In the case of
PGF2a, the additional loss of the third HOTMS group (569" -* 299") gradually
increases when nitrogen is utilized (Figure 3-6a) or levels off when argon
(Figure 3-6b) is employed, as the collision gas pressure is continually
increased. In Figure 3-7, the selected-reactions have relatively low
intensities at low collision gas pressures (< 1.0 mTorr), but increase
gradually and level off as the collision gas pressure is increased (> 1.0
mTorr).
Trace analysis by selected-reaction monitoring with MS/MS requires
optimization of the absolute intensity of a single daughter ion of the
selected parent ion. The curves in Figures 3-8 and 3-9 give an indication
of the optimum reactions and collision gas pressures which should be
selected for maximum SRM sensitivity for PGE2 and PGF2a with three
different collision gases at maximum collision energy (30 eV). This type
of curve is calculated by dividing the area of selected daughter ions, Dj,
by the area of the incident parent ion, PQ (measured in a daughter spectrum
without collision gas). The reaction with the highest CAD efficiency
should be selected to yield the highest sensitivity for selected reaction
monitoring (SRM) trace determination of PGs. For example, in the case of
PGF2a, choice of the 569" -* 299 selected reaction with argon (Figure 3-
9b) would be the optimum (overall efficiency of -2%) at a collision
pressure of 1.5 mtorr and collision energy of 30 eV. This reaction
corresponds to the [M-PFB]" -* [(M-PFB) 3(HOTMS) ]"for the derivatized
carboxylate anion of PGF2(J. Note that this overall CAD efficiency (-2%)
is obtained at the optimum pressure for any of the three gases. The more


71
13n
Nz Collision Gas
Collision Energy
30 eV
(a)
x
Optimum A
ooooo 524"-*
434"
.
524 -*
344
CL
A A A A A 524 -*
313"
\
Q
ooooo 524 ->
268"
5-
0.0 1.0 2.0 3.0
Collision Gas Pressure (mTorr)
(b)
Optimum
Ar Collision Gas
Collision'Energy 30 eV
ooooo 524"
CDDOD 524"
4AAAA 524
OOOOO 524"
0.0 1.0 2.0 3.0
Collision Gas Pressure (mTorr)
434'
344'
313"
268"
13-|
(C)
Optimum
Xe Collision Gas
Collision Energy 30 eV
ooooo 524"
o_ooop 524"
A A A A A 524"
ooooo 524"
434'
344'
313'
268'
0.0 1.0 2.0 3.0
Collision Gas Pressure (mTorr)
Figure 3-8: Overall CAD efficiency for the selected-reaction
monitoring of the carboxylate anion of the MO/PFB/TMS
derivative of PGE2 with collision gas:
(a) Nitrogen (b) Argon (c) Xenon


72
(a)
2.5 ?
N2 Collision Gas
Collision Energy 30 eV
Optimum ->
0.0 1.0 2.0 3.0 4.0
Collision Gas Pressure (mTorr)
(b)
2-5 :
2.0 -
V 1-5
o
CL
\ 1.0
a
0.5
0.0
:
Ar Collision Gas
' Optimum A
Collision Energy 30 e\
ooooo 569"- 389'
/ \
aaoao 5fiQ - 317"
" / \
aaaaa 569 -* 299"
: / \
00000 569"- 273"
0.0 1.0 2.0 3.0 4.0
Collision Gas Pressure (mTorr)
(c)
Optimum
Qffl-QQQ 569'
qoDop569'
aaaaa 569'
00000 569'
389'
317'
299'
273'
Xe Collision Gos
Collision Energy 30 eV
2.0
3.0
4.0
Collision Gas Pressure (mTorr)
Figure 3-9: Overall CAD efficiency for the selected-reaction
monitoring of the carboxylate anion of the PFB/TMS
derivative of PGF^ with collision gas:
(a) Nitrogen (b) Argon (c) Xenon


73
massive the collision gas, the lower the optimum pressure. PGF2a exhibits
a slightly higher overall CAD efficiency (-2%) with xenon for the selected
reaction of 569' -* 317' (Figure 3-9c). This reaction corresponds to the
[M-PFB]" -+ [ (M-PFB) 2(HOTMS) (CH3)2Si=CH2]' for the derivatized
carboxylate anion of PGF2a. This suggests that xenon would be the optimum
CAD gas. However, xenon is quite expensive ($650/50 L of gas) and the
gain in CAD efficiency is slight; thus, argon would be a more practical
choice.
For PGE2, the [M-PFB]' - [(M-PFB) 2(H0TMS) C02 HOCH3] reaction
with argon (Figure 3-8b) is optimum at a pressure 2 times lower than for
PGF2)J. Even more notable is that the optimum CAD efficiency (D1/PQ) for
PGE2 (-10%) is significantly higher than that for PGF2a (-2%) with all
three gases employed. Note that on Figures 3-8b and 3-8c the lowest
collision gas pressure been plotted is 0.2 mTorr. This is due to the fact
that when the zero collision gas pressure data was obtained, the actual
pressure of the collision cell was 0.2 mTorr. This indicates that
residual collision gas was present in both these cases, thus allowing
residual CAD to occur.
Collision Energy Study
Argon was chosen as the collision gas for the optimization of
collision energy. The collision energy study for selected-reaction
monitoring is shown in Figure 3-10. Data for SRM with the reactions and
Argon pressure chosen as optimum in the collision gas pressure studies at
30 eV for PGE2 and PGF2a are plotted on the same graph. Three one-
microliter injections of a 500 pg//iL solution of PGE2 and PGF2a were


Area
10 J-Krr
0.0
rrfTTi 11 t iTrynm i n i [ n i 11'itt"t~]~tttt i i i i i | i i tit i d i |
5.0 10.0 15.0 20.0 25.0 50.0
Collision Energy (eV)
(524' 268')
¡sion Pressure
mTorr Argon
(569" -> 299")
¡sion Pressure
mTorr Argon
Figure 3-10: Collision energy study for the selected reactions of the M0/PFB/TMS
derivative of PGE2 and the PFB/TMS derivative of PGF^.


75
performed at collision energies of 7 to 28 eV. Optima for the selected
reactions of 524 - 268* (PGE2) and 569" -+ 299 (PGF2a) are indicated on the
graph. The optimum collision energy for PGE2 (25 eV) is slightly higher
than for PGF2a (22 eV) probably due to the difference in the collision
pressures employed for each selected reaction. These plots suggest that,
once a particular collision gas, pressure, and selected reaction are
chosen, variation of the collision energy has little effect.
PauEhter Spectra of Standards
Figures 3-11a and 3-lib show daughter ion spectra for the
carboxylate anions of the MO/PFB/TMS derivative of PGE2 and the PFB/TMS
derivative of PGF2ff. The fragment ions labeled in the spectra are
tabulated in Table 3-1 with possible assignments of the ion's identity.
Most of the fragment ions observed in both daughter spectra are
derivative specific. These ions occur at m/z 434, 344 and 313 for PGE2 and
at m/z 479, 389, 317 and 299 for PGF2a. The most intense daughter ion from
the fragmentation of the [M-PFB] ion of PGE2 is m/z 268 ion and
corresponds to the loss of (2*H0TMS-C02-CH30H) from the parent ion of 524
In the daughter spectrum of PGF2a the m/z 299 ion is the most intense
and corresponds to the loss of three HOTMS groups from the parent ion of
569". The fragment ions which occur at lower masses are ions that
correspond to backbone-specific fragments. This means these ions
correspond to fragmentation of the carbon-hydrogen skeleton in both PGE2
and PGF2a. These ions include m/z 240 and 214 for PGE2 and m/z 255, 215,
201 and 161 for PGF.


% Relative Abundance
100%!
268~
CHjO-N
(a)
100%-i
(b)
m/z 100
Figure 3-11:
-j
as
Daughter ion spectra of the [M-PFB]' ions (ra/z 524 and 569) of:
(a) PGE2 MO/PFB/TMS derivative at 1.0 mTorr argon and at 28.2 eV
(b) PGF^ PFB/TMS derivative at 1.5 mTorr argon and at 28.2 eV


77
Table 3-1: Daughter Ions of [M-PFB]"
PGE2 MO/PFB/TMS and PGF2a
(P) of
PFB/TMS
PGE-, MO/PFB/TMSa
Ion Assignment
m/z
%RA'
P'
524
5
[P-HOTMS]*
434
2
[P-2H0TMS]*
344
21
[P-2H0TMS-OCHj]'
313
32
[P-2H0TMS-C02]'
300
4
[p-2hotms-co2-ch2o]'
270
11
[P-2H0TMS-C02-CHjOH ]'
268
100
[ P 2H0TMS C02- CHjOH C2H4 ]'
240
5
[ P 2H0TMS C02 CH3OH C4H6 ]'
214
12
PGF-^ PFB/TMSb
Ion Assignment
m/z
%RA
P'
569
36
[P-HOTMS]"
479
4
[P-2H0TMS]*
389
18
[ P 2H0TMS (CH3) 2S i=CH2 ]'
317
24
[P-3H0TMS]
299
100
[ P 2H0TMS C02 (CH3) 2S i=CH2 ]"
273
56
[P.-3H0TMS-C02]
255
36
[p-3hotms-co2-c3h4]'
215
21
[p-3hotms-co2-c4h6]"
201
12
[p-3hotms-co2-c7h10]"
161
18
8 At a collision gas pressure of 1.0 mTorr argon
and collision energy of 28.0 eV.
b At a collision gas pressure of 1.5 mTorr argon
and collision energy of 28.0 eV.
c 1 Relative Abundance


78
Considerations for choice of a particular selected reaction for
monitoring has been discussed recently by Strife (77). This report along
with other studies have shown that backbone-specific fragmentation confers
superior selectivity over derivative-specific fragmentation in the
analysis of biological samples. For example, when SRM is based on a
derivative-specific fragmentation, any component in a SIM chromatogram
that is derivatized has an enhanced probability of appearing in a SRM
chromatogram. However, the backbone-specific fragmentation has a lower
relative daughter ion intensity in EC-NCI/GC/MS/MS than for derivative-
specific fragmentation. Therefore, if the backbone-specific fragmentation
was chosen for SRM analysis the sensitivity would be lower than that for
the derivative-specific fragmentation found in Figure 3-8 and Figure 3-9
for PGE2 and PGF2a.
Selected-Reaction Monitoring Calibration Curve
A selected-reaction monitoring (SRM) calibration curve for PGE2
(524" -+ 268") is shown in Figure 3-12. This curve indicates the linearity
and limit of detection for PGE2 with SRM. Three one-microliter injections
at seven different concentrations were performed. The limit of detection
was calculated from the calibration data, the corresponding amount of PGE2
which gives a GC peak area three times greater than the average area
obtained with a derivatized blank. The use of SRM with standard PGE2
produced a limit of detection of approximately 14 pg, as indicated on the
curve. The calibration curve showed good linearity above the limit of
detection in the range of concentrations expected for endogenous PGE2 in
urine (100 to 400 pg/mL) (71,78). The linear dynamic range of the curve


Figure 3-12: Selected-reaction monitoring calibration curve for the 524* -+ 268
reaction of the MO/PFB/TMS derivative of PGE2-


80
is from 20 pg to 5 ng (solid line) and the slope of the linear regression
best fit line is 1.007 with a correlation coefficient of 0.9989. Precision
of the GC/MS/MS method utilizing SRM was determined by performing ten one
microliter injections of a 500 pg//iL solution of PGE2. The percent
relative standard deviation (%RSD) of the ten injections was 3.9%.
Calibration curves for PGF2a, PGD2 and DHKF2q were similar, with varying
limits of detection in the range of 5 to 30 pg. The results for this
study agree well with literature reports, which have shown LODs utilizing
EC-NCI/MS/MS of about 1 to 20 pg (19,20,76,77).
Conclusions
The optimum conditions for GC/MS electron-capture negative chemical
ionization (EC-NCI) with SIM and GC/MS/MS with SRM are summarized in Table
3-2. The optimum collision gas pressure for both qualitative and
quantitative (SRM) analysis of PGE2 are lower than the optima found for
PGF2a. The dramatically lower CAD efficiency for the carboxylate anion
of PGF2a (Figure 3-8b) compared to that of PGE2 (Figure 3-7b) clearly
indicates its greater stability under CAD conditions.
This study demonstrates the need for evaluating the CAD efficiency
in the trace analysis of PGs. Optimization of both collision energy and
collision gas pressure is essential in obtaining an accurate qualitative
daughter spectrum "rich" in structural information. The CAD reaction with
the highest CAD efficiency should be selected to yield the sensitivity for
SRM determination of PGs.
Examining the calibration curves (Figures 3-4 and 3-11) differences
between SIM and SRM are noted. Sensitivity is greater with SIM than with


81
Table 3-2: Otimum Conditions for Electron-Capture Negative
Chemical Ionization Mass Spectrometry
and Tandem Mass Spectrometry
Electron-Capture Negative Chemcial
Parameter
Ion Source Pressure
Ion Source Temperature
PGE:
0.50 Torr
190C
Ionization
££F 2a
0.50 Torr
190C
Tandem Mass Spectrometry
Qualitative Daughter Spectrum
Parameter
Collision Gas
Collision Gas Pressure
Collision Energy
pge2
Argon
1.0 mTorr
28.1 eV
L2a
Argon
1.5 mTorr
28.1 eV
Quantitative
Parameter
Collision Gas
Selected Reaction
Collision Gas Pressure
Collision Energy
Selected-Reaction Monitoring
pge2
Argon
524' 268
1.0 mTorr
25.0 eV
PG£2a
Argon
569' 299
1.5 mTorr
22.2 eV


82
SRM. The limit of detection for SIM (94 fg) is slightly more than 2
orders of magnitude lower than for SRM (14 pg). Comparing the relative
peak areas of SIM and SRM at 20 pg the SIM peak area is approximately 10
times higher than the peak area of 20 pg with SRM. In addition, at higher
levels of PGE2, 500 pg, the SIM peak area is approximately 40 times higher
than the SRM peak area. The lower sensitivity of SRM is expected due to
the limited efficiency of the CAD conversion of the parent ion to the
daughter ion (approximately 12% for 524' -* 268") of interest, as well as
transmission losses inherent in adding a second stage of mass analysis
(typically 10 times). However, the selectivity gained by the parent-
daughter reaction should reduce the chemical noise, in a sample matrix,
to a greater extent than the analytical signal, thus, compensating for the
lost sensitivity.


CHAPTER 4
DIFFERENCES IN THE COLLISIONALLY ACTIVATED DISSOCIATION OF
STRUCTURALLY SIMILAR PROSTAGLANDINS
Introduction
The ions formed by electron ionization (El) of the methyl ester/
methoxime/trimethyl silyl ether derivatives of prostaglandins (PGs) show
considerable fragmentation in the collisionally activated dissociation
(CAD) process (74,75). However, the carboxylate anions of certain PGs
produced by EC-NCI have been reported to be extremely stable when
subjected to CAD (76).
It has been observed that the carboxylate anions of certain PGs
exhibit little fragmentation even at high collision energies (>20 eV) and
pressures (1.5 mTorr N2). Subtle differences among the structures of
prostaglandins E2 (PGE2), F2a (PGF2a) D2 (PGD2) and 13,14-dihydro-15-keto
F2a (DHKF2a) (Figure 4-1) yield enormous differences in CAD efficiency.
The CAD efficiency for the [MO/TMS-PFB] , [M-PFB]' and [M-H] carboxylate
anions is significantly different for closely related PGs. The low
fragmentation and CAD efficiencies of the carboxylate anions of PGF2a and
DHKF2a compared to those of PGE2 and PGD2 clearly indicate the greater
stability of these species. In this chapter these differences are
evaluated and explained in relation to the structural differences between
the carboxylate anions for the PGs.
83


84
Figure 4-1: Structures of the four prostaglandins studied:
(a) Prostaglandin F2a (PGF2a) (b) Prostaglandin E2 (PGE2)
(c) Prostaglandin D2 (PGD2) (d) 13,14-dihydro-15-keto F2
(DHKF2a)


85
Experimental
Prostaglandins and Reagents
The prostaglandins E2, F2a, D2 and 13,14-dihydro-15-keto F2a, as well
as O-methylhydroxylamine hydrochloride, N,N-diisopropylethyl-amine,
pyridine, and acetonitrile (analytical grade) were all purchased from
Sigma Chemical Co.. Pentafluorobenzylbromide (PFBBr) and bis(trimethyl-
silyl)trifluoroacetamide (BSTFA) were purchased from Pierce Chemical Co..
The methane (>99%) used as the chemical ionization reagent gas was
purchased from Matheson Gas Products, Inc.. Helium used as GC carrier
gas and nitrogen used as CAD collision gas were commercial grade, with
their purity checked by mass spectrometry.
Derivatization
The methoxime/pentafluorobenzyl ester/trimethylsilyl (MO/PFB/TMS)
derivatives (Figure 4-2) formed for the GC/MS/MS studies were prepared
according to the method in chapter 2. The trimethylsilyl derivative was
formed by adding 100 tL of BSTFA and allowed to stand overnight at room
temperature. Dilutions were made from this solution so that a 500 pg//xL
solution of each PG was used for injections. The solids probe/MS/MS
studies were performed either by analyzing the standards without
derivatization or as the PFB derivative, using only the PFBBr
esterification step above.


86
(a)
(b)
(c)
(d)
Figure 4
TMSO
CHjO-N
TMSO
TMSO
2: Structures of the methoxime-pentafluorobenzyl-
trimethylsilyl (MO/PFB/TMS) derivatives of the four
prostaglandins:
(a) PGF2a (b) PGE2 (c) PGD2 (d) DHKF2(J


87
Instrumental Conditions
GC was carried out on a short J&W Scientific (Folsom, CA)
DB-1 (3 m long, 0.25 mm i.d., 0.25 /an film thickness) capillary column in
the splitless mode with helium carrier gas at an inlet pressure of 4-6
psi. The initial temperature of 200C was held for 30 s, then increased
at 20C/min to 260C. The injector temperature was 300C. One-microliter
injections of a 500 pg//L solution of each PG were made in triplicate at
each condition for the GC/MS/MS studies.
The solids probe was used as the means for sample introduction to
study the PFB ester derivatives and the free (underivatized) PG standards.
The initial temperature was 50C and increased at 20C/min to 300.
Triplicate samples were analyzed for each derivatization procedure at each
condition for the MS/MS studies. Sample size was one microgram of the
underivatized PGs or 1 ng of the PFB ester derivatives.
A Finnigan MAT TSQ45 gas chromatograph/triple quadrupole mass
spectrometer was employed. Mass spectrometry conditions were: interface
and transfer line temperature 300C, ionizer temperature 190C, electron
energy 100 eV and emission current 0.3 mA. Electron-capture negative
chemical ionization (EC-NCI) was carried out with methane at an ionizer
pressure of 0.45 torr.
In the MS/MS experiments, nitrogen collision gas pressure and
collision energy were varied depending on each experiment. The [MO/TMS-
PFB]", [M-PFB] carboxylate anions were selected in the first quadrupole
(Ql) region and passed into the collision cell (Q2). In this region these
ions underwent CAD to form characteristic fragments which were then mass
analyzed in the third quadrupole (Q3) region. A full daughter spectrum


88
was acquired over the mass range of 55-600 amu. The maximum collision
energy possible on the TSQ 45 is 30 eV.
The peak areas in the daughter spectra of selected daughter ions and
the parent ion remaining after CAD were calculated by the INCOS computer
system for each GC and solids probe sample. A baseline was chosen
visually and the calculated areas were used for determining CAD
efficiencies.
Efficiency Calculations
The abundance of the daughter ions relative to that of the remaining
parent carboxylate anion in the daughter spectrum can be controlled by
varying the CAD energy or pressure; these parameters also affect
sensitivity due to scattering losses. The processes of fragmentation and
scattering can be monitored by evaluating the fragmentation (E ),
r
collection (E ), and overall CAD (E ) efficiencies given by the
\j LAD
following equations (110):
E
F
SDj
P + ED,.
fraction of ions present
following CAD which are
daughter ions
E
P + ED,.
fraction of initial parent
C
ions that is collected
following CAD as either
parent or daughter ions
E
CAD
fraction of initial parent
ion that is converted to
collectable daughter ions


89
where PQ, P, and Dj are the intensities of the parent ion prior to CAD, the
parent ion remaining after CAD, and a daughter ion resulting from CAD,
respectively. Note that n = E x Er.
GAD r G
As was stated earlier in chapter 3, the above efficiencies are
affected by collision energy and collision gas pressure. Either parameter
can be varied to maximize the CAD efficiency for a particular parent ion.
Increasing the collision energy allows for more energetic collisions,
while increasing the collision gas pressure increases the number of
collisions each ion experiences. Either approach increases the amount of
energy deposited into the parent ion, and thereby increases the
fragmentation efficiency. However, an increase in collision energy or
pressure will produce an increase in scattering losses (or possibly other
loss mechanisms such as neutralization by charge exchange) and thereby
decrease collection efficiency. The overall CAD efficiency, as the
product of fragmentation and collection efficiency, will typically first
increase then level off and even decrease as the collision energy or
pressure are increased. Systematic variation of each parameter would
provide a three-dimensional plot of efficiency vs. energy vs. pressure.
Practically, such studies involve two-dimensional slices through this
three-dimensional surface, varying one parameter while keeping the other
constant.
Collision Energy Study of the M0/TMS-PFB1' Carboxvlate Anions
In light of the dramatic differences observed in Chapter 3 of the
CAD efficiencies of the carboxylate anions of the fully derivatized PGF2a
and PGE2 (differing structurally only in the presence of a carbonyl (=0)


90
group at C-9 derivatized to a methoximine, in PGE2, rather than a hydroxyl
(OH) group at the C-9 position, derivatized to a trimethylsilyl group, in
PGF2a) two PGs similar to these were studied. The PGD2 and PGE2 isomers
vary only by the interchange of the hydroxyl (OH) and carbonyl (=0) groups
on C-9 and C-ll. DHKF2a differs from PGF2a by exchange of a carbonyl (=0)
group (derivatized to a methoximine) for the hydroxyl (OH) group
(derivatized to a trimethylsilyl) at C-15.
Figure 4-3 and Figure 4-4 presents curves for fragmentation,
collection and overall CAD efficiencies versus collision energy for the
carboxylate anions of PGE2, PGF2a, PGD2 and DHKF2(J. These curves show the
effects of varying the collision energy at two different collision gas
pressures. In Figures 4-3a, 4-3b and 4-3c, the collision pressure has
been established at 1.2 mTorr N2, a value which is typically optimum for
many MS/MS analyses. The fragmentation efficiency curve (Figure 4-3a)
indicates the dramatic differences in stability of the carboxylate anions
of the four PGs. At a collision energy of 30 eV the fragmentation
efficiencies ranges from a typical 80% down to only 2%. The collision
pressure must be increased to produce more efficient fragmentation. The
collection efficiency (Figure 4-3b) for the four PGs are similar. The
notable exception is PGD2, which has an unusually high collection
efficiency at collision energies of 10-25 eV. This explains the
difference noted between the fragmentation efficiency of PGE2 and PGD2
compared to their overall CAD efficiency.
Figures 4-4a, 4-4b and 4-4c show the overall CAD, collection and
fragmentation efficiencies at a collision gas pressure 2.5 times higher.
The fragmentation efficiency (Figure 4-4a) as well as the overall CAD


100
91
(a)
(b)
(c)
Figure 4-3: CAD efficiency of the [MO/TMS PFB]* carboxylate anions
versus collision energy at 1.2 mTorr N2:
(a) Fragmentation
(b) Collection
(c) Overall CAD


Full Text

PAGE 1

&21&(376 )25 7+( '(7(50,1$7,21 2) 35267$*/$1',16 %< 7$1'(0 0$66 63(&7520(75< %\ 72'' $//(1 *,//(63,( $ ',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

7R P\ ORYLQJ ZLIH 3DXOD

PAGE 3

$&.12:/('*(0(176 ZRXOG OLNH WR H[SUHVV P\ VLQFHUH JUDWLWXGH WR 'U 5LFKDUG $
PAGE 4

,Q DGGLWLRQ WR WKH SHRSOH PHQWLRQHG DERYH ZRXOG OLNH WR WKDQN 6WHYH %URRNV 0DUN %DUQHV DQG -LP 0LFKHOV IRU WKHLU IULHQGVKLS ZRXOG SDUWLFXODUO\ OLNH WR WKDQN P\ SDUHQWV GXULQJ DOO WKH \HDUV RI P\ HGXFDWLRQ ZKHWKHU LQ RU RXW RI WKH FODVVURRP IRU WKHLU HQGOHVV VXSSRUW 0RVW RI DOO WKDQN P\ ZRQGHUIXO FDULQJ ZLIH 3DXOD IRU KHU FRQVWDQW ORYH XQGHUVWDQGLQJ DQG SDWLHQFH WKURXJKRXW P\ \HDUV LQ JUDGXDWH VFKRRO 6KH KDV PDGH WKLV ZRUN DOO SRVVLEOH DQG ZRUWKZKLOH LY

PAGE 5

7$%/( 2) &217(176 3DJH $&.12:/('*(0(176 LLL $%675$&7 YLL &+$37(56 ,1752'8&7,21 $UDFKLGRQLF $FLG 0HWDEROLWHV 3URVWDJODQGLQVf 5HFHQW $QDO\WLFDO $GYDQFHV 6WUDWHJLHV IRU 0L[WXUH $QDO\VLV E\ 0606 2YHUYLHZ RI 7KHVLV 2UJDQL]DWLRQ 6$03/( 35(3$5$7,21 678',(6 ,QWURGXFWLRQ &RQFHSWV IRU 6ROLG3KDVH ([WUDFWLRQ &RQFHSWV IRU 'HULYDWL]DWLRQ ([SHULPHQWDO 5HVXOWV DQG 'LVFXVVLRQ &RQFOXVLRQV 237,0,=$7,21 2) *&06 $1' *&0606 &21',7,216 )25 75$&( '(7(50,1$7,21 2) 35267$*/$1',16 ,QWURGXFWLRQ ([SHULPHQWDO 0DVV 6SHFWURPHWU\ *&06f 7DQGHP 0DVV 6SHFWURPHWU\ *&0606f &RQFOXVLRQV ',))(5(1&(6 ,1 7+( &2//,6,21$//< $&7,9$7(' ',662&,$7,21 2) 6758&785$//< 6,0,/$5 35267$*/$1',16 ,QWURGXFWLRQ ([SHULPHQWDO (IILFLHQF\ &DOFXODWLRQV &ROOLVLRQ (QHUJ\ 6WXG\ RI WKH >027063)%@ &DUER[\ODWH $QLRQV Y

PAGE 6

&+$37(56 3DJH &ROOLVLRQ 3UHVVXUH 6WXG\ RI WKH >027063)%@ &DUER[\ODWH $QLRQV &ROOLVLRQ 3UHVVXUH 6WXG\ RI WKH >03)%@ &DUER[\ODWH $QLRQV &ROOLVLRQ 3UHVVXUH 6WXG\ RI WKH >0+@n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

PAGE 7

$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ &21&(376 )25 7+( '(7(50,1$7,21 2) 35267$*/$1',16 %< 7$1'(0 0$66 63(&7520(75< %\ 7RGG $OOHQ *LOOHVSLH 0D\ &KDLUPDQ 5LFKDUG $
PAGE 8

VWUXFWXUDO FKDQJHV LQ 3*V $ SRVVLEOH H[SODQDWLRQ KDV EHHQ SURSRVHG WR H[SODLQ WKHVH GUDPDWLF GLIIHUHQFHV 7KH DGYDQWDJHV DQG OLPLWDWLRQV RI LPPXQRDIILQLW\ SXULILFDWLRQ ,$f IRU VDPSOH SUHSDUDWLRQ RI 3*V LQ XULQH KDYH EHHQ LQYHVWLJDWHG 5HVXOWV VKRZ WKDW ,$ SXULILFDWLRQ FRXSOHG ZLWK D VKRUW P *& FDSLOODU\ FROXPQ XWLOL]LQJ HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f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f RI 3* DQDO\VLV 7KLV VWXG\ LQGLFDWHV WKDW WKH XWLOL]DWLRQ RI D PRUH VHOHFWLYH VDPSOH SUHSDUDWLRQ PHWKRG HJ ,$f ZLWK 0606 FDQ UHGXFH WKH FKURPDWRJUDSKLF VHSDUDWLRQ WLPH UHTXLUHG WR DFKLHYH WKH QHFHVVDU\ VHOHFWLYLW\ DQG VHQVLWLYLW\ IRU 3* DQDO\VLV LQ XULQH +RZHYHU UHVXOWV VKRZ WKDW 0606 LV QRW QHFHVVDU\ LI ,$ SXULILFDWLRQ DQG D ORQJHU FKURPDWRJUDSKLF VHSDUDWLRQ PRUH VHOHFWLYHf WHFKQLTXH DUH HPSOR\HG 7KLV V\VWHPDWLF VWXG\ VKRXOG EH DSSOLFDEOH LQ WKH HYDOXDWLRQ RI DQ\ DQDO\WLFDO SURFHGXUH IRU DQDO\VLV RI FRPSRQHQWV LQ D ELRORJLFDO VDPSOH ,Q DGGLWLRQ IXWXUH ZRUN LV SURSRVHG ZKLFK VKRXOG IXUWKHU HQKDQFH 3* DQDO\VLV E\ 0606 YLLL

PAGE 9

&+$37(5 ,1752'8&7,21 $UDFKLGRQLF $FLG 0HWDEROLWHV 3URVWDJODQGLQVf 7KH HQ]\PDWLF R[LGDWLRQ RI DUDFKLGRQLF DFLG $$f OHDGV WR D PXOWLWXGH RI ELRFKHPLFDOO\ LPSRUWDQW SURGXFWV f $PRQJ WKHVH VXEVWDQFHV DUH SURVWDJODQGLQV 3*Vf WKURPER[DQHV 7;Vf DQG OHXNRWULHQHV /7Vf &ROOHFWLYHO\ WKHVH FRPSRXQGV DUH UHIHUUHG WR DV HLFRVDQRLGV DQG FRQVWLWXWH ZKDW LV NQRZQ DV WKH DUDFKLGRQLF DFLG FDVFDGH )LJXUH f 0DQ\ RI WKHVH R[\JHQFRQWDLQLQJ PHWDEROLWHV KDYH LQWHUHVWLQJ DQG GLYHUVH SKDUPDFRORJLFDO SURSHUWLHV DQG VLJQLILFDQW PHGLFLQDO SRWHQWLDO f 6LQFH WKH LQLWLDO GHVFULSWLRQ RI 3*V LQ D YDVW ERG\ RI NQRZOHGJH KDV DFFXPXODWHG RQ WKHLU SK\VLRORJ\ DQG FKHPLVWU\ f 5HFHQWO\ DWWHQWLRQ KDV EHHQ IRFXVHG RQ 3*V RI FHUWDLQ VHULHV DV DQWLWXPRU DJHQWV f (YLGHQFH LQGLFDWHV WKDW 3*V VXFK DV SURVWDJODQGLQ ( 3*(f SOD\ DQ LPSRUWDQW UROH DV ORFDO PHGLDWRUV DQG PRGXODWRUV RI UHQDO EORRG IORZ DQG H[FUHWRU\ IXQFWLRQV f ,W KDV EHHQ VXJJHVWHG WKDW PRVW RI WKH SULPDU\ 3*V IRXQG LQ XULQH DUH GHULYHG IURP UHQDO SURGXFWLRQ f FRQn VHTXHQWO\ XULQDU\ OHYHOV RI 3*V KDYH EHHQ DSSOLHG DV DQ LQGH[ RI UHQDO 3* DFWLYLW\ LQ QXPHURXV VWXGLHV 5HFHQWO\ 3*( KDV VHHQ DSSOLFDWLRQ LQ WKH LQGXFWLRQ RI ODERU VRIWHQLQJ RI WKH FHUYL[ DQG SUHYHQWLRQ DQG WUHDWPHQW RI VWUHVV XOFHUV f :KLOH PXFK KDV EHHQ OHDUQHG DERXW 3*V

PAGE 10

‘ m‘ A&&; Y!ZQAY ZWQRI LPPRI 5f+YGURRDUR}\0 OO50n+I2URU\6 DFLG DLFRrDWDWUDDQRLH DFLG / ‘f§AZArA&22+ } 60}rORU _O669O6QULURSmURU\6O r!HRXL0UDmQRm WFR Lrm7(RU L6606K\GURD\6r DFRDDLDUDDQRm DFLG RQ !UAAF2& A 6+77ORU 66f6Q\GURD\G f rD!FRDDLDOUDDmRLF DFLG r.DWR52) RU IWNDIRRURDXJLDQGLQ LW 60 I!\DURRDURUY6m 6+K\GURU\ DDDLDLDDQRF DFmM Z}Pm L 66O6Q\2URRDURL
PAGE 11

ELRORJLFDO HIIHFWV DQG KRZ WKH\ UHODWH WR PDPPDOLDQ KHDOWK GLIILFXOW\ LQ PHDVXULQJ ORZ FRQFHQWUDWLRQV RI 3*V LQ ELRORJLFDO V\VWHPV KDV KLQGHUHG WKH SURJUHVV RI UHVHDUFK 7KH DQDO\VLV RI 3*V DQG RWKHU $$ PHWDEROLWHV FDQ EH GLYLGHG LQWR WKUHH EDVLF VWHSV VDPSOH SUHSDUDWLRQ VDPSOH LQWURGXFWLRQ DQG PHDVXUHPHQW E\ VXFK WHFKQLTXHV DV ELRDVVD\ UDGLRLPPXQRDVVD\ 5,$f KLJKSHUIRUPDQFH OLTXLG FKURPDWRJUDSK\ +3/&f JDV FKURPDWRJUDSK\ *&f DQG JDV FKURPDWRJUDSK\PDVV VSHFWURPHWU\ *&06f ,W KDV EHHQ VKRZQ WKDW ZLWK PDQ\ RI WKH DQDO\WLFDO PHWKRGV IUHTXHQWO\ XVHG 3* FRQFHQWUDWLRQV DUH RIWHQ RYHUHVWLPDWHG E\ DV PXFK DV D IDFWRU RI WHQ f 7KLV SUREOHP FDQ EH WUDFHG WR WKH ODFN RI VHOHFWLYLW\ RI WKH HQWLUH DQDO\WLFDO VFKHPH XVHG IRU DQDO\VLV 7KHUHIRUH WKH GHYHORSPHQW RI DQ DQDO\WLFDO VFKHPH ZKLFK SURYLGHV IRU DFFXUDWH VHQVLWLYH DQG VHOHFWLYH GHWHUPLQDWLRQ RI 3*V LV QHHGHG ,Q WKLV FKDSWHU D EULHI UHYLHZ RI WKH PRVW IUHTXHQWO\ HPSOR\HG WHFKQLTXHV IRU VDPSOH SUHSDUDWLRQ DQG PHDVXUHPHQW RI 3*V ZLOO EH GLVFXVVHG 0RUH WKRURXJK UHYLHZV RI VDPSOH SUHSDUDWLRQ DQG PHDVXUHPHQW WHFKQLTXHV FDQ EH IRXQG LQ WKH OLWHUDWXUH f 5HFHQWO\ D UHYLHZ RQ $$ PHWDEROLVP ZLWK H[DPSOHV RI YDULRXV DQDO\VLV PHWKRGV KDV EHHQ SXEOLVKHG f 2WKHU PRUH VSHFLILF UHYLHZV KDYH EHHQ ZULWWHQ E\ 7UDLWOHU f DQG .HOO\ f RQ PDVV VSHFWURPHWULF DQDO\VLV PHWKRGV RI HLFRVDQRLGV 6DPSOH 3UHSDUDWLRQ 7HFKQLTXHV IRU 3URVWDJODQGLQV 6DPSOH SUHSDUDWLRQ EHIRUH WKH PHDVXUHPHQW VWHS LV H[WUHPHO\ LPSRUWDQW ZLWK WKH H[WHQW RI H[WUDFWLRQ DQG SXULILFDWLRQ GUDPDWLFDOO\ DIIHFWLQJ WKH YDOLGLW\ RI WKH GDWD ,Q VDPSOH SUHSDUDWLRQ RI ELRORJLFDO

PAGE 12

IOXLGV D WUDGLWLRQDO WHFKQLTXH WKDW LV FRPPRQO\ XWLOL]HG LV OLTXLG OLTXLG VROYHQW H[WUDFWLRQ f 7KLV PHWKRG LV WLPHFRQVXPLQJ DQG XVXDOO\ \LHOGV RQO\ b WR b UHFRYHU\ RI PRVW 3*V f 7KH GHJUHH RI FOHDQXS SURYLGHG E\ VXFK H[WUDFWLRQV LV OLPLWHG IXUWKHU SXULILFDWLRQ LV RIWHQ QHFHVVDU\ IRU ERG\ IOXLGV VXFK DV XULQH $QRWKHU SRSXODU PHWKRG IRU VHSDUDWLQJ 3*V IURP ELRORJLFDO PDWUL[ FRPSRQHQWV LV VROLGSKDVH H[WUDFWLRQ 7KUHH W\SHV RI VROLGSKDVH H[WUDFWLRQ DUH FRPPRQO\ HPSOR\HG f DPEHUOLWH ;$'f FROXPQ f RFWDGHF\OVLO\O 2'6f FROXPQ &f DQG f VHOHFWLYH SDFNLQJ PDWHULDOV VXFK DV LPPXQRDQWLERGLHV %UDGORZ f GHVFULEHG WKH XVH RI DQ ;$' FROXPQ WKDW LV DGYDQWDJHRXV ZKHQ WKH ELRORJLFDO PDWUL[ FRQWDLQV D ODUJH FRQFHQWUDWLRQ RI SURWHLQV 5HFRYHULHV XVLQJ WKLV PHWKRG KDYH EHHQ UHSRUWHG DV DERXW b %RWK VROYHQW H[WUDFWLRQ DQG ;$' UHVLQ H[WUDFWLRQ SURFHGXUHV DUH WLPHFRQVXPLQJ DQG UHTXLUH HYDSRUDWLRQ RI UHODWLYHO\ ODUJH YROXPHV RI RUJDQLF VROYHQWV 0RUHRYHU WKH\ DUH QRW YHU\ VHOHFWLYH DQG JLYH H[WUDFWLRQV FRQWDLQLQJ H[WUDQHRXV PDWHULDO WKDW PXVW EH UHPRYHG VXEVHTXHQWO\ E\ YDULRXV FKURPDWRJUDSKLF SXULILFDWLRQV $ YDULHW\ RI PHWKRGV XVLQJ D & FROXPQ WR H[WUDFW 3*V IURP ELRORJLFDO VDPSOHV KDYH EHHQ GHYHORSHG E\ 3RZHOO f DQG RWKHU UHVHDUFKHUV f 7KH VROLG SKDVH H[WUDFWLRQ XVLQJ D & FROXPQ LV UDSLG HIILFLHQW DQG PRUH VHOHFWLYH WKDQ VROYHQW DQG ;$' H[WUDFWLRQV 5HFRYHU\ ZLWK WKLV PHWKRG KDV EHHQ UHSRUWHG WR EH JUHDWHU WKDQ b LQ PDQ\ FDVHV 6SHFLDOL]HG SDFNLQJ PDWHULDOV FDQ SURYLGH VLJQLILFDQWO\ PRUH VHOHFWLYH H[WUDFWLRQ RI VSHFLILF WDUJHWHG 3*V $ SKHQ\OERURQLF DFLG FROXPQ KDV EHHQ XVHG WR VHOHFWLYHO\ LVRODWH WKURPER[DQH % 7;%f DQG LWV PHWDEROLWHV f 7KH UHFRYHU\ RI UDGLRODEHOHG 7;% DIWHU H[WUDFWLRQ ZDV

PAGE 13

UHSRUWHG DW b 3RWHQWLDOO\ DQ HYHQ PRUH VHOHFWLYH DSSURDFK WR VDPSOH SUHSDUDWLRQ LV WR FRPELQH WKH H[WUDFWLRQ DQG SXULILFDWLRQ VWHSV LQWR RQH SURFHGXUH 7KLV KDV EHHQ DFFRPSOLVKHG E\ XVLQJ DQ DQWLERG\PHGLDWHG H[WUDFWLRQ SURFHGXUH GHYHORSHG E\ .UDXVH HW DO f %DVLFDOO\ WKH SURVWDJODQGLQDQWLERG\ ZDV FRXSOHG WR F\DQRJHQ EURPLGHDFWLYDWHG 6HSKDURVH % DQG XVHG DV D VWDWLRQDU\ SKDVH IRU WKH H[WUDFWLRQ RI 3* IURP WKH VDPSOHV 7KH DQWLERG\ ZDV FRXSOHG WR 6HSKDURVH DQG SDFNHG LQWR D 3DVWHXU SLSHWWH 7KH SODVPD VDPSOHV ZHUH WKHQ DSSOLHG WR WKH JHO LQ WKH FROXPQ 7KLV RQHVWHS H[WUDFWLRQSXULILFDWLRQ PHWKRG KDV VKRZQ LPSURYHG VSHFLILFLW\ DQG VHQVLWLYLW\ 6LPLODU PHWKRGV KDYH DOVR EHHQ HPSOR\HG E\ +XEEDUG f DQG 9UEDQDF f IRU WKH DQDO\VLV RI 7;% DQG NHWR3*)D LQ XULQH $QRWKHU DSSURDFK WR H[SORLW WKH KLJK VHOHFWLYLW\ RI DQWLERG\ DQWLJHQ UHDFWLRQV IRU VDPSOH H[WUDFWLRQ LV GRXEOHDQWLERG\ SUHFLSLWDWLRQ 7KLV WHFKQLTXH KDV EHHQ XVHG IRU SUHSDUDWLRQ RI SODVPD VDPSOHV EHIRUH +3/& DQDO\VLV IRU 5f PHWK\O3*( f ,Q VXPPDU\ WKH DGYDQWDJHV RI H[WUDFWLRQ HLWKHU VROYHQW RU VROLG SKDVHf DUH f LW HOLPLQDWHV VRPH H[WUDQHRXV PDWHULDO WKHUHE\ LPSDUWLQJ JUHDWHU VSHFLILFLW\ WR WKH DVVD\ DQG f LW LPSURYHV VHQVLWLYLW\ RI WKH DQDO\VLV E\ FRQFHQWUDWLQJ WKH PDWHULDO 7KH GLVDGYDQWDJHV DUH f LW LV WLPHFRQVXPLQJ f D FDUU\RYHU RI QRQHOXWHG DQDO\WH PD\ RFFXU LI WKH VDPH FROXPQ LV UHXVHGf HIIHFWLQJ WKH YDOLGLW\ RI VXEVHTXHQW DVVD\V DQG f WKH H[WUDFWLRQ HIILFLHQF\ RI WKH SURFHGXUH LV YDULDEOH 6LPSOH VROYHQW RU VROLGSKDVH H[WUDFWLRQ KDV EHHQ VKRZQ WR \LHOG VDPSOHV WKDW GR QRW SHUPLW DFFXUDWH YDOLGLW\ RI 3* TXDQWLWDWLRQ ,PSURYHG YDOLGLW\ RI VXEVHTXHQW TXDQWLWDWLRQ KDV EHHQ REVHUYHG DIWHU IXUWKHU SXULILFDWLRQ

PAGE 14

VWHSV $ PRUH GHWDLOHG H[SODQDWLRQ RI VROLGSKDVH H[WUDFWLRQ DQG LPPXQRDIILQLW\ ,$f SXULILFDWLRQ FDQ EH IRXQG LQ &KDSWHU 7KUHH W\SHV RI FKURPDWRJUDSKLF SXULILFDWLRQ DUH GHVFULEHG EHORZ f VLOLFD DFLG FROXPQ FKURPDWRJUDSK\ f WKLQOD\HU FKURPDWRJUDSK\ 7/&f DQG f +3/& *URXS VHSDUDWLRQ RI 3*V DQG UHODWHG FRPSRXQGV LV FRQYHQLHQWO\ SHUIRUPHG E\ VLOLFD DFLG FROXPQ FKURPDWRJUDSK\ f 5HFRYHULHV ZHUH UHSRUWHG IRU WKLV SXULILFDWLRQ PHWKRG RI b WR b 3*V VHSDUDWHG E\ VLOLFD DFLG FKURPDWRJUDSK\ XVXDOO\ UHTXLUH IXUWKHU SXULILFDWLRQ E\ 7/& RU +3/& SULRU WR TXDQWLWDWLRQ E\ 5,$ RU *&06 6HSDUDWLRQ RI 3*V E\ 7/& ZDV ILUVW LQYHVWLJDWHG E\ *UHHQ DQG 6DPXHOVVRQ f 7/& LV WKH PRVW FRPPRQO\ XVHG PHWKRG IRU VHSDUDWLRQ RI 3*V EHFDXVH RI LWV HIILFLHQF\ VLPSOLFLW\ DQG HFRQRP\ FRPSDUHG WR RWKHU FKURPDWRJUDSKLF SURFHGXUHV 7KH PDMRU JURXSV RI 3*V $ % ( ) DQG NHWR3*)Df ZHUH UHDGLO\ VHSDUDWHG RQ D VLOLFD JHO SODWH XVLQJ YDULRXV VROYHQW PL[WXUHV f 7KH GLVDGYDQWDJHV RI 7/& DUH LWV ORZ UHFRYHU\ \LHOGV W\SLFDOO\ bf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f 7KH FRQYHQWLRQDO WHFKQLTXHV RI FROXPQ FKURPDWRJUDSK\ DQG 7/& XVXDOO\ VXIIHU IURP SRRU FKURPDWRJUDSKLF UHVROXWLRQ DQG WKH QHHG WR XVH VHYHUDO VROYHQW V\VWHPV WR DGHTXDWHO\ VHSDUDWH DUDFKLGRQDWH PHWDEROLWHV +3/& KDV

PAGE 15

EHHQ XVHG VXFFHVVIXOO\ IRU WKH VHSDUDWLRQ DQG SXULILFDWLRQ RI 3*V IURP ELRORJLFDO VRXUFHV VLQFH f 7KLV WHFKQLTXH RIIHUV VHYHUDO DGYDQWDJHV f WKHUH LV KLJK UHVROXWLRQ RI FORVHO\ UHODWHG FRPSRXQGV f JRRG UHSURGXFLELOLW\ LV SRVVLEOH DQG f IUDFWLRQV FRQWDLQLQJ 3* SHDNV FDQ EH DXWRPDWLFDOO\ FROOHFWHG DQG ODWHU TXDQWLWDWHG E\ 5,$ *&06 RU VFLQWLOODWLRQ FRXQWLQJ RI UDGLRODEHOHG PHWDEROLWHV %RWK QRUPDOSKDVH +3/& RQ VLOLFD DFLG f DQG UHYHUVHSKDVH +3/& RQ RFWDGHF\OVLO\O VLOLFD f KDYH EHHQ XVHG WR VHSDUDWH WKH F\FORR[\JHQDVH SURGXFWV RI DUDFKLGRQLF DFLG +RZHYHU +3/& FDQ EH DQ H[WUHPHO\ OHQJWK\ WHFKQLTXH IRU SXULILFDWLRQ DQG FDQ \LHOG ORZ UHFRYHULHV RQ WKH RUGHU RI b 7HFKQLTXHV IRU 'HWHUPLQDWLRQ DQG 0HDVXUHPHQW RI 3URVWDJODQGLQV $ QXPEHU RI DQDO\WLFDO PHWKRGV KDYH EHHQ GHYHORSHG IRU WKH GHWHFWLRQ DQG PHDVXUHPHQW RI 3*V WR VWXG\ WKHLU SK\VLRORJLFDO DQG SKDUPDFRORJLFDO HIIHFWV $PRQJ WKRVH ELRDVVD\ 5,$ +3/& DQG *&06 DUH PRVW ZLGHO\ XVHG IRU WKH TXDQWLWDWLRQ RI 3*V LQ ELRORJLFDO IOXLGV %LRDVVDY %LRORJLFDO WHFKQLTXHV DQG ELRDVVD\ KDYH FRQWULEXWHG JUHDWO\ WR WKH GHYHORSPHQW RI WHFKQLTXHV IRU GHWHFWLQJ DQG TXDQWLWDWLQJ $$ PHWDEROLWHV f ,Q JHQHUDO ELRDVVD\ KDV EHHQ KLJKO\ EHQHILFLDO LQ HVWDEOLVKLQJ WKH ELRORJLFDO VLJQLILFDQFH RI WKH XQVWDEOH SURGXFWV RI $$ PHWDEROLVP +RZHYHU LW SURYLGHV RQO\ DSSUR[LPDWH TXDQWLWDWLRQ DQG UHODWLYHO\ ORZ VHOHFWLYLW\ 5DGLRLPPXQRDVVD\ 5,$f 5,$ RI 3*V ZDV LQWURGXFHG LQ E\ /HYLQH DQG 9DQ 9XQDNLV f ZLWK DVVD\V GHYHORSHG IRU 3*( DQG 3*)D 7KH OLWHUDWXUH KDV EHHQ H[SDQGLQJ UDSLGO\ DQG D ODUJH QXPEHU RI 5,$V IRU 3*V 7;V DQG /7V KDYH EHHQ UHSRUWHG 5,$ LV EDVHG RQ WKH FRPSHWLWLRQ EHWZHHQ

PAGE 16

UDGLRODEHOHG DQG XQODEHOHG PROHFXOHV RI D SDUWLFXODU FRPSRXQG IRU ELQGLQJ VLWHV RQ DQ DQWLERG\ GLUHFWHG DJDLQVW WKH VDPH FRPSRXQG 7KH DPRXQW RI ODEHOHG FRPSRXQG LV NQRZQ DQG FRQVWDQW IRU DOO WKH WXEHV LQ DQ DVVD\ ZKHUHDV WKH DPRXQW RI XQODEHOHG VXEVWDQFH LV HLWKHU NQRZQ DQG YDULHG VWDQGDUG WXEHVf RU XQNQRZQ VDPSOH WXEHVf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f XVXDOO\ QHHG WR EH SXULILHG WKURXJK H[WUDFWLRQ FROXPQ FKURPDWRJUDSK\ 7/& RU HYHQ +3/& EHIRUH DQDO\VLV E\ 5,$ $SSURSULDWH SXULILFDWLRQ VWHSV DUH WLPH

PAGE 17

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f KDYH IRXQG WKDW WKH KLJKHVW PRODU H[WLQFWLRQ FRHIILFLHQW RFFXUV DURXQG QP IRU PDMRU 3*V \LHOGLQJ GHWHFWLRQ OLPLWV LQ WKH QDQRJUDP UDQJH 5HFHQWO\ D PRUH VHQVLWLYH PHWKRG XVLQJ +3/& ZLWK D SRVWFROXPQ GHULYDWL]DWLRQ DQG IOXRUHVFHQFH GHWHFWLRQ KDV EHHQ GHYHORSHG IRU HLFRVDQRLG TXDQWLWDWLRQ :DWNLQV DQG 3HWHUVRQ f GHYHORSHG D PHWKRG WR PHDVXUH $$ PHWDEROLWHV E\ UHYHUVHSKDVH +3/& IROORZHG E\ IRUPDWLRQ RI WKH HVWHU GHULYDWLYH ZLWK 3 DQWKUR\OR[\f SKHQDF\O EURPLGH 7KH GLVDGYDQWDJHV RI +3/& DUH WKDW WKLV WHFKQLTXH FDQ EH OHQJWK\ DQG D UHODWLYHO\ ODUJH YROXPH RI VDPSOH LV UHTXLUHG IRU DGHTXDWH GHWHFWLRQ RI ORZ OHYHOV RI 3*V LQ ELRORJLFDO IOXLGV *DV FKURPDWRJUDSK\PDVV VSHFWURPHWU\ *&06f *&06 LV WKH DQDO\WLFDO PHWKRG RI FKRLFH IRU WKH LGHQWLILFDWLRQ FKDUDFWHUL]DWLRQ DQG TXDQWLWDWLRQ RI WKH SURGXFWV RI WKH DUDFKLGRQLF DFLG FDVFDGH 2IIHULQJ ERWK KLJK VHQVLWLYLW\ DQG VHOHFWLYLW\ *&06 KDV EHFRPH WKH JROG VWDQGDUG IRU WKH DQDO\VLV RI 3*V 7UDGLWLRQDOO\ *&06 ZDV XVHG IRU VWULFWO\ TXDOLWDWLYH DQDO\VLV ZLWK VWXGLHV GRQH RQ WKH GHWHUPLQDWLRQ RI WKH VWUXFWXUHV RI VHYHUDO SURVWDJODQGLQV f ,GHQWLILFDWLRQ DQG

PAGE 18

FKDUDFWHUL]DWLRQ RI PDQ\ SURVWDJODQGLQV DQG WKHLU PHWDEROLWHV ZHUH SHUIRUPHG E\ HOHFWURQ LRQL]DWLRQPDVV VSHFWURPHWU\ WKURXJK WKH HDUO\ WR PLGnV ,Q UHSRUWV RQ HLFRVDQRLGV ILUVW DSSHDUHG ZLWK OLPLWV RI GHWHFWLRQ LQ WKH ORZ QJP/ UDQJH f 7KH XVH RI VHOHFWHGLRQ PRQLWRULQJ 6,0f ZLWK SRVLWLYH FKHPLFDO LRQL]DWLRQ 3&,f DQG HOHFWURQ FDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f IRU TXDQWLWDWLRQ VLJQLILFDQWO\ LPSURYHG WKH GHWHFWLRQ OLPLWV DFKLHYHG E\ *&06 7KH GLVFXVVLRQ WKDW IROORZV ZLOO IRFXV RQ FRPSRQHQWV RI WKH DQDO\WLFDO WHFKQLTXH RI *&06 IRU WKH DQDO\VLV RI 3*V ,Q D W\SLFDO TXDOLWDWLYH RU TXDQWLWDWLYH DQDO\VLV IRU 3*V E\ *&06 WKH IROORZLQJ VWHSV DUH SHUIRUPHG f VDPSOH SUHSDUDWLRQ H[WUDFWLRQ DQG SXULILFDWLRQf f GHULYDWL]DWLRQ f JDV FKURPDWRJUDSKLF VHSDUDWLRQ f LRQL]DWLRQ DQG f PDVV VSHFWURPHWULF GHWHFWLRQ ,Q WKH IROORZLQJ SDJHV WKHVH DQDO\WLFDO VWHSV ZLOO EH GLVFXVVHG LQ UHYHUVH RUGHU KLJKOLJKWLQJ WKH PDVV VSHFWURPHWULF FRPSRQHQW RI WKH DQDO\VLV UDWKHU WKDQ VDPSOH SUHSDUDWLRQ ZKLFK ZDV GLVFXVVHG LQ GHWDLO HDUOLHU ,Q PDVV VSHFWURPHWULF DQDO\VLV WKH TXDQWLWDWLRQ RI WUDFH OHYHOV RI 3*V LV FRPPRQO\ SHUIRUPHG E\ XWLOL]LQJ DQ LVRWRSHODEHOHG DQDORJ RI WKH FRPSRXQG RI LQWHUHVW ZLWK VHOHFWLYH PRQLWRULQJ RI WKH LRQV RI HDFK 6LQFH LWV LQWURGXFWLRQ LQ VWDEOH LVRWRSH GLOXWLRQ f KDV EHHQ WKH PHWKRG RI FKRLFH IRU TXDQWLWDWLRQ 0DQ\ XVHV RI VWDEOH LVRWRSH ODEHOLQJ ZLWK 6,0 FDQ EH IRXQG LQ WKH SURVWDJODQGLQ OLWHUDWXUH f %RWK KLJK UHVROXWLRQ PDVV VSHFWURPHWU\ DQG ORZ UHVROXWLRQ PDVV VSHFWURPHWU\ KDYH EHHQ HPSOR\HG IRU DQDO\VLV RI 3*V +LJK UHVROXWLRQ FDQ UHYHDO WKH HOHPHQWDO FRPSRVLWLRQ RI LRQV ZKLFK LV KHOSIXO LQ LGHQWLI\LQJ QHZ FRPSRXQGV /RZ UHVROXWLRQ LV XVHG IRU WUDFH DQDO\VLV GHVSLWH LWV ORZHU

PAGE 19

VHOHFWLYLW\ ([DPSOHV RI ERWK WHFKQLTXHV FDQ EH IRXQG LQ WKH OLWHUDWXUH f $ JUHDW GHDO RI UHVHDUFK KDV EHHQ GHYRWHG WR WUDFH DQDO\VLV RI HLFRVDQRLGV DQG WKHLU PHWDEROLWHV LQ DOO W\SHV RI ELRORJLFDO IOXLGV ZLWK PRVW GHWHUPLQDWLRQV GRQH LQ SODVPD DQG XULQH f 7KH DPRXQWV WKDW KDYH EHHQ DQDO\]HG DUH IURP WKH ORZ QJ WR ORZ SJP/ UDQJH ZLWK OLPLWV RI GHWHFWLRQ DV ORZ DV IJ UHSRUWHG LQ RQH VWXG\ f 7KUHH W\SHV RI LRQL]DWLRQ DUH XVHG WRGD\ IRU PRVW 3*V DQDO\VHV HOHFWURQ LRQL]DWLRQ (Of SRVLWLYH FKHPLFDO LRQL]DWLRQ 3&,f DQG HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f (,06 DV GLVFXVVHG HDUOLHU LV PRVW RIWHQ XVHG IRU VWUXFWXUDO HOXFLGDWLRQ DQG LGHQWLILFDWLRQ RI QHZ FRPSRXQGV (O PDVV VSHFWUD JLYH VWUXFWXUDOO\ XVHIXO IUDJPHQWDWLRQ SDWWHUQV DOWKRXJK WKH PROHFXODU LRQ PD\ EH ZHDN RU HYHQ DEVHQW )RU WUDFH DQDO\VLV W\SLFDO OLPLWV RI GHWHFWLRQ ZLWK (O DUH DSSUR[LPDWHO\ SJP/ f 3&, DQG (&1&, DUH JHQWOHU LRQL]DWLRQ WHFKQLTXHV JHQHUDOO\ SURGXFLQJ OHVV IUDJPHQWDWLRQ ZLWK D PRUH SURPLQHQW SVHXGRf PROHFXODU LRQ 7KXV WKHVH WHFKQLTXHV DUH XVHIXO IRU FRQILUPLQJ PROHFXODU ZHLJKW DQG IRU WUDFH DQDO\VLV E\ VHOHFWHGLRQ PRQLWRULQJ 3&, KDV EHHQ VKRZQ WR EH KHOSIXO LQ FKDUDFWHUL]DWLRQ RI WKURPER[DQHV DQG SURVWDJODQGLQV f /LPLWV RI GHWHFWLRQ YDU\ IRU 3&, DQG (&1&, GHSHQGLQJ RQ ERWK WKH FRPSRXQG DQG WKH UHDJHQW JDV VHOHFWHG 0DQ\ W\SHV RI FKHPLFDO LRQL]DWLRQ UHDJHQW JDVHV KDYH EHHQ XVHG EXW PHWKDQH DQG LVREXWDQH DUH WKH PRVW FRPPRQ 0RVW WUDFH DQDO\VLV VWXGLHV DUH QRZ SHUIRUPHG ZLWK (&1&, ZLWK PHWKDQH DV WKH UHDJHQW JDV 'HWHFWLRQ OLPLWV DUH JHQHUDOO\ LQ WKH ORZ SJP/ UDQJH DOWKRXJK OLPLWV DV ORZ DV IJP/ KDYH EHHQ UHSRUWHG f 7KH WKUHH LRQL]DWLRQ WHFKQLTXHV KDYH EHHQ

PAGE 20

FRPSDUHG IRU WUDFH DQDO\VLV RI 3*V LQFOXGLQJ OLPLWV RI GHWHFWLRQ DQG VSHFWUD REWDLQHG ZLWK HDFK LRQL]DWLRQ WHFKQLTXH f *DV FKURPDWRJUDSK\ LV JHQHUDOO\ XVHG WR VHSDUDWH WKH HLFRVDQRLGV IURP HDFK RWKHU DQG IURP RWKHU SRWHQWLDO LQWHUIHUHQWV SULRU WR WKHLU LGHQWLILFDWLRQ RU GHWHFWLRQ E\ PDVV VSHFWURPHWU\ 7KH ILUVW *&06 DQDO\VHV ZHUH DFFRPSOLVKHG ZLWK SDFNHG JDV FKURPDWRJUDSK\ FROXPQV ZKLFK ZHUH XVHG H[WHQVLYHO\ XQWLO WKH GHYHORSPHQW RI IXVHG VLOLFD FDSLOODU\ FKURPDWRJUDSKLF FROXPQV 8QWLO DSSUR[LPDWHO\ HTXDO XVH ZDV PDGH RI SDFNHG DQG FDSLOODU\ FROXPQ WHFKQLTXHV EXW FDSLOODU\ FKURPDWRJUDSK\ KDV OHG WR EHWWHU VHSDUDWLRQ RI FORVHO\ UHODWHG FRPSRXQGV &RXSOHG ZLWK QHJDWLYH FKHPLFDO LRQL]DWLRQ LW KDV DOORZHG UHVHDUFKHUV WR DFKLHYH OLPLWV RI GHWHFWLRQ LQ WKH ORZ SJP/ UDQJH 7KHVH DGYDQWDJHV KDYH SURYLGHG KLJKHU VHQVLWLYLW\ DQG VHOHFWLYLW\ LQ HLFRVDQRLGV DQDO\VLV +RZHYHU SDFNHG FROXPQ FKURPDWRJUDSK\ VWLOO KDV D UROH LQ SURVWDJODQGLQ DQDO\VLV 2QH UHFHQW VWXG\ f VKRZHG WKH DGYDQWDJHV RI SDFNHG FROXPQV IRU KLJKO\ FRQWDPLQDWHG VDPSOHV WKDW H[FHHGHG WKH FDSDFLW\ RI FDSLOODU\ FROXPQV 5HVHDUFKHUV KDYH UHFHQWO\ UHFRJQL]HG WKH YDOXH RI LQWURGXFLQJ WKH FDSLOODU\ FROXPQ GLUHFWO\ LQWR WKH LRQ VRXUFH RI WKH PDVV VSHFWURPHWU\ f 7KLV DYRLGV SUREOHPV ZLWK FRQWDPLQDWLRQ DGVRUSWLRQ DQG GHFRPSRVLWLRQ RI DQDO\WHV ZKLFK FDQ EH VHYHUH ZLWK 3*Vf RQ DFWLYH VXUIDFHV LQ RWKHU *&06 LQWHUIDFHV 'HULYDWL]DWLRQ RI 3*V KDV EHHQ LPSRUWDQW LQ WKHLU DQDO\VLV ERWK WR LQFUHDVH WKHLU YRODWLOLW\ IRU JDV FKURPDWRJUDSK\ VHSDUDWLRQ DQG WR SURYLGH IRU HIILFLHQW (&1&, WR LQFUHDVH VHQVLWLYLW\ RI WKH *&06 PHWKRG 7RGD\ WKH PHWK\OHVWHUPHWKR[LPHWULPHWK\OVLO\O HWKHU RI 3*V LV WKH PRVW IUHTXHQWO\ FLWHG GHULYDWLYH LQ *&(,06 DQDO\VLV f +RZHYHU LW KDV

PAGE 21

EHHQ VKRZQ WKDW WKHVH GHULYDWLYHV DUH VXVFHSWLEOH WR K\GURO\VLV RIWHQ SURGXFLQJ LRQV WKDW DUH QRW RSWLPDO IRU VHOHFWLYHLRQ PRQLWRULQJ f 7KLV LV GXH WR WKH ORZ UHODWLYH LQWHQVLW\ RI WKH KLJK PDVV LRQV ZKLFK DUH RSWLPDO IRU TXDQWLWDWLRQ 7KH GHULYDWL]DWLRQ RI 3*V IRU *&(&1&,06 VHHPV WR EH VWDQGDUGL]LQJ RQ WKH PHWKR[LPHWULPHWK\OVLO\O HWKHUSHQWDIOXRUREHQ]\O HVWHU 027063)%f PL[HG GHULYDWLYH f 'HULYDWL]DWLRQ ZLWK SHUIOXRULQDWHG DFLG DQK\GULGHV KDV EHHQ LQFUHDVLQJO\ XVHG IRU ERWK TXDOLWDWLYH DQG TXDQWLWDWLYH ZRUN f 7KHVH DQK\GULGHV XVXDOO\ LQFRUSRUDWH D VLO\ODWLQJ UHDJHQW VXFK DV 1WHWUDEXW\OGLPHWK\OVLO\Of1PHWK\OWULIOXRURDFHWDPLGHf 7KLV JLYHV K\GURO\WLF VWDELOLW\ DQG LQFUHDVHV KLJK PDVV LRQ LQWHQVLW\ IRU RSWLPDO XVH RI VHOHFWLYHLRQ PRQLWRULQJ 7KH XVH RI VXFK GHULYDWLYHV DOVR HOLPLQDWHV GHWHFWLRQ RI PDQ\ QRQSURVWDJODQGLQ FDUER[\OLF DFLGV GXH WR WKHLU DELOLW\ WR GHULYDWL]H ZLWK WKH FDUERQ\O UDWKHU WKDQ RU LQ DGGLWLRQ WR WKH FDUER[\O JURXS 7KLV PDNHV WKHVH GHULYDWLYHV KLJKO\ DWWUDFWLYH IRU GHWHFWLQJ WUDFH TXDQWLWLHV RI SURVWDJODQGLQV LQ ELRORJLFDO PDWULFHV f 5HFHQW $QDO\WLFDO $GYDQFHV *&06 UHPDLQV WKH ZRUNKRUVH WHFKQLTXH RI 3* UHVHDUFK KRZHYHU WDQGHP PDVV VSHFWURPHWU\ 0606f DQG VRIW LRQL]DWLRQ WHFKQLTXHV VXFK DV IDVW DWRP ERPEDUGPHQW )$%f RU OLTXLG VHFRQGDU\ LRQ PDVV VSHFWURPHWU\ /6,06f DQG OLTXLG FKURPDWRJUDSK\PDVV VSHFWURPHWU\ /&06f DUH EHLQJ HIIHFWLYHO\ HPSOR\HG 7KH VHQVLWLYLW\ DQG VHOHFWLYLW\ RI *&0606 FRPSDUHG WR *&06 KDV EHHQ VWXGLHG LQ UHSRUWV f XWLOL]LQJ ERWK (O DQG (&1&, 7KH DGYDQWDJHV RI *&0606 KDYH UHFHQWO\ EHHQ H[SORLWHG IRU

PAGE 22

WKH WUDFH DQDO\VLV RI 3*V LQ ELRORJLFDO VDPSOHV f 7KHVH VWXGLHV KDYH EHHQ SHUIRUPHG RQ ERWK VHFWRU DQG TXDGUXSROH LQVWUXPHQWV 7KH KLJK VHOHFWLYLW\ RI 0606 PDNHV LW SRVVLEOH WR SHUIRUP DQDO\VHV ZLWK PLQLPDO VDPSOH SUHSDUDWLRQ 0606 DOVR PLQLPL]HV RU HOLPLQDWHV WKH QHHG IRU FKURPDWRJUDSKLF VHSDUDWLRQ LQ PDQ\ FDVHV PDNLQJ WKH DQDO\VLV H[WUHPHO\ UDSLG 0606 H[SHULPHQWV KDYH UHFHQWO\ EHHQ UHSRUWHG LQ WKH OLWHUDWXUH IRU DQDO\VLV RI XQGHULYDWL]HG SURVWDJODQGLQV f ,Q DGGLWLRQ ZLWK LPSURYHG LQVWUXPHQWDWLRQ KDV FRPH WKH WHFKQLTXH RI )$% RU /6,06 f 7KLV PHWKRG KDV DLGHG VWUXFWXUDO HOXFLGDWLRQ DV ZHOO DV FKDUDFWHUL]DWLRQ RI PDQ\ 3*V /&06 KDV EHFRPH LQFUHDVLQJO\ SRSXODU LQ WKH DQDO\VLV RI 3*V f DV LQ DOO DUHDV RI FKHPLVWU\ /&06 KDV WKH DELOLW\ WR DQDO\]H SRODU WKHUPDOO\ ODELOH DQG KLJK PROHFXODU ZHLJKW HLFRQVDQRLGV DQG LW VDYHV WLPH LQ VDPSOH SUHSDUDWLRQ /&06 ZLWK WKHUPRVSUD\ LRQL]DWLRQ 763/&06f KDV EHHQ XVHG E\ VHYHUDO UHVHDUFKHUV WR GHWHFW 3*V DQG 7;% DW OLPLWV RI GHWHFWLRQ DV ORZ DV SJ RQ FROXPQf DIWHU GHULYDWL]DWLRQ ZLWK GLHWK\ODPLQRfHWK\O FKORULGH f $ VHULHV RI 3* VWDQGDUGV ZHUH DQDO\]HG DQG LQYHVWLJDWHG WR VKRZ WKH LQFUHDVH LQ VHQVLWLYLW\ UHVXOWLQJ IURP D SRVWFROXPQ GHULYDWL]DWLRQ ZKLFK IRUPHG WKH PHWK\O HVWHU f 7KH VHQVLWLYLW\ LV VWLOO QRW HTXDO WR WKH *&06 PHWKRGV FRPPRQO\ HPSOR\HG 7KLV LV WKH OLPLWLQJ IDFWRU RI /&06 IRU WKH DQDO\VLV RI 3*V KRZHYHU WKHUH LV UHDVRQ WR EHOLHYH WKDW WKH QHFHVVDU\ LPSURYHPHQWV LQ VHQVLWLYLW\ FDQ HYHQWXDOO\ EH REWDLQHG /&06 LV D JRRG TXDOLWDWLYH WHFKQLTXH ZKLFK LV VWLOO LQ LWV LQIDQF\ 7KH DGYDQWDJHV WR EH JDLQHG LQ VLPSOLILHG VDPSOH SUHSDUDWLRQ DQG WKH DELOLW\ WR GLUHFWO\ DQDO\]H WKH PRUH SRODU HLFRQVDQRLGV ZLOO VWLPXODWH IXUWKHU LPSURYHPHQWV

PAGE 23

$QRWKHU UHFHQW 0606 WHFKQLTXH ZKLFK LV SURPLVLQJ LV LRQ WUDS ,7f0606 7KH ,706 RIIHUV WKH SRWHQWLDO IRU YHU\ VHOHFWLYH DQG VHQVLWLYH *&0606 DQDO\VLV ,Q WKH LRQ WUDS LRQ IRUPDWLRQ DQG PDVV DQDO\VLV RFFXU LQ WKH VDPH UHJLRQ WDQGHPLQWLPHf ZKHUHDV LQ WDQGHP PDVV VSHFWURPHWU\ WKHVH WZR SURFHVVHV RFFXU LQ GLIIHUHQW UHJLRQV WDQGHPLQVSDFHf 7KH DQDO\VLV RI 3*V E\ WKLV PHWKRG KDV EHHQ UHSRUWHG E\ 6WULIH f 7KLV ZRUN VKRZV WKH XQLTXH DGYDQWDJHV RI KLJK VHQVLWLYLW\ 0606ZLWK QHDUO\ b FRQYHUVLRQ HIILFLHQFLHV RI SDUHQW WR GDXJKWHU LRQ LQ 0606 H[SHULn PHQWV 7KLV VHFWLRQ RI &KDSWHU KDV VKRZQ WKDW PXFK SURJUHVV KDV EHHQ PDGH LQ WKH DUHD RI 3* VDPSOH SUHSDUDWLRQ DQG TXDQWLWDWLRQ 0DQ\ OLPLWDWLRQV UHPDLQ HVSHFLDOO\ ZKHQ WKH VDPSOH VL]H LV OLPLWHG ,Q WKH FKDSWHUV WR IROORZ VRPH RI WKHVH OLPLWDWLRQV ZLOO EH DGGUHVVHG DQG QHZ DQDO\WLFDO VFKHPHV ZLOO EH HYDOXDWHG 6WUDWHHLHV IRU 0L[WXUH $QDO\VLV E\ 0606 6LQFH WKH GHYHORSPHQW RI WDQGHP PDVV VSHFWURPHWU\ 0606f LQ WKH nV LW KDV UHFHQWO\ JDLQHG UDSLG DFFHSWDQFH DV DQ H[FHSWLRQDO DQDO\WLFDO WRRO IRU PL[WXUH DQDO\VLV f 0606 KDV WKH DELOLW\ WR SURYLGH UDSLG VHQVLWLYH DQG VHOHFWLYH DQDO\VLV RI FRPSOH[ ELRORJLFDO VDPSOHV RIWHQ ZLWK PLQLPDO VDPSOH FOHDQXS f 7KH 0606 VFDQ PRGHV XWLOL]HG LQ WKHVH VWXGLHV DUH GHSLFWHG LQ )LJXUH ,Q PL[WXUH DQDO\VLV FKHPLFDO LRQL]DWLRQ RI D PL[WXUH LV RIWHQ XWLOL]HG LQ WKH LRQ VRXUFH RI WKH PDVV VSHFWURPHWHU WR SURGXFH LRQV FKDUDFWHULVWLF RI WKH FRPSRQHQWV LQ WKH PL[WXUH DQG WR DFKLHYH D VSHFWUXP ZLWK IHZ IUDJPHQWV 6HSDUDWLRQ RI WKH DQDO\WH IURP WKH PDWUL[ FRPSRQHQWV

PAGE 24

Df 4 )XOO 6FDQ Ff 6HOHFWHG,RQ 0RQLWRULQJ 6,0f 4 4 4 4 4, 4 Ef 'DXJKWHU 6FDQ 6HOHFWHG5HDFWLRQ 0RQLWRULQJ 650f 4 4 )LJXUH 7DQGHP PDVV VSHFWURPHWU\ VFDQ PRGHV

PAGE 25

LV DFKLHYHG E\ WKH PDVV VHOHFWLRQ RI D FKDUDFWHULVWLF LRQ RI WKH DQDO\WH E\ WKH ILUVW PDVV DQDO\]HU 4Of 7KH VHOHFWHG SDUHQW LRQ XQGHUJRHV FROOLVLRQDOO\ DFWLYDWHG GLVVRFLDWLRQ &$'f WKURXJK FROOLVLRQV ZLWK QHXWUDO JDV PROHFXOHV LQ WKH IUDJPHQWDWLRQ UHJLRQ 4f WR \LHOG YDULRXV IUDJPHQW RU GDXJKWHU LRQV 6XEVHTXHQW PDVV DQDO\VLV RI WKH GDXJKWHU LRQV E\ WKH VHFRQG PDVV DQDO\]HU 4f UHVXOWV LQ WKH DQDO\WLFDO VLJQDO 7KLV PHWKRG RI 0606 DQDO\VLV FRUUHVSRQGV WR D GDXJKWHU VFDQ )LJXUH OEf $OWKRXJK WKLV RSHUDWLRQDO PRGH LV KLJKO\ VHOHFWLYH WKLV IXOOVFDQ GDXJKWHU PDVV VSHFWUXP XVXDOO\ GRHV QRW H[KLELW VXIILFLHQW VHQVLWLYLW\ IRU WUDFH DQDO\VLV RI DQ DQDO\WH LQ D FRPSOH[ PDWUL[ 7KHUHIRUH WKH VFDQ PRGH RI VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f LV FRPPRQO\ HPSOR\HG )LJXUH OGf $ FKDUDFWHULVWLF GDXJKWHU LRQ W\SLFDOO\ WKH PRVW DEXQGDQW UHVXOWLQJ IURP WKH IUDJPHQWDWLRQ RI WKH VHOHFWHG SDUHQW LRQ RI WKH DQDO\WH LV VHOHFWHG E\ WKH VHFRQG PDVV DQDO\]HU IRU PRQLWRULQJ 650 LV DQDORJRXV WR WKH VHOHFWHGLRQ PRQLWRULQJ 6,0f )LJXUH OFf FRPPRQO\ XVHG WR REWDLQ PD[LPXP VHQVLWLYLW\ LQ FRQYHQWLRQDO *&06 7KXV DQ HQKDQFHPHQW LQ VHQVLWLYLW\ LV REWDLQHG DW WKH H[SHQVH RI D JDLQ LQ VHOHFWLYLW\ ,Q DGGLWLRQ WR WKHVH 0606 PRGHV WKH WDQGHP PDVV VSHFWURPHWHU FDQ EH RSHUDWHG DV D QRUPDO 06 E\ DOORZLQJ DOO LRQV WR SDVV WKURXJK RQH PDVV DQDO\]HU 4O RU 4f DQG WKH FROOLVLRQ FHOO 4f WKHQ VFDQ WKH RWKHU PDVV DQDO\]HU 4 RU 4Of WR SURGXFH D QRUPDO PDVV VSHFWUXP )LJXUH ODf 2SWLPL]DWLRQ RI PDQ\ RI WKHVH RSHUDWLRQDO PRGHV KDYH EHHQ HYDOXDWHG WKURXJKRXW WKHVH VWXGLHV DQG ZLOO EH GLVFXVVHG LQ IXUWKHU GHWDLO DV WR WKHLU VLJQLILFDQFH LQ WKH WUDFH GHWHUPLQDWLRQ RI 3*V

PAGE 26

,PSRUWDQW 3DUDPHWHUV IRU 7UDFH $QDO\VLV ,Q RUGHU WR SHUIRUP WUDFH DQDO\VHV VXFFHVVIXOO\ LW LV QHFHVVDU\ WR WKLQN LQ WHUPV RI WKH IRXU 6nV RI DQDO\VLV f VHQVLWLYLW\ f VHOHFWLYLW\ f VSHHG RU DQDO\VLV WLPH DQG f e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f 7KH OLPLW RI GHWHFWLRQ /2'f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nV VSHHG RI WKH DQDO\VLV DQG FRVW HIIHFWLYHQHVV PD\ QRW EH RSWLPXP

PAGE 27

7KH )RXU 6WHSV ,QYROYHG LQ 7UDFH 0L[WXUH $QDO\VLV 7KH DQDO\WLFDO VFKHPH IRU WUDFH GHWHUPLQDWLRQ RI DQ DQDO\WH LQ D ELRORJLFDO VDPSOH E\ 0606 LQYROYHV IRXU EDVLF VWHSV f VDPSOH SUHSDUDWLRQ f VDPSOH VHSDUDWLRQLQWURGXFWLRQ f LRQL]DWLRQ DQG f GHWHFWLRQ :KHQ GHYHORSLQJ DQ DFFXUDWH UHOLDEOH DQG VSHFLILF PHWKRG IRU PL[WXUH DQDO\VLV D UDQJH RI VHOHFWLYLW\ VHQVLWLYLW\ WLPH DQG FRVW DUH REVHUYHG IRU WKH IRXU VWHSV ,Q VDPSOH SUHSDUDWLRQ D UDSLG ORZ FRVW DQG VHOHFWLYH SURFHGXUH LV GHVLUHG 7KLV FDQ EH DFKLHYHG WKURXJK WKH SURSHU FKRLFH RI H[WUDFWLRQ SXULILFDWLRQ RU GHULYDWL]DWLRQ PHWKRGV ZKLFK VDWLVI\ DQ\ RU DOO RI WKH IRXU 6nV 7KH VHFRQG VWHS LQYROYHV VHSDUDWLRQ RI WKH DQDO\WH RI LQWHUHVW IURP DQ\ PDWUL[ FRPSRQHQWV ZKLFK KDYH QRW EHHQ HOLPLQDWHG E\ WKH VDPSOH SUHSDUDWLRQ PHWKRGV 7\SLFDOO\ LQ 0606 JDV FKURPDWRJUDSK\ LV HPSOR\HG IRU VHSDUDWLRQ LI WKH DQDO\WH H[KLELWV VXIILFLHQW YRODWLOLW\ 6HSDUDWLRQ RI FRPSRQHQWV FDQ EH DFFRPSOLVKHG RQ VKRUW FDSLOODU\ *& FROXPQV P RU OHVVf ZKHQ WKH VDPSOH KDV EHHQ DGHTXDWHO\ FOHDQHGXS f 6KRUW *& FROXPQV FDQ RQO\ EH XWLOL]HG IRU VHSDUDWLRQ RI FRPSOH[ VDPSOHV LI WKH VDPSOH SUHSDUDWLRQ PHWKRGV KDYH WKH QHFHVVDU\ VHOHFWLYLW\ 7KH FKRLFH RI DQ LRQL]DWLRQ PHWKRG LV EDVHG RQ WKH W\SH RI DQDO\VLV UHTXLUHG DQG WKH DQDO\WH ZKLFK LV WR EH DQDO\]HG ,Q WKH ORZ OHYHO WUDFH GHWHUPLQDWLRQ RI DQDO\WHV LQ ELRORJLFDO VDPSOHV D VRIW LRQL]DWLRQ PHWKRG HJ FKHPLFDO LRQL]DWLRQf LV XVXDOO\ VHOHFWHG ZKLFK \LHOGV DQ LQWHQVH PROHFXODU LRQ ZLWK IHZ IUDJPHQWV )XUWKHUPRUH IRU DQDO\WHV ZKLFK DUH KLJKO\ HOHFWURQn FDSWXULQJ RU FDQ EH GHULYDWL]HGf HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f PD\ EH FKRVHQ LQ RUGHU WR DFKLHYH WKH KLJKHVW VHQVLWLYLW\ )LQDOO\ WKH GHWHFWLRQ E\ 0606 LQYROYHV WKH RSWLPL]DWLRQ

PAGE 28

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f DQG VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f IRU 3*( DQG 3*)D DUH GHVFULEHG DQG WKH UHVXOWV GLVFXVVHG &KDSWHU SUHVHQWV D VWXG\ RI WKH GLIIHUHQFHV LQ WKH &$' HIILFLHQF\ RI WZR VWUXFWXUDOO\ VLPLODU 3*V 3*( DQG 3*)Tf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f RI 3* DQDO\VLV &KDSWHU LQFOXGHV DQ HYDOXDWLRQ RI WKH UDSLG DQDO\VLV WHFKQLTXHV RI GLUHFW VROLGV SUREH0606 DQG GLUHFW FKHPLFDO LRQL]DWLRQ '&,f0606

PAGE 29

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

PAGE 30

&+$37(5 6$03/( 35(3$5$7,21 678',(6 ,QWURGXFWLRQ 6DPSOH SUHSDUDWLRQ LV DQ LPSRUWDQW VWHS LQ DQ\ DQDO\WLFDO PHWKRGRORJ\ 7KLV VWHS SUHSDUHV WKH VDPSOH IRU WKH GHWHFWLRQ PHWKRG DQG FDQ GUDPDWLFDOO\ DIIHFW WKH YDOLGLW\ RI WKH GDWD REWDLQHG 7KH WZR PDLQ SDUWV RI VDPSOH SUHSDUDWLRQ IRU JDV FKURPDWRJUDSK\PDVV VSHFWURPHWU\ *&06f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f PDNHV LW LPSRVVLEOH IRU WKHP WR SDVV WKURXJK D *& FROXPQ LQWDFW ZLWKRXW ILUVW XQGHUJRLQJ GHULYDWL]DWLRQ 7KLV GHULYDWL]DWLRQ LQFUHDVHV WKH YRODWLOLW\ RI WKH FRPSRXQG DQG UHGXFHV WKH LQWHUDFWLRQ RI WKH SRODU VXEVWLWXHQWV RQ WKH FRPSRXQG ZLWK WKH VWDWLRQDU\ SKDVH RI WKH *& FROXPQ ,Q DGGLWLRQ GHULYDWL]DWLRQ FDQ DGG VHQVLWLYLW\ DQGRU VHOHFWLYLW\ IRU GHWHFWLRQ RI D FRPSRXQG 0DQ\ RUJDQLF GHULYDWL]DWLRQ UHDFWLRQV ZLWK 3*V HQKDQFH WKH HIILFLHQF\ RI HOHFWURQ

PAGE 31

FDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f PDVV VSHFWURPHWU\ f (OHFWURQFDSWXUH 1&, ZLWK GHULYDWL]DWLRQ SURGXFHV PXFK VLPSOHU PDVV VSHFWUD DQG WKH PDMRU IUDJPHQW LRQV RFFXU DW WKH KLJK PDVV UDQJH f 7KXV WKHVH WZR IHDWXUHV FRPELQHG ZLWK WKH KLJKHU LRQL]DWLRQ HIILFLHQF\ RI (&1&, SURYLGH DGGHG VHQVLWLYLW\ DQG VHOHFWLYLW\ QHHGHG LQ WUDFH GHWHUPLQDWLRQ RI 3*V &RQFHSWV IRU 6ROLG3KDVH ([WUDFWLRQ 6ROLGSKDVH H[WUDFWLRQ 63(f KDV HPHUJHG LQ WKH ODVW WHQ \HDUV DV WKH PHWKRG RI FKRLFH IRU LVRODWLRQ DQG SXULILFDWLRQ RI DUDFKLGRQLF DFLG PHWDEROLWHV f 63( KDV WKH DGYDQWDJH RI XVLQJ ORZ YROXPHV RI VROYHQWV DQG KLJK UHFRYHULHV RI b WR b IRU PRVW 3*V 5DSLG H[WUDFWLRQV DUH XVXDOO\ SRVVLEOH ZLWK VLPSOH SURFHGXUHV 7KLV UHVXOWV LQ D UDSLG LQH[SHQVLYH H[WUDFWLRQ WHFKQLTXH 7KH FRQFHSW RI 63( LV EDVHG RQ WKH VHOHFWLYH UHWHQWLRQ RI WKH DQDO\WH E\ D VRUEHQW EHG DV D VROYHQW LQ ZKLFK WKH DQDO\WH LV GLVVROYHG LV SDVVHG WKURXJK WKH FROXPQ 7KLV LGHD LV GLVSOD\HG JUDSKLFDOO\ LQ )LJXUH $ VDPSOH FRQWDLQLQJ DQDO\WHV $f DQG LQWHUIHUHQFHV t 0f LV SDVVHG WKURXJK WKH VRUEHQW 7KH VRUEHQW VHOHFWLYHO\ UHWDLQV DQDO\WHV $f DQG VRPH LQWHUIHUHQFHV ,f +RZHYHU DW WKH VDPH WLPH PDQ\ LQWHUIHUHQFHV 0f SDVV XQUHWDLQHG WKURXJK WKH VRUEHQW $SSURSULDWH VROYHQWV DUH WKHQ XVHG WR ZDVK WKH VRUEHQW VHOHFWLYHO\ HOXWLQJ SUHYLRXVO\ UHWDLQHG LQWHUIHUHQFHV ,f ZKLOH WKH DQDO\WHV $f UHPDLQ RQ WKH VRUEHQW EHG 3XULILHG FRQFHQWUDWHG DQDO\WHV $f DUH WKHQ HOXWHG IURP WKH VRUEHQW

PAGE 32

)LJXUH &RQFHSW RI VROLGSKDVH H[WUDFWLRQ $ DQDO\WH t 0 LQWHUIHUHQFHV

PAGE 33

6RUEHQW$QDO\WH ,QWHUDFWLRQV 7KUHH W\SHV RI FKHPLFDO LQWHUDFWLRQV DUH FRPPRQO\ HPSOR\HG LQ VROLG SKDVH H[WUDFWLRQV f 7KH ILUVW LV WKH QRQSRODU LQWHUDFWLRQ ZKLFK RFFXUV EHWZHHQ WKH FDUERQK\GURJHQ ERQGV RI WKH DQDO\WH DQG WKDW RI WKH VRUEHQW 9LUWXDOO\ DOO RUJDQLF FRPSRXQGV KDYH VRPH QRQSRODU FKDUDFWHU WKXV WKHVH W\SHV RI LQWHUDFWLRQV DUH WKH PRVW FRPPRQO\ XVHG WR UHWDLQ DQDO\WHV RQ VRUEHQWV 7KH IRUFHV ZKLFK DUH LQYROYHG LQ VXFK QRQSRODU LQWHUDFWLRQV DUH YDQ GHU :DDOV RU GLVSHUVLRQ IRUFHV f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f 3RODU LQWHUDFWLRQV LQFOXGH K\GURJHQ ERQGLQJ GLSROHGLSROH SLn SL DQG PDQ\ PRUH LQWHUDFWLRQV LQ ZKLFK WKH GLVWULEXWLRQ RI HOHFWURQV LV XQHTXDO LQ WKH DWRPV RI WKH IXQFWLRQDO JURXSV 7KLV SURSHUW\ RI SRODU VRUEHQWV DOORZV DQ DQDO\WH ZKLFK FRQWDLQV D SRODU IXQFWLRQDO JURXS WR

PAGE 34

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f LQWHUDFWV ZLWK D VRUEHQW FDUU\LQJ D FKDUJH RSSRVLWH WR WKDW RI WKH DQDO\WH ,RQLF LQWHUDFWLRQV DUH PRUH VHOHFWLYH WKDQ QRQSRODU DQG SRODU LQWHUDFWLRQV DQG FDQ EH FRQWUROOHG E\ DGMXVWLQJ WKH S+ RI WKH VDPSOH VROXWLRQ ,W LV HVVHQWLDO WR NQRZ DERXW WKH IXQFWLRQDO JURXSV RQ WKH VRUEHQW DQG WKH DQDO\WH EHFDXVH ERWK RI WKHVH QHHG WR EH FKDUJHG WR IDFLOLWDWH LRQLF LQWHUDFWLRQ 7ZR FODVVHV RI LRQ H[FKDQJH LQWHUDFWLRQ H[LVW FDWLRQLF SRVLWLYHO\ FKDUJHGf DQG DQLRQLF QHJDWLYHO\ FKDUJHGf ([DPSOHV RI FDWLRQLF LQWHUDFWLRQV LQFOXGH WKH LQWHUDFWLRQ RI DPLQHV DQG FHUWDLQ LQRUJDQLF FDWLRQV ZLWK FDUER[\PHWK\O VXOIRQ\OSURS\O DQG EHQ]HQHVXOIRQ\OSURS\O VRUEHQWV $QLRQLF LQWHUDFWLRQV RFFXU ZKHQ VRUEHQWV FRQWDLQLQJ SULPDU\ VHFRQGDU\ WHUWLDU\ DQG TXDWHUQDU\ DPLQHV LQWHUDFW ZLWK FDUER[\OLF DQG VXOIRQLF DFLGV SKRVSKDWHV DQG VLPLODU JURXSV RQ DQ DQDO\WH 5HFHQWO\ FRYDOHQW LQWHUDFWLRQV KDYH EHHQ H[SORLWHG IRU H[WUDFWLRQ RI VSHFLILF W\SHV RI FRPSRXQGV f &RYDOHQW FKURPDWRJUDSK\ LV KLJKO\ FKHPLFDOO\ VHOHFWLYH LQYROYLQJ DQ LQWHUDFWLRQ RI JUHDWHU HQHUJ\ WKDQ LV HPSOR\HG LQ WKH RWKHU H[WUDFWLRQ PHWKRGV 5HWHQWLRQ RI WKH DQDO\WH RFFXUV

PAGE 35

ZKHQ D FRYDOHQW ERQG FDQ IRUP EHWZHHQ LW DQG WKH VRUEHQW $ FKDQJH LQ WKH VROYHQW HQYLURQPHQW IDFLOLWDWHV HOXWLRQ RI WKH DQDO\WH 7KLV LV FRPPRQO\ DFFRPSOLVKHG WKURXJK WKH XVH RI VROYHQWV ZLWK YDULRXV S+nV 2QH H[DPSOH LV SKHQ\O ERURQLF DFLG 3%$f ZKLFK KDV EHHQ LPPRELOL]HG IRU WKH VHOHFWLYH UHWHQWLRQ RI FRPSRXQGV ZLWK RU GLROV VXFK DV FDWHFKRODPLQHV DQG WKURPER[DQHV f 0DQ\ RI WKH VRUEHQWV GLVFXVVHG DERYH PD\ H[KLELW PRUH WKDQ RQH LQWHUDFWLRQ %RWK SRODU DQG LRQLF LQWHUDFWLRQV GXH WR WKH VLOLFD VXEVWUDWH XVHG FDQ RFFXU LQ DOO VRUEHQWV ,Q WKH FDVH RI WKH 3%$ QRQn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f 7KH VRUEHQWV ZKLFK ZHUH FKRVHQ IRU WKH VWXG\ ZHUH GHWHUPLQHG E\ H[DPLQLQJ SURSHUWLHV RI WKH DQDO\WH 3*Vf DQG WKH PDWUL[ XULQHf )LUVW WKH GHWHUPLQDWLRQ RI WKH LQWHUDFWLRQV ZKLFK 3*V FRXOG XQGHUJR ZDV H[DPLQHG $UHDV RI FDUERQK\GURJHQ FRQWHQW ZLWK DON\O FKDLQV VXJJHVWHG WKDW QRQSRODU UHWHQWLRQ ZDV SUREDEOH 7KH SUHVHQFH RI VXFK SRODU JURXSV

PAGE 36

DV K\GUR[\OV 2+f DQG FDUERQ\OV f LQGLFDWHG D SRWHQWLDO IRU UHWHQWLRQ E\ SRODU LQWHUDFWLRQV ,RQLF LQWHUDFWLRQ ZDV LQGLFDWHG E\ WKH SUHVHQFH RI WKH FDUER[\OLF DFLG PRLHW\ +RZHYHU WKLV PHWKRG ZDV QRW HYDOXDWHG IRU WKH DQDO\VLV RI 3*V LQ XULQH GXH WR WKH H[FHVVLYH TXDQWLWLHV RI FRPSRXQGV LQ XULQH ZKLFK ZRXOG XQGHUJR DQLRQLF DQG FDWLRQLF LQWHUDFWLRQV &RQVLGHULQJ WKDW 3%$ KDV EHHQ XVHG IRU VHSDUDWLRQ RI WKH DUDFKLGRQLF DFLG PHWDEROLWH WKURPER[DQH % 7;%f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f )LUVW HDFK VRUEHQW QHHGHG WR EH SUHSDUHG 7KLV ZDV DFFRPSOLVKHG E\ ZDVKLQJ WKH VRUEHQW EHG ILUVW DQG DOORZLQJ WKH IXQFWLRQDO JURXSV RQ WKH VRUEHQW WR LQWHUDFW ZLWK WKH VROYHQW 7KH QH[W VWHS ZDV WR UHPRYH WKH ZDVK VROYHQW DQG FUHDWH DQ HQYLURQPHQW WKDW IDFLOLWDWHG WKH DQDO\WHV 3*Vf UHWHQWLRQ $IWHU WKLV SURFHVV WKH WHVWLQJ SURFHGXUH EHJDQ DQG LQYROYHG ILYH VWHSV 6WDQGDUGV ZHUH SUHSDUHG LGHQWLFDO WR D UHDO VDPSOH DQG DSSOLHG WR WKH FROXPQ VRUEHQWf 7KH VWDQGDUGV ZHUH WKHQ ZDVKHG ZLWK WKH VDPH VROYHQW LQ ZKLFK WKH\ ZHUH GLVVROYHG DQG WKH HOXHQW FROOHFWHG 7KH HOXHQW ZDV WKHQ FKHFNHG IRU WKH SUHVHQFH RI DQDO\WH LQGLFDWLQJ VRUEHQWV ZKLFK GLG QRW SURYLGH DGHTXDWH UHWHQWLRQ RI WKH DQDO\WH 1H[W VWURQJ

PAGE 37

2SWLPL]H 5HWHQWLRQ RI 6WDQGDUGV 2SWLPL]H (OXWLRQ RI 6WDQGDUGV ,GHQWLI\ :DVK 6ROYHQWV 7HVW %ODQN 0DWUL[ 8VH :DVK 6ROYHQWV 7HVW 6SLNHG 0DWUL[ 7URXEOHVKRRW LI 1HFHVVDU\ )LJXUH 6RUEHQW WHVWLQJ VFKHPH

PAGE 38

HOXWLRQ VROYHQWV ZHUH FKRVHQ RI ZKLFK VPDOO YROXPHV FDQ EH XWLOL]HG WR FRPSOHWHO\ HOXWH WKH UHWDLQHG DQDO\WH 'XULQJ WKLV SURFHVV VROYHQWV ZKLFK ZRXOG QRW HOXWH WKH DQDO\WH ZHUH LGHQWLILHG IRU XVH DV ZDVK VROYHQWV 7KHVH ZHUH WHVWHG QH[W ZLWK D EODQN PDWUL[ XULQHf WR GHWHUPLQH WKH VROYHQWVf ZKLFK SURGXFHG WKH FOHDQHVW H[WUDFW &OHDUO\ WKLV ZDV IDU PRUH GLIILFXOW WR HYDOXDWH WKDQ WKH GHWHUPLQDWLRQ RI DQDO\WH UHFRYHU\ $IWHU GHYHORSLQJ D SURFHGXUH ZKLFK SURYLGHG VXIILFLHQW DQDO\WH UHWHQWLRQ DQG HOXWLRQ DV ZHOO DV DGHTXDWH FOHDQXS RI WKH PDWUL[ WKH PHWKRG ZDV WHVWHG ZLWK D VDPSOH XULQHf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f 7KH QHFHVVLW\ RI IXUWKHU SXULILFDWLRQ RI WKH H[WUDFWV EHIRUH FKURPDWRJUDSKLF DQDO\VLV PDNHV WKH DQDO\WLFDO SURFHGXUHV PRUH FRPSOH[ ODERULRXV DQG WLPHFRQVXPLQJ WR GHYHORS 7KLV SUREOHP KDV EHHQ DYRLGHG LQ PDQ\ FDVHV E\ WDNLQJ DGYDQWDJH RI LPPXQR DGVRUSWLRQ WHFKQLTXHV WR VLPSOLI\ H[WUDFWLRQ DQG FOHDQXS SURFHGXUHV IRU *&06 DQDO\VLV f 5HSRUWV KDYH VKRZQ WKDW WKH VHOHFWLYLW\ RI WKH LPPXQRDGVRUSWLRQ SURFHGXUHV PD\ SHUPLW WKH GLUHFW DQDO\VLV RI H[WUDFWV DQG HOLPLQDWH WKH QHHG IRU LQWHUPHGLDWH FKURPDWRJUDSKLF FOHDQXS

PAGE 39

$QWLERGLHV KDYH EHHQ XVHG IRU PDQ\ \HDUV IRU WKH DQDO\VLV RI 3*V E\ UDGLRLPPXQRDVVD\ 5,$f 8QIRUWXQDWHO\ WKH SUHVHQFH RI VXEVWDQFHV ZLWKLQ WKH VDPSOH PDWUL[ ZKLFK H[KLELW FURVVUHDFWLYLW\ ZLWK WKH SRO\FORQDO DQWLERG\ FDQ EH FRQVLGHUDEOH f )RU H[DPSOH DQWLERGLHV IRU FDUERQ 3*V DQG WKHLU PHWDEROLWHV PD\ DOVR ELQG WKH FRUUHVSRQGLQJ GLQRU PHWDEROLWHV SUHVHQW LQ WKH PDWUL[ f 7KXV +3/& LV IUHTXHQWO\ HPSOR\HG DV D VHSDUDWLRQ WHFKQLTXH SULRU WR 5,$ WR DYRLG FURVVUHDFWLYLW\ 5HSRUWV KDYH VKRZQ WKDW ZLWKRXW VHSDUDWLRQ RI FURVVUHDFWLQJ FRPSRQHQWV E\ +3/& 3* OHYHOV KDYH EHHQ IRXQG WLPHV KLJKHU WKDQ WKH DFWXDO OHYHOV SUHVHQW f ,PPXQRDGVRUSWLRQ SXULILFDWLRQ KDV EHHQ XWLOL]HG DV ZHOO SULRU WR 3* DQDO\VLV E\ 5,$ f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f 7KH EDVLF SULQFLSOH RI DQWLERG\ DIILQLW\ H[WUDFWLRQ LV GLVSOD\HG LQ )LJXUH ,Q D W\SLFDO DIILQLW\ FKURPDWRJUDSKLF VHSDUDWLRQ WKH DQWLERG\ LV FRXSOHG WR D VWDWLRQDU\ SKDVH WKH PRVW SRSXODU LV DJDURVH JHOf 7KH VHOHFWLYLW\ RI DIILQLW\ VHSDUDWLRQV LV EDVHG RQ WKH SULQFLSOH RI ORFN DQG NH\ ELQGLQJ ZKLFK

PAGE 40

$GVRUE 5HJHQHUDWH :DVK )LJXUH %DVLF SULQFLSOH RI DQWLERG\ DIILQLW\ H[WUDFWLRQ $ DQDO\WH t 0 LQWHUIHUHQFHV

PAGE 41

RFFXUV LQ ELRORJLFDO V\VWHPV ([WUDFWLRQ RI WKH VDPSOH LV DFFRPSOLVKHG E\ SDVVLQJ WKH VROXWLRQ FRQWDLQLQJ DQDO\WHV DQG LQWHUIHUHQFHVf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f $V UHSRUWHG HDUOLHU LQ &KDSWHU WKH PRVW FRPPRQO\ XVHG GHULYDWLYH IRU

PAGE 42

TXDQWLWDWLYH DQDO\VLV E\ *&06 LV WKH PHWKR[LPHSHQWDIOXRUREHQ]\OWUL PHWK\OVLO\O 023)%706f GHULYDWLYH 7KH NHWR JURXS RQ 3*( LV FRQYHUWHG WR WKH PHWKR[LPH GHULYDWLYH WR SUHYHQW VLO\ODWLRQ ZKLFK FDQ LQWHUIHUH ZLWK TXDQWLWDWLRQ E\ SURGXFLQJ DGGLWLRQDO GHULYDWLYHV 3HQWDIOXRUREHQ]\O 3)%f HVWHUV DUH FUHDWHG WR HQKDQFH WKH HIILFLHQF\ RI LRQL]DWLRQ E\ (&1&, LQ RUGHU WR DFKLHYH ORZ OHYHO GHWHUPLQDWLRQV RI 3*V 7KHVH 3)% HVWHUV KDYH EHHQ IRXQG WR JLYH DERXW WZLFH WKH VHQVLWLYLW\ RI WKH PHWK\O HVWHU GHULYDWLYH f 5HDFWLRQ WLPHV DUH IDVW PLQf DQG TXDQWLWDWLYH bf IRU WKLV GHULYDWL]DWLRQ SURFHGXUH 7KH K\GUR[\O JURXSV DUH FRQYHUWHG WR WULPHWK\OVLO\O 706f HWKHUV XVLQJ ELVWULPHWK\OVLO\OfWULIOXRURDFHWDPLGH %67)$f 7KLV 706 GRQRU KDV WKH DGGLWLRQDO DGYDQWDJH RI FUHDWLQJ H[WUHPHO\ YRODWLOH UHDFWLRQ E\SURGXFWV ZKLFK XVXDOO\ HOXWH ZLWK WKH VROYHQW IURQW LQ WKH *& WUDFH (YHQ WKRXJK WKH GHULYDWL]DWLRQ IRU TXDQWLWDWLYH DQDO\VLV RI 3*V E\ *&06 KDV EHHQ WKRURXJKO\ GRFXPHQWHG WKHUH DUH PDQ\ YDULDWLRQV LQ WKH OLWHUDWXUH ,W KDV EHHQ UHSRUWHG WKDW E\ SHUIRUPLQJ WKH PHWKR[LPDWLRQ EHIRUH WKH HVWHUILFDWLRQ D ILYHIROG LQFUHDVH LQ WKH GHULYDWLYH \LHOG FDQ EH REWDLQHG f +RZHYHU PDQ\ UHVHDUFKHUV VWLOO SHUIRUP WKH HVWHU ILFDWLRQ VWHS ILUVW LQ WKH GHULYDWL]DWLRQ SURFHGXUH f 5HDFWLRQ WLPHV IRU WKH PHWKR[LPDWLRQ VWHS YDU\ LQ WKH OLWHUDWXUH UDQJLQJ IURP RQH KRXU DW r WR KRXUV DW URRP WHPSHUDWXUH 7KHVH GLIIHUHQFHV LQ DGGLWLRQ WR WKH FRPSDULVRQ RI WHFKQLTXHV IRU WKH UHPRYDO RI H[FHVV GHULYDWLYH UHDJHQWV E\ OLTXLGOLTXLG H[WUDFWLRQ DQG QLWURJHQ HYDSRUDWLRQ ZHUH H[SORUHG LQ WKLV VWXG\

PAGE 43

([SHULPHQWDO 3URVWDJODQGLQV DQG 5HDJHQWV $OO VROYHQWV ZHUH UHDJHQW RU +3/& JUDGH 3URVWDJODQGLQ ( 3*(f ZDV SXUFKDVHG IURP 6LJPD &KHPLFDO &R 6W /RXLV 02f > +@3*( DQG 5LDIOXRU OLTXLG VFLQWLOODWRU ZHUH IURP 1HZ (QJODQG 1XFOHDU %RVWRQ 0$f DQG ZHUH D JLIW IURP 'U 1HX RI WKH 'HSDUWPHQW RI 3HGLDWULFV 8QLYHUVLW\ RI )ORULGD *DLQHVYLOOH )/f 7KH VROLGSKDVH H[WUDFWLRQ FROXPQV ZHUH SXUFKDVHG IURP $QDO\WLFKHP ,QWHUQDWLRQDO ,QF +DUERU &LW\ &$f DQG :DWHUV $VVRF 6HS3DN FROXPQV 0LOIRUG 0$f nn+f 3*( DQG WKH DQWLERG\ DIILQLW\ VRUEHQW ZHUH JLIWV IURP 'UV -9UEDQDF DQG '5 .QDSS RI WKH 'HSDUWPHQW RI 3KDUPDFRORJ\ 0HGLFDO 8QLYHUVLW\ RI 6RXWK &DUROLQD &KDUOHVWRQ 6&f 7KH GHULYDWL]DWLRQ UHDJHQWV DQG VROYHQWV S\ULGLQH 2PHWK\OK\GUR[\ODPLQH K\GURFKORULGH DFHWRQLWULOH DQG 11GLLVRSURS\OHWK\O DPLQH IRU *&06 SHUFHQW UHFRYHU\ VWXGLHV ZHUH DOO SXUFKDVHG IURP 6LJPD &KHPLFDO &R 3HQWDIOXRUREHQ]\O EURPLGH 3)%%Uf DQG ELVWULPHWK\OVLO\OfWULIOXRURDFHWDPLGH %67)$f ZHUH SXUFKDVHG IURP 3LHUFH &KHPLFDO &R 5RFNIRUG ,/f 8ULQH ZDV REWDLQHG IURP WKH DXWKRU $OO JODVVZDUH ZDV VLODQL]HG ZLWK D VROXWLRQ RI b GLPHWK\OGLFKORURVLODQH LQ WROXHQH 7KHVH WZR FKHPLFDOV ZHUH ERWK SXUFKDVHG IURP 6LJPD &KHPLFDO &R +HOLXP XVHG DV *& FDUULHU JDV DQG PHWKDQH !bf XVHG DV WKH FKHPLFDO LRQL]DWLRQ UHDJHQW JDV ZHUH IURP 0DWKHVRQ *DV 3URGXFWV ,QF 2UODQGR )/f 6DPSOH 3UHSDUDWLRQ 7KH VRUEHQWV IRU WKH SHUFHQW UHFRYHU\ VWXGLHV ZHUH FKRVHQ DQG WHVWHG DFFRUGLQJ WR WKH SURFHGXUHV GLVFXVVHG HDUOLHU LQ WKLV FKDSWHU ([WUDFWLRQ

PAGE 44

SURFHGXUHV ZHUH GHWHUPLQHG IRU WKH QRQSRODU SRODU DQG SKHQ\O ERURQLF DFLG FROXPQV E\ GHWHFWLRQ RI WKH WULWLXPODEHOHG 3*( E\ VFLQWLOODWLRQ FRXQWLQJ 7KH VRUEHQWV FKRVHQ DUH OLVWHG ZLWK WKH ILQDO H[WUDFWLRQ SURFHGXUH XVHG IRU WKH SHUFHQW UHFRYHU\ VWXGLHV IRU ERWK VFLQWLOODWLRQ FRXQWLQJ DQG *&06 1RQSRODU FROXPQV RFW\O &f RFWDGHF\O &f DQG SKHQ\O 3+f f &RQGLWLRQHG WKH FROXPQ ZLWK P/ RI +3/& ZDWHU DQG P/ RI PHWKDQRO f 3DVVHG VROXWLRQ RI 3*( DFLGLILHG WR S+ ZLWK IRUPLF DFLGf WKURXJK WKH FROXPQ f :DVKHG WKH FROXPQ ZLWK P/ RI +3/& ZDWHU DQG P/ SHWUROHXP HWKHU f (OXWHG 3*( ZLWK P/ RI HWK\O DFHWDWH 3RODU FROXPQV VLOLFD 6,f F\DQRSURS\O &1f DPLQRSURS\O 1+f DQG GLRO +f f &RQGLWLRQHG WKH FROXPQ ZLWK P/ RI EHQ]HQHHWK\O DFHWDWH YROXPHYROXPHf f 3DVVHG VROXWLRQ RI 3*( DFLGLILHG WR S+ ZLWK IRUPLF DFLGf WKURXJK WKH FROXPQ f :DVKHG WKH FROXPQ ZLWK P/ EHQ]HQHHWK\O DFHWDWH YYf f (OXWHG 3*( ZLWK P/ EHQ]HQHHWK\O DFHWDWHPHWKDQRO YYYf 3KHQ\O ERURQLF DFLG FROXPQ 3%$f f &RQGLWLRQHG WKH FROXPQ ZLWK P/ RI 0 K\GURFKORULF DFLG DQG P/ RI 0 VRGLXP K\GUR[LGH

PAGE 45

f 3DVVHG VDPSOH RI 3*( DGMXVWHG WR S+ ZLWK 0 SKRVSKDWH EXIIHU 3%6ff WKURXJK WKH FROXPQ f :DVKHG WKH FROXPQ ZLWK P/ RI PHWKDQRO DQG P/ RI +3/& ZDWHU f (OXWHG 3*( ZLWK P/ RI 0 3%6 S+ f 7KH DQWLERG\ DIILQLW\ FROXPQV ZHUH WHVWHG DQG SHUFHQW UHFRYHU\ GDWD FDOFXODWHG RQO\ ZLWK *&06 $QWLERG\ DIILQLW\ FROXPQ >,PPXQRDIILQLW\ ,$f@ f &RQGLWLRQHG WKH FROXPQ ZLWK P/ RI 3%6 S+ f f 3DVVHG VROXWLRQ RI 3*( DFLGLILHG WR S+ ZLWK IRUPLF DFLGf WKURXJK WKH FROXPQ f $OORZHG WKH VDPSOH WR VHWWOH LQWR WKH VRUEHQW EHG IRU PLQ DW URRP WHPSHUDWXUH f :DVKHG WKH FROXPQ ZLWK P/ RI 3%6 S+ f DQG P/ +3/& ZDWHU 5HPRYHG DOO UHPDLQLQJ ZDWHU LQ WKH FROXPQ f (OXWHG 3*( ZLWK P/ RI b DFHWRQLWULOH VROXWLRQ YYf f :DVKHG FROXPQ ZLWK DQ DGGLWLRQDO P/ RI b DFHWRQLWULOH WR DVVXUH UHPRYDO RI DOO WKH 3*( f ,PPHGLDWHO\ ULQVHG WKH FROXPQ ZLWK P/ RI +3/& ZDWHU DQG P/ RI 3%6 S+ f 6FLQWLOODWLRQ &RXQWLQJ $ VWRFN VROXWLRQ RI +3*( ZDV XVHG IRU WKH SHUFHQW UHFRYHU\ VWXGLHV 7KLV VROXWLRQ ZDV PLFURFXULHV L&LfPLFUROLWHU M/f DQG KDG D VSHFLILF DFWLYLW\ RI A&LPLOOLPROH 6L[ PLFUROLWHUV RI WKLV RULJLQDO VROXWLRQ ZDV GLOXWHG ZLWK / RI DEVROXWH HWK\O DOFRKRO FUHDWLQJ D VROXWLRQ RI [ n L&LL/ 7HQ PLFUROLWHUV RI WKLV

PAGE 46

VWDQGDUG VROXWLRQ FRUUHVSRQGLQJ WR [ n PPROHV RU PJ ZDV SDVVHG WKURXJK HDFK FROXPQ WHVWHG )ROORZLQJ WKH H[WUDFWLRQ SURFHGXUHV WKH HOXHQW ZDV FROOHFWHG DQG WKH VROYHQW HYDSRUDWHG ZLWK QLWURJHQ 7KH +3*( ZDV WKHQ GLOXWHG ZLWK W/ RI 3%6 S+ f $GGLWLRQDOO\ P/ RI 5LDIOXRU OLTXLG VFLQWLOODWRU ZHUH DGGHG WR WKH [ f &L VROXWLRQ RI +3*( EHIRUH WKH FRXQWLQJ SURFHVV (DFK H[WUDFWLRQ ZDV SHUIRUPHG WKUHH WLPHV ZLWK WKUHH LQGLYLGXDO FROXPQV $ FDOLEUDWLRQ FXUYH ZDV SUHSDUHG LQ WKH VDPH PDQQHU ZLWK WKH H[FHSWLRQ RI WKH DFWXDO H[WUDFWLRQ VWHS )LJXUH Df $OLTXRWV RI DQG PLFUROLWHUV RI WKH [ f L&LL/ VROXWLRQ ZHUH DGGHG WR VHSDUDWH YLDOV DQG HDFK GLOXWHG ZLWK L/ RI WKH 3%6 S+ f ,Q DGGLWLRQ D EODQN FRQWDLQLQJ RQO\ W/ RI WKH 3%6 S+ f ZDV SUHSDUHG 7KH 5LDIOXRU OLTXLG VFLQWLOODWRU ZDV DGGHG DQG WKH VWDQGDUGV FRXQWHG DQG XVHG WR FDOFXODWH WKH SHUFHQW UHFRYHU\ YDOXHV IRU WKH GLIIHUHQW FROXPQV WHVWHG *DV &KURPDWRJUDSK\0DVV 6SHFWURPHWU\ *&06f 7HQ QDQRJUDPV QJf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f DQG LQFUHDVLQJ DPRXQWV RI 3*( LQ WKH

PAGE 47

)LJXUH &DOLEUDWLRQ FXUYHV Df 6FLQWLOODWLRQ FRXQWLQJ Ef *DV FKURPDWRJUDSK\PDVV VSHFWURPHWU\ *&06f ZLWK VHOHFWHGLRQ PRQLWRULQJ 6,0f

PAGE 48

7DEOH &DOLEUDWLRQ &XUYH 'LOXWLRQV IRU *&06 fKSJH $GGHG QJf SJH $GGHG QJf 9ROXPH RI 'LOXWLRQ /f &RQFHQWUDWLRQ RI +3*( SJL/f &RQFHQWUDWLRQ RI 3*( SJ$L/f

PAGE 49

VROXWLRQ )LJXUH Ef 7DEOH OLVWV WKH DPRXQWV RI +A3*( DQG VWDQGDUG 3*( DGGHG WR HDFK YLDO DQG WKH ILQDO FRQFHQWUDWLRQV DIWHU GLOXWLRQ ZLWK L/ RI VLODQL]LQJ UHDJHQW 'HULYDWL]DWLRQ IRU *&06 7KH PHWKR[LPHSHQWDIOXRUREHQ]\O HVWHUWULPHWK\OVLO\O 023)%706f GHULYDWLYHV ZHUH IRUPHG IRU WKH *&06 SHUFHQW UHFRYHU\ DQG GHULYDWL]DWLRQ VWXGLHV 7KH PHWKRG XVHG ZDV VLPLODU WR WKH GHULYDWL]DWLRQ RI + / +XEEDUG HW DO f 7KH VWDQGDUGV DQG VDPSOHV RI +3*( DQG 3*( DIWHU HYDSRUDWLRQ ZHUH WUHDWHG ZLWK L/ RI PHWK\OK\GUR[\ODPLQH +& LQ GU\ S\ULGLQH PJP/f DOORZHG WR VWDQG RYHUQLJKW DW URRP WHPSHUDWXUH WKHQ HYDSRUDWHG XQGHU QLWURJHQ XQWLO GU\ (DFK VDPSOH ZDV DFLGLILHG E\ DGGLQJ L/ RI ,1 IRUPLF DFLG H[WUDFWHG ZLWK WZR P/ DOLTXRWV RI HWK\O DFHWDWH DQG WKH H[WUDFW GULHG XQGHU QLWURJHQ 7KHQ L/ RI DFHWRQLWULOH L/ RI b 3)%%U LQ DFHWRQLWULOH DQG L/ RI b 11 GLLVRSURS\OHWK\ODPLQH LQ DFHWRQLWULOH ZHUH DGGHG WR WKH GULHG PHWKR[LPH GHULYDWLYH (DFK VROXWLRQ ZDV DOORZHG WR VWDQG IRU PLQXWHV DW URRP WHPSHUDWXUH EHIRUH WKH UHDJHQWV ZHUH HYDSRUDWHG ZLWK QLWURJHQ ([FHVV GHULYDWL]LQJ UHDJHQW ZDV UHPRYHG E\ GLVVROYLQJ WKH VDPSOH LQ L/ RI GLVWLOOHG ZDWHU DQG H[WUDFWLQJ ZLWK WZR P/ DOLTXRWV RI D PHWK\OHQH FKORULGHKH[DQH YYf VROXWLRQ WKH H[WUDFW ZDV WKHQ GULHG XQGHU QLWURJHQ 7KH WULPHWK\OVLO\O GHULYDWLYH WKHQ ZDV IRUPHG E\ DGGLQJ W/ RI %67)$ WR WKH VWDQGDUGV IRU WKH FDOLEUDWLRQ FXUYH DQG L/ WR WKH H[WUDFWLRQ VDPSOHV DQG DOORZLQJ WKH VROXWLRQV WR VWDQG RYHUQLJKW DW URRP WHPSHUDWXUH 2QHPLFUROLWHU LQMHFWLRQV FRQWDLQLQJ SJ RI +3*( ZHUH PDGH RI HDFK VWDQGDUG DQG VDPSOH

PAGE 50

,QVWUXPHQWDWLRQ $ %HFNPDQ /6 OLTXLG VFLQWLOODWLRQ FRXQWHU DQG D )LQQLJDQ 0$7 WULSOH VWDJH TXDGUXSROH 764f JDV FKURPDWRJUDSKPDVV VSHFWURPHWHU ZHUH XVHG LQ WKHVH VWXGLHV *DV FKURPDWRJUDSK\ ZDV FDUULHG RXW RQ D FRQYHQWLRQDO -t: 6FLHQWLILF )ROVRP &$f '% P ORQJ PP LG DQ ILOP WKLFNQHVVf FDSLOODU\ FROXPQ LQ WKH VSOLWOHVV PRGH ZLWK KHOLXP FDUULHU JDV DW D IORZ UDWH RI FPV LQOHW SUHVVXUH SVLf 7KH LQLWLDO WHPSHUDWXUH RI r& ZDV KHOG IRU V WKHQ LQFUHDVHG DW r&PLQ WR r& IRU WKH FDOLEUDWLRQ FXUYH DQG SHUFHQW UHFRYHU\ VWXGLHV RI VWDQGDUGV 8ULQH SHUFHQW UHFRYHU\ GDWD ZHUH REWDLQHG ZLWK DQ LQLWLDO WHPSHUDWXUH RI r& KHOG IRU V LQFUHDVHG DW r&PLQ WR r& WKHQ LQFUHDVHG DJDLQ DW r&PLQ WR r& 0DVV VSHFWURPHWU\ FRQGLWLRQV ZHUH LQWHUIDFH DQG WUDQVIHU OLQH WHPSHUDWXUH r& LRQL]HU WHPSHUDWXUH r& HOHFWURQ HQHUJ\ H9 DQG HPLVVLRQ FXUUHQW P$ (OHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f ZDV FDUULHG RXW ZLWK PHWKDQH DW DQ LRQL]HU SUHVVXUH RI WRUU ,Q WKH *&06 SHUFHQW UHFRYHU\ DQG GHULYDWL]DWLRQ VWXGLHV D VSHFLILF LRQ IRU 3*( f >027063)%@ff DQG IRU +3*( >027063)%@nf ZHUH VHOHFWHG DQG PRQLWRUHG WKURXJKRXW WKHVH VWXGLHV 7KH VHOHFWHG LRQ PRQLWRULQJ PRGH 6,0f ZLWK TXDGUXSROH RQH ZDV XVHG RQ WKH PDVV VSHFWURPHWHU $ EDVHOLQH ZDV FKRVHQ YLVXDOO\ RQ WKH *& WUDFH DQG WKH DUHDV IRU 3*( DQG +A3*( FDOFXODWHG E\ WKH ,1&26 FRPSXWHU V\VWHP IRU WKH FDOLEUDWLRQ FXUYH DQG SHUFHQW UHFRYHU\ VDPSOHV 7KH DUHD RI 3*( GLYLGHG E\ WKH DUHD RI +A3*( LQ WKH VWDQGDUGV JLYHV D UDWLR ZKLFK LV XVHG LQ WKH FDOLEUDWLRQ FXUYH 7KH DPRXQW RI 3*( UHFRYHUHG WKURXJK HDFK FROXPQ ZDV

PAGE 51

FDOFXODWHG E\ FRPSDULQJ WKH UDWLR RI WKHVH LRQV DIWHU WKH H[WUDFWLRQ SURFHGXUH WR WKDW RI WKH FDOLEUDWLRQ FXUYH 5HVXOWV DQG 'LVFXVVLRQ 3HUFHQW 5HFRYHU\ 6WXGLHV 6FLQWLOODWLRQ &RXQWLQJf 7DEOH VKRZV WKH SHUFHQW UHFRYHU\ UHVXOWV IRU WKH GLIIHUHQW VRUEHQWV WHVWHG 7KHVH UHFRYHULHV ZHUH GHWHUPLQHG E\ VFLQWLOODWLRQ FRXQWLQJ RI +3*( VWDQGDUGV 7KUHH VDPSOHV ZHUH H[WUDFWHG IRU HDFK VRUEHQW DQG WKH DYHUDJH DQG SHUFHQW UHODWLYH VWDQGDUG GHYLDWLRQ b56'f FDOFXODWHG ([DPLQDWLRQ RI 7DEOH LQGLFDWHV WKDW D ZLGH UDQJH RI UHFRYHULHV ZDV IRXQG IRU WKH GLIIHUHQW VRUEHQWV WHVWHG 7KH QRQSRODU VRUEHQWV LQYHVWLJDWHG ZHUH RFW\O &f RFWDGHF\O &f DQG SKHQ\O 3+f 7KH & FROXPQV KDG WKH KLJKHVW SHUFHQW UHFRYHULHV bf ZLWK WKH & bf DQG WKH 3+ bf FROXPQV KDYLQJ ORZHU UHFRYHULHV 7KHVH ORZ UHFRYHU\ YDOXHV IRU WKH & DQG 3+ FROXPQV VLJQLI\ HLWKHU f 3*( ZDV XQUHWDLQHG DV WKH LQLWLDO VWDQGDUG VROXWLRQ ZDV SDVVHG WKURXJK WKH FROXPQ f 3*( ZDV HOXWHG GXULQJ WKH ZDVK SURFHGXUH RU f 3*( ZDV LUUHYHUVLEO\ ERXQG WR WKH FROXPQ RU QRW HIIHFWLYHO\ HOXWHG 7KH UHDVRQV IRU SRRU UHFRYHU\ ZHUH LQYHVWLJDWHG E\ H[DPLQLQJ DOO WKH HOXHQWV ZKLFK ZHUH SDVVHG WKURXJK WKH UHVSHFWLYH FROXPQV WR GHWHUPLQH WKH SUHVHQFH RI 3*( ,W ZDV GLVFRYHUHG WKDW WKH & DQG 3+ FROXPQV GLG QRW LQLWLDOO\ UHWDLQ 3*( 2FWDGHF\O FROXPQV H[KLELWHG WKH VPDOOHVW YDULDWLRQ IURP FROXPQ WR FROXPQ ZLWK D b56' RI 3RODU VRUEHQWV WHVWHG ZHUH VLOLFD 6,f F\DQRSURS\O &1f DPLQRSURS\O 1+f DQG GLRO +f $V ZLWK WKH QRQSRODU FROXPQV D ZLGH UDQJH RI UHFRYHULHV ZHUH GLVFRYHUHG IRU WKH GLIIHUHQW SRODU LQWHUDFWLRQV WHVWHG

PAGE 52

7DEOH b 5HFRYHU\ RI 6WDQGDUG 3*( E\ 6FLQWLOODWLRQ &RXQWLQJ b 5HFRYHU\ 'DWD &ROXPQ &ROXPQ $YHUDJH b 5HFRYHUY b56'f & 2FW\OfE & 2FWDGHF\Of 3+ 3KHQ\Of 6, 6LOLFDf &1 &\DQRSURS\Of 1+ $PLQRSURS\Of 2+ 'LROf 3%$ 3KHQ\O %RURQLF $FLGf D b 5HODWLYH 6WDQGDUG 'HYLDWLRQ E $OO FROXPQV ZHUH SXUFKDVHG IURP $QDO\WLFKHP

PAGE 53

7KH WZR VRUEHQWV WKDW H[KLELWHG JUHDWHU WKDQ b UHFRYHU\ ZHUH WKH 6, bf DQG + bf 7KH UHFRYHULHV IRU WKHVH FROXPQV ZHUH IRXQG WR EH PXFK KLJKHU WKDQ WKRVH IRXQG IRU &1 bf DQG 1+ bf FROXPQV 7KLV GLIIHUHQFH LQ UHFRYHULHV PD\ EH DWWULEXWHG WR WKH LQWHUDFWLRQ RI WKH SRODU JURXSV RQ 3*( SDUWLFXODUO\ WKH K\GUR[\OVf ZLWK WKH K\GUR[\O JURXSV RQ WKH 6, DQG + UDWKHU WKDQ ZLWK WKH FDUERQQLWURJHQ LQWHUDFWLRQ ZLWK &1 RU WKH DPLQH JURXS ZLWK WKH 1+ ,QYHVWLJDWLRQ RI WKH HOXHQWV VKRZHG WKDW 3*( ZDV QRW HIIHFWLYHO\ UHWDLQHG LQLWLDOO\ IRU WKH &1 DQG 1+ FROXPQV 7KH YDULDWLRQ IURP FROXPQ WR FROXPQ b56'f IRU WKH 6, bf DQG + bf ZHUH OHVV WKDQ WKDW IRXQG IRU &1 bf DQG 1+ bf ,Q DGGLWLRQ SKHQ\O ERURQLF DFLG FROXPQV ZHUH WHVWHG 7KH SHUFHQW UHFRYHU\ IRXQG XVLQJ WKLV W\SH RI LQWHUDFWLRQ ZDV b ZHOO EHORZ WKH UHFRYHU\ YDOXHV IRXQG IRU & 6, DQG + FROXPQV 7KLV H[WUDFWLRQ WHFKQLTXH LV EDVHG RQ WKH SUHPLVH WKDW WKH WHWUDKHGUDO DQLRQLF IRUP RI ERURQDWHV FRQGHQVH ZLWK RU GLROV WR IRUP ILYH RU VL[ PHPEHUHG FRYDOHQW FRPSOH[HV f 7KH ORZ UHFRYHU\ RI 3*( REVHUYHG IRU WKH 3%$ FROXPQ FDQ SRVVLEO\ EH H[SODLQHG E\ WKH LQDELOLW\ RI WKH ERURQDWH WR FRQGHQVH ZLWK WKH GLROV RQ WKH F\FORSHQWDQH ULQJ RI 3*( WR IRUP D VWDEOH FRPSOH[ $Q H[SODQDWLRQ IRU WKH LQDELOLW\ RI 3*V WR FRQGHQVH ZLWK WKH 3%$ FROXPQ ZDV UHSRUWHG E\ /DZVRQ HW DO f 7KH\ EHOLHYH WKDW WKH WHQGHQF\ RI WKH SODQDU SKHQ\O JURXSV WR RULHQW VR WKDW WKHLU SL MWf RUELWDOV DOLJQ RU DUH VWDFNHG WKHUHE\ IRUFLQJ WKH ERURQLF DFLG JURXSV WR EH WRR FORVH WRJHWKHU QRW DOORZLQJ WKH VWHULFDOO\ IL[HG F\FOLF GLROV RQ 3*V IUHH DFFHVV 'DWD REWDLQHG IURP WHVWLQJ WKHVH VRUEHQWV VXJJHVWV WKDW 3*( KDV SUHIHUHQFH IRU UHWHQWLRQ RQ VSHFLILF QRQSRODU &f DQG SRODU 6, DQG

PAGE 54

+f VRUEHQWV (YHQ VRUEHQWV ZLWK WKH VDPH W\SH RI LQWHUDFWLRQV GHPRQVWUDWH YDULHG UHWHQWLRQ IRU 3*( 5HFRYHULHV IRU WKH & 6, DQG + FROXPQV DUH VLPLODU DQG GHPRQVWUDWH DGHTXDWH UHWHQWLRQ !bf RI 3*( WR MXVWLI\ IXUWKHU LQYHVWLJDWLRQ 3HUFHQW 5HFRYHU\ 6WXGLHV *&06f 3HUFHQW UHFRYHU\ GDWD IRU VWDQGDUG 3*( E\ *&06 LV OLVWHG LQ 7DEOH 7KH FROXPQV WHVWHG LQ WKLV VWXG\ ZHUH WKRVH WKDW KDG EHHQ IRXQG WR SURYLGH DGHTXDWH UHWHQWLRQ !bf IRU 3*( LQ WKH SUHYLRXV VFLQWLOODWLRQ FRXQWLQJ H[SHULPHQWV ,Q DGGLWLRQ WKLV VWXG\ VKRZV UHFRYHU\ GDWD IRU DQRWKHU EUDQG RI RFWDGHF\O VRUEHQW 6HS3DNf DQG D YHU\ VHOHFWLYH VRUEHQW XVLQJ DQWLERG\DQWLJHQ LQWHUDFWLRQ LPPXQRDIILQLW\f $V LQ WKH LQLWLDO UHFRYHU\ VWXG\ 7DEOH f WKUHH LQGLYLGXDO FROXPQV ZHUH HDFK XVHG WR H[WUDFW WKUHH VDPSOHV RI VWDQGDUG 3*( 7KUHH LQMHFWLRQV RI HDFK VDPSOH ZHUH PDGH LQWR WKH *&06 7KH DYHUDJH RI WKH WKUHH LQMHFWLRQV DQG WKH WKUHH VDPSOHV LQ DGGLWLRQ WR WKH b56' LV OLVWHG LQ 7DEOH &RPSDULQJ WKH UHFRYHU\ GDWD LQ 7DEOH WR WKH GDWD LQ 7DEOH WKH DYHUDJH UHFRYHU\ YDOXHV IRU WKH & 6, DQG + DUH VLPLODU 7KH YDOXHV GHWHUPLQHG E\ *&06 DUH FRQVLVWHQWO\ b ORZHU WKDQ WKRVH GHWHUPLQHG E\ VFLQWLOODWLRQ FRXQWLQJ +RZHYHU WKLV VOLJKW GLIIHUHQFH FRXOG EH DWWULEXWHG WR WKH EDVLF GLIIHUHQFH LQ FDOFXODWLQJ FRXQWLQJ GDWD DQG DUHDV RI *&06 7KH YDULDWLRQ EHWZHHQ FROXPQV LV DJDLQ VPDOO bf IRU DOO VRUEHQWV WHVWHG 7KH LPPXQRDIILQLW\ FROXPQ GHPRQVWUDWHG D SHUFHQW UHFRYHU\ bf TXLWH DGHTXDWH IRU UHWHQWLRQ RI 3*( 2FWDGHF\O FROXPQV IURP WZR GLIIHUHQW VXSSOLHUV ZHUH FRPSDUHG WR H[DPLQH GLIIHUHQFHV LQ UHWHQWLRQ DQG VHOHFWLYLW\ 7KH UHFRYHU\ GDWD IRU WKH 6HS3DN :DWHUVf

PAGE 55

7DEOH b 5HFRYHU\ RI 6WDQGDUG 3*( E\ *DV &KURPDWRJUDSK\0DVV VSHFWURPHWU\ $YHUDJH b 5HFRYHU\ 'DWD $YHUDJH b 5HFRYHU\ b56'D &ROXPQ &ROXPQ 0 *& ,QLHFWLRQ $ b 5HFRYHUY b56'D RI RI &ROXPQV &ROXPQV ^ 6HS3DN 2FWDGHF\Of & 2FWDGHF\Of ‘3r 6, 6LOLFDf 2+ 'LROf ,$ ,PPXQXQRDIILQLW\f D b 5HODWLYH 6WDQGDUG 'HYLDWLRQ

PAGE 56

FROXPQV ZHUH VOLJKWO\ ORZHU WKDQ WKDW IRXQG IRU WKH & $QDO\WLFKHPf FROXPQV 7KLV PD\ EH DWWULEXWHG WR H[SHULPHQWDO HUURU LQ WKH H[WUDFWLRQ SURFHGXUH KRZHYHU UHSRUWV VXJJHVW WKDW 6HS3DNV KDYH FRQVLGHUDEOH IDXOWV FRPSDUHG WR RFWDGHF\O VRUEHQWV IURP RWKHU PDQXIDFWXUHUV f 7DEOH FRQWDLQV WKH SHUFHQW UHFRYHU\ UHVXOWV RI VWDQGDUG 3*( VSLNHG LQWR XULQH E\ *&06 DQDO\VLV 7KH FROXPQV WHVWHG LQ WKLV VWXG\ ZHUH & 6, + DQG D FRPELQDWLRQ RI & SOXV LPPXQRDIILQLW\ ,$f %LRORJLFDO VDPSOHV FDQ EH GLUHFWO\ DSSOLHG WR WKH ,$ FROXPQ KRZHYHU IRU 3* DQDO\VLV .QDSS DQG 9UEDQDF f KDYH IRXQG DQ DGYDQWDJH LQ SUHFHHGLQJ WKH ,$ SXULILFDWLRQ SURFHGXUH ZLWK D & FROXPQ H[WUDFWLRQ 7KH DGYDQWDJH LV WKDW HPSOR\LQJ WKH & H[WUDFWLRQ ILUVW UHPRYHV ODUJH FRQFHQWUDWLRQV RI H[WUHPHO\ SRODU LPSXULWLHV IRXQG LQ XULQH ZKLFK FDQ QRQVSHFLILFDOO\ ELQG WR WKH ,$ FROXPQ $YHUDJHV DQG b56' DUH OLVWHG LQ WKH WDEOH IRU WKUHH LQMHFWLRQV RI HDFK VDPSOH DQG WKH WKUHH H[WUDFWLRQV ZKLFK ZHUH SHUIRUPHG RQ LQGLYLGXDO FROXPQV 7KH GDWD LQGLFDWH WKDW WKH FROXPQV 6, DQG +f ZKLFK XWLOL]H SRODU LQWHUDFWLRQV DUH QRW HIIHFWLYH IRU UHWHQWLRQ RI 3*( LQ XULQH HYHQ WKRXJK WKH\ ZHUH VXFFHVVIXO IRU 3*( VWDQGDUGV 7KLV LV SUHVXPDEO\ GXH WR FRPSHWLWLRQ IRU ELQGLQJ VLWHV RQ WKH VRUEHQW EHWZHHQ PDWUL[ FRPSRQHQWV LQ WKH XULQH DQG 3*( 7KH QRQSRODU & FROXPQ DQG WKH & FROXPQ FRXSOHG ZLWK WKH ,$ FROXPQ SURYLGHG VLPLODU UHFRYHULHV IRU 3*( LQ XULQH DV LQ VWDQGDUGV 7KH YDULDWLRQ IURP FROXPQ WR FROXPQ LV ORZ IRU DOO FDVHV bf LQFOXGLQJ WKH & DQG ,$ VDPSOHV ,Q WKH FDVH RI WKH ,$ FROXPQ GDWD WKH VDPH VRUEHQW EHG RU FROXPQf ZDV XVHG IRU DOO WKUHH VDPSOHV 7KH b56' IRU WKH WKUHH VDPSOHV LQ DGGLWLRQ WR WKH WKUHH DYHUDJH UHFRYHU\ YDOXHV GHPRQVWUDWH WKH UHXVDELOLW\ RI WKH ,$ VRUEHQW 7KH VOLJKW GHFUHDVH LQ WKH UHFRYHU\ YDOXHV EHWZHHQ VDPSOHV LQGLFDWHV

PAGE 57

7DEOH b 5HFRYHU\ RI 6WDQGDUG 3*( LQ 8ULQH E\ *DV &KURPDWRJUDSK\0DVV 6SHFWURPHWU\ &ROXPQVf &ROXPQ b 5HFRYHU\ 'DWD *& ,QLHFWLRQ b $YHUDJH 5HFRYHUY b56'D b 5HFRYHU\ RI b56'D RI &ROXPQV &ROXPQV & 2FWDGHF\Of 6, 6LOLFDf ‘3n 92 2+ 'LROf & ,$E D b 5HODWLYH 6WDQGDUG 'HYLDWLRQ E 7KUHH GLIIHUHQW & FROXPQV EXW WKH RQO\ RQH ,$ FROXPQ

PAGE 58

WKDW QR FDUU\RYHU RI 3*( RFFXUUHG IURP VDPSOH WR VDPSOH 7KXV WKH ,$ VRUEHQW FDQ EH UHXVHG IRU PDQ\ XULQH VDPSOHV LQ FRPELQDWLRQ ZLWK D & FROXPQ ZLWKRXW ORVV RI DIILQLW\ IRU 3*( 7KH DELOLW\ RI ,$ WR HIIHFWLYHO\ VHSDUDWH XULQH PDWUL[ FRPSRQHQWV IURP 3*( ZLOO EH GLVFXVVHG LQ D ODWHU FKDSWHU 'HULYDWL]DWLRQ 6WXGLHV 7DEOH OLVWV WKH UHVXOWV RI WKH VWXG\ RI GLIIHUHQW GHULYDWL]DWLRQ SURFHGXUHV 7KH *&06 SHDN DUHDV IRU WKUHH VDPSOHV DUH OLVWHG DORQJ ZLWK WKHLU DYHUDJH DQG b56' (DFK VDPSOH LQMHFWHG RQWR WKH *& FROXPQ FRQWDLQHG SJ RI 3*( &RPSDULQJ WKH GLIIHUHQW UHVXOWV WKH PRVW HIIHFWLYH PHWKRG RI GHULYDWL]DWLRQ FDQ EH GHWHUPLQHG 7KH ILUVW PHWKRG OLVWHG IROORZHG WKH GHULYDWL]DWLRQ SURFHGXUH GLVFXVVHG LQ WKH H[SHULPHQWDO VHFWLRQ &RPSDULQJ WKDW PHWKRG WR D VHFRQG PHWKRG LQ ZKLFK D PRUH UDSLG PHWKR[LPDWLRQ DW DQ HOHYDWHG WHPSHUDWXUH KU DW r&f ZDV XVHG WKH SHDN DUHD RI PHWKRG RQH ZDV WLPHV JUHDWHU ZKHQ WKH KRXU PHWKR[LPDWLRQ ZDV HPSOR\HG 7KLV VXJJHVWV WKDW DW ORQJHU UHDFWLRQ WLPHV PRUH FRPSOHWH PHWKR[LPDWLRQ RFFXUV 5HFHQWO\ D VWXG\ RI WKH PHWKR[LPDWLRQ RI YDULRXV 3*V ZDV UHSRUWHG LQ WKH OLWHUDWXUH f 7KHVH UHVXOWV VKRZHG WKDW HIILFLHQW PHWKR[LPDWLRQ RI 3*( E\ D SURFHGXUH VLPLODU WR PHWKRG RQH ZDV WLPHV JUHDWHU WKDQ PHWKRG WZR ZLWK D b56' RI b 7KLV FRUUHVSRQGV WR WKH YDOXHV ZKLFK ZHUH REWDLQHG LQ WKLV VWXG\ $QRWKHU TXHVWLRQ DGGUHVVHG E\ WKLV VWXG\ LV ZKHWKHU WR SHUIRUP WKH PHWKR[LPDWLRQ VWHS EHIRUH RU DIWHU WKH 3)% HVWHULILFDWLRQ ([DPLQLQJ WKH SHDN DUHDV REWDLQHG IRU PHWKRG WKUHH DQG FRPSDULQJ WKHP WR PHWKRG RQH VLPLODU DUHDV ZHUH FDOFXODWHG IRU SJ 7KH GDWD VXJJHVW WKDW HLWKHU

PAGE 59

7DEOH 6WXG\ RI 'LIIHUHQW 'HULYDWL]DWLRQ 3URFHGXUHV IRU 3*( E\ *&06 ZLWK 6,0 IRU WKH >03)%@f LRQ 3HDN $UHD RI 3*( FRXQWVf 0HWKRG 6DPSOH 6DPOH 6DPSOH $YHUDJH b56'n OE [ [ ; ; & [ [ ; ; G [ [ ; ; H [ [ ; ; I [ [ ; ; D b 5HODWLYH 6WDQGDUG 'HYLDWLRQ E 3URFHGXUH GHVFULEHG RQ SDJH F 0HWKR[LPDWLRQ IRU KU DW r& G (VWHULILFDWLRQ SHUIRUPHG EHIRUH PHWKR[LPDWLRQ H 1LWURJHQ HYDSRUDWLRQ RQO\ DIWHU WKH PHWKR[LPDWLRQ VWHS I 1LWURJHQ HYDSRUDWLRQ SHUIRUPHG DIWHU DOO VWHSV QR OLTXLGOLTXLG H[WUDFWLRQ ZDV SHUIRUPHGf

PAGE 60

VWHS PHWKR[LPDWLRQ RU WKH 3)% HVWHULILFDWLRQf FDQ EH SHUIRUPHG ILUVW 7KH RWKHU TXHVWLRQ SURSRVHG LQ WKLV VWXG\ ZDV WKH XVH RI OLTXLGOLTXLG H[WUDFWLRQ WR UHPRYH H[FHVV GHULYDWL]LQJ UHDJHQWV RU WKH VLPSOHU PRUH UDSLG PHWKRG RI RQO\ QLWURJHQ HYDSRUDWLRQ 7ZR PHWKRGV ZHUH VWXGLHG RQH LQ ZKLFK RQO\ QLWURJHQ HYDSRUDWLRQ ZDV SHUIRUPHG DIWHU WKH PHWKR[LPDWLRQ VWHS WKHQ OLTXLGOLTXLG H[WUDFWLRQ DIWHU WKH HVWHULILFDWLRQ PHWKRG f DQG WKH RWKHU LQ ZKLFK RQO\ QLWURJHQ HYDSRUDWLRQ ZDV SHUIRUPHG DIWHU DOO GHULYDWL]DWLRQ VWHSV PHWKRG f &RPSDULQJ WKHVH WZR PHWKRGV ZLWK PHWKRG RQH WKH DUHDV IRU SJ IRU ERWK PHWKRG IRXU DQG ILYH ZHUH DSSUR[LPDWHO\ b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

PAGE 61

HIIHFW RQ WKH DUHD FDOFXODWHG IRU 3*( 5HVXOWV IURP WKLV VWXG\ GHPRQVWUDWH WKH DGYDQWDJH RI XVLQJ OLTXLGOLTXLG H[WUDFWLRQ PHWKRGV WR UHPRYH WKH H[FHVV GHULYDWL]DWLRQ UHDJHQWV DIWHU HDFK VWHS LQ WKH GHULYDWL]DWLRQ SURFHGXUH

PAGE 62

&+$37(5 237,0,=$7,21 2) *&06 $1' *&0606 &21',7,216 )25 75$&( '(7(50,1$7,21 2) 35267$*/$1',16 ,QWURGXFWLRQ 0DQ\ UHSRUWV RI *&06 DQDO\VLV RI SURVWDJODQGLQV 3*Vf FDQ EH IRXQG LQ WKH OLWHUDWXUH f 7KH FRQGLWLRQV HPSOR\HG LQ HDFK FDVH YDU\ GHSHQGLQJ RQ WKH W\SH RI DQDO\VLV TXDOLWDWLYH RU TXDQWLWDWLYHf VDPSOH PDWUL[ XULQH VHUXP HWFf DQG WDUJHWHG FRQFHQWUDWLRQ ,Q WKH WUDFH GHWHUPLQDWLRQ RI 3*V RSWLPL]DWLRQ RI FRQGLWLRQV LV FULWLFDO 'HWHFWLRQ RI ORZ OHYHOV RI 3*V SJP/f LQ XULQH UHTXLUHV D WHFKQLTXH WKDW LV ERWK VHQVLWLYH DQG VHOHFWLYH 7KH PDQ\ SDUDPHWHUV ZKLFK H[LVW LQ *&06 DQG *&0606 FDQ EH YDULHG DFFRUGLQJ WR WKH DQDO\VLV WR HQKDQFH HLWKHU VHQVLWLYLW\ RU VHOHFWLYLW\ 7KXV WR DFKLHYH WKH SURSHU FRQGLWLRQV IRU WUDFH GHWHUPLQDWLRQ RI 3*V WKH YDULRXV SDUDPHWHUV PXVW EH FKDUDFWHUL]HG DQG RSWLPL]HG ([SHULPHQWDO 3URVWDJODQGLQV DQG 5HDJHQWV $OO VROYHQWV ZHUH UHDJHQW RU +3/& JUDGH 3URVWDJODQGLQ ( 3*(f DQG SURVWDJODQGLQ )D 3*)Df ZDV SXUFKDVHG IURP 6LJPD &KHPLFDO &R 6W /RXLV 02f 7KH GHULYDWL]DWLRQ UHDJHQWV S\ULGLQH 2PHWK\OK\GUR[\ODPLQH K\GURFKORULGH DFHWRQLWULOH DQG 11GLLVRSURS\OHWK\O DPLQH ZHUH DOO

PAGE 63

SXUFKDVHG IURP 6LJPD &KHPLFDO &R 3HQWDIOXRUREHQ]\OEURPLGH 3)%%Uf DQG ELVWULPHWK\OVLO\OfWULIOXRURDFHWDPLGH %67)$f ZHUH SXUFKDVHG IURP 3LHUFH &KHPLFDO &R 5RFNIRUG ,/f $OO JODVVZDUH ZDV VLODQL]HG ZLWK D VROXWLRQ RI b GLPHWK\OGLFKORURVLODQH LQ WROXHQH 7KHVH WZR FKHPLFDOV ZHUH ERWK SXUFKDVHG IURP 6LJPD &KHPLFDO &R +HOLXP XVHG DV *& FDUULHU JDV PHWKDQH !bf DV FKHPLFDO LRQL]DWLRQ UHDJHQW JDV DQG QLWURJHQ DUJRQ DQG [HQRQ XVHG DV FROOLVLRQ JDVHV ZHUH IURP 0DWKHVRQ *DV 3URGXFWV ,QF 2UODQGR )/f 'HULYDWL]DWLRQ 7KH 023)%706 GHULYDWLYH RI 3*( DQG WKH 3)%706 GHULYDWLYH RI 3*)ZHUH SUHSDUHG E\ WKH VDPH SURFHGXUH DV LQ &KDSWHU ,QVWUXPHQWDO &RQGLWLRQV $ )LQQLJDQ 0$7 WULSOH VWDJH TXDGUXSROH 764f JDV FKURPDWRJUDSK PDVV VSHFWURPHWHU ZDV HPSOR\HG 0DVV VSHFWURPHWU\ FRQGLWLRQV ZHUH LQWHUIDFH DQG WUDQVIHU OLQH WHPSHUDWXUH r& LRQL]HU WHPSHUDWXUH r& HOHFWURQ HQHUJ\ H9 DQG HPLVVLRQ FXUUHQW P$ *& ZDV FDUULHG RXW RQ D VKRUW -t: 6FLHQWLILF )ROVRP &$f '% P ORQJ PP LG LP ILOP WKLFNQHVVf FDSLOODU\ FROXPQ LQ WKH VSOLWOHVV PRGH ZLWK KHOLXP FDUULHU JDV DW DQ LQOHW SUHVVXUH RI SVL 7KH LQLWLDO WHPSHUDWXUH RI r& ZDV KHOG IRU V WKHQ LQFUHDVHG DW r&PLQ WR r& 7KH LQMHFWRU WHPSHUDWXUH ZDV r& %RWK IXOO VFDQ PDVV VSHFWUD DQG VHOHFWHGLRQ PRQLWRULQJ 6,0f ZHUH XVHG LQ WKH *&06 VWXGLHV $Q HOHFWURQ PXOWLSOLHU (0f VHWWLQJ RI 9 ZDV XVHG IRU WKH IXOO VFDQ VSHFWUD DQG D SUHDPS JDLQ RI n $9 $ EDVHOLQH ZDV FKRVHQ YLVXDOO\ RQ WKH *& WUDFH DQG WKH DUHD IRU 3*( rf

PAGE 64

DQG 3*)D ff FDOFXODWHG E\ WKH ,1&26 FRPSXWHU V\VWHP LQ WKH 6,0 PRGH RI RSHUDWLRQ ,Q *&0606 RSWLPL]DWLRQ VWXGLHV IXOO GDXJKWHU VSHFWUD DQG VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f ZHUH HPSOR\HG DQG DUHDV FDOFXODWHG E\ WKH VDPH PHWKRG DV GHVFULEHG IRU *&06 7KH (0 ZDV VHW DW 9 IRU WKH IXOO GDXJKWHU VSHFWUD REWDLQHG DQG D SUHDPS JDLQ RI 9$ ,Q WKH *&0606 RSWLPL]DWLRQ WKH >03)%@n FDUER[\ODWH DQLRQV RI 3*( DQG 3*)D ZHUH VHOHFWHG LQ WKH ILUVW TXDGUXSROH 4Of UHJLRQ DQG SDVVHG LQWR WKH FROOLVLRQ FHOO 4f ,Q WKLV UHJLRQ WKHVH LRQV XQGHUZHQW &$' WR IRUP FKDUDFWHULVWLF IUDJPHQWV ZKLFK ZHUH WKHQ PDVV DQDO\]HG LQ WKH WKLUG TXDGUXSROH 4f $ IXOO GDXJKWHU VSHFWUXP ZDV DFTXLUHG RYHU WKH PDVV UDQJH RI DPX &DOLEUDWLRQ FXUYHV ZHUH SUHSDUHG IRU ERWK *&06 DQG *&0606 DIWHU RSWLPL]DWLRQ RI WKH YDULRXV SDUDPHWHUV 6HOHFWHGLRQ PRQLWRULQJ DQG VHOHFWHGUHDFWLRQ PRQLWRULQJ ZHUH XVHG WR GHWHUPLQH OLQHDULW\ SUHFLVLRQ DQG OLPLWV RI GHWHFWLRQ IRU VWDQGDUG 3*( XWLOL]LQJ *&06 DQG *&0606 7KH (0 ZDV VHW DW 9 IRU ERWK WKH 6,0 DQG 650 FDOLEUDWLRQ FXUYH GDWD 4 ZLWK D SUHDPS JDLQ RI 9$ 0DVV 6SHFWURPHWU\ *&06f &KRLFH RI WKH DSSURSULDWH LRQL]DWLRQ PHWKRG LV HVVHQWLDO IRU WUDFH GHWHUPLQDWLRQ RI 3*V E\ *&06 (OHFWURQ LRQL]DWLRQ (Of KDV EHHQ UHSRUWHG LQ WKH GHWHUPLQDWLRQ DQG LGHQWLILFDWLRQ RI YDULRXV 3*V f 6WUXFWXUDO LQIRUPDWLRQ LV REWDLQHG E\ WKLV WHFKQLTXH GXH WR WKH DEXQGDQFH RI IUDJPHQW LRQV ZKLFK DUH SURGXFHG +RZHYHU LQ WUDFH DQDO\VLV RI 3*V WKH FUHDWLRQ RI D VLQJOH LRQ ZLWK D PD[LPL]HG LQWHQVLW\ LV SUHIHUUHG

PAGE 65

&KHPLFDO LRQL]DWLRQ &Of KDV WKH DGYDQWDJH RI XVXDOO\ SURGXFLQJ IHZ IUDJPHQW LRQV DQG D YHU\ LQWHQVH PROHFXODU LRQ 0DQ\ UHSRUWV RI FKHPLFDO LRQL]DWLRQ *&06 IRU 3* DQDO\VLV DSSHDU LQ WKH OLWHUDWXUH f %RWK SRVLWLYH DQG QHJDWLYH &O KDYH EHHQ LQFRUSRUDWHG IRU 3* DQDO\VLV 7KH OLWHUDWXUH UHSRUWV WKDW DSSURSULDWH GHULYDWL]DWLRQ RI 3*V FRXSOHG ZLWK HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f UHVXOWV LQ WKH GHWHFWLRQ RI ORZ OHYHOV RI 3*V f 7KHVH UHSRUWV JHQHUDOO\ HPSOR\ PHWKDQH &+Af DV D UHDJHQW JDV IRU LWV DELOLW\ WR WKHUPDOL]H HOHFWURQV 7KXV ERWK WKH *&06 DQG *&0606 RSWLPL]DWLRQ VWXGLHV KDYH XWLOL]HG (& 1&, ZLWK PHWKDQH DV WKH UHDJHQW JDV ,RQL]HU 3UHVVXUH 6WXG\ $OWKRXJK WKH OLWHUDWXUH LQFOXGHV QXPHURXV H[DPSOHV RI PHWKDQH DV D UHDJHQW JDV IRU (&1&, PDQ\ GUDPDWLFDOO\ GLIIHUHQW LRQ VRXUFH SUHVVXUHV KDYH EHHQ HPSOR\HG 7KLV VWXG\ ZDV SHUIRUPHG WR GHWHUPLQH WKH RSWLPXP LRQL]HU SUHVVXUH DW ZKLFK WKH >03)%@n LRQV RI 3*( DQG 3*)D DUH SURGXFHG LQ WKH LRQ VRXUFH )LJXUH VKRZV WKH DYHUDJH DUHDV GHWHUPLQHG DW GLIIHUHQW LRQL]HU SUHVVXUHV RI PHWKDQH IRU WKH n LRQ 3*(f DQG LRQ 3*)Df f 7KH DYHUDJH RI WKUHH RQHPLFUROLWHU LQMHFWLRQV RI D SJ/ VROXWLRQ RI ERWK 3*( DQG 3*)D KDYH EHHQ SORWWHG RQ WKH JUDSK 7KH RSWLPXP LRQ VRXUFH SUHVVXUH IRU 3*( DQG 3*)D RFFXUV DW 7RUU RI PHWKDQH $W LRQL]HU SUHVVXUHV ORZHU WKDQ 7RUU WKH >03)%@n LRQ KDV D ORZHU SHUFHQW UHODWLYH LQWHQVLW\ FRPSDUHG WR WKH UHFRQVWUXFWHG LRQ FXUUHQW 5,&f IRU ERWK 3*( DQG 3*)D $V WKH LRQ VRXUFH SUHVVXUH LV JUDGXDOO\ LQFUHDVHG DERYH 7RUU IUDJPHQW LRQV EHJLQ WR LQFUHDVH LQ UHODWLYH

PAGE 66

$YHUDJH $UHD r r FRXQWVf T XVR U LR a a W O L L L L L L L L L L L L f LWaUW ‘ L WaI O OnL7nW > , Lf L L L L L L L L L L O ,RQ 6RXUFH 3UHVVXUH f 7RUUf ILJXUH L ,RQ VRXUFH SUHVVXUH VWXG\ RI WKH >03I%@n ,RQ RI 3*IF DQG 32)A

PAGE 67

LQWHQVLW\ DQG FRQWULEXWH PRUH WR WKH 5,& WKXV GHFUHDVLQJ WKH UHODWLYH LQWHQVLW\ RI WKH >03)%@f LRQ FRPSDUHG WR WKH 5,& ,RQL]HU 7HPSHUDWXUH 6WXG\ 5HSRUWV LQ WKH OLWHUDWXUH KDYH FLWHG LRQ VRXUFH WHPSHUDWXUHV IRU (&1&,*&06 DQG (&1&,*&0606 LQ WKH UDQJH RI r& WR r& f )LJXUH LQGLFDWHV WKH RSWLPXP LRQ VRXUFH WHPSHUDWXUH REVHUYHG LQ WKLV VWXG\ IRU WKH DQDO\VLV RI 3*( DQG 3*)D 6HOHFWHGLRQ PRQLWRULQJ 6,0f RI WKH n 3*(f DQG LRQ 3*)Df ZDV XVHG RYHU D UDQJH RI LRQ VRXUFH WHPSHUDWXUHV IURP r& WR r& 7KUHH RQHPLFUROLWHU LQMHFWLRQV RI D SJL/ VROXWLRQ RI 3*( DQG 3*)D ZHUH SHUIRUPHG DW WHQ GLIIHUHQW LRQ VRXUFH WHPSHUDWXUHV 7KH DYHUDJH RI WKH WKUHH LQMHFWLRQV LV SORWWHG RQ WKH JUDSK %RWK 3*( DQG 3*)D KDYH DQ RSWLPXP LRQ VRXUFH WHPSHUDWXUH DW r& 7KXV WKH >03)%@fFDUER[\ODWH DQLRQ RI 3*( DQG 3*)D RSWLPL]H DW WKH PD[LPXP LRQ VRXUFH WHPSHUDWXUH RI WKH LQVWUXPHQW 7KH SHUFHQW UHODWLYH LQWHQVLW\ RI WKH >03)%@n LRQ FRPSDUHG WR WKH 5,& LQFUHDVHV ZLWK DQ LQFUHDVH LQ WKH LRQ VRXUFH WHPSHUDWXUH DQG UHDFKHV D PD[LPXP DW r& ,Q DGGLWLRQ IUDJPHQW LRQV LQFUHDVH DV WKH WHPSHUDWXUH LV HOHYDWHG WR DERXW r& WR r& WKHQ WKHVH IUDJPHQWV JUDGXDOO\ GHFUHDVH DV WKH LRQ VRXUFH WHPSHUDWXUH LV UDLVHG DERYH r& 7KHVH WZR REVHUYDWLRQV OHDG WR WKH RSWLPXP LRQ VRXUFH WHPSHUDWXUH RI r& IRU WKH >03)%@n LRQ (OHFWURQ&DSWXUH 1HJDWLYH &KHPLFDO ,RQL]DWLRQ 0DVV 6SHFWUD 7KH PDVV VSHFWUD RI VWDQGDUG 3*( DQG 3*)D REWDLQHG DW WKH RSWLPXP LRQ VRXUFH SUHVVXUH DQG WHPSHUDWXUH DUH VKRZQ LQ )LJXUH D DQG )LJXUH E %RWK VSHFWUD GHPRQVWUDWH WKH DGYDQWDJH RI HPSOR\LQJ (&1&, IRU

PAGE 68

$YHUDJH $UHD r FRXQWVf ,RQ 6RXUFH 7HPSHUDWXUH &f )LJXUH ,RQ VRXUFH WHPSHUDWXUH VWXG\ RI WKH >03)%@ LRQ RI 3*( 21 R DQG 3*)

PAGE 69

b 5HODWLYH $EXQGDQFH )LJXUH (OHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ PDVV VSHFWUD RI Df 3*( 023)%706 GHULYDWLYH Ef 3*)A 3)%706 GHULYDWLYH

PAGE 70

SURVWDJODQGLQ DQDO\VLV 2QH LQWHQVH SHDN WKH >03)%@n LRQ GRPLQDWHV HDFK PDVV VSHFWUXP 7KLV LRQ 3*( ff DQG 3*)D rf FDQ EH XWLOL]HG IRU 6,0 2WKHU ORZ LQWHQVLW\ IUDJPHQW LRQV FDQ EH VHHQ LQ WKH PDVV VSHFWUXP RI 3*( FRUUHVSRQGLQJ WR WKH ORVV RI GHULYDWLYHV DWWDFKHG WR 3*( ,Q DGGLWLRQ QR IUDJPHQWV RI JUHDWHU WKDQ b UHODWLYH DEXQGDQFH DUH REVHUYHG LQ WKH PDVV VSHFWUXP RI 3*)W 7KH 0f LRQ IRU ERWK 3*( P] f DQG 3*)D P] f LV UDUHO\ SUHVHQW LQ WKH (&1&, PDVV VSHFWUD WKXV LW PXVW EH OHVV WKDQ b UHODWLYH DEXQGDQFH ,Q DGGLWLRQ WKH 3)%r LRQ P] f RFFXUV LQ WKH (& 1&, PDVV VSHFWUD RI ERWK 3*V DW OHVV WKDQ b DEXQGDQFH 6HOHFWHG,RQ 0RQLWRULQJ &DOLEUDWLRQ &XUYH $ FDOLEUDWLRQ FXUYH IRU 3*( ff LV VKRZQ LQ )LJXUH 7KLV FXUYH LQGLFDWHV WKH OLQHDULW\ DQG OLPLW RI GHWHFWLRQ IRU 3*( ZLWK 6,0 7KUHH RQHPLFUROLWHU LQMHFWLRQV DW QLQH GLIIHUHQW FRQFHQWUDWLRQV ZHUH SHUIRUPHG 7KH OLPLW RI GHWHFWLRQ ZDV FDOFXODWHG IURP WKH FDOLEUDWLRQ GDWD DQG FRUUHVSRQGHG WR WKH DPRXQW RI 3*( ZKLFK FRXOG JLYH D *& SHDN DUHD WKUHH WLPHV JUHDWHU WKDQ WKH DYHUDJH DUHD REWDLQHG ZLWK D GHULYDWL]HG EODQN 7KH XVH RI 6,0 ZLWK VWDQGDUG 3*( SURGXFHG D OLPLW RI GHWHFWLRQ RI DSSUR[LPDWHO\ IJ IHPWRJUDPVf DQG LV LQGLFDWHG RQ WKH FXUYH 7KH FDOLEUDWLRQ FXUYH VKRZHG JRRG OLQHDULW\ DERYH WKH OLPLW RI GHWHFWLRQ LQ WKH UDQJH RI FRQFHQWUDWLRQV H[SHFWHG IRU HQGRJHQRXV 3*( LQ XULQH WR SJP/f f 7KH OLQHDU G\QDPLF UDQJH RI WKH FXUYH LV IURP IJ WR QJ VROLG OLQHf DQG WKH VORSH RI WKH OLQHDU UHJUHVVLRQ EHVW ILW OLQH LV ZLWK D FRUUHODWLRQ FRHIILFLHQW RI 7KH QRQOLQHDULW\ DW WKH ORZ HQG RI WKH FDOLEUDWLRQ FXUYH PD\ EH GXH WR DGVRUSWLRQ RQ WKH

PAGE 71

R R &' 3*( &RQFHQWUDWLRQ Jf DV X! )LJXUH 6HOHFWHGLRQ PRQLWRULQJ FDOLEUDWLRQ FXUYH IRU WKH >03)%@f LRQ RI WKH 023)%706 GHULYDWLYH RI 3*(

PAGE 72

FROXPQ VHSWXP RU LQMHFWLRQ SRUW DQG VXEVHTXHQW DGVRUSWLRQ E\ WKH QH[W LQMHFWLRQ 3UHFLVLRQ RI WKH *&06 PHWKRG XWLOL]LQJ 6,0 ZDV GHWHUPLQHG E\ SHUIRUPLQJ WHQ RQHPLFUROLWHU LQMHFWLRQV RI D SJL/ VROXWLRQ RI 3*( 7KH SHUFHQW UHODWLYH VWDQGDUG GHYLDWLRQ b56'f RI WKH WHQ LQMHFWLRQV ZDV b &DOLEUDWLRQ FXUYHV IRU 3*)D 3*' DQG '+.)D ZHUH VLPLODU ZLWK YDU\LQJ OLPLWV RI GHWHFWLRQ LQ WKH UDQJH RI WR IJ 7KH UHVXOWV IRU WKLV VWXG\ DJUHH ZHOO ZLWK WKH OLWHUDWXUH 5HSRUWV KDYH VKRZQ /2'V XVLQJ (,06 DW DERXW SJ IRU WKH 0f f DQG XWLOL]LQJ (&1&,06 DERXW IJ f IRU WKH >03)%@n LRQ 7DQGHP 0DVV 6SHFWURPHWU\ *&0606nf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f ZDV RSWLPL]HG WR GHWHUPLQH ZKLFK FROOLVLRQ JDV DQG SUHVVXUH ZHUH WKH PRVW HIILFLHQW IRU VHOHFWHGUHDFWLRQ PRQLWRULQJ DW WKH PD[LPXP DYDLODEOH FROOLVLRQ HQHUJ\ RI H9 3UHVVXUHUHVROYHG EUHDNGRZQ FXUYHV IRU VHOHFWHG LRQV RI WKH 023)%706 GHULYDWLYH RI 3*( DUH VKRZQ LQ )LJXUHV

PAGE 73

Df &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ H9 RRR4R 63 OD n n$-! n n f n f &ROOLVLRQ *DV 3UHVVXUH UQ7RUUf Ef &/ &O Z DL O2SWLPXP $U &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ H ? V ? 22224 } R ’ R R ’ r $t$$$ } f } f &ROOLVLRQ *DV 3UHVVXUH UQ7RUU $Uf Ff HH &/ W D 4 : 2SWLPXP ;H &ROOLVLRQ *DV ? &ROOLVLRQ (QHUJ\ f§ H9 44444 L ’ ’ DRD $ $ $ $ $ fr ‘ ; 2f c L -2 &ROOLVLRQ *DV 3UHVVXUH UQ7RUUf )LJXUH 3UHVVXUHUHVROYHG EUHDNGRZQ FXUYH RI WKH FDUER[\ODWH DQLRQ RI WKH 023)%706 GHULYDWLYH RI 3*( ZLWK FROOLVLRQ JDV Df 1LWURJHQ Ef $UJRQ Ff ;HQRQ

PAGE 74

Df Ef $U &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ f§ H9 RRRRR n ’ ’’’’ r n $$$$ n f &ROOLVLRQ *DV 3UHVVXUH P7RUUf Ff 2SWLPXP ;H &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ f§ H9 RRRRR n} n 2''' $2} n n n &ROOLVLRQ *DV 3UHVVXUH P7RUUf )LJXUH 3UHVVXUHUHVROYHG EUHDNGRZQ FXUYH RI WKH FDUER[\ODWH DQLRQ RI WKH 3)%706 GHULYDWLYH RI 3*)A ZLWK FROOLVLRQ JDV Df 1LWURJHQ Ef $UJRQ Ff ;HQRQ

PAGE 75

D E DQG F DQG IRU WKH 3)%706 GHULYDWLYH RI 3*)D LQ )LJXUHV D E DQG F 7KH RSWLPXP FROOLVLRQ JDV SUHVVXUH LV LQGLFDWHG RQ HDFK FXUYH 7KLV W\SH RI FXUYH FDQ EH FDOFXODWHG E\ GLYLGLQJ WKH DUHD RI D VHOHFWHG GDXJKWHU LRQ E\ WKH DUHD RI DOO WKH LRQV LQ WKH GDXJKWHU VSHFWUXP '\I'M 3@f DW HDFK SUHVVXUH 7KH SRLQW ZKLFK LV FKRVHQ DV WKH RSWLPXP LV WKH SUHVVXUH ZKHUH RQH FDQ REWDLQ D TXDOLWDWLYH GDXJKWHU VSHFWUXP ZKLFK LV ULFK LQ VWUXFWXUDO LQIRUPDWLRQ ZLWK D QXPEHU RI UHDVRQDEO\ DEXQGDQW GDXJKWHU LRQV 7KH RSWLPD LQGLFDWHG RQ )LJXUHV D E DQG F RFFXU DW D FROOLVLRQ SUHVVXUH RI DQG P7RUU IRU 1 $U DQG ;H UHVSHFWLYHO\ +RZHYHU LQ WKH FDVH RI 3*)D WKH RSWLPD RFFXU DW VLJQLILFDQWO\ KLJKHU SUHVVXUHV DQG P7RUU IRU 1 $U DQG ;H )LJXUHV D E DQG Ff &RPSDULQJ )LJXUH D WR D WKH RSWLPDO XVH RI QLWURJHQ DV D FROOLVLRQ JDV UHTXLUHV D SUHVVXUH ILYH WLPHV KLJKHU IRU 3*)D WKDQ IRU 3*( 7KLV GUDPDWLF GLIIHUHQFH LQ RSWLPXP FROOLVLRQ SUHVVXUH H[LVWV EHWZHHQ WZR VWUXFWXUDOO\ VLPLODU 3*V 7KH UHODWLYH GLIIHUHQFHV LQ WKH RSWLPXP FROOLVLRQ JDV SUHVVXUH IRU 3*)D ZLWK WKH YDULRXV FROOLVLRQ JDVHV FDQ EH H[SODLQHG E\ WKH UHODWLYH PDVV RI WKH WKUHH GLIIHUHQW FROOLVLRQ JDVHV 7KH JUHDWHU VL]H RI WKH DUJRQ DQG [HQRQ JDV PROHFXOHV LQFUHDVHV WKH HQHUJ\ GHSRVLWHG LQWR WKH SDUHQW LRQ WKHUHIRUH LQFUHDVLQJ WKH IUDJPHQWDWLRQ HIILFLHQF\ 7KHUHIRUH WKH RSWLPXP FROOLVLRQ SUHVVXUH GHFUHDVHV ZLWK DQ LQFUHDVH LQ WKH PDVV RI WKH JDV PROHFXOHV EHFDXVH WKH DEXQGDQFH RI WKH PRVW SURPLQHQW IUDJPHQW LRQV RFFXU DW ORZHU SUHVVXUHV 1RWLFH WKH VLJQLILFDQW GLIIHUHQFHV LQ WKH PD[LPXP UHODWLYH LQWHQVLW\ RI WKH GDXJKWHU LRQV IRU WKH WKUHH FROOLVLRQ JDVHV 7KH FXUYHV ZLWK

PAGE 76

QLWURJHQ )LJXUHV D DQG Df VKRZ D KLJKHU PD[LPXP UHODWLYH LQWHQVLW\ IRU WKH VHOHFWHG UHDFWLRQV OLVWHG )LJXUH F IRU 3*)XWLOL]LQJ [HQRQ DV WKH FROOLVLRQ JDV LV SDUWLFXODUO\ LQWHUHVWLQJ 7KH UHODWLYH LQWHQVLW\ RI WKH GDXJKWHU LRQV VHOHFWHG DUH WLPHV ORZHU WKDQ WKH LQWHQVLW\ RI WKH VDPH GDXJKWHU LRQV GLVSOD\HG LQ )LJXUH D IRU QLWURJHQ ,Q DGGLWLRQ WKH UHODWLYH LQWHQVLW\ RI WKH GDXJKWHU LRQV DSSURDFK ]HUR DW KLJKHU FROOLVLRQ JDV SUHVVXUHV P7RUUf 7KXV HLWKHU WKH SDUHQW LRQ FDUER[\ODWH DQLRQf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f rf n FRUUHVSRQGLQJ WR D EDFNERQH IUDJPHQWDWLRQ $ JHQHUDO WUHQG DSSHDUV LQ DOO WKH ILJXUHV IRU ERWK 3*( DQG 3*)7KH ORVV RI RQH DQG WZR +2706 JURXSV IURP WKH >03)%@f LRQ WHQG WR PD[LPL]H WRJHWKHU DW ORZ FROOLVLRQ JDV SUHVVXUHV IRU WKH WKUHH FROOLVLRQ JDVHV 6XEVHTXHQWO\ WKHVH VHOHFWHGUHDFWLRQV JUDGXDOO\ GHFUHDVH WRZDUGV ]HUR DW KLJKHU FROOLVLRQ JDV SUHVVXUHV 7KH IRXU VHOHFWHGUHDFWLRQV IRU 3*( LQ

PAGE 77

Df Ef RR f§ 2SWLPXP ;H &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ f§ H9 RRRRR } n ’ ’’’’ $ $ $ $ $ n W U W W UP L L L L L P L Q L US r W 7_ &ROOLVLRQ *DV 3UHVVXUH P7RUUf )LJXUH 3UHVVXUHUHVROYHG EUHDNGRZQ FXUYH RI WKH FDUER[\ODWH DQLRQ RI WKH 3)%706 GHULYDWLYH RI 3*)A ZLWK FROOLVLRQ JDV Df 1LWURJHQ Ef $UJRQ

PAGE 78

)LJXUH DOO LQFUHDVH DW ORZ FROOLVLRQ JDV SUHVVXUHV DQG WKHQ JUDGXDOO\ GHFUHDVH DV KLJKHU FROOLVLRQ JDV SUHVVXUHV DUH HPSOR\HG ,Q WKH FDVH RI 3*)D WKH DGGLWLRQDO ORVV RI WKH WKLUG +2706 JURXS r‘ f JUDGXDOO\ LQFUHDVHV ZKHQ QLWURJHQ LV XWLOL]HG )LJXUH Df RU OHYHOV RII ZKHQ DUJRQ )LJXUH Ef LV HPSOR\HG DV WKH FROOLVLRQ JDV SUHVVXUH LV FRQWLQXDOO\ LQFUHDVHG ,Q )LJXUH WKH VHOHFWHGUHDFWLRQV KDYH UHODWLYHO\ ORZ LQWHQVLWLHV DW ORZ FROOLVLRQ JDV SUHVVXUHV P7RUUf EXW LQFUHDVH JUDGXDOO\ DQG OHYHO RII DV WKH FROOLVLRQ JDV SUHVVXUH LV LQFUHDVHG P7RUUf 7UDFH DQDO\VLV E\ VHOHFWHGUHDFWLRQ PRQLWRULQJ ZLWK 0606 UHTXLUHV RSWLPL]DWLRQ RI WKH DEVROXWH LQWHQVLW\ RI D VLQJOH GDXJKWHU LRQ RI WKH VHOHFWHG SDUHQW LRQ 7KH FXUYHV LQ )LJXUHV DQG JLYH DQ LQGLFDWLRQ RI WKH RSWLPXP UHDFWLRQV DQG FROOLVLRQ JDV SUHVVXUHV ZKLFK VKRXOG EH VHOHFWHG IRU PD[LPXP 650 VHQVLWLYLW\ IRU 3*( DQG 3*)D ZLWK WKUHH GLIIHUHQW FROOLVLRQ JDVHV DW PD[LPXP FROOLVLRQ HQHUJ\ H9f 7KLV W\SH RI FXUYH LV FDOFXODWHG E\ GLYLGLQJ WKH DUHD RI VHOHFWHG GDXJKWHU LRQV 'M E\ WKH DUHD RI WKH LQFLGHQW SDUHQW LRQ 34 PHDVXUHG LQ D GDXJKWHU VSHFWUXP ZLWKRXW FROOLVLRQ JDVf 7KH UHDFWLRQ ZLWK WKH KLJKHVW &$' HIILFLHQF\ VKRXOG EH VHOHFWHG WR \LHOG WKH KLJKHVW VHQVLWLYLW\ IRU VHOHFWHG UHDFWLRQ PRQLWRULQJ 650f WUDFH GHWHUPLQDWLRQ RI 3*V )RU H[DPSOH LQ WKH FDVH RI 3*)D FKRLFH RI WKH r‘ f VHOHFWHG UHDFWLRQ ZLWK DUJRQ )LJXUH Ef ZRXOG EH WKH RSWLPXP RYHUDOO HIILFLHQF\ RI bf DW D FROOLVLRQ SUHVVXUH RI PWRUU DQG FROOLVLRQ HQHUJ\ RI H9 7KLV UHDFWLRQ FRUUHVSRQGV WR WKH >03)%@ rf >03)%f +2706f @IRU WKH GHULYDWL]HG FDUER[\ODWH DQLRQ RI 3*)1RWH WKDW WKLV RYHUDOO &$' HIILFLHQF\ bf LV REWDLQHG DW WKH RSWLPXP SUHVVXUH IRU DQ\ RI WKH WKUHH JDVHV 7KH PRUH

PAGE 79

Q 1] &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ H9 Df [ 2SWLPXP f§ $ RRRRR r ’ ’’’’ r &/ $ $ $ $ $ rf ? 4 RRRRR &ROOLVLRQ *DV 3UHVVXUH P7RUUf Ef 2SWLPXP $U &ROOLVLRQ *DV &ROOLVLRQn(QHUJ\ f§ H9 RRRRR &''2' $$$$ f 22222 &ROOLVLRQ *DV 3UHVVXUH P7RUUf n n &f 2SWLPXP ;H &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ f§ H9 RRRRR RBRRRS $ $ $ $ $ RRRRR n n n n &ROOLVLRQ *DV 3UHVVXUH P7RUUf )LJXUH 2YHUDOO &$' HIILFLHQF\ IRU WKH VHOHFWHGUHDFWLRQ PRQLWRULQJ RI WKH FDUER[\ODWH DQLRQ RI WKH 023)%706 GHULYDWLYH RI 3*( ZLWK FROOLVLRQ JDV Df 1LWURJHQ Ef $UJRQ Ff ;HQRQ

PAGE 80

Df 1 &ROOLVLRQ *DV &ROOLVLRQ (QHUJ\ H9 2SWLPXP &ROOLVLRQ *DV 3UHVVXUH P7RUUf Ef 9 R &/ ? D $U &ROOLVLRQ *DV n 2SWLPXPf§ $ &ROOLVLRQ (QHUJ\ H? RRRRR } n ? DDRDR IL4 } ? DDDDD r ? &ROOLVLRQ *DV 3UHVVXUH P7RUUf Ff f§ 2SWLPXP 4IIO444 n TR'RSn DDDDD n n n n n n ;H &ROOLVLRQ *RV &ROOLVLRQ (QHUJ\ f§ H9 &ROOLVLRQ *DV 3UHVVXUH P7RUUf )LJXUH 2YHUDOO &$' HIILFLHQF\ IRU WKH VHOHFWHGUHDFWLRQ PRQLWRULQJ RI WKH FDUER[\ODWH DQLRQ RI WKH 3)%706 GHULYDWLYH RI 3*)A ZLWK FROOLVLRQ JDV Df 1LWURJHQ Ef $UJRQ Ff ;HQRQ

PAGE 81

PDVVLYH WKH FROOLVLRQ JDV WKH ORZHU WKH RSWLPXP SUHVVXUH 3*)D H[KLELWV D VOLJKWO\ KLJKHU RYHUDOO &$' HIILFLHQF\ bf ZLWK [HQRQ IRU WKH VHOHFWHG UHDFWLRQ RI n rf n )LJXUH Ff 7KLV UHDFWLRQ FRUUHVSRQGV WR WKH >03)%@ > 03)%f +2706f &+f6L &+@n IRU WKH GHULYDWL]HG FDUER[\ODWH DQLRQ RI 3*)D 7KLV VXJJHVWV WKDW [HQRQ ZRXOG EH WKH RSWLPXP &$' JDV +RZHYHU [HQRQ LV TXLWH H[SHQVLYH / RI JDVf DQG WKH JDLQ LQ &$' HIILFLHQF\ LV VOLJKW WKXV DUJRQ ZRXOG EH D PRUH SUDFWLFDO FKRLFH )RU 3*( WKH >03)%@n }f >03)%f +706f & +2&+@f UHDFWLRQ ZLWK DUJRQ )LJXUH Ef LV RSWLPXP DW D SUHVVXUH WLPHV ORZHU WKDQ IRU 3*)f(YHQ PRUH QRWDEOH LV WKDW WKH RSWLPXP &$' HIILFLHQF\ '34f IRU 3*( bf LV VLJQLILFDQWO\ KLJKHU WKDQ WKDW IRU 3*)D bf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

PAGE 82

$UHD -.UU UUI77L W L7U\QP L Q L > Q L nLWWWa@aWWWW L L L L L L L WLW L G L &ROOLVLRQ (QHUJ\ H9f n nf cVLRQ 3UHVVXUH P7RUU $UJRQ f cVLRQ 3UHVVXUH P7RUU $UJRQ )LJXUH &ROOLVLRQ HQHUJ\ VWXG\ IRU WKH VHOHFWHG UHDFWLRQV RI WKH 03)%706 GHULYDWLYH RI 3*( DQG WKH 3)%706 GHULYDWLYH RI 3*)A

PAGE 83

SHUIRUPHG DW FROOLVLRQ HQHUJLHV RI WR H9 2SWLPD IRU WKH VHOHFWHG UHDFWLRQV RI f } r 3*(f DQG f 3*)Df DUH LQGLFDWHG RQ WKH JUDSK 7KH RSWLPXP FROOLVLRQ HQHUJ\ IRU 3*( H9f LV VOLJKWO\ KLJKHU WKDQ IRU 3*)D H9f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nV LGHQWLW\ 0RVW RI WKH IUDJPHQW LRQV REVHUYHG LQ ERWK GDXJKWHU VSHFWUD DUH GHULYDWLYH VSHFLILF 7KHVH LRQV RFFXU DW P] DQG IRU 3*( DQG DW P] DQG IRU 3*)D 7KH PRVW LQWHQVH GDXJKWHU LRQ IURP WKH IUDJPHQWDWLRQ RI WKH >03)%@f LRQ RI 3*( LV P] LRQ DQG FRUUHVSRQGV WR WKH ORVV RI r+706&&++f IURP WKH SDUHQW LRQ RI f ,Q WKH GDXJKWHU VSHFWUXP RI 3*)D WKH P] LRQ LV WKH PRVW LQWHQVH DQG FRUUHVSRQGV WR WKH ORVV RI WKUHH +2706 JURXSV IURP WKH SDUHQW LRQ RI 7KH IUDJPHQW LRQV ZKLFK RFFXU DW ORZHU PDVVHV DUH LRQV WKDW FRUUHVSRQG WR EDFNERQHVSHFLILF IUDJPHQWV 7KLV PHDQV WKHVH LRQV FRUUHVSRQG WR IUDJPHQWDWLRQ RI WKH FDUERQK\GURJHQ VNHOHWRQ LQ ERWK 3*( DQG 3*)D 7KHVH LRQV LQFOXGH P] DQG IRU 3*( DQG P] DQG IRU 3*)

PAGE 84

b 5HODWLYH $EXQGDQFH b a &+M21 Df bL Ef P] )LJXUH ‘M DV 'DXJKWHU LRQ VSHFWUD RI WKH >03)%@n LRQV UD] DQG f RI Df 3*( 023)%706 GHULYDWLYH DW P7RUU DUJRQ DQG DW H9 Ef 3*)A 3)%706 GHULYDWLYH DW P7RUU DUJRQ DQG DW H9

PAGE 85

7DEOH 'DXJKWHU ,RQV RI >03)%@ 3*( 023)%706 DQG 3*)D 3ff RI 3)%706 3*( 023)%706D ,RQ $VVLJQPHQW P] b5$n 3n >3+2706@r >3+706@r >3+7062&+M@n >3+706&@n >SKRWPVFRFKR@n >3+706&&+M2+ @n > 3 +706 & &+M2+ &+ @n > 3 +706 & &+2+ &+ @n 3*)A 3)%706E ,RQ $VVLJQPHQW P] b5$ 3n >3+2706@ >3+706@r > 3 +706 &+f 6 L &+ @n >3+706@f > 3 +706 & &+f 6 L &+ @ >3+706&@f >SKRWPVFRFK@n >SKRWPVFRFK@ >SKRWPVFRFK@ $W D FROOLVLRQ JDV SUHVVXUH RI P7RUU DUJRQ DQG FROOLVLRQ HQHUJ\ RI H9 E $W D FROOLVLRQ JDV SUHVVXUH RI P7RUU DUJRQ DQG FROOLVLRQ HQHUJ\ RI H9 F 5HODWLYH $EXQGDQFH

PAGE 86

&RQVLGHUDWLRQV IRU FKRLFH RI D SDUWLFXODU VHOHFWHG UHDFWLRQ IRU PRQLWRULQJ KDV EHHQ GLVFXVVHG UHFHQWO\ E\ 6WULIH f 7KLV UHSRUW DORQJ ZLWK RWKHU VWXGLHV KDYH VKRZQ WKDW EDFNERQHVSHFLILF IUDJPHQWDWLRQ FRQIHUV VXSHULRU VHOHFWLYLW\ RYHU GHULYDWLYHVSHFLILF IUDJPHQWDWLRQ LQ WKH DQDO\VLV RI ELRORJLFDO VDPSOHV )RU H[DPSOH ZKHQ 650 LV EDVHG RQ D GHULYDWLYHVSHFLILF IUDJPHQWDWLRQ DQ\ FRPSRQHQW LQ D 6,0 FKURPDWRJUDP WKDW LV GHULYDWL]HG KDV DQ HQKDQFHG SUREDELOLW\ RI DSSHDULQJ LQ D 650 FKURPDWRJUDP +RZHYHU WKH EDFNERQHVSHFLILF IUDJPHQWDWLRQ KDV D ORZHU UHODWLYH GDXJKWHU LRQ LQWHQVLW\ LQ (&1&,*&0606 WKDQ IRU GHULYDWLYH VSHFLILF IUDJPHQWDWLRQ 7KHUHIRUH LI WKH EDFNERQHVSHFLILF IUDJPHQWDWLRQ ZDV FKRVHQ IRU 650 DQDO\VLV WKH VHQVLWLYLW\ ZRXOG EH ORZHU WKDQ WKDW IRU WKH GHULYDWLYHVSHFLILF IUDJPHQWDWLRQ IRXQG LQ )LJXUH DQG )LJXUH IRU 3*( DQG 3*)D 6HOHFWHG5HDFWLRQ 0RQLWRULQJ &DOLEUDWLRQ &XUYH $ VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f FDOLEUDWLRQ FXUYH IRU 3*( f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f f 7KH OLQHDU G\QDPLF UDQJH RI WKH FXUYH

PAGE 87

)LJXUH 6HOHFWHGUHDFWLRQ PRQLWRULQJ FDOLEUDWLRQ FXUYH IRU WKH r UHDFWLRQ RI WKH 023)%706 GHULYDWLYH RI 3*(

PAGE 88

LV IURP SJ WR QJ VROLG OLQHf DQG WKH VORSH RI WKH OLQHDU UHJUHVVLRQ EHVW ILW OLQH LV ZLWK D FRUUHODWLRQ FRHIILFLHQW RI 3UHFLVLRQ RI WKH *&0606 PHWKRG XWLOL]LQJ 650 ZDV GHWHUPLQHG E\ SHUIRUPLQJ WHQ RQH PLFUROLWHU LQMHFWLRQV RI D SJL/ VROXWLRQ RI 3*( 7KH SHUFHQW UHODWLYH VWDQGDUG GHYLDWLRQ b56'f RI WKH WHQ LQMHFWLRQV ZDV b &DOLEUDWLRQ FXUYHV IRU 3*)D 3*' DQG '+.)T ZHUH VLPLODU ZLWK YDU\LQJ OLPLWV RI GHWHFWLRQ LQ WKH UDQJH RI WR SJ 7KH UHVXOWV IRU WKLV VWXG\ DJUHH ZHOO ZLWK OLWHUDWXUH UHSRUWV ZKLFK KDYH VKRZQ /2'V XWLOL]LQJ (&1&,0606 RI DERXW WR SJ f &RQFOXVLRQV 7KH RSWLPXP FRQGLWLRQV IRU *&06 HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f ZLWK 6,0 DQG *&0606 ZLWK 650 DUH VXPPDUL]HG LQ 7DEOH 7KH RSWLPXP FROOLVLRQ JDV SUHVVXUH IRU ERWK TXDOLWDWLYH DQG TXDQWLWDWLYH 650f DQDO\VLV RI 3*( DUH ORZHU WKDQ WKH RSWLPD IRXQG IRU 3*)D 7KH GUDPDWLFDOO\ ORZHU &$' HIILFLHQF\ IRU WKH FDUER[\ODWH DQLRQ RI 3*)D )LJXUH Ef FRPSDUHG WR WKDW RI 3*( )LJXUH Ef FOHDUO\ LQGLFDWHV LWV JUHDWHU VWDELOLW\ XQGHU &$' FRQGLWLRQV 7KLV VWXG\ GHPRQVWUDWHV WKH QHHG IRU HYDOXDWLQJ WKH &$' HIILFLHQF\ LQ WKH WUDFH DQDO\VLV RI 3*V 2SWLPL]DWLRQ RI ERWK FROOLVLRQ HQHUJ\ DQG FROOLVLRQ JDV SUHVVXUH LV HVVHQWLDO LQ REWDLQLQJ DQ DFFXUDWH TXDOLWDWLYH GDXJKWHU VSHFWUXP ULFK LQ VWUXFWXUDO LQIRUPDWLRQ 7KH &$' UHDFWLRQ ZLWK WKH KLJKHVW &$' HIILFLHQF\ VKRXOG EH VHOHFWHG WR \LHOG WKH VHQVLWLYLW\ IRU 650 GHWHUPLQDWLRQ RI 3*V ([DPLQLQJ WKH FDOLEUDWLRQ FXUYHV )LJXUHV DQG f GLIIHUHQFHV EHWZHHQ 6,0 DQG 650 DUH QRWHG 6HQVLWLYLW\ LV JUHDWHU ZLWK 6,0 WKDQ ZLWK

PAGE 89

7DEOH 2WLPXP &RQGLWLRQV IRU (OHFWURQ&DSWXUH 1HJDWLYH &KHPLFDO ,RQL]DWLRQ 0DVV 6SHFWURPHWU\ DQG 7DQGHP 0DVV 6SHFWURPHWU\ (OHFWURQ&DSWXUH 1HJDWLYH &KHPFLDO 3DUDPHWHU ,RQ 6RXUFH 3UHVVXUH ,RQ 6RXUFH 7HPSHUDWXUH 3*( 7RUU r& ,RQL]DWLRQ ee) D 7RUU r& 7DQGHP 0DVV 6SHFWURPHWU\ 4XDOLWDWLYH 'DXJKWHU 6SHFWUXP 3DUDPHWHU &ROOLVLRQ *DV &ROOLVLRQ *DV 3UHVVXUH &ROOLVLRQ (QHUJ\ SJH $UJRQ P7RUU H9 r1/D $UJRQ P7RUU H9 4XDQWLWDWLYH 3DUDPHWHU &ROOLVLRQ *DV 6HOHFWHG 5HDFWLRQ &ROOLVLRQ *DV 3UHVVXUH &ROOLVLRQ (QHUJ\ 6HOHFWHG5HDFWLRQ 0RQLWRULQJ SJH $UJRQ n P7RUU H9 3*eD $UJRQ n P7RUU H9

PAGE 90

650 7KH OLPLW RI GHWHFWLRQ IRU 6,0 IJf LV VOLJKWO\ PRUH WKDQ RUGHUV RI PDJQLWXGH ORZHU WKDQ IRU 650 SJf &RPSDULQJ WKH UHODWLYH SHDN DUHDV RI 6,0 DQG 650 DW SJ WKH 6,0 SHDN DUHD LV DSSUR[LPDWHO\ WLPHV KLJKHU WKDQ WKH SHDN DUHD RI SJ ZLWK 650 ,Q DGGLWLRQ DW KLJKHU OHYHOV RI 3*( SJ WKH 6,0 SHDN DUHD LV DSSUR[LPDWHO\ WLPHV KLJKHU WKDQ WKH 650 SHDN DUHD 7KH ORZHU VHQVLWLYLW\ RI 650 LV H[SHFWHG GXH WR WKH OLPLWHG HIILFLHQF\ RI WKH &$' FRQYHUVLRQ RI WKH SDUHQW LRQ WR WKH GDXJKWHU LRQ DSSUR[LPDWHO\ b IRU n r‘ f RI LQWHUHVW DV ZHOO DV WUDQVPLVVLRQ ORVVHV LQKHUHQW LQ DGGLQJ D VHFRQG VWDJH RI PDVV DQDO\VLV W\SLFDOO\ WLPHVf +RZHYHU WKH VHOHFWLYLW\ JDLQHG E\ WKH SDUHQW GDXJKWHU UHDFWLRQ VKRXOG UHGXFH WKH FKHPLFDO QRLVH LQ D VDPSOH PDWUL[ WR D JUHDWHU H[WHQW WKDQ WKH DQDO\WLFDO VLJQDO WKXV FRPSHQVDWLQJ IRU WKH ORVW VHQVLWLYLW\

PAGE 91

&+$37(5 ',))(5(1&(6 ,1 7+( &2//,6,21$//< $&7,9$7(' ',662&,$7,21 2) 6758&785$//< 6,0,/$5 35267$*/$1',16 ,QWURGXFWLRQ 7KH LRQV IRUPHG E\ HOHFWURQ LRQL]DWLRQ (Of RI WKH PHWK\O HVWHU PHWKR[LPHWULPHWK\O VLO\O HWKHU GHULYDWLYHV RI SURVWDJODQGLQV 3*Vf VKRZ FRQVLGHUDEOH IUDJPHQWDWLRQ LQ WKH FROOLVLRQDOO\ DFWLYDWHG GLVVRFLDWLRQ &$'f SURFHVV f +RZHYHU WKH FDUER[\ODWH DQLRQV RI FHUWDLQ 3*V SURGXFHG E\ (&1&, KDYH EHHQ UHSRUWHG WR EH H[WUHPHO\ VWDEOH ZKHQ VXEMHFWHG WR &$' f ,W KDV EHHQ REVHUYHG WKDW WKH FDUER[\ODWH DQLRQV RI FHUWDLQ 3*V H[KLELW OLWWOH IUDJPHQWDWLRQ HYHQ DW KLJK FROOLVLRQ HQHUJLHV H9f DQG SUHVVXUHV P7RUU 1f 6XEWOH GLIIHUHQFHV DPRQJ WKH VWUXFWXUHV RI SURVWDJODQGLQV ( 3*(f )D 3*)Df 3*'f DQG GLK\GURNHWR )D '+.)Df )LJXUH f \LHOG HQRUPRXV GLIIHUHQFHV LQ &$' HIILFLHQF\ 7KH &$' HIILFLHQF\ IRU WKH >027063)%@ f >03)%@n DQG >0+@f FDUER[\ODWH DQLRQV LV VLJQLILFDQWO\ GLIIHUHQW IRU FORVHO\ UHODWHG 3*V 7KH ORZ IUDJPHQWDWLRQ DQG &$' HIILFLHQFLHV RI WKH FDUER[\ODWH DQLRQV RI 3*)D DQG '+.)D FRPSDUHG WR WKRVH RI 3*( DQG 3*' FOHDUO\ LQGLFDWH WKH JUHDWHU VWDELOLW\ RI WKHVH VSHFLHV ,Q WKLV FKDSWHU WKHVH GLIIHUHQFHV DUH HYDOXDWHG DQG H[SODLQHG LQ UHODWLRQ WR WKH VWUXFWXUDO GLIIHUHQFHV EHWZHHQ WKH FDUER[\ODWH DQLRQV IRU WKH 3*V

PAGE 92

)LJXUH 6WUXFWXUHV RI WKH IRXU SURVWDJODQGLQV VWXGLHG Df 3URVWDJODQGLQ )D 3*)Df Ef 3URVWDJODQGLQ ( 3*(f Ff 3URVWDJODQGLQ 3*'f Gf GLK\GURNHWR ) '+.)Df

PAGE 93

([SHULPHQWDO 3URVWDJODQGLQV DQG 5HDJHQWV 7KH SURVWDJODQGLQV ( )D DQG GLK\GURNHWR )D DV ZHOO DV 2PHWK\OK\GUR[\ODPLQH K\GURFKORULGH 11GLLVRSURS\OHWK\ODPLQH S\ULGLQH DQG DFHWRQLWULOH DQDO\WLFDO JUDGHf ZHUH DOO SXUFKDVHG IURP 6LJPD &KHPLFDO &R 3HQWDIOXRUREHQ]\OEURPLGH 3)%%Uf DQG ELVWULPHWK\O VLO\OfWULIOXRURDFHWDPLGH %67)$f ZHUH SXUFKDVHG IURP 3LHUFH &KHPLFDO &R 7KH PHWKDQH !bf XVHG DV WKH FKHPLFDO LRQL]DWLRQ UHDJHQW JDV ZDV SXUFKDVHG IURP 0DWKHVRQ *DV 3URGXFWV ,QF +HOLXP XVHG DV *& FDUULHU JDV DQG QLWURJHQ XVHG DV &$' FROOLVLRQ JDV ZHUH FRPPHUFLDO JUDGH ZLWK WKHLU SXULW\ FKHFNHG E\ PDVV VSHFWURPHWU\ 'HULYDWL]DWLRQ 7KH PHWKR[LPHSHQWDIOXRUREHQ]\O HVWHUWULPHWK\OVLO\O 023)%706f GHULYDWLYHV )LJXUH f IRUPHG IRU WKH *&0606 VWXGLHV ZHUH SUHSDUHG DFFRUGLQJ WR WKH PHWKRG LQ FKDSWHU 7KH WULPHWK\OVLO\O GHULYDWLYH ZDV IRUPHG E\ DGGLQJ W/ RI %67)$ DQG DOORZHG WR VWDQG RYHUQLJKW DW URRP WHPSHUDWXUH 'LOXWLRQV ZHUH PDGH IURP WKLV VROXWLRQ VR WKDW D SJ[/ VROXWLRQ RI HDFK 3* ZDV XVHG IRU LQMHFWLRQV 7KH VROLGV SUREH0606 VWXGLHV ZHUH SHUIRUPHG HLWKHU E\ DQDO\]LQJ WKH VWDQGDUGV ZLWKRXW GHULYDWL]DWLRQ RU DV WKH 3)% GHULYDWLYH XVLQJ RQO\ WKH 3)%%U HVWHULILFDWLRQ VWHS DERYH

PAGE 94

Df Ef Ff Gf )LJXUH 7062 &+M21 7062 7062 6WUXFWXUHV RI WKH PHWKR[LPHSHQWDIOXRUREHQ]\O WULPHWK\OVLO\O 023)%706f GHULYDWLYHV RI WKH IRXU SURVWDJODQGLQV Df 3*)D Ef 3*( Ff 3*' Gf '+.)-

PAGE 95

,QVWUXPHQWDO &RQGLWLRQV *& ZDV FDUULHG RXW RQ D VKRUW -t: 6FLHQWLILF )ROVRP &$f '% P ORQJ PP LG DQ ILOP WKLFNQHVVf FDSLOODU\ FROXPQ LQ WKH VSOLWOHVV PRGH ZLWK KHOLXP FDUULHU JDV DW DQ LQOHW SUHVVXUH RI SVL 7KH LQLWLDO WHPSHUDWXUH RI r& ZDV KHOG IRU V WKHQ LQFUHDVHG DW r&PLQ WR r& 7KH LQMHFWRU WHPSHUDWXUH ZDV r& 2QHPLFUROLWHU LQMHFWLRQV RI D SJ/ VROXWLRQ RI HDFK 3* ZHUH PDGH LQ WULSOLFDWH DW HDFK FRQGLWLRQ IRU WKH *&0606 VWXGLHV 7KH VROLGV SUREH ZDV XVHG DV WKH PHDQV IRU VDPSOH LQWURGXFWLRQ WR VWXG\ WKH 3)% HVWHU GHULYDWLYHV DQG WKH IUHH XQGHULYDWL]HGf 3* VWDQGDUGV 7KH LQLWLDO WHPSHUDWXUH ZDV r& DQG LQFUHDVHG DW r&PLQ WR r 7ULSOLFDWH VDPSOHV ZHUH DQDO\]HG IRU HDFK GHULYDWL]DWLRQ SURFHGXUH DW HDFK FRQGLWLRQ IRU WKH 0606 VWXGLHV 6DPSOH VL]H ZDV RQH PLFURJUDP RI WKH XQGHULYDWL]HG 3*V RU QJ RI WKH 3)% HVWHU GHULYDWLYHV $ )LQQLJDQ 0$7 764 JDV FKURPDWRJUDSKWULSOH TXDGUXSROH PDVV VSHFWURPHWHU ZDV HPSOR\HG 0DVV VSHFWURPHWU\ FRQGLWLRQV ZHUH LQWHUIDFH DQG WUDQVIHU OLQH WHPSHUDWXUH r& LRQL]HU WHPSHUDWXUH r& HOHFWURQ HQHUJ\ H9 DQG HPLVVLRQ FXUUHQW P$ (OHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f ZDV FDUULHG RXW ZLWK PHWKDQH DW DQ LRQL]HU SUHVVXUH RI WRUU ,Q WKH 0606 H[SHULPHQWV QLWURJHQ FROOLVLRQ JDV SUHVVXUH DQG FROOLVLRQ HQHUJ\ ZHUH YDULHG GHSHQGLQJ RQ HDFK H[SHULPHQW 7KH >02706 3)%@ >03)%@f FDUER[\ODWH DQLRQV ZHUH VHOHFWHG LQ WKH ILUVW TXDGUXSROH 4Of UHJLRQ DQG SDVVHG LQWR WKH FROOLVLRQ FHOO 4f ,Q WKLV UHJLRQ WKHVH LRQV XQGHUZHQW &$' WR IRUP FKDUDFWHULVWLF IUDJPHQWV ZKLFK ZHUH WKHQ PDVV DQDO\]HG LQ WKH WKLUG TXDGUXSROH 4f UHJLRQ $ IXOO GDXJKWHU VSHFWUXP

PAGE 96

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f U FROOHFWLRQ ( f DQG RYHUDOO &$' ( f HIILFLHQFLHV JLYHQ E\ WKH ?M /$' IROORZLQJ HTXDWLRQV f ( ) 6'M 3 (' IUDFWLRQ RI LRQV SUHVHQW IROORZLQJ &$' ZKLFK DUH GDXJKWHU LRQV ( 3 (' IUDFWLRQ RI LQLWLDO SDUHQW & LRQV WKDW LV FROOHFWHG IROORZLQJ &$' DV HLWKHU SDUHQW RU GDXJKWHU LRQV ( f&$' IUDFWLRQ RI LQLWLDO SDUHQW LRQ WKDW LV FRQYHUWHG WR FROOHFWDEOH GDXJKWHU LRQV

PAGE 97

ZKHUH 34 3 DQG 'M DUH WKH LQWHQVLWLHV RI WKH SDUHQW LRQ SULRU WR &$' WKH SDUHQW LRQ UHPDLQLQJ DIWHU &$' DQG D GDXJKWHU LRQ UHVXOWLQJ IURP &$' UHVSHFWLYHO\ 1RWH WKDW Q (f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f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07063)%n &DUER[YODWH $QLRQV ,Q OLJKW RI WKH GUDPDWLF GLIIHUHQFHV REVHUYHG LQ &KDSWHU RI WKH &$' HIILFLHQFLHV RI WKH FDUER[\ODWH DQLRQV RI WKH IXOO\ GHULYDWL]HG 3*)D DQG 3*( GLIIHULQJ VWUXFWXUDOO\ RQO\ LQ WKH SUHVHQFH RI D FDUERQ\O f

PAGE 98

JURXS DW & GHULYDWL]HG WR D PHWKR[LPLQH LQ 3*( UDWKHU WKDQ D K\GUR[\O 2+f JURXS DW WKH & SRVLWLRQ GHULYDWL]HG WR D WULPHWK\OVLO\O JURXS LQ 3*)Df WZR 3*V VLPLODU WR WKHVH ZHUH VWXGLHG 7KH 3*' DQG 3*( LVRPHUV YDU\ RQO\ E\ WKH LQWHUFKDQJH RI WKH K\GUR[\O 2+f DQG FDUERQ\O f JURXSV RQ & DQG &OO '+.)D GLIIHUV IURP 3*)D E\ H[FKDQJH RI D FDUERQ\O f JURXS GHULYDWL]HG WR D PHWKR[LPLQHf IRU WKH K\GUR[\O 2+f JURXS GHULYDWL]HG WR D WULPHWK\OVLO\Of DW & )LJXUH DQG )LJXUH SUHVHQWV FXUYHV IRU IUDJPHQWDWLRQ FROOHFWLRQ DQG RYHUDOO &$' HIILFLHQFLHV YHUVXV FROOLVLRQ HQHUJ\ IRU WKH FDUER[\ODWH DQLRQV RI 3*( 3*)D 3*' DQG '+.)7KHVH FXUYHV VKRZ WKH HIIHFWV RI YDU\LQJ WKH FROOLVLRQ HQHUJ\ DW WZR GLIIHUHQW FROOLVLRQ JDV SUHVVXUHV ,Q )LJXUHV D E DQG F WKH FROOLVLRQ SUHVVXUH KDV EHHQ HVWDEOLVKHG DW P7RUU 1 D YDOXH ZKLFK LV W\SLFDOO\ RSWLPXP IRU PDQ\ 0606 DQDO\VHV 7KH IUDJPHQWDWLRQ HIILFLHQF\ FXUYH )LJXUH Df LQGLFDWHV WKH GUDPDWLF GLIIHUHQFHV LQ VWDELOLW\ RI WKH FDUER[\ODWH DQLRQV RI WKH IRXU 3*V $W D FROOLVLRQ HQHUJ\ RI H9 WKH IUDJPHQWDWLRQ HIILFLHQFLHV UDQJHV IURP D W\SLFDO b GRZQ WR RQO\ b 7KH FROOLVLRQ SUHVVXUH PXVW EH LQFUHDVHG WR SURGXFH PRUH HIILFLHQW IUDJPHQWDWLRQ 7KH FROOHFWLRQ HIILFLHQF\ )LJXUH Ef IRU WKH IRXU 3*V DUH VLPLODU 7KH QRWDEOH H[FHSWLRQ LV 3*' ZKLFK KDV DQ XQXVXDOO\ KLJK FROOHFWLRQ HIILFLHQF\ DW FROOLVLRQ HQHUJLHV RI H9 7KLV H[SODLQV WKH GLIIHUHQFH QRWHG EHWZHHQ WKH IUDJPHQWDWLRQ HIILFLHQF\ RI 3*( DQG 3*' FRPSDUHG WR WKHLU RYHUDOO &$' HIILFLHQF\ )LJXUHV D E DQG F VKRZ WKH RYHUDOO &$' FROOHFWLRQ DQG IUDJPHQWDWLRQ HIILFLHQFLHV DW D FROOLVLRQ JDV SUHVVXUH WLPHV KLJKHU 7KH IUDJPHQWDWLRQ HIILFLHQF\ )LJXUH Df DV ZHOO DV WKH RYHUDOO &$'

PAGE 99

Df Ef Ff )LJXUH &$' HIILFLHQF\ RI WKH >02706 3)%@r FDUER[\ODWH DQLRQV YHUVXV FROOLVLRQ HQHUJ\ DW P7RUU 1 Df )UDJPHQWDWLRQ Ef &ROOHFWLRQ Ff 2YHUDOO &$'

PAGE 100

Df Ef Ff &$' HIILFLHQF\ RI WKH >02706 3)%@ FDUER[\ODWH DQLRQV YHUVXV FROOLVLRQ HQHUJ\ DW P7RUU 1 Df )UDJPHQWDWLRQ Ef &ROOHFWLRQ Ff 2YHUDOO &$' )LJXUH

PAGE 101

HIILFLHQF\ )LJXUH Ff FXUYHV GHPRQVWUDWH WKH GLIIHUHQFHV LQ WKH VWDELOLW\ RI WKH FDUER[\ODWH DQLRQV GXULQJ WKH &$' SURFHVV $W WKHVH KLJK FROOLVLRQ JDV SUHVVXUHV HYHQ DW D FROOLVLRQ HQHUJ\ DV ORZ DV H9 OLWWOH RU QR SDUHQW LRQ LV OHIW IRU 3*( DQG 3*' \LHOGLQJ D IUDJPHQWDWLRQ HIILFLHQF\ RI QHDUO\ b )LJXUH Df 7KH LQHIILFLHQW IUDJPHQWDWLRQ QRWHG LQ )LJXUH Df IRU 3*)D DQG '+.)D LV VWLOO REVHUYHG 1RWH WKDW DW WKH KLJKHU FROOLVLRQ JDV SUHVVXUH VFDWWHULQJ ORVVHV EHFRPH VLJQLILFDQW HVSHFLDOO\ DW KLJKHU FROOLVLRQ HQHUJLHV \LHOGLQJ DQ RSWLPXP FROOLVLRQ HQHUJ\ EHORZ WKH PD[LPXP DYDLODEOH H9 &ROOLVLRQ 3UHVVXUH 6WXG\ RI WKH I027063)%On &DUER[\ODWH $QLRQV 7KH IUDJPHQWDWLRQ HIILFLHQFLHV ( f IRU WKH FDUER[\ODWH DQLRQV RI U WKH IRXU 3*V DV D IXQFWLRQ RI FROOLVLRQ JDV SUHVVXUH DW WKH PD[LPXP DYDLODEOH FROOLVLRQ HQHUJ\ H9f DUH VKRZQ LQ )LJXUH D $W ORZ FROOLVLRQ JDV SUHVVXUHV 3*( KDV D IUDJPHQWDWLRQ HIILFLHQF\ WLPHV JUHDWHU WKDQ WKDW IRU 3*)D DQG '+.)D 7KHUH DUH QR GUDPDWLF GLIIHUHQFHV LQ WKH FROOHFWLRQ HIILFLHQF\ )LJXUH Ef RI WKH IRXU 3*V DOWKRXJK DW ORZ FROOLVLRQ JDV SUHVVXUHV P7RUU 1f '+.)D KDV WKH KLJKHVW (F EXW DW KLJK FROOLVLRQ JDV SUHVVXUHV WKH ORZHVW ( 6LQFH WKH PDVV RI WKH FDUER[\ODWH DQLRQV DUH DSSUR[LPDWHO\ WKH VDPH WKH LQFUHDVHG ORVV RI LRQV LV SUREDEO\ QRW GXH WR VFDWWHULQJ EXW UDWKHU GXH WR QHXWUDOL]DWLRQ RI WKH DQLRQ E\ HOHFWURQ GHWDFKPHQW 7KH RYHUDOO &$' HIILFLHQFLHV )LJXUH Ff IRU WKH FDUER[\ODWH DQLRQV RI WKH IRXU 3*V GHPRQVWUDWH WKH GLIIHUHQFHV LQ WKHLU EHKDYLRU 3*( KDV D PD[LPXP (AA RI b ZKLFK LV WLPHV JUHDWHU WKDQ WKDW IRU 3*' WLPHV EHWWHU WKDQ 3*)D DQG WLPHV JUHDWHU WKDQ '+.)D

PAGE 102

Df Ef &$' HIILFLHQF\ RI WKH >02706 3)%@ FDUER[\ODWH DQLRQV YHUVXV FROOLVLRQ JDV SUHVVXUH DW D FROOLVLRQ HQHUJ\ RI H9 Df )UDJPHQWDWLRQ Ef &ROOHFWLRQ Ff 2YHUDOO &$' )LJXUH

PAGE 103

7KH HIILFLHQF\ FXUYHV IRU WKH IRXU 3*V GHPRQVWUDWH WKDW GLIIHUHQFHV GR H[LVW EHWZHHQ )VHULHV 3*V DQG 3*( DQG 3*' +RZHYHU E\ H[DPLQLQJ )LJXUHV D E DQG F VLPLODULWLHV FDQ EH QRWHG IRU FHUWDLQ 3*V 3*' KDV D IUDJPHQWDWLRQ FROOHFWLRQ DQG RYHUDOO &$' HIILFLHQF\ EHKDYLRU HVVHQWLDOO\ WKH VDPH DV 3*( 7KH EHKDYLRU RI '+.)D FORVHO\ UHVHPEOHV WKDW RI 3*)B 7KH QRWDEOH GLIIHUHQFH LV WKDW '+.) KDV DQ (f DQG (B$U p D ) &$' HYHQ ORZHU WKDQ WKDW RI 3*)D 7KHVH UHVXOWV VXJJHVW WKDW WKH SUHVHQFH RI WZR 706 JURXSV RQ WKH F\FORSHQW\O ULQJ SRVLWLRQV & DQG &OOf RI 3*)D DQG '+.)DGG WR WKH VWDELOLW\ RI WKH >03)%@f FDUER[\ODWH DQLRQ GXULQJ &$' H[SHULPHQWV &ROOLVLRQ 3UHVVXUH 6WXG\ RI WKH I03)%On &DUER[\ODWH $QLRQV ,Q RUGHU WR WHVW WKLV K\SRWKHVLV WKH 3)% HVWHU GHULYDWLYHV ZLWKRXW PHWKR[LPH RU WULPHWK\OVLO\O JURXSVf RI WKH 3*V ZHUH H[DPLQHG $ FRQYHQWLRQDO VROLGV SUREH ZDV XVHG WR LQWURGXFH WKH GHULYDWL]HG 3*V VLQFH ZLWK RQO\ 3)% GHULYDWL]DWLRQ WKH 3*V ZHUH QR ORQJHU DPHQDEOH WR *& VHSDUDWLRQ 7KH &$' HIILFLHQF\ GDWD IURP WKLV VWXG\ DUH VKRZQ LQ )LJXUH 7KH IUDJPHQWDWLRQ EHKDYLRU )LJXUH Df RI WKH FDUER[\ODWH DQLRQV RI WKH 3)%RQO\ GHULYDWLYHV LV VLPLODU WR WKDW REVHUYHG IRU WKH IXOO\ GHULYDWL]HG 3*V )LJXUH Df 7KH 3*)D3)% DQG '+.)-3)% GHULYDWLYHV IUDJPHQW HYHQ OHVV HIILFLHQWO\ WKDQ WKH 023)%706 GHULYDWLYHV DW FROOLVLRQ SUHVVXUHV P7RUU 1 7KLV QRWHG GLIIHUHQFH LQ WKH IUDJPHQWDWLRQ HIILFLHQF\ RI WKH 3)% GHULYDWLYHV LV UHIOHFWHG LQ WKH H[WUHPHO\ ORZ RYHUDOO &$' HIILFLHQF\ )LJXUH Ff RI 3*)D DQG '+.)T 7KH UHVXOWV IURP WKLV VWXG\ VXJJHVW WKDW WKH SUHVHQFH RU DEVHQFH RI 706 DQG 02 JURXSV RI WKH IXOO\ GHULYDWL]HG 3*)-3)%706 KDV OLWWOH RU QR

PAGE 104

Df Ef &ROOLVLRQ *DV 3UHVVXUH P7RUU 1f )LJXUH &$' HIILFLHQF\ RI WKH >0 3)%@r FDUER[\ODWH DQLRQV YHUVXV FROOLVLRQ JDV SUHVVXUH DW D FROOLVLRQ HQHUJ\ RI H9 Df )UDJPHQWDWLRQ Ef &ROOHFWLRQ Ff 2YHUDOO &$'

PAGE 105

Df Ef )LJXUH 6NHWFK RI EDOODQGVWLFN PRGHOV RI Df 3*)D Ef 3*( &RORUHG EDOOV UHSUHVHQW R[\JHQ DWRPV

PAGE 106

HIIHFW RQ WKH REVHUYHG GLIIHUHQFHV LQ WKH IUDJPHQWDWLRQ EHKDYLRU RI 3*( DQG 3*)D ,W LV K\SRWKHVL]HG WKDW WKH GLIIHUHQFH QRWHG EHWZHHQ WKH (S RI 3*( DQG 3*)D LV GXH RQO\ WR WKH SUHVHQFH RI WZR K\GUR[\O RU 2706f JURXSV RQ WKH F\FORSHQW\O ULQJ RI WKH )VHULHV 3*V 7KLV LV VHHQ LQ )LJXUH ZKLFK FRQWDLQV VNHWFKHV RI EDOODQGVWLFN PRGHOV RI 3*( DQG 3*)D )LJXUH D VKRZV RQH SRVVLEOH FRQILJXUDWLRQ RI 3*)D GHPRQVWUDWLQJ KRZ WKH FDUER[\ODWH JURXS FDQ LQWHUDFW ZLWK WKH WZR K\GUR[\O 2+f JURXSV RQ & DQG &OO ,Q FRQWUDVW WKH 3*( FRQILJXUDWLRQ )LJXUH Ef VKRZV WKDW ZLWK RQO\ RQH K\GUR[\O 2+f JURXS WKH LQWHUDFWLRQ ZLWK WKH FDUER[\ODWH JURXS PD\ QRW EH DV VWURQJ 7KXV WKH VWDELOLW\ RI WKH FDUER[\ODWH DQLRQV RI WKH )VHULHV 3*V ZRXOG EH H[SHFWHG WR EH JUHDWHU GXULQJ &$' WKDQ WKDW RI 3*( DQG 3*' &ROOLVLRQ 3UHVVXUH 6WXG\ RI WKH I0+On &DUER[\ODWH $QLRQV 8QGHULYDWL]HG 3*V ZHUH H[DPLQHG WR ORRN DW WKH IUDJPHQWDWLRQ DQG &$' HIILFLHQF\ RI WKH >0+@f FDUER[\ODWH DQLRQV 7KHVH LRQV KDYH QRPLQDOO\ WKH VDPH VWUXFWXUHV DV WKH >03)%@ FDUER[\ODWH DQLRQV IRUPHG E\ GLVVRFLDWLYH HOHFWURQ FDSWXUH IURP WKH 3)%GHULYDWL]HG FRPSRXQGV $ FRQYHQWLRQDO VROLGVSUREH ZDV XVHG IRU WKLV VWXG\ DV LQ WKH H[SHULPHQWV GRQH RQ WKH 3)%RQO\ GHULYDWLYHV >03)%@ff 7KH >0+@f LRQV RI 3*( DQG 3*' FRXOG QRW EH VWXGLHG GXH WR WKHLU ORZ DEXQGDQFH b UHODWLYH WR >0+@nf LQ WKH (&1&, PDVV VSHFWUXP KRZHYHU ERWK 3*)T DQG '+.)D SURGXFHG DQ >0+@f LRQ LQWHQVH HQRXJK WR SHUPLW &$' DQDO\VLV 7KH ( ( DQG ( IRU WKHVH XQGHULYDWL]HG >0+@n LRQV DUH VKRZQ LQ )LJXUH 7KH FXUYH IRU ( )LJXUH Ef RI WKH >0+@f LRQ IRU '+.)T LV VLPLODU WR WKDW IRXQG IRU WKH >03)%@f LRQ LQ )LJXUH E %XW IRU 3*)D DW ORZHU FROOLVLRQ

PAGE 107

Df Ef Ff &ROOLVLRQ *DV 3UHVVXUH P7RUU 1f )LJXUH &$' HIILFLHQF\ RI WKH >0 +@ FDUER[\ODWH DQLRQV YHUVXV FROOLVLRQ JDV SUHVVXUH DW D FROOLVLRQ HQHUJ\ RI H9 Df )UDJPHQWDWLRQ Ef &ROOHFWLRQ Ff 2YHUDOO &$'

PAGE 108

SUHVVXUHV P7RUU 1f WKH (F LV WLPHV KLJKHU WKDQ LQ WKH FDVH RI )LJXUH E /RRNLQJ DW )LJXUH D DQG F WKH IUDJPHQWDWLRQ DQG &$' HIILFLHQFLHV DUH VKRZQ WR EH VLPLODU WR WKRVH IRXQG LQ )LJXUHV D DQG F 7KH (S DQG (T$' IRU 3*)D DQG '+.)D DUH WLPHV JUHDWHU LQ WKH FDVH RI WKH >0+@n LRQ WKDQ IRU WKH >03)%@n LRQ 7KLV VOLJKW GLIIHUHQFH EHWZHHQ WKH LRQV PD\ EH H[SODLQHG E\ WKH LQFUHDVHG LQWHUQDO HQHUJ\ LQ WKH >0+@f LRQ SURGXFHG XQGHU (&1&, FRPSDUHG WR WKDW RI WKH >03)%@ LRQ SURGXFHG E\ GLVVRFLDWLRQ HOHFWURQ FDSWXUH &RQFOXVLRQV 7KH GLIIHUHQFHV LQ IUDJPHQWDWLRQ EHKDYLRU RI 3*( DQG 3*)D ZHUH H[DPLQHG WKURXJK WKH XVH RI IUDJPHQWDWLRQ FROOHFWLRQ DQG RYHUDOO &$' HIILFLHQF\ VWXGLHV :H KDYH IRXQG WKDW WKH &$' HIILFLHQF\ IRU WKH >027063)%@f >03)%@ DQG >0+@f FDUER[\ODWH DQLRQV LV VLJQLILFDQWO\ GLIIHUHQW IRU FORVHO\ UHODWHG 3*V 7KURXJK WKH XVH RI WKHVH FXUYHV ZH KDYH VKRZQ WKDW )VHULHV 3*V IUDJPHQW OHVV HIILFLHQWO\ WKDQ 3*( DQG 3*' $ SRVVLEOH H[SODQDWLRQ KDV EHHQ SURSRVHG WR H[SODLQ WKHVH GUDVWLF GLIIHUHQFHV VHHQ LQ WKH IUDJPHQWDWLRQ EHKDYLRU RI VWUXFWXUDOO\ VLPLODU FDUER[\ODWH DQLRQV RI 3*V ,W LV EHOLHYHG WKDW )VHULHV 3*V DUH PRUH VWDEOH GXULQJ &$' GXH WR WKH LQWHUDFWLRQ RI WKH FDUER[\ODWH JURXS ZLWK WKH WZR K\GUR[\O 2+f JURXSV LQ WKH F\FORSHQW\O ULQJ

PAGE 109

&+$37(5 (9$/8$7,21 2) 62/,'3+$6( (;75$&7,21 *&06 $1' *&0606 )25 7+( $1$/<6,6 2) (1'2*(1286 35267$*/$1',1 ( ,1 85,1( ,QWURGXFWLRQ 7KH WUDFH GHWHUPLQDWLRQ RI SURVWDJODQGLQV 3*Vf LQYROYHV WKUHH EDVLF VWHSV VDPSOH SUHSDUDWLRQ VDPSOH LQWURGXFWLRQ DQG GHWHFWLRQ $ ORJLFDO FRPELQDWLRQ RI WKHVH WKUHH VWHSV FDQ SURGXFH DQ DQDO\WLFDO PHWKRG ZLWK WKH UHTXLUHG VHOHFWLYLW\ VHQVLWLYLW\ DQG WRWDO DQDO\VLV WLPH IRU WKH GHWHFWLRQ RI HQGRJHQRXV OHYHOV RI 3*( LQ XULQH $V ZDV SRLQWHG RXW LQ HDUOLHU FKDSWHUV YDULRXV VDPSOH SUHSDUDWLRQ PHWKRGV FRXSOHG ZLWK *&06 KDYH EHHQ UHSRUWHG H[WHQVLYHO\ LQ WKH OLWHUDWXUH f +RZHYHU WKH IRUPDWLRQ RI WKH 023)%706 GHULYDWLYH IROORZHG E\ VXEVHTXHQW DQDO\VLV ZLWK *&HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f 06 XWLOL]LQJ VHOHFWHGLRQ PRQLWRULQJ 6,0f VRPHWLPHV SURGXFHV PDQ\ LQWHUIHULQJ SHDNV ZKLFK SUHYHQW UHOLDEOH TXDQWLWDWLRQ f 7KHVH LQWHUIHUHQFHV RIWHQ UHIHUUHG WR DV FKHPLFDO QRLVH f FDQ VWDQG LQ WKH ZD\ RI DFKLHYLQJ UHTXLUHG GHWHFWLRQ OLPLWV RU UHTXLUH PRUH H[WHQVLYH VDPSOH FOHDQXS 7ZR PHWKRGV FDQ EH XVHG WR UHGXFH WKLV FKHPLFDO QRLVH .QDSS DQG 9UEDQDF KDYH WDNHQ WKH DSSURDFK RI LPPXQRDIILQLW\ ,$f FROXPQ SXULILFDWLRQ ZLWK *&(&1&,06 WR JLYH D YHU\ VHOHFWLYH DQDO\VLV f 7KLV PHWKRG XWLOL]HV D VHOHFWLYH VDPSOH FOHDQXS DQG SXULILFDWLRQ LQ D UHODWLYHO\

PAGE 110

UDSLG WZRVWHS SURFHGXUH WR UHGXFH WKH FKHPLFDO QRLVH )LUVW DQ RFWDGHF\O VLO\O &f VROLGSKDVH H[WUDFWLRQ FROXPQ LV HPSOR\HG IRU FOHDQn XS WR FRQYHQLHQWO\ FRQFHQWUDWH D ODUJH YROXPH RI XULQH WR D PDQDJHDEOH YROXPH DQG WR SURYLGH D FOHDU VROXWLRQ IUHH RI SUHFLSLWDWHV IRU DSSOLFDWLRQ WR WKH ,$ FROXPQ WKH VHFRQG VWHS LQ WKH FOHDQXSf )XUWKHU UHGXFWLRQ RI WKH FKHPLFDO QRLVH FDQ EH DFFRPSOLVKHG E\ *& LQ FRQMXQFWLRQ ZLWK WDQGHP PDVV VSHFWURPHWU\ 0606f XWLOL]LQJ WKH VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f PRGH f 5HFHQWO\ *&0606 DQDO\VLV RI VHOHFWHG 3*V LQ ELRORJLFDO PDWULFHV KDV EHHQ UHSRUWHG XVLQJ YDULRXV LRQL]DWLRQ DQG GHULYDWL]DWLRQ PHWKRGV f 7KH FRPELQDWLRQ RI ERWK WKHVH FKHPLFDO QRLVH UHGXFWLRQ PHWKRGV KDV EHHQ H[SORLWHG E\ .QDSS DQG 9UEDQDF f LQ WKH DQDO\VLV RI 3*V E\ *&HOHFWURQLPSDFW (,f0606 XVLQJ 650 +RZHYHU (O ODFNV WKH VHQVLWLYLW\ QHHGHG LQ PDQ\ FDVHV IRU WKH ORZ OHYHO GHWHUPLQDWLRQ RI 3*nV ,QYHVWLJDWLRQ RI DOO WKUHH EDVLF VWHSV VDPSOH SUHSDUDWLRQ LQWURGXFWLRQ DQG DQDO\VLVf ZKLFK FRPSULVH WKH DQDO\VLV LV QHFHVVDU\ WR GHWHUPLQH WKH PRVW VHQVLWLYH DQG VHOHFWLYH PHWKRG IRU WKH GHWHUPLQDWLRQ RI 3*V LQ D ELRORJLFDO PDWUL[ ,W LV RIWHQ REVHUYHG WKDW WUDGHRIIV LQ VHOHFWLYLW\ VHQVLWLYLW\ DQG WRWDO DQDO\VLV WLPH H[LVW LQ WKH WKUHH EDVLF VWHSV RI DQ\ WUDFH DQDO\WLFDO PHWKRG 3UHYLRXV ZRUN LQ RXU UHVHDUFK JURXS KDV VKRZQ WKH DGYDQWDJHV DQG GLVDGYDQWDJHV RI VKRUW P DQG FRQYHQWLRQDO P *& FDSLOODU\ FROXPQV IRU *&06 DQG *&0606 f +RZHYHU QR V\VWHPDWLF VWXG\ KDV EHHQ SHUIRUPHG IRU WKH HQWLUH DQDO\WLFDO SURFHGXUH ,Q WKLV VWXG\ GLIIHUHQW FRPELQDWLRQV RI VDPSOH SUHSDUDWLRQ *& FROXPQ OHQJWKV DQG PDVV VSHFWURPHWU\ GHWHFWLRQ VFKHPHV KDYH EHHQ LQYHVWLJDWHG 7KH WUDGHn RIIV EHWZHHQ VHOHFWLYLW\ VHQVLWLYLW\ DQG WLPH RI DQDO\VLV WKURXJKRXW WKH

PAGE 111

DQDO\WLFDO PHWKRGRORJ\ KDYH EHHQ HYDOXDWHG LQ WKLV FKDSWHU ,Q DGGLWLRQ TXDQWLWDWLRQ RI HQGRJHQRXV 3*( LQ XULQH KDV EHHQ SHUIRUPHG ZLWK VHYHUDO GLIIHUHQW PHWKRGV ([SHULPHQWDO 3URVWDJODQGLQV DQG 5HDJHQWV $OO VROYHQWV ZHUH UHDJHQW RU +3/& JUDGH 3URVWDJODQGLQ ( 3*(f ZDV SXUFKDVHG IURP 6LJPD &KHPLFDO &R 6W /RXLV 02f 7KH VROLGSKDVH H[WUDFWLRQ FROXPQV ZHUH SXUFKDVHG IURP $QDO\WLFKHP ,QWHUQDWLRQDO ,QF +DUERU &LW\ &$f n n+Af 3*( DQG WKH DQWLERG\ DIILQLW\ VRUEHQW ZHUH JLIWV IURP 'UV -9UEDQDF DQG '5 .QDSS RI WKH 'HSDUWPHQW RI 3KDUPDFRORJ\ 0HGLFDO 8QLYHUVLW\ RI 6RXWK &DUROLQD &KDUOHVWRQ 6&f 7KH GHULYDWL]DWLRQ UHDJHQWV DQG VROYHQWV S\ULGLQH 2PHWK\OK\GUR[\ODPLQH K\GURFKORULGH DFHWRQLWULOH DQG 11GLLVRSURS\OHWK\O DPLQH IRU *&06 SHUFHQW UHFRYHU\ VWXGLHV ZHUH DOO SXUFKDVHG IURP 6LJPD &KHPLFDO &R 3HQWDIOXRUREHQ]\OEURPLGH 3)%%Uf DQG ELVWULPHWK\OVLO\OfWULIOXRUR DFHWDPLGH %67)$f ZHUH SXUFKDVHG IURP 3LHUFH &KHPLFDO &R 5RFNIRUG ,/f 7KH XULQH ZDV FROOHFWHG RQ WZR VHSDUDWH GD\V IURP WKH DXWKRU $OO JODVVZDUH ZDV VLODQL]HG ZLWK D VROXWLRQ RI b GLPHWK\OGLFKORURVLODQH LQ WROXHQH 7KHVH WZR FKHPLFDOV ZHUH ERWK SXUFKDVHG IURP 6LJPD &KHPLFDO &R +HOLXP XVHG DV *& FDUULHU JDV PHWKDQH !bf XVHG DV WKH FKHPLFDO LRQL]DWLRQ UHDJHQW JDV DQG DUJRQ XVHG DV &$' FROOLVLRQ JDV ZHUH IURP 0DWKHVRQ *DV 3URGXFWV ,QF 2UODQGR )/f

PAGE 112

P/ 8ULQH 6SLNHG ZLWK QJ RI +A3*( $FLGLILHG ZLWK )RUPLF $FLG WR S+ ([WUDFWHG )RXU P/ 8ULQH 6DPSOHV ZLWK 6HSDUDWH & &ROXPQV (YDSRUDWHG (OXHQWV IURP & &ROXPQV ZLWK 1 7ZR 6DPSOHV 7ZR 6DPSOHV 'HULYDWL]HG 'LOXWHG ZLWK P/ RI 3%6 S+ f ([WUDFWHG ZLWK 6HSDUDWH ,$ &ROXPQV (YDSRUDWHG (OXHQWV IURP ,$ &ROXPQV ZLWK 1 'HULYDWL]HG )LJXUH 6DPSOH SUHSDUDWLRQ VFKHPH IRU XULQH

PAGE 113

6DPSOH 3UHSDUDWLRQ 7ZR GLIIHUHQW XULQH VSHFLPHQV IURP GLIIHUHQW GD\V ZHUH SUHSDUHG IRU WKH TXDQWLWDWLRQ VWXG\ 6DPSOHV DQG ZHUH IURP WKH ILUVW XULQH VSHFLPHQ DQG VDPSOH ZDV IURP WKH VHFRQG XULQH VSHFLPHQ 7KH ILUVW WZR XULQH VDPSOHV ZHUH SUHSDUHG DFFRUGLQJ WR WKH VFKHPH LQ )LJXUH )RU VDPSOH IURP WKH VHFRQG XULQH VSHFLPHQ RQO\ WZR & FROXPQV ZHUH XWLOL]HG DQG D GLIIHUHQW LPPXQRDIILQLW\ ,$f FROXPQ WKDQ WKDW IRU VDPSOHV DQG ZDV XVHG $ P/ XULQH VDPSOH ZDV DFLGLILHG ZLWK IRUPLF DFLG WR S+ DIWHU DGGLWLRQ RI L/ RI D QJL/ VROXWLRQ RI +A3*( ([WUDFWLRQ WKHQ IROORZHG ZLWK IRXU P/ VDPSOHV RI WKH VSLNHG XULQH LQWURGXFHG RQWR IRXU VHSDUDWH & FROXPQV 3UHSDUDWLRQ DQG H[WUDFWLRQ RI WKH 3*( XWLOL]LQJ WKH & FROXPQV ZDV DFFRPSOLVKHG XVLQJ WKH IROORZLQJ PHWKRG f &RQGLWLRQHG WKH FROXPQ ZLWK P/ RI +3/& ZDWHU DQG P/ RI PHWKDQRO f 3DVVHG VROXWLRQ RI 3*( DFLGLILHG WR S+ ZLWK IRUPLF DFLGf WKURXJK WKH FROXPQ f :DVKHG WKH FROXPQ ZLWK P/ RI +3/& ZDWHU DQG P/ SHWUROHXP HWKHU f (OXWHG 3*( ZLWK P/ RI HWK\O DFHWDWH $IWHU WKH & H[WUDFWLRQ DOO IRXU VDPSOHV ZHUH HYDSRUDWHG ZLWK 1 7ZR RI WKH VDPSOHV ZHUH WKHQ IXUWKHU SXULILHG ZLWK VHSDUDWH ,$ FROXPQV 7KHVH UHVLGXHV ZHUH GLOXWHG ZLWK DSSUR[LPDWHO\ P/ RI D SKRVSKDWH EXIIHU VROXWLRQ S+ f 7KLV VROXWLRQ ZDV WKHQ DSSOLHG WR WKH ,$ FROXPQ DQG H[WUDFWHG DV IROORZV f &RQGLWLRQHG WKH FROXPQ ZLWK P/ RI 3%6 S+ f

PAGE 114

f 3DVVHG VROXWLRQ RI 3*( DFLGLILHG WR S+ ZLWK IRUPLF DFLGf WKURXJK WKH FROXPQ f $OORZHG WKH VDPSOH WR VHWWOH LQWR WKH VRUEHQW EHG IRU PLQ DW URRP WHPSHUDWXUH f :DVKHG WKH FROXPQ ZLWK P/ RI 3%6 S+ f DQG P/ +3/& ZDWHU 5HPRYHG DOO UHPDLQLQJ ZDWHU LQ WKH FROXPQ f (OXWHG 3*( ZLWK P/ RI b DFHWRQLWULOH VROXWLRQ YYf f :DVKHG FROXPQ ZLWK DQ DGGLWLRQDO P/ RI b DFHWRQLWULOH WR DVVXUH UHPRYDO RI DOO WKH 3*( f ,PPHGLDWHO\ ULQVHG WKH FROXPQ ZLWK P/ RI +3/& ZDWHU DQG P/ RI 3%6 S+ f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

PAGE 115

,QVWUXPHQWDO &RQGLWLRQV $ )LQQLJDQ 0$7 WULSOH VWDJH TXDGUXSROH 764f JDV FKURPDWRJUDSK WDQGHP PDVV VSHFWURPHWHU ZDV XVHG IRU WKHVH VWXGLHV *DV FKURPDWRJUDSK\ ZDV FDUULHG RXW RQ YDULRXV OHQJWKV RI -t: 6FLHQWLILF )ROVRP &$f '% DQG PHWHU ORQJ PP LG P ILOP WKLFNQHVVf FDSLOODU\ FROXPQV 7KH GLIIHUHQW OHQJWKV RI *& FROXPQV ZHUH XVHG LQ WKH VSOLWOHVV PRGH ZLWK KHOLXP FDUULHU JDV DW WKH IROORZLQJ FRQGLWLRQV P *& FROXPQ ZDV RSHUDWHG DW D IORZ UDWH RI FPV LQOHW SUHVVXUH SVLf ZLWK DQ LQLWLDO WHPSHUDWXUH RI r& KHOG IRU V LQFUHDVHG DW r&PLQ WR r& WKHQ LQFUHDVHG DJDLQ DW r&PLQ WR r& WKH P *& FROXPQ ZDV RSHUDWHG DW D IORZ UDWH RI FPV LQOHW SUHVVXUH SVLf ZLWK WKH VDPH WHPSHUDWXUH SURJUDP H[FHSW IRU DQ LQLWLDO WHPSHUDWXUH RI r& WKH P *& FROXPQ ZDV RSHUDWHG DW DQ LQOHW SUHVVXUH RI SVL ZLWK DQ LQLWLDO WHPSHUDWXUH RI r& KHOG IRU V WKHQ LQFUHDVHG DW r&PLQ WR r& 7KH LQMHFWRU WHPSHUDWXUH ZDV r& IRU DOO WKUHH *& FROXPQ OHQJWKV 0DVV VSHFWURPHWU\ FRQGLWLRQV ZHUH LQWHUIDFH DQG WUDQVIHU OLQH WHPSHUDWXUH r& LRQL]HU WHPSHUDWXUH r& HOHFWURQ HQHUJ\ H9 DQG HPLVVLRQ FXUUHQW P$ (OHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f ZDV FDUULHG RXW ZLWK PHWKDQH DW DQ LRQL]HU SUHVVXUH RI 7RUU $UJRQ ZDV HPSOR\HG DV WKH FROOLVLRQ JDV DW D SUHVVXUH RI P7RUU DQG D FROOLVLRQ HQHUJ\ RI H9 ZDV XWLOL]HG IRU WKH VHOHFWHGUHDFWLRQ PRQLWRULQJ VWXGLHV RI 3*(! 7KH *&06 DQDO\VLV XWLOL]LQJ 6,0 XVHG DQ HOHFWURQ PXOWLSOLHU (0f VHWWLQJ RI 9 DQG D SUHDPS JDLQ RI 9$ *&0606 H[SHULPHQWV ZLWK 650 HPSOR\HG DQ (0 VHWWLQJ RI 9 DQG D SUHDPS JDLQ LGHQWLFDO WR WKH 6,0 DQDO\VLV

PAGE 116

7DEOH $QDO\WLFDO 6FKHPHV 8VHG IRU WKH 'HWHUPLQDWLRQ RI (QGRJHQRXV /HYHOV RI 3*( LQ 8ULQH 0HWKRG 6DPSOH 3UHSDUDWLRQ *& &ROXPQ /HQJWK 'HWHFWLRQ 0HWKRG $D & &ROXPQ PHWHU 6,0E %D & &ROXPQ PHWHU 650& &D &O F ,$G &ROXPQV PHWHU 6,0 'D & t ,$ &ROXPQV PHWHU 650 ( & &ROXPQ PHWHU 6,0 ) & &ROXPQ PHWHU 650 *D & t ,$ &ROXPQV PHWHU 6,0 +D & F ,$ &ROXPQV PHWHU 650 & &ROXPQ PHWHU 650 & F ,$ &ROXPQV PHWHU 6,0 .D & F ,$ &ROXPQV PHWHU 650 0HWKRGV H 6HOHFWHG 6HOHFWHG PSOR\HG IRU TXDQWLWDWLRQ VWXG\ RI LRQ PRQLWRULQJ UHDFWLRQ PRQLWRULQJ WKH e QGRJHQRXV OHYHO RI 3*( LQ XULQH G ,PPXQRDIILQLQW\ SXULILFDWLRQ

PAGE 117

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f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b RI WKH SJ RI +3*( 7KH TXDQWLWDWLRQ RI WKH HQGRJHQRXV OHYHOV RI 3*( LQ WKH H[WUDFWHG XULQH VDPSOH ZDV DFFRPSOLVKHG E\ VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f DQG VHOHFWHGLRQ PRQLWRULQJ 6,0f 7ZR JDV FKURPDWRJUDSKLF SHDNV DSSHDU IRU GHULYDWL]HG 3*( LQ WKH FKURPDWRJUDPV LQ WKLV FKDSWHU 7KHVH FRUUHVSRQG

PAGE 118

7DEOH &DOLEUDWLRQ &XUYH 'LOXWLRQV IRU WKH 4XDQWLWDWLRQ RI 3*( eKSJH $GGHG QJf SJH $GGHG QJf 9ROXPH RI 'LOXWLRQ /f &RQFHQWUDWLRQ RI ?3*( SJ[/f &RQFHQWUDWLRQ RI 3*( SJA/f

PAGE 119

&0 )LJXUH &DOLEUDWLRQ FXUYH XWLOL]LQJ D P *& FROXPQ ZLWK 6,0 ,OO

PAGE 120

WR WKH V\Q DQG DQWLPHWKR[LPH LVRPHUV RI WKH GHULYDWL]HG 3*( f 7KH PDMRU DQWLPHWKR[LPH LVRPHU RI 3*( WKH VHFRQG SHDNf ZDV XVHG IRU TXDQWLWDWLRQ LQ WKHVH VWXGLHV 7KH >03)%@f LRQV RI 3*( ff DQG + 3*( rf ZHUH PRQLWRUHG IRU VHOHFWHGLRQ PRQLWRULQJ VWXGLHV 2SWLPXP FRQGLWLRQV IURP &KDSWHU ZHUH XVHG IRU WKH DQDO\VLV RI 3*( DQG +A3*( 7KH VHOHFWHGUHDFWLRQV PRQLWRUHG IRU WKH DQDO\VLV RI HQGRJHQRXV OHYHOV RI 3*( LQ XULQH ZHUH f r‘ f IRU 3*( DQG r r‘ n IRU WKH LQWHUQDO VWDQGDUG +3*( $ EDVHOLQH ZDV FKRVHQ YLVXDOO\ RQ WKH *& WUDFH DQG WKH SHDN DUHDV IRU 3*( DQG +3*( FDOFXODWHG E\ WKH ,1&26 FRPSXWHU V\VWHP IRU WKH VWDQGDUGV DQG WKH H[WUDFWHG XULQH VDPSOHV 7KH DUHD RI 3*( GLYLGHG E\ WKH DUHD RI +3*( LQ WKH VWDQGDUGV JLYHV D UDWLR WKDW LV XVHG LQ WKH FDOLEUDWLRQ FXUYH 7KH DPRXQW RI 3*( LQ HDFK XULQH VDPSOH ZDV FDOFXODWHG E\ FRPSDULQJ WKH UDWLR RI WKHVH LRQV WR WKDW RI WKH FDOLEUDWLRQ FXUYH $ W\SLFDO 6,0 FKURPDWRJUDP P *&f RI D XULQH H[WUDFW FOHDQHG XS E\ & DQG ,$f LV VKRZQ LQ )LJXUH D WKH UHVXOWV ZLWK RQO\ & FOHDQXS DUH VKRZQ LQ )LJXUH E 7KH DPRXQW RI 3*( LQ WKH VDPSOH LV FDOFXODWHG IURP WKH UDWLR RI WKH SHDN DUHD VKDGHG LQ EODFNf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

PAGE 121

b 5HODWLYH ,QWHQVLW\ b 5HODWLYH ,QWHQVLW\ b PSJH 7LPH X L U f§L r } f f )LJXUH 7\SLFDO 6,0 FKURPDWRJUDP RI D XULQH H[WUDFW VKRZLQJ ERWK WKH HQGRJHQRXV 3*( nf DQG +A3*( rf ZLWK Df & DQG ,$ SXULILFDWLRQ Ef & H[WUDFWLRQ RQO\ 7KH LQWHJUDWHG SHDN DUHDV DUH VKDGHG LQ EODFN

PAGE 122

5HVXOWV IURP WKH 4XDQWLWDWLRQ 6WXG\ RI 3*(A LQ 8ULQH 4XDQWLWDWLRQ 6WXG\ 7KH VHYHQ DQDO\WLFDO VFKHPHV HPSOR\HG IRU TXDQWLWDWLRQ RI 3*( LQ XULQH DQG WKH UHVXOWV RI WKH VWXG\ DUH VKRZQ LQ 7DEOH 7KH WKUHH VDPSOHV GLVFXVVHG HDUOLHU ZHUH DQDO\]HG E\ HDFK PHWKRG RQ WKH VDPH GD\ 7KUHH LQMHFWLRQV RI HDFK VDPSOH ZHUH PDGH DQG WKH DYHUDJH DQG b56' FDOFXODWHG ,Q DGGLWLRQ WKH DYHUDJH RI VDPSOHV DQG IURP WKH VDPH XULQH VSHFLPHQf LV OLVWHG DV ZHOO DV WKH DYHUDJH RI DOO WKUHH VDPSOHV DQG WKH b56' 7KLV WDEOH SURYLGHV D JUHDW GHDO RI LQIRUPDWLRQ DERXW WKH PHWKRGV XVHG IRU WKH TXDQWLWDWLRQ RI 3*( LQ XULQH )LUVW WKH TXDQWLWLHV IRXQG IRU WKH HQGRJHQRXV 3*( LQ XULQH DJUHH ZHOO ZLWK QRUPDO YDOXHV UHSRUWHG LQ WKH OLWHUDWXUH f 5HSRUWV KDYH VKRZQ WKDW WKH FRQFHQWUDWLRQ RI 3*( LQ XULQH RI YDULRXV VXEMHFWV UDQJHV IURP WR SJP/ 4XDQWLWLHV GHWHFWHG LQ WKLV VWXG\ ZLWK WKH VHYHQ GLIIHUHQW DQDO\WLFDO VFKHPHV DOO DUH ZLWKLQ WKLV UDQJH 7KH DYHUDJH YDOXH RI WKH VHYHQ GLIIHUHQW PHWKRGV ZDV SJ ZLWK D b56' RI b 7KH DYHUDJH YDOXHV RI WKH GLIIHUHQW PHWKRGV HPSOR\HG YDULHG RQO\ VOLJKWO\ UDQJLQJ IURP SJP/ WR SJP/ 7KLV LQGLFDWHV WKDW DOO WKH VHOHFWHG PHWKRGV PD\ EH HPSOR\HG IRU WKH DQDO\VLV RI 3*( LQ XULQH DW WKHVH OHYHOV 7KH YDULDWLRQ LQ WKH VHYHQ PHWKRGV LV REVHUYHG LQ WKH b56' IRXQG IURP DYHUDJLQJ WKH UHVXOWV IURP WKH VHYHQ GLIIHUHQW PHWKRGV HPSOR\HG IRU WKH WKUHH XULQH VDPSOHV 7KHVH DYHUDJH YDOXHV YDU\ RQO\ VOLJKWO\ ZLWK D b56' UDQJLQJ IURP b IRU XULQH VDPSOH WR D KLJK RI b IRU XULQH VDPSOH ,Q DGGLWLRQ WKLV WDEOH SURYLGHV LQIRUPDWLRQ DERXW WKH YDULRXV

PAGE 123

7DEOH 4XDQWLWDWLRQ 6WXG\ RI (QGRJHQRXV 3*( LQ 8ULQH 8WLOL]LQJ 9DULRXV $QDO\WLFDO 6FKHPHV 4XDQWLW\ RI 3*( $YHUDJH 0HWKRG 6DPSOH *& SJP/f ,QMHFWLRQ RI ,QM b56'E $YHUDJH RI t $YHUDJH RI $OO b56' RI DOO $ % & D 5HIHU WR 7DEOH IRU H[SODQDWLRQ RI DQDO\WLFDO VFKHPHV E b 5HODWLYH 6WDQGDUG 'HYLDWLRQ

PAGE 124

7DEOH FRQWLQXHG 0HWKRG 6DPSOH 4XDQWLW\ RI 3*( SJP/f *& ,QMHFWLRQ $YHUDJH RI ,QM b56'E $YHUDJH RI t $YHUDJH RI $OO b56' RI DOO + 8ULQH 6DPSOH $YHUDJH IURP 0HWKRGV SHP/f b56' D 5HIHU WR 7DEOH IRU H[SODQDWLRQ RI DQDO\WLFDO VFKHPHV E b 5HODWLYH 6WDQGDUG 'HYLDWLRQ

PAGE 125

VDPSOH SUHSDUDWLRQV DQG PDVV VSHFWURPHWULF DQDO\VLV PHWKRGV HPSOR\HG )RU H[DPSOH FRPSDULQJ WKH FRQFHQWUDWLRQV IRXQG E\ PHWKRG & ,$ P *& 6,0f DQG PHWKRG % & ,$ P 650f D GLIIHUHQFH LV QRWHG EHWZHHQ WKH 6,0 DQG 650 DQDO\VLV PHWKRGV 7KH PHWKRG XWLOL]LQJ 6,0 \LHOGHG FRQFHQWUDWLRQV IRU HQGRJHQRXV 3*( DSSUR[LPDWHO\ b KLJKHU WKDQ IRU WKH PHWKRG XWLOL]LQJ 650 7KLV PD\ EH GXH WR WKH LQWHUIHUHQFHV WKDW DUH SUHVHQW LQ WKH 6,0 FKURPDWRJUDP RYHUODSSLQJ ZLWK WKH 3*( SHDN FUHDWLQJ GLIILFXOW\ LQ WKH DFFXUDWH GHWHUPLQDWLRQ RI WKH DFWXDO 3*( SHDN DUHD 7KH XVH RI 650 HOLPLQDWHV PDQ\ RI WKH FKHPLFDO LQWHUIHUHQFHV WKXV UHGXFLQJ WKH SUREOHP RI LQDFFXUDWH SHDN DUHD GHWHUPLQDWLRQ $QRWKHU LPSRUWDQW GLIIHUHQFH REVHUYHG LQ WKH WDEOH RFFXUV EHWZHHQ PHWKRGV $ & P *& 6,0f DQG & & ,$ P *& 6,0f IRU DOO WKUHH XULQH VDPSOHV 7KH FRQFHQWUDWLRQV RI HQGRJHQRXV 3*( GHWHUPLQHG E\ PHWKRG $ DUH FRQVLVWHQWO\ b KLJKHU WKDQ WKRVH IRXQG E\ PHWKRG & 7KLV PD\ EH H[SODLQHG E\ WKH UHPRYDO RI XULQH PDWUL[ FRPSRQHQWV ZLWK WKH DGGLWLRQ RI ,$ LQ PHWKRG & SHUPLWWLQJ PRUH DFFXUDWH FDOFXODWLRQ RI WKH 3*( SHDN DUHD 1RWH WKDW WKH DGGLWLRQDO VHOHFWLYLW\ RI 650 PHWKRGV % DQG 'f UHGXFHV WKH QHHG IRU ,$ FOHDQXS WKHUHIRUH UHGXFLQJ WKH GLIIHUHQFH EHWZHHQ WKH UHVXOWV REWDLQHG IURP PHWKRGV % DQG /LPLW RI 'HWHFWLRQ &/2'f DQG 6HQVLWLYLW\ 6WXGLHV 7DEOH JLYHV WKH DSSUR[LPDWH /2' IRXQG IRU +3*( LQ XULQH DQG WKH VHQVLWLYLW\ YDOXHV VORSHV RI WKH FDOLEUDWLRQ FXUYHV LQ FRXQWVSJf IRU 3*( VWDQGDUGV 7KH /2' VWXG\ ZDV DFFRPSOLVKHG E\ GLOXWLQJ WKH XULQH H[WUDFWV XVHG DERYH FRQWDLQLQJ SJ// RI +3*( WR DQG SJL/ DQG PRQLWRULQJ +A3*( SHDN DUHD 7KH /2'V UHSRUWHG LQ 7DEOH

PAGE 126

7DEOH D /LPLW RI 'HWHFWLRQ 6WXG\ RI +3*( LQ 8ULQH IRU 9DULRXV $QDO\WLFDO 6FKHPHV 0HWKRG /LPLW RI 'HWHFWLRQ SJP/f $ % & + 7DEOH E 6HQVLWLYLW\ 6WXG\ RI 3*( 6WDQGDUGV 8WLOL]LQJ WKH 6ORSHV RI WKH &DOLEUDWLRQ &XUYHV 6ORSH RU 6HQVLWLYLWY FRXQWV SJf *& &ROXPQ /HQJWK 6,0 650 P F G P F G P H H 5HIHU WR 7DEOH IRU H[SODQDWLRQ RI DQDO\WLFDO VFKHPH E $SSUR[LPDWLRQ IURP WKH GLOXWLRQ RI WKH H[WUDFWHG XULQH VDPSOHV WR SURGXFH D SHDN DUHD WLPHV WKDW RI D GLOXWHG XULQH EODQN F (OHFWURQ PXOWLSOLHU VHWWLQJ DW 9 G (OHFWURQ PXOWLSOLHU VHWWLQJ DW 9 H (OHFWURQ PXOWLSOLHU VHWWLQJ DW 9

PAGE 127

b 5HODWLYH ,QWHQVLW\ b b bW 7LPH )LJXUH 650 FKURPDWRJUDPV RI +3*( LQ XULQH H[WUDFWHG ZLWK D &,6 FROXPQ DQG VHSDUDWHG ZLWK D P *& FROXPQ DQG GLOXWHG WR \LHOG Df SJ +3*( Ef SJ ?3*( Ff 8ULQH EODQN QR +3*(f

PAGE 128

D DUH WKH FRQFHQWUDWLRQV RI +3*( LQ XULQH ZKLFK SURGXFH D SHDN DUHD WKUHH WLPHV WKH DUHD FDOFXODWHG IURP D EODQN XULQH VDPSOH FRQWDLQLQJ QR +A3*( GLOXWHG ZLWK WKH VDPH SURFHGXUH $Q H[DPSOH RI D /2' FDOFXODWLRQ IRU PHWKRG %f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f RQO\ VHUYHV WR ZRUVHQ WKH /2' &RPSDULQJ PHWKRGV + DQG KRZHYHU LQGLFDWHV WKDW WKH EHVW OLPLWV RI GHWHFWLRQ FDQ EH UHJDLQHG ZLWK 650 E\ VLPSOH UHGXFLQJ WKH DPRXQW RI *& VHSDUDWLRQ WKDW LV HPSOR\HG 7KHVH UHVXOWV VLPSO\ FRQILUP WKH IDFW WKDW WKH /2' LQ D UHDO VDPSOH LV D IXQFWLRQ RI ERWK VHQVLWLYLW\ DQG VHOHFWLYLW\ :KHWKHU DGGLQJ DQRWKHU VWHS WR HQKDQFH WKH VHOHFWLYLW\ HJ 650f ZLWK WKH FRQFRPLWDQW ORVV LQ VHQVLWLYLW\ HJ WKH OHVVWKDQ XQLW\ &$' HIILFLHQF\ DQG WUDQVPLVVLRQ HIILFLHQF\ WKURXJK D VHFRQG PDVV DQDO\]HUf ZLOO LPSURYH RU GHJUDGH WKH /2' LV D IXQFWLRQ RI WKH LQWHUIHUHQFHV ZKLFK UHPDLQ LQ WKH VDPSOH 'LIIHUHQFHV LQ WKH /2' IRU YDULRXV VDPSOH SUHSDUDWLRQV *& FROXPQ OHQJWKV DQG PDVV VSHFWURPHWULF GHWHFWLRQ PRGHV DUH GLVFXVVHG LQ GHWDLO WKURXJKRXW WKLV FKDSWHU 7KH VORSHV RI WKH VL[ FDOLEUDWLRQ FXUYHV IRU 3*( VWDQGDUG XWLOL]LQJ 6,0 DQG 650 ZLWK GLIIHUHQW FROXPQ OHQJWKV DUH OLVWHG LQ 7DEOH E

PAGE 129

1RWH WKDW QRW DOO RI WKHVH VHQVLWLYLWLHV FDQ EH GLUHFWO\ FRPSDUHG GXH WR WKH YDULRXV HOHFWURQ PXOWLSOLHU YROWDJHV HPSOR\HG &RPSDULVRQ RI WKH VORSHV IRU 650 DQG 6,0 XVLQJ D P *& FROXPQ \LHOGV D VHQVLWLYLW\ UDWLR RI RU b 7KLV FRUUHVSRQGV WR DSSUR[LPDWHO\ D WLPHV GHFUHDVH LQ VHQVLWLYLW\ IRU 650 DQDO\VLV FRPSDUHG WR 6,0 'LIIHUHQFHV LQ WKH VHQVLWLYLW\ IRU WKH YDULRXV *& FROXPQ OHQJWKV ZLOO EH GLVFXVVHG LQ GHWDLO LQ D ODWHU VHFWLRQ RI WKLV FKDSWHU 6XPPDU\ RI 5HVXOWV 7KH FRQFHQWUDWLRQV RI HQGRJHQRXV 3*( LQ XULQH IRXQG XWLOL]LQJ WKH VHYHQ GLIIHUHQW DQDO\WLFDO VFKHPHV DJUHHV IDYRUDEO\ ZLWK WKRVH LQ WKH OLWHUDWXUH $OO WKH UHVXOWV DUH VLPLODU ZLWK DQ DYHUDJH RI SJP/ DQG D b56' RI b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

PAGE 130

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f

PAGE 131

b 5HODWLYH ,QWHQVLW\ )LJXUH r P *& FROXPQ 6,0 FKURPDWRJUDPV RI HQGRJHQRXV 3*(J LQ XULQH H[WUDFWHG ZLWK Df & FROXPQ Ef t ,$ FROXPQV

PAGE 132

b 5HODWLYH ,QWHQVLW\ ba? b L 7LPH Df )LJXUH P *& FROXPQ 6,0 FKURPDWRJUDPV RI HQGRJHQRXV 3*( LQ XULQH H[WUDFWHG ZLWK Df & FROXPQ Ef & t ,$ FROXPQV

PAGE 133

b 5HODWLYH ,QWHQVLW\ b Q b Q Ef 3*( 7LPH )LJXUH P *& FROXPQ 650 FKURPDWRJUDPV RI HQGRJHQRXV 3*( LQ XULQH H[WUDFWHG ZLWK Df & FROXPQ Ef & t ,$ FROXPQV

PAGE 134

,I D GLIIHUHQW PDVV VSHFWURPHWULF WHFKQLTXH LV HPSOR\HG WKH GLIIHUHQFHV EHWZHHQ WKH WZR VDPSOH SUHSDUDWLRQV UHPDLQ SURPLQHQW ,Q )LJXUH VHSDUDWLRQ RQ D P *& FROXPQ LV XVHG ZLWK 650 7KH FKURPDWRJUDP XWLOL]LQJ RQO\ & H[WUDFWLRQ )LJXUH Df VKRZV D UHGXFWLRQ LQ WKH FKHPLFDO QRLVH GXH WR WKH XVH RI 0606 EXW ZLWK WKH ODFN RI VHSDUDWLRQ RI WKH P *& FROXPQ HYHQ 650 FDQQRW JLYH DGHTXDWH GHWHFWLRQ RI HQGRJHQRXV OHYHOV RI 3*( LQ XULQH )LJXUH E GHPRQVWUDWHV WKDW ZLWK & DQG ,$ VDPSOH SUHSDUDWLRQ DQG WKH DGGLWLRQDO UHGXFWLRQ LQ FKHPLFDO QRLVH E\ XWLOL]DWLRQ RI 650 3*( LQ XULQH FDQ EH HDVLO\ GHWHFWHG 7KH VHQVLWLYLW\ DQG VHOHFWLYLW\ RI WKH GLIIHUHQW VDPSOH SUHSDUDWLRQV DUH UHIOHFWHG LQ WKH OLPLWV RI GHWHFWLRQ /2'f LQ 7DEOH D 7KH UHVXOWV REWDLQHG IURP WKLV VWXG\ VKRZ QR GLIIHUHQFH LQ WKH /2' IRU RQO\ WKH & H[WUDFWLRQ DQG WKH & DQG ,$ SXULILFDWLRQ ZKHQ XWLOL]LQJ D P *& FROXPQ ZLWK 6,0 7KH /2' IRXQG IRU & DQG ,$ SXULILFDWLRQ XVLQJ D P ZLWK 650 SJf ZDV VOLJKWO\ ZRUVH WKDQ IRU RQO\ & H[WUDFWLRQ ZLWK WKH VDPH FRQGLWLRQV ,Q WKHRU\ LI WKH & H[WUDFWLRQ DORQH ZLWK P *&0606 SURYLGHG DGHTXDWH VHSDUDWLRQ RI XULQH PDWUL[ FRPSRQHQWV IURP WKH HQGRJHQRXV 3*( WKHQ DGGLWLRQ RI DQRWKHU XQQHHGHGf H[WUDFWLRQ VWHS ,$f RQO\ VHUYHV WR UHGXFH WKH VHQVLWLYLW\ GXH WR OHVV WKDQ b UHFRYHU\ RI WKH 3*( LQ XULQH $QRWKHU LPSRUWDQW IDFWRU WR FRQVLGHU LV WKH WLPH WR SUHSDUH WKH VDPSOH EHIRUH WKH GHULYDWL]DWLRQ 7KH & H[WUDFWLRQ LV VLPSOH DQG UDSLG RQO\ UHTXLULQJ DSSUR[LPDWHO\ WR PLQXWHV IRU D P/ XULQH VDPSOH WR EH SUHSDUHG 7KH DGGLWLRQDO ,$ SXULILFDWLRQ UHTXLUHV DSSUR[LPDWHO\ PLQXWHV SHU VDPSOH WKXV DQ HQWLUH VDPSOH SUHSDUDWLRQ WLPH RI WR PLQXWHV +RZHYHU WKH ,$ SXULILFDWLRQ LV VWLOO PRUH UDSLG WKDQ

PAGE 135

7RWDO 7LPH PLQf b 5HTXLUHG 6HOHFWLYLW\ Df )LJXUH 6XPPDU\ RI WKH UHODWLYH GLIIHUHQFHV LQ VDPSOH SUHSDUDWLRQ PHWKRGV IRU Df 6HOHFWLYLW\ Ef 7RWDO WLPH

PAGE 136

FRQYHQWLRQDO FKURPDWRJUDSKLF SXULILFDWLRQ PHWKRGV )XUWKHUPRUH WKH DGGLWLRQDO WLPH IRU WKH ,$ VWHS LV D ZRUWKZKLOH WUDGHRII IRU WKH FRQVLGHUDEOH JDLQ LQ VHOHFWLYLW\ WKDW LV DFKLHYHG E\ WKLV PHWKRG 7KH GLIIHUHQFHV LQ UHODWLYH VHOHFWLYLW\ DQG WLPH RI DQDO\VLV DUH VXPPDUL]HG LQ )LJXUH 7KH WRS OLQH RQ )LJXUH D UHSUHVHQWV WKH VHOHFWLYLW\ UHTXLUHG WR GHWHFW HQGRJHQRXV OHYHOV RI 3*( LQ XULQH DSSUR[LPDWHO\ SJP/f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f LQFUHDVHV WKH VHOHFWLYLW\ RI WKH PHWKRG DOEHLW DW D FRVW RI ORQJHU DQDO\VLV WLPH 8OWLPDWHO\ D P *& FROXPQ SRVVHVV WKH JUHDWHVW VHOHFWLYLW\ IRU WKLV DQDO\VLV +RZHYHU DV ZDV GLVFXVVHG SUHYLRXVO\ WKH XWLOL]DWLRQ RI & DQG ,$ IRU VDPSOH SUHSDUDWLRQ SURGXFHV D FOHDQ HQRXJK VDPSOH WKDW VHOHFWLYLW\ VHSDUDWLRQf RI D P *& FROXPQ LV DGHTXDWH IRU VHSDUDWLRQ RI XULQH PDWUL[ FRPSRQHQWV IURP 3*( )LJXUH F VKRZV WKDW ZLWK WKLV PHWKRG RI DQDO\VLV KRZHYHU

PAGE 137

b 5HODWLYH ,QWHQVLW\ )LJXUH 6,0 FKURPDWRJUDPV RI HQGRJHQRXV 3*( LQ XULQH H[WUDFWHG ZLWK & DQG ,$ FROXPQV DQG VHSDUDWHG ZLWK Df P *& Ef P *& Ff P *&

PAGE 138

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b DV VHQVLWLYH DV WKDW ZLWK WKH P *& FROXPQ ,Q DGGLWLRQ SHDN DUHDV IRU WKH SJ RI +A3*( LQWHUQDO VWDQGDUG XWLOL]LQJ D P *& FROXPQ DUH DSSUR[LPDWHO\ IRXU WLPHV ODUJHU WKDQ IRU D P *& FROXPQ 7KHUHIRUH WKHVH UHVXOWV VXJJHVW WKDW JUHDWHU WKDQ b RI WKH GHULYDWL]HG 3*( LV ORVW VRPHZKHUH DORQJ WKH P *& FROXPQ 7KLV PD\ RFFXU GXH WR DGVRUSWLRQ RQ WKH *& FROXPQ RU GHFRPSRVLWLRQ RI WKH GHULYDWL]HG 3*( RQ WKH FROXPQ 6LPLODU REVHUYDWLRQV ZHUH PDGH LQ DQ HDUOLHU UHSRUW ZLWK D P *& FROXPQ f 7KH UHVHDUFKHUV UHSRUWHG WKDW DIWHU UHSHDWHG DQDO\VHV RI GHUYLDWL]HG 3* VDPSOHV RQ D P *& FROXPQ VXEVWDQWLDO ORVV RI SDUWLFXODU 3*V HJ

PAGE 139

3*( EXW QRW 3*)Df RFFXUHG &RQVHTXHQWO\ 3*( ZRXOG KDYH OHVV WLPH DQG OHQJWK RI FROXPQ WR LQWHUDFW ZLWK WKH VWDWLRQDU\ SKDVH ZKHQ VKRUWHU *& FROXPQ OHQJWKV HJ P RU Pf DUH XWLOL]HG 7KH FKURPDWRJUDPV LQ )LJXUH VKRZ WKH REYLRXV WLPH GLIIHUHQWLDO EHWZHHQ WKH WKUHH OHQJWKV RI *& FROXPQ $QDO\VLV RI 3*( ZLWK D P *& FROXPQ UHTXLUHV PLQ ZLWK D P *& FROXPQ PLQ DQG ZLWK D P *& FROXPQ PLQ 6LQFH WKHVH FKURPDWRJUDPV XWLOL]H WKH VDPH VDPSOH SUHSDUDWLRQ PHWKRG WKH RQO\ GLIIHUHQFH LQ WKH WLPH RI DQDO\VLV LV EDVHG RQ WKH OHQJWK RI WKH *& FROXPQ )XUWKHUPRUH WKH P *& FROXPQ UHTXLUHV KLJKHU HOHYDWHG WHPSHUDWXUHV IRU HOXWLRQ RI 3*( LQ XULQH ar&f WKDQ D P ar&f RU P ar&f *& FROXPQ 7KLV HOHYDWHG WHPSHUDWXUH FRUUHVSRQGV WR DQ DGGLWLRQDO WLPH LQFUHDVH UHTXLUHG WR FRRO WKH RYHQ WR WKH LQLWLDO VWDUWLQJ WHPSHUDWXUH RI r& ,I ZH FRPSDUH WKH WRWDO *& DQDO\VLV WLPH DQ DQDO\VLV XWLOL]LQJ D P *& FROXPQ )LJXUH Df ZRXOG UHTXLUH PLQ EHIRUH LQMHFWLQJ WKH QH[W VDPSOH FRPSDUHG WR PLQ IRU D P *& FROXPQ 7KLV FRUUHVSRQGV WR WKH DQDO\VLV RI VDPSOHV D GD\ ZLWK D P *& FROXPQ ZLWK WKHVH FRQGLWLRQV FRPSDUHG WR VDPSOHV D GD\ ZLWK D P *& FROXPQ 7KXV IRU D VOLJKW ORVV LQ VHOHFWLYLW\ ZLWK D P *& FROXPQ WZLFH WKH QXPEHU RI VDPSOHV FDQ EH TXDQWLWDWHG LQ D GD\ IRU 3*( LQ XULQH $ VXPPDU\ VLPLODU WR WKH RQH SUHVHQWHG HDUOLHU IRU VDPSOH SUHSDUDWLRQ )LJXUH f LV VKRZQ LQ )LJXUH IRU VDPSOH LQWURGXFWLRQ 7KLV ILJXUH LQGLFDWHV JUDSKLFDOO\ WKH UHODWLYH WUDGHRIIV EHWZHHQ WKH VHOHFWLYLW\ DQG WLPH RI DQDO\VLV IRU WKH WKUHH GLIIHUHQW *& FROXPQV )LJXUH D VKRZV WKDW D P FROXPQ SRVVHVVHV WKH JUHDWHVW VHOHFWLYLW\ KRZHYHU )LJXUH E GLVSOD\V WKH IDFW WKDW WKLV VDPH OHQJWK RI *& FROXPQ

PAGE 140

Df !! R \ 2f HQ ‘R FU f FU P *& P *& P *& *& &GXPQ /HQJWK Ef ne ( f§ R R *& &ROXPQ /HQJWK )LJXUH 6XPPDU\ RI WKH UHODWLYH GLIIHUHQFHV LQ *& FROXPQ OHQJWKV IRU Df 6HOHFWLYLW\ Ef 7RWDO WLPH EHWZHHQ *& LQMHFWLRQV

PAGE 141

KDV D WRWDO DQDO\VLV WLPH WZLFH DV ORQJ DV D P *& FROXPQ )LQDOO\ WKH WKUHH *& FROXPQV GR QRW SRVVHVV HQRXJK VHOHFWLYLW\ ZLWKRXW VDPSOH SUHSDUDWLRQ DQG D GHWHFWLRQ VFKHPH WR UHDFK WKH UHTXLUHG VHOHFWLYLW\ OLQH RQ WKH ILJXUH 0DVV 6SHFWURPHWULF $QDO\VLV 6,0 YV 650 7KH DGYDQWDJHV RI XVLQJ 650 IRU PL[WXUH DQDO\VLV KDYH EHHQ SRLQWHG RXW HDUOLHU LQ &KDSWHU 8WLOL]DWLRQ RI 650 UHGXFHV WKH FKHPLFDO QRLVH LQKHUHQW LQ DQDO\VLV RI FRPSOH[ ELRORJLFDO PDWULFHV f )LJXUH FRPSDUHV WKH 6,0 FKURPDWRJUDP WR WKH 650 FKURPDWRJUDP RI HQGRJHQRXV 3*( LQ XULQH HPSOR\LQJ & H[WUDFWLRQ ZLWK D P *& FROXPQ 7KH UHGXFWLRQ RI WKH FKHPLFDO LQWHUIHUHQFH VLJQDO E\ 650 )LJXUH OLEf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

PAGE 142

b 5HODWLYH ,QWHQVLW\ b b 7LPH )LJXUH P *& FROXPQ FKURPDWRJUDPV RI HQGRJHQRXV 3*( LQ XULQH H[WUDFWHG ZLWK D & FROXPQ XWLOL]LQJ Df 6,0 Ef 650

PAGE 143

b 5HODWLYH ,QWHQVLW\ bQ b L 7LPH Df )LJXUH P *& FROXPQ FKURPDWRJUDPV RI HQGRJHQRXV 3*( LQ XULQH H[WUDFWHG ZLWK & DQG ,$ FROXPQV XWLOL]LQJ Df 6,0 Ef 650

PAGE 144

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b IRU WKH VHOHFWHGUHDFWLRQ FKRVHQ ,Q DGGLWLRQ IRU 650 WKH VHFRQG PDVV DQDO\]HU 4f LV XVHG DV D PDVV ILOWHU UDWKHU WKDQ DQ 5) RQO\ TXDGUXSROH WKXV D ORZHU WUDQVPLVVLRQ HIILFLHQF\ LV H[SHFWHG W\SLFDOO\ bf +RZHYHU WKH VHOHFWLYLW\ JDLQHG E\ WKH SDUHQWGDXJKWHU UHDFWLRQ UHGXFHV WKH FKHPLFDO QRLVH WR D JUHDWHU H[WHQW WKDQ WKH DQDO\WLFDO VLJQDO LQ D VDPSOH PDWUL[ RIWHQ FRPSHQVDWLQJ IRU WKH ORVW VHQVLWLYLW\ 7KH GLIIHUHQFHV LQ WKH /2' IRU GLIIHUHQW VDPSOH SUHSDUDWLRQV DQG *& FROXPQ OHQJWKV XWLOL]LQJ 6,0 DQG 650 FDQ EH IRXQG LQ 7DEOH D 7KH ORZHVW OLPLWV RI GHWHFWLRQ SJf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

PAGE 145

5HTXLUHG 6HOHFWLYLW\ 0DVV 6SHFWURPHWULF 'HWHFWLRQ 0HWKRGV )LJXUH 6XPPDU\ RI WKH UHODWLYH GLIIHUHQFHV LQ VHOHFWLYLW\ IRU 6,0 DQG 650

PAGE 146

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f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f GHWHFWLRQ PHWKRGV )LJXUH Df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

PAGE 147

Df b AA 6DUD 3UHR *& &FLPUWV 'HWHFWDQ Ef ! m 7M f 6n &e &O t ,$ &P *& P *& 60 W L L 650 $QG\WLFG 6FKHPHV )LJXUH 6XPPDU\ RI WKH UHODWLYH GLIIHUHQFHV LQ Df 6HOHFWLYLW\ IRU YDULRXV SDUDPHWHUV Ef 6HOHFWLYLW\ IRU YDULRXV DQDO\WLFDO VFKHPHV Ff 7RWDO WLPH RI DQDO\VLV IRU YDULRXV DQDO\WLFDO VFKHPHV

PAGE 148

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f IRU VDPSOH SUHSDUDWLRQ DQG LQWURGXFWLRQ PHWKRGV UHTXLUH ORQJHU WLPHV RI DQDO\VLV 7KH WRWDO DQDO\VLV WLPH IRU PHWKRGV & DQG LV VKRZQ LQ )LJXUH F &RPSDULQJ WKLV ILJXUH ZLWK )LJXUH E IRU VHOHFWLYLW\ WKH REYLRXV WUDGHRIIV EHWZHHQ WRWDO DQDO\VLV WLPH DQG VHOHFWLYLW\ IRU WKHVH

PAGE 149

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

PAGE 150

&+$37(5 (9$/8$7,21 2) 62/,'3+$6( (;75$&7,21 352%(0606 )25 7+( $1$/<6,6 2) (1'2*(1286 35267$*/$1',1 ( ,1 85,1( ,QWURGXFWLRQ ,Q &KDSWHU WKH XVH RI & DQG LPPXQRDIILQLW\ ,$f SXULILFDWLRQ FRXSOHG WR D VKRUW P *& FROXPQ ZLWK VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f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f FDQQRW EH VHSDUDWHG E\ *& ZLWK RQO\ 3)% GHULYDWL]DWLRQ LW ZRXOG EH SRVVLEOH WR HPSOR\ D OHVV VHOHFWLYH VDPSOH LQWURGXFWLRQ WHFKQLTXH VXFK DV FRQYHQWLRQDO VROLGV SURGH 06 RU GLUHFW FKHPLFDO LRQL]DWLRQ SUREH '&,f 8QIRUWXQDWHO\ WKH WRWDO F\FOH WLPH IRU SUREH VDPSOH LQWURGXFWLRQ LV DFWXDOO\ ORQJHU WKDQ IRU VKRUW *& FROXPQ LQWURGXFWLRQ GLVFXVVHG LQ &KDSWHU )XUWKHUPRUH WKH IDFW WKDW HVVHQWLDOO\ DOO PL[WXUH FRPSRQHQWV GHVRUE LQWR WKH LRQ VRXUFH DW QHDUO\ WKH VDPH WLPH LQFUHDVHV WKH SUREDELOLW\ RI TXHQFKLQJ RI WKH HOHFWURQ

PAGE 151

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f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/ RI HWK\O DFHWDWH WR WKH XULQH VDPSOHV

PAGE 152

DQG r/ WR WKH VWDQGDUGV IRU WKH FDOLEUDWLRQ FXUYH 2QHPLFUROLWHU LQMHFWLRQV FRQWDLQLQJ SJ RI +A3*( ZHUH HLWKHU GLUHFWO\ SODFHG LQ VDPSOH YLDOV IRU WKH VROLGV SUREH RU FRDWHG RQWR WKH ZLUH ORRS RI WKH '&, SUREH ,QVWUXPHQWDO &RQGLWLRQV $ )LQQLJDQ 0$7 WULSOH VWDJH TXDGUXSROH 764f JDV FKURPDWRJUDSK WDQGHP PDVV VSHFWURPHWHU ZDV XVHG IRU WKHVH VWXGLHV 0DVV VSHFWURPHWU\ FRQGLWLRQV ZHUH LQWHUIDFH DQG WUDQVIHU OLQH WHPSHUDWXUH r& LRQL]HU WHPSHUDWXUH r& HOHFWURQ HQHUJ\ H9 DQG HPLVVLRQ FXUUHQW P$ (OHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ (&1&,f ZDV FDUULHG RXW ZLWK PHWKDQH DW DQ LRQL]HU SUHVVXUH RI WRUU $UJRQ ZDV HPSOR\HG DV WKH FROOLVLRQ JDV DW D SUHVVXUH RI P7RUU D FROOLVLRQ HQHUJ\ RI H9 ZDV XWLOL]HG IRU WKH VHOHFWHGUHDFWLRQ PRQLWRULQJ VWXGLHV RI 3*( 7KH 650 H[SHULPHQWV HPSOR\HG DQ (0 VHWWLQJ RI 9 DQG D SUHDPS JDLQ RI R 9$ $ FDOLEUDWLRQ FXUYH ZDV REWDLQHG IRU WKH '&, VWXGLHV E\ DQDO\]LQJ VWDQGDUG VROXWLRQV FRQWDLQLQJ D FRQVWDQW DPRXQW RI +A3*( QJf DQG LQFUHDVLQJ DPRXQWV RI 3*( DV OLVWHG LQ 7DEOH LQ &KDSWHU 7KH TXDQWLWDWLRQ RI WKH HQGRJHQRXV OHYHOV RI 3*( LQ XULQH ZDV DFFRPSOLVKHG E\ VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f RI n f IRU 3*( DQG f f IRU WKH LQWHUQDO VWDQGDUG +A3*( $ EDVHOLQH ZDV FKRVHQ YLVXDOO\ RQ WKH VROLGV SUREH RU '&, SUREH WUDFH DQG WKH DUHDV IRU 3*( DQG S +A3*( FDOFXODWHG E\ WKH ,1&26 FRPSXWHU V\VWHP IRU WKH FDOLEUDWLRQ FXUYH DQG WKH H[WUDFWHG XULQH VDPSOHV 7KH DUHD RI 3*( GLYLGHG E\ WKH DUHD RI +A3*( LQ WKH VWDQGDUGV JLYHV D UDWLR ZKLFK LV XVHG LQ WKH FDOLEUDWLRQ FXUYH 7KH DPRXQW RI 3*( LQ HDFK XULQH VDPSOH ZDV FDOFXODWHG DFFRUGLQJ

PAGE 153

WR WKH PHWKRG GHVFULEHG HDUOLHU LQ &KDSWHU 7KH VROLGV SUREH DQDO\VLV ZDV SHUIRUPHG E\ SODFLQJ WKH GLOXWHG XULQH VDPSOH RU VWDQGDUG LQWR D VPDOO JODVV YLDO DQG HYDSRUDWLQJ WKH HWK\O DFHWDWH LQ DLU 7KH SUREH WHPSHUDWXUH ZDV LQLWLDOO\ VHW DW r& DQG WKHQ LQFUHDVHG DW r&PLQ WR r& IRU WKH VWDQGDUGV XULQH EODQN DQG XULQH VDPSOHV DQDO\]HG 7KH '&, DQDO\VLV ZDV SHUIRUPHG E\ FRDWLQJ WKH ZLUH ORRS RI WKH )LQQLJDQ GLUHFW H[SRVXUH SUREH ZLWK WKH VDPSOH DQG DOORZLQJ WKH HWK\O DFHWDWH WR HYDSRUDWH LQ DLU 7KH KHDWLQJ FXUUHQW LQLWLDOO\ P$ ZLWK WKH SUREH DW URRP WHPSHUDWXUHf ZDV LQFUHDVHG DW P$V r&PLQf IRU PLQ 6ROLGV 3UREH $QDO\VLV (&1&, DQG 'DXJKWHU 6SHFWUD RI 6WDQGDUG 3*( 7KH (&1&, PDVV VSHFWUXP IRU VWDQGDUG 3*( ZLWK QR GHULYDWL]DWLRQ LV VKRZQ LQ )LJXUH OD 7KLV PDVV VSHFWUXP RI QJ RI 3*( LV GRPLQDWHG E\ LRQV FRUUHVSRQGLQJ WR WKH ORVV RI RQH ff DQG WZR f ZDWHU PROHFXOHV IURP WKH 0f LRQ 7KH 0n LRQ RI 3*( ff KDV D ORZ UHODWLYH DEXQGDQFH RI RQO\ b FRPSDUHG WR WKH LQWHQVH LRQV REVHUYHG IURP WKH ORVV RI RQH DQG WZR ZDWHU PROHFXOHV 7KH ODUJH UHODWLYH DEXQGDQFH RI WKH DQG LRQV VXJJHVWV WKDW GHK\GUDWLRQ RI WKH 3*( PROHFXOHV PD\ RFFXU EHIRUH WKH LRQL]DWLRQ SURFHVV DV WKH\ DUH GHVRUEHG IURP WKH JODVV VDPSOH YLDO DV WKH SUREH LV KHDWHG ,Q DGGLWLRQ SRVLWLYH FKHPLFDO LRQL]DWLRQ 3&,f ZDV SHUIRUPHG DQG HYDOXDWHG 7KH UHVXOWV IURP WKVH H[SHULPHQWV VKRZ WKDW ZLWKRXW GHULYDWL]DWLRQ WKH 3&, PDVV VSHFWUXP KDV D PXFK ORZHU VHQVLWLYLW\ WKDQ WKDW RI (&1&,

PAGE 154

b 5HODWLYH $EXQGDQFH b U Df f b Ef P] >0+ @ U 6ROLGV SUREH HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ PDVV VSHFWUXP RI Df 8QGHULYDWL]HG 3*( VWDQGDUG OSJf Ef 3)% HVWHU GHULYDWLYH RI 3*( QJf )LJXUH

PAGE 155

7KH 3)% GHULYDWLYH RI 3*( ZDV SUHSDUHG DQG HYDOXDWHG WR FRPSDUH WKH VHQVLWLYLW\ XWLOL]LQJ WKLV DEEUHYLDWHG GHULYDWL]DWLRQ SURFHGXUH WR WKDW RI WKH XQGHULYDWL]HG VWDQGDUG )LJXUH OE VKRZV WKH (&1&, PDVV VSHFWUXP RI QJ RI WKH 3)% HVWHU GHULYDWLYH RI 3*( 7KLV PDVV VSHFWUXP LV VLPLODU WR )LJXUH OD RI WKH XQGHULYDWL]HG 3*( KRZHYHU WKH PRVW DEXQGDQW LRQ LV WKH >03)%+@ LRQ UDWKHU WKDQ WKH >0+@n LRQ 7KH >03)%+@ LRQ LV DOVR SURPLQHQW LQ )LJXUH OE ZLWK RWKHU OHVV LQWHQVH LRQV bf SUHVHQW LQ WKH PDVV VSHFWUXP $JDLQ WKHVH LRQV PD\ UHIOHFW WKHUPDO GHK\GUDWLRQ DV WKH 3)% GHULYDWL]HG 3*( LV YDSRUL]HG RII WKH SUREH 7KH n LRQ FRUUHVSRQGV WR WKH >03)%@n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n LRQ LQ WKH (& 1&, PDVV VSHFWUXP VXEVHTXHQWO\ SURGXFHV D ORZ LQWHQVLW\ GDXJKWHU VSHFWUXP RI WKH >03)%@n LRQ )LJXUH f $ GDXJKWHU VSHFWUXP ZLWK PDQ\ ORZ LQWHQVLW\ IUDJPHQW LRQV LV VKRZQ LQ )LJXUH 7KH PRVW DEXQGDQW LRQ LQ WKH VSHFWUXP LV WKH n LRQ FRUUHVSRQGLQJ WR >03)%+&@n 6XEVHTXHQWO\ WKLV LRQ ZDV FKRVHQ IRU VHOHFWHGUHDFWLRQ PRQLWRULQJ RI 3*( LQ XULQH 7KH RWKHU SURPLQHQW GDXJKWHU LRQV DUH OLVWHG LQ 7DEOH ZLWK WKH b UHODWLYH DEXQGDQFH DQG SUREDEOH LRQ DVVLJQPHQW 1RWH WKDW WKH

PAGE 156

b 5HODWLYH $EXQGDQFH )LJXUH 6ROLGV SUREH GDXJKWHU LRQ VSHFWUXP RI WKH >03)%@n LRQ RI WKH 3)% HVWHU GHULYDWLYH RI 3*( QJf DW P7RUU RI DUJRQ DQG H9 FROOLVLRQ HQHUJ\

PAGE 157

7DEOH 'DXJKWHU ,RQV RI >03)%@f 3ff RI 3*( 3)% (VWHU $QDO\]HG E\ 'LUHFW 6ROLGV 3UREH ,RQ $VVLJQPHQW P] 5$f >3@n >3+@f >3+@n >3+&@n >3+&&+Mr >3+&&+@ RU >3+2&2&+@ ‘a r f r D b 5HODWLYH DEXQGDQFH DW D FROOLVLRQ JDV SUHVVXUH RI P7RUU DUJRQ DQG FROOLVLRQ HQHUJ\ RI H9

PAGE 158

>03)%+@ LRQ LQ WKH (&1&, PDVV VSHFWUXP FRXOG KDYH EHHQ FKRVHQ IRU 0606 ZLWK DQ LQFUHDVH LQ VHQVLWLYLW\ RI DSSUR[LPDWHO\ 6WXG\ RI (QGRJHQRXV /HYHOV RI 3*(A LQ 8ULQH )LJXUH VKRZV WKH 650 WUDFHV RI D SJ 3*( VWDQGDUG D XULQH EODQN FRQWDLQLQJ HQGRJHQRXV OHYHOV RI 3*( ZLWK QR +3*( DGGHGf DQG D XULQH VDPSOH FRQWDLQLQJ SJ RI +A3*( 7KH XULQH EODQN DQG VDPSOH ZHUH SUHSDUHG E\ HVVHQWLDOO\ WKH VDPH PHWKRG ZLWK & DQG ,$ SXULILFDWLRQ WKHQ GHULYDWL]HG WR WKH 3)% HVWHU RI 3*( 7KLV H[SHULPHQW ZDV SHUIRUPHG ZLWK D WHPSHUDWXUH UDPS RI r&PLQ DV GHVFULEHG LQ WKH H[SHULPHQWDO VHFWLRQ RI WKLV FKDSWHU 7KH WUDFH IRU WKH 3*( VWDQGDUG )LJXUH Df VKRZV RQH GLVWLQFW SHDN ZLWK D ORZ OHYHO RI QRLVH )LJXUH E VKRZV WKH FKURPDWRJUDP RI WKH XULQH EODQN ZLWK WKH VDPH FRQGLWLRQV DV WKH VWDQGDUG LQ )LJXUH D $ GLVWLQFW SHDN IRU HQGRJHQRXV 3*( LV QRWLFHG EXW LQ WKLV FDVH WKH QRLVH OHYHO KDV LQFUHDVHG GUDVWLFDOO\ FRPSDUHG WR WKH UHODWLYH LQWHQVLW\ RI WKH 3*( SHDN 7KH SHDN DUHD RI WKH 3*( VWDQGDUG LQ )LJXUH D LV WLPHV JUHDWHU WKDQ WKH SHDN DUHD RI WKH HQGRJHQRXV OHYHO RI 3*( LQ WKH XULQH EODQN )LJXUH Ef 5HVXOWV IURP &KDSWHU LQGLFDWH WKDW HQGRJHQRXV OHYHOV RI 3*( LQ XULQH DUH DSSUR[LPDWHO\ WR SJP/ 7KHUHIRUH WKH SHDN DUHD IRU WKH XULQH EODQN VKRXOG EH DSSUR[LPDWHO\ WKH VDPH DV WKDW RI WKH SJ 3*( VWDQGDUG LQ )LJXUH D 7KLV VXJJHVWV WKDW 3*( PD\ KDYH EHHQ ORVW GXULQJ WKH VDPSOH SUHSDUDWLRQ SURFHGXUH RU WKH UHPDLQLQJ XULQH PDWUL[ FRPSRQHQWV LQ WKH H[WUDFWHG VDPSOH LQWHUIHUH ZLWK WKH HIILFLHQW LRQL]DWLRQ RI WKH >03)%@r LRQ 7KLV VHFRQG SRVVLEOH H[SODQDWLRQ LV UHIIHUHG WR DV TXHQFKLQJ DQG PD\

PAGE 159

b 5HODWLYH ,QWHQVLW\ )LJXUH 6ROLGV SUREH 650 WUDFH RI D 3)% GHULYDWL]HG Df SJ 3*( VWDQGDUG Ef ([WUDFWHG XULQH EODQN Ff ([WUDFWHG XULQH VDPSOH FRQWDLQLQJ SJ RI +3*( LQWHUQDO VWDQGDUG

PAGE 160

RFFXU LQ WKH DQDO\VLV RI ELRORJLFDO VDPSOHV ZKHQ (&1&, LV XWLOL]HG ZLWKRXW H[WHQVLYH FKURPDWRJUDSKLF FOHDQXS f 7KH WUDFH IRU D XULQH VDPSOH ZKLFK FRQWDLQHG DQ DGGLWLRQDO SJ RI +A3*( ZKLFK ZDV QRW SUHVHQW LQ WKH XULQH EODQN )LJXUH Ef LV VKRZQ LQ )LJXUH F 7KH SHDN VKDSH IRU 3*( LV QRW DV GLVWLQFW DV LQ )LJXUHV D DQG E DQG WKH VLJQDO WR QRLVH UDWLR KDV GHFUHDVHG FRQVLGHUDEO\ IURP WKH SJ VWDQGDUG LQ )LJXUH F &RPSDULQJ WKH 3*( VWDQGDUG LQ )LJXUH D WR WKH XULQH VDPSOH WKH SHDN DUHD LV DSSUR[LPDWHO\ WLPHV ORZHU WKDQ WKDW FDOFXODWHG IRU WKH 3*( VWDQGDUG ,Q DGGLWLRQ WKH SHDN DUHD RI WKH XULQH EODQN )LJXUH Ef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

PAGE 161

DSSDUHQWO\ OHDG WR TXHQFKLQJ RI WKH >03)%@n LRQ GXULQJ WKH LRQL]DWLRQ SURFHVV UHVXOWLQJ LQ LQHIILFLHQW 650 7KHUHIRUH DIWHU H[DPLQLQJ WKHVH UHVXOWV DQG H[SHULPHQWLQJ IXUWKHU ZLWK GLIIHUHQW WHPSHUDWXUH UDPSV WKH VROLGV SUREH0606 PHWKRG ZDV QRW HPSOR\HG IRU TXDQWLWDWLRQ RI 3*( LQ XULQH 'LUHFW &KHPLFDO ,RQL]DWLRQ $QDO\VLV &RQFHSW RI 'LUHFW &KHPLFDO ,RQL]DWLRQ '&,f 7KH WHFKQLTXH RI '&, DOVR FDOOHG LQ EHDP RU GHVRUSWLRQ FKHPLFDO LRQL]DWLRQ PDVV VSHFWURPHWU\ ZDV ILUVW LQWURGXFHG E\ %DOGZLQ DQG 0F/DIIHUW\ f DQG DSSHDUV WR EH XVHIXO LQ WKH DQDO\VLV RI PHGLXP PROHFXODUZHLJKW SRODU FRPSRXQGV f 7\SLFDOO\ WKH WHFKQLTXH LQYROYHV FRDWLQJ D ZLUH SUREH ZLWK D VDPSOH ZKLFK LV WKHQ GLUHFWO\ LQVHUWHG LQWR WKH LRQ SODVPD LQ WKH FKHPLFDO LRQL]DWLRQ VRXUFH 7KH SUREH LV XVXDOO\ KHDWHG ZLWK DQ HOHFWULF FXUUHQW WR WHPSHUDWXUHV LQ H[FHVV RI r& ,Q PRVW FDVHV SRODU RUJDQLFV DUH YRODWLOL]HG LQWDFW IURP WKH SUREH WLS DW WHPSHUDWXUHV PXFK ORZHU WKDQ WKLV r& WR r&f 5HFHQWO\ WKLV WHFKQLTXH KDV EHHQ XWLOL]HG IRU ERWK SRVLWLYH DQG QHJDWLYH DPPRQLD '&, PDVV VSHFWURPHWU\ RI D QXPEHU RI 3*V ZLWKRXW SULRU GHULYDWL]DWLRQ f 7KLV UHSRUW GHPRQVWUDWHG WKH DGYDQWDJHV RI '&, PDVV VSHFWURPHWU\ LQ DQDO\]LQJ VWDQGDUG SURVWDJODQGLQV ZLWKRXW GHULYDWL]DWLRQ DQG WKH PHFKDQLVWLF DVSHFWV RI WKH JDVSKDVH FKHPLVWU\ LQYROYHG +RZHYHU RQO\ 3* VWDQGDUGV ZHUH LQYHVWLJDWHG DQG DW OHYHOV QJ RU PRUHf ZHOO DERYH HQGRJHQRXV OHYHOV RI 3*( LQ XULQH 7KHUHIRUH WKLV UDSLG VDPSOH LQWURGXFWLRQ WHFKQLTXH ZLWK D VKRUW GHULYDWL]DWLRQ SURFHGXUH ZDV HYDOXDWHG IRU GHWHUPLQLQJ HQGRJHQRXV 3*( LQ XULQH

PAGE 162

b 5HODWLYH F &2 7 & Q ?L" X )LJXUH 'LUHFW FKHPLFDO LRQL]DWLRQ HOHFWURQFDSWXUH QHJDWLYH FKHPLFDO LRQL]DWLRQ PDVV VSHFWUXP RI 3)% GHULYDWL]HG 3*( VWDQGDUG

PAGE 163

(&1&, DQG 'DXHKWHU 6SHFWUD RI 6WDQGDUG 3*( )LJXUH VKRZV WKH (&1&, PDVV VSHFWUXP RI SJ RI D 3)% GHULYDWL]HG 3*( VWDQGDUG 7KLV VSHFWUXP GLIIHUV IURP WKDW RI WKH 3)% GHULYDWL]HG 3*( XVLQJ WKH VROLGV SUREH )LJXUH OEf LQ WKDW WKH PRVW SURPLQHQW LRQ LV WKH >03)%@n FDUER[\ODWH DQLRQ ff UDWKHU WKDQ WKH LRQV FRUUHVSRQGLQJ WR D ORVV RI RQH RU WZR ZDWHU PROHFXOHV 7KH LPSRUWDQFH RI DFTXLULQJ DQ LQWHQVH SDUHQW LRQ >03)%@f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f LRQ RI D QJ 3)%GHULYDWL]HG 3*( VWDQGDUG XVLQJ WKH VROLGV SUREH FRUUHVSRQGLQJ WR D WLPHV KLJKHU VHQVLWLYLW\ IRU '&, 7KHUHIRUH WKLV PHWKRG VKRXOG SURYLGH DGHTXDWH VHQVLWLYLW\ IRU WKH DQDO\VLV RI 3*( DQG PD\ EH FRPSDUDEOH WR WKDW IRXQG IRU D P *& FROXPQ XWLOL]LQJ 650 LQ &KDSWHU 'DXJKWHU LRQ VSHFWUD RI WKH >03)%@ LRQ ff XQGHU GLIIHUHQW &$' FRQGLWLRQV DUH VKRZQ LQ )LJXUH D DQG )LJXUH E 7KH ILUVW )LJXUH Df GDXJKWHU VSHFWUXP ZDV REWDLQHG ZLWK D FROOLVLRQ HQHUJ\ RI H9 DQG D FROOLVLRQ JDV SUHVVXUH RI P7RUU RI DUJRQ )LJXUH E ZDV REWDLQHG

PAGE 164

b 5HODWLYH $EXQGDQFH b U Df b Ef P] Lrr L ‘ffn f_ 9n fQU ‘ LX}Uf X U ‘ L L n ‘ U ‘ L L QU ‘ ffnfL ‘ fWf} UrrL Lr QU PQ7Q L U L n n L L n L L )LJXUH 'LUHFW FKHPLFDO LRQL]DWLRQ GDXJKWHU LRQ VSHFWUD RI WKH >03)%@f LRQ RI WKH 3)% HVWHU GHULYDWLYH RI 3*( DW Df P7RUU RI DUJRQ DQG H9 Ef P7RUU RI DUJRQ DQG H9

PAGE 165

7DEOH 'DXJKWHU ,RQV RI >03)%@r 3ff RI 3*( 3)% (VWHU $QDO\]HG E\ 'LUHFW &KHPLFDO ,RQL]DWLRQ '&,f ,RQ $VVLHQPHQW P] b5$D bUDn >3@n >SK@ >3+@n >3+&@f >3+&&+@n RU >3+&&@f >3+&&+@f RU >3+2&2&+@ D b 5HODWLYH DEXQGDQFH DW D FROOLVLRQ JDV SUHVVXUH RI P7RUU DUJRQ DQG FROOLVLRQ HQHUJ\ RI H9 E ; 5HODWLYH DEXQGDQFH DW D FROOLVLRQ JDV SUHVVXUH RI P7RUU DUJRQ DQG FROOLVLRQ HQHUJ\ RI H9

PAGE 166

ZLWK D FROOLVLRQ HQHUJ\ RI H9 DQG D FROOLVLRQ JDV SUHVVXUH RI P7RUU RI DUJRQ 7KH SURPLQHQW LRQV LQ ERWK GDXJKWHU VSHFWUD DUH WKH VDPH DQG DUH OLVWHG LQ 7DEOH ZLWK WKH b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f WKH VSHFWUD DUH VLPLODU 7KLV LV WR EH H[SHFWHG VLQFH WKH &$' FRQGLWLRQV ZHUH LGHQWLFDO LQ ERWK FDVHV 7KH GLIIHUHQFHV LQ WKH LRQV UHODWLYH LQWHQVLW\ PD\ EH DWWULEXWHG WR WKH XVH RI GLIIHUHQW PHWKRGV RI VDPSOH LQWURGXFWLRQ DQG WKH PXFK ORZHU VLJQDOWRQRLVH UDWLR LQ )LJXUH 6WXG\ RI (QGRJHQRXV /HYHOV RI 3*( LQ 8ULQH )LJXUH VKRZV WKH 650 WUDFHV RI D SJ 3*( VWDQGDUG )LJXUH Df DV ZHOO DV D XULQH EODQN )LJXUH Ef DQG D XULQH VDPSOH FRQWDLQLQJ SJ RI +A3*( LQWHUQDO VWDQGDUG )LJXUH Ff SUHSDUHG E\ & DQG ,$ SXULILFDWLRQ 7KHVH WKUHH VDPSOHV ZHUH DQDO\]HG ZLWK '&, XWLOL]LQJ D r&PLQ WHPSHUDWXUH UDPS DV GHVFULEHG LQ WKH H[SHULPHQWDO VHFWLRQ 7KH 650 WUDFHV RI RI DOO WKUHH VDPSOHV VKRZV D GLVWLQFW SHDN

PAGE 167

b 5HODWLYH ,QWHQVLW\ )LJXUH 'LUHFW FKHPLFDO LRQL]DWLRQ 650 WUDFH RI D 3)% GHULYDWL]HG Df SJ 3*( VWDQGDUG Ef ([WUDFWHG XULQH EODQN Ff ([WUDFWHG XULQH VDPSOH FRQWDLQLQJ SJ RI +3*( LQWHUQDO VWDQGDUG

PAGE 168

ZKLFK YDSRUL]HV RII WKH '&, SUREH DSSUR[LPDWHO\ V DIWHU WKH KHDWLQJ KDV VWDUWHG &RPSDULQJ )LJXUH D WR )LJXUH E WKH SJ 3*( VWDQGDUG KDV D SHDN DUHD WR WLPHV JUHDWHU WKDQ WKH SHDN DUHD RI WKH HQGRJHQRXV 3*( LQ WKH XULQH EODQN 7KH SHDN DUHD RI WKH XULQH EODQN VKRXOG EH DSSUR[LPDWHO\ WKH VDPH DV WKH SJ VWDQGDUG IRU WKH UHDVRQV GHVFULEHG LQ WKH VROLGV SUREH VHFWLRQ ,Q DGGLWLRQ WKH SHDN DUHD RI WKH XULQH VDPSOH FRQWDLQLQJ SJ RI +3*( )LJXUH Ff ZDV WLPHV ORZHU WKDQ WKH SHDN DUHD RI WKH XULQH EODQN )LJXUH Ef DQG WLPHV ORZHU WKDQ WKH SHDN DUHD RI WKH VWDQGDUG )LJXUH Df ZLWK D GUDPDWLFDOO\ ORZHU VLJQDOWRQRLVH UDWLR 7KH TXHQFKLQJ HIIHFW QRWHG DERYH LV PRUH SURPLQHQW IRU WKH XULQH VDPSOH FRQWDLQLQJ WKH SJ RI +A3*( 7KH TXDQWLWLHV RI HQGRJHQRXV 3*( LQ XULQH REWDLQHG E\ XWLOL]LQJ '&,0606 ZLWK D r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b RI WKH SJ RI +A3*( 5HVXOWV IURP WKLV VWXG\ HVWDEOLVK WKH IDFW WKDW WKH XULQH PDWUL[ FRPSRQHQWV YDSRUL]H RII WKH '&, SUREH DW WKH VDPH WLPH DV WKH HQGRJHQRXV 3*( 7KH DYHUDJH YDOXHV REWDLQHG IRU WKH WKUHH VDPSOHV DUH DSSUR[LPDWHO\ WLPHV ODUJHU WKDQ WKH YDOXHV IRXQG IRU WKH VDPH XULQH

PAGE 169

1 )LJXUH &DOLEUDWLRQ FXUYH XWLOL]LQJ GLUHFW FKHPLFDO LRQL]DWLRQ ZLWK 650

PAGE 170

7DEOH 4XDQWLWDWLRQ 6WXG\ RI (QGRJHQRXV 3*( LQ 8ULQH 8WLOL]LQJ 'LUHFW &KHPLFDO ,RQL]DWLRQ '&,f0606D &RQFHQWUDWLRQ RI 3*( SJP/f 8ULQH 6DPSOH '&, ,QLHFWLRQ $YH RI ,QL b56'n $YHUDJH RI 8ULQH 6DPSOHV t SJP/ $YHUDJH RI 8ULQH 6DPSOHV SJP/ b56' RI 6DPSOHV & DQG ,$ SXULILFDWLRQ SHUIRUPHG RQ DOO XULQH VDPSOHV E b 5HODWLYH 6WDQGDUG 'HYLDWLRQ

PAGE 171

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f ZKLFK RFFXU GXULQJ WKH ,$ SXULILFDWLRQ SURFHGXUH 7KHVH LQWHUDFWLRQV ZHUH GLVFXVVHG HDUOLHU LQ &KDSWHU DQG WKH FRQVHTXHQFHV RI WKHVH LQWHUDFWLRQV DUH REYLRXV IURP WKH UHVXOWV RI WKH '&,0606 VWXGLHV 7KH XWLOL]DWLRQ RI DQ DGGLWLRQDO FOHDQn XS WHFKQLTXH DIWHU WKH VHOHFWLYH ,$ SXULILFDWLRQ VWHS ZDV HYDOXDWHG $QRWKHU ,$ FROXPQ ZDV HPSOR\HG ZKLFK KDG LPPXQRDIILQLW\ IRU SURVWDJODQGLQ NHWR)D DIWHU WKH ,$ SXULILFDWLRQ RI 3*( 7KH HOXHQW ZKLFK ZDV QRW

PAGE 172

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

PAGE 173

&+$37(5 &21&/86,216 $1' 68**(67,216 )25 )8785( :25. 6XPPDU\ $Q HYDOXDWLRQ RI WKH FRQFHSWV IRU WKH WUDFH GHWHUPLQDWLRQ RI SURVWDJODQGLQV 3*Vf E\ WDQGHP PDVV VSHFWURPHWU\ 0606f KDV EHHQ DFKLHYHG 5HVXOWV IURP WKH VWXGLHV LQ &KDSWHU GHPRQVWUDWH WKH LPSRUWDQFH RI WKH RSWLPL]DWLRQ RI YDULRXV SDUDPHWHUV LQ WKH FROOLVLRQDOO\DFWLYDWHG GLVVRFLDWLRQ &$'f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f >03)%@ DQG >0+@ FDUER[\ODWH DQLRQV LV VLJQLILFDQWO\ GLIIHUHQW IRU VXEWOH VWUXFWXUDO FKDQJHV LQ 3*V 7KURXJK WKH XVH RI WKHVH

PAGE 174

FXUYHV ZH KDYH VKRZQ WKDW )VHULHV 3*V IUDJPHQW OHVV HIILFLHQWO\ WKDQ 3*( DQG 3*'! $ SRVVLEOH H[SODQDWLRQ KDV EHHQ SURSRVHG WR H[SODLQ WKHVH GUDPDWLF GLIIHUHQFHV VHHQ LQ WKH IUDJPHQWDWLRQ EHKDYLRU RI VWUXFWXUDOO\ VLPLODU FDUER[\ODWH DQLRQV RI 3*V ,W LV EHOLHYHG WKDW )VHULHV 3*V DUH PRUH VWDEOH GXULQJ &$' GXH WR WKH LQWHUDFWLRQ RI WKH FDUER[\ODWH JURXS ZLWK WKH WZR 2+ JURXSV LQ WKH F\FORSHQW\O ULQJ 7KH DGYDQWDJHV DQG OLPLWDWLRQV RI LPPXQRDIILQLW\ SXULILFDWLRQ ,$f IRU VDPSOH SUHSDUDWLRQ RI 3*V LQ XULQH KDYH EHHQ LQYHVWLJDWHG 5HVXOWV VKRZ WKDW ,$ SXULILFDWLRQ FRXSOHG ZLWK D VKRUW P *& FDSLOODU\ FROXPQ XWLOL]LQJ (&1&, VHOHFWHGUHDFWLRQ PRQLWRULQJ 650f FDQ SURYLGH D VHOHFWLYH VHQVLWLYH DQG UDSLG PHWKRG RI DQDO\VLV IRU HQGRJHQRXV OHYHOV RI 3*( LQ XULQH 7KH VWXGLHV SHUIRUPHG LQ &KDSWHUV DQG GHPRQVWUDWH WKH UHXVDELOLW\ RI WKH ,$ VRUEHQW DQG LWV FDSDELOLWLHV LQ YDULRXV DQDO\WLFDO VFKHPHV +RZHYHU GDWD IURP &KDSWHU VKRZV WKDW ,$ SXULILFDWLRQ VWLOO KDV OLPLWDWLRQV 7KH QRQVSHFLILF ELQGLQJ ZKLFK RFFXUV GXH WR VHFRQGDU\ LQWHUDFWLRQV LQ WKH ,$ SURFHGXUH FUHDWHV GLIILFXOWLHV LQ DQDO\VLV ZKHQ OHVV VHOHFWLYH VDPSOH LQWURGXFWLRQ GLUHFW SUREH RU '&,f RU GHWHFWLRQ VFKHPHV VHOHFWHGLRQ PRQLWRULQJf DUH HPSOR\HG 7KH V\VWHPDWLF VWXG\ ZKLFK ZDV SHUIRUPHG LQ &KDSWHU GHPRQVWUDWHV WKH UHODWLYH WUDGHRIIV ZKLFK H[LVW WKURXJKRXW WKH HQWLUH DQDO\WLFDO SURFHGXUH 7KLV VWXG\ LQGLFDWHV WKDW WKH XWLOL]DWLRQ RI D PRUH VHOHFWLYH VDPSOH SUHSDUDWLRQ PHWKRG ,$f ZLWK 0606 FDQ UHGXFH WKH FKURPDWRJUDSKLF VHSDUDWLRQ WLPH UHTXLUHG WR DFKLHYH WKH QHFHVVDU\ VHOHFWLYLW\ DQG VHQVLWLYLW\ IRU 3* DQDO\VLV LQ XULQH +RZHYHU UHVXOWV VKRZ WKDW 0606 LV QRW QHFHVVDU\ LI ,$ SXULILFDWLRQ DQG D ORQJHU FKURPDWRJUDSKLF VHSDUDWLRQ PRUH VHOHFWLYLW\f WHFKQLTXH DUH HPSOR\HG ,Q DGGLWLRQ

PAGE 175

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f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

PAGE 176

GLUHFW FKHPLFDO LRQL]DWLRQ '&,f DV D SRVVLEOH UDSLG VDPSOH LQWURGXFWLRQ WHFKQLTXH 'HULYDWL]DWLRQ SURFHGXUHV IRU 650 DOVR QHHG WR EH DGGUHVVHG 7KH XVH RI (&1&, *&06 XWLOL]HV WKH 023)%706 GHULYDWLYH IRU DQDO\VLV 7KLV DSSURDFK KDV VHUYHG DV WKH EDVLV RI WKH PRUH VHQVLWLYH DQG VHOHFWLYH DQDO\VLV E\ 6,0 f ,Q WKLV ZRUN LW ZDV IRXQG WKDW WKH LQWHQVH FDUER[\ODWH DQLRQ IRUPHG IURP WKLV GHULYDWL]DWLRQ SURGXFHG LQHIILFLHQW RYHUDOO &$' bf IRU )VHULHV 3*V )XUWKHUPRUH ZLWK (&1&, GHULYDWLYHVSHFLILF IUDJPHQWDWLRQ LV SURPLQHQW ZLWK OLWWOH WR QR EDFNERQHVSHFLILF IUDJPHQWDWLRQ SUHVHQW 7KHUHIRUH IXUWKHU H[DPLQDWLRQ RI PRUH HIIHFWLYH GHULYDWL]DWLRQ SURFHGXUHV ZLWK YDULRXV LRQL]DWLRQ PHWKRGV IRU 650 DQDO\VLV QHHG WR EH SHUIRUPHG $ORQJ WKHVH OLQHV 6WULIH f KDV SHUIRUPHG SUHOLPLQDU\ VWXGLHV ZLWK WKH 0(02706 GHULYDWLYH XWLOL]LQJ WKH LRQ WUDS PDVV VSHFWURPHWHU ,706f GLVFXVVHG LQ &KDSWHU 7KH ,706 RIIHUV DFFHVV WR EDFNERQH VSHFLILF IUDJPHQWDWLRQ EXW DW KLJK &$' HIILFLHQFLHV RI b f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

PAGE 177

/,7(5$785( &,7(' 1HOVRQ 1 $ .HOO\ 5 & &KHP (QJ 1HZV 6DPXHOVVRQ % *R G\QH 0 *UDQVWUP ( +DPEHUJ 0 +DPPDUVWUP 6 0DOPVWHQ & $QQ 5HY %LRFKHP %UHJPDQ 0 0H\VNHQV ) / &DQFHU 5HV f /HYHQVRQ 6LPPRQV & ( %UHQQHU % 0 $P 0HG )UOLFK & :LOVRQ 7 : 6ZHHWPDQ % 6PLJHO 0 1LHV $ 6 &DUU :DWVRQ 7 2DWHV $ &OLQ ,QYHVW %ODLU $ %DUURZ 6 ( :DGGHOO $ /HZLV 3 'ROOHU\ & 7 3URVWDJODQGLQV $GYDQFHV LQ 3URVWDJODQGLQV DQG 7KRPER[DQH 5HVHDUFK )UOLFK $ (G 5DYHQ 3UHVV 1HZ
PAGE 178

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

PAGE 179

9DQ 5ROOLQV 0 +R 6 + *UHHQZDOG ( $OH[DQGHU 0 'RUPDQ 1 :RQJ / +RUURFNV / $ 3URVWDJODQGLQV 7HUUDJQR $ 5\G]LN 5 7HUUDJQR 1 $ 3URVWDJODQGLQV +HUEDF]\QVND&HGUR %DQH 5 &LUF 5HV /RQLJUR $ 7HUUDJQR 1 $ 0DOLN 8 0F*LII & 3URVWDJODQGLQV /HYLQH / 9DQ 9XQDNLV + %LRFKHP %LRSKYV 5HV &RPPXQ 0LGJOH\ $ 5 -U 1LVZHQGHU 5HEDU 5 : $FWD (QGRFULQRO :DWNLQV : 3HUWHUVRQ 0 % $QDO %LRFKHP %HUJVWURP 6 5\KDJH 5 6DPXHOVVRQ % 6MYDOO %LRO &KHP 6DPXHOVVRQ % +DPEHUJ 0 6ZHHOH\ & & $QDO %LRFKHP *UHQ 6DPXHOVVRQ % ,Q 3URVWDJODQGLQ 6\PSRVLXP RI WKH :RUFHVWHU )RXQGDWLRQ IRU ([SHULHPHQWDO %LRORJ\ 5DPZHOO 3 : 6KDZ ( (G ,QWHUVFLHQFH 1HZ
PAGE 180

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
PAGE 181

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
PAGE 182

6WULIH 5 .HOO\ 3 ( :HEHU*UDEDX 0 3URF WK $QQ &RQI 0DVV 6SHFWURP $OOLHG 7RS 'HQYHU 6WULIH 5 6LPPV 5 3URF WK $QQ &RQI 0DVV 6SHFWURP $OOLHG 7RS 6DQ )UDQFLVFR .UXJHU 7 / /LWWRQ ) .RQGUDW 5 : &RRNV 5 $QDO &KHP .RQGUDW 5 : &RRNV 5 $QDO &KHP $ 0F/DIIHUW\ ) : %RFNKRII ) 0 $QDO &KHP
PAGE 183

8]LHO 0 6PLWK / + 7D\ORU 6 $ &OLQ &KHP -XQN $ $YHU\ 0 5LFKDUG $QDO &KHP 6KLQGR 1 7RPRNR 6 0XUD\DPD %LRPHG (QYLURQ 0DVV 6RHFWURP
PAGE 184

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
PAGE 185

, 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\ $LFKDUG $
PAGE 186

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

PAGE 187

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


UNIVERSITY OF FLORIDA
3 1262 08554 2792


CONCEPTS FOR THE DETERMINATION OF PROSTAGLANDINS
BY TANDEM MASS SPECTROMETRY
By
TODD ALLEN GILLESPIE
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
1989

To my loving wife, Paula

ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to Dr. Richard A. Yost
for his guidance, direction, and friendship during this research. His
editorial assistance during the preparation of this dissertation and
various papers is very much appreciated.
I would like to express my gratitude to Dr. Joe Neu in the
Department of Neonatology at the University of Florida for his initiation
of this project and provision of supplies for the scintillation counting
work. Also I would like to express my sincere heartfelt thanks to Dr. Jim
Vrbanac, who, while at the Medical University of South Carolina in
Charleston, supplied samples, immunoaffinity gel, and expert advice as
well as a valued friendship during this collaborative research. In
addition, I thank Merrell Dow Research Institute for their support of this
work.
I acknowledge the members of my research committee, Drs. John G.
Dorsey, Anna Brajter-Toth, Samuel 0. Colgate and Joe Neu for their various
contributions to my thesis work and education at the University of
Florida.
This research would not have been possible or as much fun without
the support of and discussions with my friends and co-workers in the Yost
research group. I would especially like to thank Mark Hail, David
Berberich and Jodie Johnson for many helpful discussions about this work.
iii

In addition to the people mentioned above, I would like to thank Steve
Brooks, Mark Barnes and Jim Michels for their friendship.
I would particularly like to thank my parents, during all the years
of my education whether in or out of the classroom, for their endless
support. Most of all, I thank my wonderful, caring wife Paula, for her
constant love, understanding and patience throughout my years in graduate
school. She has made this work all possible and worthwhile.
iv

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
ABSTRACT vii
CHAPTERS
1 INTRODUCTION 1
Arachidonic Acid Metabolites
(Prostaglandins) 1
Recent Analytical Advances 13
Strategies for Mixture Analysis by MS/MS 15
Overview of Thesis Organization 20
2 SAMPLE PREPARATION STUDIES 22
Introduction 22
Concepts for Solid-Phase Extraction 23
Concepts for Derivatization 33
Experimental 35
Results and Discussion 43
Conclusions 52
3 OPTIMIZATION OF GC/MS AND GC/MS/MS CONDITIONS
FOR TRACE DETERMINATION OF PROSTAGLANDINS 54
Introduction 54
Experimental 54
Mass Spectrometry (GC/MS) 56
Tandem Mass Spectrometry (GC/MS/MS) 64
Conclusions 80
4 DIFFERENCES IN THE COLLISIONALLY ACTIVATED
DISSOCIATION OF STRUCTURALLY SIMILAR
PROSTAGLANDINS 83
Introduction 83
Experimental 85
Efficiency Calculations 88
Collision Energy Study of the [MO/TMS-PFB]"
Carboxylate Anions 89
v

CHAPTERS
Page
Collision Pressure Study of the
[MO/TMS-PFB]" Carboxylate Anions 93
Collision Pressure Study of the [M-PFB]"
Carboxylate Anions 95
Collision Pressure Study of the [M-H]'
Carboxylate Anions 98
Conclusions 100
5 EVALUATION OF SOLID-PHASE EXTRACTION GC/MS
AND GC/MS/MS FOR THE ANALYSIS OF ENDOGENOUS
PROSTAGLANDIN E2 IN URINE 101
Introduction 101
Experimental 103
Results from the Quantitation Study
of PGE2 in Urine 114
Trade-offs in the Steps of
the Analytical Procedure 121
Conclusions 138
6 EVALUATION OF SOLID-PHASE EXTRACTION
PROBE/MS/MS FOR THE ANALYSIS OF ENDOGENOUS
PROSTAGLANDIN E2 IN URINE 142
Introduction 142
Experimental 143
Solids Probe Analysis 145
Direct Chemical Ionization Analysis 153
Conclusions 164
7 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 165
Summary 165
Future Directions 167
LITERATURE CITED 169
BIOGRAPHICAL SKETCH 176
vi

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
CONCEPTS FOR THE DETERMINATION OF PROSTAGLANDINS
BY TANDEM MASS SPECTROMETRY
By
Todd Allen Gillespie
May, 1989
Chairman: Richard A. Yost
Major Department: Chemistry
An evaluation of the concepts for the trace determination of
prostaglandins (PGs) by tandem mass spectrometry (MS/MS) has been
achieved. Results from this work demonstrate the importance of the
optimization of various parameters in the collisionally-activated
dissociation (CAD) process before performing trace analysis. Dramatic
differences in the optimum collision gas pressure for selected-reaction
monitoring (SRM) with MS/MS for the determination of prostaglandins E2 and
F2a were observed. The differences in fragmentation behavior were examined
through the use of fragmentation, collection and overall CAD efficiency
studies. This work shows that the CAD efficiency for the derivatized and
underivatized carboxylate anions is significantly different for subtle
vii

structural changes in PGs. A possible explanation has been proposed to
explain these dramatic differences.
The advantages and limitations of immunoaffinity purification (IA) for
sample preparation of PGs in urine have been investigated. Results show
that IA purification coupled with a short 3 m GC capillary column
utilizing electron-capture negative chemical ionization (EC-NCI) SRM can
provide a selective, sensitive and rapid method of analysis for endogenous
levels of PGE2 in urine.
A systematic study was performed demonstrating the relative trade-offs
which exist throughout the entire analytical procedure. Eleven different
analytical schemes were systematically evaluated for the trade-offs in
sensitivity, selectivity, and total time of analysis. These trade-offs
are discussed in relation to how they affect the three basic steps (sample
preparation, sample introduction and mass spectrometric detection) of PG
analysis. This study indicates that the utilization of a more selective
sample preparation method (e.g., IA) with MS/MS can reduce the
chromatographic separation time required to achieve the necessary
selectivity and sensitivity for PG analysis in urine. However, results
show that MS/MS is not necessary if IA purification and a longer
chromatographic separation (more selective) technique are employed. This
systematic study should be applicable in the evaluation of any analytical
procedure for analysis of components in a biological sample. In addition,
future work is proposed which should further enhance PG analysis by MS/MS.
viii

CHAPTER 1
INTRODUCTION
Arachidonic Acid Metabolites (Prostaglandins)
The enzymatic oxidation of arachidonic acid (AA) leads to a
multitude of biochemically important products (1). Among these substances
are prostaglandins (PGs), thromboxanes (TXs) and leukotrienes (LTs).
Collectively, these compounds are referred to as eicosanoids and
constitute what is known as the arachidonic acid cascade (Figure 1-1).
Many of these oxygen-containing metabolites have interesting and diverse
pharmacological properties and significant medicinal potential (2).
Since, the initial description of PGs in 1935, a vast body of
knowledge has accumulated on their physiology and chemistry (1,2).
Recently, attention has been focused on PGs of certain series as antitumor
agents (3). Evidence indicates that PGs such as prostaglandin E2 (PGE2) ,
play an important role as local mediators and modulators of renal blood
flow and excretory functions (4). It has been suggested that most of the
primary PGs found in urine are derived from renal production (5); con¬
sequently, urinary levels of PGs have been applied as an index of renal
PG activity in numerous studies. Recently, PGE2 has seen application in
the induction of labor, softening of the cervix and prevention and
treatment of stress ulcers (1). While much has been learned about PGs
1

2
rs=—
/=-—«■ -^C >»^w>^*^COOH COON
li-NTHor
,lSSM5-*y«»Op»ror»-5.lL (15SHS-hv 11.1>-*ico**tair*ancx acd 11.1 >«»i4Hir«too< b
1
2SM2-f>yaroo*rorv-S.*,lO. (12S)-12-f’vO'ory-5.B.1 k-aicoaaiat/aanoc ac>d ' «-•c tc*3
uh
/=^-<-^^COOl
S-HTHEor
|SS)-S-nydro*y-8 •.
11.' Miouminnoe acid
S-HRCTlor
i SS(-S-nyOroparoay-« l
II.IMiCaMWUMflOC *c
B-fc#«oproaUgland*n f.m
OH
S-HyOrory-l
i.l1i^ «O Oh
y-C—■s^^COOH
TT
M.12-Tnhydforr-«.10. •iH.12-Tnhydr®*y-S.t.
â–¼
OH
^-<^=s^^COOH
Vr
HO OH
Kid 1 Micoulntno* a<
nan*
I *«os*i*tra*r>
•COOH
LTA, or lauKolnan* A,
S ^O.hydro«y-ri.11.14
COOH
>->- i. —
(SS.12R and SS.12S>-S.12-
Oihydrory-d • IO-fr#nj-14-
LTV, or Wuaotnan* 8,
A 1
corCHjjj-cM-cooH
Hfi-CH-CONMCH,COOH
.TC.or
IWranj-tauKouian* C,
CO(CH,|,-¿H-COOH
IÑ-CH-CONHCHjCOOH
r
:ooh
or LTC, or lauiiotnana C,
h,N-CH-CONhCh,COOH
CH,
j^vV'-aoi
T
COOH
LTD, or iau«ou>ao* 0.
(^^I^COOH
" —
LTV, or lautolnana E,
Figure 1-1: Arachidonic acid cascade

3
biological effects and how they relate to mammalian health, difficulty in
measuring low concentrations of PGs in biological systems has hindered
the progress of research.
The analysis of PGs and other AA metabolites can be divided into
three basic steps; sample preparation, sample introduction and measurement
by such techniques as bioassay, radioimmunoassay (RIA), high-performance
liquid chromatography (HPLC), gas chromatography (GC) and gas
chromatography/mass spectrometry (GC/MS). It has been shown that with
many of the analytical methods frequently used, PG concentrations are
often overestimated by as much as a factor of ten (6). This problem can
be traced to the lack of selectivity of the entire analytical scheme used
for analysis. Therefore, the development of an analytical scheme which
provides for accurate, sensitive and selective determination of PGs is
needed.
In this chapter, a brief review of the most frequently employed
techniques for sample preparation and measurement of PGs will be
discussed. More thorough reviews of sample preparation and measurement
techniques can be found in the literature (7,8). Recently, a review on
AA metabolism with examples of various analysis methods has been published
(9). Other, more specific reviews have been written by Traitler (10) and
Kelly (11) on mass spectrometric analysis methods of eicosanoids.
Sample Preparation Techniques for Prostaglandins
Sample preparation before the measurement step is extremely
important, with the extent of extraction and purification dramatically
affecting the validity of the data. In sample preparation of biological

4
fluids, a traditional technique that is commonly utilized is liquid-
liquid solvent extraction (7). This method is time-consuming and usually
yields only 80% to 90% recovery of most PGs (12). The degree of clean-up
provided by such extractions is limited; further purification is often
necessary for body fluids such as urine.
Another popular method for separating PGs from biological matrix
components is solid-phase extraction. Three types of solid-phase
extraction are commonly employed: (1) amberlite (XAD-2) column; (2)
octadecylsilyl (ODS) column (C18); and (3) selective packing materials,
such as immunoantibodies. Bradlow (13) described the use of an XAD-2
column that is advantageous when the biological matrix contains a large
concentration of proteins. Recoveries using this method have been
reported as about 90%. Both solvent extraction and XAD-2 resin extraction
procedures are time-consuming and require evaporation of relatively large
volumes of organic solvents. Moreover, they are not very selective and
give extractions containing extraneous material that must be removed
subsequently by various chromatographic purifications. A variety of
methods using a C18 column to extract PGs from biological samples have
been developed by Powell (8,14) and other researchers (15,16). The solid-
phase extraction using a C18 column is rapid, efficient and more selective
than solvent and XAD-2 extractions. Recovery with this method has been
reported to be greater than 90% in many cases.
Specialized packing materials can provide significantly more
selective extraction of specific targeted PGs. A phenylboronic acid
column has been used to selectively isolate thromboxane B2 (TXB2) and its
metabolites (17). The recovery of radio-labeled TXB2 after extraction was

5
reported at 90%. Potentially, an even more selective approach to sample
preparation is to combine the extraction and purification steps into one
procedure. This has been accomplished by using an antibody-mediated
extraction procedure developed by Krause et al. (18). Basically, the
prostaglandin-antibody was coupled to cyanogen bromide-activated Sepharose
4B and used as a stationary phase for the extraction of PG from the
samples. The antibody was coupled to Sepharose and packed into a Pasteur
pipette. The plasma samples were then applied to the gel in the column.
This one-step extraction-purification method has shown improved
specificity and sensitivity. Similar methods have also been employed by
Hubbard (19) and Vrbanac (20) for the analysis of TXB2 and 6-keto-PGF1a in
urine. Another approach to exploit the high selectivity of antibody-
antigen reactions for sample extraction is double-antibody precipitation.
This technique has been used for preparation of plasma samples before HPLC
analysis for (15R)-15 methyl-PGE2 (21).
In summary, the advantages of extraction (either solvent or solid-
phase) are: (1) it eliminates some extraneous material, thereby imparting
greater specificity to the assay; and (2) it improves sensitivity of the
analysis by concentrating the material. The disadvantages are: (1) it is
time-consuming; (2) a "carry-over" of non-eluted analyte may occur (if the
same column is reused) effecting the validity of subsequent assays: and
(3) the extraction efficiency of the procedure is variable. Simple
solvent or solid-phase extraction has been shown to yield samples that do
not permit accurate validity of PG quantitation. Improved validity of
subsequent quantitation has been observed after further purification

6
steps. A more detailed explanation of solid-phase extraction and
immunoaffinity (IA) purification can be found in Chapter 2.
Three types of chromatographic purification are described below: (1)
silica acid column chromatography; (2) thin-layer chromatography (TLC);
and (3) HPLC. Group separation of PGs and related compounds is
conveniently performed by silica acid column chromatography (22,23).
Recoveries were reported for this purification method of 85% to 90%. PGs
separated by silica acid chromatography usually require further
purification by TLC or HPLC prior to quantitation by RIA or GC/MS.
Separation of PGs by TLC was first investigated by Green and
Samuelsson (24). TLC is the most commonly used method for separation of
PGs because of its efficiency, simplicity and economy compared to other
chromatographic procedures. The major groups of PGs (A, B, D, E, F and
6-keto-PGF1a) were readily separated on a silica gel plate using various
solvent mixtures (25-27). The disadvantages of TLC are its low recovery
yields (typically 80%) and the lengthy procedures required for separation
of closely related compounds. Prostaglandin-related compounds with
similar behavior are often observed to migrate in a similar way even in
different solvent systems. Such problems can be avoided by using two-
dimensional TLC. A considerable improvement of resolution is achieved by
combining two solvent systems with different chromatographic properties.
Two-dimensional TLC analysis of PGs and related compounds has been
reported from a few laboratories (8,28-30).
The conventional techniques of column chromatography and TLC usually
suffer from poor chromatographic resolution and the need to use several
solvent systems to adequately separate arachidonate metabolites. HPLC has

7
been used successfully for the separation and purification of PGs from
biological sources since 1976 (31). This technique offers several
advantages: (1) there is high resolution of closely related compounds; (2)
good reproducibility is possible; and (3) fractions containing PG peaks
can be automatically collected and later quantitated by RIA, GC/MS or
scintillation counting of radio-labeled metabolites. Both normal-phase
HPLC on silica acid (32-34) and reverse-phase HPLC on octadecylsilyl
silica (35,36) have been used to separate the cyclooxygenase products of
arachidonic acid. However, HPLC can be an extremely lengthy technique for
purification and can yield low recoveries on the order of 60%.
Techniques for Determination and Measurement of Prostaglandins
A number of analytical methods have been developed for the detection
and measurement of PGs to study their physiological and pharmacological
effects. Among those, bioassay, RIA, HPLC and GC/MS are most widely used
for the quantitation of PGs in biological fluids.
Bioassav. Biological techniques and bioassay have contributed
greatly to the development of techniques for detecting and quantitating
AA metabolites (37,38). In general, bioassay has been highly beneficial
in establishing the biological significance of the unstable products of
AA metabolism. However, it provides only approximate quantitation and
relatively low selectivity.
Radioimmunoassay (RIA) . RIA of PGs was introduced in 1970 by Levine
and Van Vunakis (39) with assays developed for PGE1 and PGF2a. The
literature has been expanding rapidly, and a large number of RIAs for PGs,
TXs and LTs have been reported. RIA is based on the competition between

8
radio-labeled and unlabeled molecules of a particular compound for binding
sites on an antibody directed against the same compound. The amount of
labeled compound is known and constant for all the tubes in an assay,
whereas the amount of unlabeled substance is either known and varied
(standard tubes) or unknown (sample tubes). A tube with no antibody
present is required as a "zero binding" tube. A tube containing no
unlabeled substance is also required as a "maximal binding" tube. When
larger amounts of unlabeled substance are present, the radioactive
molecules are displaced from the binding sites. The radioactivities of
the unbound fraction and antibody-bound fractions are usually separated
by dextran-coated charcoal or double-antibody methods, and the
radioactivity of either or both fractions is determined. The amount of
unlabeled compound in a sample tube is then obtained by comparison with
the standard tubes.
RIA has certain advantages over other quantitative methods, the most
important being its high sensitivity, with detection limits as low as a
picogram per sample. The precision and accuracy frequently compare
favorably with other methods. RIA is relatively rapid and also has high
sample capacity; for example, 100 samples can be analyzed within one or
two days, including radioactivity measurements and data processing.
RIA also has some drawbacks. First, the method is not entirely
specific under all circumstances. It is difficult to obtain a specific
antibody with a minimum of cross-reactivity and high affinity. Biological
samples, especially biological fluids (urine or plasma), usually need to
be purified through extraction, column chromatography, TLC, or even HPLC
before analysis by RIA. Appropriate purification steps are time-

9
consuming, but frequently necessary to remove most interfering compounds
and yield a specific assay with valid results. Other disadvantages of RIA
include the potential risk inherent in using radioactive materials and the
high cost of using disposable glassware, utensils, counting vials and
large volumes of scintillation fluid.
High-performance liquid chromatography (HPLO. HPLC has proven to
be useful for purification of PGs after an initial extraction procedure.
The HPLC technique is a good qualitative method; however, quantitation is
rather limited, especially for PGs. Terragno et al. (36) have found that
the highest molar extinction coefficient occurs around 192.5 nm for major
PGs, yielding detection limits in the nanogram range. Recently, a more
sensitive method using HPLC with a postcolumn derivatization and
fluorescence detection has been developed for eicosanoid quantitation.
Watkins and Peterson (41) developed a method to measure AA metabolites by
reverse-phase HPLC followed by formation of the ester derivative with P-
(9-anthroyloxy) phenacyl bromide. The disadvantages of HPLC are that this
technique can be lengthy and a relatively large volume of sample is
required for adequate detection of low levels of PGs in biological fluids.
Gas chromatography/mass spectrometry (GC/MS). GC/MS is the
analytical method of choice for the identification, characterization, and
quantitation of the products of the arachidonic acid cascade. Offering
both high sensitivity and selectivity, GC/MS has become the "gold
standard" for the analysis of PGs. Traditionally, GC/MS was used for
strictly qualitative analysis, with studies done on the determination of
the structures of several prostaglandins (42). Identification and

10
characterization of many prostaglandins and their metabolites were
performed by electron ionization/mass spectrometry through the early to
mid-1960's. In 1967, reports on eicosanoids first appeared, with limits
of detection in the low ng/mL range (42,43). The use of selected-ion
monitoring (SIM) with positive chemical ionization (PCI) and electron-
capture negative chemical ionization (EC-NCI) for quantitation
significantly improved the detection limits achieved by GC/MS.
The discussion that follows will focus on components of the
analytical technique of GC/MS for the analysis of PGs. In a typical
qualitative or quantitative analysis for PGs by GC/MS, the following steps
are performed: (1) sample preparation (extraction and purification); (2)
derivatization; (3) gas chromatographic separation; (4) ionization; and
(5) mass spectrometric detection. In the following pages, these
analytical steps will be discussed in reverse order, highlighting the mass
spectrometric component of the analysis, rather than sample preparation
which was discussed in detail earlier.
In mass spectrometric analysis, the quantitation of trace levels of
PGs is commonly performed by utilizing an isotope-labeled analog of the
compound of interest, with selective monitoring of the ions of each.
Since its introduction in 1967, stable isotope dilution (44) has been the
method of choice for quantitation. Many uses of stable isotope labeling
with SIM can be found in the prostaglandin literature (45-54). Both high
resolution mass spectrometry and low resolution mass spectrometry have
been employed for analysis of PGs. High resolution can reveal the
elemental composition of ions, which is helpful in identifying new
compounds. Low resolution is used for trace analysis despite its lower

11
selectivity. Examples of both techniques can be found in the literature
(55-59). A great deal of research has been devoted to trace analysis of
eicosanoids and their metabolites in all types of biological fluids, with
most determinations done in plasma and urine (48,49,60-63). The amounts
that have been analyzed are from the low ng to low pg/mL range, with
limits of detection as low as 50 fg reported in one study (64).
Three types of ionization are used today for most PGs analyses:
electron ionization (El), positive chemical ionization (PCI), and
electron-capture negative chemical ionization (EC-NCI). EI/MS, as
discussed earlier, is most often used for structural elucidation and
identification of new compounds. El mass spectra give structurally useful
fragmentation patterns, although the molecular ion may be weak or even
absent. For trace analysis, typical limits of detection with El are
approximately 100 pg/mL (57). PCI and EC-NCI are "gentler" ionization
techniques, generally producing less fragmentation, with a more prominent
(pseudo-) molecular ion. Thus, these techniques are useful for confirming
molecular weight, and for trace analysis by selected-ion monitoring. PCI
has been shown to be helpful in characterization of thromboxanes and
prostaglandins (65). Limits of detection vary for PCI and EC-NCI,
depending on both the compound and the reagent gas selected. Many types
of chemical ionization reagent gases have been used, but methane and
isobutane are the most common. Most trace analysis studies are now
performed with EC-NCI with methane as the reagent gas. Detection limits
are generally in the low pg/mL range, although limits as low as 50 fg/mL
have been reported (59). The three ionization techniques have been

12
compared for trace analysis of PGs, including limits of detection and
spectra obtained with each ionization technique (49,57).
Gas chromatography is generally used to separate the eicosanoids
from each other and from other potential interferents prior to their
identification or detection by mass spectrometry. The first GC/MS
analyses were accomplished with packed gas chromatography columns, which
were used extensively until the development of fused silica capillary
chromatographic columns. Until 1982, approximately equal use was made of
packed and capillary column techniques, but capillary chromatography has
led to better separation of closely related compounds. Coupled with
negative chemical ionization, it has allowed researchers to achieve limits
of detection in the low pg/mL range. These advantages have provided
higher sensitivity and selectivity in eicosanoids analysis. However,
packed column chromatography still has a role in prostaglandin analysis.
One recent study (66) showed the advantages of packed columns for highly
contaminated samples that exceeded the capacity of capillary columns.
Researchers have recently recognized the value of introducing the
capillary column directly into the ion source of the mass spectrometry
(67) . This avoids problems with contamination, adsorption, and
decomposition of analytes (which can be severe with PGs) on active
surfaces in other GC/MS interfaces.
Derivatization of PGs has been important in their analysis, both to
increase their volatility for gas chromatography separation and to provide
for efficient EC-NCI to increase sensitivity of the GC/MS method. Today,
the methylester/methoxime/trimethylsilyl ether of PGs is the most
frequently cited derivative in GC/EI/MS analysis (63,64). However, it has

13
been shown that these derivatives are susceptible to hydrolysis, often
producing ions that are not optimal for selective-ion monitoring (68).
This is due to the low relative intensity of the high mass ions which are
optimal for quantitation.
The derivatization of PGs for GC/EC-NCI/MS seems to be standardizing
on the methoxime/trimethylsilyl ether/pentafluorobenzyl ester (MO/TMS/PFB)
mixed derivative (50,51,69-72). Derivatization with perfluorinated acid
anhydrides has been increasingly used for both qualitative and
quantitative work (69). These anhydrides usually incorporate a silylating
reagent such as N-(tetra-butyldimethylsilyl)/N-(methyltrifluoroacetamide).
This gives hydrolytic stability and increases high mass ion intensity for
optimal use of selective-ion monitoring. The use of such derivatives also
eliminates detection of many nonprostaglandin carboxylic acids, due to
their ability to derivatize with the carbonyl, rather than, or in addition
to, the carboxyl group. This makes these derivatives highly attractive
for detecting trace quantities of prostaglandins in biological matrices
(73).
Recent Analytical Advances
GC/MS remains the workhorse technique of PG research; however,
tandem mass spectrometry (MS/MS) and soft ionization techniques such as
fast atom bombardment (FAB) or liquid secondary ion mass spectrometry
(LSIMS) and liquid chromatography/mass spectrometry (LC/MS) are being
effectively employed. The sensitivity and selectivity of GC/MS/MS
compared to GC/MS has been studied in reports (74-76) utilizing both El
and EC-NCI. The advantages of GC/MS/MS have recently been exploited for

14
the trace analysis of PGs in biological samples (20,77,78). These studies
have been performed on both sector and quadrupole instruments. The high
selectivity of MS/MS makes it possible to perform analyses with minimal
sample preparation. MS/MS also minimizes or eliminates the need for
chromatographic separation in many cases, making the analysis extremely
rapid. MS/MS experiments have recently been reported in the literature
for analysis of underivatized prostaglandins (79,80).
In addition, with improved instrumentation has come the technique
of FAB or LSIMS (81-83). This method has aided structural elucidation,
as well as characterization of many PGs. LC/MS has become increasingly
popular in the analysis of PGs (84,85), as in all areas of chemistry.
LC/MS has the ability to analyze polar, thermally labile, and high
molecular weight eiconsanoids, and it saves time in sample preparation.
LC/MS with thermospray ionization (TSP-LC/MS) has been used by several
researchers to detect PGs and TXB2 at limits of detection as low as 10-
300 pg (on column), after derivatization with (diethylamino)ethyl chloride
(86). A series of PG standards were analyzed and investigated to show the
increase in sensitivity resulting from a post-column derivatization which
formed the methyl ester (87) . The sensitivity is still not equal to the
GC/MS methods commonly employed. This is the limiting factor of LC/MS
for the analysis of PGs; however, there is reason to believe that the
necessary improvements in sensitivity can eventually be obtained. LC/MS
is a good qualitative technique which is still in its infancy. The
advantages to be gained in simplified sample preparation and the ability
to directly analyze the more polar eiconsanoids will stimulate further
improvements.

15
Another recent MS/MS technique which is promising is ion trap
(IT)MS/MS. The ITMS offers the potential for very selective and sensitive
GC/MS/MS analysis. In the ion trap, ion formation and mass analysis occur
in the same region (tandem-in-time), whereas, in tandem mass spectrometry
these two processes occur in different regions (tandem-in-space). The
analysis of PGs by this method has been reported by Strife (88,89). This
work shows the unique advantages of high sensitivity MS/MS,with nearly
100% conversion efficiencies of parent to daughter ion in MS/MS experi¬
ments .
This section of Chapter 1 has shown that much progress has been made
in the area of PG sample preparation and quantitation. Many limitations
remain, especially when the sample size is limited. In the chapters to
follow some of these limitations will be addressed and new analytical
schemes will be evaluated.
Strateeies for Mixture Analysis by MS/MS
Since the development of tandem mass spectrometry (MS/MS) in the
1970's, it has recently gained rapid acceptance as an exceptional
analytical tool for mixture analysis (90-93). MS/MS has the ability to
provide rapid, sensitive and selective analysis of complex biological
samples, often with minimal sample clean-up (94,95).
The MS/MS scan modes utilized in these studies are depicted in
Figure 1-2. In mixture analysis, chemical ionization of a mixture is
often utilized in the ion source of the mass spectrometer to produce ions
characteristic of the components in the mixture and to achieve a spectrum
with few fragments. Separation of the analyte from the matrix components

(a) Q3 Full Scan
Ql Q2 Q3
»
1
y
\
i
r»»t
~iyr
N2 i
QI
Selected-Ion
Monitoring (SIM)
Q2
Q3
(b) Daughter Scan
Selected-Reaction
Monitoring (SRM)
Q2 Q3
Figure 1-2: Tandem mass spectrometry scan modes

17
is achieved by the mass selection of a characteristic ion of the analyte
by the first mass analyzer (Ql). The selected parent ion undergoes
collisionally activated dissociation (CAD) through collisions with neutral
gas molecules in the fragmentation region (Q2) to yield various fragment
or daughter ions. Subsequent mass analysis of the daughter ions by the
second mass analyzer (Q3) results in the analytical signal. This method
of MS/MS analysis corresponds to a daughter scan (Figure l-2b).
Although this operational mode is highly selective, this full-scan
daughter mass spectrum usually does not exhibit sufficient sensitivity for
trace analysis of an analyte in a complex matrix. Therefore, the scan
mode of selected-reaction monitoring (SRM) is commonly employed (Figure
l-2d). A characteristic daughter ion, typically the most abundant,
resulting from the fragmentation of the selected parent ion of the
analyte, is selected by the second mass analyzer for monitoring. SRM is
analogous to the selected-ion monitoring (SIM) (Figure l-2c) commonly used
to obtain maximum sensitivity in conventional GC/MS. Thus, an enhancement
in sensitivity is obtained at the expense of a gain in selectivity. In
addition to these MS/MS modes, the tandem mass spectrometer can be
operated as a normal MS by allowing all ions to pass through one mass
analyzer (Ql or Q3) and the collision cell (Q2), then scan the other mass
analyzer (Q3 or Ql) to produce a normal mass spectrum (Figure 2-la).
Optimization of many of these operational modes have been evaluated
throughout these studies and will be discussed in further detail as to
their significance in the trace determination of PGs.

18
Important Parameters for Trace Analysis
In order to perform trace analyses successfully, it is necessary to
think in terms of the four "S's" of analysis: (1) sensitivity; (2)
selectivity; (3) speed or analysis time; and (4) £ or cost. In the
determination of pure analytes, sensitivity can be a very useful
criterion; however, when required to determine an analyte in a complex
matrix, sensitivity alone may become meaningless. This is due to the fact
that chemical interferents in the matrix may themselves produce a response
or interfere with the signal of the analyte. Therefore, the factor which
may determine the smallest amount of analyte which can be determined
accurately is the second "S", selectivity. The selectivity can be
described as the ability of the method to distinguish the signal of the
analyte from that of the chemical interferents (so-called chemical noise).
The limit of detection (LOD), which depends upon both the selectivity and
sensitivity, is defined as the smallest amount of analyte which can be
detected.
The LOD required in trace analyses can be achieved by improving the
selectivity of the analytical scheme. Normally, this is accomplished
through the use of extensive sample clean-up and separation to enhance the
analyte signal with respect to the matrix components signal. These
extractions and purifications increase the possibility of sample
contamination and sample loss. Additionally, the methods necessary to
increase selectivity may become time-consuming and expensive, thus the
final two "S's", speed of the analysis and cost effectiveness may not be
optimum.

19
The Four Steps Involved in Trace Mixture Analysis
The analytical scheme for trace determination of an analyte in a
biological sample by MS/MS involves four basic steps: (1) sample
preparation; (2) sample separation/introduction; (3) ionization; and (4)
detection. When developing an accurate, reliable and specific method for
mixture analysis, a range of selectivity, sensitivity, time and cost are
observed for the four steps.
In sample preparation, a rapid, low cost and selective procedure is
desired. This can be achieved through the proper choice of extraction,
purification or derivatization methods which satisfy any or all of the
four "S's". The second step involves separation of the analyte of
interest from any matrix components which have not been eliminated by the
sample preparation methods. Typically, in MS/MS, gas chromatography is
employed for separation, if the analyte exhibits sufficient volatility.
Separation of components can be accomplished on short capillary GC columns
(3 m or less), when the sample has been adequately cleaned-up (96). Short
GC columns can only be utilized for separation of complex samples if the
sample preparation methods have the necessary selectivity. The choice of
an ionization method is based on the type of analysis required and the
analyte which is to be analyzed. In the low level trace determination of
analytes in biological samples, a "soft" ionization method (e.g., chemical
ionization) is usually selected which yields an intense molecular ion with
few fragments. Furthermore, for analytes which are highly electron¬
capturing (or can be derivatized), electron-capture negative chemical
ionization (EC-NCI) may be chosen in order to achieve the highest
sensitivity. Finally, the detection by MS/MS involves the optimization

20
of the parameters which constitute the operational modes which were
discussed above.
Overview of Thesis Organization
This thesis is divided into seven chapters. Chapter 2 describes
the sample preparation concepts and methods employed for this work.
Results from recovery studies on various types of extraction columns and
their characteristics are discussed in detail. The concept of
immunoaffinity purification is introduced and investigated.
The third chapter emphasizes the importance of optimizing MS/MS
parameters for trace determination of PGs. Optimization studies for
selected-ion monitoring (SIM) and selected-reaction monitoring (SRM) for
PGE2 and PGF2a are described and the results discussed.
Chapter 4 presents a study of the differences in the CAD efficiency
of two structurally similar PGs (PGE2 and PGF2q) . Collision energy and
collision gas pressure studies of the carboxylate anions of four PGs are
evaluated and hypotheses for the differences noted are put forth.
The results of the quantitation study of endogenous PGE2 in urine can
be found in Chapter 5. The advantages and disadvantages of various
analytical schemes are pointed out. These schemes are systematically
evaluated for the trade-offs in sensitivity, selectivity and time of
analysis. The trade-offs are discussed in relation to how they are
affected by the three basic steps (sample preparation, sample introduction
and detection) of PG analysis.
Chapter 6 includes an evaluation of the rapid analysis techniques
of direct solids probe/MS/MS and direct chemical ionization (DCI)/MS/MS

21
utilizing an abbreviated derivatization procedure. The advantages and
limitations are discussed and the results of a quantitation study of
endogenous PGE2 in urine are presented.
The final chapter reviews the conclusions which were drawn from this
work. This chapter points out the potential of GC/MS/MS with selective
sample preparation and short GC capillary columns to determine endogenous
levels of PGE2 in urine. The importance of a systematic study of the
entire analytical scheme is finalized. In addition, future work is
proposed which should further enhance PG analysis by MS/MS.

CHAPTER 2
SAMPLE PREPARATION STUDIES
Introduction
Sample preparation is an important step in any analytical
methodology. This step prepares the sample for the detection method and
can dramatically affect the validity of the data obtained. The two main
parts of sample preparation for gas chromatography/mass spectrometry
(GC/MS) are sample purification and derivatization. When considering
sample purification, selectivity and speed of the method are of vital
importance. A method which is extremely selective can eliminate matrix
interferences and reduce the separation needed in GC. Sample throughput
is always an important factor in any analytical method. A rapid sample
purification step can greatly reduce the total time of analysis.
The other main part of sample preparation is derivatization. Many
compounds are not directly amenable to GC. The thermal lability of
prostaglandins (PGs) makes it impossible for them to pass through a GC
column intact without first undergoing derivatization. This
derivatization increases the volatility of the compound and reduces the
interaction of the polar substituents on the compound with the stationary
phase of the GC column. In addition, derivatization can add sensitivity
and/or selectivity for detection of a compound. Many organic
derivatization reactions with PGs enhance the efficiency of electron-
22

23
capture negative chemical ionization (EC-NCI) mass spectrometry (51,
70-72). Electron-capture NCI with derivatization produces much simpler
mass spectra and the major fragment ions occur at the high mass range
(50,69). Thus, these two features combined with the higher ionization
efficiency of EC-NCI provide added sensitivity and selectivity needed in
trace determination of PGs.
Concepts for Solid-Phase Extraction
Solid-phase extraction (SPE) has emerged, in the last ten years, as
the method of choice for isolation and purification of arachidonic acid
metabolites (8,14-16). SPE has the advantage of using low volumes of
solvents and high recoveries of 90% to 100% for most PGs. Rapid
extractions are usually possible with simple procedures. This results in
a rapid inexpensive extraction technique. The concept of SPE is based on
the selective retention of the analyte by a sorbent bed as a solvent in
which the analyte is dissolved is passed through the column. This idea
is displayed graphically in Figure 2-1. A sample containing analytes (A)
and interferences (I & M) is passed through the sorbent. The sorbent
selectively retains analytes (A) and some interferences (I). However, at
the same time, many interferences (M) pass unretained through the sorbent.
Appropriate solvents are then used to wash the sorbent, selectively
eluting previously retained interferences (I), while the analytes (A)
remain on the sorbent bed. Purified, concentrated analytes (A) are then
eluted from the sorbent.

24
Figure 2-1: Concept of solid-phase extraction:
A - analyte; I & M - interferences.

25
Sorbent/Analyte Interactions
Three types of chemical interactions are commonly employed in solid-
phase extractions (97). The first is the non-polar interaction which
occurs between the carbon-hydrogen bonds of the analyte and that of the
sorbent. Virtually all organic compounds have some non-polar character,
thus these types of interactions are the most commonly used to retain
analytes on sorbents. The forces which are involved in such non-polar
interactions are "van der Waals" or dispersion forces (97,98). The most
widely used sorbent in non-polar interactions is octadecyl silane bonded
to a silica substrate which is called C18. Many compounds can be retained
by a C18 sorbent, thus it is a very non-selective sorbent. In general,
non-polar solid-phase extraction is the least selective extraction
procedure. The concept of non-polar interaction is comparable to that of
reverse-phase chromatography. Retention of the analyte by non-polar
interaction is facilitated by a solvent more polar than that of the
non-polar sorbent. Elution is then accomplished by utilizing a solvent
with sufficient non-polar character to release the retained analyte from
its interaction with the sorbent.
Other interactions which are common for SPE are polar interactions.
These interactions are exhibited between many sorbents and functional
groups on analytes. All bonded silica exhibits polar interaction due to
the polar nature of the silica substrate to which the sorbent is bound
(97,98). Polar interactions include hydrogen bonding, dipole/dipole, pi¬
pi and many more interactions in which the distribution of electrons is
unequal in the atoms of the functional groups. This property of polar
sorbents allows an analyte which contains a polar functional group to

26
interact with a polar group on the sorbent. Groups that exhibit these
types of interactions include hydroxyls, amines, carbonyls and other
groups containing hetero-atoms such as oxygen, nitrogen, sulfur and
phosphorous. The most common polar sorbents are silica, diol, aminopropyl
and cyanopropyl. Polar sorbents function similarly to the interactions
found in normal-phase chromatography. Non-polar solvents are used to
promote retention of the analyte on the polar sorbent. Then a solvent,
more polar than the sorbent, is utilized to elute the analyte.
The third type of interaction is ionic. This occurs when an analyte
carrying a charge (either positive or negative) interacts with a sorbent
carrying a charge opposite to that of the analyte. Ionic interactions are
more selective than non-polar and polar interactions and can be controlled
by adjusting the pH of the sample solution. It is essential to know about
the functional groups on the sorbent and the analyte because both of these
need to be charged to facilitate ionic interaction. Two classes of ion-
exchange interaction exist, cationic (positively charged) and anionic
(negatively charged). Examples of cationic interactions include the
interaction of amines and certain inorganic cations with carboxymethyl,
sulfonylpropyl and benzenesulfonylpropyl sorbents. Anionic interactions
occur when sorbents containing primary, secondary, tertiary and quaternary
amines interact with carboxylic and sulfonic acids, phosphates and similar
groups on an analyte.
Recently, covalent interactions have been exploited for extraction
of specific types of compounds (99). Covalent chromatography is highly
chemically selective, involving an interaction of greater energy than is
employed in the other extraction methods. Retention of the analyte occurs

27
when a covalent bond can form between it and the sorbent. A change in the
solvent environment facilitates elution of the analyte. This is commonly
accomplished through the use of solvents with various pH's. One example
is phenyl boronic acid (PBA) which has been immobilized for the selective
retention of compounds with 1,2- or 1,3-diols such as catecholamines and
thromboxanes (17,100).
Many of the sorbents discussed above may exhibit more than one
interaction. Both polar and ionic interactions due to the silica
substrate used can occur in all sorbents. In the case of the PBA, non¬
polar, polar and ionic interactions can occur as secondary interactions
within the sorbent. The interactions which occur with a particular
sorbent are a function of the sample matrix and the solvent used for
washes and elution.
Sorbent Selection
The problem encountered in this analysis was to develop a solid-
phase extraction to selectively isolate PGs from interferences in urine.
Evaluation of different sorbents followed two fundamental steps. First,
sorbents were selected which in theory have the capability to retain PGs
from urine. Next, the different sorbents chosen were tested to evaluate
their actual ability to selectively retain the PGs of interest (97).
The sorbents which were chosen for the study were determined by
examining properties of the analyte (PGs) and the matrix (urine). First,
the determination of the interactions which PGs could undergo was
examined. Areas of carbon/hydrogen content with alkyl chains suggested
that non-polar retention was probable. The presence of such polar groups

28
as hydroxyls (OH) and carbonyls (=0) indicated a potential for retention
by polar interactions. Ionic interaction was indicated by the presence
of the carboxylic acid moiety. However, this method was not evaluated for
the analysis of PGs in urine due to the excessive quantities of compounds
in urine which would undergo anionic and cationic interactions.
Considering that PBA has been used for separation of the arachidonic acid
metabolite, thromboxane B2 (TXB2), covalent interaction with some PGs
appears possible due to the 1,3-diol present on the cyclopentane ring.
Next, the properties of the matrix and the potential interfering
components which are contained in urine were considered. Urine is an
aqueous media which contains many proteins, salts and solids. Components
with polar and non-polar functionalities can be found throughout urine
samples. This suggested that the interferences would undergo the same
interactions with the sorbents as the PGs. Therefore, to determine which
interactions would work most effectively, the sorbents required testing.
A sorbent testing scheme is shown in Figure 2-2 (97). First, each
sorbent needed to be prepared. This was accomplished by washing the
sorbent bed first and allowing the functional groups on the sorbent to
interact with the solvent. The next step was to remove the wash solvent
and create an environment that facilitated the analytes (PGs) retention.
After this process, the testing procedure began and involved five steps.
Standards were prepared identical to a "real" sample and applied to
the column (sorbent). The standards were then washed with the same
solvent in which they were dissolved, and the eluent collected. The
eluent was then checked for the presence of analyte, indicating sorbents
which did not provide adequate retention of the analyte. Next, strong

29
Optimize Retention of Standards
Optimize Elution of Standards
- Identify Wash Solvents
Test Blank Matrix
- Use Wash Solvents
Test Spiked Matrix
Troubleshoot if Necessary
Figure 2-2: Sorbent testing scheme.

30
elution solvents were chosen of which small volumes can be utilized to
completely elute the retained analyte. During this process, solvents
which would not elute the analyte were identified for use as wash
solvents. These were tested next with a blank matrix (urine) to determine
the solvent(s) which produced the cleanest extract. Clearly, this was far
more difficult to evaluate than the determination of analyte recovery.
After developing a procedure which provided sufficient analyte retention
and elution, as well as adequate clean-up of the matrix, the method was
tested with a sample (urine) spiked with analyte. Recoveries found in
this step were similar to those obtained with the standards. However, if
problems had been encountered, either the sorbent, wash solvents or
elution solvents may have been changed to provide for adequate retention
and elution of the analyte in the matrix.
Antibody Affinity Extraction
Extraction methods for PGs based on liquid-liquid or solid-phase
extraction are relatively nonselective and the final extracts are
frequently unsuitable for direct analysis, even by highly specific GC/MS
quantitation methods (7,101). The necessity of further purification of
the extracts before chromatographic analysis makes the analytical
procedures more complex, laborious and time-consuming to develop. This
problem has been avoided in many cases by taking advantage of immuno-
adsorption techniques to simplify extraction and clean-up procedures for
GC/MS analysis (18-21,102). Reports have shown that the selectivity of
the immunoadsorption procedures may permit the direct analysis of extracts
and eliminate the need for intermediate chromatographic clean-up.

31
Antibodies have been used for many years for the analysis of PGs by
radio-immunoassay (RIA). Unfortunately, the presence of substances within
the sample matrix which exhibit cross-reactivity with the polyclonal
antibody can be considerable (39,103). For example, antibodies for 20
carbon PGs and their metabolites may also bind the corresponding dinor
metabolites present in the matrix (19). Thus, HPLC is frequently employed
as a separation technique prior to RIA to avoid cross-reactivity. Reports
have shown that without separation of cross-reacting components by HPLC,
PG levels have been found 20 times higher than the actual levels present
(7,8). Immunoadsorption purification has been utilized as well prior to
PG analysis by RIA (104,105). However, this method has the disadvantage
of combining a purification procedure based on immunoaffinity with a
measurement procedure based upon the same principle. The advantage of
utilizing immunoadsorption for purification before GC/MS analysis is that
the highly specific antibody will enhance the selectivity by providing
discrimination which is unrelated and complements the characteristics of
GC/MS. This results in an analysis method for PGs which has a higher
degree of specificity than RIA.
These ideas have been incorporated in the sample preparation of PGs.
The inherent selectivity of the antibody-antigen interactions has been
exploited for PG analysis by Knapp and Vrbanac to obtain relatively pure
sample extracts (20,78). The basic principle of antibody affinity
extraction is displayed in Figure 2-3. In a typical affinity
chromatographic separation, the antibody is coupled to a stationary phase
(the most popular is agarose gel). The selectivity of affinity
separations is based on the principle of "lock and key" binding which

32
Figure 2-3: Basic principle of antibody affinity extraction
A - analyte; I & M - interferences.

33
occurs in biological systems. Extraction of the sample is accomplished
by passing the solution (containing analytes and interferences) through
the sorbent bed; the PGs which have affinity for the antibody are adsorbed
while other components pass through unretained. The retained or adsorbed
PGs are then eluted by changing the solvent.
Additional, secondary interactions are possible with immunoaffinity
chromatography. One important interaction discussed earlier is due to the
cross-reactivity of the polyclonal antibodies. Furthermore, non-specific
binding of interfering components may occur during the immunoadsorption
procedure. The bulk protein carrying the antibody has the potential for
interaction of components in the sample matrix. In addition, polar
interactions are possible between the silica stationary phase and any
polar functionalities found in the sample matrix.
In general, antibody affinity purification can decrease significant
loss of sample which can occur in TLC and HPLC. This method of sample
preparation is relatively rapid and requires no additional purification
of biological samples to obtain an adequate interference free GC trace.
The greatest advantage is the significant selectivity of the separation
process for antibody affinity purification compared to other conventional
chromatographic methods.
Concepts for Derivatization
Derivatization of PGs has been important in their analysis by GC/MS,
both to increase their volatility for GC separation and to provide for
efficient EC-NCI to increase sensitivity of the GC/MS method. Many
different derivatives have been used in the analysis for PGs (10,11). As
reported earlier in Chapter 1, the most commonly used derivative for

34
quantitative analysis by GC/MS is the methoxime/pentafluorobenzyl/tri-
methylsilyl (MO/PFB/TMS) derivative.
The keto group on PGE2 is converted to the methoxime derivative to
prevent silylation which can interfere with quantitation by producing
additional derivatives. Pentafluorobenzyl (PFB) esters are created to
enhance the efficiency of ionization by EC-NCI in order to achieve low
level determinations of PGs. These PFB esters have been found to give
about twice the sensitivity of the methyl ester derivative (106) . Reaction
times are fast (-20 min) and quantitative (-100%) for this derivatization
procedure. The hydroxyl groups are converted to trimethylsilyl (TMS)
ethers using 0-bis(trimethylsilyl)-trifluoroacetamide (BSTFA). This TMS
donor has the additional advantage of creating extremely volatile reaction
by-products which usually elute with the solvent front in the GC trace.
Even though the derivatization for quantitative analysis of PGs by
GC/MS has been thoroughly documented, there are many variations in the
literature. It has been reported that by performing the methoximation
before the esterfication a fivefold increase in the derivative yield can
be obtained (47). However, many researchers still perform the ester-
fication step first in the derivatization procedure (10,11,74). Reaction
times for the methoximation step vary in the literature ranging from one
hour at 60° to 24 hours at room temperature. These differences, in
addition to the comparison of techniques for the removal of excess
derivative reagents by liquid-liquid extraction and nitrogen evaporation
were explored in this study.

35
Experimental
Prostaglandins and Reagents
All solvents were reagent or HPLC grade. Prostaglandin E2 (PGE2) was
purchased from Sigma Chemical Co. (St. Louis, MO). [5,6,8,11,12,14,15 -
3H2]-PGE2 and Riafluor liquid scintillator were from New England Nuclear
(Boston, MA) and were a gift from Dr. J. Neu of the Department of
Pediatrics, University of Florida (Gainesville, FL) . The solid-phase
extraction columns were purchased from Analytichem International, Inc.
(Harbor City, CA) and Waters Assoc. (Sep-Pak columns; Milford, MA).
3,3',4,4'-(2H4) PGE2 and the antibody affinity sorbent were gifts from
Drs. J.J. Vrbanac and D.R. Knapp of the Department of Pharmacology,
Medical University of South Carolina (Charleston, SC) . The derivatization
reagents and solvents pyridine, O-methylhydroxylamine hydrochloride,
acetonitrile, and N,N-diisopropylethyl amine for GC/MS percent recovery
studies were all purchased from Sigma Chemical Co.. Pentafluorobenzyl-
bromide (PFBBr) and bis(trimethylsilyl)-trifluoroacetamide (BSTFA) were
purchased from Pierce Chemical Co. (Rockford, IL). Urine was obtained
from the author. All glassware was silanized with a solution of 5%
dimethyldichlorosilane in toluene. These two chemicals were both
purchased from Sigma Chemical Co.. Helium used as GC carrier gas and
methane (>99%) used as the chemical ionization reagent gas were from
Matheson Gas Products, Inc. (Orlando, FL).
Sample Preparation
The sorbents for the percent recovery studies were chosen and tested
according to the procedures discussed earlier in this chapter. Extraction

36
procedures were determined for the non-polar, polar and phenyl boronic
acid columns by detection of the tritium-labeled PGE2 by scintillation
counting. The sorbents chosen are listed with the final extraction
procedure used for the percent recovery studies for both scintillation
counting and GC/MS.
Non-polar columns: octyl (C8), octadecyl (C18) and phenyl (PH)
(1) Conditioned the column with 10 mL of HPLC water and 10 mL of
methanol.
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Washed the column with 10 mL of HPLC water and 10 mL petroleum
ether.
(4) Eluted PGE2 with 10 mL of ethyl acetate.
Polar columns: silica (SI), cyanopropyl (CN), aminopropyl (NH2) and
diol (20H)
(1) Conditioned the column with 10 mL of benzene:ethyl acetate
(80:20 volume:volume).
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Washed the column with 10 mL benzene:ethyl acetate (60:40 v:v).
(4) Eluted PGE2 with 10 mL benzene:ethyl acetate:methanol
(60:40:30 v:v:v).
Phenyl boronic acid column (PBA)
(1) Conditioned the column with 5 mL of 0.1 M hydrochloric acid and
5 mL of 0.1 M sodium hydroxide.

37
(2) Passed sample of PGE2 (adjusted to pH 8.5 with 0.1 M phosphate
buffer (PBS)) through the column.
(3) Washed the column with 5 mL of methanol and 5 mL of HPLC water.
(4) Eluted PGE2 with 5 mL of 0.1 M PBS (pH 6.5).
The antibody affinity columns were tested and percent recovery data
calculated only with GC/MS.
Antibody affinity column [Immunoaffinity (IA)]
(1) Conditioned the column with 20 mL of PBS (pH 7.4).
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Allowed the sample to settle into the sorbent bed for 15 min at
room temperature.
(4) Washed the column with 25 mL of PBS (pH 7.4) and 10 mL HPLC
water. Removed all remaining water in the column.
(5) Eluted PGE2 with 15 mL of 95% acetonitrile solution (v:v).
(6) Washed column with an additional 10 mL of 95% acetonitrile to
assure removal of all the PGE2.
(7) Immediately rinsed the column with 10 mL of HPLC water and
15 mL of PBS (pH 7.4).
Scintillation Counting
A stock solution of 3H-PGE2 was used for the percent recovery
studies. This solution was 0.09375 microcuries (/iCi)/microliter (/jL) and
had a specific activity of 169.5 ^Ci/millimole. Six microliters of this
original solution was diluted with 100 /¿L of absolute ethyl alcohol
creating a solution of 5.625 x 10’3 /iCi//iL. Ten microliters of this

38
standard solution, corresponding to 3.319 x 10'4 mmoles or 0.1218 mg was
passed through each column tested. Following the extraction procedures
the eluent was collected and the solvent evaporated with nitrogen. The
3H-PGE2 was then diluted with 100 /tL of PBS (pH 7.4). Additionally, 3.5
mL of Riafluor liquid scintillator were added to the 9.375 x 10’3 /¿Ci
solution of 3H-PGE2 before the counting process. Each extraction was
performed three times with three individual columns.
A calibration curve was prepared in the same manner with the
exception of the actual extraction step (Figure 2-4a). Aliquots of 4,
5.5, 8, 10.5, 12 and 13.5 microliters of the 5.625 x 10'3 /iCi//iL solution
were added to separate vials and each diluted with 100 /iL of the PBS (pH
7.4). In addition, a blank containing only 100 /tL of the PBS (pH 7.4) was
prepared. The Riafluor liquid scintillator was added and the standards
counted and used to calculate the percent recovery values for the
different columns tested.
Gas Chromatography/Mass Spectrometry (GC/MS)
Ten nanograms (ng) of PGE2 were passed through each column for the
percent recovery studies of standards. Following the extraction procedure
for the columns tested, 10 ng of 2H4-PGE2 were added and the solutions were
evaporated to dryness with nitrogen. The same procedure was followed for
extraction of PGE2 in urine for percent recovery studies except that the
10 ng of PGE2 added to the urine is in addition to the endogenous levels
present.
Calibration curves for the GC/MS analysis were prepared by adding
a constant amount of 2H^-PGE2 (25 ng) and increasing amounts of PGE2 in the

39
Figure 2-4: Calibration curves: (a) Scintillation counting
(b) Gas chromatography/mass spectrometry (GC/MS)
with selected-ion monitoring (SIM).

Table 2-1: Calibration Curve Dilutions for GC/MS
‘h4-pge2
Added (ng)
pge2
Added (ng)
Volume of
Dilution (/¿L)
Concentration
of 2H4-PGE2 (pg//iL)
Concentration
of PGE2 (pg/AiL)
25.0
0.0
50.0
500.0
0.0
25.0
0.25
50.0
500.0
5.0
25.0
2.5
50.0
500.0
50.0
25.0
5.0
50.0
500.0
100.0
25.0
12.5
50.0
500.0
250.0
25.0
25.0
50.0
500.0
500.0
25.0
37.5
50.0
500.0
750.0
25.0
50.0
50.0
500.0
1000.0

41
solution (Figure 2-4b). Table 2-1 lists the amounts of 2H^-PGE2 and
standard PGE2 added to each vial and the final concentrations after
dilution with 50 /iL of silanizing reagent.
Derivatization for GC/MS
The methoxime/pentafluorobenzyl ester/trimethylsilyl (MO/PFB/TMS)
derivatives were formed for the GC/MS percent recovery and derivatization
studies. The method used was similar to the derivatization of H. L.
Hubbard et al. (19). The standards and samples of 2H4-PGE2 and PGE2 after
evaporation were treated with 100-200 /iL of methylhydroxylamine HC1 in dry
pyridine (4 mg/mL), allowed to stand overnight at room temperature, then
evaporated under nitrogen until dry. Each sample was acidified by adding
200 /iL of IN formic acid, extracted with two 1 mL aliquots of ethyl
acetate, and the extract dried under nitrogen. Then 50 /iL of
acetonitrile, 30 /iL of 30% PFBBr in acetonitrile, and 15 /iL of 10% N,N-
diisopropylethylamine in acetonitrile were added to the dried methoxime
derivative. Each solution was allowed to stand for 30 minutes at room
temperature before the reagents were evaporated with nitrogen. Excess
derivatizing reagent was removed by dissolving the sample in 200 /iL of
distilled water and extracting with two 1 mL aliquots of a methylene
chloride:hexane (50:50 v:v) solution; the extract was then dried under
nitrogen. The trimethylsilyl derivative then was formed by adding 50 /tL
of BSTFA to the standards for the calibration curve and 20 /iL to the
extraction samples and allowing the solutions to stand overnight at room
temperature. One-microliter injections containing 500 pg of 2H4-PGE2 were
made of each standard and sample.

42
Ins trumentation
A Beckman LS 3800 liquid scintillation counter and a Finnigan MAT
triple stage quadrupole (TSQ45) gas chromatograph/mass spectrometer were
used in these studies. Gas chromatography was carried out on a
conventional J&W Scientific (Folsom, CA) DB-1 (30 m long, 0.25 mm i.d.,
0.25 /an film thickness) capillary column in the splitless mode with helium
carrier gas at a flow rate of 41 cm/s (inlet pressure 18-20 psi). The
initial temperature of 250°C was held for 30 s, then increased at 20°C/min
to 310°C for the calibration curve and percent recovery studies of
standards. Urine percent recovery data were obtained with an initial
temperature of 100°C held for 30 s, increased at 25°C/min to 250°C, then
increased again at 5°C/min to 310°C.
Mass spectrometry conditions were: interface and transfer line
temperature 300°C, ionizer temperature 190°C, electron energy 100 eV and
emission current 0.3 mA. Electron-capture negative chemical ionization
(EC-NCI) was carried out with methane at an ionizer pressure of 0.45 torr.
In the GC/MS percent recovery and derivatization studies, a specific
ion for PGEZ (524‘; [MO/TMS-PFB]’) and for 2H4-PGE2 (528; [MO/TMS-PFB]')
were selected and monitored throughout these studies. The selected ion
monitoring mode (SIM) with quadrupole one was used on the mass
spectrometer. A baseline was chosen visually on the GC trace and the
areas for PGE2 and H^-PGE2 calculated by the INCOS computer system for the
calibration curve and percent recovery samples. The area of PGE2 divided
by the area of 2H4-PGE2 in the standards gives a ratio which is used in the
calibration curve. The amount of PGE2 recovered through each column was

43
calculated by comparing the ratio of these ions after the extraction
procedure to that of the calibration curve.
Results and Discussion
Percent Recovery Studies (Scintillation Counting)
Table 2-2 shows the percent recovery results for the different
sorbents tested. These recoveries were determined by scintillation
counting of 3H-PGE2 standards. Three samples were extracted for each
sorbent and the average and percent relative standard deviation (%RSD)
calculated. Examination of Table 2-2 indicates that a wide range of
recoveries was found for the different sorbents tested.
The non-polar sorbents investigated were octyl (C8), octadecyl (C18)
and phenyl (PH). The C18 columns had the highest percent recoveries
(97.2%) with the C8 (81.8%) and the PH (8.8%) columns having lower
recoveries. These low recovery values for the C8 and PH columns signify
either: (1) PGE2 was unretained as the initial standard solution was passed
through the column; (2) PGE2 was eluted during the wash procedure; or (3)
PGE2 was irreversibly bound to the column or not effectively eluted. The
reasons for poor recovery were investigated by examining all the eluents
which were passed through the respective columns to determine the presence
of PGE2. It was discovered that the C8 and PH columns did not initially
retain PGE2. Octadecyl columns exhibited the smallest variation from
column to column with a %RSD of 0.6.
Polar sorbents tested were silica (SI), cyanopropyl (CN) aminopropyl
(NH2) and diol (20H). As with the non-polar columns, a wide range of
recoveries were discovered for the different polar interactions tested.

Table 2-2: % Recovery of Standard PGE2 by Scintillation Counting
%
Recovery
Data
Column
Column 4
Average
% Recoverv
%RSD‘
1
2
3
C8 (Octyl)b
80.11
82.17
83.08
81.8
1.9
C18 (Octadecyl)
97.91
96.99
96.84
97.2
0.6
PH (Phenyl)
8.35
9.20
8.78
8.8
4.8
SI (Silica)
97.89
100.03
103.01
100.4
2.5
CN (Cyanopropyl)
24.02
27.92
22.82
24.9
10.7
NH2 (Aminopropyl)
12.75
13.96
11.12
12.6
11.3
2OH (Diol)
89.19
93.44
98.55
93.7
5.0
PBA (Phenyl
40.72
38.23
41.08
40.0
3.9
Boronic Acid)
a % Relative Standard
Deviation
b All columns were purchased from Analytichem.

45
The two sorbents that exhibited greater than 90% recovery were the SI
(100.4%) and 20H (93.7%). The recoveries for these columns were found to
be much higher than those found for CN (24.9%) and NH2 (12.6%) columns.
This difference in recoveries may be attributed to the interaction of the
polar groups on PGE2 (particularly the hydroxyls) with the hydroxyl groups
on the SI and 20H, rather than with the carbon/nitrogen interaction with
CN or the amine group with the NH2. Investigation of the eluents showed
that PGE2 was not effectively retained initially for the CN and NH2
columns. The variation from column to column (%RSD) for the SI (2.5%) and
20H (5.0%) were less than that found for CN (10.7%) and NH2 (11.3%).
In addition, phenyl boronic acid columns were tested. The percent
recovery found using this type of interaction was 40.0%, well below the
recovery values found for C18, SI and 20H columns. This extraction
technique is based on the premise that the tetrahedral anionic form of
boronates condense with 1,2- or 1,3-diols to form five- or six- membered
covalent complexes (107). The low recovery of PGE2 observed for the PBA
column can possibly be explained by the inability of the boronate to
condense with the diols on the cyclopentane ring of PGE2 to form a stable
complex. An explanation for the inability of PGs to condense with the PBA
column was reported by Lawson et al. (17). They believe that the tendency
of the planar phenyl groups to orient so that their pi (jt) orbitals align
or are stacked, thereby forcing the boronic acid groups to be too close
together, not allowing the sterically fixed cyclic 1,3-diols on PGs free
access.
Data obtained from testing these sorbents suggests that PGE2 has
preference for retention on specific non-polar (C18) and polar (SI and

46
20H) sorbents. Even sorbents with the same type of interactions
demonstrate varied retention for PGE2. Recoveries for the C18, SI and 20H
columns are similar and demonstrate adequate retention (>90%) of PGE2 to
justify further investigation.
Percent Recovery Studies (GC/MS)
Percent recovery data for standard PGE2 by GC/MS is listed in Table
2-3. The columns tested in this study were those that had been found to
provide adequate retention (>90%) for PGE2 in the previous scintillation
counting experiments. In addition, this study shows recovery data for
another brand of octadecyl sorbent (Sep-Pak) and a very selective sorbent
using antibody-antigen interaction (immunoaffinity). As in the initial
recovery study (Table 2-2), three individual columns were each used to
extract three samples of standard PGE2. Three injections of each sample
were made into the GC/MS. The average of the three injections and the
three samples, in addition to the %RSD is listed in Table 2-3.
Comparing the recovery data in Table 2-2 to the data in Table 2-3,
the average recovery values for the C18, SI and 20H are similar. The
values determined by GC/MS are consistently 3-10% lower than those
determined by scintillation counting. However, this slight difference
could be attributed to the basic difference in calculating counting data
and areas of GC/MS. The variation between columns is again small (<5.0%)
for all sorbents tested. The immunoaffinity column demonstrated a percent
recovery (93.1%) quite adequate for retention of PGE2. Octadecyl columns
from two different suppliers were compared to examine differences in
retention and selectivity. The recovery data for the Sep-Pak (Waters)

Table 2-3: % Recovery of Standard PGE2 by Gas Chromatography/Mass spectrometry
Average
% Recovery Data Average % Recovery %RSDa
Column
Column 4
GC
Iniection
A
% Recoverv
%RSDa
of 3
of 3
1
1
91.85
2
91.72
3
91.15
91.6
0.4
Columns
Columns
Í
Sep-Pak
2
86.30
84.60
84.12
85.0
1.4
89.11
4.0
(Octadecyl)
3
89.01
92.63
90.09
90.6
2.1
1
89.43
89.59
92.67
90.6
2.0
C18
2
95.63
94.98
95.06
95.2
0.4
92.8
2.5
(Octadecyl)
3
92.51
91.82
93.17
92.5
0.7
1
96.52
93.02
96.09
95.2
1.9
â– P*
SI
2
82.04
94.11
92.21
89.5
7.3
90.8
4.3
(Silica)
3
86.29
86.79
90.49
87.9
2.6
1
92.35
91.76
92.07
92.1
0.3
2 OH
2
90.44
88.69
91.13
90.1
1.4
90.0
2.4
(Diol)
3
88.58
86.90
87.88
87.8
1.0
1
88.50
98.18
102.02
96.2
7.2
IA
2
91.11
87.88
88.34
89.1
2.0
93.1
3.9
(Immununoaffinity)
3
90.67
89.55
101.60
93.9
7.1
a % Relative Standard Deviation

48
columns were slightly lower than that found for the C18 (Analytichem)
columns. This may be attributed to experimental error in the extraction
procedure; however, reports suggest that Sep-Paks have considerable faults
compared to octadecyl sorbents from other manufacturers (108).
Table 2-4 contains the percent recovery results of standard PGE2
spiked into urine by GC/MS analysis. The columns tested in this study
were C18, SI, 20H and a combination of C18 plus immunoaffinity (IA).
Biological samples can be directly applied to the IA column; however, for
PG analysis Knapp and Vrbanac (78) have found an advantage in preceeding
the IA purification procedure with a C18 column extraction. The advantage
is that employing the C18 extraction first removes large concentrations
of extremely polar impurities found in urine which can non-specifically
bind to the IA column. Averages and %RSD are listed in the table for
three injections of each sample and the three extractions which were
performed on individual columns. The data indicate that the columns (SI
and 20H) which utilize polar interactions are not effective for retention
of PGE2 in urine, even though they were successful for PGE2 standards.
This is presumably due to competition for binding sites on the sorbent
between matrix components in the urine and PGE2. The non-polar C18 column
and the C18 column coupled with the IA column provided similar recoveries
for PGE2 in urine as in standards. The variation from column to column is
low for all cases (<7%) including the C18 and IA samples. In the case of
the IA column data, the same sorbent bed (or column) was used for all
three samples. The %RSD for the three samples, in addition to the three
average recovery values, demonstrate the reusability of the IA sorbent.
The slight decrease in the recovery values between samples 1-3 indicates

Table 2-4:
% Recovery of
Standard PGE2 in
Urine by Gas
Chromatography/Mass
Spectrometry
Column(s)
Column #
%
Recovery Data
GC Iniection # %
Average
Recoverv
%RSDa
% Recovery
of 3
%RSDa
of 3
1
2
3
Columns
Columns
1
89.95
84.13
88.66
87.9
3.5
C18
2
96.88
99.66
99.16
98.6
1.5
92.1
6.3
(Octadecyl)
3
90.74
90.33
89.20
90.1
0.9
1
9.58
10.22
10.88
10.2
6.4
SI
2
10.35
10.81
10.51
10.6
2.2
10.6
4.0
(Silica)
3
10.67
10.91
11.62
11.1
4.5
â– P'
VO
1
23.27
18.61
26.82
22.9
18.0
2 OH
2
21.29
24.48
23.82
23.2
7.3
22.2
6.8
(Diol)
3
21.09
20.46
19.81
20.5
3.1
1
81.25
93.65
102.7
92.5
11.6
C18 + IAb
2
87.15
92.08
87.46
88.9
3.1
89.7
2.8
3
87.50
88.65
86.97
87.7
1.0
a % Relative Standard Deviation
b Three different C18 columns, but the only one IA column.

50
that no carry-over of PGE2 occurred from sample to sample. Thus, the IA
sorbent can be reused for many urine samples in combination with a C18
column without loss of affinity for PGE2. The ability of IA to effectively
separate urine matrix components from PGE2 will be discussed in a later
chapter.
Derivatization Studies
Table 2-5 lists the results of the study of different derivatization
procedures. The GC/MS peak areas for three samples are listed along with
their average and %RSD. Each sample injected onto the GC column contained
500 pg of PGE2. Comparing the different results, the most effective method
of derivatization can be determined.
The first method listed followed the derivatization procedure
discussed in the experimental section. Comparing that method to a second
method, in which a more rapid methoximation at an elevated temperature (1
hr at 60°C) was used, the peak area of method one was 1.4 times greater
when the 24 hour methoximation was employed. This suggests that at longer
reaction times more complete methoximation occurs. Recently, a study of
the methoximation of various PGs was reported in the literature (109).
These results showed that efficient methoximation of PGE2 by a procedure
similar to method one was 1.1 times greater than method two with a %RSD
of 11.8%. This corresponds to the values which were obtained in this
study. Another question addressed by this study is whether to perform the
methoximation step before or after the PFB esterification. Examining the
peak areas obtained for method three and comparing them to method one,
similar areas were calculated for 500 pg. The data suggest that either

Table 2-5: Study of Different Derivatization Procedures for PGE2
by GC/MS with SIM for the [M-PFB]‘ ion
Peak
Area of PGE,
(counts)
Method
Sample 1
Sample 2
Sample
3
Average
%RSD'
lb
1.64
x 106
2.21 x 106
2.01
X
106
1.95
X
106
14.8
2C
1.29
x 106
1.58 x 106
1.44
X
106
1.44
X
106
10.1
3d
2.16
x 106
1.74 x 106
2.00
X
106
1.97
X
106
10.8
4e
1.14
x 106
1.14 x 106
1.16
X
106
1.15
X
106
1.0
5f
1.21
x 106
1.14 x 106
1.12
X
106
1.15
X
106
4.1
a % Relative Standard Deviation
b Procedure described on page 41
c Methoximation for 1 hr at 60°C
d Esterification performed before methoximation
e Nitrogen evaporation only after the methoximation step
f Nitrogen evaporation performed after all steps
(no liquid-liquid extraction was performed)

52
step (methoximation or the PFB esterification) can be performed first.
The other question proposed in this study was the use of liquid-liquid
extraction to remove excess derivatizing reagents or the simpler, more
rapid method of only nitrogen evaporation. Two methods were studied, one
in which only nitrogen evaporation was performed after the methoximation
step, then liquid-liquid extraction after the esterification (method 4)
and the other in which only nitrogen evaporation was performed after all
derivatization steps (method 5). Comparing these two methods with method
one, the areas for 500 pg for both method four and five were approximately
40% less than method one. This suggests that removal of the excess
derivatizing reagents by liquid-liquid extraction is essential prior to
GC/MS, despite the increase in sample preparation time. The concentration
of PGE2 in urine is 100 to 400 pg/mL, thus having an effective
derivatization procedure which enhances the sensitivity of PGE2 is vital,
even at the expense of additional analysis time.
Conclusions
The optimum sample preparation for PGE2 in urine has been determined
in this chapter. Extraction and purification procedures as well as
derivatization steps have been investigated. The results from recovery
studies show that the use of either a C18 column or a combination of C18
and IA columns achieve adequate quantitative recoveries for PGE2 in urine.
Derivatization study results indicate that the time and temperature of the
methoximation reaction are important and appears to be optimum at longer
reaction times with lower temperatures. Performing either methoximation
or PFB esterification first in the derivatization procedure has little

53
effect on the area calculated for PGE2- Results from this study
demonstrate the advantage of using liquid-liquid extraction methods to
remove the excess derivatization reagents after each step in the
derivatization procedure.

CHAPTER 3
OPTIMIZATION OF GC/MS AND GC/MS/MS CONDITIONS
FOR TRACE DETERMINATION OF PROSTAGLANDINS
Introduction
Many reports of GC/MS analysis of prostaglandins (PGs) can be found
in the literature (2,17,48,62,101). The conditions employed in each case
vary depending on the type of analysis (qualitative or quantitative),
sample matrix (urine, serum, etc.), and targeted concentration. In the
trace determination of PGs, optimization of conditions is critical.
Detection of low levels of PGs (100-400 pg/mL) in urine requires a
technique that is both sensitive and selective. The many parameters which
exist in GC/MS and GC/MS/MS can be varied according to the analysis to
enhance either sensitivity or selectivity. Thus, to achieve the proper
conditions for trace determination of PGs the various parameters must be
characterized and optimized.
Experimental
Prostaglandins and Reagents
All solvents were reagent or HPLC grade. Prostaglandin E2 (PGE2) and
prostaglandin F2a (PGF2a) was purchased from Sigma Chemical Co. (St. Louis,
MO). The derivatization reagents pyridine, O-methylhydroxylamine
hydrochloride, acetonitrile and N,N-diisopropylethyl amine were all
54

55
purchased from Sigma Chemical Co. Pentafluorobenzylbromide (PFBBr) and
bis(trimethylsilyl)trifluoroacetamide (BSTFA) were purchased from Pierce
Chemical Co. (Rockford, IL). All glassware was silanized with a solution
of 5% dimethyldichlorosilane in toluene. These two chemicals were both
purchased from Sigma Chemical Co. Helium used as GC carrier gas, methane
(>99%) as chemical ionization reagent gas and nitrogen, argon and xenon
used as collision gases were from Matheson Gas Products, Inc. (Orlando,
FL).
Derivatization
The MO/PFB/TMS derivative of PGE2 and the PFB/TMS derivative of PGF2fl
were prepared by the same procedure as in Chapter 2.
Instrumental Conditions
A Finnigan MAT triple stage quadrupole (TSQ45) gas chromatograph/
mass spectrometer was employed. Mass spectrometry conditions were:
interface and transfer line temperature 300°C, ionizer temperature 190°C,
electron energy 100 eV and emission current 0.3 mA. GC was carried out
on a short J&W Scientific (Folsom, CA) DB-1 (3 m long, 0.25 mm i.d., 0.25
/im film thickness) capillary column in the splitless mode with helium
carrier gas at an inlet pressure of 4-6 psi. The initial temperature of
200°C was held for 30 s, then increased at 20°C/min to 260°C. The
injector temperature was 300°C.
Both full scan mass spectra and selected-ion monitoring (SIM) were
used in the GC/MS studies. An electron multiplier (EM) setting of 900 V
was used for the full scan spectra and a preamp gain of 10'8 A/V. A
baseline was chosen visually on the GC trace and the area for PGE2 (524*)

56
and PGF2a (569’) calculated by the INCOS computer system in the SIM mode
of operation. In GC/MS/MS optimization studies full daughter spectra and
selected-reaction monitoring (SRM) were employed and areas calculated by
the same method as described for GC/MS. The EM was set at 1500 V for the
full daughter spectra obtained and a preamp gain of 108 V/A. In the
GC/MS/MS optimization the [M-PFB]* carboxylate anions of PGE2 and PGF2(J
were selected in the first quadrupole (Ql) region and passed into the
collision cell (Q2) . In this region these ions underwent CAD to form
characteristic fragments which were then mass analyzed in the third
quadrupole (Q3). A full daughter spectrum was acquired over the mass
range of 100-600 amu.
Calibration curves were prepared for both GC/MS and GC/MS/MS after
optimization of the various parameters. Selected-ion monitoring and
selected-reaction monitoring were used to determine linearity, precision
and limits of detection for standard PGE2 utilizing GC/MS and GC/MS/MS.
The EM was set at 1700 V for both the SIM and SRM calibration curve data
Q
with a preamp gain of 10 V/A.
Mass Spectrometry (GC/MS)
Choice of the appropriate ionization method is essential for trace
determination of PGs by GC/MS. Electron ionization (El) has been reported
in the determination and identification of various PGs (42,43,57).
Structural information is obtained by this technique due to the abundance
of fragment ions which are produced. However, in trace analysis of PGs
the creation of a single ion with a maximized intensity is preferred.

57
Chemical ionization (Cl) has the advantage of usually producing few
fragment ions and a very intense molecular ion. Many reports of chemical
ionization GC/MS for PG analysis appear in the literature (65-72). Both
positive and negative Cl have been incorporated for PG analysis. The
literature reports that appropriate derivatization of PGs coupled with
electron-capture negative chemical ionization (EC-NCI) results in the
detection of low levels of PGs (69-72). These reports generally employ
methane (CH^) as a reagent gas for its ability to thermalize electrons.
Thus, both the GC/MS and GC/MS/MS optimization studies have utilized EC-
NCI with methane as the reagent gas.
Ionizer Pressure Study
Although the literature includes numerous examples of methane as a
reagent gas for EC-NCI, many dramatically different ion source pressures
have been employed. This study was performed to determine the optimum
ionizer pressure at which the [M-PFB]' ions of PGE2 and PGF2a are produced
in the ion source. Figure 3-1 shows the average areas determined at
different ionizer pressures of methane for the 524' ion (PGE2) and 569" ion
(PGF2a) • The average of three one-microliter injections of a 100 pg//¿L
solution of both PGE2 and PGF2a have been plotted on the graph. The
optimum ion source pressure for PGE2 and PGF2a occurs at 0.50 Torr of
methane.
At ionizer pressures lower than 0.50 Torr the [M-PFB]' ion has a
lower percent relative intensity compared to the reconstructed ion current
(RIC) for both PGE2 and PGF2a. As the ion source pressure is gradually
increased above 0.50 Torr, fragment ions begin to increase in relative

Figure 3-1 i Ion source pressure study of the [M-PFB]' ion of PGF2 and PGF.
r*
Average Area * 10° (counts)
tv
O
O)
a
oo
o
o
o
NO
O
-N
O
CO
o
CO
o
ro
b
o
Q-Ull I I I I I I I I I I I I [ I I I I I I I I 1 I I I I I I I I I I I I I l I II < â–  ; ' i ! ; ! | | | | | | i | i | i i i i i i , , i |
o-
O
Z5
CA
O
a
CD
o -i
ÑO¬
CO
p
a
"0
CD
05
05
C
T
CD
O
Oi
a»>
a
pH
ba-
o
o-
o
85
‘Optimum

59
intensity and contribute more to the RIC, thus decreasing the relative
intensity of the [M-PFB]‘ ion compared to the RIC.
Ionizer Temperature Study
Reports in the literature have cited ion source temperatures for
EC-NCI/GC/MS and EC-NCI/GC/MS/MS in the range of 110°C to 200°C (69-78).
Figure 3-2 indicates the optimum ion source temperature observed in this
study for the analysis of PGE2 and PGF2a< Selected-ion monitoring (SIM)
of the 524' (PGE2) and 569" ion (PGF2a) was used over a range of ion source
temperatures from 100°C to 190°C. Three one-microliter injections of a
500 pg//iL solution of PGE2 and PGF2a were performed at ten different ion
source temperatures. The average of the three injections is plotted on
the graph. Both PGE2 and PGF2a have an optimum ion source temperature at
190°C. Thus, the [M-PFB]‘carboxylate anion of PGE2 and PGF2a optimize at
the maximum ion source temperature of the instrument.
The percent relative intensity of the [M-PFB]' ion compared to the
RIC increases with an increase in the ion source temperature and reaches
a maximum at 190°C. In addition fragment ions increase, as the
temperature is elevated to about 140°C to 150°C, then these fragments
gradually decrease as the ion source temperature is raised above 150°C.
These two observations lead to the optimum ion source temperature of 190°C
for the [M-PFB]' ion.
Electron-Capture Negative Chemical Ionization Mass Spectra
The mass spectra of standard PGE2 and PGF2a, obtained at the optimum
ion source pressure and temperature, are shown in Figure 3-3a and Figure
3-3b. Both spectra demonstrate the advantage of employing EC-NCI for

Average Area * 10 (counts)
Ion Source Temperature (C)
Figure 3-2: Ion source temperature study of the [M-PFB]" ion of PGE2
ON
o
and PGF.

% Relative Abundance
Figure 3-3: Electron-capture negative chemical ionization mass spectra of:
(a) PCE2 MO/PFB/TMS derivative
(b) PGF^ PFB/TMS derivative

62
prostaglandin analysis. One intense peak, the [M-PFB]' ion, dominates
each mass spectrum. This ion, PGE2 (524’) and PGF2a (569*), can be utilized
for SIM. Other low intensity fragment ions can be seen in the mass
spectrum of PGE2, corresponding to the loss of derivatives attached to
PGE2. In addition, no fragments of greater than 1% relative abundance are
observed in the mass spectrum of PGF2(t.
The M’ ion for both PGE2 (m/z 705) and PGF2a (m/z 750) is rarely
present in the EC-NCI mass spectra, thus it must be less than 0.1%
relative abundance. In addition, the PFB* ion (m/z 181) occurs in the EC-
NCI mass spectra of both PGs at less than 0.5% abundance.
Selected-Ion Monitoring Calibration Curve
A calibration curve for PGE2 (524’) is shown in Figure 3-4. This
curve indicates the linearity and limit of detection for PGE2 with SIM.
Three one-microliter injections at nine different concentrations were
performed. The limit of detection was calculated from the calibration
data and corresponded to the amount of PGE2 which could give a GC peak area
three times greater than the average area obtained with a derivatized
blank. The use of SIM with standard PGE2 produced a limit of detection of
approximately 94 fg (femtograms) and is indicated on the curve. The
calibration curve showed good linearity above the limit of detection in
the range of concentrations expected for endogenous PGE2 in urine (100 to
400 pg/mL) (71,78). The linear dynamic range of the curve is from 500 fg
to 1 ng (solid line) and the slope of the linear regression best fit line
is 1.266 with a correlation coefficient of 0.9925. The non-linearity at
the low end of the calibration curve may be due to adsorption on the

10
10
PGE2 Concentration (g)
as
u>
Figure 3-4:
Selected-ion monitoring calibration curve for the
[M-PFB]' ion of the MO/PFB/TMS derivative of PGE2.

64
column, septum or injection port and subsequent adsorption by the next
injection. Precision of the GC/MS method utilizing SIM was determined by
performing ten one-microliter injections of a 50 pg//iL solution of PGE2.
The percent relative standard deviation (%RSD) of the ten injections was
5.5%. Calibration curves for PGF2a, PGD2 and DHKF2a were similar, with
varying limits of detection, in the range of 50 to 200 fg.
The results for this study agree well with the literature. Reports
have shown LODs using EI/MS at about 20 pg for the M+’ (6,17,48,62,101) and
utilizing EC-NCI/MS about 100 fg (19,20,76,77) for the [M-PFB]' ion.
Tandem Mass Spectrometry (GC/MS/MS)
Monitoring the efficiencies of the collisionally activated
dissociation processes can help in determining optimum MS/MS conditions
for trace determination of PGs. These efficiencies are affected by
collision energy and collision gas pressure. Either parameter can be
varied to maximize the CAD efficiency for a particular parent ion.
Increasing the collision energy allows for more energetic collisions,
while increasing the collision gas pressure increases the number of
collisions each ion experiences.
Collision Gas Pressure Studies
The collision gas pressure for three different gases (N2, Ar, and Xe)
was optimized to determine which collision gas and pressure were the most
efficient for selected-reaction monitoring at the maximum available
collision energy of 30 eV. Pressure-resolved breakdown curves for
selected ions of the MO/PFB/TMS derivative of PGE2 are shown in Figures

(a)
Collision Gas
Collision Energy - 30 eV
oooQo 524
SP 524"
524'
lAQ 524'
434'
344’
313'
268’
0.0 1.0 2.0 3.0
Collision Gas Pressure (mTorr)
(b)
Optimum
Ar Collision Gas
Collision Energy - 30 eV
QoooQ 524”-» 43-4"
□ anon 524”-» 344'
4AAAA 524'-+ 313'
0 0000 524 -» 268'
0.0 1.0 2.0
Collision Gas Pressure (mTorr Ar)
(c)
ee
CL
t ®
Q
W
1 Optimum
1
Xe
Collision Gas
: /
\ Collision Energy — 30 eV
: /
QQ-QQQ 524 -> 434
i /
a â–¡ a o a 524 -> 344
- /
524'-+ 313"
â– 1 X
0 524 - 268'
¿ i
0.0 1.0 2.0 JO
Collision Gas Pressure (mTorr)
Figure 3-5: Pressure-resolved breakdown curve of the carboxylate
anion of the MO/PFB/TMS derivative of PGE2 with
collision gas: (a) Nitrogen (b) Argon (c) Xenon

(a)
(b)
Ar Collision Gas
Collision Energy — 30 eV
ooooo 569 -*
339'
â–¡ â–¡â–¡â–¡â–¡ 569 -*
317'
A6AAA 569
299'
00000 569”-+
273"
Collision Gas Pressure (mTorr)
(c)
Optimum
Xe Collision Gas
Collision Energy — 30 eV
ooooo 569'-»
389'
ODDDÜ ñAO--»
317"
299'
00000 569'-
273'
Collision Gas Pressure (mTorr)
Figure 3-6: Pressure-resolved breakdown curve of the carboxylate
anion of the PFB/TMS derivative of PGF^ with
collision gas: (a) Nitrogen (b) Argon (c) Xenon

67
3-5a, 3-5b and 3-5c and for the PFB/TMS derivative of PGF2a in Figures 3-
6a, 3-6b and 3-6c. The optimum collision gas pressure is indicated on
each curve. This type of curve can be calculated by dividing the area of
a selected daughter ion by the area of all the ions in the daughter
spectrum (DyfüDj + P]) at each pressure. The point which is chosen as the
optimum is the pressure where one can obtain a qualitative daughter
spectrum which is "rich" in structural information with a number of
reasonably abundant daughter ions.
The optima indicated on Figures 3-5a, 3-5b and 3-5c occur at a
collision pressure of 0.5, 1.0 and 0.5 mTorr for N2, Ar, and Xe
respectively. However, in the case of PGF2a, the optima occur at
significantly higher pressures, 2.5, 1.5, and 1.0 mTorr for N2, Ar, and Xe
(Figures 3-6a, 3-6b and 3-6c). Comparing Figure 3-5a to 3-6a, the optimal
use of nitrogen as a collision gas requires a pressure five times higher
for PGF2a than for PGE2. This dramatic difference in optimum collision
pressure exists between two structurally similar PGs.
The relative differences in the optimum collision gas pressure for
PGF2a with the various collision gases can be explained by the relative
mass of the three different collision gases. The greater size of the
argon and xenon gas molecules increases the energy deposited into the
parent ion, therefore increasing the fragmentation efficiency. Therefore,
the optimum collision pressure decreases with an increase in the mass of
the gas molecules, because the abundance of the most prominent fragment
ions occur at lower pressures.
Notice the significant differences in the maximum relative intensity
of the daughter ions for the three collision gases. The curves with

68
nitrogen (Figures 3-5a and 3-6a) show a higher maximum relative intensity
for the selected reactions listed. Figure 3-6c for PGF2(J, utilizing xenon
as the collision gas, is particularly interesting. The relative intensity
of the daughter ions selected are 12 times lower than the intensity of the
same daughter ions displayed in Figure 3-6a for nitrogen. In addition,
the relative intensity of the daughter ions approach zero at higher
collision gas pressures (> 1.0 mTorr). Thus, either the parent ion
(carboxylate anion) is increasing at higher pressures or other daughter
ions are more abundant with argon and xenon at these collision gas
pressures. Clearly, for the CAD process, the parent ion decreases as the
collision gas pressure is increased. Therefore, various daughter ions not
listed in these figures must be prominent with argon and xenon at higher
collision gas pressures.
This is apparent from examining Figure 3-7, which shows the
pressure-resolved breakdown curves for different selected ions with the
PFB/TMS derivative of PGF2a with argon and xenon as collision gases.
Comparing Figure 3-7a and Figure 3-7b to Figure 3-6a the relative
intensity of the daughter ions for argon and xenon in this case are
similar to that found for nitrogen. The most intense reaction in both
cases in Figure 3-7 is the selected-reaction of 569’ -*• 89', corresponding
to a back-bone fragmentation.
A general trend appears in all the figures for both PGE2 and PGF2a>
The loss of one and two HOTMS groups from the [M-PFB]’ ion tend to maximize
together at low collision gas pressures for the three collision gases.
Subsequently, these selected-reactions gradually decrease towards zero at
higher collision gas pressures. The four selected-reactions for PGE2 in

69
(a)
(b)
o.o
— Optimum
Xe Collision Gas
Collision Energy — 30 eV
ooooo 569 -»
255'
â–¡ â–¡â–¡â–¡â–¡ 569
215
A A A A A 569
161"
00000 569 -*
89'
t[ m m mTTTTTTm t~h * t
1.0 2.0 3.0
ti
4.0
Collision Gas Pressure (mTorr)
Figure 3-7: Pressure-resolved breakdown curve of the carboxylate
anion of the PFB/TMS derivative of PGF^ with
collision gas: (a) Nitrogen (b) Argon

70
Figure 3-5 all increase at low collision gas pressures and then gradually
decrease as higher collision gas pressures are employed. In the case of
PGF2a, the additional loss of the third HOTMS group (569" -*â–  299") gradually
increases when nitrogen is utilized (Figure 3-6a) or levels off when argon
(Figure 3-6b) is employed, as the collision gas pressure is continually
increased. In Figure 3-7, the selected-reactions have relatively low
intensities at low collision gas pressures (< 1.0 mTorr), but increase
gradually and level off as the collision gas pressure is increased (> 1.0
mTorr).
Trace analysis by selected-reaction monitoring with MS/MS requires
optimization of the absolute intensity of a single daughter ion of the
selected parent ion. The curves in Figures 3-8 and 3-9 give an indication
of the optimum reactions and collision gas pressures which should be
selected for maximum SRM sensitivity for PGE2 and PGF2a with three
different collision gases at maximum collision energy (30 eV). This type
of curve is calculated by dividing the area of selected daughter ions, Dj,
by the area of the incident parent ion, PQ (measured in a daughter spectrum
without collision gas). The reaction with the highest CAD efficiency
should be selected to yield the highest sensitivity for selected reaction
monitoring (SRM) trace determination of PGs. For example, in the case of
PGF2a, choice of the 569" -*■ 299’ selected reaction with argon (Figure 3-
9b) would be the optimum (overall efficiency of -2%) at a collision
pressure of 1.5 mtorr and collision energy of 30 eV. This reaction
corresponds to the [M-PFB]" -*• [(M-PFB) - 3(HOTMS) ]"for the derivatized
carboxylate anion of PGF2(J. Note that this overall CAD efficiency (-2%)
is obtained at the optimum pressure for any of the three gases. The more

71
13n
(a)
Nz Collision Gas
â– 
Collision Energy — 30 eV
10-
JK,
Optimum — A
ooooo 524--* 434"
□ □□□□ 524 -» 344
CL
\
Q
A A A A A 524 -* 313
OOOOO 524 -> 268"
o.o 1.0 J.O 3.0
Collision Gas Pressure (mTorr)
(b)
Optimum
Ar Collision Gas
Collision'Energy — 30 eV
ooooo 524"
â–¡ DODO 524"
A A 524“
OOOOO 524"
0.0 1.0 2.0 3.0
Collision Gas Pressure (mTorr)
434'
344'
313"
268"
1S-|
(C)
Optimum
Xe Collision Gas
Collision Energy — 30 eV
ooooo 524"
o_ooop 524"
A AAA A 524"
OOOOO524"
434'
344'
313'
268'
0.0 1.0 2.0 3.0
Collision Gas Pressure (mTorr)
Figure 3-8: Overall CAD efficiency for the selected-reaction
monitoring of the carboxylate anion of the MO/PFB/TMS
derivative of PGE2 with collision gas:
(a) Nitrogen (b) Argon (c) Xenon

72
(a)
2.5 ?
N2 Collision Gas
Collision Energy - 30 eV
Optimum ->
0.0 1.0 2.0 3.0 4.0
Collision Gas Pressure (mTorr)
(b)
2-5 :
2.0 :
V *-5
o
CL
\ 1.0
a
0.5
0.0
:
Ar Collision Gas
' Optimum— A
Collision Energy - 30 e\
ooooo 569~-> 389'
/ \
aaoao 5fiQ -» 317"
/ \
569 -* 299"
: / \
00000 569"- 273"
0.0 1.0 2.0 3.0 4.0
Collision Gas Pressure (mTorr)
(c)
— Optimum
Qffl-QQQ 569'
oanno 569'
aaaaa 569'
00000 569'
389'
317'
299'
273'
Xe Collision Gos
Collision Energy — 30 eV
2.0
3.0
4.0
Collision Gas Pressure (mTorr)
Figure 3-9: Overall CAD efficiency for the selected-reaction
monitoring of the carboxylate anion of the PFB/TMS
derivative of PGF^ with collision gas:
(a) Nitrogen (b) Argon (c) Xenon

73
massive the collision gas, the lower the optimum pressure. PGF2a exhibits
a slightly higher overall CAD efficiency (-2%) with xenon for the selected
reaction of 569' -*• 317' (Figure 3-9c). This reaction corresponds to the
[M-PFB]" -+ [ (M-PFB) - 2(HOTMS) - (CH3)2Si=CH2]' for the derivatized
carboxylate anion of PGF2a. This suggests that xenon would be the optimum
CAD gas. However, xenon is quite expensive ($650/50 L of gas) and the
gain in CAD efficiency is slight; thus, argon would be a more practical
choice.
For PGE2, the [M-PFB]' -*• [(M-PFB) - 2(H0TMS) - C02 - H0CH3]‘ reaction
with argon (Figure 3-8b) is optimum at a pressure 2 times lower than for
PGF2(J. Even more notable is that the optimum CAD efficiency (D1/PQ) for
PGE2 (-10%) is significantly higher than that for PGF2a (-2%) with all
three gases employed. Note that on Figures 3-8b and 3-8c the lowest
collision gas pressure been plotted is 0.2 mTorr. This is due to the fact
that when the zero collision gas pressure data was obtained, the actual
pressure of the collision cell was 0.2 mTorr. This indicates that
residual collision gas was present in both these cases, thus allowing
residual CAD to occur.
Collision Energy Study
Argon was chosen as the collision gas for the optimization of
collision energy. The collision energy study for selected-reaction
monitoring is shown in Figure 3-10. Data for SRM with the reactions and
Argon pressure chosen as optimum in the collision gas pressure studies at
30 eV for PGE2 and PGF2a are plotted on the same graph. Three one-
microliter injections of a 500 pg//iL solution of PGE2 and PGF2a were

Area
1 O ° ~ i 11 11 11 i i 11 ■ i 11 t ill | M 11 i t TTTfri i 11' i TT~rj~rn~T i i i i i | i i i i i i 11 11
0.0
5.0
10.0
15.0
20.0
25.0
50.0
Collision Energy (eV)
(524' 268')
¡sion Pressure
mTorr Argon
(569" -> 299")
¡sion Pressure
mTorr Argon
Figure 3-10: Collision energy study for the selected reactions of the M0/PFB/TMS
derivative of PGE2 and the PFB/TMS derivative of PGF^.

75
performed at collision energies of 7 to 28 eV. Optima for the selected
reactions of 524’ -*• 268* (PGE2) and 569" -+ 299’ (PGF2a) are indicated on the
graph. The optimum collision energy for PGE2 (25 eV) is slightly higher
than for PGF2a (22 eV) , probably due to the difference in the collision
pressures employed for each selected reaction. These plots suggest that,
once a particular collision gas, pressure, and selected reaction are
chosen, variation of the collision energy has little effect.
PauEhter Spectra of Standards
Figures 3-11a and 3-lib show daughter ion spectra for the
carboxylate anions of the MO/PFB/TMS derivative of PGE2 and the PFB/TMS
derivative of PGF2ff. The fragment ions labeled in the spectra are
tabulated in Table 3-1 with possible assignments of the ion's identity.
Most of the fragment ions observed in both daughter spectra are
derivative - specific. These ions occur at m/z 434, 344 and 313 for PGE2 and
at m/z 479, 389, 317 and 299 for PGF2a. The most intense daughter ion from
the fragmentation of the [M-PFB]’ ion - of PGE2 is m/z 268 ion and
corresponds to the loss of (2*H0TMS-C02-CH30H) from the parent ion of 524’
In the daughter spectrum of PGF2a the m/z 299 ion is the most intense
and corresponds to the loss of three HOTMS groups from the parent ion of
569". The fragment ions which occur at lower masses are ions that
correspond to backbone-specific fragments. This means these ions
correspond to fragmentation of the carbon-hydrogen skeleton in both PGE2
and PGF2a. These ions include m/z 240 and 214 for PGE2 and m/z 255, 215,
201 and 161 for PGF.

% Relative Abundance
100%-i
268~
CHjO-N
(a)
100%-i
(b)
m/z 100
Figure 3-11:
â– -j
as
Daughter ion spectra of the [M-PFB]' ions (ra/z 524 and 569) of:
(a) PGE2 MO/PFB/TMS derivative at 1.0 mTorr argon and at 28.2 eV
(b) PGF^ PFB/TMS derivative at 1.5 mTorr argon and at 28.2 eV

77
Table 3-1: Daughter Ions of [M-PFB]’
PGE2 MO/PFB/TMS and PGF2a
PFB/TMS
PGE-, MO/PFB/TMSa
Ion Assignment
m/z
%RA'
P'
524
5
[P-HOTMS]*
434
2
[P-2H0TMS]‘
344
21
[P-2H0TMS-OCHj]"
313
32
[P-2H0TMS-C02]"
300
4
[P-2H0TMS-C02-CH20]'
270
11
[P-2H0TMS-C02-CHjOH ]'
268
100
[ P - 2H0TMS - C02- CHjOH - C2H4 ]'
240
5
[ P - 2H0TMS - C02 - CHjOH - C4H6 ]'
214
12
PGF-^ PFB/TMSb
Ion Assignment
m/z
%RA
P*
569
36
[P-HOTMS]‘
479
4
[P-2H0TMS]*
389
18
[ P - 2H0TMS - (CH3) 2S i=CH2 ]'
317
24
[P-3H0TMS]’
299
100
[ P - 2H0TMS - C02 - (CH3) 2S i=CH2 ]'
273
56
[ P.- 3H0TMS - C02 ] *
255
36
[P-3H0TMS-C02-C3H4]'
215
21
[p-3hotms-co2-c4h6]‘
201
12
[p-3hotms-co2-c7h10]'
161
18
8 At a collision gas pressure of 1.0 mTorr argon
and collision energy of 28.0 eV.
b At a collision gas pressure of 1.5 mTorr argon
and collision energy of 28.0 eV.
c % Relative Abundance

78
Considerations for choice of a particular selected reaction for
monitoring has been discussed recently by Strife (77). This report along
with other studies have shown that backbone-specific fragmentation confers
superior selectivity over derivative-specific fragmentation in the
analysis of biological samples. For example, when SRM is based on a
derivative-specific fragmentation, any component in a SIM chromatogram
that is derivatized has an enhanced probability of appearing in a SRM
chromatogram. However, the backbone-specific fragmentation has a lower
relative daughter ion intensity in EC-NCI/GC/MS/MS than for derivative-
specific fragmentation. Therefore, if the backbone-specific fragmentation
was chosen for SRM analysis the sensitivity would be lower than that for
the derivative-specific fragmentation found in Figure 3-8 and Figure 3-9
for PGE2 and PGF2a.
Selected-Reaction Monitoring Calibration Curve
A selected-reaction monitoring (SRM) calibration curve for PGE2
(524"-* 268") is shown in Figure 3-12. This curve indicates the linearity
and limit of detection for PGE2 with SRM. Three one-microliter injections
at seven different concentrations were performed. The limit of detection
was calculated from the calibration data, the corresponding amount of PGE2
which gives a GC peak area three times greater than the average area
obtained with a derivatized blank. The use of SRM with standard PGE2
produced a limit of detection of approximately 14 pg, as indicated on the
curve. The calibration curve showed good linearity above the limit of
detection in the range of concentrations expected for endogenous PGE2 in
urine (100 to 400 pg/mL) (71,78). The linear dynamic range of the curve

Figure 3-12: Selected-reaction monitoring calibration curve for the 524* -+ 268
reaction of the MO/PFB/TMS derivative of PGE2-

80
is from 20 pg to 5 ng (solid line) and the slope of the linear regression
best fit line is 1.007 with a correlation coefficient of 0.9989. Precision
of the GC/MS/MS method utilizing SRM was determined by performing ten one
microliter injections of a 500 pg//iL solution of PGE2. The percent
relative standard deviation (%RSD) of the ten injections was 3.9%.
Calibration curves for PGF2a, PGD2 and DHKF2q were similar, with varying
limits of detection in the range of 5 to 30 pg. The results for this
study agree well with literature reports, which have shown LODs utilizing
EC-NCI/MS/MS of about 1 to 20 pg (19,20,76,77).
Conclusions
The optimum conditions for GC/MS electron-capture negative chemical
ionization (EC-NCI) with SIM and GC/MS/MS with SRM are summarized in Table
3-2. The optimum collision gas pressure for both qualitative and
quantitative (SRM) analysis of PGE2 are lower than the optima found for
PGF2a. The dramatically lower CAD efficiency for the carboxylate anion
of PGF2a (Figure 3-8b) compared to that of PGE2 (Figure 3-7b) clearly
indicates its greater stability under CAD conditions.
This study demonstrates the need for evaluating the CAD efficiency
in the trace analysis of PGs. Optimization of both collision energy and
collision gas pressure is essential in obtaining an accurate qualitative
daughter spectrum "rich" in structural information. The CAD reaction with
the highest CAD efficiency should be selected to yield the sensitivity for
SRM determination of PGs.
Examining the calibration curves (Figures 3-4 and 3-11) differences
between SIM and SRM are noted. Sensitivity is greater with SIM than with

81
Table 3-2: Otimum Conditions for Electron-Capture Negative
Chemical Ionization Mass Spectrometry
and Tandem Mass Spectrometry
Electron-Capture Negative Chemcial
Parameter
Ion Source Pressure
Ion Source Temperature
PGE:
0.50 Torr
190°C
Ionization
0.50 Torr
190°C
Tandem Mass Spectrometry
Qualitative Daughter Spectrum
Parameter
Collision Gas
Collision Gas Pressure
Collision Energy
pge2
Argon
1.0 mTorr
28.1 eV
Argon
1.5 mTorr
28.1 eV
Quantitative
Parameter
Collision Gas
Selected Reaction
Collision Gas Pressure
Collision Energy
Selected-Reaction Monitoring
pge2
Argon
524' - 268
1.0 mTorr
25.0 eV
PG£2a
Argon
569' - 299
1.5 mTorr
22.2 eV

82
SRM. The limit of detection for SIM (94 fg) is slightly more than 2
orders of magnitude lower than for SRM (14 pg). Comparing the relative
peak areas of SIM and SRM at 20 pg the SIM peak area is approximately 10
times higher than the peak area of 20 pg with SRM. In addition, at higher
levels of PGE2, 500 pg, the SIM peak area is approximately 40 times higher
than the SRM peak area. The lower sensitivity of SRM is expected due to
the limited efficiency of the CAD conversion of the parent ion to the
daughter ion (approximately 12% for 524' -*â–  268") of interest, as well as
transmission losses inherent in adding a second stage of mass analysis
(typically 10 times). However, the selectivity gained by the parent-
daughter reaction should reduce the chemical noise, in a sample matrix,
to a greater extent than the analytical signal, thus, compensating for the
lost sensitivity.

CHAPTER 4
DIFFERENCES IN THE COLLISIONALLY ACTIVATED DISSOCIATION OF
STRUCTURALLY SIMILAR PROSTAGLANDINS
Introduction
The ions formed by electron ionization (El) of the methyl ester/
methoxime/trimethyl silyl ether derivatives of prostaglandins (PGs) show
considerable fragmentation in the collisionally activated dissociation
(CAD) process (74,75). However, the carboxylate anions of certain PGs
produced by EC-NCI have been reported to be extremely stable when
subjected to CAD (76).
It has been observed that the carboxylate anions of certain PGs
exhibit little fragmentation even at high collision energies (>20 eV) and
pressures (1.5 mTorr N2). Subtle differences among the structures of
prostaglandins E2 (PGE2), F2a (PGF2a) , D2 (PGD2) and 13,14-dihydro-15-keto
F2a (DHKF2a) (Figure 4-1) yield enormous differences in CAD efficiency.
The CAD efficiency for the [MO/TMS-PFB] ‘, [M-PFB]' and [M-H]‘ carboxylate
anions is significantly different for closely related PGs. The low
fragmentation and CAD efficiencies of the carboxylate anions of PGF2a and
DHKF2a compared to those of PGE2 and PGD2 clearly indicate the greater
stability of these species. In this chapter these differences are
evaluated and explained in relation to the structural differences between
the carboxylate anions for the PGs.
83

84
Figure 4-1: Structures of the four prostaglandins studied:
(a) Prostaglandin F2a (PGF2a) (b) Prostaglandin E2 (PGE2)
(c) Prostaglandin D2 (PGD2) (d) 13,14-dihydro-15-keto F2
(DHKF2a)

85
Experimental
Prostaglandins and Reagents
The prostaglandins E2, F2a, D2 and 13,14-dihydro-15-keto F2a, as well
as O-methylhydroxylamine hydrochloride, N,N-diisopropylethyl-amine,
pyridine, and acetonitrile (analytical grade) were all purchased from
Sigma Chemical Co.. Pentafluorobenzylbromide (PFBBr) and bis(trimethyl-
silyl)trifluoroacetamide (BSTFA) were purchased from Pierce Chemical Co..
The methane (>99%) used as the chemical ionization reagent gas was
purchased from Matheson Gas Products, Inc.. Helium used as GC carrier
gas and nitrogen used as CAD collision gas were commercial grade, with
their purity checked by mass spectrometry.
Derivatization
The methoxime/pentafluorobenzyl ester/trimethylsilyl (MO/PFB/TMS)
derivatives (Figure 4-2) formed for the GC/MS/MS studies were prepared
according to the method in chapter 2. The trimethylsilyl derivative was
formed by adding 100 /¿L of BSTFA and allowed to stand overnight at room
temperature. Dilutions were made from this solution so that a 500 pg//xL
solution of each PG was used for injections. The solids probe/MS/MS
studies were performed either by analyzing the standards without
derivatization or as the PFB derivative, using only the PFBBr
esterification step above.

86
(a)
(b)
(c)
(d)
Figure 4
TMSO
CHjO-N
TMSO
TMSO
2: Structures of the methoxime-pentafluorobenzyl-
trimethylsilyl (MO/PFB/TMS) derivatives of the four
prostaglandins:
(a) PGF2a (b) PGE2 (c) PGD2 (d) DHKF2(J

87
Instrumental Conditions
GC was carried out on a short J&W Scientific (Folsom, CA)
DB-1 (3 m long, 0.25 mm i.d., 0.25 /xm film thickness) capillary column in
the splitless mode with helium carrier gas at an inlet pressure of 4-6
psi. The initial temperature of 200°C was held for 30 s, then increased
at 20°C/min to 260°C. The injector temperature was 300°C. One-microliter
injections of a 500 pg//xL solution of each PG were made in triplicate at
each condition for the GC/MS/MS studies.
The solids probe was used as the means for sample introduction to
study the PFB ester derivatives and the free (underivatized) PG standards.
The initial temperature was 50°C and increased at 20°C/min to 300°.
Triplicate samples were analyzed for each derivatization procedure at each
condition for the MS/MS studies. Sample size was one microgram of the
underivatized PGs or 1 ng of the PFB ester derivatives.
A Finnigan MAT TSQ45 gas chromatograph/triple quadrupole mass
spectrometer was employed. Mass spectrometry conditions were: interface
and transfer line temperature 300°C, ionizer temperature 190°C, electron
energy 100 eV and emission current 0.3 mA. Electron-capture negative
chemical ionization (EC-NCI) was carried out with methane at an ionizer
pressure of 0.45 torr.
In the MS/MS experiments, nitrogen collision gas pressure and
collision energy were varied depending on each experiment. The [MO/TMS-
PFB]", [M-PFB]" carboxylate anions were selected in the first quadrupole
(Ql) region and passed into the collision cell (Q2). In this region these
ions underwent CAD to form characteristic fragments which were then mass
analyzed in the third quadrupole (Q3) region. A full daughter spectrum

88
was acquired over the mass range of 55-600 amu. The maximum collision
energy possible on the TSQ 45 is 30 eV.
The peak areas in the daughter spectra of selected daughter ions and
the parent ion remaining after CAD were calculated by the INCOS computer
system for each GC and solids probe sample. A baseline was chosen
visually and the calculated areas were used for determining CAD
efficiencies.
Efficiency Calculations
The abundance of the daughter ions relative to that of the remaining
parent carboxylate anion in the daughter spectrum can be controlled by
varying the CAD energy or pressure; these parameters also affect
sensitivity due to scattering losses. The processes of fragmentation and
scattering can be monitored by evaluating the fragmentation (E ),
r
collection (E ), and overall CAD (E ) efficiencies given by the
I» UAD
following equations (110):
E
F
EDj
P + ED.
fraction of ions present
following CAD which are
daughter ions
E
P + ED,.
fraction of initial parent
C
ions that is collected
following CAD as either
parent or daughter ions
E
’CAD
fraction of initial parent
ion that is converted to
collectable daughter ions

89
where PQ, P, and Dj are the intensities of the parent ion prior to CAD, the
parent ion remaining after CAD, and a daughter ion resulting from CAD,
respectively. Note that n = E„ x Er.
GAD r G
As was stated earlier in chapter 3, the above efficiencies are
affected by collision energy and collision gas pressure. Either parameter
can be varied to maximize the CAD efficiency for a particular parent ion.
Increasing the collision energy allows for more energetic collisions,
while increasing the collision gas pressure increases the number of
collisions each ion experiences. Either approach increases the amount of
energy deposited into the parent ion, and thereby increases the
fragmentation efficiency. However, an increase in collision energy or
pressure will produce an increase in scattering losses (or possibly other
loss mechanisms such as neutralization by charge exchange) and thereby
decrease collection efficiency. The overall CAD efficiency, as the
product of fragmentation and collection efficiency, will typically first
increase then level off and even decrease as the collision energy or
pressure are increased. Systematic variation of each parameter would
provide a three-dimensional plot of efficiency vs. energy vs. pressure.
Practically, such studies involve two-dimensional slices through this
three-dimensional surface, varying one parameter while keeping the other
constant.
Collision Energy Study of the ÍM0/TMS-PFB1' Carboxvlate Anions
In light of the dramatic differences observed in Chapter 3 of the
CAD efficiencies of the carboxylate anions of the fully derivatized PGF2a
and PGE2 (differing structurally only in the presence of a carbonyl (=0)

90
group at C-9 derivatized to a methoximine, in PGE2, rather than a hydroxyl
(OH) group at the C-9 position, derivatized to a trimethylsilyl group, in
PGF2a) two PGs similar to these were studied. The PGD2 and PGE2 isomers
vary only by the interchange of the hydroxyl (OH) and carbonyl (=0) groups
on C-9 and C-ll. DHKF2a differs from PGF2a by exchange of a carbonyl (=0)
group (derivatized to a methoximine) for the hydroxyl (OH) group
(derivatized to a trimethylsilyl) at C-15.
Figure 4-3 and Figure 4-4 presents curves for fragmentation,
collection and overall CAD efficiencies versus collision energy for the
carboxylate anions of PGE2, PGF2a, PGD2 and DHKF2(J. These curves show the
effects of varying the collision energy at two different collision gas
pressures. In Figures 4-3a, 4-3b and 4-3c, the collision pressure has
been established at 1.2 mTorr N2, a value which is typically optimum for
many MS/MS analyses. The fragmentation efficiency curve (Figure 4-3a)
indicates the dramatic differences in stability of the carboxylate anions
of the four PGs. At a collision energy of 30 eV the fragmentation
efficiencies ranges from a typical 80% down to only 2%. The collision
pressure must be increased to produce more efficient fragmentation. The
collection efficiency (Figure 4-3b) for the four PGs are similar. The
notable exception is PGD2, which has an unusually high collection
efficiency at collision energies of 10-25 eV. This explains the
difference noted between the fragmentation efficiency of PGE2 and PGD2
compared to their overall CAD efficiency.
Figures 4-4a, 4-4b and 4-4c show the overall CAD, collection and
fragmentation efficiencies at a collision gas pressure 2.5 times higher.
The fragmentation efficiency (Figure 4-4a) as well as the overall CAD

100
91
(a)
(b)
(c)
Figure 4-3: CAD efficiency of the [MO/TMS - PFB]* carboxylate anions
versus collision energy at 1.2 mTorr N2:
(a) Fragmentation
(b) Collection
(c) Overall CAD

92
(a)
(b)
(c)
CAD efficiency of the [MO/TMS - PFB]" carboxylate anions
versus collision energy at 3.0 mTorr N2:
(a) Fragmentation
(b) Collection
(c) Overall CAD
Figure 4-4:

93
efficiency (Figure 4-4c) curves demonstrate the differences in the
stability of the carboxylate anions during the CAD process. At these
high collision gas pressures, even at a collision energy as low as 4.0 eV,
little or no parent ion is left for PGE2 and PGD2, yielding a fragmentation
efficiency of nearly 100% (Figure 4-4a). The inefficient fragmentation
(noted in Figure 4-3a) for PGF2a and DHKF2a is still observed. Note that,
at the higher collision gas pressure, scattering losses become
significant, especially at higher collision energies, yielding an optimum
collision energy below the maximum available 30 eV.
Collision Pressure Study of the fMO/TMS-PFBl' Carboxylate Anions
The fragmentation efficiencies (E ) for the carboxylate anions of
r
the four PGs as a function of collision gas pressure at the maximum
available collision energy (30 eV) are shown in Figure 4-5a. At low
collision gas pressures, PGE2 has a fragmentation efficiency 20 times
greater than that for PGF2a and DHKF2a. There are no dramatic differences
in the collection efficiency (Figure 4-5b) of the four PGs, although at
low collision gas pressures (<0.5 mTorr N2), DHKF2a has the highest Ec,
but at high collision gas pressures the lowest E . Since the mass of the
carboxylate anions are approximately the same, the increased loss of ions
is probably not due to scattering, but rather due to neutralization of the
anion by electron detachment. The overall CAD efficiencies (Figure 4-5c)
for the carboxylate anions of the four PGs demonstrate the differences in
their behavior; PGE2 has a maximum E^^ of 35%, which is 2 times greater
than that for PGD2, 5 times better than PGF2a and 20 times greater than
DHKF2a-

(a)
(b)
CAD efficiency of the [MO/TMS - PFB]‘ carboxylate anions
versus collision gas pressure at a collision energy of 30 eV
(a) Fragmentation
(b) Collection
(c) Overall CAD
Figure 4-5:

95
The efficiency curves for the four PGs demonstrate that differences
do exist between F-series PGs and PGE2 and PGD,. However, by examining
Figures 4-5a, 4-5b and 4-5c, similarities can be noted for certain PGs.
PGD2 has a fragmentation, collection and overall CAD efficiency behavior
essentially the same as PGE2. The behavior of DHKF2a closely resembles
that of PGF,_. The notable difference is that DHKF- has an E„ and E_Ar,
2® 2a F CAD
even lower than that of PGF2a> These results suggest that the presence of
two TMS groups on the cyclopentyl ring (positions C-9 and C-ll) of PGF2a
and DHKF2(J add to the stability of the [M-PFB]’ carboxylate anion during
CAD experiments.
Collision Pressure Study of the fM-PFBl' Carboxylate Anions
In order to test this hypothesis, the PFB ester derivatives (without
methoxime or trimethylsilyl groups) of the PGs were examined. A
conventional solids probe was used to introduce the derivatized PGs, since
with only PFB derivatization the PGs were no longer amenable to GC
separation. The CAD efficiency data from this study are shown in
Figure 4-6. The fragmentation behavior (Figure 4-6a) of the carboxylate
anions of the PFB-only derivatives is similar to that observed for the
fully derivatized PGs (Figure 4-5a). The PGF2a/PFB and DHKF2(J/PFB
derivatives fragment even less efficiently than the MO/PFB/TMS derivatives
at collision pressures > 2.0 mTorr N2. This noted difference in the
fragmentation efficiency of the PFB derivatives is reflected in the
extremely low overall CAD efficiency (Figure 4-6c) of PGF2a and DHKF2q.
The results from this study suggest that the presence or absence of
TMS and MO groups of the fully derivatized PGF2(J/PFB/TMS has little or no

(a)
(b)
Collision Gas Pressure (mTorr N2)
Figure 4-6: CAD efficiency of the [M - PFB]* carboxylate anions versus
collision gas pressure at a collision energy of 30 eV:
(a) Fragmentation
(b) Collection
(c) Overall CAD

97
(a)
(b)
Figure 4-7: Sketch of ball-and-stick models of: (a) PGF2a (b) PGE2
Colored balls represent oxygen atoms.

98
effect on the observed differences in the fragmentation behavior of PGE2
and PGF2a. It is hypothesized that the difference noted between the Ep of
PGE2 and PGF2a is due only to the presence of two hydroxyl (or -OTMS)
groups on the cyclopentyl ring of the F-series PGs. This is seen in
Figure 4-7 which contains sketches of ball-and-stick models of PGE2 and
PGF2a. Figure 4-7a shows one possible configuration of PGF2a demonstrating
how the carboxylate group can interact with the two hydroxyl (OH) groups
on C-9 and C-ll. In contrast, the PGE2 configuration (Figure 4-7b) shows
that, with only one hydroxyl (OH) group, the interaction with the
carboxylate group may not be as strong. Thus, the stability of the
carboxylate anions of the F-series PGs would be expected to be greater
during CAD than that of PGE2 and PGD2.
Collision Pressure Study of the fM-Hl' Carboxylate Anions
Underivatized PGs were examined to look at the fragmentation and CAD
efficiency of the [M-H]‘ carboxylate anions. These ions have nominally the
same structures as the [M-PFB]" carboxylate anions formed by dissociative
electron capture from the PFB-derivatized compounds. A conventional
solids-probe was used for this study, as in the experiments done on the
PFB-only derivatives ([M-PFB]'). The [M-H]' ions of PGE2 and PGD2 could
not be studied due to their low abundance (0.1% relative to [M-H20]') in
the EC-NCI mass spectrum; however, both PGF2q and DHKF2a produced an
[M-H]" ion intense enough to permit CAD analysis. The E E and E for
these underivatized [M-H]' ions are shown in Figure 4-8. The curve for E
G
(Figure 4-8b) of the [M-H]" ion for DHKF2q is similar to that found for
the [M-PFB]' ion in Figure 4-6b. But, for PGF2a,
at lower collision

100 -J
99
(a)
(b)
(c)
Collision Gas Pressure (mTorr N2)
Figure 4-8: CAD efficiency of the [M - H] carboxylate anions versus
collision gas pressure at a collision energy of 30 eV:
(a) Fragmentation
(b) Collection
(c) Overall CAD

100
pressures (< 1.0 mTorr N2), the Ec is 3 times higher than in the case of
Figure 4-6b. Looking at Figure 4-8a and 4-8c, the fragmentation and CAD
efficiencies are shown to be similar to those found in Figures 4-6a and
4-6c. The Ep and EqAD for PGF2a and DHKF2a are 2-4 times greater in the
case of the [M-H]' ion than for the [M-PFB]' ion. This slight difference
between the ions may be explained by the increased internal energy in the
[M-H]‘ ion produced under EC-NCI compared to that of the [M-PFB]" ion
produced by dissociation electron capture.
Conclusions
The differences in fragmentation behavior of PGE2 and PGF2a were
examined through the use of fragmentation, collection and overall CAD
efficiency studies. We have found that the CAD efficiency for the
[MO/TMS-PFB]’, [M-PFB]" and [M-H]‘ carboxylate anions is significantly
different for closely related PGs. Through the use of these curves, we
have shown that F-series PGs fragment less efficiently than PGE2 and PGD2.
A possible explanation has been proposed to explain these drastic
differences seen in the fragmentation behavior of structurally similar
carboxylate anions of PGs. It is believed that F-series PGs are more
stable during CAD due to the interaction of the carboxylate group with the
two hydroxyl (OH) groups in the cyclopentyl ring.

CHAPTER 5
EVALUATION OF SOLID-PHASE EXTRACTION GC/MS AND GC/MS/MS FOR
THE ANALYSIS OF ENDOGENOUS PROSTAGLANDIN E2 IN URINE
Introduction
The trace determination of prostaglandins (PGs) involves three basic
steps; sample preparation, sample introduction and detection. A logical
combination of these three steps can produce an analytical method with the
required selectivity, sensitivity and total analysis time for the
detection of endogenous levels of PGE2 in urine. As was pointed out in
earlier chapters, various sample preparation methods coupled with GC/MS
have been reported extensively in the literature (10,11). However, the
formation of the MO/PFB/TMS derivative followed by subsequent analysis
with GC/electron-capture negative chemical ionization (EC-NCI) MS
utilizing selected-ion monitoring (SIM) sometimes produces many
interfering peaks which prevent reliable quantitation (6,17,48). These
interferences, often referred to as chemical noise (91,111), can stand in
the way of achieving required detection limits, or require more extensive
sample clean-up.
Two methods can be used to reduce this chemical noise. Knapp and
Vrbanac have taken the approach of immunoaffinity (IA) column purification
with GC/EC-NCI/MS to give a very selective analysis (19,20). This method
utilizes a selective sample clean-up and purification in a relatively
101

102
rapid two-step procedure to reduce the chemical noise. First, an
octadecyl silyl (C18) solid-phase extraction column is employed for clean¬
up to conveniently concentrate a large volume of urine to a manageable
volume and to provide a clear solution free of precipitates for
application to the IA column (the second step in the clean-up). Further
reduction of the chemical noise can be accomplished by GC in conjunction
with tandem mass spectrometry (MS/MS) utilizing the selected-reaction
monitoring (SRM) mode (91,111). Recently, GC/MS/MS analysis of selected
PGs in biological matrices has been reported using various ionization and
derivatization methods (74,76,77). The combination of both these chemical
noise reduction methods has been exploited by Knapp and Vrbanac (78) in
the analysis of PGs by GC/electron-impact (EI)/MS/MS using SRM. However,
El lacks the sensitivity needed in many cases for the low level
determination of PG's. Investigation of all three basic steps (sample
preparation, introduction and analysis) which comprise the analysis is
necessary to determine the most sensitive and selective method for the
determination of PGs in a biological matrix.
It is often observed that trade-offs in selectivity, sensitivity
and total analysis time exist in the three basic steps of any trace
analytical method. Previous work in our research group has shown the
advantages and disadvantages of short 3 m and conventional 30 m GC
capillary columns for GC/MS and GC/MS/MS (96). However, no systematic
study has been performed for the entire analytical procedure. In this
study, different combinations of sample preparation, GC column lengths and
mass spectrometry detection schemes have been investigated. The trade¬
offs between selectivity, sensitivity and time of analysis throughout the

103
analytical methodology have been evaluated in this chapter. In addition,
quantitation of endogenous PGE2 in urine has been performed with several
different methods.
Experimental
Prostaglandins and Reagents
All solvents were reagent or HPLC grade. Prostaglandin E2 (PGE2) was
purchased from Sigma Chemical Co. (St. Louis, MO). The solid-phase
extraction columns were purchased from Analytichem International, Inc.
(Harbor City, CA). 3,3' ,4,4'-(2H^) PGE2 and the antibody affinity sorbent
were gifts from Drs. J.J. Vrbanac and D.R. Knapp of the Department of
Pharmacology, Medical University of South Carolina (Charleston, SC). The
derivatization reagents and solvents pyridine, O-methylhydroxylamine
hydrochloride, acetonitrile, and N,N-diisopropylethyl amine for GC/MS
percent recovery studies were all purchased from Sigma Chemical Co..
Pentafluorobenzyl-bromide (PFBBr) and bis(trimethylsilyl)trifluoro-
acetamide (BSTFA) were purchased from Pierce Chemical Co. (Rockford, IL).
The urine was collected on two separate days from the author. All
glassware was silanized with a solution of 5% dimethyldichlorosilane in
toluene. These two chemicals were both purchased from Sigma Chemical Co..
Helium used as GC carrier gas, methane (>99%) used as the chemical
ionization reagent gas, and argon used as CAD collision gas were from
Matheson Gas Products, Inc. (Orlando, FL).

200 mL Urine
Spiked with 300 ng of 2H^-PGE2
I
Acidified with Formic Acid to pH 3.5
I
Extracted Four 20 mL Urine Samples with Separate C18 Columns
I
Evaporated Eluents from C18 Columns with N2
Two Samples Two Samples
Derivatized Diluted with 5 mL of PBS (pH 7.4)
Extracted with Separate IA Columns
I
Evaporated Eluents from IA Columns with N2
I
Derivatized
Figure 5-1: Sample preparation scheme for urine.
104

105
Sample Preparation
Two different urine specimens from different days were prepared for
the quantitation study. Samples 1 and 2 were from the first urine
specimen and sample 3 was from the second urine specimen. The first two
urine samples were prepared according to the scheme in Figure 5-1. For
sample 3 from the second urine specimen, only two C18 columns were
utilized, and a different immunoaffinity (IA) column than that for samples
1 and 2 was used.
A 200 mL urine sample was acidified with formic acid to pH 3.5 after
addition of 300 (iL of a 1 ng//iL solution of 2H^-PGE2. Extraction then
followed with four 20 mL samples of the spiked urine introduced onto four
separate C18 columns. Preparation and extraction of the PGE2 utilizing
the C18 columns was accomplished using the following method:
(1) Conditioned the column with 10 mL of HPLC water
and 10 mL of methanol.
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Washed the column with 10 mL of HPLC water
and 10 mL petroleum ether.
(4) Eluted PGE2 with 10 mL of ethyl acetate.
After the C18 extraction all four samples were evaporated with N2.
Two of the samples were then further purified with separate IA columns.
These residues were diluted with approximately 5 mL of a phosphate buffer
solution (pH 7.4). This solution was then applied to the IA column and
extracted as follows:
(1) Conditioned the column with 20 mL of PBS (pH 7.4).

106
(2) Passed solution of PGE2 (acidified to pH 3.5 with formic acid)
through the column.
(3) Allowed the sample to settle into the sorbent bed for 15 min at
room temperature.
(4) Washed the column with 25 mL of PBS (pH 7.4) and 10 mL HPLC
water. Removed all remaining water in the column.
(5) Eluted PGE2 with 15 mL of 95% acetonitrile solution (v:v).
(6) Washed column with an additional 10 mL of 95% acetonitrile to
assure removal of all the PGE2.
(7) Immediately rinsed the column with 10 mL of HPLC water and
15 mL of PBS (pH 7.4).
The eluents were then evaporated with N2>
Derivatization
The evaporated samples were then derivatized according to the
procedure in Chapter 2. The amount of reagents used to derivatize the
urine samples was tripled for the methoximation and PFB esterification
steps compared to the amount used to derivatize standards to assure
efficient derivatization of the analyte in the presence of urine matrix
components which could also be derivatized.. The trimethylsilyl
derivative then was formed by adding 60 /¿L of BSTFA to the esterfied urine
samples and 50 /¿L to the standards for the calibration curves and allowing
the solutions to stand overnight at room temperature. One-microliter
injections containing 500 pg of 2H^-PGE2 were made of each standard and
sample.

107
Instrumental Conditions
A Finnigan MAT triple stage quadrupole (TSQ45) gas chromatograph/
tandem mass spectrometer was used for these studies. Gas chromatography
was carried out on various lengths of J&W Scientific (Folsom, CA) DB-1
(30, 10, and 3 meter long, 0.25 mm i.d., 0.25 /¿m film thickness) capillary
columns. The different lengths of GC columns were used in the splitless
mode with helium carrier gas at the following conditions: 30 m GC column
was operated at a flow rate of 41 cm/s (inlet pressure 18-20 psi) with an
initial temperature of 100°C held for 30 s, increased at 25°C/min to
250°C, then increased again at 5°C/min to 310°C; the 10 m GC column was
operated at a flow rate of 50 cm/s (inlet pressure 10-12 psi) with the
same temperature program except for an initial temperature of 200°C; the
3 m GC column was operated at an inlet pressure of 4-6 psi, with an
initial temperature of 200°C held for 30 s, then increased at 20°C/min to
260°C. The injector temperature was 300°C for all three GC column
lengths.
Mass spectrometry conditions were: interface and transfer line
temperature 300°C, ionizer temperature 190°C, electron energy 100 eV and
emission current 0.3 mA. Electron-capture negative chemical ionization
(EC-NCI) was carried out with methane at an ionizer pressure of 0.50 Torr.
Argon was employed as the collision gas at a pressure of 1.0 mTorr and a
collision energy of 25 eV was utilized for the selected-reaction
monitoring studies of PGE2> The GC/MS analysis utilizing SIM used an
electron multiplier (EM) setting of 1500 V and a preamp gain of 108 V/A.
GC/MS/MS experiments with SRM employed an EM setting of 2000 V and a
preamp gain identical to the SIM analysis.

Table 5-1: Analytical Schemes Used for the Determination of
Endogenous Levels of PGE2 in Urine
Method
Sample Preparation GC
Column Length
Detection Method
Aa
C18 Column
30
meter
SIMb
Ba
C18 Column
30
meter
SRMC
Ca
Cl8 & IAd Columns
30
meter
SIM
Da
C18 & IA Columns
30
meter
SRM
E
C18 Column
10
meter
SIM
F
C18 Column
10
meter
SRM
Ga
C18 & IA Columns
10
meter
SIM
Ha
C18 & IA Columns
10
meter
SRM
I
C18 Column
3
meter
SRM
J
C18 & IA Columns
3
meter
SIM
Ka
C18 & IA Columns
3
meter
SRM
Methods e
Selected-
Selected-
mployed for quantitation study of
ion monitoring
reaction monitoring
the £
;ndogenous
level of PGE2 in urine.
d Immunoaffininty purification
108

109
Eleven different analytical schemes were investigated for the study
of PGE2 in urine. These methods are listed in Table 5-1 with the sample
preparation, GC column length and the mass spectrometric analysis method
employed. Seven of the methods examined were employed for the
quantitation of the endogenous levels of PGE2 in urine. The schemes
selected for quantitation are noted in the table.
Standard calibration curves for the seven quantitation methods were
prepared by analyzing solutions containing a constant amount of 2H^-PGE2
(25 ng) and increasing amounts of PGE2. Table 5-2 lists the amounts of
2
H^-PGE2 and standard PGE2 added to each vial and the final concentrations
after dilution with 50 jíL of silylating reagent. An example of a
calibration curve that was obtained with a 10 m GC column utilizing SIM,
is shown in Figure 5-2. Six different calibration curves were obtained
for the three lengths of GC columns employed utilizing either SIM or SRM.
The calibration curve shown demonstrates good linearity with a slope of
1.06, similar to the expected value of 1.00 for this calibration curve.
The five other calibration curves obtained exhibit similar linearity with
slopes similar to that found for the calibration curve shown in Figure
5-2. Extrapolation of the x-intercept from the best fit line yields the
amount of PGE2 in 500 pg of the 2H^-PGE2 internal standard. The average
intercept obtained from the six calibration curves corresponded to
approximately 6 pg of PGE2 which is 1.1% of the 500 pg of 2H4-PGE2.
The quantitation of the endogenous levels of PGE2 in the extracted
urine sample was accomplished by selected-reaction monitoring (SRM) and
selected-ion monitoring (SIM). Two gas chromatographic peaks appear for
derivatized PGE2 in the chromatograms in this chapter. These correspond

Table 5-2: Calibration Curve Dilutions for the Quantitation of PGE2
£h4-pge2
Added (ng)
pge2
Added (ng)
Volume of
Dilution (/¿L)
Concentration
of \-PGE2 (pg//xL)
Concentration
of PGE2 (pg/^L)
25
0.0
50
500.0
0.0
25
1.0
50
500.0
20.0
25
2.5
50
500.0
50.0
25
5.0
50
500.0
100.0
25
10.0
50
500.0
200.0
25
20.0
50
500.0
400.0
25
25.0
50
500.0
500.0
I
110

CM
Figure 5-2: Calibration curve utilizing a 10 m GC column with SIM.
Ill

112
to the syn- and anti-methoxime isomers of the derivatized PGE2 (75). The
major anti-methoxime isomer of PGE2 (the second peak) was used for
quantitation in these studies. The [M-PFB]’ ions of PGE2 (524’) and 2H4-
PGE2 (528’), were monitored for selected-ion monitoring studies. Optimum
conditions from Chapter 3 were used for the analysis of PGE2 and 2H^-PGE2.
The selected-reactions monitored for the analysis of endogenous levels of
PGE2 in urine were 524’ -*■ 268’ for PGE2 and 528* -*■ 272' for the internal
standard H4-PGE2. A baseline was chosen visually on the GC trace and the
peak areas for PGE2 and 2H4-PGE2 calculated by the INCOS computer system
for the standards and the extracted urine samples. The area of PGE2
divided by the area of 2H4-PGE2 in the standards gives a ratio that is used
in the calibration curve. The amount of PGE2 in each urine sample was
calculated by comparing the ratio of these ions to that of the calibration
curve. A typical SIM chromatogram (30 m GC) of a urine extract (cleaned-
up by C18 and IA) is shown in Figure 5-3a; the results with only C18
clean-up are shown in Figure 5-3b. The amount of PGE2 in the sample is
calculated from the ratio of the peak area (shaded in black) in the top
trace to that of 2H4-PGE2 in the bottom trace. The 2H4-PGE2 is used both
as an internal standard for quantitation and as a retention time marker
for identification of the endogenous PGE2 peak which may not be fully
resolved, as in Figure 5-3b. Note that the derivatized 2H4-PGE2 elutes
approximately 5 to 6 seconds before derivatized PGE2. The amount of PGE2
found from the calibration curve was then multiplied by the dilution
factor of 60. This indicates the amount of endogenous PGE2 in the 20 mL
urine sample. Dividing this amount by 20 results in the amount of
endogenous PGE2 per mL of urine.

% Relative Intensity % Relative Intensity
113
100%-,
m4-pge2
Time u:49
i 1 r
—i 1 * 1 1 1 »
15:11 15:33 15:55
Figure 5-3: Typical SIM chromatogram of a urine extract showing both the
endogenous PGE2 (524') and 2H^-PGE2 (528*) with:
(a) C18 and IA purification (b) C18 extraction only
The integrated peak areas are shaded in black.

114
Results from the Quantitation Study of PGE^ in Urine
Quantitation Study
The seven analytical schemes employed for quantitation of PGE2 in
urine and the results of the study are shown in Table 5-3. The three
samples discussed earlier were analyzed by each method on the same day.
Three injections of each sample were made and the average and %RSD
calculated. In addition, the average of samples 1 and 2 (from the same
urine specimen) is listed, as well as the average of all three samples and
the %RSD.
This table provides a great deal of information about the methods
used for the quantitation of PGE2 in urine. First, the quantities found
for the endogenous PGE2 in urine agree well with normal values reported in
the literature (71,77,78). Reports have shown that the concentration of
PGE2 in urine of various subjects ranges from 100 to 400 pg/mL. Quantities
detected in this study with the seven different analytical schemes all are
within this range. The average value of the seven different methods was
315.2 pg with a %RSD of 3.7%. The average values of the different methods
employed varied only slightly, ranging from 302.4 pg/mL to 330.8 pg/mL.
This indicates that all the selected methods may be employed for the
analysis of PGE2 in urine at these levels.
The variation in the seven methods is observed in the %RSD found
from averaging the results from the seven different methods employed for
the three urine samples. These average values vary only slightly, with
a %RSD ranging from 3.5% for urine sample 2 to a high of 5.3% for urine
sample 3. In addition, this table provides information about the various

Table 5-3: Quantitation Study of Endogenous PGE2 in Urine
Utilizing Various Analytical Schemes
Quantity of PGE2 Average
Method8
Sample #
GC
(pg/mL)
Injection //
of
3 Inj.
%RSDb
Average
of 1 & 2
Average
of All 3
%RSD
of all 3
1
1
363.2
2
348.3
3
360.3
357.3
2.2
337.0
A
2
321.8
310.5
317.6
316.6
1.8
327.8
7.9
3
312.8
307.2
308.8
309.6
0.9
1
363.0
372.8
352.1
362.6
2.9
340.7
B
2
326.0
320.5
309.6
318.7
2.6
319.9
13.1
3
279.6
270.1
285.2
278.3
2.7
1
344.8
332.7
317.5
331.7
4.1
322.3
C
2
302.5
321.8
314.9
312.9
3.1
302.4
11.8
3
262.0
267.7
259.6
262.7
1.5
1
348.5
371.5
313.7
344.6
8.4
329.2
D
2
323.0
304.3
313.7
313.7
3.0
316.3
8.6
3
284.1
292.3
295.7
290.7
2.1
a Refer to Table 5-1 for explanation of analytical schemes.
b % Relative Standard Deviation
115

Table 5-3: --continued
Method3
Sample #
Quantity of PGE2
(pg/mL)
GC Injection #
Average
of
3 Inj .
%RSDb
Average
of 1 & 2
Average
of All 3
%RSD
of all 3
1
1
379.1
2
364.7
3
344.5
362.8
4.8
348.6
G
2
345.1
333.8
324.3
334.4
3.1
330.8
10.3
3
299.6
297.4
288.6
295.2
2.0
1
338.7
314.8
342.6
332.0
4.5
314.3
H
2
287.4
322.3
280.0
296.6
7.6
303.1
8.7
3
270.9
266.5
304.5
280.6
7.4
1
376.5
295.2
347.7
339.8
12.1
326.4
K
2
273.7
267.3
364.2
312.9
18.0
306.0
10.4
3 285.3
264.4
279.5
276.4 3.9
Urine Sample #
Average
from 7
Methods (oe/mL)
%RSD
1
347.3
3.9
2
315.1
3.5
3
284.8
5.3
a Refer to Table 5-1 for explanation of analytical schemes.
b % Relative Standard Deviation
116

117
sample preparations and mass spectrometric analysis methods employed.
For example, comparing the concentrations found by method G (C18 +
IA + 10 m GC + SIM) and method B (C18 + IA + 30 m + SRM) a difference is
noted between the SIM and SRM analysis methods. The method utilizing SIM
yielded concentrations for endogenous PGE2 approximately 10% higher than
for the method utilizing SRM. This may be due to the interferences that
are present in the SIM chromatogram overlapping with the PGE2 peak,
creating difficulty in the accurate determination of the actual PGE2 peak
area. The use of SRM eliminates many of the chemical interferences, thus
reducing the problem of inaccurate peak area determination.
Another important difference observed in the table occurs between
methods A (C18 + 30 m GC + SIM) and C (C18 + IA + 30 m GC + SIM) for all
three urine samples. The concentrations of endogenous PGE2 determined by
method A are consistently 10% higher than those found by method C. This
may be explained by the removal of urine matrix components with the
addition of IA in method C, permitting more accurate calculation of the
PGE2 peak area. Note that the additional selectivity of SRM (methods B and
D) reduces the need for IA clean-up, therefore reducing the difference
between the results obtained from methods B and D.
Limit of Detection CLOD) and Sensitivity Studies
Table 5-4 gives the approximate LOD found for 2H^-PGE2 in urine and
the sensitivity values (slopes of the calibration curves in counts/pg) for
PGE2 standards. The LOD study was accomplished by diluting the urine
extracts used above containing 500 pg//LL of 2H4-PGE2 to 100, 50, 25 and 13
pg//iL and monitoring 2H4-PGE2 peak area. The LODs reported in Table

118
Table 5-4a: Limit of Detection Study of 2H4-PGE2 in Urine
for Various Analytical Schemes
Method3
Limit of Detection13 (pg/mL)
A
B
C
D
G
H
K
20
20
20
35
20
75
25
Table 5-4b: Sensitivity Study of PGE2 Standards Utilizing
the Slopes of the Calibration Curves
Slope or Sensitivitv
(counts/ne)
GC Column Length
SIM
SRM
30 m
0.032c
0.0089d
10 m
0.145c
0.031d
3 m
0.805e
0.028e
3 Refer to Table 5-1 for explanation of analytical scheme.
b Approximation from the dilution of the extracted urine
samples to produce a peak area 3 times that of a
diluted urine blank.
c Electron multiplier setting at 1500 V.
d Electron multiplier setting at 2000 V.
e Electron multiplier setting at 1700 V.

% Relative Intensity
119
100% 1
956,417
100%
100%-t
Time
165,120
89,216
23,232
14:27
15:11
Figure 5-4: SRM chromatograms of 2H4-PGE2 in urine extracted with a CIS
column and separated with a 30 m GC column and diluted to
yield: (a) 25 pg 2H,-PGE2 (b) 13 pg \-PGE-,
(c) Urine blank (no 2H4-PGE2)

120
5-4a are the concentrations of H4-PGE2 in urine which produce a peak area
three times the area calculated from a blank urine sample containing no
2H^-PGE2 diluted with the same procedure. An example of a LOD calculation
(for method B) is shown in Figure 5-4, with the peak areas used for the
calculation marked off on the three chromatograms. Figure 5-4a shows the
SRM chromatogram of 25 pg injected on column that produces a peak area
approximately 5 times the peak area of the blank. Figure 5-4b shows the
SRM chromatogram of 13 pg of 2H^-PGE2 which produces a peak area
approximately twice that of the urine blank shown in Figure 5-4c.
Examination of the LODs in Table 5-4a show interesting trends. First,
comparing methods C and D or G and H, it is apparent that utilization of
SRM in a case where the clean-up is already highly selective (i.e., IA)
only serves to worsen the LOD. Comparing methods H and K, however,
indicates that the best limits of detection can be regained with SRM by
simple reducing the amount of GC separation that is employed. These
results simply confirm the fact that the LOD in a real sample is a
function of both sensitivity and selectivity. Whether adding another step
to enhance the selectivity (e.g., SRM) with the concomitant loss in
sensitivity (e.g., the less-than unity CAD efficiency and transmission
efficiency through a second mass analyzer) will improve or degrade the LOD
is a function of the interferences which remain in the sample.
Differences in the LOD for various sample preparations, GC column lengths
and mass spectrometric detection modes are discussed in detail throughout
this chapter.
The slopes of the six calibration curves for PGE2 standard utilizing
SIM and SRM with 3 different column lengths are listed in Table 5-4b.

121
Note that not all of these sensitivities can be directly compared due to
the various electron multiplier voltages employed. Comparison of the
slopes for SRM and SIM using a 3 m GC column yields a sensitivity ratio
of 0.035 or 3.5%. This corresponds to approximately a 30 times decrease
in sensitivity for SRM analysis compared to SIM. Differences in the
sensitivity for the various GC column lengths will be discussed in detail
in a later section of this chapter.
Summary of Results
The concentrations of endogenous PGE2 in urine found utilizing the
seven different analytical schemes agrees favorably with those in the
literature. All the results are similar, with an average of 315.2 pg/mL
and a %RSD of 3.7%. The LOD varies from a low of 20 pg for four of the
methods, including C18 and IA purification coupled to a 10 m GC column
with SIM, to a high of 75 pg for C18 and IA purification coupled to a 10
m GC column with SRM. These data indicate that any of these methods could
be used for the analysis of normal levels of urinary PGE2.
Trade-offs in the Steps of the Analytical Procedure
The sample preparation, sample introduction and mass spectrometric
detection method all affect the overall selectivity, sensitivity and the
time of analysis for the determination of PGE2 in urine. The eleven
different analytical schemes listed in Table 5-1 were used to evaluate the
trade-offs which result from various combinations of the three basic steps
of the analytical procedure. This systematic study was then used to
determine the optimum analytical scheme for the analysis of PGE2 in urine.

122
Sample Preparation
The differences in sample preparation between a simple C18
extraction only and a C18 extraction with IA purification is shown in
Figure 5-5. This analysis employed a 30 m GC column with SIM. These
chromatograms demonstrate the additional selectivity enhancement of
employing IA purification with a simple C18 extraction. In Figure 5-5a,
a large number of interfering components from the urine matrix remain at
concentrations much higher than PGE2, which are not present in the case of
Figure 5-5b utilizing C18 and IA. This can be observed by examining the
absolute counts obtained for the chromatogram in Figure 5-5a that are
approximately 13 times higher than that observed for Figure 5-5b for the
major urine matrix components still present. In addition, the endogenous
PGE2 in not completely separated from the interferences present in the
urine Figure 5-5a. Figure 5-5b demonstrates the effectiveness of IA
purification to separate urine matrix components from endogenous PGE2. The
advantage of utilizing IA purification is even greater when employing
shorter lengths of GC columns. Figure 5-6 shows the differences of these
same sample preparations using a 10 m GC column with SIM. Figure 5-6a is
the chromatogram employing only C18 extraction. This indicates the many
interferences which are still present from the urine and are not
distinguishable from the endogenous PGE2. In addition, the concentrations
of the interferences in Figure 5-6a that remain produce an absolute count
value 5 times higher than that observed in Figure 5-6b. However, even
with a 10 m GC column using SIM, PGE2 can be separated from components in
the urine matrix by the addition of IA purification (Figure 5-6b).

% Relative Intensity
Figure 5*5:
30 m GC column SIM chromatograms of endogenous PGEg in urine
extracted with: (a) C18 column (b) C18 & IA columns
123

% Relative Intensity
100%~\
289,792
100% -i
Time
(a)
:44
2:12
3:40
59,392
5:10
Figure 5-6:
10 m GC column SIM chromatograms of endogenous PGE2 in urine
extracted with: (a) C18 column (b) C18 & IA columns
124

% Relative Intensity
100% n
1,960
100% n
(b)
PGE-
Time
20,096
m*UJbM
:56
2:50
4:42
Figure 5-7: 10 m GC column SRM chromatograms of endogenous PGE2 in urine
extracted with: (a) C18 column (b) C18 & IA columns
125

126
If a different mass spectrometric technique is employed, the
differences between the two sample preparations remain prominent. In
Figure 5-7, separation on a 10 m GC column is used with SRM. The
chromatogram utilizing only C18 extraction (Figure 5-7a) shows a reduction
in the chemical noise due to the use of MS/MS, but with the lack of
separation of the 10 m GC column even SRM cannot give adequate detection
of endogenous levels of PGE2 in urine. Figure 5-7b demonstrates that with
C18 and IA sample preparation and the additional reduction in chemical
noise by utilization of SRM PGE2 in urine can be easily detected.
The sensitivity and selectivity of the different sample preparations
are reflected in the limits of detection (LOD) in Table 5-4a. The results
obtained from this study show no difference in the LOD for only the C18
extraction and the C18 and IA purification when utilizing a 30 m GC column
with SIM. The LOD found for C18 and IA purification using a 30 m with SRM
(35 pg) was slightly worse than for only C18 extraction with the same
conditions. In theory, if the C18 extraction alone with 30 m GC/MS/MS
provided adequate separation of urine matrix components from the
endogenous PGE2, then addition of another (unneeded) extraction step (IA)
only serves to reduce the sensitivity due to less than 100% recovery of
the PGE2 in urine.
Another important factor to consider is the time to prepare the
sample before the derivatization. The C18 extraction is simple and rapid,
only requiring approximately 10 to 15 minutes for a 20 mL urine sample to
be prepared. The additional IA purification requires approximately 30
minutes per sample, thus an entire sample preparation time of 40 to 45
minutes. However, the IA purification is still more rapid than

Total Time (min) % Required Selectivity
127
(a)
Figure 5-8: Summary of the relative differences in sample preparation
methods for: (a) Selectivity (b) Total time

128
conventional chromatographic purification methods. Furthermore, the
additional time for the IA step is a worthwhile trade-off for the
considerable gain in selectivity that is achieved by this method.
The differences in relative selectivity and time of analysis are
summarized in Figure 5-8. The top line on Figure 5-8a represents the
selectivity required to detect endogenous levels of PGE2 in urine
(approximately 100 pg/mL). All the methods employed for the quantitation
study possessed adequate limits of detection to detect endogenous levels
of PGE2 in urine. Figure 5-8b shows the time required for a C18 extraction
compared to C18 and IA purification. The optimum is obviously the one
which is the most rapid, possessing adequate selectivity for reliable
analysis.
Sample Introduction
The various lengths of GC columns employed demonstrate considerable
differences in selectivity. Figure 5-9 shows the use of C18 and IA sample
preparation coupled to 30 m, 10 m and 3 m GC columns with SIM.
Differences in the separation of urine matrix components from endogenous
PGE2 is evident in the chromatograms. The additional separation ability
of a 30 m GC column (Figure 5-9a) increases the selectivity of the method,
albeit at a cost of longer analysis time. Ultimately, a 30 m GC column
possess the greatest selectivity for this analysis. However, as was
discussed previously, the utilization of C18 and IA for sample preparation
produces a clean enough sample that selectivity (separation) of a 10 m GC
column is adequate for separation of urine matrix components from PGE2.
Figure 5-9c shows that with this method of analysis, however,

% Relative Intensity
129
66,176
Figure 5-9: SIM chromatograms of endogenous PGE2 in urine extracted with
C18 and IA columns and separated with:
(a) 30 m GC (b) 10 m GC (c) 3 m GC

130
a 3 m GC column does not possess adequate selectivity for the analysis of
PGE2 in urine.
The sensitivity and selectivity for the different lengths of columns
with different analysis methods are reflected in the detection limits
presented in Table 5-4a. In theory, if the same temperature programs were
employed for the three lengths of GC columns, a 3 m column should produce
shorter retention times and possibly narrower, taller peaks, therefore
producing higher sensitivity. However, the selectivity will be lower, and
thus the LOD may increase or decrease, depending upon the complexity of
the sample. Table 5-4a shows that the LOD for different lengths of GC
columns are similar. However, dramatic differences are observed in the
slopes of the calibration curves for the different lengths of GC columns
in Table 5-4b. The ratio of the slopes of the calibration curves for the
30 m GC column divided by the 10 m GC column for standard PGE2 utilizing
SIM is 0.22 and for SRM is 0.29. This indicates that analysis with the
30 m GC column is approximately 26% as sensitive as that with the 10 m GC
column. In addition, peak areas for the 500 pg of 2H^-PGE2 internal
standard utilizing a 10 m GC column are approximately four times larger
than for a 30 m GC column. Therefore, these results suggest that greater
than 75% of the derivatized PGE2 is lost somewhere along the 30 m GC
column. This may occur due to adsorption on the GC column or
decomposition of the derivatized PGE2 on the column. Similar observations
were made in an earlier report with a 30 m GC column (112). The
researchers reported that after repeated analyses of derviatized PG
samples on a 30 m GC column, substantial loss of particular PGs (e.g.,

131
PGE2, but not PGF2a) occured. Consequently, PGE2 would have less time and
length of column to interact with the stationary phase when shorter GC
column lengths (e.g., 3 m or 10 m) are utilized.
The chromatograms in Figure 5-9 show the obvious time differential
between the three lengths of GC column. Analysis of PGE2 with a 30 m GC
column requires -15 min., with a 10 m GC column -5 min and with a 3 m GC
column -3.5 min. Since these chromatograms utilize the same sample
preparation method, the only difference in the time of analysis is based
on the length of the GC column. Furthermore, the 30 m GC column requires
higher, elevated temperatures for elution of PGE2 in urine (~305°C), than
a 10 m (~260°C) or 3 m (~240°C) GC column. This elevated temperature
corresponds to an additional time increase required to cool the oven to
the initial starting temperature of 100°C. If we compare the total GC
analysis time, an analysis utilizing a 30 m GC column (Figure 5-9a) would
require -25 min before injecting the next sample compared to -12 min for
a 10 m GC column. This corresponds to the analysis of 20 samples a day
with a 30 m GC column with these conditions compared to 40 samples a day
with a 10 m GC column. Thus, for a slight loss in selectivity with a 10
m GC column, twice the number of samples can be quantitated in a day for
PGE2 in urine.
A summary similar to the one presented earlier for sample
preparation (Figure 5-8) is shown in Figure 5-10 for sample introduction.
This figure indicates graphically the relative trade-offs between the
selectivity and time of analysis for the three different GC columns.
Figure 5-10a shows that a 30 m column possesses the greatest selectivity;
however, Figure 5-10b displays the fact that this same length of GC column

132
(a)
GC Column Length
(b)
'£
.£
I—
o
o
GC Column Length
Figure 5-10: Summary of the relative differences in GC column lengths
for: (a) Selectivity (b) Total time between GC injections

133
has a total analysis time twice as long as a 10 m GC column. Finally,
the three GC columns do not possess enough selectivity without sample
preparation and a detection scheme to reach the required selectivity line
on the figure.
Mass Spectrometric Analysis: SIM vs SRM
The advantages of using SRM for mixture analysis have been pointed
out earlier in Chapter 1. Utilization of SRM reduces the chemical noise
inherent in analysis of complex biological matrices (94,95). Figure 5-11
compares the SIM chromatogram to the SRM chromatogram of endogenous PGE2
in urine employing C18 extraction with a 30 m GC column. The reduction
of the chemical interference signal by SRM (Figure 5-lib) is apparent.
This allows for more reliable quantitation of PGE2 in urine. In addition,
with SRM, in this case, the use of 2H^-PGE2 is not required as a "marker
compound" to mark the retention time of the trace level of endogenous PGEg.
The additional selectivity of SRM is even more apparent in Figure 5-12.
This analysis method employs C18 and IA for sample preparation with a 3
m GC column. In Figure 5-12a with SIM, the endogenous level of PGE2 is
only slightly visible above the chemical interferents present. However,
Figure 5-12b demonstrates the advantage of SRM for this analysis. The
chemical interferences are completely eliminated, allowing for accurate,
reliable quantitation of endogenous levels of PGE2 in urine.
The sensitivity of SIM compared to SRM was discussed earlier in
Chapter 3. The sensitivity for SIM should be greater than SRM when the
analyte signal is efficiently separated from the chemical interference
signal present in a chromatogram. In Table 5-4b, the slope of the

% Relative Intensity
100%
100%
Time
Figure 5-11: 30 m GC column chromatograms of endogenous PGE2 in urine extracted
with a C18 column utilizing: (a) SIM (b) SRM
134

% Relative Intensity
100%n
61,184
100%
Time
Figure 5-12: 3 m GC column chromatograms of endogenous PGE2 in urine extracted
with C18 and IA columns utilizing: (a) SIM (b) SRM
135

136
calibration curve for SIM and SRM utilizing a 3 m GC column may be
compared to determine the relative difference in sensitivity between SIM
and SRM. The ratio of the SRM slope to that of the SIM slope is 0.035.
This indicates that the sensitivity of SIM is 30 times greater than SRM
for derivatized standard PGE2. The lower sensitivity of SRM is expected
due to the inefficiency of the CAD conversion of the parent ion to the
daughter ion of interest. This was investigated and discussed in detail
in Chapter 3 for PGE2, resulting in an overall CAD efficiency of
approximately 12% for the selected-reaction chosen. In addition, for SRM
the second mass analyzer (Q3) is used as a mass filter rather than an RF
only quadrupole, thus, a lower transmission efficiency is expected
(typically 10%). However, the selectivity gained by the parent-daughter
reaction reduces the chemical noise to a greater extent than the
analytical signal in a sample matrix, often compensating for the lost
sensitivity.
The differences in the LOD for different sample preparations and GC
column lengths utilizing SIM and SRM can be found in Table 5-4a. The
lowest limits of detection (20 pg) found were with methods A, B, C, and
G, which employed C18 and IA sample preparation with a 10 m GC column
using SIM. The LODs for all the analytical schemes vary by only 15 pg,
except for method H which employed C18 and IA extraction with a 10 m GC
column using SRM.
The time for analysis by SIM or SRM is essentially the same;
however, as was pointed out earlier in Chapter 3, optimization of the
selected reactions to be employed in the analysis is essential. This
optimization requires an additional amount of time in the beginning of an

Required Selectivity
137
Mass Spectrometric Detection Methods
Figure 5-13: Summary of the relative differences in selectivity
for SIM and SRM.

138
analysis, but once accomplished can give an enhancement in selectivity
which is worthwhile. More importantly, the use of SRM rather than SIM may
provide for shorter analysis times due to possible reduction of extensive
sample preparation and chromatographic separation.
Figure 5-13 graphically summarizes the relative selectivity
differences observed between SIM and SRM for analysis of PGE2 in urine.
This graph is similar to the previous figures; however, the time of
analysis for SRM and SIM (essentially the same) is not shown. Therefore,
SRM possesses greater selectivity than SIM and requires the same amount
of time.
Conclusions
The basic steps in the analytical scheme for the determination of
endogenous PGE2 in urine have been systematically investigated and
evaluated for their selectivity, sensitivity and time of analysis. The
selectivity of the techniques investigated have been summarized throughout
the chapter. Comparing the relative selectivity of the sample
preparation, GC column lengths, and mass spectrometric (MS) detection
methods (Figure 5-14a) the various parameters individually lack the
necessary selectivity to analyze PGE2 in urine. However, by combining
these methods into a logical analytical scheme the selectivity required
for the analysis may be achieved. Figure 5-14b shows the selectivity of
various combinations of sample preparations, GC column lengths and MS
detection methods. In method C, the use of C18 and IA purification with
a 30 m GC column utilizing SIM produces the selectivity required to
analyze endogenous levels of PGE2. Method K uses the same sample

100
139
(a)
%
^^3
Sara Preo.
GC Ccirms
Detection
(b)
>,
>
«
Tj
(/I
cc
140
Andyticd Schemes
Cl 8 & IA
3Cm GC
3m GC
SM
t: •1 M 11 i-3
SRM
Andyticd Schemes
Figure 5-14: Summary of the relative differences in:
(a) Selectivity for various parameters
(b) Selectivity for various analytical schemes
(c) Total time of analysis for various analytical schemes

140
preparation as A, but utilizes a shorter 3 m GC column with SRM. This
combination of parameters also achieves the necessary selectivity.
However in method J, using the same sample preparation and GC column, but
with SIM rather than SRM, the needed selectivity is not achieved.
Therefore, many combinations of parameters may be explored to achieve the
required selectivity for a particular analysis.
Sensitivity must also be considered in an analytical scheme. In
the case of the analysis of PGE2 in urine, all of the methods utilizing SIM
have greater sensitivity than the methods employing SRM. In addition, the
results in this chapter demonstrate the advantage of utilizing shorter GC
column lengths to obtain greater sensitivity. However, if urine matrix
components interfere with the determination of endogenous levels of PGE2,
then both sensitivity and selectivity are critical. Therefore, once
combinations of parameters are found which achieve the needed selectivity
for an analysis, the particular method with the greater sensitivity can
be selected. In this case, the 10 m GC column with SIM using C18 and IA
for sample preparation could be utilized.
The time of analysis for particular methods was summarized for
sample preparation and GC column lengths earlier in this chapter. The
trade-offs between selectivity, sensitivity, and the total analysis time
can be compared by examining the chromatograms throughout the chapter.
Overall higher selectivity (and therefore lower LODs) for sample
preparation and introduction methods require longer times of analysis.
The total analysis time for methods C, K and J is shown in Figure 5-14c.
Comparing this figure with Figure 5-14b for selectivity, the obvious
trade-offs between total analysis time and selectivity for these

141
particular methods can be observed. As was discussed earlier, for a
slight decrease in selectivity, a large decrease in the analysis time can
be achieved. For example, the selectivity and sensitivity difference is
quite small when comparing method C to method K; however, method K
utilizing a 3 m GC column and SRM is 20 min faster per sample than method
C with a 30 m GC column with SIM or SRM. This corresponds to analysis of
approximately 3 to 4 times as many samples per day for a slight decrease
in selectivity which does not affect the quantitation of PGE2 in urine.
Thus, trade-offs are necessary between the different steps in an analysis
scheme to achieve the optimum technique.

CHAPTER 6
EVALUATION OF SOLID-PHASE EXTRACTION PROBE/MS/MS FOR THE
ANALYSIS OF ENDOGENOUS PROSTAGLANDIN E2 IN URINE
Introduction
In Chapter 5, the use of C18 and immunoaffinity (IA) purification
coupled to a short 3 m GC column with selected-reaction monitoring (SRM)
was shown to be a rapid analysis method with the required selectivity and
sensitivity for the determination of PGE2 in urine. However, the
derivatization procedure required for GC sample introduction is both
lengthy and tedious. If a sample introduction method which did not
require such derivatization were employed, total analysis times could be
reduced dramatically. Note, however, that it would still be attractive
to retain the PFB derivatization, since it provides the opportunity to
utilize the advantage of increased sensitivity and selectivity inherent
in EC-NCI. Although prostaglandins (PGs) cannot be separated by GC with
only PFB derivatization, it would be possible to employ a less selective
sample introduction technique, such as conventional solids prode MS or
direct chemical ionization probe (DCI). Unfortunately, the total cycle
time for probe sample introduction is actually longer than for short GC
column introduction discussed in Chapter 5. Furthermore, the fact that
essentially all mixture components desorb into the ion source at nearly
the same time increases the probability of quenching of the electron-
142

143
capture process. This ionization interference leads to decreased ion
signals and poor limits of detection, especially in samples containing
complex matrices in which an enormous number of compounds may have been
derivatized which can undergo electron-capture. The objective of this
study was to evaluate the capability of IA purification coupled to the
sample introduction techniques of solids probe and DCI with SRM to analyze
endogenous levels of PGE2 in urine.
Experimental
Sample Preparation
The prostaglandins and reagents were identical to those described
in Chapter 2. Urine samples (identical to the three in Chapter 5) and
standards for a calibration curve were prepared by the same method as was
explained in Chapter 5. Note that a constant amount of 2H4-PGE2 was added
as an internal standard to the urine before extraction. In these
experiments, C18 and IA purification was utilized for all the urine
samples.
Derivatization
The purified samples were evaporated and then derivatized to the
PFB ester according to the procedure in Chapter 2. The methoximation and
silylation steps of the procedure were not employed for this study. The
amount of PFB esterification reagents used to derivatize the urine samples
was tripled for the same reason as was explained in Chapter 5. After
evaporation of the excess PFB esterification reagents, the derivatized
samples were diluted by adding 60 /¿L of ethyl acetate to the urine samples

144
and 50 /*L to the standards for the calibration curve. One-microliter
injections containing 500 pg of 2H^-PGE2 were either directly placed in
sample vials for the solids probe or coated onto the wire loop of the DCI
probe.
Instrumental Conditions
A Finnigan MAT triple stage quadrupole (TSQ45) gas chromatograph/
tandem mass spectrometer was used for these studies. Mass spectrometry
conditions were: interface and transfer line temperature 300°C, ionizer
temperature 190°C, electron energy 100 eV and emission current 0.3 mA.
Electron-capture negative chemical ionization (EC-NCI) was carried out
with methane at an ionizer pressure of 0.50 torr. Argon was employed as
the collision gas at a pressure of 1.0 mTorr; a collision energy of 25 eV
was utilized for the selected-reaction monitoring studies of PGE2. The
SRM experiments employed an EM setting of 2000 V and a preamp gain of
o
10 V/A. A calibration curve was obtained for the DCI studies by analyzing
standard solutions containing a constant amount of 2H^-PGE2 (25 ng) and
increasing amounts of PGE2, as listed in Table 5-2 in Chapter 5.
The quantitation of the endogenous levels of PGE2 in urine was
accomplished by selected-reaction monitoring (SRM) of 351' -+ 271’ for PGE2
and 355’ -+ 275’ for the internal standard, 2H^-PGE2. A baseline was chosen
visually on the solids probe or DCI probe trace and the areas for PGE2 and
p
H^-PGE2 calculated by the INCOS computer system for the calibration curve
and the extracted urine samples. The area of PGE2 divided by the area of
2
H^-PGE2 in the standards gives a ratio which is used in the calibration
curve. The amount of PGE2 in each urine sample was calculated according

145
to the method described earlier in Chapter 5.
The solids probe analysis was performed by placing the diluted urine
sample or standard into a small glass vial and evaporating the ethyl
acetate in air. The probe temperature was initially set at 50°C and then
increased at 60°C/min to 300°C for the standards, urine blank and urine
samples analyzed. The DCI analysis was performed by coating the wire loop
of the Finnigan direct exposure probe with the sample and allowing the
ethyl acetate to evaporate in air. The heating current (initially 0 mA
with the probe at room temperature) was increased at 10 mA/s (600°C/min)
for 1 min.
Solids Probe Analysis
EC-NCI and Daughter Spectra of Standard PGE.,
The EC-NCI mass spectrum for standard PGE2 with no derivatization
is shown in Figure 6-la. This mass spectrum of 1 ng of PGE2 is dominated
by ions corresponding to the loss of one (334‘) and two (316") water
molecules from the M"‘ ion. The M"' ion of PGE2 (351‘) has a low relative
abundance of only 0.5% compared to the intense ions observed from the loss
of one and two water molecules. The large relative abundance of the 334"
and 316" ions suggests that dehydration of the PGE2 molecules may occur
before the ionization process, as they are desorbed from the glass sample
vial as the probe is heated. In addition, positive chemical ionization
(PCI) was performed and evaluated. The results from thse experiments show
that without derivatization, the PCI mass spectrum has a much lower
sensitivity than that of EC-NCI.

% Relative Abundance
100%
334"
r1,676,080
(a) •
100%
(b)
m/z
[M-H20 ]
r1,001,470
Solids probe electron-capture negative chemical
ionization mass spectrum of:
(a) Underivatized PGE2 standard (lpg)
(b) PFB ester derivative of PGE2 (5 ng).
Figure 6-1:
146

147
The PFB derivative of PGE2 was prepared and evaluated to compare the
sensitivity utilizing this abbreviated derivatization procedure to that
of the underivatized standard. Figure 6-lb shows the EC-NCI mass spectrum
of 5 ng of the PFB ester derivative of PGE2. This mass spectrum is similar
to Figure 6-la of the underivatized PGE2; however, the most abundant ion
is the [M-PFB-2H20]" ion rather than the [M-H20]' ion. The [M-PFB-H20]" ion
is also prominent in Figure 6-lb, with other less intense ions (< 5%)
present in the mass spectrum. Again, these ions may reflect thermal
dehydration as the PFB derivatized PGE2 is vaporized off the probe. The
351' ion corresponds to the [M-PFB]' ion produced by dissociation electron
capture, and has a low intensity compared to the other ions in the
spectrum. Comparing the absolute counts observed for the base peaks in
Figure 6-la with Figure 6-lb, the underivatized PGE2 signal is 1.7 times
larger than that for the PFB derivatized PGE2 standard; however, the
underivatized PGE2 sample had a concentration 200 times greater than the
PFB-derivatived PGE2. Thus, the sensitivity for the PFB-derivatized PGE2
is approximately 100 times greater than that of the underivatized
standard.
The extremely low relative abundance of the [M-PFB]' ion in the EC-
NCI mass spectrum, subsequently produces a low intensity daughter spectrum
of the [M-PFB]' ion (Figure 6-2). A daughter spectrum with many low
intensity fragment ions is shown in Figure 6-2. The most abundant ion in
the spectrum is the 271' ion corresponding to [M-PFB-2H20-C02]'.
Subsequently, this ion was chosen for selected-reaction monitoring of PGE2
in urine. The other prominent daughter ions are listed in Table 6-1 with
the % relative abundance and probable ion assignment. Note that the

% Relative Abundance
Figure 6-2: Solids probe daughter ion spectrum of the [M-PFB]' ion
of the PFB ester derivative of PGE2 (5 ng) at 1.0 mTorr of
argon and 25 eV collision energy.
,372
148

149
Table 6-1: Daughter Ions of [M-PFB]’ (P‘) of PGE2 PFB Ester
Analyzed by Direct Solids Probe
Ion Assignment
m/z
2RA‘
[P]'
351
32
[P-H20]‘
333
23
[P-2H20]'
..315
31
[P-2H20-C02]'
271
100
[P-2H20-C02-C2H2j*
235
28
[P-2H20-C02-C5H60]"
189
85
or
[P-2H2O-CO2-C6H10]-
a % Relative abundance
at a collision gas pressure
of
1.0 mTorr argon and collision energy of 25 eV.

150
[M-PFB-H20]" ion in the EC-NCI mass spectrum could have been chosen for
MS/MS, with an increase in sensitivity of approximately 100.
Study of Endogenous Levels of PGE^ in Urine
Figure 6-3 shows the SRM traces of a 350 pg PGE2 standard, a urine
blank (containing endogenous levels of PGE2 with no H4-PGE2 added) and a
urine sample containing 500 pg of 2H^-PGE2. The urine blank and sample
were prepared by essentially the same method with C18 and IA purification
then derivatized to the PFB ester of PGE2. This experiment was performed
with a temperature ramp of 60°C/min, as described in the experimental
section of this chapter. The trace for the PGE2 standard (Figure 6-3a)
shows one distinct peak with a low level of noise. Figure 6-3b shows the
chromatogram of the urine blank with the same conditions as the standard
in Figure 6-3a. A distinct peak for endogenous PGE2 is noticed, but in
this case the noise level has increased drastically compared to the
relative intensity of the PGE2 peak. The peak area of the PGE2 standard
in Figure 6-3a is 5 times greater than the peak area of the endogenous
level of PGE2 in the urine blank (Figure 6-3b). Results from Chapter 5
indicate that endogenous levels of PGE2 in urine are approximately 300 to
350 pg/mL. Therefore, the peak area for the urine blank should be
approximately the same as that of the 350 pg PGE2 standard in Figure
6-3a. This suggests that PGE2 may have been lost during the sample
preparation procedure or the remaining urine matrix components in the
extracted sample interfere with the efficient ionization of the [M-PFB]*
ion. This second possible explanation is reffered to as quenching and may

% Relative Intensity
151
99,840
24,896
19,392
Figure 6-3: Solids probe SRM trace of a PFB derivatized:
(a) 350 pg PGE2 standard
(b) Extracted urine blank
(c) Extracted urine sample containing
500 pg of 2H4-PGE2 internal standard

152
occur in the analysis of biological samples when EC-NCI is utilized,
without extensive chromatographic clean-up (111).
The trace for a urine sample which contained an additional 500 pg
of H^-PGE2 which was not present in the urine blank (Figure 6-3b) is shown
in Figure 6-3c. The peak shape for PGE2 is not as distinct as in Figures
6-3a and 6-3b and the signal to noise ratio has decreased considerably
from the 350 pg standard in Figure 6-3c. Comparing the PGE2 standard in
Figure 6-3a to the urine sample, the peak area is approximately 7 times
lower than that calculated for the PGE2 standard. In addition, the peak
area of the urine blank (Figure 6-3b) is 1.5 times greater than the peak
area of the urine sample containing the H^-PGE2. These results suggest
that the urine matrix components in the urine samples leads to the
quenching effect discussed above.
Slower temperature ramps were evaluated to determine if PGE2 could
possibly be separated from the urine matrix interferences present in the
extract. However, the quenching effect noted in the figures above was
still a prominent problem. In addition, calculation of an accurate peak
area was extremely difficult due to the low signal to noise ratio observed
for urine samples.
Figure 6-3 indicates the difficulty in determination of PGE2 in urine
by utilizing the solids probe for sample introduction. This technique
lacks the selectivity and sensitivity required for the analysis of
endogenous levels of PGE2. The rapid process of heating the probe and
vaporization of the sample from the vial results in a lack of separation
of the PGE2 from the urine matrix components present even after IA
purification. In addition, the remaining urine matrix components

153
apparently lead to quenching of the [M-PFB]' ion during the ionization
process, resulting in inefficient SRM. Therefore, after examining these
results and experimenting further with different temperature ramps, the
solids probe/MS/MS method was not employed for quantitation of PGE2 in
urine.
Direct Chemical Ionization Analysis
Concept of Direct Chemical Ionization (DCI)
The technique of DCI, also called "in beam" or "desorption chemical
ionization", mass spectrometry was first introduced by Baldwin and
McLafferty (113) and appears to be useful in the analysis of medium-
molecular-weight polar compounds (114,115). Typically, the technique
involves coating a wire probe with a sample which is then directly
inserted into the ion plasma in the chemical ionization source. The probe
is usually heated with an electric current to temperatures in excess of
1000°C. In most cases, polar organics are volatilized intact from the
probe tip at temperatures much lower than this (100°C to 300°C).
Recently, this technique has been utilized for both positive and negative
ammonia DCI mass spectrometry of a number of PGs, without prior
derivatization (80,116). This report demonstrated the advantages of DCI
mass spectrometry in analyzing standard prostaglandins without
derivatization and the mechanistic aspects of the gas-phase chemistry
involved. However, only PG standards were investigated, and at levels (50
ng or more) well above endogenous levels of PGE2 in urine. Therefore, this
rapid sample introduction technique with a short derivatization procedure
was evaluated for determining endogenous PGE2 in urine.

% Relative
c
(0
T3
C
D
n
<
Figure 6-4: Direct chemical ionization electron-capture negative
chemical ionization mass spectrum of PFB derivatized
PGE2 standard.
154

155
EC-NCI and Dauehter Spectra of Standard PGE-,
Figure 6-4 shows the EC-NCI mass spectrum of 500 pg of a PFB
derivatized PGE2 standard. This spectrum differs from that of the PFB-
derivatized PGE2 using the solids probe (Figure 6-lb) in that the most
prominent ion is the [M-PFB]' carboxylate anion (351‘), rather than the
ions corresponding to a loss of one or two water molecules. The
importance of acquiring an intense parent ion ([M-PFB]") was discussed
earlier. In the case of DCI, since the [M-PFB]" carboxylate anion is the
most abundant ion in the EC-NCI mass spectrum, the sensitivity should be
enhanced compared to the solids probe. Differences in the EC-NCI mass
spectra of PFB derivatized PGE2 standard using solids probe and DCI may be
attributed to the binding of the PG sample to the glass vial used in
solids probe analysis, as was discussed earlier in this chapter. The loss
of one and two water molecules from the [M-PFB]" are present in the mass
spectrum as well as a few low intensity "backbone" fragment ions. The
absolute counts for the [M-PFB]" ion of a 500 pg sample of PFB derivatized
PGE2 using DCI was 1.5 times greater than the counts for the [M-PFB-2H20]‘
ion of a 5 ng PFB-derivatized PGE2 standard using the solids probe,
corresponding to a 15 times higher sensitivity for DCI. Therefore, this
method should provide adequate sensitivity for the analysis of PGE2 and may
be comparable to that found for a 3 m GC column utilizing SRM in Chapter
5.
Daughter ion spectra of the [M-PFB]" ion (351‘) under different CAD
conditions are shown in Figure 6-5a and Figure 6-5b. The first (Figure
6-5a) daughter spectrum was obtained with a collision energy of 28 eV and
a collision gas pressure of 1.5 mTorr of argon. Figure 6-5b was obtained

% Relative Abundance
700% 1
r 264,192
(a) -
700%-i
(b) -
/ **
m/z 700
271
189
I 1- f r-y1’-^ *|- r
233
,1..,. ü.n^Lp., j.f.,
315
‘1 ■•t »• i r
315
333
*1 ' r
351“
T ' ' ’ ' ' T ’ I • |
271
189
r ’ i *
233
y » r * H » » ♦"T4 i * » rn~i~i
200
300
r891,904
333 351
t~’~i
TT »
r t-*-]' ’ *-1 "n*
400
Figure 6-5: Direct chemical ionization daughter ion spectra of the
[M-PFB]* ion of the PFB ester derivative of PGE2 at:
(a) 1.5 mTorr of argon and 28 eV
(b) 1.0 mTorr of argon and 25 eV
156

157
Table 6-2:
Daughter Ions of [M-PFB]* (P‘) of PGE2 PFB Ester
Analyzed by Direct Chemical Ionization (DCI)
Ion Assienment
m/z
%RAa
%ra'
[P]'
351
8
77
[p-h20]-
333
39
69
[P-2H20]'
315
47
100
[P-2H20-C02]‘
271
100
49
[P-2H20-C02-C2H4]'
or
[P-2H20-C02-C0]'
233
12
13
[P-2H20-C02-C5H60]‘
or
[P-2H2O-CO2-C6H10]-
189
45
19
a % Relative abundance at a collision gas pressure of
1.5 mTorr argon and collision energy of 28 eV.
b X Relative abundance at a collision gas pressure of
1.0 mTorr argon and collision energy of 25 eV.

158
with a collision energy of 25 eV and a collision gas pressure of 1.0 mTorr
of argon. The prominent ions in both daughter spectra are the same and
are listed in Table 6-2 with the % relative abundances and possible ion
assignments. The fragment ions which occur at lower mass are ions that
correspond to backbone-specific fragments, due to fragmentation of the
carbon-hydrogen skeleton in PGE2. Differences in the relative intensity
of the ions in the two daughter spectra are noted, particularly the major
ions of m/z 351, 333, 315 and 271. As was explained in Chapters 3 and 4,
increasing the collision energy allows for more energetic collisions,
while increasing the collision gas pressure increases the number of
collisions each ion experiences. This explains the differences noted in
the two daughter spectra. In addition, comparing Figure 6-5b to the
daughter spectrum of the PFB-derivatized PGE2 standard utilizing the solids
probe (Figure 6-2), the spectra are similar. This is to be expected since
the CAD conditions were identical in both cases. The differences in the
ions relative intensity may be attributed to the use of different methods
of sample introduction, and the much lower signal-to-noise ratio in Figure
6-2.
Study of Endogenous Levels of PGE., in Urine
Figure 6-6 shows the SRM traces of a 350 pg PGE2 standard (Figure
6-6a), as well as a urine blank (Figure 6-6b) and a urine sample
containing 500 pg of 2H^-PGE2 internal standard (Figure 6-6c) prepared by
C18 and IA purification. These three samples were analyzed with DCI
utilizing a 600°C/min temperature ramp as described in the experimental
section. The SRM traces of of all three samples shows a distinct peak

% Relative Intensity
159
Figure 6-6: Direct chemical ionization SRM trace of a PFB
derivatized:
(a) 350 pg PGE2 standard
(b) Extracted urine blank
(c) Extracted urine sample containing
500 pg of 2H4-PGE2 internal standard

160
which vaporizes off the DCI probe approximately 20-30 s after the heating
has started. Comparing Figure 6-6a to Figure 6-6b, the 350 pg PGE2
standard has a peak area 6 to 7 times greater than the peak area of the
endogenous PGE2 in the urine blank. The peak area of the urine blank
should be approximately the same as the 350 pg standard for the reasons
described in the solids probe section. In addition, the peak area of the
urine sample containing 500 pg of H4-PGE2 (Figure 6-6c) was 3 times lower
than the peak area of the urine blank (Figure 6-6b) and 18 times lower
than the peak area of the standard (Figure 6-6a), with a dramatically
lower signal-to-noise ratio. The quenching effect, noted above, is more
p
prominent for the urine sample containing the 500 pg of H^-PGE2.
The quantities of endogenous PGE2 in urine obtained by utilizing
DCI/MS/MS with a 600°C/min vaporization rate are listed in Table 6-3. The
three urine samples were the same as reported earlier in Chapter 5.
Quantitation was performed utilizing the method listed above in the
experimental section. The calibration curve used to determine the amount
of endogenous PGE2 in urine is shown in Figure 6-7. The calibration curve
shown demonstrates good linearity with a slope of 1.06, similar to the
expected value of 1.00 for this calibration curve. Extrapolation of the
x-intercept from the best fit line yields the amount of PGE2 in 500 pg of
the 2H4-PGE2 internal standard. The x-intercept obtained from this
calibration curve corresponded to approximately 26 pg of PGE2 which is 5.2%
of the 500 pg of 2H^-PGE2. Results from this study establish the fact that
the urine matrix components vaporize off the DCI probe at the same time
as the endogenous PGE2. The average values obtained for the three samples
are approximately 3 times larger than the values found for the same urine

Figure 6-7: Calibration curve utilizing direct chemical ionization
with SRM.
161

162
Table 6-3: Quantitation Study of Endogenous PGE2 in Urine Utilizing
Direct Chemical Ionization (DCI)/MS/MSa
Concentration of PGE2
(pg/mL)
Urine Sample 4
DCI
Iniection 4
Ave. of 3 Ini .
%RSD'
1
1
1063.3
2
1144.5
3
1172.1
1126.6
5.0
2
1134.0
913.8
1066.4
1038.1
10.9
3
985.7
1085.2
1191.1
1087.3
9.4
Average of Urine Samples 1 & 2: 1082.4 pg/mL
Average of 3 Urine Samples: 1084.0 pg/mL
%RSD of 3 Samples: 4.1
3 C18 and IA purification performed on all 3 urine samples.
b % Relative Standard Deviation

163
samples derivatized and analyzed by GC/MS/MS in Chapter 5. Therefore,
the selectivity of this method is inadequate for the analysis of PGE2 in
urine. Sensitivity of the method was investigated by the same method
employed in Chapter 5. The slope of the calibration curve of standard PGE2
derivatized with PFB was 0.0023 counts/pg, approximately 4 times lower
than that found for a 30 m GC column utilizing SRM. Consequently, the
sensitivity may not be adequate for the analysis of endogenous PGE2 in
urine. However, examining the LOD for PGE2 in urine, 100 to 125 pg/mL
was detectable with a signal-to-noise ratio of 3. Therefore, if the
selectivity of this technique could be enhanced, the LOD of DCI/MS/MS is
sufficient for the determination of endogenous levels of PGE2 in urine.
Slower temperature ramps were evaluated to determine if PGE2 could
possibly be separated from the urine matrix interferences present in the
extract. The results were similar to those found for the solids probe
analysis. The signal-to-noise ratios utilizing the slower temperature
ramps were inadequate to reliably measure the peak area of the endogenous
PGE2 in urine.
The urine matrix components which interfere with the analysis of PGE2
and may cause quenching are still present in the extracts due to secondary
interactions (non-specific adsorption) which occur during the IA
purification procedure. These interactions were discussed earlier in
Chapter 2 and the consequences of these interactions are obvious from the
results of the DCI/MS/MS studies. The utilization of an additional clean¬
up technique after the selective IA purification step was evaluated.
Another IA column was employed, which had immunoaffinity for prostaglandin
6-ketoF1a, after the IA purification of PGE2< The eluent which was not

164
retained by the 6-ketoF1a IA column was collected and analyzed for PGE2.
This technique allowed the PGE2 to pass unretained through this IA column,
while hopefully retaining the urine matrix components which were
originally non-specifically bound to the PGE2 IA column. It was observed
that the selectivity of the DCI analysis was not enhanced appreciably by
this additional clean-up step.
Conclusions
The utility of solids probe/MS/MS and DCI/MS/MS for the analysis of
endogenous levels of PGE2 in urine has been evaluated in this chapter.
An abbreviated derivatization method has been employed, allowing for more
rapid preparation of urine samples. This advantage, coupled with the
ability of DCI to vaporize samples rapidly, yields a method which reduces
overall analysis times dramatically. However, as was pointed out in the
introduction to this chapter, the total cycle time for probe sample
introduction is actually longer than for short GC column introduction.
Hence, the only savings in time results from the reduced derivatization
necessary. Another drawback of the DCI probe is that the rapid
vaporization of the urine sample allows a large number of urine matrix
components to be vaporized into the ion source at the same time, causing
quenching and creating difficult, inaccurate quantitation of endogenous
levels of PGE2, as was observed in Table 6-3. The use of DCI/MS/MS for
accurate determination of PGE2 in urine will require further investigation
of more efficient and selective methods of sample preparation to eliminate
the possible secondary interactions which occur in IA purification.

CHAPTER 7
CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK
Summary
An evaluation of the concepts for the trace determination of
prostaglandins (PGs) by tandem mass spectrometry (MS/MS) has been
achieved. Results from the studies in Chapter 3 demonstrate the
importance of the optimization of various parameters in the
collisionally-activated dissociation (CAD) process before performing trace
analysis. Optimization of both collision energy and collision gas
pressure is essential in obtaining an accurate qualitative daughter
spectrum "rich" in structural information. Choice of a particular
daughter ion for SRM is essential and can affect the sensitivity and/or
selectivity of an analysis. The CAD reaction with the highest CAD
efficiency should be selected to yield the highest sensitivity for SRM
determination of PGs. A dramatic difference in the optimum collision gas
pressure for SRM with MS/MS for the determination of PGE2 and PGF2a has
been observed and discussed.
The differences in fragmentation behavior of PGE2 and PGF2a were
examined through the use of fragmentation, collection and overall CAD
efficiency studies. This work showed that the CAD efficiency for the
[MO/TMS-PFB]‘, [M-PFB]" and [M-H]" carboxylate anions is significantly
different for subtle structural changes in PGs. Through the use of these
165

166
curves, we have shown that F-series PGs fragment less efficiently than
PGE2 and PGD2> A possible explanation has been proposed to explain these
dramatic differences seen in the fragmentation behavior of structurally
similar carboxylate anions of PGs. It is believed that F-series PGs are
more stable during CAD due to the interaction of the carboxylate group
with the two -OH groups in the cyclopentyl ring.
The advantages and limitations of immunoaffinity purification (IA)
for sample preparation of PGs in urine have been investigated. Results
show that IA purification coupled with a short 3 m GC capillary column
utilizing EC-NCI selected-reaction monitoring (SRM) can provide a
selective, sensitive and rapid method of analysis for endogenous levels
of PGE2 in urine. The studies performed in Chapters 2 and 5 demonstrate
the reusability of the IA sorbent and its capabilities in various
analytical schemes. However, data from Chapter 6 shows that IA
purification still has limitations. The non-specific binding which occurs
due to secondary interactions in the IA procedure creates difficulties in
analysis when less selective sample introduction (direct probe or DCI) or
detection schemes (selected-ion monitoring) are employed.
The systematic study which was performed in Chapter 5 demonstrates
the relative trade-offs which exist throughout the entire analytical
procedure. This study indicates that the utilization of a more selective
sample preparation method (IA) with MS/MS can reduce the chromatographic
separation time required to achieve the necessary selectivity and
sensitivity for PG analysis in urine. However, results show that MS/MS
is not necessary if IA purification and a longer chromatographic
separation (more selectivity) technique are employed. In addition,

167
dramatic differences in sensitivity were observed for PGE2 for the three
different lengths of GC columns employed. This type of systematic study
should be applicable in the evaluation of any analytical procedure for
analysis of components in a biological sample.
Future Directions
Validation of the accuracy and effectiveness of IA purification
coupled with a 3 m GC capillary column and SRM needs to be performed on
samples which have already been analyzed with another method, such as
radioimmunoassay (RIA). Another aspect of IA which requires immediate
attention is the applicability to other matrices, especially human milk
samples. This will possibly require an optimization of the extraction
technique with the use of different solvents. In addition, the
sensitivity of this method requires further examination, if it is to be
employed for the routine analysis of small prenatal samples.
A number of studies are still needed to establish an optimum method
of analysis for PGs in biological samples utilizing MS/MS. Various sample
preparations, derivation procedures, ionization and measurement methods
need to be evaluated. Even though IA purification is a reliable,
selective method for sample preparation, the optimization of an even
simpler, selective, more rapid extraction procedure would be highly
advantageous. The commercial availability of monoclonal antibodies for
PG analysis would reduce sample preparation time even more and possibly
reduce the non-specific binding problems observed with the polyclonal
immunoafffinity columns tested. This would allow further evaluation of

168
direct chemical ionization (DCI) as a possible rapid sample introduction
technique.
Derivatization procedures for SRM also need to be addressed. The
use of EC-NCI GC/MS utilizes the MO/PFB/TMS derivative for analysis. This
approach has served as the basis of the more sensitive and selective
analysis by SIM (48-52). In this work, it was found that the intense
carboxylate anion formed from this derivatization produced inefficient
overall CAD (< 2.0%) for F-series PGs. Furthermore, with EC-NCI,
derivative-specific fragmentation is prominent with little to no
"backbone-specific" fragmentation present. Therefore, further examination
of more effective derivatization procedures with various ionization
methods for SRM analysis need to be performed.
Along these lines, Strife (90) has performed preliminary studies
with the ME/MO/TMS derivative utilizing the ion trap mass spectrometer
(ITMS), discussed in Chapter 1. The ITMS offers access to "backbone-
specific" fragmentation, but at high CAD efficiencies of 50% (91). This
method of measurement has the additional advantage of not sacrificing
sensitivity for selectivity when using the MS/MS mode of operation. In
initial trials, he has observed excellent sensitivity for less than 75-pg
quantities of PGs injected on column.
From these studies and the literature, it is clear that much work
remains to be performed in the systematic optimization of the analytical
scheme for the analysis of endogenous levels of PGs in biological samples.
The principles discussed in this work, coupled with new analytical
techniques may help to influence future studies in PG analysis.

LITERATURE CITED
1. Nelson, N. A.; Kelly, R. C. Chem. Eng. News 1982, 60, 30.
2. Samuelsson, B. ; Go1dyne, M. ; Granstróm, E. ; Hamberg, M.;
Hammarstróm, S.; Malmsten, C. Ann, Rev. Biochem. 1978, 47, 997.
3.
Bregman, M. D.;
Meyskens,
F.
L. Cancer Res. 1983. 43. 1642
•
4.
Levenson, D. J.
; Simmons,
C.
E.; Brenner, B. M. Am. J. Med.
1982,
72, 354.
5.
Frólich, J. C.;
Wilson, T
. W
.; Sweetman, B. J.; Smigel, M.;
Nies,
A. S. ; Carr, K.
; Watson,
J.
T. ; Oates. J. A. J. Clin. Invest.
1975, 55, 763.
6. Blair, J. A.; Barrow, S. E.; Waddell, K. A.; Lewis, P. J.; Dollery,
C. T. Prostaglandins 1982, 23, 579.
7. "Advances in Prostaglandins and Thomboxane Research";
Frólich, J. A., Ed.; Raven Press: New York, 1978, Vol. 5.
8. "Methods in Enzymology Prostaglandins and Arachidonate
Metabolites"; Lands, W. E. M.; Smith, W. L. , Eds.¡Academic:
Orlando, 1982, Vol. 86, Section 5.
9. Powell, W. S.; Funk, C. D. Prog. Lipid Res. 1987, 26, 183.
10. Traitler, K. Prog. Lipid Res. 1987, 26, 257.
11. Kelley, R. W. In "Mass Spectrometry - Applications in Clinical
Biochemistry"; Lawson, A. M., Ed.; de Gruyter 1988.
12. Henke, D. C.; Kouzan, S.; Eling, T. E. Anal. Biochem. 1984, 140,
87.
13. Bradlow, H. L. Steroids 1968, 11, 265.
14. Powell, W. Prostaglandins 1980, 20, 947.
15. Vesterquist, 0.; Gréen, K. Prostaglandins 1984, 28, 139.
16. Berens, M. E.; Salmon, S. E.; Davis, T. P. J. Chromatogr. 1984,
307, 251.
169

170
17. Lawson, J. A.; Brash A. R. ; Doran, J.; FitzGerald, G. A. Anal.
Biochem. 1985, 150, 463.
18. Krause, W.; Jakobs, U. Schulze, P. E.; Nieuweboer, B.; Hümpel, M.
Prostaglandins Leukotriene Med. 1985, 17, 167.
19. Hubbard, H. L.; Eller, T. D.; Mais, D. E.; Halushka, P. V.;
Baker, R. H. ; Blair, I. A.; Vrbanac, J. J.; Knapp, D. R.
Prostaglandins 1987, 33, 149.
20. Vrbanac, J. J.; Eller, T. D.; Knapp, D. R. J. Chromatogr. 1988,
69, 1.
21. Cox, V. W.; Pullen R. H.; Royer M. E. Anal. Chem. 1985, 57, 2365.
22. Auletta, F. J.; Zusman, R. M. Caldwell, B. V. Clin. Chem, 1974,
20, 1580.
23. Hamberg, M.; Svensson, J.; Wakabayashi, T.; Samuelsson, B. Proc,
Natl. Acad. Sci. USA 1974, 71, 345.
24. Green, K.; Samuelson, B. J. Lipid Res. 1964, 5, 117.
25. Kiefer, H. C.; Johnson, C. R.; Arora, K. L. Anal. Biochem. 1975,
68, 336.
26. Deshpande, Y. G.; Kaminski, D. L. Prostaglandins 1980, 20, 367.
27. Greenwald, J. E.; Alexander, M. S.; Van Rollins M.; Wong, L. K.;
Bianchine, J. R. Prostaglandins 1981, 21, 33.
28. Lagarde, M.; Gharib, A.; Dechavanne, M. Clin. Chem. Acta. 1977,
79, 255.
29. Bailey, J. M. ; Bryant, R. W. ; Feinmark, S. J.; Makheja, A. N.
Prostaglandins 1977, 13, 479.
30. Vincent, J.E.; Zijlstra, F. J. Prostaglandins 1977, 14, 1043.
31. Carr, K. ; Sweetman, B. J. ; Frolich, J. C. Prostaglandins 1976, 11,
3.
32. Whorton, A. R.; Carr, K.; Smigel, M.; Walker, L.; Ellis, K.;
Oates, J. A. J. Chromatogr. 1979, 163, 64.
33. Alam, I.; Ohuchi, K.; Levine, L. Anal. Biochem. 1979, 93, 339.
34. Boeynaems, J.; Brash, A. R. ; Oates, J. Al; Hubbard, W. C. Anal.
Biochem. 1980, 104, 259.

171
35. Van Rollins, M.; Ho S. H. K.; Greenwald, J. E.; Alexander, M.;
Dorman, N. J.; Wong, L. K.; Horrocks, L. A. Prostaglandins 1980,
20, 571.
36. Terragno, A.; Rydzik, R. ; Terragno, N. A. Prostaglandins 1981, 21,
101.
37. Herbaczynska-Cedro, K.; Bane, J. R. Circ. Res. 1973, 33, 428.
38. Lonigro, A. J.; Terragno, N. A.; Malik, K. U. ; McGiff, J. C.
Prostaglandins 1973, 3, 595.
39. Levine, L.; Van Vunakis, H. Biochem. Biophvs, Res. Commun. 1970,
41, 1171. ~
40. Midgley, A. R. Jr.; Niswender, G. D. ; Rebar, R. W. Acta.
Endocrinol. 1969, 63, 163.
41. Watkins, W. D.; Perterson, M. B. Anal. Biochem. 1982, 125, 30.
42. Bergstrom, S.; Ryhage, R.; Samuelsson, B.; Sjóvall, J. J. Biol.
Chem. 1963, 238, 3555.
43. Samuelsson, B.; Hamberg, M.; Sweeley, C. C. Anal. Biochem. 1970,
38, 301.
44. Gréen, K. ; Samuelsson, B. In "Prostaglandin Symposium of the
Worcester Foundation for Experiemental Biology"; Ramwell, P. W. ;
Shaw, J. E. Ed.; Interscience: New York, 1967, 389.
45. Watson, J. T.; Hubbard, W. C.; Sweetman, B. J.; Pelster, D. R.
In "Advances in Mass Spectrometry in Biochemistry and Medicine";
Frigerio, A. Ed.; Halsted: New York, 1976, Vol. 2, 495.
46. Erlenmaier, T.; Muller, H.; Seyberth, H. W. J. Chrornatogr. 1979,
163, 289.
47. Claeys, M.; Van Have, C.; Dachateau, A.; Herman, A. G. Biomed.
Mass Spectrom 1980, 7, 544.
48. Fischer, C.; Meese, C. 0. Biomed. Mass Spectrom. 1985, 12, 399.
49. Fischer, C. Biomed. Mass Spectrom. 1984, 11, 114.
50. Hubbard, W. C.; Litterst, C. L.; Liu, M. C.; Bleeker, E. R.;
Eggleston, J. C.; McLemore, T. L.; Boyd, M. R. Prostaglandins
1986, 32, 889.
51. Leis, H. J.; Malle, E.;Mayer, B.; Kostner, G. M.; Esterbauer, H.;
Gleispach, H. Anal. Biochem. 1987, 162, 337.

172
52. Leis, H. J.; Hohenester, E.; Gleispach, H.; Malle, E.; Mayer, B.
Biomed. Environ. Mass Spectrom, 1987, 14, 617.
53. Hubbard, W. C.; Watson, J. T. Prostaglandins 1976, 12, 21.
54. Falardeau, P. ; Oates, J. A.; Brash, A. R. Anal. Biochem, 1981,
115, 359.
55.
Middleditch,
B. S. ;
Desiderio. D. M. Adv.
Mass Spectrom.
1974, 6,
173.
56.
Middleditch,
B. S. ;
Desiderio. D. M. Anal.
Biochem. 1973.
55, 509.
57.
Horvath, G.
Biomed
. Mass Snectrom. 1976.
3, 4.
58. Oliw, E. W.; Sprecher, H.; Hamberg, M. J. Biol. Chem. 1986, 261,
2675.
59.
Oliw, E. W.; Fahlstadius, P.;
261, 9216.
Hamberg, M.
J. Biol.
Chem. 1986.
60.
Walker, R. W. ; Garber, V. F. ;
1980, 181, 85.
Pile, J.;
et al. J,
Chromatogr.
61. Ferretti, A.; Flanagan, V. P.; Roman, J. M. Anal. Biochem. 1983,
128, 351.
62. Waddell, K. A.; Blair, I. A.; Wellby, J. Biomed. Mass Spectrom.
1983, 10, 83.
63. Ferretti, A.; Flanagan, V. P.; Reeves, V. B. Anal, Biochem. 1987,
167, 174.
64. Wilson, B. W. ; Snedden, W. ; Parker, R. B. In "Advances in Mass
Spectrometry in Biochemistry and Medicine"; Frigerio, A. Ed.;
Halsted: New York, 1976, Vol. 2, 487.
65. Morita, I.; Murota, S-I.; Suzuki, M.; Ariga, T.; Miyatake, T.
J. Chromatogr. 1978, 154, 285.
66. Rubio, F.; Garland, W. A. J, Chromatogr. 1985, 339, 313.
67. Gleispach, H. ; Mayer, B.; Rauter, L. ; Wurtz, E. J. Chromatogr.
1983, 273, 166.
68. Buzan, A. C.; Knapp, D. R. J. Chromatogr. 1982, 236, 201.
69. Gleispach, H.; Moser, R. ; Leis, H. J. J, Chromatogr. 1985, 342,
245.

173
70. Westcott, J. Y.; Chang, S.; Balazy, M.; Stene, D. 0.;
Pradelles, P. ; Maclouf, J.; Voeikei, N. F.; Murphy, R. C.
Prostaglandins 1986, 32, 857.
71. Martineau, A.; Falardeau, P. J. J. Chrornatogr. 1987, 417, 1.
72. Mayer, B.; Gleispach, H.; Kukovetz, W. R. Biochim, Biophvs. Acta
1987, 918, 209.
73. Leffler, C. W.; Desiderio, D. M.; Wakelyn, C. E. Prostaglandins
1981, 21, 227.
74. Schweer, H. ; Seyberth, H. W. ; Shubert, R. Biomed. Environ. Mass
Spectrom, 1986, 13, 611.
75. Schweer, H.; Seyberth, H. W.; Meese, C. 0. Biomed. Environ. Mass
Spectrom. 1988, 15, 129.
76. Schweer, H.; Seyberth, H. W. ; Meese, C. 0.; Fürst, 0. Biomed.
Environ. Mass Spectrom. 1988, 15, 143.
77. Strife, R. J.; Simms, J. R. Anal. Chem, 1988, 60, 1800.
78. Vrbanac, J. J.; Knapp, D. R. Proc. 35th Ann. Conf. Mass Spectrom.
Allied Top., Denver, 1987, 7.
79. Zilletti, L.; Cuiffi, M.; Frahi-Micheli, S.; Moneti, G.; Luzzi, S.
Adv. Mass Spectrom. 1986, 10, 1583.
80. Schilling, A. B. ; Zulak, I. M. ; Puttemans, M. L. ; Hall, E. R. ;
Venton, D. L. Biomed. Mass Spectrom. 1986, 13, 545.
81. Burlinggame, A. L. ; Baillie, T. A.; Chizhov, 0. S. Anal. Chem.
1980, 52, 214R.
82. Chilton, F. H. ; Murphy, R. C. Biomed. Environ. Mass Spectrom,
1986, 13, 71.
83. Chilton, F. H. ; Murphy, R. C. Prostaglandins Leukotrienes Med.
1986, 23, 141.
84. Weerasinghe, C. A.; Locke, L. A.; Wang, R. Proc. 35th Ann. Conf.
Mass Spectrom. Allied Top., Denver, 1987, 451.
85. Kim, H. Y.; Yergey, J. A.; Salem, N. , Jr. J. Chromatogr. 1987,
394, 155.
86. Voyksner, R. D. ; Bush, E. D. ; Brent, D. Biomed. Environ. Mass
Spectrom, 1987, 14, 523.
87. Voyksner, R. D.; Bush, E. D. Biomed. Environ. Mass Spectrom. 1987,
14, 213.

174
88. Strife, R. J.; Kelly, P. E.; Weber-Grabau, M. Proc. 35th Ann.
Conf. Mass Spectrom. Allied Top., Denver, 1987, 9.
89. Strife, R. J.; Simms, J. R. Proc. 35th Ann. Conf. Mass Spectrom.
Allied Top., San Francisco, 1988, 1114.
90. Kruger, T. L.; Litton, J. F.; Kondrat, R. W.; Cooks, R. G. Anal.
Chem. 1976, 48, 2113.
91. Kondrat, R. W.; Cooks, R. G. Anal. Chem. 1978, 50, 81A.
92. McLafferty, F. W.; Bockhoff, F. M. Anal. Chem. 1978, 50, 69.
93. Yost, R. A.; Enke, C. J. Anal. Chem. 1979, 51, 1251A.
94. Glish, G. L. ; Shaddock, V. M. ; Harmon, K. ; Cooks, R. G. Anal.
Chem. 1980, 52, 165.
95. Brotherton, H . 0.; Yost, R. A. Anal. Chem. 1983, 55, 549.
96. Trehy, M. L.; Yost, R. A. Anal. Chem. 1984, 56, 1281.
97. Van Horne, K. C. "Sorbent Extraction Technology"; Analytichem
International, Inc., Cambridge: England, 1985.
98. Harris, P. A. Presented at the Second Annual International
Symposium on Sample Preparation and Isolation Using Bonded Silicas,
Philadelphia, January 14-15, 1985, pp 3.
99. Stolowitz, M. L. Presented at the Second Annual International
Symposium on Sample Preparation and Isolation Using Bonded Silicas,
Philadelphia, January 14-15, 1985, pp 41.
100. Maestas, R.; Prieto, J.; Duehn, G.; Hageman, J. J. Chromatogr.
1980, 189, 225.
101. Barrow, S. E.; Waddell, K. A.; Ennis, M.; Dollery, C. T.;
Blair, I. A. J. Chromatogr. 1982, 239, 71.
102. Gaskell, S. J.; Brownsey, B. G. Clin. Chem. 1983, 29, 677.
103. Wilson, T. W. ; McCauley, F. A.; Tuchek, J. M. J. Chromatogr. 1984,
306, 351.
104. Dyas, J.; Turkes, A.; Read, G. F. ; Riad-Fahmy, D. Ann. Clin.
Biochem. 1981, 18, 37.
105. Glencross, R. G.; Abeywardene, S. A.; Corney, S. J.; Morris, H. S.
J, Chromatogr. 1981, 223, 193.
106. Knapp, D. R. "Handbook of Analytical Derivatization Reactions";
Wiley: New York, 1979, 530.

175
107. Uziel, M.; Smith, L. H. ; Taylor, S. A. Clin. Chem. 1976, 22, 1451.
108.
Junk, G. A.;
1347.
; Avery, M. J.
; Richard, J. J.
Anal. Chem. 1988. 60.
109.
Shindo, N. ;
Tomoko, S. ;
Murayama, K.
Biomed. Environ. Mass
Soectrom. 1988, 15, 25.
110. Yost, R. A.; Enke, C. G.; McGilvery, D. C.; Smith, D.;
Morrison, J. D. Int. J. Mass Spectrom. Ion Phvs. 1979, 30, 127.
111. Johnson, J. V.; Yost, R. A. Anal. Chem. 1985, 758A.
112. Gleispach, H. ; Moser, R. ; Leis, H. J. J. Chrornatogr. 1985, 342,
245.
113. Baldwin, M. A.; McLafferty, F. W. Org. Mass Spectrom. 1973, 7, 7.
114. Reinhold, V. N.; Carr, S. A. Anal. Chem. 1982, 54, 503.
115. Ayanoglu, E.; Wegmann, A.; Pilet, 0.; Marbury, G. D.; Haas, J. R.;
Djerassi, C. J. Am. Chem. Soc. 1984, 106, 5246.
116. Cepa, S. R.; Hall, E. R.; Venton, D. L. Prostaglandins. 1984, 27,
645.

BIOGRAPHICAL SKETCH
Todd Allen Gillespie was born in Portland, Indiana on January 13,
1962. He attended Jay County High School, graduating in 1980 as the
senior class president. From 1980 to 1984 while attending the University
of Indianapolis, he lettered four years on the collegiate tennis team and
was head statistician for the football and basketball teams from 1983 to
1984. During his senior year at U. of I. he acquired an interest in
analytical chemistry while employed as a co-op at Merrell Dow
Pharmaceutical, Inc. in Indianapolis. He graduated Cum Laude in May 1984
with a B.S. degree in chemistry and mathematics. In August of 1988, he
began his graduate school studies at the University of Florida under the
direction of Dr. Richard A. Yost. During the spring of 1987, he married
his beautiful wife Paula E. Hannon at the University of Indianapolis.
Upon graduation his wife and him will be moving to Cincinnati, Ohio where
Todd will be employed at Merrell Dow Research Institute.
176

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.
áichard A. Yostq Chairman
Associate 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.
Dorsey
ate Professor of Chemistry
1 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.
A
Anna Brajter-Toth
Associate 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.
Samuel 0. Colgate
Associate 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.
yJOse^Neu
"Associate Professor of Pediatrics
This dissertation was submitted to the Graduate Faculty of the
Department of Chemistry in the College of Liberal Arts and Sciences and
to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
May, 1989
Dean, Graduate School

UNIVERSITY OF FLORIDA
3 1262 08554 2792



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 E1B2C2L3N_W5AOP3 INGEST_TIME 2011-11-08T19:53:58Z PACKAGE AA00004803_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES