Pharmacokinetic-pharmacodynamic modeling of piperacillin-tazobactam combinations

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Title:
Pharmacokinetic-pharmacodynamic modeling of piperacillin-tazobactam combinations
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ix, 147 leaves : ill. ; 29 cm.
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English
Creator:
Dalla Costa, Teresa Cristina Tavares, 1962-
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Subjects

Subjects / Keywords:
Piperacillin -- pharmacokinetics   ( mesh )
Piperacillin -- pharmacology   ( mesh )
Penicillanic Acid -- analogs & derivatives   ( mesh )
Penicillanic Acid -- pharmacology   ( mesh )
Penicillanic Acid -- pharmacokinetics   ( mesh )
Antibiotics, Combined -- pharmacokinetics   ( mesh )
Antibiotics, Combined -- pharmacology   ( mesh )
Drug Therapy, Combination   ( mesh )
Models, Chemical   ( mesh )
Escherichia coli -- pathogenicity   ( mesh )
Dose-Response Relationship, Drug   ( mesh )
Department of Pharmaceutics thesis Ph.D   ( mesh )
Dissertations, Academic -- College of Pharmacy -- Department of Pharmaceutics -- UF   ( mesh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaves 132-146).
Additional Physical Form:
Also available online.
Statement of Responsibility:
by Teresa Cristina Tavares Dalla Costa.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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oclc - 48651742
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Full Text











PHARMACOKINETIC-PHARMACODYNAMIC MODELING OF PIPERACILLIN-
TAZOBACTAM COMBINATIONS














By


TERESA CRISTINA TAVARES DALLA COSTA












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

1996



























Dedicated to my parents Ligia and Ddrio Dalla Costa.




















ACKNOWLEDGMENTS


I would like to offer my appreciation and sincere thanks to Dr. Hartmut Derendorf

for his continuous encouragement since I met him in 1986 in his first official invitation to

teach pharmacokinetics in my College in Brazil. I think we have come a long way until I

finally completed this Ph.D. program, and his guidance was always very helpful. I also

would like to thank the members of my supervisory committee, Dr. Gayle Brazeau, Dr.

Guenther Hochhaus, and Dr. Kenneth Rand, for their advice and suggestions throughout

my doctoral research. I would like to specially thank Dr. Hochhaus for his friendship and

concern about me.

I would like to thank the secretaries of the Department of Pharmaceutics, in

particular Mrs. Patricia Khan, for their technical support at all times. I also would like to

thank Mrs. Marjorie Rigby for helping to keep the laboratory organized and in working

conditions.

The completion of the animal experiments for this project was done thanks to the

help of Dr. Arno Nolting, my fellow graduate student at that time, and Dr. Andreas

Kovar. I am very thankful for their support. I would like extend my thanks to all

graduate students who were my colleagues in the "battle front" and will always be my

friends. Very special thanks to my dear friend Maritza de Cediel, who brought the "Latin

blood" back to my life and to the laboratory.




iii















Apart from the department I would like to thank Prof. Paul Doering and his family
for giving me and my husband a little taste of the American way of life and a great deal of

friendship and support.

Finally I would like to thank my parents for supporting me ever since I can

remember in everything I tried and in any way they could. A very special thanks to Regis

who understood how important this project was for me. I could not have received this

degree without him.

































iv















TABLE OF CONTENTS


page

ACKN OW LED GEM EN TS....................................................... ....... ............................iii

AB STRA CT ...... ............. .... .................. ...... ............... .................. ............. viii

CHAPTERS

1 INTRODUCTION .......................... ................... ......... ...... ............. .. 1

Im portance of the Study....................................................... ....................... 1
H ypotheses ........................................................................ ................ ..... 4

2 LITERATURE REVIEW.......................................................................... 5

Piperacillin ............. .............. ............................................................... 5
0-Lactam Antibiotic and P-Lactamase Inhibitor Combination ....................... 9
Tazobactam ... ..................................................................................... 11
Piperacillin-Tazobactam Combinations ................................................... 13
M icrodialysis.............................. ............................................................ 15
In vitro Models to Assess Antibacterial Activity ......................................... 22
PK-PD Modeling of Antiinfective Agents ................... ....................... 33

3 ANALYTICAL DETERMINATION OF PIPERACILLIN AND
TAZOBACTAM....................................................... ........... 39

Specific Aims of the Analytical Studies.............................. ..................... 39
M aterial and M ethods ................................................................................ 39
D rug A ssay ...................................................................................... ... 39
Chem icals and Reagents ..................................... ..................... ... 39
Instrum entation ................................. ....................................... 40
TZB Sample Preparation .................. ......... .......... ..... ..... 40
TZB Chromatographic Conditions..................... ....................... 40
PIP Sample Preparation ..... ........................................... 41
PIP Chromatographic Conditions....................................... 41
A ssay V alidation.................................. ................................. ........ 4 1
TZB Stability Studies ................. ................... ............ 42
Results and Discussion ...................... ....... .............................. 43


V









Assay Validation...................................................... ...................... .. 43
TZB Stability Studies ................................................ ................. 44
C onclusions............................................. ............................ 45

4 PHARMACOKINETICS OF PIPERACILLIN AND TAZOBACTAM
CO M BIN A TION S ................................................................................. .. 47

Specific Aims of the Pharmacokinetic Studies.................... ................ 47
M aterial and M ethods................. ..... ........................... .................... 47
Experim ental D esign..................................................... ........................ 47
Surgical Procedure .............................................................................. 48
M icrodialysis Conditions ....................... ............ .... ....................... 49
Microdialysis System and Probe Calibration In Vitro............................. 49
TZB Protein Binding Determination ............................................... 50
Microdialysis Probe Calibration In Vivo.............................................. 51
Estimation of Pharmacokinetic Parameters......................................... 52
Statistical Analysis............................................................................ 53
R esults and D iscussion ................................................... ......................... ... 54
Piperacillin Pharmacokinetics......................................... ................... 54
TZB Probe Calibration In Vivo........ ........ ....................................... 56
Protein Binding D eterm ination.................................. ........................... 58
Tazobactam Pharmacokinetics............................... ................. .... 59
C onclusions............................. . ............... ....... ................................. ..... 67

5 IN VITRO PHARMACODYNAMICS OF PIPERACILLIN AND
TAZOBACTAM COMBINATIONS ..................................... ................... 71

Specific Aims of the Pharmacodynamic Studies........................................ 71
M aterial and M ethods ................................................................................ 71
Drugs ..................... ......... ................ .................. 71
Bacteria................... .................... ................. 71
In Vitro M odel of Infection............................................. .................. 72
Bacterial Q uantification ..................... ........ ........ .......... .......... 73
Comparison Between Human Tissue Levels and In Vitro Levels............. 73
Piperacillin Stability In The In Vitro Model....................... .............. 74
TZB Minimum Effective Concentration..................................... ... 74
Experim ental D esign.......................................................................... 75
R e su lts ........ .............. .. ................ ................................................................ 8 0
Comparison Between Human Tissue Levels and In Vitro Levels............. 80
Piperacillin Stability In The In Vitro Model..................... .... ............ 80
TZB Minimum Effective Concentration............................................ 83
Simulation of Constant Intravenous Infusion.............................. .. 84
Simulation ofi.v. Bolus Multiple Dosing..................... ................ .... 89
C onclusions.................................... ...................... ................... 99




vi









6 PHARMACOKINETIC-PHARMACODYNAMIC MODELING.............. 100
Specific Aims of the PK-PD Modeling.......................................... ............. 100
PK-PD Analysis for Piperacillin alone ....................................................... 102
Effect of Tazobactam Concentration ............................. .................. 105
Simulation of Constant Infusion........................................ 110
Simulation of i.v. M ultiple Dosing ............................................................ 113
Conclusions ............................................... 122

7 FINAL CONCLUSIONS ........................... ................. 124

REFERENCES..................... ...................................... ...................... .....132

BIOGRAPHICAL SKETCH........................................................................... 147







































vii















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


PHARMACOKINETIC-PHARMACODYNAMIC MODELING OF PIPERACILLIN-
TAZOBACTAM COMBINATIONS

By

Teresa Cristina Tavares Dalla Costa

August, 1996

Chairman: Hartmut Derendorf, Ph.D.
Major Department: Pharmaceutics


The treatment of infections is mainly based on experience rather than on rational

design. Although some attempts have been made to correlate pharmacokinetic and

pharmacodynamic parameters of antibiotics in order to predict the outcome of

antiinfective therapy, the results to date are still not satisfactory. A more detailed

evaluation of the antimicrobial effect can be obtained by using a pharmacokinetic-

pharmacodynamic model. Therefore, it was the aim of the present study to model the

pharmacokinetic and pharmacodynamic data of different combinations of piperacillin, a 3-

lactam antibiotic, combined with tazobactam, a P-lactamase inhibitor, against E. coli in

order to optimize the dosing regimen for this combination. In the first part of the study,

the pharmacokinetics of piperacillin and tazobactam alone and in different combinations

were investigated in rats after single i.v. bolus administration. Total plasma concentrations

were monitored and microdialysis in the muscle was used to monitor free interstitial

concentrations. Concentration-time profiles in plasma were adequately described by a



viii










two-compartment body model. Predictions of free tissue levels were possible for both

drugs, alone and in combination, based on parameters derived from plasma data. In the

second part of the study, free concentrations expected in tissue after i.v. bolus multiple

dose and constant infusion were calculated based on human pharmacokinetic parameters.

Escherichia coli ATCC 35218, a P-lactamase producing strain, was exposed to these

concentrations in an in vitro model of infection. Bacterial counts were monitored for up

to twenty-four hours. A modified Emax-model was used to link the pharmacokinetics to

the pharmacodynamics and describe the number of bacteria as a function of time. The

results showed a decreased EC50 for piperacillin when combined with TZB in comparison

to the value obtained for piperacillin alone. The decreased EC50 is a result of

pharmacokinetic and possibly pharmacodynamic effects. Tazobactam protects piperacillin

from degradation by the p-lactamase and may also enhance piperacillin's bactericidal

effect. The comparison of different doses and dosing regimens suggested that as the

dosing interval is shortened the antiinfective effect can be enhanced. When using a high

dose of tazobactam, twice a day administration of piperacillin-tazobactam combination

may be possible.






















ix















CHAPTER 1
INTRODUCTION


Importance of the Study

The treatment of infections is mainly based on clinical experience rather than on

rational design. This is because the appropriate selection and use of an antimicrobial agent

depends on characteristics of the infection, the host, and the drug. Although many

attempts have been made to correlate all these factors in order to predict the outcome of

infections the results to date are still not satisfactory for many antibiotics. If one can find a

way to adjust dose and dosing regimen for treating infections it will be possible to reduce

the risks of side effects and also the cost of antibiotic therapy. The use of an adequate

dose and dosing interval from the beginning of the treatment on may reduce the chance of

development of bacterial resistance which has become a very important issue lately. It can

also have an impact on patient compliance if it can be shown that less frequent

administration of some of the current antibiotics has the same efficacy as frequent and

rather tedious dosing schedules. An important step in addressing this question is the

combination of pharmacokinetic parameters of the antibiotic (PK) with its

pharmacodynamic properties against bacteria (PD) in a PK-PD model. Both parts

together (PK and PD) can be used to predict the effect as a function of time and allow a

systematic study of interactions between drug and microorganism. By using a PK-PD

model different doses and dosing regimens can be compared and predictions can be made

based on a scientific approach.

It has been reported that the antimicrobial activity of 1-lactam antibiotics

correlates better with the time that plasma concentrations are maintained above the



1






2


minimum antibiotic concentration (MIC) than with any other pharmacokinetic parameter.

Apparently, once the concentration exceeds a critical value (4-5 times MIC), bacterial
killing proceeds at zero-order rate, and increasing drug concentrations does not result in a

proportional change in the microbial death rate (1). This critical concentration is easily

achieved in vivo using current therapy. Furthermore, p-lactam antibiotics do not produce

a post-antibiotic effect (PAE) in Gram-negative bacteria emphasizing that the presence of

certain level of the antibiotic is indispensable for the activity (2). This behavior differs

from that of aminoglycosides, for instance, that exhibit concentration-dependent killing.

The killing rate of these drugs continues to increase with concentration up to 16-32 times

the minimum bactericidal concentration (MBC). Since relatively low levels of these

antibiotics are obtained in vivo compared to their MBCs, a linear relationship between

dose and bacterial rate can be observed in the therapeutic range. Aminoglycosides also

produce a concentration-dependent PAE. Combining these two factors one can conclude

that aminoglycosides show antiinfective activity which is mainly dependent on the initial

high drug concentrations. p-lactam antibiotics are therefore frequently referred to as

concentration-independent and time-dependent agents while aminoglycosides are named

concentration-dependent (3). Since it is known that most of the P-lactam antibiotics have

a short half-life, more frequent administration of lower doses will result in a better

antiinfective effect (because it prolongs the exposure of bacteria to the desirable drug

concentrations) than high doses administered less frequently (for which the high drug

levels obtained will not translate into a more effective bacterial killing). It was also shown

in in vitro experiments that for this class of antibiotics the total daily dose can be reduced

if the dosing interval is increased concomitantly. For the P-lactam antibiotic piperacillin

studied in vitro using Escherichia coli, 6 g of the drug given as 1 g six times a day had an

effect equivalent to 15.6 g given as 5.2 g three times a day (4). The problem associated

with increasing the number of daily administrations is the decrease in patient compliance

or the increase in personnel cost for hospitalized patients.






3


Bacteria can develop resistance against 0-lactam antibiotics mainly by producing

P-lactamases (5). In order to overcome this resistance, p-lactam antibiotics are frequently

combined with p-lactamase inhibitors. One of the most effective combinations in this class

is piperacillin (PIP) and tazobactam (TZB), a P-lactamase inhibitor. For the treatment of

infections with PIP-TZB combination, it was suggested that the same total daily doses of

both drugs can be administered less frequently without loss of efficacy (6). In this study

bacteria were exposed to fluctuating total concentrations of piperacillin alone or in

combination with tazobactam in an in vitro model of infection which simulates drug levels

obtained in humans. It was shown that the combination of piperacillin and tazobactam (3

g/0.375 g) administered four times a day is as effective against 0-lactamase producer E.

coli as piperacillin and tazobactam (4 g/0.5 g) administered three times a day. However,

these studies were conducted exposing bacteria to the total drug concentrations observed

in plasma rather than to the concentrations observed in interstitial fluid which is the most

common site of infection. It is known that drug concentrations in blood may not reflect

the concentrations at the cellular level due to the degree of protein binding, capillary and

membrane permeability, and physico-chemical properties of the drug.

The suggested efficacy for treatment of infections with PIP-TZB using longer

dosing intervals opens the possibility of less frequent administration of 1-lactam antibiotics

in humans. However, before any inferences can be made, a more detailed investigation of

the pharmacokinetic and pharmacodynamic aspects of this combination is necessary.

Different doses, dose ratios and dosing regimens have to be investigated in simulations of

achievable free tissue levels. A PK-PD model has to be devised that allows comparison of
the different doses and dosing regimens investigated. The model can also be used to make

predictions about the efficacy of doses and dosing regimens of this combination.






4


Hypotheses


The hypothesis for this research project were as follows: firstly, free piperacillin

and tazobactam tissue concentrations, alone and in combination, can be predicted from

their respective plasma concentrations based on a diffusion-driven pharmacokinetic model,

secondly, a pharmacodynamic Emax-model can be used to describe the antiinfective effect

of piperacillin-tazobactam combinations in different doses, thirdly, in contrast to the

current recommendations, piperacillin combined with tazobactam can be administered less

frequently without loss of efficacy, and finally that the possibility of less frequent dosing of

piperacillin combined with tazobactam is not related to changes in piperacillin

pharmacokinetics but is rather due to the pharmacodynamic effect of the combination.

In order to test these hypotheses this research project was divided in four parts:

analytical studies, pharmacokinetic studies, pharmacodynamic studies, and PK-PD

modeling. Each part is presented in the subsequent chapters.














CHAPTER 2
LITERATURE REVIEW


Piperacillin

Piperacillin is a semi-synthetic acylureido-penicillin that was developed in 1977 and

originally referred to as T-1220. The basic structure of piperacillin, like other penicillins,

is the nucleus with fused 0-lactam and thiazolidine rings (7). Piperacillin's chemical name

is [2S-[2a,5a,6p(S*)]]-6-[[[[(4-ethyl-2,3-dioxo-l-piperazinyl)carbonyl]-

amino]phenylacetyl]amino]-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo-[3.2.0]heptane-2-

carboxylic acid (8). The presence of an intact p-lactam ring is essential for its antiinfective

activity. The ureido structure in the side chain provides the diverse physico-chemical and

biological properties of PIP compared to other penicillins (Figure 2-1). The pKa of

piperacillin is 4.14. The pH of an aqueous solution ofpiperacillin sodium is 5.5-7.0 (8).

The pH range of highest stability is 4-6. The sodium salt of PIP is highly water soluble

(714 g per 1 L).

Piperacillin is not absorbed from the gastrointestinal tract and has to be

administered either intravenously or intramuscularly. PIP pharmacokinetics has been

described by either a one-compartment (9-10) or a two-compartment body models (11).

After intravenous administration in humans, piperacillin kinetics is characterized by high

maximum plasma concentrations, a small volume of distribution, a short half-life and a

rapid decay in plasma concentrations (12). After intravenous bolus administrations of 15,

30, and 60 mg/kg mean peak plasma concentrations in healthy volunteers were 102

pg/mL, 232 Vg/mL, and 522 lg/mL, respectively (11).




5






6




HNH NN HNI
H: s H- 3 O H 3
L/CH3 N CH3
H5C2 COOH COOH

Piperaillin N- desethyl Piperacillin
Piperacillin

H COOH

N H2N
jCH L/ CH3 S
O-/OH
COOH
Tazobactam Tazobactam Metabolite MI

Figure 2-1. Chemical structures of piperacillin, N-desethyl piperacillin, tazobactam, and
tazobactam metabolite (MI).



Piperacillin 4 g given by infusion over 30 min to healthy subjects results in a mean peak

concentration of 244 pg/mL (9). Intramuscular injection of 0.5 g and 2 g resulted in 70 to

80% bioavailability Peak concentrations were reached within 45 min and averaged from

5.13 to 30 pg/mL, respectively (13).

PIP apparent volume of distribution at steady state (Vdss) averaged 30.5 L after 1

g dose, 27.5 L after 2 g, and 21.2 L after 4 g administered as i.v. bolus injection (14).

The volume of distribution for the elimination phase (Vdarea) is also dose-dependent (15).

After intramuscular injection of 1 g of piperacillin the Vdarea obtained was 38.6 L/1.73m2

(15).

Total body clearances after both intravenous and intramuscular administration

decreased with increasing PIP dose: 24.52 L/h and 12.58 L/h after intravenous doses of 1

g and 6 g, respectively (15). In patients with normal renal function PIP is primarily

eliminated via the kidneys (80%) by glomerular filtration and tubular secretion. Most of






7


the given dose, 60 to 80%, is recovered unchanged in the urine. The percentage of

recovery is lower after i.m. than after i.v. administration of the drug (15). Average renal

clearances of 245.7 mL/min and 186.9 mL/min are reported after 1 and 6 g doses,

respectively (15). The renal clearance exceeds the glomerular filtration rate by far,

suggesting that tubular secretion is the major factor affecting the dose-dependent behavior

shown by piperacillin (11). Less than 1% of the dose is metabolized to N-desethyl-

piperacillin, an active metabolite (8) (Figure 2-1). About 20% of the dose is excreted

through the biliary tract producing concentrations in the bile up to forty times of those in

the serum (16-17).

Serum half-lives are slightly dose-dependent with values ranging from 0.6 to 1.05

h after i.v. bolus administration of 1 and 6 g, respectively (15). After i.m. injection the

half-lives are higher (1.2 h for 1 g and 1.3 h for 6 g of PIP). The prolongation of half-life

with increasing dose is not clinically significant (9).

Piperacillin protein binding is approximately 21% (9-10). This relatively low

protein binding explains the extent with which PIP diffuses into tissues and other body

fluids. Therapeutic concentrations of piperacillin are achieved in a variety of tissue and

body fluids including cerebrospinal fluid, bronchial mucosa, kidney, bone, subcutaneous

tissue, peritoneal fluid, heart tissue, aqueous humor, gallbladder wall and female genital

tissue (13, 16, 18-23). Penetration into the amniotic fluid is not as high as that into the

umbilical cord, and passage into the breast milk is negligible (13).

Piperacillin pharmacokinetics is altered in children, pregnant women and elderly

subjects. The elimination half-life is shorter in children than in adults (24). It was also

shown that the younger the child the shorter the half-life. The total body clearance in

infants (1 to 6 months) was also lower than in older children (5 to 10 years) (25). In

children, the mean renal clearance of the drug represented 63% of the total body clearance

suggesting a substantial non-renal route of elimination for piperacillin (24-25). In elderly

subjects the total clearance of PIP is reduced by 15% and the volume of distribution is






8


increased by 43% compared to young adults. As a result the mean residence time of PIP

in the body is doubled in elderly subjects (2.09 0.15 h) compared to young adults (1.15

+ 0.04 h) (26). Larger volumes of distribution and higher clearance rates are observed for

piperacillin during pregnancy. Thus, higher doses may be required for effective treatment

of serious infections in pregnant women near the term (27).

The elimination half-life of piperacillin is increased from 60 min in normal patients

to 96 min in patients with mild renal insufficiency (creatinine clearance 50 to 80 mL/min).

With moderate renal failure (creatinine clearance 15 to 50 mL/min) it increases to

approximately 130 min and reaches 150 min in patients with severe renal insufficiency

(creatinine clearance 9 to 15 mL/min). Then, the diminution of kidney function to less

than one-tenth of the normal value is accompanied by only a 3-fold increase of the

elimination half-life of piperacillin (28). The urinary recovery of PIP decreases with the

degree of renal insufficiency from approximately 80% of the dose in normal subjects to

practically zero in patients with end-stage renal insufficiency (29). The non-renal or biliary

clearance probably compensates for the renal elimination in renal compromised patients

(29). In renal impaired patients undergoing hemodialysis the half-life of PIP is decreased

on average 60.5% compared to patients not undergoing dialysis (30). This confirms that

piperacillin can readily be removed by dialysis. A dose reduction or an increased interval

between doses is indicated according to the degree of renal impairment. Doses must also

be adjusted to account for a reduced renal clearance between hemodialysis treatment as

well as for removal of the drug during hemodialysis (29).

Piperacillin is a bactericidal drug that demonstrates a broad spectrum of
antibacterial activity (9, 31). The mechanism of action is related to its effect on the

bacterial cell wall. In Gram-negative microorganisms, PIP binds covalently to the penicillin

binding proteins (PBP) located between the layers of the cell membrane. The PBP are

enzymes that constitute the system responsible for the synthesis of the bacterial cell wall.






9


The cell wall is responsible for the shape and integrity of the bacteria. Piperacillin

has a high degree of affinity to PBP 3, which is important for the bacterial cell division, to

PBP la and Ib, responsible for the cell wall integrity and to PBP 2, responsible for the cell

wall shape (5, 32). At low concentrations piperacillin produces bacterial filamentation

without any lytic activity (33). Cell lysis occurs at high concentrations without any

appreciable filamentation.

Piperacillin demonstrates a wide range of antibacterial activity against Gram-

positive and Gram-negative aerobic and anaerobic organisms. It is effective against

Proteus, Enterobacter, Serratia and Actinobacter species. It exhibits good activity

against clinical isolates of Pseudomonas, Proteus, Klebsiella, Serratia, Bacteroides and

Enterococci. Haemophilus influenza and Neisseria gonorrhoeae also have demonstrated

a marked sensitivity to piperacillin (13).


B-Lactam Antibiotic and 1-Lactamase Inhibitor Combination

Bacterial resistance have rendered some of the older P-lactam antibiotics obsolete.
The antibacterial effect of p-lactam antibiotics depends on their capacity to resist or avoid

the barriers opposed by the bacteria (5). There are three mechanisms by which bacteria

resist the action of P-lactam antibacterial agents: production of enzymes that mediate

antibiotic degradation, alteration of outer membrane permeability, and decreased

penicillin-binding protein affinity (34). Three classes of enzymes can hydrolyze 3-lactam

antibiotics: P-lactamases, acylases, and esterases (5). P-Lactamase mediated hydrolysis of

the P-lactam nucleus is the most common and important mechanism of bacterial resistance

to P-lactam antibiotics. P-Lactamases are produced by some Gram-positive and all Gram-

negative bacteria (12). Gram-negative bacilli produce both chromosomally encoded and

plasmid-encoded 3-lactamases (5). For Gram-positive bacteria only the production of 0-

lactamase and the alteration of the PBP affinity are available mechanisms of resistance






10


because of the location of the PBP on the exterior surface of the cytoplasmic membrane

(35). The PBP on Gram-negative bacteria are located in the inner membrane. The

antibiotic has to cross the outer membrane and avoid the enzymatic degradation at the

periplasmic space in order to reach its target. For these microorganisms the interplay

between the permeability of the outer membrane (OM) and the degradation rate by the P-

lactamase is very important (36). If the antibiotic penetrates the OM slowly and the

enzymatic activity is low, sufficient drug concentration can build up in the periplasmic

space to bind to the PBP. For an agent that penetrates faster, the concentration in the

periplasmic space approaches that in the external medium unless a very fast inactivation

process occurs inside the cell. Thus, for most agents the decisive factor is not the absolute

rate of OM penetration but the balance between the penetration rate and the subsequent

inactivation rate. The difference in 3-lactam concentration on either side of the OM

depends on these two factors (37). In general P-lactam agents cross the OM through
porin channels. Diffusion of some agents is limited by molecular weight and electrostatic

charges; diffusion of others is limited by bulky substituents on the acyl side chain of the 3-

lactam nucleus (38-39). Two outer membrane proteins (Omps) have been identified and

characterized for E. coli. (OmpF and OmpC). The difference between the two proteins is

the diameter of the channel. The bacteria can mutate to produce only OmpC (narrowest

diameter) in order to resist to the penetration of p-lactams (40).

The co-administration of a non-antimicrobial drug capable of inhibiting 3-

lactamase activity in conjunction with a P-lactam antibiotic is a strategy that has been used

to overcome P-lactamase-mediated resistance. The inactivation of the P-lactam antibiotic

by the P-lactamase and the inhibition of the P-lactamase by the p-lactamase inhibitor can

occur in a competitive, non-competitive, or terminal (suicide) fashion (41). Competitive

inactivation involves the formation of a reversible enzyme-inhibitor or enzyme-antibiotic

complex. Even though the enzyme complex is reversible, the bacteria can be killed if the

enzyme is bound long enough for the antibiotic to bind to PBP and initiate the lethal






11


effect. Non-competitive inhibition is progressive and time dependent. This mechanism

does not seem to be viable for either of the drugs in combination. Suicide inhibition

results in the formation of a stable acylated complex between the 1-lactamase and the
inhibitor. The product can be either a hydrolyzed inhibitor and a reactivated enzyme or an

inert complex. Although the reaction may be in fact reversible in some situations, the

enzyme is complexed for such a long period of time that, for all practical purpose, the

reaction is permanent. All P-lactam inhibitors clinically used up to now are irreversible

inhibitors of the 3-lactamases (42).

Two 1-lactam inhibitors widely used are sulbactam, co-administered with

ampicillin, and clavulanic acid, used in combination with ticarcillin. Piperacillin has been

introduced recently combined with tazobactam to treat infections caused by 3-lactamase

producing bacteria.


Tazobactam

Tazobactam (TZB) is a p-lactamase inhibitor from the class of penicillanic acid

sulfones developed by R.G. Micetich and Taiho Pharmaceutical Company (Tokushima,

Japan) and originally referred to as YTR-830 (43). TZB's chemical name is [2S-

(2a,30,5a)]-3-methyl-7-oxo-3-(1H-1,2,3-triazol-1-ylmethyl)-4-thia-l-azabicyclo-
[3.2.0]heptane-2-carboxylic acid (Figure 2-1). The pKa of TZB is 2.1 and hence it is

ionized in tissues and body fluids except in the acidic conditions of the stomach (8). TZB

is very soluble in water (500g of the sodium salt dissolves in 1 L of water).

Tazobactam has inhibitory activity against Richmond and Sykes types II, III, IV,

and V p-lactamases, staphylococcal penicillinase and extended-spectrum 3-lactamases. All

these enzymes are plasmid encoded (34). Tazobactam also has activity against class Ic

chromosomally-mediated enzymes, but limited activity against other class I enzymes. It

acts as an irreversible inhibitor against the major P-lactamase classes. Unlike clavulanic






12


acid, TZB has only weak to moderate enzyme inducing activity (44). TZB seems to be

more effective than sulbactam and clavulanic acid in inhibintig some of the most common

plasmid encoded 3-lactamases like TEM-1, TEM-2 and SHV-1 enzymes (45).

Tazobactam binds to PBP 2 of Gram-negative organisms but its antibacterial activity is

negligible (46).

Tazobactam has been shown to extend the spectrum of activity of piperacillin

against bacteria producing both chromosomal and plasmid-mediated 3-lactamases (34, 47-

50). Piperacillin-tazobactam possesses a broad spectrum of activity including Gram-

positive and Gram-negative aerobic and anaerobic organisms (51). Gram-negative

bacteria include many Enterobacteriaceae and Pseudomonas aeruginosa. Susceptible

Gram-positive bacteria include Enterococcusfecalis, Listeria monocytogenes and

streptococci. This combination has good activity against Bacterioidesfragilis and other

anaerobes (34). Piperacillin-tazobactam is, overall, the most active p-lactam-p-lactamase

inhibitor combination as demonstrated by in vitro studies (52-53). It is recommended for

the treatment of polymicrobial infections (54). Decreased susceptibility to piperacillin-

tazobactam is observed in organisms with more than one mechanism of resistance (34).

Tazobactam pharmacokinetics investigated in humans over the dose range of 0.1

to 1.0 g was found to be typical of those for other P-lactam (8, 12) (Table 2-1). The

maximum plasma concentrations obtained at the end of an infusion were approximately

proportional to the dose administered. As the dose was increased, total clearance

decreased and, consequently, the AUC rose more than proportionally to the dose

administered. The volume of distribution for the lowest dose (0.1 g) is approximately

13 L and increased by 20% for the highest dose (1 g). The amount of TZB excreted

unchanged by the kidney increased from 60.3% to 77.0% over the dose range studied.

The half-life increased significantly with dose. Tazobactam is metabolized by cleavage of

the P-lactam ring to produce the metabolite M1 (Figure 2-1) which is further broken down

to a butanoic acid derivate. On average, 26% of the dose is transformed to M1 which has






13 13


no 3-lactamase activity; the metabolism is suggested to take place predominantly in the

hepatocytes (8). The protein binding of 14C-tazobactam in human plasma by

ultrafiltration was found to be 20-23% over a concentration range of 1-100 g.g/mL (8).


Piperacillin-Tazobactam Combinations

The effect of co-administration of piperacillin and tazobactam on the

pharmacokinetic behavior of each of these agents was investigated for combinations of

PIP-TZB 2 g a g, g and 4 g/0.5 g (8, 12, 34). The pharmacokinetics of

piperacillin remained unaffected after co-administration with tazobactam in a ratio 1:4 and

1:8 (8). The pharmacokinetics of TZB, on the other hand, was significantly affected by

the presence of PIP. A summary of these results is shown in Table 1. The plasma

concentrations and the half-life of TZB were increased after co-administration with

piperacillin when compared to TZB administration alone. The half-life of TZB when

administered in combination is similar to the half-life of PIP and the plasma levels of the

two compounds parallel one another. The changes observed in TZB pharmacokinetics

when administered in combination are related to the fact that both drugs are eliminated by

tubular secretion and since PIP was given in an 8:1 ratio, there is a competitive inhibition

for transport at the renal site in favor of piperacillin.

Renal elimination of tazobactam and piperacillin accounts for 50-60% of the dose

after combined administration (8). Since piperacillin and tazobactam are eliminated

primarily through the kidneys their dosage may be adjusted according to the renal

function. The administration of PIP and TZB to patients with compromised renal function

showed that reduction in creatinine clearance has a greater effect on the total clearance of

tazobactam than on that of piperacillin (55). This is because in normal healthy volunteers

the renal excretion of unchanged TZB is higher than that of PIP. However the difference

between changes in total clearance of TZB and PIP are not of sufficient magnitude to






14

Table 2-1. Pharmacokinetic parameters of tazobactam in healthy volunteers after
administration alone and in combination with piperacillin (means and CV).

No. of Infusion Cmax AUCO-oo CLT Vdss Half- Urinary
Dose (g) subjects time (mg/L) (mg*h/L) (mL/min) (L) life excretion
(min) (h) (%)
TZB 0.1 4 30 5.5 4.1 418 12.8 0.35 60
(25) (22) (22) (17) (18) (42)
TZB 0.25 3 30 14.0 11.7 358 13.1 0.45 71.0
(23) (12) (11) (8) (7) (7)
TZB 0.5 4 30 23.5 20.8 415 14.6 0.44 70.9
(15) (20) (24) (12) (17) (5)
TZB 1.0 3 30 51.0 53.5 327 15.8 0.63 77.0
(6) (29) (26) (11) (32) (9)
PIP 2/ 8 5 16.2 12.4 339 23.2 0.88 65.7
TZB 0.25 (24)a (11) (11) (6) (31) (16)
PIP 4/ 6 30 34.4 41.4 202 12.6 0.78 55.4
TZB 0.5 (6) (4) (4) (7) (9) (14)
Adapted from SOrgel and Kinzig (1993) (8)
aEstimated concentration at the end of 5 min infusion



warrant adjustment of the dose of tazobactam independent of that of piperacillin (55).

Thus, in renal failure the dosage of this combination should be adjusted in the same

manner as adjustments are made for piperacillin alone in renal compromised patients.

An injectable combination product containing piperacillin sodium and tazobactam

sodium was approved by the FDA in 1994 (56-57). This product is available from Lederle

Laboratories under the name of Zosyn. Zosyn is supplied in two different

combinations: PIP and TZB 1:4 (2 g/0.5 g or 3 g/0.375 g) or PIP and TZB 1:8 (4 g/0.5

g). The combination product is indicated for the treatment of moderate to severe infection

caused by P-lactamase-producing strains of microorganisms that are resistant to PIP alone

but are susceptible to the combination of PIP and TZB. Specific indications include

appendicitis and peritonitis caused by E. coli, or Bacteroides spp.; uncomplicated and

complicated infections of the skin and skin structure caused by Staphylococcus aureus;

post-partum endometritis and pelvic inflammatory disease caused by E. coli; and moderate

cases of community acquired pneumonia caused by Haemophilus influenzae. The dosage






15


regimen for this combination varies according to the type and severity of the infection

treated. The dosage of PIP-TZB most commonly recommended in adults and children

(>12 years) with severe infections is 4/0.5 g every 8 hours. For patients who have mild to

moderate infections the recommended dose is 2/0.5 every 8 hours (51).


Microdialysis


The antibiotic concentrations in plasma are indirectly related to the cure of

infections. Only the free drug concentrations present at the site of infection are

responsible for the antiinfective effect. The antibiotics have to distribute from the blood

into the infected tissue in order to be active against microorganisms. Only the free,

unbound fraction of the antibiotic is capable of passing through capillary fenestrations and

can be available to interact with bacteria. Hence, the determination of plasma

pharmacokinetics must be conducted together with the determination of free levels of the

drug in the tissue. Monitoring free antibiotic concentrations in tissue was done in the past

using different techniques that were volume-demanding and traumatic such as fibrin clots,

tissue chambers and skin blister (58-59). These techniques can alter the normal

distribution patterns of the drug in the tissue. Also, due to the large volumes involved,

often times rapid changes in concentrations could not be measured with these techniques.

Microdialysis is a sampling technique which offers some advantages for

pharmacokinetic studies. First, no physiologic disturbance is produced in the investigated

tissue allowing the determination of actual free drug levels observed in normal conditions.

Second, many samples can be withdrawn from the same experimental animal in acute or

chronic experiments since the technique does not produce animal fluid loss. Third, the

method provides the ability to monitor pharmacokinetics in several organs at the same

time using a single experimental animal. Finally, no sample preparation is required prior to

the analysis of the compound of interest. Microdialysis gives direct access to the






16


extracellular fluid in many tissues. For the study of drugs acting on cell surface bound

structures or on extracellular structures such as enzymes or microorganisms, direct access

to the biophase free levels of the drug is obtained (60).

Microdialysis is a technique for measurement of unbound concentrations of

compounds present in the tissue interstitial space that was introduced in 1966 for use in

experimental brain research (61). Many additional contributions were made over the years

in investigations of changing endogenous substance levels due to diseases or special

conditions as well as in monitoring free levels of administered drugs. Microdialysis has

been used to investigate other tissues besides brain such as muscle, adipose and

subcutaneous tissue, liver, lungs, kidneys, and blood in a variety of experiments with

different species of animals in anesthetized or conscious conditions (62-67). The

technique, first restricted to animals, has also been applied to humans. In human studies

endogenous substances such as glycerol (68), amino acids (69) and glucose (70) were

monitored. The pharmacokinetics of exogenous compounds like propranolol (71),

caffeine (72), ethanol (73), acetaminophen and gentamicin (74) have been investigated in

humans by using this technique. Microdialysis in humans was performed in subcutaneous

(68, 70-71, 73,75) and adipose tissues (72), skin (73), muscle (74), and brain (76). The

use ofmicrodialysis as a clinical tool has been reported for the monitoring of plasma levels

of lactate, pyruvate, glucose, creatinine, urea, adenosine, inosine, and hypoxantine in

intensive care patients (77). A method for routine monitoring of disturbances in brain

energy metabolism in patients in the neurosurgical intensive care unit by using

intracerebral microdialysis was also investigated (78).

The potential use ofmicrodialysis in pharmacokinetic studies is not restricted to

the determination of drug concentrations in tissue. This technique can be used to monitor

changes in protein binding of drugs by directly investigating blood levels over a period of

time after drug administration in vivo (79). It can also be used for the determination of

protein binding in vitro. It has been shown that the results obtained with microdialysis are






17


similar to the ones obtained using ultrafiltration for a number of drugs (80). Microdialysis,

however, is not suitable for all compounds, due to their physico-chemical properties and

analytical limitations (81).

The microdialysis technique uses the dialysis principle and consists of a membrane

permeable to water and small solutes which is continuously flushed on one side with a

solution devoid of the substance of interest, whereas the other side faces the interstitial

space. A concentration gradient is created causing diffusion of substances from the

interstitial space into the dialysis probe. The continuous flow through the probe carries

substances to the sampling site for further analysis (61). These samples are devoid of

proteins and can be directly analyzed. On-line analysis of drugs can be performed by

combining microdialysis with mass spectrometry (82) or other analytical equipment such

as capillary eletrophoresis or HPLC.

The microdialysis probe can be of two types having the inlet and outlet tubes in a

serial arrangement or positioned in parallel. The pore size of the dialysis membrane

determines the molecular weight cut off of the compounds entering the probe (83).

The perfusion fluids used for flushing the microdialysis probe vary widely with

respect to composition and pH, depending on the tissue studied. However, they should

always be isotonic with plasma and mimic as much as possible the composition of the fluid

surrounding the tissue under investigation (61, 84).

Since microdialysis is performed under sink conditions, a true equilibrium between

perfusate solution and interstitial space concentrations will never be reached. However,

the concentrations of drugs in the dialysate are proportional to the true free interstitial

concentrations. For quantitative analysis, it is necessary to determine the relative recovery

of the microdialysis probes for specific conditions and drugs. The relative recovery is

defined as the ratio between the concentration in the dialysate and the concentration of the

substance outside the probe (83).






18


The relative recovery is influenced by factors such as temperature, perfusion flow

rate, dialysis membrane area and composition, time after the beginning of the perfusion,

and diffusion coefficient (61, 83). The relative recovery obtained for different substances

using the same microdialysis probe is known to vary. This may be due to difference in the

molecular weight and consequently differences in diffusion coefficients. Furthermore, the

diffusion coefficients are known to increase with temperature increasing consequently the

recovery. For this reason determinations of recovery in vitro should always be performed

at temperatures identical to the tissue (37 o C).

The perfusion flow rate is inversely proportional to the relative recovery.

Increasing the flow rates proportionally decreased the drug concentration in the dialysate.

A compromise has to be achieved between the flow rate and the limit of quantification of

the analytical method used. Flow rates between 1 and 5 Ag/mL are generally acceptable.

The in vitro performance of the microdialysis probe depends on the characteristics
of the semipermeable membrane. Polyacrylonitrile membranes have the highest extraction

in vitro. However, the performance in vivo does not differ significantly for the different

kinds of membranes available (85). The explanation for this finding is that the main factor

limiting extraction in vitro is the membrane resistance to diffusion, whereas in vivo, tissue

resistance to diffusion is the limiting step. In conclusion, in vitro measurements of

microdialysis probe extraction are not a reliable way of calibrating in vivo performance.

As expected, relative recovery is directly proportional to the size of the dialysis membrane

area. By increasing the membrane area, lower concentrations can be detected using

reasonable perfusion flow rates. The increase in membrane area, however, is limited by

the size of the tissue or organ under investigation.

The relative recovery is time dependent (61). Initially, the recovery is high but it
rapidly decreases. This is probably due to a steep concentration gradient across the

dialysis membrane when the probe is first inserted into the tissue. The gradient gradually

declines due to the drainage of the immediate vicinity of the membrane. After perfusion of






19


the probe for about one hour this constitutes a minor factor (< 1%) and can be neglected

for practical purposes (83).

The relative recovery can be determined in vitro and in vivo. The in vitro recovery

is used to estimate the in vivo value. However, the recovery determined in vitro generally

overestimates the free concentration in tissues. This occurs because diffusion rate in

tissues is usually smaller than diffusion in vitro due to tortuosity and limited volume

fraction of the extracellular space (86-88). Hence, the evaluation of the correlation

between in vitro and in vivo recoveries is fundamental in order to accurately determine the

free tissue concentrations.

The most common techniques used for the determination of in vivo recovery are

the extrapolation to zero flow rate method, the point of no net flux method, the slow

perfusion rate method, and the internal reference method (89).

The extrapolation to zero flow rate method was developed in 1985 by Jacobson

and co-workers (90). This method is based on the relationship between recovery and flow

rate. If the tissue concentration is kept constant due to a continuous i.v. infusion of the

drug, changes in perfusion flow rate will produce proportional changes in the relative

recoveries obtained. The free tissue concentration can be estimated by nonlinear

regression to a set ofdialysate concentrations measured at different flow rates. The in

vivo recovery is calculated as the dialysate concentration obtained for one specific flow

rate divided by the tissue concentration estimated by nonlinear regression.

The point of no net flux method was developed by Lonnroth and co-workers in

1987 (75). The method is based on determining mass transport of the analyte across the

microdialysis membrane as a function of perfusate concentration. The experiment is

performed under steady-state conditions obtained by constant i.v. infusion. When the

concentration of the analyte is lower in the perfusate than in the external media, the

direction of diffusion is from the media into the probe. The situation is reversed when the

concentration is higher in the perfusate, in which case the analyte diffuses out of the probe






20


to the external media. The point of no net flux is the condition at which external and

internal concentrations are equal. This point can be determined by linear regression of the

net transport for different perfusate concentrations. Net transport across the membrane is

calculated by subtracting the concentration of analyte recovered in the dialysate from the

concentration that was added to the perfusate solution. The slope of the linear regression

line is equal to the relative recovery. This method is considered by some authors to be one

of the most adequate and precise methods to determine true interstitial concentrations (91-

93). The disadvantage of this method, as well as of the previous one described, is the

amount of time necessary to calibrated the probe. For four different flow rates or four

different concentrations in the perfusate solution at least 8 to nine hours of experiment are

needed for the calibration of a single probe. This fact limits the application of these two

methods as a routine calibration procedure for every microdialysis probe.

The slow perfusion rate method was proposed by Menacherry and co-workers in

1992. The method is based on the fact that at very slow perfusion rate the concentration

of analyte in the dialysate is near equilibrium with the external concentration (91). While

theoretically it would require zero flow rate for concentrations to equilibrate, in practice

better than 90% efficiency is obtained at slow perfusion rates around 50 nL/min. The in

vivo concentration estimated at this very low rate is used to establish the relative recovery

at other flow rates. Although this method is less time consuming than the other two

described previously, some major drawbacks are associated to it such as: lack of sufficient

sample for analysis, sample evaporation during long collection times, and difficulties in

obtaining a reliable constant flow rate.

The three methods described so far require the calibration of the microdialysis

probe previous to the actual experiment to determine the pharmacokinetics of the drug

under investigation. Retrodialysis is a method that allows for continuous assessment of

recovery in vivo during the study period (94-95). Retrodialysis involves the measurement

of diffusive loss of molecules (retrodialysis calibrator or internal standard) from the






21


perfusate solution into the environment surrounding the probe, under sink conditions. The

drug under investigation and the calibrator should have similar physico-chemical

properties to assure similar diffusion characteristics. The relative loss, by analogy to the

relative recovery, is the ratio of calibrator concentration difference between perfusate and

dialysate over the perfusate concentration. A similar concept was developed in 1991 by

Scheller and Kolb for the internal reference method (96). In this approach the calibrator is

the labeled form of the compound of interest. Both methods assume that the diffusion of

the analyte across the microdialysis membrane is not altered by the diffusion of the

calibrator and vice-versa. Retodialysis (74) and the method of no net flux (71) have been

used for in vivo probe calibration in human experiments.

Free tissue concentrations of 1-lactam antibiotics were investigated by

microdialysis by Deguchi and co-workers (69). The purpose of the study was to

demonstrate the rapid equilibration between vascular and extravascular concentrations of

free drug. Two 1-lactam antibiotics were investigated in rats: SY5555, a penem

antibiotic, and cefminox, a cephalosporin. Total tissue levels for lung, muscle and liver

were determined and compared with free levels determined by microdialysis. The results

showed that total levels can vary significantly according to the type of tissue investigated.

The free tissue levels, however, were similar for all three different tissues studied. The

results illustrate that total drug levels should not be used to compare or design dosing

regimens since they do not reflect the active concentrations at the site of action.

In a study using piperacillin alone some of the issues related to use of microdialysis

for determination of free tissue concentrations were addressed (97). It was shown that the

microdialysis probe recovery is constant for different external concentrations and that the

probes are capable of responding swiftly to changes in the outside concentrations. It was
also shown that under the investigated conditions PIP relative recovery in vitro was

equivalent to the in vivo recovery determined in rat muscle using the point of no net flux

method. Therefore, for piperacillin the in vitro recovery could be used as a good






22


approximation of the in vivo recovery. The pharmacokinetic results from the study

demonstrated that piperacillin concentration-time profiles after i.v. bolus administration

can be fitted to a two compartment body model. The distribution of the drug between

central and peripheral compartments is a diffusion driven process. Finally, it was shown

that free concentrations in the interstitial fluid measured by microdialysis can be predicted

from pharmacokinetic parameters of the drug estimated from plasma data.

In summary, the knowledge of free drug concentrations at the site of action is very

important for pharmacodynamic studies since it is the free drug that exerts the

pharmacological effect. Pharmacological effects based on total plasma levels would be

overestimated because the pharmacologically inactive fraction of the drug is also being

considered. Microdialysis allows for the investigation of free tissue levels of drugs

without disturbing the physiological conditions. Its application to pharmacokinetic studies

has a great potential. The use of free drug levels in a PK-PD model should result in better

predictions of the bactericidal effect for different doses and dosing regimens compared to
the predictions obtained using total drug concentrations.


In vitro Models to Assess Antibacterial Activity

Unlike other diseases, the causative agent of many infections can be isolated from

the patient and its interaction with drugs can be studied in vitro (98). The efficacy of

antibiotics studied in vitro does not necessarily translate into efficacy in patients. On the

other hand, comparisons of treatments for bacterial infections in patients is difficult

because outcomes are a function of multiple variables related to the microorganism, drug

administered and patient general conditions. The use of volunteers for this type of study is

limited for ethical reasons. The use of animal models has also been investigated. The

drawback of animal models is the fact that they do not often truly reflect human

pharmacokinetics. Pharmacokinetic parameters like volume of distribution, elimination






23


rates or protein binding may vary considerably among species. Elimination half-lives of

most antibiotics are much shorter in animals than in humans (99). Therefore, animal

models may suggest optimal dosing regimens for antibiotics that are not applicable to

human therapy.

Several in vitro models have been developed over the years in an attempt to

determine antiinfective activity of single or combined drugs, to compare doses and dosing

regimens, to compare new and older drugs, and to optimize therapy in preclinical studies.

In vitro models can closely mimic infections observed in neutropenic patients because they

permit the study of interactions of bacteria and antibiotic without the presence of host

defense. In vitro models of infections offer some advantages over animal models in the

study of antibiotic efficacy. In these models many variables that occur during treatment

can be independently evaluated. Effect of dosing, pharmacokinetics and culture conditions

can be analyzed outside the host (99). Furthermore, the use of in vitro models may reduce

the number of animals required for drug dosage investigations.

Commonly used parameters to quantify the activity of antibiotics against a certain

bacteria are the minimum inhibitory concentration (MIC), the minimum bactericidal

concentration (MBC), and the minimum antibiotic concentration (MAC). The MIC is

defined as the minimum concentration that prevents visible growth, i.e., zero net change in

the number of organisms over time. The MIC only estimates the growth inhibition and its

efficacy in vivo relies on the host immune system to eradicate the pathogen. The MBC is

the minimum antibiotic concentration that kills 99.9% of the original number of bacteria.

Hence, the MBC reflects not only the antibiotic ability to inhibit growth but also its killing

effect. It is used to assess antiinfective activity in clinical situations where the host

immune system is less effective in eradicating the pathogen, such as endocarditis,

osteomyelitis, meningitis, and infections in neutropenic patients (2). The MAC is the

smallest concentration found in vitro that exhibits any influence on the rate of growth of

bacteria when compared with control cultures without antibiotic. The MAC may be many






24


times lower than the MIC proving the assumption that the MIC value is a threshold for

antibiotic bacterial activity is not valid (2).

When the MIC and the MBC of an antibiotic have similar order of magnitude the

agent is called bactericidal. Drugs included in this class are 3-lactam antibiotics,

aminoglycosides, and quinolones. When the antibiotic does not produce a reliable

bactericidal effect at concentrations close to the MIC it is called bacteriostatic. In this

situations the MBC can largely exceed the MIC. Examples of this class are macrolides,

tetracyclines, and chloramphenicol. Because the MBC is not routinely determined,

bacteriostatic drugs are avoided when treating infections where bactericidal activity is

required (2). The MIC, the MBC, and the MAC are determined under standardized

conditions using constant drug concentrations. However, the constancy of drug levels

does not reflect the in vivo situation where the bacteria are exposed to fluctuating

concentrations due to the metabolism and elimination in the body. For this reason, some

in vitro systems were developed in order to simulate more closely the in vivo conditions

and to better characterize the antiinfective effect.

The in vitro models can be divided into three groups according to the way drug

concentrations are investigated: the first group investigates the bacterial behavior under

constant concentration of the antibiotics, the second group simulates changing drug

concentration by means of dilution, and the third group uses diffusion or dialysis as the

mechanism to simulate fluctuating antibiotic concentrations. Since the MIC only reflects

the bacterial activity at one specific concentration and time (18-24 h), some investigators

studied the antibacterial effect of bacteriostatic and bactericidal drugs by exposing bacteria

to constant drug concentrations and collecting samples at specific intervals over a period

of time (100-102). From the killing curves obtained (in presence of drug) compared to the

control (growth rate curves), it was possible to mathematically describe the activity of the

antibiotic. Any change in the normal first-order growth rate constant observed in the

absence of the drug would be due to the presence of the antibiotic and will produce a new






25


apparent growth rate constant for the bacteria (kapp). These apparent growth rate

constants for bacteriostatic antibiotics were described mathematically and classified into

four classes according to Garrett (103). Class I interactions describe antibiotic activity

using a linear relationship between kapp and drug concentration. In Class II interactions

the apparent growth rate (kapp) decreases with increasing drug concentration to

asymptotically approach zero. Class III interactions are characterized by a Class I

behavior at low antibiotic concentrations and decreasing rates of change in kapp at higher

concentrations. Class IV interactions show S-shaped plots of kapp vs. drug concentration

probably due to drug binding to nutrients at low concentrations.

For bactericidal drugs (such as P-lactam antibiotics) the kapp may assume negative

values because killing is induced above certain concentrations. The killing rate shows a

linear relationship with the difference between the actual drug concentration and the

minimum drug concentrations necessary to produce effect (104). The killing effect shows

a lag time due to the relatively slow onset of full bactericidal activity presented by these

antibiotics. Mattie and co-workers (105-108) used another mathematical approach to

describe the observed effect. Growth curves in the presence of antibiotic were described

as a quadratic function of time, with initial growth rates and killing rates as concentration-

dependent variables. Since the growth rate is assumed constant, the killing rates depend

only on drug concentration.

Although it was possible to mathematically describe the effect of antibiotics against

bacteria when exposed to constant concentrations, the correlation of this result to the in

vivo situation was not possible. In clinical treatment of infections in patients, bacteria are

exposed to continuously changing antibiotic concentration. Various designs of in vitro

models have been proposed to expose bacteria to changing antiinfective concentrations.

These models try to simulate the concentration-time profiles of antibiotics using

pharmacokinetic parameters of the drug observed in humans.






26


The simplest technique used to simulate the continuous change in concentration

patterns which occurs in vivo is the stepwise dilution. In these experiments bacteria are

exposed to drug concentrations which approximate the concentration-time curves in

human serum seen during clinical therapy. The bacterial inoculum is incubated with an

antibiotic concentration that is kept constant for a while, then diluted according to the

half-life of the drug, incubated again and so on. The smaller the dilution step the closer

the model simulates the drug elimination profile observed in vivo. The bacteria can either

be diluted with the dilution steps used for the drug (109) or remain undiluted due to use of

filters (4). Stepwise dilutions are time consuming. On the other hand, the technique is

simple to perform and does not require pumps to simulate different concentration profiles.

A model that reproduced more closely the serum kinetics of the antibiotics was

first described by Sanfilippo and co-workers in 1968 (110). In this model, a dose of the

antibiotic was injected into the culture flask when bacterial inoculum was in the log-

growth phase. Sterile plain broth solution was pumped at a fixed rate into the flask,

diluting the antibiotic in a linear fashion. The volume of the culture flask increased during

the experiment causing the dilution of the antibiotic as well as the bacterial inoculum. This

dilution method is able to simulate any concentration-time profile, however when the

difference between peak and trough is 10 to 100-fold within one dosing interval, the

culture volume has to be expanded in the same way, which creates a practical problem.

Grasso and co-workers described in 1978 a one-compartment open model that

simulated the pharmacokinetics of drugs after intravenous administration (111). The same

dilution method was used as described previously. Two flasks were connected by tubing

to a peristaltic pump. From the reservoir flask sterile broth solution was pumped at a

constant rate into the flask that contained bacteria and drug. The flask that contained the

culture was connected to a vessel to collect the excess fluid resulting from the dilution.

The antibiotic concentrations decreased exponentially in the culture flask simulating the

half-life of the antibiotic in human serum. The initial antibiotic concentration in the system






27


was calculated to mimic the peak concentration of the drug expected for the dose under

investigation. Grasso also introduced a modification of this model in order to simulate

first order absorption kinetics as it would be obtained after oral or intramuscular

administration (111). In this model, a third flask that contains the antibiotic solution was

placed between the reservoir of plain broth solution and the culture flask. The antibiotic

solution is pumped into the culture flask simulating the absorption rate constant of the

drug. The concentration in the culture flask increases until a maximum when it equals the

concentration in the antibiotic flask. Eventually the concentration in the culture flask

decreases exponentially. Bergan and co-workers introduced a modification of the method

by adapting a photometer in the path of the antibiotic-bacteria mixture to continuously

measure the bacterial level by turbidity (112-114). In this way the bacterial plating and

counting for determination of colony forming units (CFU) was not necessary. These

dilution models, with small modifications, were used by several investigators (115-117).

Ledergerber and co-workers modified the Grasso model by introducing computer drive

control to apply the appropriate antibiotic infusion rate and to record the turbidity (117).

The major drawback of these dilution methods is that the bacterial inoculum is diluted

with the antibiotic. When the dilution rate constant is lower than the bacterial growth

rate, the growth curve does not differ substantially from that observed in a static situation

(111). However, when the dilution rate is higher than the bacterial growth rate the

artificially increased bacterial clearance has to be taken into account. Some authors have

proposed equations to mathematically correct the bacterial count (118-119). It is

important to mention that the effect of dilution can be corrected mathematically only if the

cultures are increasing or decreasing exponentially.

In order to overcome the bacterial dilution problem some authors modified the

one-compartment model to include a filter that keeps the bacteria within the cell culture

(120). Al-Asadi and co-workers proposed the use of two glass tubes connected by a

cellulose acetate membrane (121). One tube had the bacteria in the log-growth phase and






28


the other tube had the antibiotic solution. The antibiotic is allowed to diffuse into the

compartment containing the bacteria. To reverse the diffusion process, broth solution was

pumped into the compartment containing the culture. This created a flow of broth across

the membrane into the antibiotic-containing compartment from which accumulated broth

was continuously removed by a second pump. Because of the flow across the membrane

the half-life of the drug could be simulated and the bacterial inoculum remained essentially

constant. The disadvantage of using filters is that they tend to clog after some time due to

the presence of increasing inoculum or debris produced by the bacteria multiplication

making it difficult to control a constant infusion rate using pumps (99).

All the models described so far simulate the elimination of the drug following a

monoexponential profile. However, some antibiotics show a short distribution phase

followed by a longer elimination phase. To closely mimic the biexponential decline of

serum kinetics following intravenous administrations Murakawa and co-workers

introduced a two compartment model that utilizes a bi-directional flow between the central

and peripheral compartments (122). At the beginning of the experiment antibiotic and

bacteria are placed into the central compartment. Due to continuous mixing of the

contents of the central and peripheral compartment, as well as dilution of the central

compartment with plain broth solution, a biexponential decline of the drug in the central

compartment is achieved. Bacteria are diluted out of the central compartment into the

peripheral compartment and out of the system. The dilution of the bacterial inoculum has

to be corrected mathematically.

In the one-compartment model bacteria are exposed to serum concentration-time

profiles observed in humans. However, except for septicemia, the site of infection is the

tissue water. It is more relevant then to simulate concentration-time profiles that mimic

those observed in interstitial fluid or tissue rather than in serum. The diffusion models are

basically two-compartment models. The bacteria are kept at constant inoculum in the

"tissue" compartment and the drug is diluted in the "central" compartment simulating the






29


half-life of the antibiotic. A membrane is used to separate the two compartments. The

antibiotic has to diffuse from the "central" to the peripheral "compartment" simulating in

this way the build up as well as the elimination of the drug in the tissue. Using the

diffusion principle several models were described in the literature (123-127). The main

problem with some of these models were the large volumes that were necessary in order

to reproduce the kinetics of the drug. A more sophisticated model was devised by Blaser

and co-workers in 1985 (128). The extravascular infection sites are represented by

artificial capillary units which contain the bacterial cultures within the peripheral

compartments. The capillary unit consists of a plastic shell through which runs a bundle of

150 artificial capillaries. The capillaries are hollow fibers ofpolysulfone with porous walls

acting as membranes. The peripheral compartment interfaces with the central

compartment through the porous capillary walls which allow for bi-directional penetration

of antibiotics but prevent the passage of bacteria. Bacteria are placed into the outer

chamber of the capillary unit. Several capillary units are placed in series and are connected

with plastic tubing to the central compartment which consists of the central reservoir plus

the lumen of the capillaries and the tubing connecting the units. The antibiotic is

administered into the central compartment. The antibiotic-broth is continuously pumped

through the capillaries and penetrates into the peripheral chambers containing bacteria.

Sterile plain broth is continuously pumped into the central compartment at a flow rate set

to simulate the elimination half-life of the drug in humans. The volume of the central

compartment remains constant but the concentration changes over time. The volume of

the peripheral compartment is in general 10 mL. Samples are withdrawn from the

peripheral compartment for bacteria counting. This model can be used to simulate

continuous and intermittent administration of drugs (129). It can be also used to simulate

oral or intramuscular administration of an antibiotic by inserting an absorption chamber

before the central compartment (130). One of the main advantages of this model is the

possibility of studying combinations of antibiotics with different half-lives (131-136).






30


More specific models were developed over the years in order to simulate in vivo

conditions observed in special infection sites. Some examples of these models are the

artificial bladder model (137), the model used to simulate acute otitis media (138), and the

in vitro pharmacodynamic model of endocarditis (139). To study the treatment of

infections in implants in vitro models were devised to investigate the activity of

antimicrobials not only on suspended bacteria but also on the biofilm formed by adherent

bacteria (140-141).

Although some in vitro models were designed considering the fact that most of the

infections occur in the interstitial fluid, few investigators realized that only the free

concentration present in the tissue is available to produce antiinfective effect. The first

researcher to address the problem of protein binding in in vitro infection models was Lintz

(142). This author derived equations to predict total and free tissue concentrations and

showed that in vitro simulations of total plasma concentrations and even total tissue

concentrations would expose the bacteria to much higher levels of the antibiotics than

those obtained in interstitial fluid. This could explain why some in vitro predictions of

activity did not correspond to the clinical outcome observed in patients (142). To what

extent protein binding affects the antibiotic activity is an issue for discussion. Some

authors consider that only protein binding higher than 80% can cause a significant

difference in the drug activity (143). Some experiments in vitro showed that differences in

the effect time course can be observed between simulations of total serum concentrations

and free interstitial concentrations for the same antibiotic even when the protein binding is

lower than 80% (116). The results of a study to determine the importance of extracellular

protein binding with highly protein-bound drugs suggested that the onset of antibacterial

effect for this kind of drugs is delayed in the presence of proteins in the site of infection.

On the other hand, a more prolonged effect after the cessation of the treatment can be

observed since drug concentrations tend to decline more slowly under these conditions






31


(144). How these differences observed in vitro affect the in vivo outcome of infections is

still to be determined.

Few experiments were design to assess the host defense mechanisms in the

presence of oscillating drug concentrations against bacterial cultures. Shah studied the

activity of imipenem against Gram-negative bacteria using human blood as culture media

instead of broth solution (145). The effect ofenoxacin against S. aureus in the presence

or absence ofleukocytes was studied by Blaser and co-workers using the two-

compartment capillary model (99). The presence of leukocytes increased bacterial killing

ten times after the first two hours but no significant difference was observed after six

hours. Leukocyte administration was more effective when given after six hours of

antibiotic administration. These findings are consistent with more recent studies showing

enhanced leukocyte killing against resistant bacterial subpopulations which were selected

during exposure to aminoglycosides and quinolones in conventional in vitro experiments

(146). The mechanism by which preexposure to antibiotics influences leukocyte bacterial

killing is not clear although potentiation ofopsonization is a possibility (146). The

increased leukocyte activity seems to be linked to bacterial resistance. Subinhibitory

concentrations of antibiotics can induce morphological and biochemical changes in

bacteria which might render these organisms more vulnerable to leukocytes. These

resistant organisms should not represent a problem to the immune competent hosts.

However the use of aminoglycosides alone in immune compromised patients may not

result in successful therapy. Conventional in vitro models do not address these kind of

problems because in general they test the antibiotic effect in the absence of host defense

which represents a greater challenge to their antibacterial activity compared to the in vivo

situation. However, the example illustrates the importance of careful analysis of the in

vitro results when making extrapolations to in vivo situations.

The result of the in vitro experiment is the determination of viable bacteria as a

function of time and the influence of the antibiotic administered on the microorganism






32


kinetics. Different methods can be used to follow bacteria multiplication or death. The

turbidity method relies on the good correlation between the optical density of a suspension

and the number of particles per unit volume (113). A refinement of this approach is to use

a Coulter counter to count the actual number of particles. Both methods are not very

reliable because the number of particles counted may not represent the number of viable

microorganisms. Furthermore, it is not clear whether the change in the form of the

bacteria that have been exposed to antibiotics results in a change in their optical qualities

(108). To overcome this problem it was suggested that the total living bacterial cell mass

could be estimated by measuring the intracellular adenosine triphosphate (ATP).

Although this method has been used for measuring the effect of antibiotics on bacterial

growth some data published showed that antibiotics profoundly affect the ATP content of

live microorganisms (108). Because of this consideration the counting of the live

microorganism as colony forming units (CFU) remains the more reliable method for

determining bacterial viability in the presence of bactericidal drugs (108) whereas the

photometry is a suitable alternative when studying bacteriostatic agents (113).

The in vitro models discussed here simulate infections in neutropenic patients and

can be used for preclinical studies with antibiotics, studies of optimal dosing and dosing

regimen, effect of specific factors like protein binding and post-antibiotic effect as well as

antibiotic combinations. These models cannot replace the in vivo animal models or the

clinical investigation of antibiotic activities, but they allow a reduction of such experiments

and may complement assessment of antibiotic activity. Discrepancies between in vitro and

in vivo results may be due to numerous causes: differences in bacterial growth rate in vitro

and in vivo, difference in medium composition and limitation of some substract for

bacterial growth in vitro, the fact that in vitro experiments bacteria are floating in the

medium in opposition to some in vivo situation where bacteria can adhere to implants or

other structures, differences in temperature maintained for the in vitro studies, changes in

the morphology and physiology of the microorganism in order to adapt to the in vitro






33


conditions among others (147). One has always to keep in mind that the in vitro models

of infection are very useful to investigate the interaction between bacteria and antibiotic

but extrapolation of the results to in vivo situations has to be made with great care.

An in vitro model was devised in our group to study the pharmacodynamic effect

of piperacillin alone against E. coli following administration of constant or fluctuating

concentrations (4). A one-compartment in vitro model was used to simulate only the free

interstitial concentrations obtained in humans after different doses and dosing regimens.

The free tissue concentrations were estimated based on human plasma pharmacokinetics.

To simulate drug elimination, broth solution containing piperacillin and the bacteria was

withdrawn through sterile filters and replaced by free sterile broth. In this way the

antibiotic half-life was simulated in a stepwise fashion. The number of bacteria was not

affected by the withdrawal of samples due to the use of the sterile filter. The number of

viable cells was determined by counting the CFU after overnight incubation. This in vitro

model will be used for this project in order to allow the comparison of different dosing

regimens of PIP and TZB.



PK-PD Modeling of Antiinfective Agents

The appropriate selection and use of an antimicrobial agent is based on

characteristics of the infection, the host, and the antiinfective agent (148). Important

features of the infection are the characteristics of the infecting agent and its susceptibility

to the antimicrobial agent. Important information about the host are the site of infection,

the host immune status and the host's general ability to absorb and metabolize drugs.

With respect to the drug two aspects have to be considered: its pharmacokinetic

properties such as absorption, distribution into the infected tissues, and elimination, and

its pharmacodynamic features such as mechanism of action, the cidal or static nature of the

antimicrobial effect and the rate at which it occurs. An approach that incorporates all






34


these factors in designing the best therapy is currently not available. An important step in

this direction is the combination of the pharmacokinetic and pharmacodynamic properties

of the antibiotic in order to predict the outcome of a specific therapy.

The pharmacokinetic parameters used to characterize the time course of the

antibiotic concentration in plasma include the area under the curve (AUC), the peak

concentration and the half-life. The duration of time that the plasma concentration

exceeds a threshold value, generally the MIC, is also used (t > MIC). The AUC, the peak

level over MIC and the t > MIC are dose and dosing interval dependent parameters. For a

given total daily dose the AUC over 24 h is independent of the administration schedule.

The same daily dose given at longer dosing intervals will result in larger peak/MIC ratios

but smaller t > MIC periods of time. The opposite will occur when smaller doses are

administered more frequently. The difference observed with different dosing schedules

will be most marked with drugs with short half-lives.

As discussed previously, parameters commonly used to quantify the activity of

antiinfective agents are the MIC and the MBC. These measurements of activity are

inadequate to completely characterize an antibiotic's pharmacodynamic properties because

they reflect the net drug effect following a fixed time of incubation The result is often

viewed as a yes or no phenomena: growth vs. no growth, killing vs. no killing. These

parameters do not account for the time course of the antimicrobial activity.

Another pharmacodynamic parameter used to describe the activity of antibiotic

after its removal from the in vitro system is the postantibiotic effect (PAE) (149). It is

defined as the delay in bacterial regrowth which occurs as a result of transient antibiotic

exposure after the removal of the antimicrobial (2). The PAE is observed with almost all

antibiotics. However, not all antimicrobial agent produce a PAE with all microorganisms.

In general, antibiotics for which the mechanism of action is related to protein synthesis or

inhibition of DNA or RNA synthesis exert PAE with most bacteria. Some examples are

aminoglycosides, quinolones and chloramphenicol. Inhibitors of cell wall synthesis such as






35


p-lactams antibiotics may produce PAE with some Gram-positive stains, but rarely

produce PAE with Gram-negative bacteria. The PAE is considered an important

parameter in designing dosing regimens. The presence of PAE for an antibiotic implies

that the infrequent dosing resulting in temporary very low levels of the drug is possible

without compromising drug efficacy.

Based on these pharmacokinetic and pharmacodynamic parameters and

experimental results from animal and in vitro studies the antibiotics are generally referred

to as concentration-dependent or time-dependent agents (3). When the contribution on

the killing process is more affected by increasing the peak/MIC ratio than by prolonging

the exposure time of the bacteria to the antibiotic, the antiinfective agent is called

concentration dependent (150). These antibiotics have relatively long PAEs. The

relationship observed between efficacy and the period that the drug concentration remains

above the MIC (t > MIC) is less significant than the pronounced killing effect observed

with high dose. The antibiotics in this group are aminoglycosides and fluoroquinolones.

In an attempt to maximize the peak/MIC ratio, the concept of once a day administration

for aminoglycosides has evolved (151). Avoidance of toxicity provides additional

incentive for less-frequent administration of aminoglycosides (152).

Some antiinfective agents such as P-lactmas and vancomycin appear to have a

different bacterial killing profile. Apparently when the concentration exceeds a critical

value 4 to 5 times the MIC), killing proceeds at zero order rate, and increasing drug

concentration does not result in a proportional change in the microbial death rate (3).

These antibiotics are called concentration-independent or time-dependent. For them the

most important PK-PD relationship is the t > MIC. If the dosing interval for these drugs

is short in relationship to their half-lives, the t > MIC will be maximized, as will bacterial

eradication. Some strategies for achieving this goal are using frequent dosing of the

antibiotic or administering the antibiotic by continuous infusion (153-154). The

applicability of constant infusion as the optimal method for the administration of P-lactam






36


antibiotics has to be clinically investigated with respect to emergence of bacterial

resistance, incidence of side effects and patient outcome (154). The prediction of the best

antibiotic dosing interval by adding up the expected t > MIC (based on the dose and the

antibiotic pharmacokinetics and the MIC) and the PAE (when quantifiable) was also

suggest in the literature (155).

Although the PK-PD correlations are used presently to better dose antibiotics

(156), the approaches are still more descriptive than predictive of the antiinfective activity.

An attempt to obtain a general method to optimize the dosing schedules for the treatment

of infections with (3-lactam antibiotics, quinolones or aminoglycosides was proposed by

Schentag and co-workers (157). They postulated a target value of 125 h for the area

under the inhibitory curve (AUIC) over 24 hours. The AUIC can be easily calculated as

the ratio of 24-hours AUC (for time points with respective concentrations above the MIC)

and the MIC. In a systematic evaluation of this approach we showed that different serum

concentration profiles can result in the same AUIC although some of the dosing regimens

are known to be ineffective (158). We also derived a precise equation for the calculation

of AUIC and showed that for the situation when the trough concentration at the end of the

dosing interval equals the MIC, the AUIC is independent of the MIC, dose and drug

concentration in serum and it is determined only by the half-life of the drug, the time of

infusion and the dosing interval. Consequently, it does not seem valid to accept any single

AUIC target breakpoint for the dosing of antibiotics in these three classes investigated.

The need to devise a better approach to compare and optimize antibiotic doses and

dosing regimens is obvious. An important contribution to this end is the combination of

pharmacokinetics and pharmacodynamic properties of the antibiotic in a PK-PD model.

By using this approach more detailed information can be obtained about the time course of

the antimicrobial effect. A systematic comparison of different dosing regimens can be

obtained and predictions can be made about the efficacy of treatments prior to clinical

testing.






37


Pharmacokinetic/pharmacodynamic modeling is used to describe the effect of a

drug as a function of time, where the pharmacokinetic part gives information about the

concentration-time profile of the drug in the body, and the pharmacodynamic part offers
information about the concentration-effect relationship. The known relationship between

dose, concentration of the drug in plasma, and drug effects may be used as a starting point

in dosage individualization.

Some of the pharmacodynamic models described in the literature are the fixed-
effect model, the linear model, the log-linear model, the Eax-model and the sigmoid-Emax"

model (159). These models can also be used as a starting point to develop more complex

and sophisticated structures in order to describe the data. The fixed effect model is that

where the observed effect is either present or absent. The degree of the effect is not

important, rather the critical element is whether or not the effect occurs. The linear model

describes an effect that is directly proportional to drug concentration. This model,

however, lacks the ability to define the maximum effect. The log-linear model describes

an effect that is directly proportional to the log of the concentration. It has the same

restrictions as the linear model. The Emax -model is the simplest model that describes

drug effect over the whole range of concentrations by a hyperbolic relationship. This

model has two important properties: it predicts the maximum effect a drug can achieve
and it predicts no effect when drug is absent. The sigmoid-Emax -model is a variation of

the Emax-model where the effect/concentration curve cannot be described by a simple

hyperbolic form. In this case a parameter has to be added to the traditional Emax-model

to account for the different slopes of the curve.

The most common approach to link the PK and PD parts of the model is usually
the use of an effect compartment (160). This approach assumes that the drug enters and

leaves the effect site by first order process. Using this approach the effect compartment is

allowed to float during the fitting process to make both data sets match ("soft link") (161).

Another approach described is the "hard link" model which allows a true prediction of the






38


pharmacodynamic data based on the pharmacokinetic data and information from in vitro

studies (161) (bacterial killing rates in this case). In this way, the pharmacodynamic data

is not used for the characterization of the model but it is predicted. A further and

important step when using this approach is to validate the model with pharmacodynamic

data obtained from studies with patients.

A modified Emax-model was derived to describe the bactericidal effect of

piperacillin against E. coli in vitro simulations of free fluctuating concentrations expected

in human tissue after i.v. bolus administration (4). A set of parameters were derived which

allowed the simulation of the bactericidal effects of any given dose or dosing regimen.

The same model will be investigated to describe the antimicrobial effect of PIP-TZB

combinations in the present study.















CHAPTER 3
ANALYTICAL DETERMINATION OF PIPERACILLIN AND TAZOBACTAM


Specific Aims of the Analytical Studies


The specific aims of the analytical studies were to develop a sensitive and specific

assay to quantify tazobactam in rat plasma and in microdialysis dialysate, and to study the

stability oftazobactam in different media: water, phosphate buffer, rat plasma, rat plasma

filtrate, and Miiller-Hinton Broth solution (MHB) in the presence and absence of E. coli

ATCC 25922.


Material and Methods



Drug Assay

The assay for determination of TZB in biological fluids by HPLC was developed

based on previously published procedures (162-163). The HPLC assay used for PIP was

previously described (97).


Chemicals and Reagents

Piperacillin, p-aminobenzoic acid polyester were purchased from Sigma Chemical

Company (St. Louis, MO), and used as received. Tazobactam was donated by Lederle

(Divisional Laboratory, Cyanamid of Great Britain, Hampshire, England). Antipyrine was

purchased from Aldrich Chemical Company (Milwaukee, WI). HPLC grade acetonitrile

and tetrabutylammonium hydroxide (TBA) were purchased from Fisher Scientific (Fair




39






40


Lawn, NJ). All other reagents were of analytical grade and purchased from Fisher

Scientific.


Instrumentation

The chromatographic system consisted of a Constametric III G high pressure

pump (LDC Milton Roy, Riviera Beach, FL), a Perkin Elmer auto sampler (model ISS-
100, Norwalk, CT), fitted with a 100 [LL injection loop, a 15 cm x 4.6. mm i.d., 5 Ptm

particle size Spherisorb C18 column (PhaseSep, Quensferry, UK), a UV LDC Milton Roy

detector (Riviera Beach, FL), and a Hewlett Packard integrator (model 3392A, Palo Alto,

CA). A pre-column filled with ODS packing material was placed before the analytical

column.


TZB Sample Preparation

To 100 tL of rat plasma 500 plL of ice cold acetonitrile with 1% of formic acid 0.5

M and 50 IlL ofantipyrine 2 mg/mL (internal standard) were added. This step was

performed in an ice bath. The mixture was vortexed for 10 seconds and then centrifuged

at 3000 rpm for 20 min. The supernatant was evaporated to dryness under nitrogen. The

residue was reconstituted in 200 pL of water and 100 IL were injected into the HPLC

system. Tissue samples obtained by microdialysis were injected directly using a manual

injector with a 20 uL loop.


TZB Chromatographic Conditions

TZB was analyzed using an ion pair reversed phase HPLC system. The mobile

phase consisted of a mixture of 5 mM TBA, 0.04 M sodium phosphate monobasic

solution and acetonitrile (46.5:46.5:7 % V:V). The pH was adjusted to 6.6. The mobile

phase was filtered through a 0.2 mm nylon filter and degassed by sonication before use.






41


The flow rate was 1 mL/min and the wave length used for detection was 220 nm. Typical

blank plasma and TZB chromatograms obtained after extraction are shown in Figure 3-la.


PIP Sample Preparation

To 100 pL of rat plasma 200 .tL of methanol containing 15 .g/mL ofp-

aminobenzoic acid propylester (internal standard) were added. The mixture was vortexed

for 15 seconds and subsequently centrifuged at 3000 rpm for 15 min. An aliquot of 100

jiL of the supernatant was injected into the HPLC system. Tissue samples from

microdialysis were injected directly using a manual injector with a 20 liL loop.


PIP Chromatographic Conditions

For PIP analysis, reversed phase chromatography was performed. The mobile

phase consisted of 0.05 M phosphate buffer and acetonitrile (80:20 % V:V). The pH was

adjusted to 7. The mobile phase was filtered and degassed as described for TZB mobile

phase. The flow rate was 1 mL/min and the UV detection was also performed at 220 nm.

Figure 3-1b. shows a typical PIP chromatogram after extraction and the respective blank

plasma chromatogram.


Assay Validation


Both assays described above were validated in plasma by preparing three

calibration curves each day for three different days and analyzing quality control samples.

For TZB a linear calibration curve could be obtained for peak height ratio in the range of 3

to 200 Ig/mL. For PIP a linear calibration curve could be obtained for peak area ratio in

the range of 2 to 500 tg/mL. In both cases the correlation coefficients obtained were

0.996 or more. Inter- and intraday variability were determined by using four different






42


quality control concentrations for TZB (3, 30, 75 and 150 .tg/mL) and three for PIP (30,

100 and 300 I.g/mL).









S13.04










a b

Figure 3-1. Representative chromatograms of tazobactam and piperacillin in rat plasma: a)
shows blank plasma and tazobactam (RT 6.54 min) with internal standard (RT
11.70 min); b) shows blank plasma and piperacillin (RT 6.09 min) with
internal standard (RT 13.04 min).




TZB Stability Studies


The stability of TZB was determined in different media and conditions. Wistar rat

plasma was spiked with TZB to obtain a final concentration of 100 gg/mL and kept at

room temperature or at 37 C up to three hours. Aliquots (100 gL) were taken at time

zero, 15, 30, 60, 90, 120 and 180 min and immediately analyzed using the analytical

method described above. The stability of TZB in rat plasma filtrate was investigated at

room temperature. Rat plasma filtrate was obtained by ultracentrifugation of untreated






43


plasma using an ultra-microcentrifuge tube filter unit (PGC Scientifics, Gaiterburg, MD)

with a molecular weight cut off of 5000 D. Centrifugation was performed in an

ultracentrifuge (Marathon 13K/M, Fisher, Fair Lawn, NJ) at 4500 rpm for 20 min. The

rat plasma filtrate was spiked with TZB to obtain a final concentration of 100 pig/mL.

Samples (100 tL) were taken at time zero, 5, 10, 15, 30 and 60 min. The filtrate was

analyzed using the same method described for blood samples. All the experiments for the

stability studies were replicated three times.

TZB stability was also determined in water, phosphate buffer 0.05 M pH 7 and

Miller-Hinton Broth solution (MHB). Solutions containing TZB at final concentrations

of 100 lg/mL were prepared in water and phosphate buffer and kept at 4 o C for 72 h.

Samples (100 pL) were taken at time zero, 1, 2, 3, 24, 48 and 72 h and analyzed by

HPLC. The stability of TZB in MHB was checked at 37 C in presence or absence of

Escherichia coli ATCC 25922 (piperacillin sensitive, 3-lactamase negative). TZB was

dissolved in MHB to obtain a solution with a final concentration of 100 pg/mL. In the

media containing E. coli the bacteria was added to produce an inoculum of 5 x 105

bacteria/mL. From this solution aliquots (100 tL) were taken at time zero, 1, 2, 3, 4, 5, 6,

7, 8, and 24 h. The samples were extracted in the same way as blood samples and

analyzed by HPLC using a calibration curve prepared in broth solution.


Results and Discussion


Assay Validation

The results of the inter- and intraday variability in plasma for tazobactam and

piperacillin are shown in Tables 3-1 and 3-2, respectively.

Based on the results of the validation, both assays were considered adequate for

the purpose of this study. The limit of quantification (LOQ) for piperacillin and






44


Table 3-1. Inter- and intraday variability for tazobactam assay (n = 9).

Theoretical Measured Intraday Variability Interday Variability
Concentration Concentration (SD) (%) (%)
(ptg/mL) (ig/mL)
3 3.8(0.72) 10.0 18.7
30 31.4(2.8) 4.4 8.9
75 72.2 (2.0) 5.5 2.8
150 152.8 (15.8) 3.9 10.3



Table 3-2. Inter- and intraday variability for piperacillin assay (n = 9).

Theoretical Measured Intraday Variability Interday Variability
Concentration Concentration (SD) (%) (%)
(pg/mL) (gg/mL)
30 28.9 (1.9) 2.7 6.6
100 96.0 (4.3) 3.6 4.5
300 296 (4.2) 1.6 4.2



tazobactam in plasma, determined as the lowest concentration that produced an interday

variability smaller than 20%, were 2 pg/mL and 3 pg/mL, respectively. For the

microdialysis studies the LOQ was 1 tg/mL for both drugs.


TZB Stability Studies

The results of the stability studies of TZB in rat plasma and rat plasma filtrate are

shown in Figure 3-2. The half-lives of TZB in rat plasma at room temperature and at

37 C were estimated to be 62 ( 9) min and 34 ( 2) min, respectively. In rat plasma

filtrate at room temperature the half-life was 84 (+ 10) min.

The concentrations of TZB in water and phosphate buffer after 72 h at 4 O C
dropped by an average of 12% and 6%, respectively. In broth solution, 85% of the initial






45


concentration is available after 24 h at 37 O C. The presence ofE. coli ATCC 25922 did

not change the rate of TZB degradation under these conditions.

Based on these results and literature data on the instability of TZB in plasma kept

at -20 C (164) it was concluded that plasma samples from the pharmacokinetic studies

should be extracted immediately after they are obtained. It was also shown that the

determination of protein binding by ultrafiltration is problematic since TZB is not stable in

plasma and in plasma filtrate.


Conclusions

It can be concluded that the HPLC assays for piperacillin and tazobactam are

precise and accurate.

Tazobactam rapidly degrades in plasma at room temperature and 37 C as well as

in plasma ultrafiltrate. Hence, the determination of TZB protein binding by ultrafiltration

does not seem feasible. Tazobactam is stable in Miller-Hinton Broth solution in the

conditions that will be used for the pharmacodynamic studies, in the absence and presence

of non P-lactamase producer E. coli.








46




103




102




8 101'-
0
U



0 20 40 60 80 100 120
Time (min)

103
b



- 102




101
0



100 I
0 50 100 150 200
Time (min)

103




Oib 102




o 101
0


100 .... .... ........ .... .... ....
0 10 20 30 40 50 60
Time (min)
Figure 3-2. Stability of tazobactam: a) in rat plasma at room temperature (half-life 62 9
min); b) in rat plasma at 37 C (half-life 34 2 min); c) in rat plasma filtrate
at room temperature (half-life 84 + 10 min). Mean SD of 3 experiments.














CHAPTER 4
PHARMACOKINETICS OF PIPERACILLIN AND TAZOBACTAM
COMBINATIONS


Specific Aims of the Pharmacokinetic Studies

The specific aims of the pharmacokinetic studies were: to elucidate the

pharmacokinetics oftazobactam in rats using plasma data and free interstitial

concentrations obtained by microdialysis, to determine the pharmacokinetics of

tazobactam combined with piperacillin when administered to rats in different dose

combinations (1:4 and 1:8) using plasma and free interstitial concentrations obtained by

microdialysis, to validate the hypothesis that the concentration-time profile of piperacillin

in plasma and tissue is not affected by the administration oftazobactam. Dose ratios of

tazobactam-piperacillin 1:2 and 1:4 will be investigated. Furthermore, the

pharmacokinetic studies inteds to show that diffusion is the mechanism that drives the

distribution oftazobactam between blood and tissues when administered alone or in

combination with piperacillin, to correlate free levels of the combination tazobactam and

piperacillin in blood with those in tissue obtained by microdialysis, and to predict tissue

concentrations of both drugs alone and in combination based on plasma data.


Material and Methods


Experimental Design

Tazobactam and piperacillin are administered to humans in two dose ratios: 1:4

and 1:8. In a previous study wich investigated the pharmacokinetics of piperacillin alone



47






48


in rats, two different doses were used: 60 and 120 mg/kg (97). The dose ratios studied in

this project are based on the same doses ofpiperacillin in order to allow for comparisons.

Male Wistar rats weighing 270-310 g were divided into 7 groups with 6 animals

per group. The pharmacokinetics of tazobactam alone was studied for three different

doses: 15 mg/kg, 30 mg/kg or 60 mg/kg body weight. For the determination of

piperacillin's influence on tazobactam pharmacokinetics, three combinations were studied:

TZB 15 mg/kg and PIP 60 mg/kg (1:4) or PIP 120 mg/kg body weight (1:8), and TZB 30

mg/kg and PIP 120 mg/kg body weight (1:4). The influence oftazobactam on piperacillin

pharmacokinetics was determined for two combinations: TZB 15 mg/kg or 30 mg/kg and

PIP 60 mg/kg body weight (1:4 or 1:2). Although the TZB-PIP dose ratio 1:2 is not used

for treatment of infections, it was investigated in this project to determine if higher doses

of tazobactam would have an effect on piperacillin pharmacokinetics. In all studies the

drugs were administered as an i.v. bolus injection.


Surgical Procedure

The animal procedure was approved by the Institutional Animal Care and Use

Committee of the University of Florida (IACUC). Rats were anesthetized with

ethylcarbamate (1.25 mg/kg i.p.). After complete anesthesia the animals were immobilized

in a supine position and a catheter was inserted into the carotid artery (polyethylene

catheter with an inner diameter of 0.3 mm and an outer diameter of 0.7 mm). The artery

was irrigated with heparinized saline. The left hind leg muscle was used for the insertion

of the microdialysis probe after skin removal. The microdialysis probe was allowed to

equilibrate inside the muscle for one hour before drug administration. Drugs were injected
as i.v. bolus injection (0.5 mL/100 g) via the femoral vein of the right hind leg. After the

completion of the injection (time zero), blood and microdialysis tissue samples were

drawn. Microdialysis samples were collected over 20 min intervals. Blood samples were






49


collected right before drug administration and at 2, 5, 10, 15, 20, 30, 45, 60, 90, and 120

minutes. Blood samples (400-500 iL) were harvested into heparinized tubes. Plasma

samples for TZB analysis were immediately extracted as described in analytical

methodology. Plasma samples for PIP analysis were frozen and stored at -5 o C until

assayed.


Microdialysis Conditions

Microdialysis was used to determine free tissue concentrations of the drugs under

investigation. A single microdialysis probe was inserted into the left leg muscle of the rat

when TZB was administered alone. For the investigation of tissue concentrations after

administration of the combination of TZB and PIP two probes were inserted in the same

muscle. Each probe was previously calibrated in vitro for either PIP or TZB. The

microdialysis pump was set at a flow rate of 1.5 pl/min. Ringer's solution was used as

perfusion fluid. Dialysate samples were collected over 20 min time intervals and

immediately analyzed by HPLC. Since microdialysate concentrations are time-averaged

over the collection interval these values were translated into concentration at a single time

point by assuming that the concentration obtained is the actual concentration at the midle-

point of the time interval.


Microdialysis System and Probe Calibration In Vitro

The microdialysis system consisted of a Harvard Apparatus Pump 22 connected to

a microliter syringe (1 mL, gas-tight) to provide the perfusate solution. The syringe was

connected to the flexible loop probe (tip length 4 mm, molecular weight cut off6000 D)

(ESA, Inc., Bedford, MA) by using fused-silica connecting tubes. The lag time due to the

dead volume between the sampling site and the point ofdialysate collection was calculated






50


to be 27 sec. The lag time was considered negligible and no corrections were made in the

time-points.

Prior to each in vivo experiment the microdialysis probes were calibrated in vitro.

The recovery obtained was used to normalize the in vivo data. The probes were put into

Ringer's solution containing either TZB or PIP 100 lg/mL and allowed to equilibrate for

one hour at 37 o C. Ringer's solution was perfused at 1.5 pL/min. After the equilibration

period 3 samples were collected at 20 min intervals and analyzed by HPLC. The recovery

was determined as the ratio ofdialysate concentration over outside concentration x 100.

Under these conditions the recoveries of TZB and PIP were found to be in the range of

18-32% and 8-14%, respectively.


TZB Protein Binding Determination

The determination of protein binding by ultrafiltration was not feasible since it was

shown that TZB degradation is rapid in rat plasma and rat plasma ultrafiltrate. The

protein binding was determined as the ratio between free tissue concentration and total

plasma concentration obtained at steady state following a constant intravenous infusion.

At steady state the free concentrations of the drug in tissue and plasma are in equilibrium

and the ratio between free concentration in tissue and total concentration in plasma can be

used to assess the fraction bound to plasma proteins.

For the infusion experiments a loading dose followed by a maintenance dose of

TZB alone were given in order to reach a steady state concentration in plasma of 50

pg/mL. Seventy five minutes after the TZB loading dose, piperacillin was also

administered to the same animal in order to determine the influence on this drug on the

protein binding of TZB. Piperacillin was administered as a loading dose followed by a

maintenance dose to reach a steady state concentration in plasma of 200 lg/mL (1:4 TZB-

PIP ratio). The maintenance doses were given in form of a constant intravenous infusion






51


in the femoral vein. A flow rate of 2 mL/h was maintained using a volumetric infusion

pump Flo-Gard 8000 (Travenol Laboratories, Deerfield, IL). Microdialysis was

performed as described for the single dose administration. One hour of probe

equilibration in the muscle was allowed before drug administration. Microdialysis samples

were collected over 20 min intervals. Blood samples were collected before dosing and at

15, 30, 45, 60, 75 min to analyze TZB levels administered alone and at 85, 100, 120, 140,

180, 210, and 240 min for analysis of TZB administered in combination. A total of 3

animals were used for the infusion studies.

The loading and maintenance doses were calculated based on pharmacokinetic

parameters estimated from single intravenous dose administration of TZB or PIP using the

following equations:


LD=Vc.Cpss (4-1)



where Vc is the volume of distribution of the central compartment and Cpss is the target

concentration in plasma. The infusion rate was calculated using eq. 4-2:


Ko = Cpss CL (4-2)


where CL is the total clearance.


Microdialysis Probe Calibration In Vivo

The in vivo recovery of the microdialysis probe for tazobactam was determined by

using the point of no net flux method. For one group of three animals, a loading dose

followed by a maintenance dose of TZB alone were administered to obtain a steady state

concentration of 50 tg/mL. The same infusion conditions described for protein binding

determination were followed. One hour after the LD was administered (steady state






52


condition established), three microdialysis samples were collected using plain Ringer's

solution as perfusate. For the subsequent samples, TZB was added in different

concentrations (7.5, 15 or 30 pg/mL) to the perfusion fluid. After one hour equilibration

with the new perfusate concentration, the net dialysate concentration was determined for

three samples by HPLC. The net concentration in the dialysate solution was plotted

against the initial perfusate concentration. The intercept of the plot with the x-axis equals
the free concentration of TZB in the tissue at steady state. The slope of the line is the in

vivo recovery. The same probe was calibrated in vitro, prior to the experiment, and in

vivo using the conditions describe above. A correction factor was calculated and used to

normalize all TZB microdialysis data before estimation ofpharmacokinetic parameters.

No correction factor was used for piperacillin since it was shown that the in vitro and in

vivo recoveries were similar in the experimental conditions described (97).


Estimation of Pharmacokinetic Parameters

The pharmacokinetic parameters of TZB alone and in combination as well as the

parameters of PIP in combination were estimated for each animal using classical non-

compartmental equations (165). The terminal elimination rate constant (ke) was estimated

from the log-linear plot of concentration versus time. The area under the concentration-

time curve (AUC) and the area under the first moment curve (AUMC) were calculated

using the trapezoidal rule. The following parameters were also determined: mean

residence time (MRT), the half-life (t1/2), the volumes of distribution (Vc, Vdss and

Vdarea) and the total clearance (CL).
The compartmental analysis was performed using the computer program
SCIENTIST (Micromath, Salt Lake City, UT). The average data for both drugs alone
and in combination were fitted using a two compartment body model according to eq. 4-3:






53


Cp = A.e-at +B.e-t (4-3)



where Cp is the total plasma concentration at time t, a and 0 are the hybrid constants for

the distribution and elimination phases, respectively, and A and B are the corresponding

zero-time intercepts. All data points were weighted equally for the compartmental fitting.

The concentrations of free piperacillin and tazobactam in the peripheral

compartment were predicted based on plasma pharmacokinetic parameters obtained from

the plasma data using the following equation (166):


fu-D-k
C Dk21 (e-3."t e-a t (4-4)
tissue- Vc. (a 3p)


where D.k21 =A.+B.a (4-5)
Vc


where fu is the fraction unbound of the drug in plasma, D is the dose administered as i.v.

bolus injection, k21 is the first-order rate constant from the peripheral to the central

compartment.


Statistical Analysis

The values of pharmacokinetic parameters obtained from the non-compartmental

approach were compared using analysis of variance (ANOVA). When significant

differences were observed Duncan's multiple range test was applied for individual

comparisons. For the compartmental analysis the model selection criteria (MSC) was

used to determine the goodness of the curve fit.






54


Results and Discussion



Piperacillin Pharmacokinetics

Since the in vitro and in vivo recoveries for PIP were similar (8 to 14%), no

correction factor was used to normlize PIP microdialysis data. The results of the non-

compartmental analysis of PIP 60 mg/kg in plasma and in tissue, alone (97) and in




Table 4-1. Pharmacokinetic parameters of piperacillin 60 mg/kg alone and in combination
with tazobactam 30 mg/kg (1:2) (n = 6), tazobactam 15 mg/kg (1:4) (n = 6),
and average of both combinations pooled (n = 12). (Mean SD).



Pharmacokinetic Piperacillin PIP/TZB PIP/TZB PIP/TZB
Parameters Alone a (1:2) (1:4) Average

AUC Plasma 4662 + 1899 4863 2244 4110 2020 4342 2027
([g.min/mL)
MRT Plasma 32 8 42 25 38 21 39 21
(min)
Half-life Plasma 33 6 42 + 16 38 15 39 15
(min)
Vc 0.17 0.03b 0.22 0.02 0.26 0.06b 0.25 0.06b
(L/kg)
Vdss 0.33 0.20 0.49 0.12 0.56 0.14 0.54 0.13
(L/kg)
Vdarea 0.51 0.34 0.81 0.34 0.84 0.23 0.83 0.25
(L/kg)
CL 11.7 8.3 14.8 7.2 17.9 8.2 16.9 7.7
(mL/min/kg)
AUC Tissue 2533 942 2515 817 3562 1474 3143 1327
(tg.min/ mL)
MRT Tissue 35 11 39 16 46 14 43 14
(min)
Half-life Tissue 30 7 27 9 31 10 29 9
(min)__
aFrom Nolting et al. (1996) (97); b p<0.05.






55


combination with TZB 15 and 30 mg/kg (1:4 and 1:2 ratios) are summarized in Table 4-1.

There were no statistically significant differences between the non-compartmental

parameters estimated for PIP in either combination (1:2 and 1:4), leading to the

conclusion that if TZB has an affect of PIP pharmacokinetics this effect is not dose

dependent. For this reason, the concentration-time profiles for these two ratios were

pooled together and the average of the pharmacokinetic parameters were estimated for

PIP combined. The results are also shown in Table 4-1. When PIP alone was compared

to PIP in combination no significant difference was observed, showing that the

administration of TZB does not affect PIP pharmacokinetics. The volume of distribution

in the central compartment (Vc) was the only parameter that showed significant difference

when PIP alone was compared to PIP (1:4) or PIP combined average.

Concentration time profiles of free PIP in plasma and tissue after administration of

60 mg/kg in combination with TZB are shown in Fig. 4-1. The values shown represent

the average of all 12 animals from the two groups (1:2 and 1:4). As can be seen in Figure

4-1 the free plasma concentration-time profile of PIP could be fitted to a two-

compartment body model like it was earlier shown for PIP alone (97). The MSC for this

fit was higher than 6. Free concentrations in tissue were predicted by using eq. 4-4 and

are also shown in Fig. 4-1 together with the free interstitial levels measured by

microdialysis. The hybrid constants used for these predictions were obtained from the

plasma fitting: A = 261.5 + 6.3 pg/mL, B = 59.3 5.4 pg/mL, a = 0.236 0.134 min-1,

and p = 0.025 0.003 min-1. The value used for fraction unbound of PIP (fu = 0.55) was

determined previously for PIP alone (97). It can be seen that the predicted line is in good

agreement with the measured free interstitial concentrations proving that diffusion is the

process that governs the transfer of free PIP between blood and tissue. After a short

distribution phase, the concentrations in tissue and plasma are in equilibrium. The

concentration in the peripheral compartment is higher than the concentration in the central

compartment due to elimination from the central compartment only. As expected from a






56


diffusion driven process the slopes of the terminal phases are statistically similar showing

that the disappearance of the drug from both compartments occurs at similar rates.




103





E 102 -


0









10 'I 'I 'I ' '
0 20 40 60 80 100 120

Time (min)

Figure 4-1. Concentration-time profiles for free piperacillin levels in plasma (0) and
interstitial fluid (0) after administration of 60 mg/kg i.v. bolus combined
with tazobactam in two different ratios (1:2 and 1:4). Plasma concentrations
were fitted to a two-compartment body model. The line for free tissue levels
represents the prediction based on plasma data. Points represent mean SD
of 12 animals.





TZB Probe Calibration In Vivo


The results of the in vivo calibration for TZB according to the point of no net flux

are shown in Figure 4-2 for a representative experiment. In this example, the in vitro






57


recovery determined prior to the experiment with this probe was 24%. The point of no

net flux which equals the free interstitial concentration was calculated as 9 hg/mL. The in

vivo recovery calculated based on the slope of the regression line was found to be 23%.

For the other two experiments, the in vitro recoveries were determined to be 30% and

32%, with the respective in vivo recoveries of 24% and 27%. The correction factor was

calculated to be in average 1.16. This factor was used to normalize the microdialysis data

for TZB administered alone or in combination with PIP.





3
2
1
0 1
3 -1 10 20 30
1-2--V


-4
-5
-6

Concentration (pgmL)



Figure 4-2. Tazobactam in vivo calibration using point of no net flux method in a single
rat. Plot of initial perfusion fluid concentrations of TZB versus net changes in
the dialysate concentrations. Intercept at 9 pg/mL represents free interstitial
concentration. In vivo recovery of 23% calculated from the slope.






58


Protein Binding Determination


Tazobactam protein binding was calculated as the ratio between free interstitial

concentration and total plasma concentration obtained after intravenous constant infusion.

The average levels in plasma and tissue obtained after three experiments are shown in

Figure 4-3. The free interstitial levels were normalized for the in vivo probe calibration.

Under these conditions the fraction unbound was determined to be 0.32 0.03 for TZB

administered alone and 0.26 0.04 for TZB in combination with PIP. Since no significant

statistical difference was observed, the overall fraction unbound was calculated as 0.28

0.05.





103





1





1 102
0





10'
C)





0 50 100 150 200 250

Time (min)

Figure 4-3. Tazobactam total plasma concentrations (U) and free interstitial
concentrations (0) at steady state following a constant i.v. infusion. TZB
administered alone followed by LD of piperacillin and maintenance doses
of TZB and PIP (1:4) at 75 min. Points represent mean SD of 3 animals.






59


The average total plasma concentration of TZB alone under the infusion conditions

described above was 35 2 tg/mL. Assuming this total plasma concentration and the

fraction unbound determined, one can expect a free interstitial concentration of TZB to be

in the range of 9.2 to 10.4 Lg/mL. The free concentration determined during the in vivo

calibration (9 tg/mL) is very close to this range, considering that those two concentrations

were determined in different animals. This fact further validates the protein binding value

for TZB determined in this study.


Tazobactam Pharmacokinetics


Tazobactam alone

Tazobactam alone was administered in three different doses: 15, 30 and 60 mg/kg.

Total plasma concentration-time profiles of these three doses are shown in Figure 4-4. As

can be seen from the plot a two-compartment body model sufficiently describes the data in

all three cases. Results of the compartmental analysis performed with the average data are

shown in Table 4-2. The MSC and the correlation coefficients obtained for these fittings

confirm the choice of the two-compartment model.

Results of the non-compartmental analysis of the plasma and tissue data are

summarized in Table 4-3. Linear pharmacokinetics can be observed for the two lowest

doses: 15 and 30 mg/kg. As expected, the AUC doubled when the dose was increased

from 15 to 30 mg/kg. A trend of decreasing clearance with increasing concentration was

observed, but the differences did not prove to be significant, probably due to the high

variability observed in these experiments. All the other parameters estimated were not

statistically different.

Non-linear pharmacokinetics was observed between the 30 and 60 mg/kg doses.
The AUC increased more than three times between these two doses and was statistically

significant. The average half-life and MRT also increased although the differences were






60


not statistically significant. The increase in half-life for the highest dose can also be

observed in Figure 4-4.





103 -





102 -





101





100
0 20 40 60 80 100 120

Time (min)

Figure 4-4. Total plasma concentration-time profile oftazobactam alone: 15 mg/kg (0),
30 mg/kg (0) and 60 mg/kg(A). Points represent mean SD of 6 animals.



The same differences showed for the plasma pharmacokinetics were also observed

for the tissue data. No data is reported in tissue for TZB 15 mg/kg because the levels

were very close to the limit of quantification of the analytical method. The results of the

non-compartmental analysis in tissue for the two highest doses are shown in Table 4-3.

The AUC tissue increased more than three times from 30 to 60 mg/kg following the

results observed in plasma. The MRT and the half-life in tissue showed a significant






61

Table 4-2. Pharmacokinetic parameters obtained by compartmental analysis of the average
concentration-time profiles ofTZB alone or in combination with PIP. (Mean +
SD).


Drug A B a P r2 MSC
Combination (pg/mL) (tg/mL) (min-1) (min'1)
(mg/kg)

TZB alone 15 48.2 15.8 0.35 0.022 0.99 8.0
(0.8) (0.3) (0.01) (0.001)

TZB alone 30 82.2 44.7 0.29 0.026 0.99 7.7
(1.8) (1.1) (0.01) (0.001)

TZB alone 60 176.0 63.8 0.22 0.011 0.99 3.4
(12.5) (3.9) (0.02) (0.001)

TZB 15/PIP 60 59.1 30.0 0.22 0.020 0.99 5.7
(1:4) (2.6) (2.2) (0.02) (0.002)

TZB 15/PIP 120 75.2 35.9 0.30 0.018 0.99 4.8
(1:8) (9.8) (2.2) (0.05) (0.001)

TZB 30/PIP 120 108.9 65.6 0.28 0.024 0.99 4.4
(1:4) (11.4) (6.3) (0.06) (0.003)



increase confirming the trend observed for the plasma data. As expected, the MRT and

the half-life did not differ significantly between plasma and tissue for each dose analyzed

individually. Since the AUC increased proportionally in plasma and tissue, the fraction

unbound determined by the ratio between AUC tissue and AUC plasma was similar for

both doses. These values are in good agreement with the TZB protein binding determined
previously in the infusion experiments. According to the results presented, one can infer

that the observed TZB non-linearity between these two doses (30 and 60 mg/kg) is not

related to saturation of protein binding sites.
The predicted free tissue concentrations of TZB 30 mg/kg and 60 mg/kg






62


Table 4-3. Pharmacokinetic parameters of tazobactam alone determined by non-
compartmental analysis. (Mean SD).


Pharmacokinetic TZB 15 mg/kg TZB 30 mg/kg TZB 60 mg/kg
Parameters

AUC Plasma 1179 + 688a 2621 1133a 8538 3863a
(pg.min/mL)
MRT Plasma 76 52 53 32 119 70
(min)
Half-life Plasma 51 32 43 24 90 51
(min)
Vc 0.41 0.12 0.33 0.11 0.31 0.03
(L/kg)______
Vdss 0.91 0.27 0.61 + 0.29 0.80 0.21
(L/kg)_____
Vdarea 0.94 0.23 0.72 0.35 0.88 0.22
(L/kg)______________________
CL 19.1 14.2 13.5 5.8 8.3 3.8
(mL/min/kg)
AUC Tissue nd 543 125a 2045 477a
(Lg.min/ mL)
MRT Tissue nd 54 + 21a 95 35a
(min)
Half-life Tissue nd 40 15a 71 + 26a
(min)
Fraction Unbound nd 0.24 0.10 0.26 0.06

a p<0.05; nd = not determined




administered alone based on total plasma data together with the free plasma

concentrations are shown in Fig. 4-5. The predictions were calculated by using eq. 4-4

and the hybrid constants shown in Table 4-2 obtained from plasma data. The fraction

unbound used in each case is reported in Table 4-3. As observed for PIP, after

equilibrium is reached between free concentrations in tissue and free concentrationsin

plasma, the concentrations in tissue are slightly higher than that in plasma due to the






63




103



102



o 10'



U 100




0 20 40 60 80 100 120

Time (min)

103





102





o 101-
Uo




0 20 40 60 80 100 120

Time (min)

Figure 4-5. Concentration-time profiles of free tazobactam levels in plasma (filled
symbols) and interstitial fluid (open symbols) after administration of 30
mg/kg (circles) or 60 mg/kg (triangles) i.v. bolus. Plasma concentrations
fitted to a two compartment body model. The line for free tissue levels
represents the prediction based on plasma data. Points represent mean + SD
of 6 animals.






64


elimination from the central compartment. The slopes of the terminal phases are similar in

both cases showing that diffusion is the process that drives the distribution of TZB

between blood and tissue. It can be seen that the predictions are in good agreement with

the measured free tissue concentrations proving that it is possible to use pharmacokinetic

parameters estimated from total plasma data to predict free interstitial concentrations of

TZB administered alone.

Tazobactam combined with piperacillin

Tazobactam 15mg/kg was administered combined with PIP in two different ratios:

1:4 and 1:8. The concentration-time profiles of plasma data for these two combinations as

well as for the same dose administered alone are shown in Figure 4-6. The results of the

curve fitting are presented in Table 4-2. TZB administered in combination with PIP

showed higher plasma concentrations than when administered alone. A two compartment

body model can be used to describe the data in all cases. The goodness of fit presented in

Table 4-2 confirms the appropriateness of the model.

The results of the non-compartmental analysis performed for these two

combinations are shown in Table 4-4. The results for TZB 15 mg/kg alone are shown in

Table 4-3. There is a trend of increasing AUC by increasing the proportion of PIP in the

combination. The difference prove to be significant for the combination TZB-PIP 1:8

where the AUC doubled. A statistically significant decrease in TZB volumes of

distribution (Vc, Vdss and Vdarea) is observed when PIP is administered in combination

compared to TZB alone. As observed for humans, the co-administration of PIP decreased

the clearance of TZB probably because PIP interferes with TZB tubular secretion. A

significant decrease in clearance is observed for TZB in combination. The proportion of

PIP in combination does not seem to affect TZB volume of distribution and clearance in a

different fashion since between the two combinations studied no statistically significant

difference was observed for these parameters. Once TZB volume of distribution as well as






65



103





102




U A
o 10'





100
0 20 40 60 80 100 120

Time (min)

Figure 4-6. Plasma concentration-time profile of tazobactam 15 mg/kg alone (U), and
combined with piperacillin: 60 mg/kg (1:4) (*) and 120 mg/kg (1:8) (A).
Points represent mean SD of 6 animals.




the clearance are decreased in the same order of magnitude by the administration of PIP

the half-life is expected to remain constant. The differences in half-life did not prove to be

significant when TZB alone was compared to TZB in combination. Similar MRTs were

also observed for these three cases.

A higher dose of TZB (30 mg/kg) was also administered in combination with PIP

120 mg/g (1:4). The results of the non-compartmental analysis of this combination are

shown in Table 4-4. The comparison between the AUC plasma for TZB 30 mg/kg in

combination and 30 mg/kg alone (Table 4-3) confirm the trend observed for the lower

dose. The addition of PIP in combination increased the plasma AUC of TZB, although






66


the difference was not statistically significant. The same can be said for the volumes of

distribution (Vc, Vdss and Vdarea) and clearance. These parameters were decreased by

the administration of PIP but the differences were not statistically significant. As observed

for 15 mg/kg, administration of PIP did not affect the MRT and half-life in plasma. The

analysis of the results in tissue lead to similar conclusions. PIP caused a statistically

significant increase in the TZB AUC tissue, confirming the results observed in plasma.



Table 4-4. Pharmacokinetic parameters of tazobactam in combination with piperacillin
determined by non-compartmental analysis.


Pharmacokinetic TZB 15/PIP 60 TZB 15/PIP 120 TZB 30/PIP 120
Parameters (mg/kg) (mg/kg) (mg/kg)
(1:4) (1:8) (1:4)
AUC Plasma 1965 591 2679 974 3725 1055
(pg.min/mL)
MRT Plasma 49 11 65 + 23 58 + 17
(min)
Half-life Plasma 42 8 49 16 49 13
(min)
Vc 0.21 0.08 0.19 0.03 0.23 0.02
(L/kg)
Vdss 0.40 0.15 0.37 0.09 0.47 0.12
(L/kg)
Vdarea 0.50 0.20 0.40 0.09 0.59 0.16
(L/kg)
CL 8.4 3.1 6.5 3.3 8.5 2.2
(mL/min/kg)
AUC Tissue nd nd 785 187
(pg.min/ mL)
MRT Tissue nd nd 46 + 10
(min)
Half-life Tissue nd nd 41 + 10
(min)
Fraction Unbound nd nd 0.22 0.08

nd = not determined






67




No statistically significant difference were observed for MRT and half-life in tissue when

TZB 30 mg/kg alone and in combination 1:4 with PIP were compared. The same

parameters are in good agreement when plasma and tissue data are compared for TZB

combined. Since both plasma and tissue AUC increased in average 44% by the

concomitant administration of PIP, the resulting fraction unbound estimated from these

parameters is similar to the one calculated for TZB alone.

Free interstitial concentrations for TZB 30 mg/kg combined with PIP 120 mg/kg

(1:4) were estimated based on parameters obtained from fitting plasma data to a two

compartment model (Table 4-2) by using eq. 4-4. The results of the measured free

concentrations in the interstitial fluid obtained by microdialysis and the predictions based

on plasma data are shown in Figure 4-7. The fraction unbound used for this prediction is

presented in Table 4-4.

As observed for TZB 30 mg/kg alone, TZB in combination also follows a two

compartment body model. The measured free tissue concentrations are in good agreement

with the predicted values calculated based on plasma data. The rates of drug

disappearance from the central and peripheral compartments are similar and elimination

occurs only from the central compartment. Diffusion is the process that drives distribution

of the drug between blood and interstitial space showing that it is possible to predicted

free interstitial fluid levels using plasma pharmacokinetics for TZB in combination with

PIP.


Conclusions

The main purpose of this study was to investigate the pharmacokinetics of

piperacillin and tazobactam in plasma and tissue when administered alone and in

combination. Microdialysis was used to measure the free concentrations of both drugs in






68


103






102
b :





10'





100
0 20 40 60 80 100 120

Time (min)

Figure 4-7. Concentration-time profiles of free tazobactam levels in plasma (0) and
interstitial fluid (0) after administration of 30 mg/kg i.v. bolus combined with
piperacillin 120 mg/kg (1:4). Plasma concentrations were fitted to a two-
compartment body model. The line for free tissue levels represents the
prediction based on plasma data. Points represent mean SD of 6 animals.




rat muscle interstitial fluid. The determination of free concentrations in tissue is an

important issue when dealing with antiinfective agents because only the drug unbound to

proteins is available to interact with the microorganisms in the infection site. The results

presented showed that microdialysis is a suitable technique for investigating free levels of

TZB and PIP alone and in combination. The in vivo calibration of the microdialysis

probes for each individual drug is a very important aspect that has to be considered when

using this method. In vitro and in vivo recoveries for piperacillin were similar and no

corrections had to be made for the free tissue data. For tazobactam, on the other hand,






69


recoveries in vivo were lower than recoveries in vitro and the microdialysis data had to be

normalized by a correction factor.

The determination of protein binding is another important aspect when studying

antiinfective agents. Tazobactam, a p-lactamase inhibitor, is very unstable in rat plasma

making it difficult to use standard methods for protein binding determination. It was

shown in this study that a pharmacokinetic approach can be used to estimate the protein

binding. At steady state following a constant intravenous infusion the ratio between free

concentration in tissue and total concentration in plasma is similar to the fraction unbound

of the drug. Free tissue concentrations predicted using the protein binding of TZB

determined in this way were compatible with the free concentration in the interstitial fluid

observed in the in vivo calibration of the microdialysis probes using the point of no net

flux. Further proof of the TZB protein binding estimate was obtained from the ratio

between AUC tissue and AUC total plasma. Similar results were observed in all three

approaches.

The pharmacokinetics of piperacillin in plasma and tissue were not influenced by
the co-administration oftazobactam. Even in a dose ratio higher than normally

administered to patients (1:2) piperacillin pharmacokinetic parameters were not

significantly different from the parameters estimated for PIP alone. This behavior agrees

with the results of studies performed in humans (8). Concentration-time profiles of PIP in

combination could be described by a two-compartment body model. The measured levels

of free PIP in tissue could be predicted based on plasma pharmacokinetics showing that

the distribution of this drug between blood and tissue is governed by diffusion only.

The pharmacokinetics of tazobactam alone was investigated for three different
doses. A two-compartment body model could be used to describe the data in all cases. A

linear relationship between concentration and the two lower doses was observed (15 and

30 mg/kg). There was no significant differences in the elimination half-lives from the

central compartment for both doses. A non-linear behavior was observed between 30 and






70


60 mg/kg. The protein binding for all three doses was constant indicating that the non-

linearity observed is not related to saturation of protein binding sites. The free interstitial

concentrations measured confirmed that diffusion is the force that drives TZB distribution

between blood and tissue.

The co-administration of PIP affects the pharmacokinetics of TZB in rats as it was

expected. Higher concentrations were obtained in plasma and tissue compared to TZB

administered alone. Piperacillin decreased the volume of distribution and clearance of

tazobactam. One explanation for the effect in clearance could be the interference of PIP

on the tubular secretion of TZB as it was shown previously for humans. No changes in

protein binding were observed for the combination. Tazobactam combined with PIP could

also be fitted to a two-compartment pharmacokinetic model and diffusion was again

shown to be the driving force for drug distribution.

The ultimate goal of the pharmacokinetic studies was to prove the hypothesis that

it is possible to predict free tissue levels of PIP and TZB, alone and in combination, based

on parameters derived from plasma data. The similarity observed between the measured

free interstitial concentrations for both drugs alone and in combination and the predicted

levels obtained on the basis of plasma pharmacokinetics validate this hypothesis. The

same concept observed in rats should also be applicable to humans. In this way,

concentration-time profiles of free PIP and TZB in different combinations can be predicted

based on humans plasma pharmacokinetics and simulated against microorganism in an in

vitro model of infection in order to evaluate their pharmacodynamic effect.















CHAPTER 5
IN VITRO PHARMACODYNAMICS OF PIPERACILLIN AND TAZOBACTAM
COMBINATIONS


Specific Aims of the Pharmacodynamic Studies

The specific aims of the pharmacodynamic studies were to investigate the effect of

tazobactam on Escherichia coli in vitro, to investigate the effect of combinations of

piperacillin and tazobactam (dose ratios 1:4, 1:8, and 1:16) on E. coli using in vitro

simulations of free concentration-time profiles obtained in humans after intravenous

infusion and intravenous multiple dosing, and to test the hypothesis that tazobactam

affects the pharmacodynamics of piperacillin against resistant bacteria.


Material and Methods


Drugs


Piperacillin and tazobactam stock solutions were freshly prepared in destilled water

for all experiments. The solutions were filtered through 0.2 Am sterile filters (Sterile

Accords, Gelman Sciences, Ann Arbor, MI) before their utilization in all experiments.


Bacteria

Escherichia coli ATCC 35218 was used as test strain in all experiments. This

strain is resistant to PIP alone due to the production of 0-lactamases. The resistance is

mainly due to plasmid encoded (TEM-1) although the production of a chromosomal 3-

lactamase has been reported (167). For this reason this bacteria is only susceptible to the



71






72


combination of PIP and TZB. The MIC for PIP alone against E. coli ATCC 35218 was

reported to be 32 pg/mL or larger and the MIC for the combination, 1-2 lg/mL (167-

168).

The MIC for PIP was determined by broth dilution method according to standard

procedure using Miller-Hinton Broth solution (MHB) (33). The MHB was supplemented

with Mg2+ (25 pg/mL) and Ca2+ (50 pg/mL). The concentration of TZB (0.5 pg/mL)

was kept constant in all dilution tubes. The inoculum contained 5 x 105 colony forming

units per milliliter (CFU/mL). In these conditions the MIC for PIP was found to be 1-2

pg/mL which agrees with the literature values reported.


In Vitro Model of Infection

A one-compartment in vitro model of infection was used to simulate the free

concentrations of PIP and TZB expected in human tissue based on plasma

pharmacokinetic data. Bacteria were exposed to different combinations of these two

drugs simulating constant concentrations, expected after constant intravenous infusion, as

well as fluctuating concentrations obtained after multiple dose i.v. bolus administrations.

The in vitro infection model consisted ofa 40 mL culture flask filled with 20 mL of

supplemented MHB. A syringe connected to a sterile 0.2 pm filter was adapted to the

upper side of the flask to allow the withdrawl and replacement of broth solution to the

model when simulating fluctuating concentrations. The inoculum was not affected by the

withdrawl of broth solution since this filter does not allow the passage of bacteria. In

order to reproduce the one hour half-life of PIP-TZB in humans a stepwise dilution

procedure was followed. At 15 min intervals, 3.2 mL of the in vitro media were
withdrawn from the system and replaced by fresh plain broth solution. The concentration

of the drugs was kept constant during each of these 15 min intervals. The in vitro model






73


was kept at 37 o C during the experiment. The broth solution used for the dilutions was

also maintained at the same temperature.

The inoculum was prepared from colonies incubated overnight on agar blood

plates. The colonies were diluted in 0.9% saline. The turbidity of the suspension obtained

was compared to the McFarland Equivalence Turbidity Standard (Remel Microbiology

Products, Lenexa, KS) in order to obtain a suspension of I x 108 CFU/mL. An aliquot of

this suspension (10 pl) was added to the in vitro model to produce a final inoculum of

approximately 5 x 105 CFU/mL. The model was incubated for 2 h to allow the bacteria to

reach the log-growth phase before the addition of any drug.


Bacterial Quantification

Samples (50 iL) were collected from the in vitro model and bacterial counts were

determined by plating three serial 10-fold dilutions of the sample on blood agar plates

(Blood Agar Plates TSA with 5% sheep blood, Remel, Microbiology Products, Lenexa,

KS). The dilutions were made in 0.9% saline. Aliquots (100 PL) of each dilution were

plated in duplicate. The plates were incubated at 37 C for 18 to 24 h before reading. The

average coefficient of variation for replicates done on different days was approximately

40%. This variability is acceptable since the range of measured CFU values covered up to

six orders of magnitude.


Comparison Between Human Tissue Levels and In Vitro Levels

In order to assure that the dilution method used to simulate the half-lives of PIP
and TZB in human tissue was able to reproduce the desired levels, PIP and TZB

concentrations were determined by HPLC in some experiments. Levels of PIP in the in

vitro model were measured for eight hours using a starting concentration of 100 pg/mL

combined with TZB 16 pg/mL. The experiment followed the same conditions presented






74


above without the presence of the bacteria. The half-life simulated was one hour. TZB

concentrations could not be measured in this experiment because its LOQ in broth solution

was very high (10 pg/ml). TZB and PIP levels were determined in the in vitro model

using phosphate buffer 5 mM instead ofMHB solution as media. The initial

concentrations were the same specified above. Two dosing intervals of four hours were

simulated. Three experiments were conducted in each case.


Piperacillin Stability In The In Vitro Model

The stability of piperacillin alone was investigated in the in vitro model using E.

coli ATCC 35218 and the same conditions described above for a constant concentration.

Four different initial concentrations were investigated: 8, 16, 32 and 64 pg/mL. Samples

were withdrawn at time zero (time of drug injection into the system), 0.5, 1, 1.5, 2, and

2.5 hours. The stability of PIP in combination with TZB was also investigated in the same

conditions. Piperacillin (8 pg/mL) was combined with TZB 4 tg/mL (1:2), 2 pg/mL

(1:4), and 1 pg/mL (1:8). Samples were collected at time 0, 1, 2, 4, 6, 8, 10, and 24

hours. All samples were analyzed by HPLC using the conditions described in Chapter 3.

Three experiments were conducted for each case. The bacterial counting was determined

in each experiment. A negative control with the bacteria in the absence of drugs was also

included to assure that the inoculum was active.


TZB Minimum Effective Concentration

In general, P-lactam and 3-lactamase combinations are used in only one fixed dose

ratio. Tazobactam and piperacillin are administered to patients in two dose ratios: 1:4 and

1:8. Some experiments were conducted to investigate if these two ratios have the same

efficacy in vitro as well as the minimum ratio of TZB in combination with PIP that still

produces an antiinfective activity. Concentration ratios were investigated instead of dose






75


ratios. The concentration of PIP used is in the same order of magnitude of free levels of

the drug expected at steady state after constant intravenous infusion obtained with current

therapy. The concentrations of PIP and TZB were kept constant throughout the

experiments. One single concentration of PIP was used (8 lg/mL) for all experiments.

The concentration of TZB was 4 ug/mL for the first experiment and it was decreased by a

factor of 2 up to 15 ng/mL for each subsequent experiment. In this way the concentration

ratios investigated ranged from 1:2 to 1:512. Samples were withdrawn for bacterial count

at time zero (right before drug addition to the in vitro model following two hours of

incubation), 1, 2, 4, 6, 8, 12, and 24 hours. The negative controls were bacteria in the

absence of any drug and bacteria in the presence of TZB 4tg/mL. For the positive control

PIP alone 8pg/mL was used. Each experiment was repeated on a different day.


Experimental Design


Piperacillin and tazobactam kinetics in human

Piperacillin is reported to have a dose-dependent pharmacokinetics in the dose

range used for therapy. For this reason the concentrations simulated in this study were

calculated to be in the same order of magnitude as it would be expected assuming its non-

linear behavior. For the simulation of concentration-time profiles of free piperacillin and

tazobactam in human tissue following multiple i.v. bolus administrations parameters

estimated from fitting plasma data to a two-compartment model were used in the same

equation presented in Chapter 4 (eq. 4-4). All the pharmacokinetic parameters were taken

from Bergan and Williams (11) and are presented in Table 5-1. The parameters shown for

the dose 30 mg/kg were used to calculate the free concentration-time profile for the

lowest dose of PIP (2g) simulated in vitro. The parameters shown for 60 mg/kg were

used to predict free tissue concentration-time profiles for 4 and 8 g of PIP. For the

prediction of free tissue levels after constant intravenous infusion, different clearances had






76


to be used since it was reported in the literature that PIP clearance decreases with
increasing dose. The clearance values used were taken from Tjandramaga et al. (1978)

based on similar total daily dose (15). For the infusion rates 30, 60, and 120 mg/h of PIP

the value used for clearance was 24.52 L/h. For the infusion rate 240 mg/h the value used
for clearance was 18.11 L/h. The fraction unbound used for PIP was 0.79 in all cases (9).



Table 5-1. Piperacillin pharmacokinetic parameters used for the simulations of
concentration-time profiles in human tissue after i.v. administration of
piperacillin and tazobactam combinations.

Dose (mg/kg) A (Ig/mL) B (pg/mL) a( (h) (h-1)
30 158.03 78.83 3.847 0.677
60 316.76 205.69 6.385 0.782
From Bergan and Williams (1982) (11).



Pharmacokinetic parameters derived from concentration-time profiles obtained
after administration ofTZB (375 mg) combined with PIP (3 g) in healthy volunteers were
used for the prediction of tazobactam free tissue levels after i.v. bolus administration as

well as after constant intravenous infusion. The parameters are shown in Table 5-2 and

were obtained from Cyanamid Germany (Study # 68-37 A multiple dose, open label,
non-comparative, parallel, multi-center, pharmacokinetic study of piperacillin and

tazobactam after 30 min intravenous infusion in subjects with various degrees of renal
impairment). The value used for clearance was 14.45 L/h for all the infusion rates studied.
The fraction unbound used for TZB was 0.79 (8).


Table 5-2. Tazobactam pharmacokinetic parameters used for the simulations of
concentration-time profiles in human tissue after i.v. administration of
piperacillin and tazobactam combinations.

Dose (mg) A (ig/mL) B (ig/mL) a (h-1) 3 (h-1)
375 21.53 18.33 3.61 0.91






77


Simulation of constant intravenous infusion

For the simulation of constant intravenous infusion PIP and TZB concentration at

steady state were calculated using eq. 5-1:


Cp =o (5-1)
ss CL



where ko is the infusion rate constant and CL is the total body clearance. The free

concentrations were obtained by using the fraction unbound for each drug. In order to

facilitate the preparation of solutions, rounded figures were used. The actual

concentrations simulated for PIP and TZB are shown in Table 5-3.



Table 5-3. Piperacillin and tazobactam free tissue concentrations at steady state after
constant intravenous infusion.

PIP ko 30 60 120 240
(mg/h)
PIP Cpss 1 2 4 10
(gg/mL)
TZB ko 3.75 7.5 15 30 60
(mg/h)
TZB Cpss 0.25 0.5 1 2 4
(gg/mL)




All the combinations that produced dose ratios TZB-PIP 1:4 and 1:8 with these

infusion rates were investigated. The drug concentrations in the in vitro model were kept

constant throughout the experiment. Samples for bacteria counting were withdrawn at

time zero (before drug administration), 1, 2, 4, 6, 8, 12, and 24 hours. Each experiment

was conducted in duplicate.






78

Simulation of i.v. bolus multiple dosing

Monoexponential kinetics was used for the in vitro simulation of free drug

concentrations after i.v. bolus administration. Three doses of PIP (2, 4 and 8 g) combined

with TZB (0.5 g), dose ratios 1:4, 1:8 and 1:16, were simulated in the in vitro model of

infection. The maximum free concentration in tissue after i.v. bolus administration is

obtained at tmax. The time for maximum concentration in the peripheral compartment of

a two-compartment model can be calculated using eq. 5-2:


n -
t = (5-2)
max a P



where ac and P are the hybrid constants for the distribution and elimination phases,

respectively. The value oftmax was calculated for each dose of each drug using the

parameters presented in Tables 5-1 and 5-2. Using tmax, the corresponding Cmax of free

piperacillin and tazobactam in the tissue for various dosing regimens after the first dose

was calculated using eq. 4-4. Table 5-4 displays the results. For piperacillin calculations

dose dependency was assumed as it was mentioned before.



Table 5-4. Maximum free concentrations of piperacillin and tazobactam in the tissue for
different doses after administration of the first i.v. dose.

Dose (g) PIP 2 PIP 4 PIP 8 TZB 0.5
Cmax (g/mL) 50 150 300 16



The concentrations displayed in Table 5-4 were added to the in vitro model at time

zero and at specific times depending on the dose interval being investigated in the

experiment. A monoexponential decline with a half-life of one hour after Cmax had been

reached was simulated. The distribution phase from central to peripheral compartment






79


was not simulated due to limitations of the model used. Since the distribution phase was

relatively short it was assumed that it would not influence significantly the outcome of the

experiments.

Four different dosing regimens were simulated for each one of the doses studied:

once a day administration (q24h), twice as day administration (ql2h), three times a day

administration (q8h), and four times a day administration (q6h). Samples for bacteria

counting were withdrawn at time zero (before drug administration) and every two hours

up to twenty-four hours. For the negative control, the number of bacteria was determined

in absence of any drug. For the positive controls the number of bacteria was determined

in the presence ofpiperacillin 2, 4 and 8 g alone. Each experiment was repeated on a

different day. Piperacillin concentrations was determined for all three doses alone and in

combination in the q6h experiment.

In another set of experiments, PIP (8 g) was combined with higher concentrations

of TZB, 64 and 256 tg/mL corresponding to 2 and 8 g, respectively, in a ql2h simulation.

Samples for bacteria counting were taken at the same time points specified above.

Piperacillin concentrations were determined for both combinations. Each experiment was

repeated on a different day.

The average results of the piperacillin concentration-time profiles were fitted to a

monoexponential equation using the computer program SCIENTIST (Micromath, Salt

Lake City, UT).






80

Results


Comparison Between Human Tissue Levels and In Vitro Levels

The results of the in vitro levels for PIP and TZB using a stepwise dilution method

are shown in Figure 5-1. It can be seen that in the absence of bacteria in the system, the

dilution method is able to reproduce the desired levels for both drugs with very good

accuracy. In this way, the half-life of both drugs can be simulated in vitro using the

proposed infection model.


Piperacillin Stability In The In Vitro Model

The results of the stability of constant concentrations of piperacillin alone in the

presence ofE. coli are shown in Figure 5-2. It can be seen that for the two lower

concentrations, 8 and 16 lg/mL, a monoexponential equation can be used to fit the data

with a degradation rate constant (kp) of 0.712 h-1. The half-life calculated for both

concentrations is 58 min. For the two higher concentrations, 32 and 64 lg/mL, a small

degree ofnonlinearity could be detected. The data could be fitted to a nonlinear equation

with a Michaelis-Menten constant (Km) of 20.8 pg/mL and the maximum rate of reaction

(Vmax) of 33.5 pg/h. However, when the two higher concentrations were fitted to a
linear equation the degradation rate constants 0.802 h-1 and 0.539 h-1 were obtained for

PIP 32 and 64 pg/ml, respectively. The MSC and correlation coefficient for this fit were

still very good, 2.70 and 0.98, respectively.

The pharmacodynamic effect measured for these four concentrations is displayed
in Figure 5-3. It can be observed that the killing effect is more pronounced with

increasing the concentration. The two lower concentrations showed an effect of short

duration and regrowth occurred after three hours. The other two concentrations, 32 and

64 pg/mL produced a more prolonged effect, showing regrowth after four hours.







81




103





102












100
0 2 4 6 8

Time (h)


103 -




102
ch-



101



10
U 10" '





0 2 4 6 8

Time (h)

Figure 5-1. Comparison between levels of piperacillin (0) and tazobactam (N) measured
by HPLC in the in vitro model of infection and levels calculated from human
pharmacokinetics (lines) using broth solution (upper panel) or phosphate
buffer 5 mM (lower panel). Mean SD of 3 experiments.







82



102




A




10 o






0.0 0.5 1.0 1.5 2.0 2.5
Time (h)

Figure 5-2. Piperacillin stability in the in vitro model in the presence of E. coli ATCC
35218 for four different initial concentrations: 8 jg/mL (N), 16 pg/mL (*),
32 gg/mL (*) and 64 gg/mL (A). Mean + SD of 3 experiments.





1010
109
108
107
106
105
U 104
103
102
101


0 2 4 6 8
Time (h)

Figure 5-3. Number of bacteria as a function of time for four initial concentrations of
piperacillin alone: 8 gg/mL (n), 16 gg/mL (0), 32 gg/mL (*), and 64 gg/mL
(A). Negative control in the absence of drug (0). Mean SD of 3
experiments.






83


The results of the stability studies with PIP (8 pg/mL) combined with TZB (1:2 to

1:512) are shown in Figure 5-4. The data was fitted to a monoexponential equation. The

PIP half-life was estimated to be 41 h when combined with TZB 4 pg/mL (1:2), 26 h with
TZB 2 pg/mL (1:4), and 20 h with TZB 1 g/mL (1:8). Comparing these half-lives with

the half-life of PIP alone in the same concentration (58 min) it can be concluded that TZB

is protecting piperacillin from the degradation caused by the P-lactamase.


TZB Minimum Effective Concentration

The results of the pharmacodynamic effect of piperacillin (8 pg/mL) combined
with tazobactam in different ratios are shown in Figure 5-5. The concentration ratios

investigated varied from 1:2 to 1:512. Tazobactam alone 4 pg/mL did not produce any

killing effect. As was shown previously, PIP alone (8 pg/mL) produced an effect of short

duration. The most effective killing was obtained with the combination of 4 Pg/mL of
TZB (1:2). No regrowth was observed up to twenty-four hours. The concentration ratio
1:4 also showed a very effective killing, maintaining the number of bacteria below the limit

of quantification for up to twenty-four hours. The ratio 1:8 showed a less pronounced

effect being able to control the bacterial level for up to twelve hours only. From this ratio

on, the lower the concentration of TZB in the system, the less pronounced was the PIP

effect and the faster was the bacterial regrowth.

By increasing the concentration of TZB in combination with a fixed concentration
of PIP it was possible to prolong the stability of piperacillin from a half-life of

approximately one hour (PIP 8 pg/mL alone) to a half-life of forty hours (PIP combined
with TZB 4 pg/mL 1:2). The increase in piperacillin half-life is reflected in its killing

effect against E. coli. With lower concentrations of 3-lactamase inhibitor in combination,
the protective effect of TZB is shorter because its small amount is rapidly inactivated by

the P-lactamase which is then available to interact with PIP. Thus, the more effective






84


101 -








I=
0
0o
U




0 5 10 15 20 25
Time (h)

Figure 5-4. Piperacillin (8 pg/mL) stability in the in vitro model combined with
tazobactam 1 pg/mL (A), 2 Vg/mL (*), and 4 tg/mL (0). Mean SD of 3
experiments.




combination is the one that supplies enough TZB to inhibit the p-lactamase for longer

periods of time increasing the probability of PIP to penetrate the bacterial periplasmic

space and interact with the penicillin binding proteins to produce the killing effect.


Simulation of Constant Intravenous Infusion


The pharmacodynamic effects of constant piperacillin concentrations combined

with tazobactam in different ratios simulating in vivo levels obtained in human tissue after

constant i.v. infusion are displayed in Figures 5-6 and 5-7. It can be seen in Figure 5-6

that for PIP infusion rate 30 mg/kg (1 pg/mL) combined with TZB 3.75 mg/kg (0.25

pg/mL) or TZB 7.5 mg/kg (0.5 pg/mL) the number of bacteria was initially decreased by

two-log scale but regrowth was observed after four and six hours, respectively.







85




1010 -1 ----------------------------------------'________
101




109 ---------
108


106

105
104 7

103 1

102 -

101

100
0 2 4 6 8 10 12

Time (h)


1010

109

108

107

106

5 105
U 104

103

102

101

100
0 5 10 15 20 25

Time (h)

Figure 5-5. Number of bacteria as a function of time after administration of piperacillin (8
pg/mL) alone (E) or combined with TZB: 15 ng/mL (0), 30 ng/mL (0), 60
ng/mL (0), 125 ng/mL (*), 250 ng/mL (<), 500 ng/mL (A) (upper panel)
and, 1 pg/mL (A) 2 ug/mL (0), and 4 ug/mL (E) (lower panel). Negative
control in the absence of any drug (*) and with TZB (4 pg/mL) alone (x -
dotted line). Mean SD of 2 experiments.






86


Increasing the infusion rate of PIP to 60 mg/kg (2 pg/mL) a more effective killing effect

was observed for all three dose ratios investigated. The number of bacteria was kept

constant for up to eighth hours for the two higher ratios (1:4 and 1:8) but regrowth was

observed after four hours for the lowest proportion of TZB in combination (1:16). Figure

5-7 shows that further increase in PIP infusion rate to 120 mg/kg (4 pg/mL) did not

produce more pronounced killing although bacterial regrowth was only observed after

eight hours for the combination of TZB 1:8. For the ratio 1:4, TZB concentration of 2

pg/mL, a plateau was observed up to eight hours but no regrowth was visible up to

twenty four hours. For PIP 240 mg/kg (10 pg/mL) combined with TZB 1:8 (2 pg/mL)

the same pattern shown for PIP 120 mg/kg (1:4) was observed. The most effective killing

was observed for PIP 240 mg/kg combined with TZB 60 mg/kg (4 pg/mL). The number

of bacteria was below the limit of quantification (103 CFU/mL) after one hour and except

for a count at 8 h no regrowth was observed up to twenty-four hours. In this way, the

maximum pharmacodynamic effect was obtained for E. coli in this in vitro model. Further

increase in piperacillin and tazobactam concentrations will not produce any increase in

effect.

It is important to emphasize that although the goal of the constant infusion

simulations in vitro was to keep the concentrations of both drugs constant throughout the

experiment, the concentration of PIP was shown to decrease because of the interaction

with the 3-lactamase produced by the bacteria. With lower concentrations of both drugs

the degradation rate constant should be bigger than the one estimated for PIP 8 pg/mL

combined with TZB 1, 2 and 4 pg/mL. The change in PIP levels has to be taken into

account for the PK-PD modeling.







87




1010

109

108

107

106

105

U 104

103

102

101

100 I
0 5 10 15 20 25

Time (h)

1010

109

101

107

106

S10o
U 104

103

102

101


0 5 10 15 20 25

Time (h)

Figure 5-6. Number of bacteria as a function of time for simulation of constant infusion
rates of piperacillin and tazobactam. Closed symbols represent TZB-PIP dose
ratio 1:4 and open symbols represent dose ratio 1:8. Upper panel : PIP 30
mg/kg and TZB 7.5 mg/kg (1:4) or TZB 3.75 mg/kg (1:8); Lower panel: PIP
60 mg/kg and TZB 15 mg/kg (1:4) or 7.5 mg/kg (1:8) or 3.75 mg/kg (1:16)
(x). Negative control in the absence of drugs (*). Mean SD of 2
experiments.







88




1010

109

108

107

106

5 105
U 104

103

102

101

100 ' .
0 5 10 15 20 25

Time (h)


1010 -

109

108 -

107 -

106

105

U 104

103 4

102-!

101 '
100 -
0 5 10 15 20 25

Time (h)

Figure 5-7. Number of bacteria as a function of time for simulation of constant infusion
rates ofpiperacillin and tazobactam. Closed symbols represent TZB-PIP dose
ratio 1:4 and open symbols represent dose ratio 1:8. Upper panel: PIP 120
mg/kg and TZB 30 mg/kg (1:4) or 15 mg/kg (1:8); Lower panel: PIP 240
mg/kg and TZB 60 mg/kg (1:4) or 30 mg/kg (1:8). Negative control in the
absence of drugs (*). Mean SD of 2 experiments.






89


Simulation ofi.v. Bolus Multiple Dosing


Determination of piperacillin concentration

The concentrations ofpiperacillin alone (2, 4 and 8 g) determined for the control

experiments in simulations ofq6h dosing regimen are shown in Figure 5-8. The mean data

for the three doses was simultaneously fitted to a one exponential equation using

SCIENTIST. The resulting elimination rate constant was 1.423 h-1 which represents a

half-life of approximately 30 min.




103












S10'

100 -"----2------ ----U------------------

0 2 4 6 8 10 12
Time (h)

Figure 5-8. Piperacillin concentrations in simulations of i.v. bolus multiple dosing of 2 g
(0), 4 g (0), and 8 g (A) q6h. Mean SD of 2 experiments.




Piperacillin concentrations were also determined in the q6h simulations for the

three doses studied (2, 4 and 8 g) combined with same dose of TZB (0.5 g), as well as in

the ql2h studied using higher doses of TZB in combination with PIP 8 g. Figure 5-9







90




103





102


O


o 101
U




100 I I
0 2 4 6 8 10 12

Time (h)


103





102





S10






0 5 10 15 20 25

Time (h)

Figure 5-9. Piperacillin concentrations in simulations of i.v. bolus multiple dosing. Upper
panel: PIP 2 g (0), 4 g (*), and 8 g (A) combined with TZB 0.5 g q6h.
Lower panel: PIP 8 g combined with TZB 2 g (0) and 8 g (U). Means SD
of 2 experiments.






91


displays the results for these two experiments. The average concentration-time profiles

were fitted to a monoexponential equation. Simultaneous fit was performed for the three

different doses of PIP when combined with the same dose of TZB. The elimination rate

constant obtained was 0.905 h-1 which corresponds to a half-life of 46 min. In the same

way, simultaneous fit was performed for the two different doses of TZB when combined

with the same dose of PIP. The elimination rate constant obtained for this case was 0.819

h-1 which corresponds to a half-life of 51 min.

In all multiple doses studies in vitro the dilutions were designed to produce a half-

life of one hour. The discrepancies between the simulated half-life using stepwise dilution

and the observed ones are due to degradation of piperacillin by the P-lactamase produced

by the bacteria. Subtracting the dilution rate from the obtained elimination rate constant,

one obtains the degradation rate constant of piperacillin in each case. The degradation

rate constant of PIP in the absence of TZB is 0.73 h-1. PIP degradation rate constants are

0.212 h-1 and 0.126 h-1 for the lower and higher proportion of TZB in combination,

respectively. The difference observed in the rate constants demonstrate the role of TZB in

this combination, protecting PIP from degradation which allows for this antibiotic to be

present in higher concentrations at the site of action. Higher proportions of TZB in

combination produce more effective protection of PIP. This is reflected in the different

degradation rates estimated. Piperacillin half-life observed when combined with the higher

proportions of TZB is very similar to the one simulated by dilution showing that the

maximum inhibition of the P-lactamase was reached.

Pharmacodynamic effect

The pharmacodynamic effect of PIP alone against E. coli in simulations ofi.v.

bolus multiple dosing of 2, 4 and 8 g every six hours is shown in Figure 5-10.

It can be seen that all doses produced a similar effect reducing the number of

bacteria by a two-log scale in the first two hours. After that, regrowth was observed in a