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Utilizing Mechanism-Based Pharmacokinetic and Pharmacodynamic Models to Understand and Overcome Antibiotic Resistance

Permanent Link: http://ufdc.ufl.edu/UFE0042293/00001

Material Information

Title: Utilizing Mechanism-Based Pharmacokinetic and Pharmacodynamic Models to Understand and Overcome Antibiotic Resistance
Physical Description: 1 online resource (155 p.)
Language: english
Creator: Wu, Benjamin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: antimicrobial, ciprofloxacin, dynamic, mechanism, pharmacodynamic, pharmacokinetic, pseudonomas
Pharmaceutics -- Dissertations, Academic -- UF
Genre: Pharmaceutical Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The emergence of antimicrobial resistance poses a critical challenge to public health in the 21st century. The current practice to treat microbes relies on single minimum inhibitory concentration (MIC) data to define the optimal clinical dose. This over simplified approach disregards the adaptive nature of microbial response, which leads to emergence of drug resistant microbes over time. In order to overcome antimicrobial resistance, the time course relationships of drug and microbial behavior must first be delineated. In this dissertation, the development of novel mechanism-based pharmacokinetic/ pharmacodynamic (PKPD) models was described using new molecular and genetic findings. The resulting mathematical models provide insight into the complex PKPD relationships necessary to optimize antimicrobial treatments. The two hypotheses tested were dormant and compensatory mutation hypotheses. A thorough model selection process identified the compensatory mutation model to the best model to describe the PKPD relationship. Dynamic kill-curve experiments were conducted for ciprofloxacin against a clinical isolate of Pseudomonas aeruginosa to further test the PKPD models. Aminoglycosides, but not most ?-lactams, appeared to retain the bactericidal activities against the emerged resistant strains following ciprofloxacin treatment. The induction of resistance was not limited to ciprofloxacin as shown with aztreonam. The PD model was applied to a clinical study of ceftobiprole in healthy volunteers. The free fraction of drugs collected in several tissues in this study using microdialysis techniques were used to develop a novel population PBPK model. Target attainments using relevant tissue data were predicted for various dosing schemes. Model also implied one-hour intravenous infusion can produce similar PD effects as two-hour IV infusion. Scenarios of resistance were simulated by combining the PD model with the population PBPK model to explore dosing strategy in case of resistance development. In summary, mechanism-based PKPD model was developed to test hypotheses, design laboratory experiments, and predict clinical drug resistance scenarios. Dynamic kill-curve revealed that aminoglycoside favorably suppress the resistant subpopulations emerged from ciprofloxacin treatment.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Benjamin Wu.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Derendorf, Hartmut C.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042293:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042293/00001

Material Information

Title: Utilizing Mechanism-Based Pharmacokinetic and Pharmacodynamic Models to Understand and Overcome Antibiotic Resistance
Physical Description: 1 online resource (155 p.)
Language: english
Creator: Wu, Benjamin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: antimicrobial, ciprofloxacin, dynamic, mechanism, pharmacodynamic, pharmacokinetic, pseudonomas
Pharmaceutics -- Dissertations, Academic -- UF
Genre: Pharmaceutical Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The emergence of antimicrobial resistance poses a critical challenge to public health in the 21st century. The current practice to treat microbes relies on single minimum inhibitory concentration (MIC) data to define the optimal clinical dose. This over simplified approach disregards the adaptive nature of microbial response, which leads to emergence of drug resistant microbes over time. In order to overcome antimicrobial resistance, the time course relationships of drug and microbial behavior must first be delineated. In this dissertation, the development of novel mechanism-based pharmacokinetic/ pharmacodynamic (PKPD) models was described using new molecular and genetic findings. The resulting mathematical models provide insight into the complex PKPD relationships necessary to optimize antimicrobial treatments. The two hypotheses tested were dormant and compensatory mutation hypotheses. A thorough model selection process identified the compensatory mutation model to the best model to describe the PKPD relationship. Dynamic kill-curve experiments were conducted for ciprofloxacin against a clinical isolate of Pseudomonas aeruginosa to further test the PKPD models. Aminoglycosides, but not most ?-lactams, appeared to retain the bactericidal activities against the emerged resistant strains following ciprofloxacin treatment. The induction of resistance was not limited to ciprofloxacin as shown with aztreonam. The PD model was applied to a clinical study of ceftobiprole in healthy volunteers. The free fraction of drugs collected in several tissues in this study using microdialysis techniques were used to develop a novel population PBPK model. Target attainments using relevant tissue data were predicted for various dosing schemes. Model also implied one-hour intravenous infusion can produce similar PD effects as two-hour IV infusion. Scenarios of resistance were simulated by combining the PD model with the population PBPK model to explore dosing strategy in case of resistance development. In summary, mechanism-based PKPD model was developed to test hypotheses, design laboratory experiments, and predict clinical drug resistance scenarios. Dynamic kill-curve revealed that aminoglycoside favorably suppress the resistant subpopulations emerged from ciprofloxacin treatment.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Benjamin Wu.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Derendorf, Hartmut C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042293:00001


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1 UTILIZING MECHANISM -BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODEL S TO UNDERSTAND AND OVERCOME ANTIBIOTIC RESISTANCE By BENJAMIN MON WU 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 2010

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2 2010 Benjamin Mon Wu

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3 To my f amily and f riends

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4 ACKNOWLEDGMENTS I would like to express my deepest appreciation to Professor Hartmut Derendorf for accepting me into his laboratory and his support and guidance throughout my graduate career. Professor Derendorf has given me a chance to express my potenti al as a graduate student which is one of the most important aspects of gradu ate school for me His positive encouragement teaching style alone with decades of research experience helped me excel in my learning at the University of Florida. His research topics and vision for pharmaceutical research helped me orient my career focus. I would also like to thank my supervisory committee members Dr. Kenneth Rand Dr. Charles Peloquin, and Dr. Tony Palmieri for their support and discussions They have generously provided support and collaboration. Despite their busy schedules, the y always had their doors open for me and were willing to help me. The day to day function of our program would not have been possible without the administrative staff of the Department of Pharmaceutics, especially Mrs. Patricia Khan, Mrs. Robin KeirnanSanchez, and M rs. Sarah Scheckner Finally, I would like to thank all the graduate students and post docs in the Department of Pharm aceutics for their friendship and scientific discussions.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...................................................................................................... 4 LIST OF TABLES ................................................................................................................ 8 LIST OF FIGURES ............................................................................................................ 10 ABSTRACT ........................................................................................................................ 14 CHAPTER 1 INTRODUCTION TO ANTIMICROBIAL RESISTANCE ............................................ 16 History of Antimicrobial Treatments and Resistance Classifications ........................ 16 Mechanisms of Antimicrobial Resistance .................................................................. 17 Resistance to Cell Wall Inhibitors ........................................................................ 18 Resistance to Protein Inhibitors ........................................................................... 19 Resistance to Nucleic Acid Inhibitors .................................................................. 20 Recent Hypotheses for Antimicrobial Resistance: Dormant and Compensatory Mutation Hypotheses ............................................................... 21 Specific Aims .............................................................................................................. 23 2 PRINCIPLES OF PKPD MODELING FOR ANTIMICROBIAL THERAPEUTICS .... 27 Application of PKPD Modeling in Antimicrobial Research ........................................ 27 Experimental Approaches for Studying Antimicro bial PKPD .................................... 29 MIC -Based PKPD Models ................................................................................... 29 Kill -Curve Based PKPD Models .......................................................................... 31 Models of Antimicrobial Pharmacokinetic/Pharmacodynamic .................................. 32 Modeling Constant Kill -Curve .............................................................................. 32 Modeling Dynamic Kill -curve ............................................................................... 33 Capacity limited growth. ................................................................................ 34 Drug eff ects ................................................................................................... 35 Application and Limitation of Antimicrobial PKPD Models ........................................ 37 Modeling Complex Behavior ...................................................................................... 38 Clinical Applications .................................................................................................... 38 Conclusions ................................................................................................................ 40 3 NOVEL MECHANISM -BASED PHARMACOKINETIC/PHARMACODYNAMIC MODELS FOR EMERGED ANTIBIOTIC RESISTANCE .......................................... 46 Theoretical .................................................................................................................. 46 Model Descriptions ..................................................................................................... 49 Results ........................................................................................................................ 52 Model Selections and Discussions ............................................................................ 54

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6 4 MODEL VALIDATION AND PREDICTIONS ............................................................. 72 Model Validation Using Bootstrap Statistics .............................................................. 72 Model Validation Approaches .............................................................................. 72 Bootstrap Statistics Comparisons ....................................................................... 73 Model Predictions ....................................................................................................... 73 Visual Predictive Check ....................................................................................... 73 PKPD Mul tiple Dose Simulations ........................................................................ 73 5 UTILITIES OF MODELING AND SIMULATION IN DESIGNING EXPERIMENTS .. 82 Introduction ................................................................................................................. 82 Pharmacokinetic/pharmacodynamic model descriptions .......................................... 83 Exploratory mechanism based combination therapy ................................................ 85 Discussion ................................................................................................................... 86 6 PKPD MODEL CONFIRMATION USING DYNAMIC KILL -CURVE EXPERIMENTS .......................................................................................................... 91 Introduction ................................................................................................................. 91 Material and Methods ................................................................................................. 92 Study Conduct ...................................................................................................... 92 Antimicrobial Drug Preparations .......................................................................... 92 Microbial Strain .................................................................................................... 93 Sterile Broth and Saline Preparation ................................................................... 93 Pre -Resistance S train Determination .................................................................. 93 Dynamic KillCurves ............................................................................................. 94 MIC Determination ............................................................................................... 96 Results ........................................................................................................................ 96 Pre -Resistance Strain .......................................................................................... 96 Ciprofloxacin and Ceftriaxone Kill -Curves .......................................................... 97 Cross -Resistance Evaluations with Automated Microscan ................................ 97 Ciprofloxacin, Gentamicin, and Aztreonam Kill -Curves ...................................... 98 Discussions/Conclusions ............................................................................................ 99 7 POPULATION PHYSIOLOGICALLY BASED PHARMACOKINETIC MODEL OF CEFTOBIPROLE IN HEALTHY VOLUNTEERS ..................................................... 111 Introduction ............................................................................................................... 111 Method ...................................................................................................................... 111 Study Design ...................................................................................................... 112 PBPK Model ....................................................................................................... 112 Results ...................................................................................................................... 115 Conclusions/Discussions .......................................................................................... 118 8 CONCLUSIONS ........................................................................................................ 137

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7 LIST OF REFERENCES ................................................................................................. 143 BIOGRAPHICAL SKETCH .............................................................................................. 155

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8 LIST OF TABLES Table page 1 -1 Deployment of antimicrobial drugs and the subsequent clinical observation of drug resistance2. ..................................................................................................... 25 3 -1 Endogenous toxinantitoxin (TA) molecules identified to disable and reinstate microbial replications in gram -negative and gr am -positive bacteria. ................... 57 3 -2 Model 1 parameter estimates (literature PKPD model). ....................................... 58 3 -3 Model 2 parameter estimates (Dormant PKPD model). ....................................... 58 3 -4 Model 3 parameter estimates (Compensatory Mutation PKPD model). .............. 59 3 -5 Model 4 parameter estimates (dormant and compensatory mutation combined PKPD model). ........................................................................................ 59 4 -1 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 1 (literature PKPD model). Bootstrap success rate and visual predict checks shown as the percentage of observed data outside the 90% confidence interval are presented. .......................................................... 77 4 -2 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 2 (Dormant PKPD model). Bootstrap success rate and visual predict checks shown as the percentage of observed data outside the 90% confidence interval are presented. .......................................................... 77 4 -3 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 3 (Compensatory Mutation PKPD model). Bootstrap success rate and visual predict checks shown as the percentage of observed data outside the 90% confidence interval are presented. ..................................... 78 4 -4 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 4 (Combined PKPD model). Bootstrap success rate and visual pr edict checks shown as the percentage of observed data outside the 90% confidence interval are presented. .......................................................... 78 6 -1 The susceptibilities of P. aeruginosa used in the in vitro dynamic kill -curve before and after 200 mg ciprofloxacin treatment determined by MicroScan Gram Neg BP Combo 34 panel (list of pre-resistance antimicrobial agents). ... 103 6 -2 The susceptibilities of P. aeruginosa used in the in vitro dynamic kill -curve before and after 200 mg ciprofloxacin treatment determined by MicroScan Gram Neg BP Combo 34 panel. .......................................................................... 104

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9 7 -1 Mean and standard deviation (n=12) of noncompartmental parameters of ceftobiprole in healthy volunteers. ....................................................................... 120 7 -2 Gender -specific plasma flow rate and tissue weights obtain from literature for the PBPK model144. .............................................................................................. 120 7 -3 Individual plasma flow rate calculated based on proportion of body surface area to standard values presented in Table 7 -2. ................................................ 121 7 -4 Individual tissue volume calculated based on proportion of body surface area to standard values presented in Table 7 -2. ......................................................... 121 7 -5 Population PBPK parameter estimates. .............................................................. 122

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10 LIST OF FIGURES Figure page 1 -1 The parallel relationship of increasing P. aeruginosa isolates resistant to ciprofloxacin with increasing fluoroquinolone usage (A)58. Over the same period, a trend of decreasing in the total number of newly approved antimicrobial agents was recorded (B)59. .............................................................. 26 1 -2 Baphasic killing of mycobacterium tuberculosis in murine infection model over the course of isoniazide treatment60. ............................................................. 26 2 -1 Mean (n=12) of total plasma ceftobiprole concentrations (circles), calculated unbound plasma ceftobiprole concentrations (dashline) and unbound ceftobiprole concentrations sampled from skeletal muscle (squares) and subcutaneous adipose tissue (triangles) using microdialysis probes in healthy volunteers72. ........................................................................................................... 43 2 -2 Basic structure of PKPD model for antimicrobial agents inhibiting the first order growth rate constants (ks) or stimulating the first order degradation rate constants (kd) of microorganisms. ......................................................................... 44 3 -1 Dormant hypothesis: Upregulation of endogenous toxins in the presence of antimicrobial agents prevents drug binding or tolerance to evade drug killings51. ................................................................................................................. 60 3 -5 PKPD model based on Dormant hypothsis : The susceptible population (S) has the growth and degradation rate constants of ks and kd and has nonspecific switching (ke) between the susceptible and dormant (D) populations. Drug effects denoted as (H(c(t)) stimulate the degradation rate constant of S and conversion of S to D. ................................................................ 63 3 -6 PKPD model describing Compensatory Mutation Model : The susceptible population (S) is converted to resistant population without fitness (R) with the rate con stant of kc. R population undergoes compensatory mutation with the rate constant of kc to restore the fitness to become resistant with fitness population (Rfit). The S and Rfit have the same growth and degradation rate constants (ks and kd) but different drug effects. .................................................... 64 3 -7 PKPD model describing both dormant and compensatory mutation hypotheses: Susceptible population (S) can be con verted to dormant population (D) with a rate constant of ke or resistant population (Rfit) with the rate constant of kc. The S and Rfit population exhibit the same growth and degradation rate constants (ks and kd). The drug stimulates the kd of S and conversion S to D. .................................................................................................. 65 3 -8 Observed (symbol) versus model predicted (line) values from Model 1 (literature PKPD model). ........................................................................................ 66

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11 3 -9 Observed (symbol) versus model predicted (line) values from Model 2 (dormant PKPD model). ......................................................................................... 67 3 -10 Observed (symbol) versus model predicted (line) values from Model 3 (compensatory PKPD model). ............................................................................... 68 3 -11 Observed (symbol) versus model predicted (line) values from Model 4 (dormant and compensatory mutation combined PKPD model). ......................... 69 3 -12 Subcompartmental profiles of Model 2 (dormant PKPD model): Dashline indicates ciprofloxacin concentrations, dark and light green lines indicate susceptible and dormant E.coli populations. ......................................................... 70 3 -13 Subcompartmental profiles of Model 3 (compensatory mutation PKPD model): Dashline indicates ciprofloxacin concentrations; dark, light, and median dark green lines indicate susceptible, resistant, resistant with fitness E. coli populations, respectively. ............................................................................ 71 4 -1 Subcompartmental simulation of the dormant PKPD model following 5 b.i.d. IV doses of 200 mg ciprofloxacin in E.coli. ............................................................ 79 4 -2 Subcompartmental simulation of the Compensatory Mutation PKPD model following 5 b.i.d. IV doses of 200 mg ciprofloxacin in E.coli. ................................ 80 4 -3 MIC distribution for P. aeruginosa following 200 mg ciprofloxacin b.i.d. dose106. ................................................................................................................... 81 5 -1 Use of mechanism based PKPD models for combination therapy115. ................. 88 5 -2 Utilizing the compensatory mutation PKPD model to design combination therapy for in vitro dynamic kill -curve experiments. .............................................. 89 5 -3 Model anticipated kill -curve profiles following 200 mg of ciprofloxacin at first dose then 200 mg ciprofloxacin at second dose (A), or 3-fold higher of cipr ofloxacin at second dose (B), or gentamicin at low (C), mid (D), or high (E) at second dose. ................................................................................................ 90 6 -1 In vitro dynamic kill -curves inv olving saline control, ciprofloxacin and ceftriaxone. Arrows indicate dosing. ................................................................... 1 05 6 -2 Ciprofloxacin MIC dynamics corresponding to the kill -curve experiment in Figure 61. ............................................................................................................ 106 6 -3 In vitro dynamic kill -curves involving saline control, ciprofloxacin, gentamicin, and aztreonam. Arrows indicate dosing. ............................................................ 107 6 -4 Aztreonam MIC dynamic corresponding to the kill -curve experiment in Figure 6 -3. ........................................................................................................................ 108

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12 6 -5 Ciprlfoxacin MIC dynamic corresponding to the kill -curve experiment in Figure 63. The line after 24 hour separates the dosing period and the post antibiotic period. ................................................................................................... 109 6 -6 Ciprofloxacin E -strip test for MIC determination 3 days post the last ciprofloxacin exposure (96 hr). Visible colony growth was observed in the high ciprofloxacin concentration zone, which was not present in the pre .................. 110 7 -1 Physiologically -Based Pharmacokinetic (PBPK) model. Co = plasma cardio output; M = muscle; F = fat; K=kidney; R = remainder; FP = free plasma; Q = plasma flow; KP = tissue partition coefficient; CL = clearance; V = volume. ...... 123 7 -2 Diagnostic plot of modeling the observed data: Population predicted versus observ ed (DV) values for plasma (yellow), muscle (blue) and fat (red). ............ 124 7 -3 Diagnostic plot of modeling the observed data: Individual predicted versus observed (DV) values for plasma (yellow), muscle (blue) and fat (red). ............ 124 7 -4 Diagnostic plot of modeling the observed data: Weighted residual of population mean versus population predicted values for plasma (yellow), muscle (blue) and fat (red). .................................................................................. 125 7 -5 Diagnostic plot of modeling the observed data: Visual predictive checks of unbound ceftobiprole concentrations in plasma. ................................................. 126 7 -6 Diagnostic plot of modeling the observed data: Visual predictive checks of unbound ceftobiprole concentrations in skeletal muscle. ................................... 126 7 -7 Diagnostic plot of modeling the observed data: Visual predictive checks of unbound ceftobiprole concentrations in subcutaneous adipose fat. .................. 127 7 -8 Diagnostic plot of modeling the simulated data: Population predicted versus observed (DV) values for plasma (yellow), muscle (blue) and fat (red). ............ 128 7 -9 Diagnostic plot of modeling the simulated data: Individual predicted versus observed (DV) values for plasma (yellow ), muscle (blue) and fat (red). ............ 128 7 -10 Diagnostic plot of modeling the simulated data: Weighted residual of population mean versus population predicted values for plasma (yellow), muscle (blue) and fat (red). .................................................................................. 129 7 -11 Diagnostic plot of modeling the simulated data: Visual predictive checks of unbound ceftobiprole concentrations in plasma. ................................................. 130 7 -12 Diagnostic plot of modeling the simulated data: Visual predictive checks of unbound ceftobiprole concentrations in skeletal muscle. ................................... 130

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13 7 -13 Diagnostic plot of modeling the simulated data: Visual predictive checks of unbound ceftobiprole concentrations in subcutaneous adipose fat. .................. 131 7 -14 Visual pl ots of covariate analysis of various demographic parameters. No covariate was building in the final PBPK model due to lack of demographic distribution in the 12 healthy volunteers. ............................................................. 132 7 -15 Probability of target attainment rates of ceftobiprole for 90% of population (solid line) based on 1000 Monte Carlo simulation following 2 hour intravenous infusion ceftobiprole. Dark and light gr apy bars were simulated based on time of drug concentration above MIC 25% and 50% of dosing interval. Four doses and three MIC profiles were simulated. ............................ 133 7 -16 Probability of target attainment rates of ceftobiprole for 90% of population (solid line) based on 1000 Monte Carlo simulation following 1 hour intravenous infusion ceftobiprole. Dark and light grapy bars were simulated base d on time of drug concentration above MIC 25% and 50% of dosing interval. Two doses and three MIC profiles were simulated. ............................. 133 7 -17 Integration of ceftobiprole pharmacokinetics described by the PBPK model with the Compensatory Mutation PD model for resistance evaluations. ............ 134 7 -18 Simulation of ceftobiprole pharmacodynamic profiles: MRSA in tissues without the emergence of drug resistance. ......................................................... 135 7 -19 Simulation of ceftobiprole pharmacodynamic profiles: MRSA in subcutaneous adipose tissue without the emergence of drug resistance after various doses and inoculation levels. .......................................................................................... 135 7 -20 Simulation of ceftobiprole pharmacodynamic profiles: MRSA with the emergence of drug resistance. ............................................................................ 136

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14 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 UTILIZING MECHANISM -BASED PHARMACOKINETIC/PHARMACODYNAMIC MODELING TO UNDERSTAND AND OVERCOME ANTIBIOTIC RESISTANCE By Benjamin Mon Wu December 2010 Chair: Hartmut Derendorf Major: Pharmaceutical Sciences The emergence of antimicrobial resistance pose s a critical challenge to public health in the 21stThe two hypotheses tested were d ormant and c ompensatory m utation hypotheses. A t horough m odel selection process identified the c o mpensatory m utation m odel to the best model to describe the PKPD relationship Dynamic kill-curve experiments were conducted for ciprofloxacin against a clinical isolate of Pseudomonas aeruginosa to further test the PKPD models. Aminoglycosides but not most -lactams, appeared to retain the bactericidal activities against the emerged resistant strai ns century The current practice to treat microbes relies on single minimum inhibitory concentration (MIC) data to define the optimal clinical dose This over simplified approach disregards the adaptive nature of microbial response, which leads to emergence of drug resistant microbes over time. In order to overcome antimicrobial resistance, the time course relationships of drug and microbial behavior must first be delineated. In this dissertation, the dev elopment of novel mechanism based pharmacokinetic/ pharmacodynamic (PKPD) models was described using new molecular and genetic findings. The resulting mathematical models provide insight into the complex PKPD relationships necessary to optimize antimicrobial treatments.

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15 following ciprofloxacin treatment. The induction of resistance was not limited to ciprofloxacin as shown with a ztreonam The PD model was applied to a clinical study of ceftobiprole in healthy volunteers The free fraction of drugs collected in sever al tissues in this study using microdialysis techniques were used to develop a novel population PBPK model Target attainments using relevant tissue data were predicted for various dosing schemes. Model also implied one-hour intravenous infusion can produce similar PD effects as two -hour IV infusion. Scenarios of resistance were simulated by combining the PD model with the population PBPK model to explore dosing strategy in case of resistance development. In summary, mechanism based PKPD model was dev eloped to test hypotheses, design laboratory experiments, and predict clinical drug resistance scenarios. Dynamic kill -curve revealed that aminoglycoside favorably suppress the resistant subpopulations emerged from ciprofloxacin treatment.

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16 CHAPTER 1 INTRODUCTION TO ANTI MICROBIAL RESISTANCE History of Antimicrobial Treatments and Resistance Classification s The inadvertent discove ry of the bactericidal activities of p enicillium notatum against staphylococcus aureus by Alexander Fleming in 1928 has lead to a major revolution i n the advancement of medical science s .1 In the following 80 years, major pharmaceutical companies have developed and deployed numerous new antimicrobial agents armed with different mode of actions to fight against infectious diseases .2 At first, it appears that m edical achievements ha d successfully conquered the debilitating effect s of microbial infection s However, clinical observations quickly disclaim ed the short lived victory against the m icrobes Through a range of highly adaptive mechanisms, microbes have consistently developed resistance to all the classes of antimicrobial drugs that they encountered .3 12 Clinical observance of a ntimicrobial r esistance occur s within a short period of time after the deployment of antimicrobial agents for public use; with in three years for penicillin and within a year for methici ll in (Table 1 1 ).2The documented cases of untreatable infections due to multi drug resistan t characteristics are on the rise. 13 As observed for fluoroquinolone from 1990 to 2000, the trend of increas ed usage has been associated with increas ing ly resistan t strains of Pseudomonas aeruginosa This alarming correlation is exacerbated by a decreas ing trend of new antimicrobial s approved over the same period (Figure 11) The data suggests that the current antimicrobial dosing approach disregards the adaptive nature of microbes, thereby fostering resistance development. It would be imperative to further understand the drugmicrobe interactions in order to explore new dosing strategies that

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17 consider the emergence of resistance. To achieve this goal, our main approach uses mechanistic pharmacokinetic/pharmacodynamic (PK/PD) models to aid the unders tanding of antimicrobial resistance and explore new treatment strategies Details of this approach will be discussed thoroughly in subsequent chapters Mechanisms of Antimicrobial Resistance The common mode of ant imicrobial actions can be divided into thr ee major categories : (1) targeting microbial structural cell wall, (2) nucleic acid metabolism, and (3) protein synthesis .1417 The antimicrobial d rugs target specific microbial traits which spare the toxic effects on mammalian cells and make them a relatively safe class of drugs to use. However, upon expos ure to environmental challenges such as lack of nutrients or toxic agents, microbes have the ability to adapt by changing their intrinsic regulation or alter ing their genetic cod e to favor their survival. The four main adaptive mechanisms include : (1) reduci ng drug entry by increasing efflux pump activities, (2) changing membrane permeability, (3) directly altering the chemistry of the drugs or (4 ) promoting mutation at the drug binding site s .4, 10, 11, 18 20 Besides the reactive defense mechanisms, microbes also have the intrinsic ability to deter drug actions. For example, macrolides are generally ineffective against gram -negative bacteria because their membrane morphology prevent s drug entry .21Once the antimicrobial resistan ce characteristics are developed, the genetic information can be transferred by genetic transfer to daughter cells or by mobile DNA transfer. Sharing genetic sequence is a common characteristic within a microbial community and it can be done usin g plasmid conjugation, bacteriophages (bacterial viruses) or transformation from nearby DNA 14 17, 22 In summary, when challenged with antimicrobials, any given microbial population may use one or more of these strategies

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18 to ensure the survivability of the microbial population as a whole. T he mechanisms of r esistance for each major class of antimicrobials are as follows: Resistance to Cell Wall Inhibitors The most apparent target against microbes is the structural cell wall, which is absent in the mammalian cells. The microbi al cell wall forms by utilizing special sugar residues called peptidoglycan. These residues consist of a series of subunits of N acetylglucosamine (NAG) and N acet ylmuramic acid (NAM) that make up the polymers capable of cross -linking to form the protective cell wall structure. M icrobes are classified into gram negative or gram -positive depend ing on the thickness of the polymer structure s that make up the peptidoglycan. Gram -negative bacteria with thin peptidoglycan and outer membrane will not retain crystal violet dye, while gram positive bacteria with thick peptidoglycan will stain purple.23T he cell wall synthesis consists of several steps and diffe rent antimicrobial agents have been developed to disrupt each step. First, precursors of pe p tidoglycan are synthesized in the cytoplasm. These precursors are then bound to lipids to facilitate the transport ation across the cytoplasmic membrane. Once the residue s reach the cell wall compartment, insertion and cross -peptide linkage are required to complete the cell wall formation 23Antimicrobial drugs have been designed to target each of these different steps of cell wall maturation. There are currently limited numbers of antimicrobial drugs that target the precursor form of peptidoglycan. Among these, b acitracin and cycloserine pr event the precursors from reaching the cell wall compartment 24 The majority of drugs however, target the insertion and transpeptidation of peptidoglycan in the cell wall compartment. The se drugs are mainly from the lactams and glycopeptides

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19 classes. Once they cro ss the membrane via porin protein channels, t hese drugs inhibit cell wall synthesis by covalently binding to enzymes involved in the insertion and transpeptidation of peptidoglycan. A poorly assembled bacterial cell wall is readily lysed under normal osmotic pressure.25Over time, microbes have developed resistance to -lactams in several ways. The microbes can reduce the bindin -lactams to specific enzymes They can also mutate a new form of peptidoglycan or acquire a completely new form of pepti doglycan that -lactams do not recognize. In addition, microbes can synthesize new enzymes that can hydroly z e the -lactam rings. At the membrane level, up regulation of the efflux pump as well as alternation of the membrane protein that affects the ability of lactams to enter the cell through the porin channels have also been observed. 14, 26Glycopeptide s s uch as vancomycin, disrupt the cell wall formation by binding directly to the D -Ala -D -Ala di peptide terminus of peptidoglycan, thereby preventing the addition of new subunits 27 Resistance to glycopeptides antimicrobials usually occurs through alteration of the terminus peptide; replac ing D -Ala -D Ala with D -Ala -D -Lac For vancomycin, as many as six resistance subtypes of enterococci have been described .28 Genes codes for this alteration are easily transferrable to other microbes through the plasmid pathway .29Resistance to Protein Inhibitors This poorly assembled cell wall will also lyse under normal osmotic pressure. Protein inhibitors include targeting micr obial 30s and 50s ribosom al subunits and elongation factors .30 Although the exact mechanisms of many protei n inhibitors are unclear, m icrobial ribosomal subunits are different than the mammalian counterpart

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20 Aminoglycosides and tetracyclines are the classes of bactericidal and bacteriostatic antimicrobial s that target 30s ribosomal subunits .31, 32As seen with streptomycin resistance strains microbes can alter the structure of the 30s ribosomal subunits to evade the cytotoxic effects streptomycin. The microbes can also develop resistance by producing enzymes that modify antimicrobial drugs through phosphorylation, adenylation or acetylation. Bacteriostatic antimicrobial s target ing 50s ribosomal subunits include clindamycin, chloramphenicol and macrolides Fusidic acid is a bacteriostatic agent that target s elongation factors to inhibit protein synthesis. 3335 In addit ion, enhancement of efflux pump activities has shown to prevent the entry of chloramphenicol36 38 and tetracyclines .15 Linezolid, the only approved o xazolidinone that binds microbial ribosomal subunits ha s also been observed to have lowered activity due to the mutation of 23s rRNA subunits .39Resistance to Nucleic Acid Inhibitors Antimicrobial agents targeting DNA and RNA biosynthesis have shown to be effective against gram negative and gram positive bacteria. Generally, these nucleic acid inhibitors are divided into two cla sses indirectly inhibiting DNA replication by targe ting enzymes involv ing nucleotide formation or directly targeting nucleic acid. The first category is sulfonamides, which are competitive inhibitors of dihydropteroate synthetase (DHPS) a critical enzyme involved in folate synthesis .40 In addition, certain sulfonamides are also structural analogues for paminobenzoic acid. The maturation of purine and pyrimidine bases requires paminobenzoic acid as the substrate to donate carbon groups. Through competitive i nhibition, sulfonamides disrupt further nucleotide production by interrupting the function of paminobenzoic acid.

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21 Microbes have evaded such assault by producing alternative paminobenzoic acid that has little affinity for sulfonamides, thereby render ing the drug ineffective .41 43The other class es of nucleic acid inhibitors include quinolones and rifamycins. Quinolones function by inhibiting DNA topoisomerases such as gyrA, gyrB, parC and parE 44. Rifamycins inhibit nucleic acid synthesis through disabling RNA polymerase such as rpoB .45 RNA polymerases and DNA topoisomerases are critical enzymes for transcription and translation. Similar to sulfonamide resistance mechanisms, microbes can mutate the RNA polymerases and DNA topoisomerases so that the antimicrobial agents can no longer bind or bind with reduced affinities for the new enzym es. Several clinical resistant strains of Escherichia coli have mutated gyrA that render fluoroquinolone ineffective .44, 45E xtensive studies have been conducted to s tudy fluoroquinolone resistance. Besides mutating the drug binding sites, microbes can enhance efflux pump activities and alter the membrane permeability to prevent fluoroquinolone entry 46 The resulting upregulation of efflux pump activities may explain the multidrug resistant characteristics.47 Fluoroquinolone generally enter bacterial cells through porin channels, although some have shown to directly cross the lipid bilayers. Rearrangement of membrane proteins that alters the porin channels may also minimize flu oroquinolone entry .48Recent Hypotheses for Antimicrobial Resistance: Dormant and Compensatory Mutation Hypothes e s In recent years, advancement in genetic and molecular techniques has provided additional insight s into the adaptive nature of antimicrobial resistance. Even though various mechanisms of resistance have been studied for decades, the process required

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22 to becom e a clinically relevant resistant strain w as unknown. Two relatively new hypotheses have been emphasized within the last few years, which attempt to delineate the mechanisms involve d in selection for resistant strains The first is the D ormant hypothesis. In the example of tuberculosis infection a biphasic killing was observed (Figure 12 ), characterized by a f ast killing phase followed by a prolonged killing phase It was hypothesized that the susceptible population can enter a dormant phase to escape drug killing; s ince antimicrobial s only target dividing cells, this dormant population can evade antimicrobial killing.49 53The other hypothesis is the Compensatory Mutation hypothesis which further expl ains the formation of genetic mutation discussed previously. The C ompensatory mutation hypothesis states that there is fitness cost associated with genetic mutation. Studies have shown that bacterial fitness (defined by the bacterial growth rate without drugs relative to susceptible strain) reduces when r esistan ce traits are acquired. In order for a particular resistant strain to be clinically relevant, it would need to restore the fitness while retraining the drug-resistance characteristics. During the dormant stage, cell replications are disabled through the production of intrinsic toxins that can shut down DNA and protein synthesis without inducing apoptosis. It is only when the microbes sense the clearance of drugs that they would upregulate an antitoxin to re-initiate the cell division. 54 57 This sequential mutation process may account for the genetic mutations observed across different classes of a ntimicrobial agents. Details of t hese two hypotheses and how they contribute to the development of mechanism -based PKPD models are discussed in Chapter 3

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23 Specific Aims Mathematical modeling of pharmacological responses provides : (1) quantitative approa ches to determine optimal dosing strategies, (2) mechanism hypotheses testing incorporating system biology, (3) obtain information on the determinants of variability, and (4) provide a meaningful comparison of therapeutic products. This proposal seeks to utilize mechanism based pharmacokinetics/pharmacodynamics (PK/PD) modeling and simulation to understand and overcome antimicrobial resistance. While these independent molecular and genetic approaches are being used to study resistance, there is a lack of a discipline working on establishing the correlation between these hypotheses and the optimal clinical doses that also target resistant population. The mechanism -based modeling approach can provide quantitative insight that is urgently needed to link the newly proposed microbial behavior and dose optimization. In a time of few new antimicrobial candidates, t he goal is to re evalulate the d osing strategies of existing antimicrobial s to better target both susceptible and resistant populations. The specific hypothesis behind this proposed research is that the current recommended antimicrobial doses do not consider the amplification of the resistant population. The insight gained from the final PK/PD model will be used to explore new dosing strategies that also target the resistant population. The specific aims of this dissertation are as follow : Specific Aim 1 Develop mechanism based PK/PD models mimicking the current hypotheses of anti microbial resistance using extensive in vitro kill -curves of E. coli 204 following ciprofloxacin treatment.

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24 Specific Aim 2 Examine each model using criteria such as bootstrap statistics, visual predictive check, interpolation of sub-compartmental pro files and simulation of multiple dose scenarios Specific Aim 3 Utilize modeling and simulation techniques to design laboratory experiments t hat test the PKPD models and explore new sequential combination therapy. Specific Aim 4 Develop a population physiologically based pharmacokinetic (PBPK) model for ceftobiprole in different tissue s using microdialysis probes in healthy volunteers. Prediction of clinical target attainment with different dosing regimen will be assessed using M onte Carlo simulations B ridging of the PBPK model with the mechanism based PD model will be used to explore drug effects in relevant tissues in case of antimicrobial resistance development.

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25 Table 1 1 D eployment of antimicrobial drugs and the subsequent clinical observation of drug resistance .2Antibiotic Year Deployed Resistance Observed Sulfonamides 1930s 1940s Penicillin 1943 1946 Streptomycin 1943 1959 Chloramphenicol 1947 1959 Etracycline 1948 1953 Erythromycin 1952 1988 Vancomycin 1956 1988 Methicillin 1960 1961 Ampicillin 1961 1973 Cephalosporins 1960s 1960s

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26 Figure 1 1 The parallel relationship of increasing P. aeruginosa isolates resistant to ciprofloxacin with increasing fluoroquinolone usage (A).58 Over the same period, a trend of decreasing in the total number of newly approved antimicrobial agents was recorded (B) .59 Figure 12 Baphasic killing of mycobacterium tuberculosis in murine infection model over the course of isoniazide treatment .60 Total # New Antibacterial Agents 19901993 1994 1996 1995 1997 1998 1999 2000 250 150 100 50 0 200 35 30 25 20 15 10 5 0YearsFluoroquinolone Use (kg X 103)Strains Resistant to Ciprofloxacin (%) Gram Negative Bacilli Fluoroquinolone Use P aeruginosa(A) (B )

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27 CHAPTER 2 PRINCIPLES OF PKPD MODELING FOR ANTIMICROBIAL THERAPEUTICS Application of PKPD Modeling in Antimicrobial Research Mathemati cal modeling has been used in numerous therapeutic areas to gain insight into explaining complex dynamics, understand sources of variability, predict and optimize dosing regimen, quantitative approach to decision making, test new hypotheses, and answer spe cific questions. The success of overcoming a microbial infection depends on the understanding of the complex relationship between antimicrobial agent, host, and the microbes, making this field a suitable area for applied mathematical models. Pharmacokinetics and pharmacodynamics (PK/PD) modeling has been recognized to play major roles in the development of new antimicrobial agents, aid physicians in making decisions during the course of patient therapy, and understand complex dynamics, such as the emergence of antimicrobial resistant strains. The consequences of antimicrobial treatment failure can be life threatening, as well as create a more aggressive strain of microbes, resulting in a greater danger to public health. In this chapter, we will discuss h ow mathematical modeling can aid the field of antimicrobial therapy. There has been great progress in PKPD modeling of antimicrobials over the years. For decades, the traditional PKPD model for dose selection in antimicrobial drug development was based on the relationship of drug kinetics to minimum inhibition concentration (PK MIC), from which the maximum efficacy can be classified into either time dependent or exposure (AUC or Cmax) dependent .61 Screening across different classes of anti microbial s, one can determine which dosing approach would have the highest probability of success for a given mechanism of action, based on the PK MIC

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28 relationship. For example, most of the lactams are time-dependent, and keeping sufficient levels above MIC over the dosing period would be the main determinant of a successful outcome (Table 41). Although this approach provides physicians a readily available tool to make clinical decisions, it does not consider the complexity of drug microbe relationship In reality, the interactions of microbes with host immune and therapeutic agents are not a static process. The high replication rate of microbes often creates a heterogeneous population in the presence of environmental challenges, such as starvation an d antimicrobial s. Different concentrations of drugs may result in fostering the development of different subpopulations of microbes. The MIC model, often assessed at only a single time point, would not be able to capture the complex dynamic of microbial response. Because of an increase in the emergence of resistant strains shortly after the deployment of new antimicrobial agents, which has resulted in an increase in clinical failures, recent efforts have been focused on examining the entire time course o f both drug and microbial response. In vitro models simulating the time course of clinical PK profiles, and the resulting microbial kill -curves, have now been widely used to better assess the PKPD relationships. Mathematical models can then be used to ca pture the PKPD relationship to aid the selection of optimal dose levels, route of administration, dosing frequency, and differentiation of antimicrobial candidate for a specific infection during drug development. The following sections will discuss the imp ortant considerations of PKPD modeling, from both the MIC -based approach and the kill -curve approach.

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29 Experimental Approaches for Studying Antimicrobial PKPD MIC -Based PKPD Models A physician, facing the challenge of selecting the best antimicrobial agent to treat a patient recently admitted into the emergency room, would appreciate the simple, fast, MIC based approach. Laboratory tests screening the microbial isolate across a wide range of antimicrobial s can readily identify which antimicrobial agent with in a classification would be the most effective against the infection. This individualized treatment is further verified by numerous clinical observations of how to best dose the patient for that particular antimicrobial agent, whether it be time dependent or concentrationdependent, as previously discussed. Table 41 shows the pattern of in vitro killing and the subsequent PKPD index used to aid dosing strategies .62 When in vitro killing was observed to be time dependent, keeping the drug plas ma concentration above the MIC for a certain fraction of dosing interval may achieve the best killing activity .63 66 When concentrationdependent killing is observed, it may be either the ratio of peak concentration to MIC (Cmax/MIC), or total exposure to MIC (AUC/MIC), that is critical to achieve target attainment63, 6668Although both drug potency and dosing strategy can obtained from such PKPD models, we now know that the over -simplified dosing scheme results in treatment failure, and foster the emergence of resistant populations. This concern is contributed to by inadequate information regarding both PK and PD parameters. The PK profiles obtained from these analyses are usually total plasma concentration, ignoring the protein binding and tissue distribution effects in the subjects. It is well accepted that only the free fraction of drugs is capable of exerting pharmacological effects. Upon entering the blood stream, drugs can readily bind to protein or

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30 -acid glycoprotein, lipoproteins, and/or erythrocytes .69 71 The binding process may be either linear or nonlinear. Hence, characterization of a range of drug concentration in relation to protein binding should be assessed. Most importantly, it is pr imarily the free fraction that crosses the membrane to infected tissues such as adipose tissue or, for skin infectious microbes, skeletal muscle. Using micro dialysis techniques to determine the profile of the free fraction of drug at the site of infection would be the most ideal method. Figure 4.1 shows the profiles of Ceftobiprole concentrations in different tissues .72From a perspective of a PD profile, the single point MIC is highly empirical. The MIC value for a particular antimicrobial agent varies between laboratories because it is highly dependent on the dilution factors used, lab oratory condition, and the interpretation of what constitutes no growth by the laboratory personnel. The rate of bactericidal or bacteriostatic effect with changing drug concentration is also unknown from such simplified analysis. As one can imagine, the same MIC value may result from different time course killing patterns, even though clinical outcomes may vary. Even without the dynamic kill -curve information, the inadequate MIC interpretations are sometimes revealed through post antimicrobial effects or suboptimal effects Depending on which tissue profile is used, a different dosing regimen may result from the analysis. Hence, a PKPD relationship based on total plasma concentrations alone may not always represent the free fraction needed at the site of acti on for the PK MIC relationship. 73One additiona l pitfall of the MIC approach for PKPD modeling is that only static drug concentrations are used. Using only static drug concentrations does not accurately reflect in vivo pharmacology, because it does not represent the PK profile of

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31 orally administered drugs. As a result, the PKPD relationship cannot be thoroughly understood by using only the empirical value of the MIC approach. Kill-Curve Based PKPD Models The other popular modeling approach is to assess the PKPD of antimicrobial agents using in vitro kill-curves. This provides valuable time course evaluation of bacterial population dynamic in response to drugs. A mechanistic PKPD model can then be built to describe the relationship. Parameters such as bacterial growth rate, natural death rate, and the emergence of resistant strains within a population, can be estimated. In these in vitro experiments, the antimicrobial concentrations can be static74 76 or dynamic77 79Although the dynamic kill -curve has primari ly been done using in vitro systems, similar approaches can be used for in vivo studies. The mouse thigh infection model has been widely used as the dynamic kill -curve evaluation. depending on the purpose of the study. The static kill -curve provides a quick view of the drug effects on specific strains of bacteria. However, even by capturing the dynamic microbial response, the static PK provides limited information. In order to mimic a clinically relevant scenario, the dynamic kill -curve should have drug concentration-time profiles resemble that of the free fraction of drugs in the site of infection in the relevant population. 80, 81 Although the variabil ity of the PD data often increases with animal models compared to in vitro models, the incorporation of the immune system and the different nutrients available may provide additional valuable insight into the PKPD relationship.

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32 Models of Antimicrobial Pha rmacokinetic/Pharmacodynamic Having established that the time kill -curve is a superior method for pharmacodynamic profiling of antimicrobial therapies compared to the arbitrary, singlepoint MIC method, this section will discuss the use of mathematical mod eling in characterizing these time kill -curves. Mathematical modeling of drug-response relationship provides a quantitative understanding of the complex dynamic relationships between drugs and microbial responses. This important tool benefits physicians by providing the ability to make pertinent predictions to specific questions regarding the safest and most effective dosing regimen. In the field of antimicrobial therapy, the mathematical modeling contains two major components. The first component is PK which refers to the clinically relevant free fraction of drug kinetic at the effective site of action, and second, PD, which refers to the total bacterial cell count over a time period. Because the PD parameter is the bacterial count, it is impossible t o conduct initial clinical trials in healthy volunteers to study the PKPD relationships. The PD is therefore often performed in vitro; using pertinent drug kinetics obtained from clinical studies to challenge bacteria in question, thereby allow a control study of the PKPD relationship. However, when interpreting the results, one must keep in mind that in vitro settings lack the affect that the immune system and various nutrients would have on the PD profile. In this section, we will discuss the important considerations in modeling antimicrobial drugs. Modeling Constant Kill-Curve An example of kill -curve profiles for bacteria exposed to constant drug concentrations over a period of time can be seen in Figure 4.3, showing the kill -curve profile of cefexime against H. influenza.82 Modeling of this PKPD relationship can either

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33 be described by a linear or nonlinear relationship. The idea is to capture the different growth rate between controls versus different levels of antimicrobial concentrations. If one wishes to assess the PKPD profile using a linear relationship, a minimum of three different drug levels should be used to assess the linearity relationship. When a linear relationship is assumed, the growth rate in the present of antimicrobial (kapp) can be described in equation 1: = 1 (2 -1) where ko is the growth rate of bacteria without drug tre atment, k1 is a first order inhibitory rate constant, and C is the drug concentration. If such a model is not sufficient to capture the data, a nonlinear, or saturable, process is assumed, requiring the use of equation 2: = (2 -2) where ka is an equilibrium constant between the medium and the receptor sites at steady state, and kb is the affinity constant of drug to the receptor. Again, this simplified in vitro kill -curve approach does not reflect the dynamic profiles of drug c oncentrations. The following section shows how using a kill -curve system resembling an in vivo setting incorporates the mechanistic importance of such a complex relationship. Modeling Dynamic Kill-curve In order to build a relevant PK -PD model, the behavior of bacterial cell growth and degradation must first be described. In a most simplistic term, the natural self replication and death of bacteria can be described using equation 2 3: = (2 -3)

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34 where N is the bacterial population wi th the initial count of N(0), ks is the first order rate constant for bacterial synthesis, and kdCapacity limited growth. is the first order rate constant for bacterial death. This common structure to describe bacterial growth is also used to describe viruses and cancer cell pop ulation behavior. This basic model assumes bacteria are a homogenous population with the same growth and death rate constants, which we now know may not reflect the emergence of antimicrobial resistant strains. In an in vitro se tting where the kill -curves are produced, nutrient and space availability limits do not allow the bacteria to grow indefinitely. In order to describe this capacity limited growth in equation 4, we often see an additional term added to equation 1 known as the logistic growth function: = ( 1 ) (2 -4) where Nmax is the maximum number of bacteria growth. In this equation, as N approaches Nmax = ( ) (2 -5) the growth term slows down and eventually reaches a steady state condition. The assumption of this growth model is that the maximum capacity is reached in a linear fashion. Depending on the experimental condition, it is sometimes preferable to use a no nlinear growth to describe the capacity limited growth. In this case, the first order synthesis rate is replaced with the new term in equation 2 -5: where Vmax,g is the maximum growth rate and N50 is the numbe r of bacteria at half of the maximum growth rate. In most situations, equation 2 -3 or 2 4 is sufficient to describe the in vitro kill -curve behavior.

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35 Drug e ffects Antimicrobial drug actions are divided into two major categories; drug concentrationdependent killings or time dependent killing s The concentrationdependent killing antimicrobials include aminoglycosides, quinolones, and metronidazole. Antimicrobials that exhibit time dependent killing are mostly -lactams, macrolides, oxazolidinones, and tetracyclines. Knowing these characteristics often can aid in the development of PKPD model. An antimicrobial drug with time dependent killing, identified by the traditional PKPD indices of T>MIC, can often be best described by inhibition of ks. Convers ely, an antimicrobial drug with concentrationdependent killing, identified by AUC/MIC or Cmax/MIC, can be best described by stimulation of kd. As described by Czock and Keller 2007, a minimal change in rate of killing is often observed as drug concentrat ion increase for time-dependent killing drugs. In contrast, the microbial kill rate increases substantially with increases in concentration for concentrationdependent killing. Antimicrobial drugs can reduce the overall bacterial population by inhibiting ks, which limits growth, or by stimulating kd which enhances killing. A linear drug effect can be described by simply multiplying the free drug concentration ( f Cp) by either ks*N or kd*N, and integrate the relationship over time. However, as is often the case, the drug effect is a nonlinear, saturable process. An example of direct drug effect on bacterial killing can be described by replacing the kd with a modified Michaelis -Menten term (Imax* f Cp/(IC50+ f Cp)), where Imax is the maximum drug effect and IC50 is the concentration at which half of the maximal drug effect is observed. As described previously ,83 MIC value can be relat ed to this function by first integrating the equation:

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36 = (2 -6) where t is the experimental incubation time for measuring MIC, Nt is the number of bacteria count at time t, and No is the initial inoc ulation count. Solving this equation, the MIC relationship can then be described as: = ( ) 50 (2 -7) where d is the ks -(lnNt -lnNo)/t. Although not as often done, the free drug fraction in these functions can be replaced with dose or AUC, yielding equation 2 -8: = or (2 -8) This method is generally less informative than integrating concentration-time course, because it reflects only the single parameter used. If modeling of both the ks and kd is desired, drug effects targeting ks or kd = ( 1 ) (2 -9) can also be described using equations 2 -9 and 2 -10: = 1 + (2 -10) where Imax and Smax represent maximum inhibitory or stimulatory rate and IC50 and SC50In these saturable drug effects, the fitting of pharmacodynamic curves may be improved by incorporating an exponential term (hill factor (H), often denoted as gama f C represent the concentration of drug at half of the maximal effect. p and either IC50 or SC50 of the drug effect term. The a ddition of hill factor is strictly for the purpose of improving the fit of the curve, because, by itself, it has no biological meaning.

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37 Application and Limitation of Antimicrobial PKPD Models When these PKPD models are used to describe kill -curves of diffe rent drugs against specific bacteria, a quantitative comparison of drug effects can be evaluated. This is often first done using a static kill -curve model, in which the potency of the drugs (IC50 or SC50), as well as the overall effects of the drugs (Imax or SmaxLikewise, an antimicrobial agent can be used to test across different species of Gram negative and Gram positive microorganisms to identify the relative effectiveness in each. Based on the mechanisms of action, it could be assumed that an agent that works on targeting the cell wall will not work as well in Gram -negative bacteria. However, the PKPD model can allow a quantitative distinction of a particular drug action across different species of bacteria. ), can be compared for the test article versus a standard treatment with equivalent MIC -fold exposure. For example, to compare a new antimicrobial to gentamicin for the treatment of pseudomonas aeruginosa infection, the initial free drug concentrations at 0.1, 0.5, 1, 2, 4, 8, 16X MIC can be compared. Assuming toxicity is not an issue for either, the PKPD relationship can be quantitatively compared through the modeling approach. There are several limitations that should be considered when interpreting PKPD models for antimicrobials. Different b acteria may have different growth behavior, especially when considering the presence of resistant populations. Such heterogeneous populations can result in different drug effects. As we observed with increased clinical usage of antimicrobial agents, the emergence of resistance strains has also increased. This additional phenomenon sometimes requires a more complex PD structure. Various attempts to use PKPD models to capture the complex relationship have been published.

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38 Another limitation is the differ ences between in vitro and in vivo observations. In addition to lack of an immune system in the in vitro setting, the amount of nutrients available for bacterial growth is different. If the kill rate is dependent on bacteria growth rate, the comparison o f drugs in an in vitro setting may be confounded. Likewise, if the emergence of resistance is fostered only through the artificial setting lacking the immunological component, the interpretation of the in vitro results should also be cautioned. In the fo llowing sections, we will discuss in detail the applications of PKPD models for antimicrobial agents, and the current modeling strategies to deal with resistant populations which may better explain certain kill -curve behaviors. Modeling Complex Behavior Using kill-curve data with only an empirical sigmoidal function may result in an over -simplified model. The complexity of the model greatly depends on the richness of the PD data, as well as the actual microbial behavior. Over the years, clinical observations have consistently shown that microbes have the ability to evolve and adapt in order to overcome drug challenges. This warrants using multiple populations to describe the kill -curve behavior. A dosing regimen that targets both susceptible and resist ant populations may be a key to prevent the emergence of antimicrobial resistance. Complex modeling, such as those considering the multiple populations, have been demonstrated by Campion84 and Jumbe81 and others. A mechanistic model incorporating cell cycle is to evaluate inoculation effects is published by Bulitta .85Clinical Applications In dept discussions of these topics will be covered in later chapters. As briefly discussed above, to obtain dat a for modeling a dynamic PKPD relationship, relevant free fraction of drugs concentrations in human would first need to

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39 be obtained. This information can then be used to conduct in vitro PD experiments for PKPD modeling. Many studies of antimicrobial age nts have been studied using this approach.71, 82, 8688Whenever possible, the PK profiles should be obtained at the site of actions. For cefpodoxime and cefixime, the free fraction of drugs in tissue was modeled using equations 11: The PK profiles of unbound antimicrobial concentrations were first studied in humans, then were mimicked in in vitro settings using continuous dilutions and replacement of fr esh medium technique. The effects on the bacteria of interest can then be studied using both constant and dynamic kill -curves. For these kill -curves, generally a minimum of 3 dose levels, in addition to a growth control for each drug, are needed to obtai n reliable PD parameter estimates. The frequency of the sampling time is also an important consideration to accurately obtain the curvatures of the PD profiles. In 24 hour experiment kill -curve experiments, it is frequently observed that a large segment of the kill -curve is void of samples due to logistic reasons. = ( ) ( ) ( ) ( 1 ) (2 -11) where TD is the tissue partition coefficient (AUCtissue/AUCplasma), fu is the unbound fraction in plasma, F is the bioavailability of the drug, D is the dose, ke is the elimination rate constant, ka is the absorption rate constant, Vd is the volume of distribution, and tlagFor a clinical trial, when the data are modeled with a population approach, the variants from the model can be used to predict therapeutic outcome using the Monte is the absorption lag time for the tissue. Once the PK is modeled in such a way, which takes into consideration free fraction and tissue conc entrations, the profile can be simulated in vitro to evaluate PD behavior.

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40 Carlo statistical approach8991Conclusions Typically 1,000 to 10,000 subjects can be simulated to display the population distribution using model estimated parameters and population variance. For a time-dependent drug where in vivo data show that the time of drug concentration above MIC for at least 50% of dosing interval is required to achieve efficacy can now be assess i n a more meaningful population approach. If the objective of the study is to have 95% of the population achieved this T>MIC of 50% dosing interval, Monte Carlo simulation will allow such assessment at different dose levels or dosing intervals. The best PKPD modeling is rooted in both the data collected and the understanding of the biological process. The results of model prediction cannot be stronger than the premises. Hence, thoughtful studies to obtain the most clinically relevant data are first needed. For studying the PKPD of antimicrobials, knowing the dynamic profiles of free fraction of drug concentrations at the site of action is important. The in vitro kill -curves appear to be superior to the PK MIC approach. The dynamic kill curve model allows the field of antimicrobial modeling to progress from empirical to mechanistic, thus providing a greater insight into the drug-response relationship as compared to the limited MIC approach. The examples above have shown the versatility of PKP D model in aiding different areas of antimicrobial research. Whenever possible, the model should make biological sense and concur with laboratory data in order to confirm the models validity. As we improve and explore molecular and genetic techniques to evaluate a specific question about drug-microbial response, the PKPD models can be refined and modified to incorporate the new findings. Hence, PKPD

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41 modeling for antimicrobials will remain an important tool and will integrate well with other functional areas.

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42 Table 2 1 MIC -based PKPD index .62

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43 Figure 2 1 Mean (n=12) of total plasma c eftobiprole concentrations (circles) calculated unbound plasma ceftobiprole concentrations (dashline) and unbound ceftobiprole concentrations sampled from skeletal muscle (squares) and subcutaneous adipose tissue (triangles) using microdialysis probes in healthy volunteers .72

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44 Figure 2 2 Basic structure of PKPD model for antimicrobial agent s inhibiting the first order growth rate constants ( ks) or stimulating the first order degradation rate constants ( kd ) of microorganisms N kd ksImax, IC50 for Time Dependent Killing+ Smax SC50 for Concentration Dependent Killing

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45 Figure 2 3 Example of in vitro static kill-curve .92

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46 CHAPTER 3 NOVEL MECHANISM -BASED PHARMACOKINETIC/PHARMACODYNAMIC MODELS FOR EMERGED ANTIBIOTIC RESISTANCE Theor y The major factor contributing to clinical failure in treating antimicrobial infection is that the current dosing strategy disregards the adaptability of microbes. Treatments usually impose inadequate pressure against the resistant population, which results in the promotion of a more virulent strain. The main determinants of resistance emergence over the course of antimicrobial therapy are not well understood. Over the years, t he evaluation of microbial susceptibility h as improved from point estimates (MICs ) to complete time-course approach ( dynamic kill-curve s ). However, recent advancement s in molec ular and genetic research have provided additional insights in explain ing the microbial kill -curve relationships. W ith the aid of these new findings new PKPD models can be developed to bridge basic science research to optimal dosing strategies Current ly there are two major competing hypotheses in the literature claiming to explain the process by which microbes develops resistance over the course of antimicrobial therapy. The first hypothesis is t he phenotypic variant hypothesis often referred to as the dormant or persistent population hypothesis, in the literature. This hypothesis emphasizes the importance of an endogenous toxin antitoxin regulation system that can favorably shut down cell divisions temporarily in the presence of antimicrobial dr ugs .50, 51, 53, 93, 94 The idea is depicted in Figure 3 -1 For the susceptible population, upon binding of an antimicrobial agent, the biosynthesis processes of microbes are disrupted, leading to microbial cell death. The persister population, however has up -regulated endogenous toxins that can shut down cell replication

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47 without inducing apoptosi s. Since antimicrobial agents bind only dividing cells, the dormant variant escapes the cytotoxic effects of drugs Alternatively, the ineffective ness of drug actions may be explained by a tolerance mechanism. In this case, the drug is able to bind the dormant population but exert no effect on it due to the tolerance induced from endogenous toxins .50, 51, 53A list of endogenous toxins responsible for this mechanism is summarized in Table 3 -1. Toxins such as RMF, UmuDC, SulA, RelE and HipA can inhibit translation, replication, or septation when produced. Their toxic effect s can be reverse upon the upregulation of antitoxins. W ithin th e last several years, many of th e s e inhibitory proteins have been extensively studied 53, 60, 94, 95For example, by using an inducible promoter (pBAD) for the RelE gene, the ability of E. c oli to shut down cell division s within 30 minutes of acti vating RelE expression (Figure 32 ). Three hours after inducing the RelE gene, the microbes were exposed to lethal doses of cefotaxime, ofloxacin, or tobramycin that target DNA gyrase, cell wall synthesis, or protein synthesis respectively A s ignificantly higher survival rate in the RelE induced microbes w as observed when compared to that of the non-RelE induced strain It was only when the antit oxins expression for RelE (RelEB ) was induced that microbial cell division s c ould be resumed 51. This molecular evidence supports the presence of persiste r cells that may explain the biphasic kill-curve s incomplete killings, and latent infections .60The second hypothesis is the Compensatory Mutation hypothesis The importance of mutation and fitness concept was proposed to describe the sequential process in developing antimicrobial resistance. Mutation events result in developing

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48 resistance characteristics that are often accompanied with a f itness cost (Figure 33) F itness is defined as the microbial grow rate in vitro compared to that of the susceptible strain. A h igher fitness cost result s in a lower grow t h rate of the microbes. In order for a mutated resistant strain to be clinicall y relevant, additional mutations (compensatory mutations) are needed to restore the fitness This new population would have similar growth characteristics as that of the susce ptible strain but with increased MIC due to their drug-resistan ce characteristics. This hypothesis emphasizes that genetic changes rather than phenotypic changes are responsible for the emergence of antimicrobial resistance .5457, 96102Using mechanism based models is one of the approaches used to test these hypotheses. Although in reality, both dormant and compensatory mutation resistant mechanisms could occur simultaneously the predominant mechanisms may be favorably described by a hypothesis -specific model. While these independent molecular and ge netic approaches are being used to study emergence of resistance, there is a lack of discipline establishing the correlation between these hypotheses to optim ize antimicrobial doses Because the development of resistant strains was not considered in the d osing, drug exposure may result in fostering the selection of resistant populations. A PKPD model can reveal important insights into t he recently proposed anti microbial resistance behavior with clinically relevant drug kinetics. Anticipating that few new antimicrobial s will be available in the next few years, this approach is important to maximize the efficacious potential of current drugs. Refinement of dosing strateg ies specifically target ing the drug -induced resistant population may lead to successful treatment. In this study, we developed novel mechanism based PKPD models to

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49 distinguish between competing hypothes e s for resistance emergence during drug treatment using extensive in vitro dynamic kill -curve data of ciprofloxacin and E c oli. Model Descriptions In order to develop complex mechanism based PKP D models, a rich data set with a wide range of dosing groups with frequent sampling in order to capture the timecourse of drugmicrobe dynamics were needed. In this section, t he dynamic kill -curves used for the model development were obtained from a previous publication103 using GetData Graph Digitizer 2.24 Details of the in vitro dynamic kill -curve experiments were described by previously .103 Briefly, a two -flask syste m with a constant pump was used. Flask 1 contains the Ca2+ and Mg2+ Mueller -H in ton broth. Flask 2 contains bacteria with or without antimicrobial s in the Mueller -H in ton broth. The bacteria were initially incubated for 18 h ours to reach an exponential growth rate, prior to diluting them to 106 CFU/mL for the experiment. Ciprofloxacin was then added to Flask 2 to test the drug effects. E coli 204 were subjected to ciprofloxacin treatment at 0.0, 0.1, 0.2, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0, 32.0 and 125 times the MIC A group without ciprofloxacin was used as the control. An automated pump was used to remove and replace the Flask 2 medium with fresh broth at a rate of 7 mL/hr By maintain ing a constant volume of 40 mL in the flask, the cl inical half -life of 4 hours was simulated Series of samples were taken throughout a 48 hour period for colony counting. The k ill-curve for each dose group ended when the microbial growth reached approximately 1011Four models were used to describe th e emergence of antimicrobial resistance. The first model is a commonly used model from the literature. CFU/mL. 104 The other three are novel PKPD models describing the D ormant hypothesis, C ompensatory M utation hypothesis, and a combination of these two hypotheses. Graphical descriptions of the

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50 models are shown in Figure 3 4 to Figure 37 Estimates of m odel parameter s for eac h model were computed using data from all 11 dose groups fitted simultaneously using Adapt II software .105Model 1 assumes the total microbial population consists of susceptibl e (S) and resistant (R A p roportional error model with maximum likelihood was used for all models. fit) populations Each subpopulation exhibits its own first order growth rate constant (ks or kss), and degradation rate constant (kd or kdd). The susceptible population is converted to the resistant population with a rate constant of kc. Ciprofloxacin stimulates the killings of microbes by enhancing the kill rate constants ( kd and kdd). The stimulatory drug function is described by Smax*C/(SC50 = ( 1 + ) IC = 10 +C) or denoted as H(C(t)) in Figure 3 -4 This model does not include the current in-depth knowledge of microbial resistance behaviors as discussed above The equations describing Model 1 are: 6 = ( 1 + ) + IC = 0 CFU/mL (3 -2 ) CFU/mL (3 -1 ) Where, = and = Model 2 describes the Dormant hypothsis The only observable population is t he susceptible subpopulation where the ce ll division occurs. In the absence of drug treatment s transfer between the s usceptible (S) and dormant (D) compartments occurs randomly with a rate constant of ke. The addition of ciprofloxacin promotes the conversion of S to D compartment as well as stimulates the killing of the S population. Since antibiotics target only dividing cells, no drug action is imposed on the D population It is assume d that once the antimicrobial pressure is reduced to a certain

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51 level, D population can initiat e cell division through upregulation of antitoxins and be converted back to the S population. The equations describing Model 2 are: = ( 1 + ) ( 1 + ) + IC = 10 6 = ( 1 + ) IC = 0 CFU/mL (3 -4) CFU/mL (3 -3 ) w here = and = Model 3 describes the Compensatory Mutation hypothesis where R is a mutated population with no significant growth rate The subsequent compensatory mutation restores the microbial fitness while retraining the resistance characteristics As a result, the R population is converted to an important contributing population (Rfit). The Compensatory Mutation hypothesis a ssumes the fitness is fully restored. Hence the Rfit population exhibits the same growth rate and degradation rate constant s as th ose of the S population (same ks and kd). The mutation process is described by an arbitrary kc rate constant. Although the S and Rfit = ( 1 + ) IC = 10 population have the same fitness, their responses to drug actions are different The equations describing Model 3 are: 6 = IC = 0 CFU/mL (3 -6) CFU/mL (3 -5) = + ( 1 + ) IC = 0 CFU/mL (3 -7) w here = and = Model 4 is a combination of both dormant and compensatory mutation hypotheses. Modifications to M odels 2 and 3 were done to evaluat e the multiple mechanisms simultaneously while adhering to parsimony principle. The equations describing Model 4 are:

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52 = + ( 1 + ) ( 1 ) IC = 10 6 = ( 1 + ) IC = 0 CFU/mL (3 -9 ) CFU/mL (3 -8 ) = + IC = 0 CFU/mL (3 -10 ) = and = Results The ADAPT II estimates for Models 14 are tabulated in Tables 3-2 to 3 -5 The tables show the final model output values with %CV associated for the parameter estimates. T he observ ed versus the model predicted profiles are shown in Figures 3 8 to 3 -11. The symbols are the observed microbial count and the lines are the model predictions. Model 1 has the most parameters (9 total ). T he degradation rate constants for susceptible and resistant populations were slightly lower than the respective grow th rate constants. The higher synthesis rate explains the exponential microbial growth observed in the control group. The conversion rate between the two populations was relatively small, showing kc of 0.119/hr. The overall drug effects of the susceptib le population was approximately three-fold higher than that of the resistant population (SMAX,S = 0.1 versus SMAX,R = 0.0342). The potency of the drug was slightly better in the resistant population compared to the susceptible population (0.192 versus 0.249 g/mL). The variance of the proportional error was reasonable at 0.198. The model parame ter estimates from ADAPT II revealed a good %CV (below 50%). Visual inspection of the observed versus predict ed results implies adequate fitting of the control and most dose groups.

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53 Model 2 also describe s the observed data reasonably well (Figure 39). Model 2 has 7 parameters with a growth and degradation rate constants similar to that of Model 1 enabling capture of the exponential growth of the control ( kd s lightly lower than ks). In the absence of drug concentrations minimal distribution between susceptible and dormant compartment occurs (ke = 0.108/hr). This conversion is greatly enhanced in a drug concentration dependent manner showing Smax,D of 3.61 and SC50,DModel 3 also consist s of only 7 paramet ers. It appears that Model 3 has the best model fitting as shown in Figure 3-10. T he same k of 0.263 g/mL. The variance of the proportional error was 0.212. The % CV s of the parameter estimates were slightly higher in Model 2 than in Model 1. However, all results were within a reasonable range. s and kd for the susceptible and resistant populations reveals a similar growth rate for the resistant population and the control group. The overall drug effects of the susceptible population were more than five -fold higher than that of the resistant population with restored fitness ( SMAX,S = 1.02 versus SMAX,DModel 4 consists of components of Models 2 and 3 Model 4 has the poorest fitting (Figure 311), despite having 9 parameters. In addition, t he k = 0.193). The %CV estimates of the third model were the lowest out of all four m odels, showing estimates mainly below 20% The proportional error was comparable to previous models. s valu e was 6 fold higher than the kd values The %CVs for the parameters w ere not estimated by ADAPT II. It appears that the PKPD model cannot describe the dual mechanisms u sing the richest kill-curve data set.

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54 Model Selections and Discussions S everal model selection criteria were implemented to select the best model. The se evaluations include (1) available literature data to support the hypotheses (2) objective function and Akaike criteria of the model output (3) visual inspection s of observed versus predicted plots (4) biological meaning of the model output (5) su bcompartmental profile analysis (6) simulation of multiple dose scenarios (7) model stability via bootstrap statistics and ( 8 ) model predictability via simulation of visua l predictive checks. The last three assessments are discussed in Chapter 4 as part of model validation steps For criter ion one, a wealth of data have been published in the literature to support both dormant and compensatory mutation hypothes e s. The mole cular and genetic approaches to study antimicrobial resistance are important and insightful. However, studying an isolated pathway sometimes limit s the ability to assess its contribution t o the overall clinical observations. The kill -curve data offers meaningful drugmicrobial dynamic relationships. For selecting a PKPD model, it was assumed that both hypotheses are relevant contributors to the mechanisms of antimicrobial resistance based on the literature support For each model to reach its final stage, objective functions and Akaike criteria were compared. However, they were not used to evaluate model fitting across model s due to th e fundamental differences of these models. For each model, the parsimonious modeling principle was applied while capturing the highlight of the hypothesis. The subcompartmental profiles for D ormant and C ompensatory mut ation model s are shown in Figures 312 to 313. The drug concentrations are shown in dash lines and microbial populations are shown in solid lines. I n Figure 3 12, the dynamic profiles

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55 of susceptible and dormant populations are shown as dark and light green lines over the 2 day treatment period. The simulation show s that as ciprofloxacin is administered, the susceptible population decreases in a dose dependent manner while the dormant population increases. Although the model predicted an increase in dormant population after drug exposure, the proportion of dormant population appear to be larger than what was observed in the laboratory settings. Acco rding to the literature, dormant population exceed ing the susceptible population, as indicated in the simulation, had not previously been observed The Compensatory Mutation hypothesis on the other hand suggests that following the exposure to ciprofloxac in, the susceptible population is reduced to a minimal level. The resistant population without fitness increased slightly in the presence of the drug but due to the lack of fitness, the population becom es insignificant. However, the resistant population, with fitness restored appears to dominate the overall population in the regrowth phase. This model suggests that re exposure to the same drug would have reduced effects because of the dominant RfitIn conclusion, while most of the criteria cannot concretely distinguish among models, the sub-compartmental profile simulation revealed that the Dormant Model requires a huge portion of the susceptible population be converted to the dormant population in order to describe the dynamic kill-curves. The Compensatory Mutation hypothesis provided the best explanation of the drug -microbe dynamic It suggests that a resistant population emerged after undergoing multiple mutations. Experimental designs along with the results of multiple doses used to confirm the prediction of loss population. Simulation s of multiple doses are presented in Chapter 4.

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56 drug effects from the Compensatory Mutation Model are shown i n chapters 5 and 6. The MIC dynamic will also be assessed over time to confirm the validity of selecting the Compensatory Mutation Model

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57 Table 3 1 Endogenous t oxin antitoxin (TA) molecules identified to disable and reinstate microbial replications in gram -negative and gram -positive bacteria. TA Family (locus) Toxin Antitoxin Target Phyletic Distribution ccd Ccdb CcdA DNA replication Gram neg relBE RelE RelB translation Gram neg/pos, Archaea parDE ParE ParD DNA replication Gram neg/pos higBA HigB HigA unknown Gram neg/pos mazEF MazF/Pemk MazE/Peml Translation Gram neg/pos, Archaea phd/doc doc Phd Translation Gram neg/pos, Archaea vapBC/vag VapC VapB unknown Gram pos

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58 Table 3 2 Model 1 p arameter estimates (literature PKPD model) Parameter Model Estimates %CV ks (/hr) 5.92 14.4 kd (/hr) 5.79 15.0 kc (/hr) 0.119 14.8 SMAX, S 0.100 20.0 SC50, S (g/mL) 0.249 20.7 kss (/hr) 3.06 0.873 kdd (/hr) 2.93 1.15 SMAX, R 0.0342 15.8 SC50, R (g/mL) 0.192 44.7 Proportional Error 0.198 6.71 Ks and kss = growth rate constants of susceptible and resistant populations; kd and kdd = degradation rate constants of susceptible and resistant populations; kc = conversion rate constant from susceptible to resistant population; Smax, S and Smax, R = overall drug effects on stimulating the kd or kdd; SC50,S and SC50,R = potency of drug on stimulating the kd or kdd. Table 3 3 Model 2 parameter estimates ( D ormant PKPD model) Parameter Model Estimates %CV ks (/hr) 0.921 66.1 kd (/hr) 0.709 88.5 ke (/hr) 0.108 15.5 SMAX, S 0.188 42.4 SC50, S (g/mL) 0.0588 56.4 SMAX, D 3.610 21.1 SC50, D (g/mL) 0.263 31.4 Proportional Error 0.212 6.78 Ks = growth rate constant of susce ptible population; kd = degradation rate constant of susceptible population; ke = conversion rate constant between s usceptible and dormant population s; Smax,S and Smax, D = overall drug effects on stimulating the kd or conversion of susceptible to dormant population; SC50,S and SC50, D = potency of drug on stimulating the kd or conversion of susceptible to dormant population

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59 Table 3 4 Model 3 parameter estimates ( C ompensatory M u t ation PKPD model) Parameter Model Estimates %CV ks (/hr) 0.813 14.5 kd (/hr) 0.660 18.3 kc (/hr) 0.172 10.7 SMAX, S 1.020 18.9 SC50, S (g/mL) 0.358 14.6 SMAX, R 0.193 21.3 SC50, R (g/mL) 0.113 31.6 Proportional Error 0.220 0.210 Ks = growth rate constants of susceptible or resistant with fitness populations; kd = degradation rate constants of susceptible or resistant with fitness populations; kc = conversion rate constant from susceptible to resistant population; Smax,S and Smax,R = overall drug effects on stimulating the kd of susceptible and resistant with fitness populations; SC50,S and SC50,R = potency of drug on stimulating the kd of susceptible and resistant with fitness populations. Table 3 5 Model 4 parameter estimates ( dormant and compensatory mutation combin ed PKPD model) Parameter Model Estimates %CV ks (/hr) 0.142 NA kd (/hr) 0.0235 NA ke (/hr) 0.088 NA kc (/hr) 0.00326 NA SMAX, S 28.60 NA SC50, S (g/mL) 0.374 NA SMAX, D 4.230 NA SC50, D (g/mL) 0.2680 NA Proportional Error 0.231 NA Ks = growth rate constant of susceptible population; kd = degradation rate constant of susceptible population ; ke = conversion rate constant from susceptible to dormant population ; kc = conversion rate constant from susceptible to resistant population; Smax,S and Smax, D = overall drug effects on stimulating the kd and conversion of susceptible to dormant population; SC50,S and SC50, D = potency of drug on stimulating the kd of susceptib le and conversion of susceptible to dormant population; NA = not available from ADAPT II output.

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60 Figure 31 Dormant hypothesis : U pregulation of endogenous toxins in the presence of antimicrobial agents prevents drug binding or tolerance to evade drug killing s .51 Susceptible Persister and Tolerance

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61 Figure 32 (A) In Vitro growth rate of control (triangle) and RelE induced (square) E. coli populations. The growth of RelE induced group showed growth retardation within 30 minutes. (B) Treatment with lethal doses of cefotaxime, mitomycin C, ofloxacin and tobramycin three hours after RelE induction showing greater survival rate (black bar) compared to the control (white bar) .51 Figure 33 Compensatory mutation hypothesis : Increase number of mutations leads to increase in drug resistance (A). However, the relative fitness decreases as the number of mutations increases (B) .57 RelE Induced Control (white bar) RelE Induced (black bar) Control Number of Induced Mutations

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62 Figure 34 Literature PKPD model : S usceptible (S) and resistant (Rfit) population with independent growth rate constant s (ks and kss) and degradation rate constant s (kd and kdd). Susceptible organisms can be converted to resist ant ones with the rate constant of kc. Drug effects are H ill function s denoted as H(C(t)) that work by stimulating the degradation rate constants of S and Rfit populations. ks S kd kc Rfit kdd kssH(C(t)) H(C(t)) + +

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63 Figure 35 PKPD model based on Dormant hypothsis : The susceptible population (S) has the growth and degradation rate constants of ks and kd and has nonspecific switching (ke ) between the susceptible and dormant (D) populations Drug effects denoted as (H(c(t)) sti mulate the degradation rate constant of S and conversion of S to D. Dks Ske kdH(C(t)) ke + +

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64 Figure 36 PKPD model describing Compensatory Mutation Model : The susceptible population (S) is converted to a resistant population without fitness (R) with the rate constant of kc. The R population undergoes compensatory mutation with the rate constant of kc to restore the fitness to become resistant with fitness population (Rfit). The S and Rfit have the same growth and degradation rate constants (ks and kd ) but different drug e ffects. S kd R kc kc Rfit kd ksH(C(t)) ksH(C(t)) + +

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65 Figure 37 PKPD model describing both dormant and compensatory mutation hypotheses : Susceptible population (S) can be converted to dormant population (D) with a rate constant of ke or resistant population (Rfit) wit h the rate constant of kc. The S and Rfit population exhibit the same growth and degradation rate constants (ks and kd). The drug stimulates the kd of S and conversion S to D. D ks S ke kc Rfit kd kd ks keH(C(t)) + +

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66 Figure 38 Observed (symbol) versus model predicted (line) values from Model 1 (literature PKPD model) Time (hr) 0 10 20 30 40 50 Log CSF 0 2 4 6 8 10 12 14

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67 Figure 39 Observed (symbol) versus model predicted (line) values from Model 2 (dormant PKPD model) Time (hr) 0 10 20 30 40 50 Log CSF 0 2 4 6 8 10 12 14

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68 Figure 310 Observed (symbol) versus model predicted (line) values from Model 3 (compensatory PKPD model) Time (hr) 0 10 20 30 40 50 Log CSF 0 2 4 6 8 10 12 14

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69 Figure 311 Observed (symbol) versus model predicted (line) values from Model 4 (dormant and compensatory mutation combined PKPD model) Time (hr) 0 10 20 30 40 50 Log CSF 0 2 4 6 8 10 12 14

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70 Figure 3 12 Subcompartmental profiles of Model 2 ( dormant PKPD model ): Dashline indicates ciprofloxacin concentrations, dark and light green lines indicate susceptible and dormant E.coli populations Time (hr) 0 10 20 30 40 Simulated Plasma Cipro Concentration (g/mL) 0 20 40 60 80 100 120 Log CFU 0 2 4 6 8 10 12 14 16 Cipro Concentration Susceptible Dormant

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71 Figure 3 13 Subcompartmental profiles of Model 3 ( compensatory mutation PKPD model ): Dash line indicates ciprofloxacin concentrations ; dark, light, and median dark green lines indicate susceptible, resistant, resistant with fitness E. coli populations, respectively Time (hr) 0 10 20 30 40 Simulated Plasma Cipro Concentration (g/mL) 0 20 40 60 80 100 120 Log CFU 0 2 4 6 8 10 12 14 16 Cipro Concentration Susceptible Initial Mutation Compensatory Mutation

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72 CHAPTER 4 MODEL VALIDATION AND PREDICTIONS Model Validation Using Bootstrap Statistics Model Validation Approaches The common model validation approaches include testing the model fitting or predictions using either an independent dataset or subsets of the original data that was not included in the model development. When these approaches are not feasible, bootstrap s tatistics are routinely used for model validation. The four antimicrobial resistance models described in Chapter 3 were developed using rich, dynamic kill -curve data published over 20 years ago103NONMEM VI with FOCE interactions was used to generate 1000 new datasets with each dataset equivalent in size to the original dataset. Model fittings were performed for the datasets and statistical summaries (mean and 90% confidence interval) for these are tabulated in Tables 4-1 to 44. The model estimates of the original dataset presented in Chapter 3 were compared with the bootstrap statistics. In addition, the bootstrap success rates for the models, defined by PDx POP software for consistency, are shown in the footnotes of the summary tables. The laboratory conditions and experimental procedures greatly affect the growth and degradation rates of microbes. Hence, the model validation approach to generate an independent dataset for modeling introduces inter -laboratory and inter occasion variability that would be difficult to resolve. The leave-some out approach from the original dataset was not preferred because the complex mechanism -based PKPD models require extensive data points. Thus, to validate the PKPD models, bootstrap statistics of a 1000 -runeach were performed.

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73 Bootstrap Statistics Comparisons As described in Chapter 3, Model 1 is the literature model. Model 2 is the Dormant hypothe sis model. Model 3 is the Compensatory Mutation hypothesis model. Model 4 describes the combination of Models 2 and 3. All models except for model 4, showed that the model estimates from the original dat aset were comparable to that of the bootstrap means and are mostly within the 90 % confidence interval. Model 4 serves as an example that the wellness of model prediction cannot be determined based solely on evaluating the comparison between observed and predict ed outcomes. The model estimates for Model 4 w ere not in agreement with the bootstrap statistics; the confidence intervals were large, and parameter s such as SMAX,S exhibited a large differ ence between the model estimate and bootstrap mean (28.6 versus 12.4). Not surprisingly, the bootstrap success rate was the lowest for Model 4 (61.8%). The bootstrap statistics for Models 13 were all reasonable, with the Compensatory Mutation Model having the highest success rate (83.9% versus 78.5% and 71.3%) and smallest confidence interval range. Although model selection cannot be based on bootstrap statistics alone, these analyses provide valuable information regarding model stability and precision. Model Predictions Visual Predictive Check Model predictability was evaluated using visual predictive checks (VPC) and multiple dose simulations. Visual predictive checks have been routinely used to evaluate model performance. Using the model parameters and error variances estimated from the final mode l, 1000 output s were generated using NONMEM VI. The 90th percentiles of the profile distributions were computed for each model to evaluate

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74 the distribution of the observed data within this range. To compare among the models, the percent of observed data points outside the 90th percentile were also calculated. In general, if the percentage of observed data is grossly greater than 10% outside the 90thIn comparison, the lowest percentage of observed data outside the 90 percentile distribution, the model is considered to have undesirable VPC outcome. The results of the visu al predictive checks for the models are shown in the footnotes of Tables 4 -1 to 44. thPKPD Multiple Dose Simulations percentiles infers best model performance. The VPC rankings for the four models from best to worst are: Model 4 (7.3%), Model 3 (8.3%), Model 1 (9.4%), and Model 2 (11.4%). This VPC analysis reveals the importance of not depending on a single criterion in model selection because Model 4 performed inadequately with bootstrap statis tics. Among the other models (Models 1-3), both the VPC and bootstrap statics show reasonable values. Based on these results, Models 13 were subject to further testing but Model 4 was discarded. Ciprofloxacin is adminis tered as twicea day dose. The PKPD model predicted that in an in vitro setting, the drug effect after the first dose is greatly reduced due to the emergence of resistance. Since Model 1 does not consider the emergence of resistance, it was not used for multiple dose simulation. The multiple dose PKPD profiles for Models 2 and 3 are simulated in Figures 4 -1 to 4 2. The PK profiles show the free fraction of ciprofloxacin concentrations in the plasma after a 200 mg b.i.d. dose for five doses. The corresp onding PD profiles for each subpopulation are shown for comparison (susceptible and dormant subpopulation for Model 2, and susceptible, resistance with and without fitness subpopulation for Mode 3). In addition, the total

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75 populations in Model 3 (sum of all three subpopulations) are shown as a compar ison to the susceptible population from Model 2. In both Models 2 and 3, significant losses of drug activities were predicted by the model. While a noticeable drug effect was predicted for Model 2 for all subsequent ciprofloxacin doses, Model 3 predicted a loss of killing effect after the first dose. The dormant population was predicted to increase after the initial ciprofloxacin exposure, which is consistent with the hypothesis that microbes self -induce t oxins to inhibit cell divisions when they sense a harmful substance in their environment. However, the proportion of the dormant population was predicted to be too large. There has not been any literature publication indicating that the dormant population is comparable to or larger than the susceptible population. Hence, the sub-compartmental simulation revealed that the Dormant Model did not have the biological support published in the literature. O n the other hand t he Compensatory Mutation Model appeared to provide reasonable explanation for each subpopulation. Following the initial dose of ciprofloxacin, the susceptible population was reduced to a negligible level within 12 hours. Over the next 24 hours, a resistant population without fitness developed but failed to contribute as a significant population. H owever t he resistant population with fitness was responsible for lack of drug efficacy and regrowth in the later dosing period. This model suggests that the subsequent doses of ciprofloxa cin have minimal effects on microbial killing. This explanation was consistent with the available data in the literature. Other published multiple dose in vitro kill -curves, shown in Figure 43, where the same doses of ciprofloxacin 200 mg w ere administered to P. aeruginosa, also

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76 showed the loss of drug effects by the second dose. In Dudleys study, the MIC increased over the course of ciprofloxacin therapy. Because, according to the Dormant hypothsis it is a phenotypic variant, i t has been suggested t hat the MIC may not differ once the microbes resume cellular activities following the elimination of drugs. Dudleys experiment further confirms the Compensatory Mutation Model as the superior model to explain emerged antimicrobial resistant pattern.

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77 Ta ble 4 1 Comparison of model estimates with bootstrap mean and 90% confidence interval s (CI) for Model 1 ( literature PKPD model) Bootstrap success rate and visual predict check s shown as the percentage of observed data outside the 90% confidence interval are presented. Parameter Model Estimates %CV Bootstrap Mean Bootstrap 90% CI ks (/hr) 5.92 14.4 5.80 3.18 8.77 kd (/hr) 5.79 15.0 5.64 3.13 8.65 kc (/hr) 0.119 14.8 0.126 0.0916 0.176 SMAX, S 0.100 20.0 0.120 0.0765 0.190 SC50, S (g/mL) 0.249 20.7 0.32 0.1070.753 kss (/hr) 3.06 0.873 2.97 1.88 4.29 kdd (/hr) 2.93 1.15 2.79 1.72 4.02 SMAX, R 0.0342 15.8 0.0559 0.0392 0.0969 SC50, R (g/mL) 0.192 44.7 0.114 0.0290.256 Proportional Error 0.198 6.71 0.188 0.1570.215 Bootstrap Success Rate: 78.5% Visual Predictive Check: % Observation outside 90% CI = 9.4% Ks and kss = growth rate constants of susceptible and resistant populations; kd and kdd = degradation rate constants of susceptible and resistant populations; kc = conversion rate constant from susceptible to resistant population; Smax,S and Smax,R = overall drug effects on stimulating the kd or kdd; SC50,S and SC50,R = potency of drug on stimulating the kd or kdd. Table 4 2 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 2 (Dormant PKPD model). Bootstrap success rate and visual predict checks shown as the percentage of observed data outside the 90% confidence interval are presented. Parameter Model Estimates %CV B ootstrap Mean Bootstrap 90% CI ks (/hr) 0.921 66.1 1.05 0.8111.52 kd (/hr) 0.709 88.5 0.805 0.6031.17 ke (/hr) 0.108 15.5 0.124 0.0835 0.183 SMAX, S 0.188 42.4 0.225 0.1160.365 SC50, S (g/mL) 0.0588 56.4 0.0751 0.0140 0.164 SMAX, D 3.610 21.1 3.23 1.33 4.91 SC50, D (g/mL) 0.263 31.4 0.346 0.0979 0.894 Proportional Error 0.212 6.78 0.198 0.1590.233 Bootstrap Success Rate: 71.3% Visual Predictive Check: % Observation outside 90% CI = 11.4% Ks = growth rate constant of susce ptible population; kd = degradation rate constant of susceptible population; ke = conversion rate constant between s usceptible and dormant population s; Smax,S and Smax, D = overall drug effects on stimulating the kd or conversion of susceptible to dormant populati on; SC50,S and SC50, D = potency of drug on stimulating the kd or conversion of susceptible to dormant population

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78 Table 4 3 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 3 (Compensatory Mutation PKPD model). Bootstrap success rate and visual predict checks shown as the percentage of observed data outside the 90% confidence interval are presented. Parameter Model Estimates %CV Bootstrap Mean Bootstrap 90% CI ks (/hr) 0.813 14.5 0.819 0.6540.941 kd (/hr) 0.660 18.3 0.664 0.5380.771 kc (/hr) 0.172 10.7 0.325 0.1660.565 SMAX, S 1.020 18.9 1.364 0.8902.087 SC50, S (g/mL) 0.358 14.6 0.346 0.2150.542 SMAX, R 0.193 21.3 0.215 0.1630.269 SC50, R (g/mL) 0.113 31.6 0.139 0.0636 0.365 Proportional Error 0.220 0.210 1.04 0.8121.237 Bootstrap Success Rate: 83.9% Visual Predictive Check: % Observation outside 90% CI = 8.3% Ks = growth rate constants of susceptible or resistant with fitness populations; kd = degradation rate constants of susceptible or resistant with fitness populations; kc = conversion rate constant from susceptible to resistant population; Smax,S and Smax,R = overall drug effects on stimulating the kd of susceptible and resistant with fit ness populations; SC50,S and SC50,R = potency of drug on stimulating the kd of susceptible and resistant with fitness populations. Table 4 4 Comparison of model estimates with bootstrap mean and 90% confidence intervals (CI) for Model 4 (Combined PKPD model). Bootstrap success rate and visual predict checks shown as the percentage of observed data outside the 90% confidence interval are presented. Parameter Model Estimates Bootstrap Mean Bootstrap 90% CI ks (/hr) 0.142 0.139 0.0556 0.417 kd (/hr) 0.0235 0.0447 0.0101 0.227 ke (/hr) 0.088 0.0845 0.0179 0.182 kc (/hr) 0.00326 0.0234 0.0001 0.0471 SMAX, S 28.60 12.4 1.01 44.3 SC50, S (g/mL) 0.374 0.291 0.0109 0.515 SMAX, D 4.230 3.74 0.1398.933 SC50, D (g/mL) 0.2680 2.51 0.0991 16.4 Proportional Error 0.231 0.189 0.1570.218 Bootstrap Success Rate: 61.8% Visual Predictive Check: % Observation outside 90% CI = 7.3% Ks = growth rate constant of susceptible population; kd = degradation rate constant of susceptible population ; ke = conversion rate constant from susceptible to dormant population ; kc = conversion rate constant from susceptible to resistant population; Smax,S and Smax, D = overall drug effects on stimulating the kd and conversion of susceptible to dormant population; SC50,S and SC50, D = potency of drug on stimulating the kd of susceptible and conversion of susceptible to dormant population; NA = not available from ADAPT II output.

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79 Figure 4 1 Subcompartmental simulation of the d ormant PKPD model following 5 b i d IV doses of 200 mg ciprofloxacin in E.coli. Susceptible Population CIP Conc (g/mL) Time (hr) Dormant PopulationTime (hr)Log CFU/mL PK profile

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80 Figure 4 2 Subcompartmental simulation of the Compensatory Mutation PKPD model following 5 b.i.d. IV doses of 200 mg ciprofloxacin in E.coli. Total Observable Population R with fitness R without fitness Susceptible CIP Conc (g/mL) PK profileTime (hr)Log CFU/mLTime (hr) Log CFU/mL Total Count

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81 Figure 4 3 MIC distribution for P. aeruginosa following 200 mg ciprofloxacin b.i.d. dose .106

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82 CHAPTER 5 UTILITIES OF MODELING AND SIMULATION IN DESIGNING EXPERIMENTS Introduction Regardless of the mechanisms of actions of antimicrobial classes, microbes have been able to consistently develop resistance to new drug treatments within a few years after their implementations58, 107, 108 The major factors contributing to this predicament include lack of understanding of the underlying mechanisms of antibacterial resistance and the use of suboptimal press ure specifically against the resistance population. The evaluation of antimicrobial s and microbial survival response has evolved from point estimates (minimum inhibitory concentrations) to complete time course approach (bacterial kill -curve) to reveal the drug-bacterial killing relationships .87, 92, 109, 110 However, it is only within recent years that the emphasis has shifted towards molecular and genetic approaches to understanding the mechanisms of resistance wit h additional insight on how to interpret the bacterial kill -curve relationships. It is with these new experimental findings that we propose a new mathematical model to bridge basic science research to relevant clinical usage. In this chapter we use the Co mpensatory Mutation hypothesis54 57, 99, 101, 102, 111113 as the foundation for the mechanism based pharmacokinetic/pharmacodynamics (PK/PD) model. The importance of the fitness co ncept and genetic mutation relationship were proposed to describe antimicrobial resistance. As the microbes undergo life cycle division every 20 min, selection for drug resistance mutants occurs within a short period of time following treatment. However, m utation is often associated with a fitness cost (the rate of ce ll division is reduced). It is only after multiple mutations that a drug resistant trait is acquired while further mutations occur and the mutated population becomes clinically relevant. It is this new

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83 compensated mutation population that explains the observed rising MIC over the time course of antimicrobial treatment .106We believe a quantitative modeling approach can provide the urgently needed link between the newly proposed microbial behavior and clinical dose optimization needed to better protect against infections. In the absence of adequate new antimicrobial s available in the next few years, we believe our approac h has great potential to revive some older antimicrobial s rendered useless due to resistance. The occurrence of resistance may be related to misuse of antimicrobial s that foster selection of resistance populations since this population was not considered w hen the clinical dosage was selected. In this study, we utilized a semi mechanism -based pharmacokinetic/pharmacodynamic (PK/PD) model to explore combination therapy that considers the emerged resistance population following ciprofloxacin treatment. Pharmacokinetic/pharmacodynamic model descriptions Details of the in vitro procedures have been published before.103, 114 Extensive in vitro k ill-curve data suitable for complex mechanistic modeling were obtained using GetData Graph Digitizer 2.24 software. Briefly, a two flask system with ciprofloxacin was used against Escherichia coli 204 (E. coli II), ranging from 0.0, 0.1, 0.2, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0, 32.0 and 125 times the minimum inhibitory concentration (MIC) of 0.08 ug/mL. The flask containing bacteria and drug was inoculated with 18 h-cultured bacteria followed by 2 h incubation. Ciprofloxacin was injected at the 20th hour. The inoculum size at the time of treatment was approximately106 colony forming units (CFU)/mL and the experiments ended when the total bacterial growth reached 1011 CFU/mL for each dose group. A clinical half -life of 4 h for ciprofloxacin was established

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84 in an in vitro kill -curve system by replacing 7 mL/h of fresh media in a constant 40mL flask. The monoexponential decline rate was described as: = Initial Condition = DOSE (5 -1) where kel rate constant is fixed to 0.175 h = ( 1 + ) I C =10 A graphical description of the semi mechanism based PD model is shown in Fig. 5 -1 and the respective differential equations are included below. 6 = IC = 0 CFU / mL (5 -3) CUF /mL (5 -2) = + ( 1 + ) IC = 0 CFU / mL (5 -4) w here the stimulatory function for susceptible population is described as: = (5 -5) and for Rfit = (5 -6) population as: The model describes the Compensatory Mutation hypothesis where S is the susceptible population, R is the mutated population with reduced fitness characteristic (negligible growth and degradation) and Rfit is th e resistance population after second mutation that restores fitness while retaining drug resistance characteristics. The model assumes the fitness is fully restored, showing the Rfit population exhibiting the same growth and degradation rate constant (ks and kd) as those of the S population. The multiple mutation process is described by an arbitrary kc rate constant. Ciprofloxacin has independent nonlinear killing effect on both S and Rfit population.

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85 A total of 10 ciprofloxacin treated groups and one c ontrol treated group were modeled simultaneously with the PK/PD model described above using ADPT II105Exploratory mechanism -based com bination therapy A total of 44 differential equations (sets of equations 5 1 to 5-4) were written to describe the eleven treatment groups. A proportional error model with maximum likelihood estimator in ADAPT II was impleme nted. Standard goodness of fit criteria used to obtain the final model included model convergence, Schwartz Criterion, Akaike Information Criterion, residuals versus predicted concentrations and time, and visual inspection. The final model output was tabulated in previous chapter (Table 34). The use of mechanism based PKPD models to design and predict outcome of combination therapy is shown in Figure 51. Antibiotic resistance is associated with increased MIC following drug treatment. Although MIC distribution over time was not assessed in the current study, a reduction in drug effects indirectly infers a rise of MIC during the drug exposure period. Using the time course relationship of sub -compartmental analysis from Section 2.2, additional simulations were explored to assess the feasibility of combination therapy. Figure 5 4 shows the proposed combination therapy approach using the mechanism based PK/PD model. It simulates scenarios where a second drug is inhibiting the production of bacterial synthesis with IC50 = (5 -7 ) set at 0.1, 1, and 10 n g/mL using Eq. ( 5 -7 ). where Kmax is the inhibitory equation on the synthesis rate constant of Rfit population. Imax is the maximum inhibitory effect, which was fixed to the maximum of 1 in the

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86 simulation. IC50Discussion represents the drug potency. Provided the reduction of the ciprofloxacin response after the initial dose, an antimicrobial drug from a different class that exhibits an alternat ive pharmacological action given as the second dose has greater beneficial effects compared to continuing ciprofloxacin monotherapy at the same or elevated (3X) dose. The semi mechanism -based PK/PD model mimicking the compensatory antimicrobial resistance hypothesis appears to describe the effects of eleven ciprofloxacin dose groups simultaneously reasonably well. The model captures the multiple step process needed for bacteria to develop into a clinically relevant resistant population. The resi stance without fitness compartment (R) explains the findings that mutated bacteria often lead to lower bacterial growth. Subsequent mutations that retain the drug resistance characteristics while acquiring the restoration of fitness from the clinically res istant populations that should be the target of interest. In theory, the second clinical dose would render diminished drug response with increased MIC. This phenomenon was observed previously106 using a multiple dose in vitro kill-curve system of ciprofloxacin against P. aeruginosa. Their findings show that bacterial killing at the second dose (12 hr) did not show an apparent reduction as compared to the first dose. In addition, the p rofiles of MIC distributions at 12 h were shown to increase by a large degree compared to the initial drug exposure. This multiple dose profile appears to be explainable by our compensatory PK/PD model. The multiple dose simulation from the model also did not show an apparent bacterial killing profile at a second dose given at 12 h compared to the initial drug exposure. In our simulation, a threefold increase in ciprofloxacin dosing only slightly increased bacterial killing (Figure 5 2 ). This lead us to

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87 ex plore novel dosing schemes using bacterial behavior information extracted from the PK/PD model. In general, a higher initial dose may result in a more pronounced pharmacodynamic effect, assuming maximum effects have not been reached. However, higher doses increase the risks of toxicity to patients. Hence, an alternative class of antimicrobial s with a different mode of pharmacological action may be more effective against the merged resistant population. At various potency levels (IC50In conclusion, this paper demonstrates a novel semi mechanism -based PK/PD model that describes the complex mechanisms of antimicrobial resistance using findings from recent basic science research. The microbial behavior extracted from the developed model was used to propose a study design for future experiments, predicting a different class of drug at a subsequent dose may result in superior killing of the resistant population compared to a continued treatment with ciprofloxacin. ), the model suggests a second drug with different pharmacological actions given at a subsequent dose may be more beneficial than continuation of ciprofloxacin where the bacterial have already evolved to successfully resist and grow with comparable fitness as that of the parent population.

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88 Figure 5 1 Use of mech anism -based PKPD models for combination therapy115

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89 Figure 5 2 Utilizing the compensatory mutation PKPD model to design combination therapy for in vitro dynamic kill -curve experiments S kd R kc kc Rfit kd ksH(C(t)) ksH(C(t)) + + Dose 1: CIP Dose 2: CIP OR Dose 2: GentamicinH(C(t))

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90 Figure 5 3 Model anticipated kill -curve profiles following 200 mg of ciprofloxacin at first dose then 200 mg ciprofloxacin at second dose (A) or 3 -fold higher of ciprofloxacin at second dose (B), or gentamicin at low (C), mid (D), or high (E) at second dose Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 1 2 3 4 5 6 7 A B C D E CIP CIP or Drug X ID Dose 1 Dose 2 (A) 200 mg CIP 200 mg CIP (B) 200 mg CIP 600 mg CIP (C) 200 mg CIP Low Dose X (D) 200 mg CIP Mid Dose X (E) 200 mg CIP High Dose X

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91 CHAPTER 6 PKPD MODEL CONFIRMATION USING DYNAMIC KILL -CURVE EXPERIMENTS Introduction Pseudomonas aeruginosa is infamous for being highly adaptive to their environment as well as for impos ing a significant public health threat. Within the field of infectious agent s P. aeruginosa has one of the largest genome, with the number of genes being 1.3 -fold more than that of Eschericia coli 2.2 -fold more than that of staphylococcus aureus and 3.3-fold more than that of Haemophilus influenza.116 The large genome increases the abili ty to produce a large number of functional proteins and intricate defense systems within a short period of time. The well -known antimicrobial resistan t mechanisms of P. aeruginosa include (1) decreas ing membrane permeability (2) enhanc ing efflux pump syst ems such as the mexAB oprM, mexXY oprM, mexCD oprJ and mexEF oprN117, (3) alter ing drug binding sites118, 119 and (4) modifying drug properties .118, 120130Given the adaptability of P. aeruginosa following antimicrobial administration, it is not surprisingly that the tradition antimicrobial treatment approach, which relies on single MIC time point (AUC/MIC, Cmax/MIC, or T>MIC) is bound to be ineffective over time Therefore, in vitro dynamic kill -curve and MIC dynamics were utilized in our experiments to more thoroughly elucidate the time -course of the PKPD relationship involving the emergence of resistance. The object ives of the studies are to characterize the emergence of cipr ofloxacin resistance strain using a clinical isolate of P. aeruginosa, and, once the resistance emerged, explore different treatment options to overcome the recalcitrant population. The experiments were design ed using predictions from the In reality, the phenotypic expression of resistance is likely a combination o f all mechanisms working simultaneously.

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92 compensatory mut ation PKPD model discussed in Chapter 5. Hence, t he kill -curve data also serves as a confirmatory experiment for the PKPD model. Material and Methods Study Conduct The clinical strains of pseudomonas aeruginosa used in the dynamic kill -curve and MIC assays are consider ed biohazard level 2. All experiments were conducted in a microbiology lab using the standard operating procedure (SOP) approved by the department of Environmental Health and Safety at the University of Florida. The MIC procedure s were conducted i n compliance with the Clinical and Laboratory Standards Institute (CLSI) approved standard methods. Sterile techniques and proper disposal of biohazard materials were practiced throughout the experiments. Antimicrobial Drug Preparatio ns Ciprofloxacin (CAS 85721 -33) was purchased from Sigma-Aldrich (St. Louis, MO). The original stock solution of 40 g/mL was prepared by dissolving 20 mg of ciprofloxacin in 500 mL of purified water using heat and a sonicator. Ceftriaxone (CAS 104376-7 9 6) was purchased from Sigma-Aldrich (St. Louis, MO). The stock solution of 1650 g/mL was prepared by dissolving 16.5 mg in 10 mL of purified water. Gentamicin (CAS 1405-41 0) was purchased from Sigma-Aldrich (St. Louis, MO) in the form of 50 mg/mL of deionized water. The stock solution of 1000 g/mL was prepared by diluting 1 mL of the 50 mg/mL solution with 50 mL of purified water. Aztreonam (CAS 78110380) was purchased from MP Biomedicals (Irving, CA). The stock solution of 5000 g/mL was prep ared by dissolving 10 mg in 2 mL of DMSO.

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93 Microbial Strain A clinical strain of pseudomonas aeruginosa isolated from a patient at Shands Hospital at the University of Florida was used throughout the experiments. The same microbe isolate was subcultured on agar plates throughout the kill -curve experiments to maintain the cell line. Sterile Broth and Saline Preparation A Mueller -Hinton broth (Becton Dickinson BBL) was prepared according to the manufacturers instructions Dissolved solut ion was autoclaved at 121C for 1 5 minutes then cooled to room temperature prior to use Normal saline was prepared by dissolving 9 g of sodium chloride in 1 L of double distilled water. The saline solution was then autoclaved at 121 C for 20 minutes P re -Resistance Strain Determination An agar solution was prepared by mixing 38g of agar powder in 1 L purified water. The agar solution was autoclaved at 121 C for 15 minutes then cooled to 45 -50 C. Two dose levels of ciprofloxacin were prepared for the pre-resistan t strain experiment : 0.563 mg/mL and 1.688 mg/mL of ciprofloxacin w ere prepared in purified water and 1 mL was spiked into 375 mL agar solution to obtain 1.5 and 4.5 ug/mL of ciprofloxacin concentration in the agar solution. A control of the agar group without ciprofloxacin was included. The ciprofloxacin containing agar solutions were poured into sterile petri dishes in triplicates to a 4 mm depth, and cool ed to room temperature to form agar plates Aliquots of 150 L of 108 CFU/mL bact eria w ere dispensed into tissue culture flasks containing 15 mL Mueller -Hinton broth to achieve the initial inoculation of 106 CFU/mL. For bacterial cell plating five aliquots (10 L each) from each group were

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94 pipetted onto the ciprofloxacin containing agar plates and dried at room temperature prior to being incubat ed at 37 C for 16 -20 hours for colony count ing Dynamic Kill-Curve s Two dynamic kill -curves were performed using sequential dosing scheme of two doses Experiment 1 consists of 4 groups. Group 1 received saline dose as control at time 0 and 12 hours. Group 2 received 200 mg ciprofloxacin as the first dose then 200 mg ciprofloxacin again as the second dose. Group 3 received 200 mg ciprofloxacin as the first dose th en increase to 600 mg ciprofloxacin as the second dose. Group 4 received 200 mg ciprofloxacin the first dose then switch to 2 g of Ceftriaxone as the second dose. Each group was performed in triplicates. Experiment 2 consists of 4 groups with 2 doses at 0 and 12 hours. Group 1 is the control. Group 2 received 200 mg ciprofloxacin as the first dose then 200 mg ciprofloxacin again as the second dose. Group 3 received 200 mg ciprofloxacin as the first dose then switch to 7 mg/kg gentamicin as the second d ose. Group 4 received 2 g aztreonam for both doses. The day before the experiment, P. aeruginosa w ere removed from a fridge and plated on agar plates in a 37 C incubator to obt ain the exponential growth prior to the experiment. An aliquot of bacteria w as then diluted in sterile saline to 108 CFU/mL using a calibrated turbidity meter. Aliquot s of 150 L of 108 CFU/mL bacteria w ere dispensed into 25 mL canted neck Tissue Culture Flask s containing 15 mL of Mueller Hinton broth, to achieve the initial inoculation of 106The drug profiles in the experiments were determined by clinical dose, protein binding, and clinical half -life information. To obtain the initial free fraction of CFU/mL. The bacteria and broth solution were incubated at 37 C for two hours prior to adding any drugs.

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95 ciprofloxacin concentrations (CO) of 1.5 and 3 g/mL equivalent to 200 mg and 600 mg IV bolus dose s in humans 0.563 and 1.125 mL of stock solution was spiked in cell culture flasks containing 15 mL of bacteria containing broth solutions. To obtain the free fraction of ceftriaxone with a CO of 40 g/mL after clinical dose of 2 g IV bolus dose, a 0.364 mL of stock solution was spiked into a cell culture flask containing15 mL of bacteria containing broth. To obtain the free fraction of gentamicin COFor each flask, a 5 mL syringe with a 0.22 m filter (Millipore Cat SLGV033NS Billerica, MA) was attached The dilution of drug concentrations were done manually with a syringe by drawing out appropriate sample volumes then replacing the same amount with fresh broth every 2 hours to mimic clinical half -life. The 0.22 m filters selectively remove the drug without significantly changing the bacterial population within the system. Each test group was performed in triplicate. Bacterial count was taken at 0, 2, 4, 6, 10, 12, 14, 16, 18, 22, and 24 hours post initial dru g administration. For each bacteria cell count 20 L of sample was removed from the flask and appropriate dilutions in saline (ranging from 1 to 9-fold dilutions) were performed in Corning Costar 96 Cell culture plates ( Sigm a -Aldrich, CLS3596, St. Louis, MO). The diluted samples were then aliquotted in 4 replicates (10 L each) onto agar plates. Agar plates containing 5% sheep blood w ere purchased from Remel (Lenexa, KS). The samples of 20 g/mL after clinical dose of 7 mg/kg or 490 mg IV dose for a 70 kg person, a 0.3 mL of stock solution was spiked into the cell culture flask containing 15 mL of broth and bacteria. To obtain the f ree fraction of aztreonam with Co of 40 g/mL after clinical dose of 2 g IV bolus dose a 0.12 mL of stock solution was spiked into cell culture flask containing 15 mL broth and bacteria.

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96 were dried at room temperature then incubated at 37 C for 16 20 hours for colony count. For each group, mean and standard deviation of the bacterial count was calculated for plotting with Sigma P lots 11.0 (San Jose, CA) MIC Determination Minimum inhibition concentration (MIC) for ciprofloxacin was determ ined using an E-strip test A ztreonam was determined using a disk MIC test The E -strip contains a gradient of ciprofloxacin ranging from 0.002 to 32 g/mL. The E -strip method is superior to the dilution method because the M IC value is independent of the dilution factors. The disk MIC test measures only the diameter of the area without growth so the results are shown as a percentage change relative to the pre-dose level. The samples for the MIC test were a combination of various colonies from the trip licate plating for each group so that only one MIC reading per group was obtained. For both techniques, lawn s of bacteria were platted on agar plates and the E -strip or disk was placed in the center of the plate then incubated at 37 C for 14 hours for M IC determination. For the first ciprofloxacin and ceftriaxone kill -curve experiments, MIC was determined at 0, 6, 12, and 24 hours. For the second ciprofloxacin, gentamicin, and aztreonam experiment s MIC was determined at 0, 6, 12, 16, 18 and 24 hours d uring the treatment period and 48, 72, and 96 hours for post antimicrobial effect analyses. Results Pre -Resistance Strain N o visible colony was observed on either the 200 or 600 mg groups after overnight incubation The c ontrol without drug added in the agar solution showed an abundance

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97 of colonies after overnight incubation. The control samples were not diluted and the colonies were too dense for cell counting. Ciprofloxacin and Ceftriaxone Kill-Curves The kill -curve profiles after ciprofloxacin and ceftriaxone treatment s are shown in Figure 61. The control showed an exponential growth rate reaching approximately 1011 CFU/mL by hour 12. Th e microbial concentration approximate s the maximum growth within the system and no further bacterial count was performed after the 12thThe MICs of ciprofloxacin taken throughout the kill -curve experiment are shown in Figure 62. All bacteria have a similar pre -dose MIC of 0.13 g/mL. Af ter 6 hours of 200 mg ciprofloxacin exposure, a significant increase in MIC was observed for all dose groups. The MIC values stay high throughout t he treatment period and were approximately 4 g/mL at the end of the 24 hour experiment. hour. All groups exposed to 200 mg of ciprofloxacin at the first dose exhibited an approximate 2log kill profile. The mean and standard deviation of all three groups were comparable for all time points in the first 12 hour period At the second dose, the 200 mg ciprofloxacin dose showed no apparent killing effect. Furthermore, increas ing the ciprofloxacin dose to 600 mg at second dose only slightly lowered the growth rate; no log -kill was observed. S witching from ciprofl oxacin to c eftriaxone at second dose also did not show significant killing activities (Figure 6 1). Cross -Resistance Evaluations with Automated MicroS can Micro Scan analysis determines the susceptibility of a particular microbe to an array of antimicrobial agents From the first kill -curve experiment, the 0 and 12 hour samples were submitted for M icro Scan analysis at the C linical M icrobiology L aboratory at the University of Florida. Drugs that the particular clinical isolate of P. aeruginosa are

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98 pre -resistance to are tabulated in Table 6-1. It appeared that P. aeruginosa is preresistance to many lactams, DNA inhibitor, antifolate, and tetracycline. Drugs belong to the susceptible and intermediate resistance class es are tabulated in Table 6 2. The drug class that appears to maintain effectiveness against the P. aeruginosa isolate is the aminogly cosides. The second kill -curve experiment evaluates t he effect s of gentamicin following the emergence of resistance. Ciprofloxacin, Gentamicin, and Aztreonam Kill-Curves The kill -curve profiles of the control group and drug treated groups are shown in Fi gure 63. The control group reached maximum growth of approximately 1011The percentages of MIC changed from bas eline for aztreonam are shown in Figure 64. By the 24 CFU/mL. In this experiment, G roups 2 and 3 received ciprofloxacin as the first dose then ciprofloxacin at the same dose again or switch to 7 mg/kg gentamicin. Bacterial c ell count was performed on only one of the se two groups after the initial ciprofloxacin dose due to comparable values observed in t he first kill -curve experiment. The 200 mg ciprofloxacin a gain showed no apparent drug effect after the second dose. However switchi ng to g entamicin at the second dose achieved the necessary logkill. This reduction of bacterial count is consistent with the MicroScan output that P. aeruginosa remained susceptible to gentamicin after ciprofloxacin exposure. The group that received a zt reonam a s the first and second dose showed the same loss of drug effect as observed for ciprofloxacin. However, the rate of growth after the second exposure was lower than that of ciprofloxacin or the control group. th hour, the MIC increased more than 25% from the baseline level. The MIC correlated with the same reduced drug effects as observed in the kill -curve experiment.

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99 In this kill -curve experiment, MIC v alues were obtained for ciprofloxacin during the drug exposure period and continued for another 3 days in order to assess the post antimicrobial effects. The MIC also showed a noticeable increase 6 hour s after the initial ciprofloxacin exposure and increased 56 fold by 24 hour s By the second day after drug exposure, t he MIC values had gradually been reduced to the pre-dose level (Figure 65) However, the E -strip test showed a heterogeneous P. aeruginosa population at 3 days post -dose with colonies growing in the higher drug concentration zone (Figure 6 6 ). This laboratory observation indicates that new strains of P. aeruginosa, with higher MIC s had emerged after ciprofloxacin treatment and remained within the population for days after drug had cleared. Discussions/Conclusions The first experiment examined the presence of a pre-resistance strain of P. aeruginosa to ciprofloxacin. If the particular clinical isolate is pre resistance to ciprofloxacin t he n the previous model found in the literature (Model 1 discussed in Ch a pter 3) which model ed two populations independently may be sufficient. However, since a pre-resistant population was not present a new PKPD model capable of capturing the emergence of resistance over the course of drug treatment is warranted. As described in Chapter 5, the compensatory mutation PKPD model was used to design kill -curve experiment s that evaluate the emergence of resistant characteristics. Using the single dose data, the model predicted a loss of dru g effect once the microbes were exposed to 200 mg ciprofloxacin in vitro This was confirmed by the multiple dose kill -curve experiment; Once the resistance is developed, i ncreas ing the second ciprofloxacin dose by three-fold was insufficient to exhibit the same log -kill profile as observed after the first dose. Hence, the kill -curve confirms the model predictions. In

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100 addition, the increase in MIC s further support s the compensator y mutation PKPD model; Dormant hypothsis model claims the phenotypic variance may not change the MIC once the cellular activities resume after drug exposure. Table 6 2 shows the alarming trend of several classes of susceptible antimicrobials to become resistant following exposure to c iproflox acin. Most of these -lactams As observed from the kill -curve experiment, this particular clinical P. aeruginosa isolate was intermediately resistant to ceftriaxone prior to ciprofloxacin exposure, and advanced to fully resistant following ciprofloxacin exposure. The majority of clinical isolates of P. aeruginosa are pre-resistan t to ceftriaxone. Ceftriaxone would not be a drug of choice for patients infected with P. aeruginosa Consistent with the pre-resistance strain experiment, the c linical isolate was susceptible to ciprofloxacin prior to drug exposure. Although a significant lo ss of drug effect was observed after ciprofloxacin treatment, the MicroScan results showed that clinical isolate was only an intermediate resistant strain af ter ciprofloxacin exposure. The MicroScan also revealed that a microbe population with susceptible status prior to ciprofloxacin treatment was converted to full resistance after ciprofloxacin exposure. This proved true for several antimicrobial s commonly prescribed for P. aeruginosa infections including cefepime, imipenem, and piperacillin/tazobactam These findings suggest lactams should be avoided once ciprofloxacin treatment fails. Aminoglycosides such as amikacin, gentamicin, or tobramycin, which were shown by MicroScan to retain susceptible status before and after ciprofloxacin exposure, should be used instead The second kill -curve introducing gentamicin at the second dose

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101 f urther confirms the effectiveness of this sequential dosing approach once ciprofloxacin resistance has emerged. Beta -lactams and quinolones primarily enter the bacterial cell wall through the porin channels, which are located at the outer membrane of P. aeruginosa and are permeable to small aqueous compounds. Several porin channels have been identified. T he most common, OprD, appear s to be associated with imipenem resistance when it is altered. Since different antimicrobial agents may utilize different porin channels for cell entry, alteration of a particular porin c hannel may explain drug-specific failure, despite coming from the same class of antimicrobials. A strain that relies on altering membrane proteins may not be effective against aminoglycosides, which cross the outer membrane through lipopolysaccharide (LPS ) uptake, rather than porin channels. Inevitably, P. aeruginosa can still prevents aminoglycoside entry through alteration of the LPS binding site131The induct ion of drug resistance by ciprofloxacin is not class dependent. Treatment with a -lactam such as aztreonam also showed a similar development of resistance as that observed with ciprofloxacin. This increase in response failure is also accommodated by the increase in aztreonam MIC. Besides reducing membrane permeability, lactams are often ineffective against P. aeruginosa because of their ability to upregulate the gene ampC which -lactamase 132P ost antimicrobial evaluation reveal s that the absence of drug influence leads to a reversal of the MIC values to approximately the pred -dose level. However, the visible For other classes of antimicrobial agents, P. aeruginosa can also inactivate the drug product through phosphor ylation, acetylation, or adeny lation.

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102 emergence of colonies with acquired resistance and restored fitness as described by the Compensatory Mutation hypothesis remain long after drug exposure. This observation suggests that once P. aeruginosa are exposed to ciprofloxacin, a biological memory is retained through out the subpopulation that may render future treatment more difficult. If th e s e characteristics were not recogniz ed and the same fluoroquinolone or lactams were used to treat re -infection, treatment failure may occur It appeared that a minoglycoside s would be a preferred option for treating resistance that emerged from ciprofloxacin treatment. The dose dependency of resistance emergence was not evaluated in this stud y The 200 mg ciprofloxacin used to foster resistan ce development is considered a low clinical dose. It would be informative for future studies to evaluate the different initial dose levels on the development of resistance. In addition, it would be useful to evaluate the initial inoculation effects on the emergence of resistance in order to better understand the PKPD relationship. The relationship of each antimicrobial agent with a particul ar microbe species is difficult to predict and is currently not well understood. Future experiments extending this kill -curve approach to study emergence of resistance will provide important insight into drug -microbial resistance dynamic.

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103 Table 6 1 The susceptibilities of P. aeruginosa used in the in vitro dynamic kill -curve before and after 200 mg ciprofloxacin treatment determined by MicroScan Gram Neg BP Combo 34 panel (list of pre -resistance antimicrobial agents). Antimicrobial Agent P. aerugino sa QC BREAKPOINT (ATCC 27853) 0 HR PREDOSE 12 HR CIPRO SUSCEPTIBLE (S), INTERMEDIATE (I), RESISTANCE (R) Beta Lactams (2nd generation cephalosporin) Cefoxitin >16 >16 >16 Pre Resistance Cefuroxime >16 >16 >16 Pre Resistance Cefotetan >32 >32 >32 Pre Resistance Cefazolin >16 >16 >16 Pre Resistance Beta Lactams (penicillin) Ampicillin >16 >16 >16 Pre Resistance Ampicillin/Sulbactam >16 >16 >16 Pre Resistance Beta Lactams (carbapenem) Ertapenem >4 >4 >4 Pre Resistance DNA Inhibitor Nitrofurantoin >64 >64 >64 Pre Resistance Polyketide Tetracycline 8 >8 >8 Pre Resistance Antifolate Trimethoprim/Sulfamethoxazole 8 >2 >2 Pre Resistance Carboxypenicillin Ticarcillin/K Clavulanate Pre Resistance

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104 Table 6 2 The susceptibilities of P. aeruginosa used in the in vitro dynamic kill -curve before and after 200 mg ciprofloxacin treatment determined by MicroScan Gram Neg BP Combo 34 panel Antimicrobial Agent P. aeruginosa QC BREAKPOINT (ATCC 27853) 0 HR PREDOSE 12 HR CIPRO SUSCEPTIBLE (S), INTERMEDIATE (I), RESISTANCE (R) Piperacillin/Tazobactam 64 S to R Beta Lactams (carbapenem) Meropenem S TO S Imipenem >8 S TO R Beta Lactams (3rd generation cephalosporin) Ceftriaxone 8 64, BP >32 32 >32 I TO R Cefotaxime 16 32 I TO R Ceftazidime 4 16 S TO I Beta Lactams (4th generation cephalosporin) Cefepime >16 S TO R Beta Lactams (monobactam) Aztreonam >16 S TO R Aminoglycosides Amikacin S TO S Gentamicin S TO S Tobramycin S TO S Fluoroquinolone Ciprofloxacin 2 S TO I Levofloxacin 4 S TO S

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105 Figure 6 1 In vitro dynamic kill -curves involving saline control, ciprofloxacin and ceftriaxone. Arrows indicate dosing. Time (hr) 0 4 8 12 16 20 24 28CFU/mL 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 1e+7 1e+8 1e+9 1e+10 1e+11 1e+12 1e+13 Growth Control 200 mg CIPRO then 200 mg CIPRO 200 mg CIPRO then 600 mg CIPRO 200 mg CIPRO then 2 g Ceftriaxone

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106 Figure 6 2 Ciprofloxacin MIC dynamics corresponding to the kill -curve experiment in Figure 61 Time (hr) 0 6 12 18 24 30MIC (mcg/mL) 0 1 2 3 4 5 6 Control 200 mg CIPRO then 200 mg CIPRO 200 mg CIPRO then 600 mg CIPRO 200 mg CIPRO then 2 g Ceftriaxone

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107 Figure 6 3 In vitro dynamic kill -curves involving saline control, ciprofloxacin, gentamicin, and aztreonam. Arrows indicate dosing. Time (hr) 0 4 8 12 16 20 24 28CFU/mL 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 1e+7 1e+8 1e+9 1e+10 1e+11 1e+12 1e+13 Growth Control 200 mg CIPRO then 200 mg CIPRO 200 mg CIPRO then 7 mg/kg Gentamicin 2 g Aztreonam then 2 g of Aztreonam

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108 Figure 6 4 Aztreonam MIC dynamic corresponding to the kill -curve experiment in Figure 63 Time (hr) 4 6 8 10 12 14 16 18 20 22 24 26 MIC Change (% Baseline) 0 5 10 15 20 25 30

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109 Figure 6 5 Ciprlfoxacin MIC dynamic corresponding to the kill -curve experiment in Figure 63. The line after 24 hour separates the dosing period and the post antibiotic period Time (hr) 0 24 48 72 96 MIC (mcg/mL) 0 2 4 6 8 10 12 14

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110 Figure 6 6 Ciprofloxacin E -strip test for MIC determination 3 days post the last ciprofloxacin exposure (96 hr). Visible colony growth was observed in the high ciprofloxacin concentration zone, which was not present in the p re treatment samples CIPRO -CIPRO 3 days post exposure

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111 CHAPTER 7 POPULATION PHYSIOLOGICALLY BASED PHARMACOKINETIC MODEL OF CEFTOBIPROLE IN HEALTHY VOLUNTEERS Introduction Methicillin resistant Staphylococcus aureus (MRSA) are resistan t to most of the lactam antimicrobials133 136. Ceftobiprole is a 5th generation cephalosporin for treating skin and soft tissue infections caused by either gram -negative or gram -positive bacteria It has bactericidal properties against MRSA because of its resistant characteristics to staphylococcal -lactamase. Ceftobiprole target MRSA by binding to PBP2a which is encoded by the mecA gene of lactam resistant MRSA137, 138. It is also effective against S. pneumoniae and P. aeruginosa139. Moreover, ceftobiprole is well tolerated and has reported only minor adverse effects ; n ausea, vomit ing and headaches in clinical trials140, 141Its a common practice to measure and use total plasma concentrations for PK or PKPD evaluations. However this approach, though convenient, ignores the following two important facts: ( 1) The free fraction of the drug is responsible for the observed pharmacological response. Therefore measuring free drug concentrations is more meaningful than using total drug concentrations in plasma. (2) The measured drug concentrations in plasma may no t always represent drug concentrations at the site of action. For drugs like ceftobiprole, used for treating skin and skin structure infections, the time -course of free drug concentrations at target sites can be measured using microdialysis technique. Fo r ceftobiprole, two microdialysis probes placed onto skeletal muscle and subcutaneous adipose tissue provided accurate representation of the drugs availability at its target site in humans.

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11 2 Traditionally, physiologically base pharmacokinetic (PBPK) models are developed in animals for extrapolation to predict human exposure. It is possible to predict human tissue concentrations of a drug by utilizing the known physico -chemical characteristics of the drug and available animal data. However it is advisable to use information on human tissue distribution, if available, for building a reliable PBPK model. Microdialysis, though not suitable for all tissues in clinical settings, is ideal for measuring drug distribution in adipose and muscle tissues. It also pro vided an unique opportunity for population PBPK model to gain insights into the population variance which is informative in predicting population target attainment rate. In this paper, we describe a population PBPK model for ceftobiprole using microdialys is data from muscle and adipose tissues and free drug concentrations measured in plasma. The Pop-PBPK model was then employed to assess the drugs exposures at the target sites using different dosing strategies. Method Study Design The details of the study design have been previously published72. The study was conducted at the General Clinical Resear ch Center at Shands Hospital at University of Florida (Gainesville, FL). The age of the subjects (6 males and 6 females) ranged from 20 to 34 years and no subject received any other drug treatment for at least a week prior to the study. Subjects received single dose of 500 mg ceftobiprole infused intravenously over 2 hours. Microdialysis samples were collected from skeletal muscle and subcutaneous adipose tissue according to a previously developed method142. Briefly, the microdialysis probes implanted into subcutaneous adipose and muscle tissues were perfused with lactated Ringer s solution at a flow rate of 1.5 L/min.

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113 Dialysate samples were collected at pre dose, every 20 min for 12 hours after the start of infusion and at 16 and 24 hours post dose. Retrodialysis was performed according to Stahle et al 1991143PBPK Model as a calibration measure to calculate true tissue interstitial fluid (ISF) concentrations of Ceftobiprole. Samples were collected without anesthetics to prevent drugdrug interactions. Blood samples were collected into EDTA containing tubes at predose, 40 min, and 1, 1.6, 2, 2.3, 3, 4, 6, 8, 12, 16, and 24 hours after the start of infusion for plasma Ceftobiprole concentration determination. Additional blood was samples were collected at 2 and 12 hours for protein binding determination. A validated high performance liquid chromatography with UV detection method with a limit of quatitation (LOQ) of 0.1 g/mL was used to determine drug concentrations from the microdialysis samples. A validated liquid chromatography tandem mass spectrometry with a LOQ of 0.05 g/mL was used to determine total plasma drug concentrations. The noncompartmental parameters published previously are shown in Table 71 for compar isons. Individual tissue volumes and blood flow were used for building the PBPK model. The physiological parameters for cardiac output, blood perfusion and organ weights for both male and females were obtained from Williams and Leggett (1989)144 and the relevant values used in the model are summarized in Table 72. The body surface for each subject was first calculated using DuBois & DuBois method145: BSA (m) = 0.20247 x Height (m)0.725 x Weight (kg)0.425. Individual blood perfusion rate were then calculated as BSAi/BSAaverage*organ massaverage*blood perfusionaverage*60 mins/1000. Individual cardiac output was calculated as BSAi/BSAaverage*blood flowaverage*60 mins/1000 (Table 73). Assuming the density of the tissue and blood to be 1 kg/m3,

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114 individual organ mass were calculated as BSAi/BSAaverage*organ massaverage A diagrammatic representation of the PBPK model is shown in Figure 7-1. The card iac output distributes plasma to muscle, subcutaneous (S.C.) adipose tissue, kidneys, and remainders (the rest of the body besides the ones aforementioned) with the organ specific plasma flow rates (QM, QF, QK, and QR, respectively). The QR is calculated as plasma flow of cardiac output minus the sum of plasma flow rate from other compartments (QM+QF+QK). Similarly, the remainder volume is calculated as total body volume minus other tissue volumes used for the PBPK model. The outflow of plasma from the c ompartments becomes the input of the plasma compartment. Ceftobiprole is predominantly cleared by the kidneys (80%) (Table 74). All values were then converted to plasma flow to match the free drug concentrations in plasma. The plasma flow rates and tissue weights obtained from the literature for males and females are shown in Figure 7 -2. Subject -specific plasma flow rates and tissues weight were calculated as discussed above and presented in Figure 73. 146 = ( ) / IC = 500 mg IV hence, it was assumed to be cleared only from the kidney compartment. The equations used for the PBPK model are listed below: inf = ( ) / IC = 0 (7 -2) over 2 hr (7 -1) = ( ) / IC = 0 (7 -3) = ( ) / IC = 0 (7 -4) = ( ) / IC = 0 (7 -5)

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115 w here dFP/dt, dM/dt, dF/dt, dK/dt, and dR/dt describe the time courses of unbound ceftobiprole c oncent rations in plasma, skeletal muscle, subc utaneous adipose tissue, kidney and remainder compartments respectively CO is the cardiac output, and Q, V, and KPThe population PBPK model was developed using Monolix software (INRIA, France). The estimated model parameters were tissue partition coefficients, ceftobiprole clearance, inter variabilities were initially added to all parameters and then any estimates less than 10 are the plasma flow, tissue volume, and partition coefficient for the tissues. The partition coef ficient in this case isnt a true measurement of ceftobiprole partition into tissue sites due to insufficient knowledge of protein binding and other biochemical factors occurring between plasma and tissue sites. 5 were removed from the final model. Addition of inter subject variability on parameters that failed to improve VPCs were excluded. plasma, skeletal muscle, subcutaneous adipose tissue, and kidneys, and on partition coefficient of skeletal muscle, subcutaneous adipose tissues, kidneys, and remainders, Residual error was defined by a proportional error model in the final PBPK model. In Monolix, a random seed and automatic iteration design was selected. The visual predictive check was produced from 1000 simulations. Variances of the random effects and stochastic approximation of the standard errors were select ed. The loglikelihood was estimated by linearization and fisher matrix estimation was selected to generate standard errors of parameter estimates.

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116 Since the available data had only single dose level, further model evaluation was performed by simulatin g a new random data set using the final model and fitting the simulated data set to the model to compare the parameter estimates. Monte Carlo simulations (n=1000 per group) was performed to evaluate the 90% population target attainment rate when time of drug concentration above MIC (T>MIC) at least 25% or 50% of dosing intervals for 500, 400, 300, and 250 mg doses. In addition, 2 hour infusion versus 1 hour infusion for the 500 and 400 mg dose levels were also evaluated. Results The diagnostic plots for the final model are shown in Figure s 7 2 to 7 7. The population predicted versus observed values (Figure 72 ) s hows that for each tissue, the values were evenly spread alone the line of unity. T he distribution alone the line of unity decreased for indivi dual predictions in all three tissues (Figure 7 -3). No systemic bias was observed when comparing the weighted residual population means versus the population predicted values (Figure 74). The visual predictive check s show ed that the majority of the obse rvations from all three tissues were evenly distributed within the predicted 90thThe diagnostic plots from modeling the simulated data are shown in Figures 78 to 7 -13. The simulated data contain a wider distribution compared to that of the original data set. This resulted in a larger spread of data variability compared to that of the original data set ger when modeling simulated data compared to observed data. Nonetheless, the VPC s showed a reasonable model prediction in all three tissues (Figures 7-11 to 7-13). In addition, model parameter estimates between the two approaches were similar (Table 7-5 ) percentile s with the predicted median centering the observation distributions (Figures 7 5 to 7-7).

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117 The current data set consists of small sample size with minimal age and body weight distributions Hence, no c ovariate analysis was added to the model. Nonetheless the effects of demographics on PBPK parameters were plotted for visual inspections in F igure 7 -14. Monte Carlo simulations (n=1000 per group) w ere performed to evaluate target attainment rate s T ime of ceftobiprole concentrations above MIC for at least 25% of dosing interval has been shown to achieve desirable clinical outcome. For immune compromised subjects, a stricter criterion was recommended (T>MIC at 50% of dosing interval). Using the criterion of 90% population target attainment rate, Figure 7-15 plots the outcome in all three tissues for doses ranging from 500 mg to 250 mg. To si mulate the effects of resistance development on the target attainment rate, scenarios at which the MIC increased from 1 g/mL to 2 or 4 g/mL were evaluated. When MIC = 1 g/mL, it appeared that 500 mg, the standard dose, achieved the target for all three tissues Reducing the dose to 400 mg was borderline sufficient in the adipose tissue compartment using the T>MIC 50% of dosing interval criteria If the MIC increased to 2 g/mL the desired target attainment for 90% of population would only be reached for 500 and 400 mg doses using the T>MIC of 25% criteria If the MIC increased to 4 g/mL, target attainment would not be reached for any of the dose groups in adipose tissue s even though it would be achieved in plasma tissue Reducing th e intravenous infusion time from 2 hours to 1 hour was also evaluated for target attainment. Figure 716 shows that without resistant development (MIC = 1 g/mL), 500 and 400 mg dose groups can achieve the 90% population target using the T>MIC 25% criteria. However, at T>MIC 50% criteria, only the 500 mg dose was

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118 sufficient. If increased in MIC occurred, insufficient free drug concentrations would be available to adipose tissue. Figure 717 shows the diagram of combing the PBPK model with the mechanism based PD model developed for emergence of resistance. The drug concentration profiles of Ceftobiprole in plasma, muscle, and adipose tissues were simulated to evaluate the PD profiles in case of resistance development. The growth (ks) and degradation (kd) rate constants and drug effects (Smax, SC50) of Ceftobiprole in MRSA were obtained from86Conclusions/Discussions The PD profiles in the se three tissues without resistance development are shown in Figure s 7 18. Alteration of dose levels and inoculation levels are shown in Figure 7 -19. In case of resistance development, the PD profiles are simulated to evaluate various degrees of doses inoculations, and resistance development (Figure 7 -20). The drug concentration time course of ceftobip rol e collected from tissue sites using m icrodialysis techniques in human provided a unique opportunity for clinical population PBPK modeling. The final model described the unbound drug concentrations in the plasma, skeletal muscle and subcutaneous adipose tissues reasonably well. Diagnostics plots and visual predicted checks were used to select the appropriate final m odel with inter -subject variability ( ). The clearance from the kidneys estimated from the PBPK model was similar to that of plasma clearance from the noncompartmental analysis, confirming ceftobiprol e is eliminated mainly by the kidney s (5.46 L/hr from P BPK model versus 5.15 L/hr from noncompartmental analysis ). The high partition coefficient of ceftobiprole to kidneys also contributed to the similarity. In addition, the partition coefficient values for muscle and adipose tissues estimated from

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119 the PBPK model correlated well with the unbound tissue plasma ratios (0.70 and 0.4 4 for muscle and adipose tissue from PBPK model versus 0.69 and 0.49 from f AUCtis sue/fAUCplasmaThe model revealed that if resistance occurs ( MIC increased from 1 to 4 g/mL), un bound drug concentrations at the site of action would be insufficient with the standard dose of 500 mg administered by intravenous infusion over 2 hours A higher or more frequent dose may be needed to achieve the desired dose levels at the relevant tissue sites ). In summary, using microdialysis probes in human tissues allows direct measurement of free drug concentrations in relevant tissue sites. In the majority of the clinical cases, where only plasma samples were collected, a false conclusion may be drawn for optimal dosing scheme. If tolerable, one hour instead of two hour IV infusion may be used for the standard dose of 500 mg. In the case of resistance development, a higher or more frequent dose may be needed. The PBPK model combined with mechanism based PD model furth er provided insights into the drug effects in case of resistance emergence. Th ese simulations provided insightful PKPD relationships and allow ed a djustment of dosing strategies in case of resistant development

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120 Table 7 1 Mean and standard deviation (n=12) of noncompartmental parameters of ceftobiprole in healthy volunteers Table 7 2 G ender -specific plasma flow rate and tissue weights obtain from literature for the PBPK model .144 Plasma Flow Rate Tissue Weight Male (mL/kg/min) Female (mL/kg/min) Male (kg) Female (kg) Muscle 38 38 30 18 Adipose Fat 28 28 12.5 17.5 Kidney 4000 3500 0.31 0.275 Muscle 38 38 30 18 Remainder 2634 2234 30.19 24.2 CO 6700 5800 na na PK Parameter Plasma (total) Muscle S.C. Adipose Cmax (mg/L) 25.8 2.96 14.0 3.22 9.61 4.74 Tmax (hr) 1.92 0.15 2.25 0.14 2.25 0.21 t1/2 (hr) 2.61 0.33 2.61 0.52 2.56 0.39 AUCt (hr*mg/L) 97.1 10.3 50.6 10.9 34.3 19.0 AUCinf (hr*mg/L) 98.0 10.5 53.2 11.5 36.5 19.4 CL (L/hr) 5.15 3.61 na na Vss (L) 14.6 2.17 na na AUC,tissue/AUC,plasma na 0.69 0.13 0.49 0.28 Note: Values are mean SD from noncompartmental anlaysis

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121 Table 7 3 Individual plasma flow rate calculated based on proportion of body surface area to standard values presented in Table 7 -2 Subject ID Total Body Weight (kg) Gender Height (cm) Q Fat (L/hr) Q Kidney (L/hr) Q Muscle (L/hr) Q remainder (L/hr) QCO (L/hr) 1 80.1 M 179.1 22.2 78.8 72.4 5051 426 2 68.2 F 171.2 32.6 64.1 45.6 3606 386 3 75.3 M 177.8 21.5 76.3 70.2 4894 412 4 64 F 169.7 31.6 62.0 44.1 3487 374 6 59.9 F 171.5 30.9 60.8 43.2 3417 366 7 76.3 M 180.3 21.9 77.5 71.3 4972 419 8 72.8 F 162.6 32.3 63.5 45.1 3571 383 9 76.9 F 167.6 33.8 66.5 47.2 3736 400 10 76.9 M 170.2 21.1 74.6 68.6 4784 403 12 63.5 M 179.8 20.2 71.6 65.8 4589 387 14 56.7 F 160.0 28.7 56.4 40.1 3174 340 15 78.4 M 184.4 22.5 79.7 73.3 5112 431 Mean 70.8 6m/6f 173 26.6 69.3 57.2 4199 394 SD 7.96 na 7.51 5.44 8.02 13.8 755 26.5 Table 7 4 Individual tissue volume calculated based on proportion of body surface area to standard values presented in Table 7 -2 BSA (m2) Fat Volume (L) Kidney Volume (L) Muscule Volume (L) Remainder Volume (L) Plasma Volume (L) 1.99 13.2 0.328 31.8 32.0 7.09 1.80 19.4 0.305 20.0 26.9 6.44 1.93 12.8 0.318 30.8 31.0 6.87 1.74 18.8 0.295 19.3 26.0 6.23 1.70 18.4 0.289 18.9 25.5 6.10 1.96 13.0 0.323 31.3 31.5 6.98 1.78 19.2 0.302 19.8 26.6 6.38 1.86 20.1 0.316 20.7 27.9 6.67 1.89 12.5 0.311 30.1 30.3 6.72 1.81 12.0 0.298 28.9 29.0 6.44 1.58 17.1 0.269 17.6 23.7 5.67 2.01 13.4 0.332 32.1 32.3 7.18 Note: BSA calculated using DuBois formula: BSA (m) = 0.20247 x Height(m)0.725 x Weight(kg)0.425

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122 Table 7 5 Population PBPK parameter estimates Model Estimates Parameter Description Observed Data ( %RSE ) Simulated Data ( %RSE ) KPM, Muscle Partition Coefficient 0.703 (5%) 0.733 (5%) KPF, Fat Partition Coefficient 0.436 (18%) 0.264 (19%) KPR, Remainder Partition Coefficient 0.505 0.569 KPK, Kidney Partition Coefficient 0.604 0.393 Plasma Clearance (L/hr) 5.46 (41%) 6.42 Plasma Volume 0.0118 (47%) 0.0171 (63%) Muscle Volume 0.430 (50%) 0.485 (51%) Fat Volume 0.328 (64%) 0.103 (249%) Kidney Volume 0.205 (52%) 0.0425 (127%) KPM 0.0270 (73%) 0.0214 (75%) KPF 0.365 (44%) 0.403 (41%) KPR 0.185 (85%) 0.0299 (84%) KPK 0.0724 (186%) 0.0251 CL 0.316 0.0905 (218%) Plasma Proportional Error 0.198 (18%) 0.326 (7%) Muscle Proportional Error 0.119 (9%) 0.356 (4%) Fat Proportional Error 0.145 (6%) 0.271 (4%) %RES = percent relative standard error ; is the intersubject variability, is he proportional error variance.

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123 Figure 7 1 Physiologically Based Pharmacokinetic (PBPK) model. Co = plasma cardio output; M = muscle; F = fat; K=kidney; R = remainder; FP = free plasma; Q = plasma flow; KP = tissue partition coefficient; CL = clearance; V = volume. Plasma Muscle Fat KidneysRemainderQCOQMQFQKQR CL

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124 Figure 7 2 Diagnostic plot of modeling the observed data: Population predicted versus observed (DV) values for plasma (yellow), muscle (blue) and fat (red) Figure 7 3 Diagnostic plot of modeling the observed data: Individual predicted versus observed (DV) values for plasma (yellow), muscle (blue) and fat (red).

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125 Figure 7 4 Diagnostic plot of modeling the observed data: Weighted residual of population mean versus population predicted values for plasma (yellow), muscle (blue) and fat (red).

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126 Figure 7 5 Diagnostic plot of modeling the observed data: Visual predictive checks of unbound ceftobiprole concentrations in plasma. Figure 7 6 Diagnostic plot of modeling the o bserved data: Visual predictive checks of unbound ceftobiprole concentrations in skeletal muscle.

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127 Figure 7 7 Diagnostic plot of modeling the observed data: Visual predictive checks of unbound ceftobiprole concentrations in subcutaneous adipose fat.

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128 Figure 7 8 Diagnostic plot of modeling the simulated data: Population predicted versus observed (DV) values for plasma (yellow), muscle (blue) and fat (red). Figure 7 9 Diagnostic plot of modeling the simulated data: Individual predicted versus observed (DV) values for plasma (yellow), muscle (blue) and fat (red)

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129 Figure 7 10 Diagnostic plot of modeling the simulated data: Weighted residual of population mean versus population predicted values for plasma (yellow), muscle (blue) and fat (red).

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130 Figure 7 11 Diagnostic plot of modeling the simulated data: Visual predictive checks of unbound ceftobiprole concentrations in plasma. Figure 7 12 Diagnostic plot of modeling the simulated data: Visual predictive checks of unbound ceftobiprole concentrations in skeletal muscle.

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131 Figure 7 13 Diagnostic plot of modeling the simulated data: Visual predictive checks of unbound ceftobiprole concentr ations in subcutaneous adipose fat.

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132 Figure 7 14 Visual plots of covariate analysis of various demographic parameters. No covariate was building in the final PBPK model due to lack of demographic distribution in the 12 healthy volunteers. Eta KPf vs Height [cm] 160 165 170 175 180 185 190 0.0 0.5 1.0 1.5 2.0 Eta KPf vs Weight [kg] 55 60 65 70 75 80 85 0.0 0.5 1.0 1.5 2.0 Eta KPf vs Age [ys] 20 22 24 26 28 30 32 0.0 0.5 1.0 1.5 2.0 Eta KPk vs Height [cm] 160 165 170 175 180 185 190 0.0 0.2 0.4 0.6 0.8 1.0 Eta KPk vs Weight [kg] 55 60 65 70 75 80 85 0.0 0.2 0.4 0.6 0.8 1.0 Eta KPk vs Age[ys] 20 22 24 26 28 30 32 0.0 0.2 0.4 0.6 0.8 1.0 Eta CL vs Height [cm] 160 165 170 175 180 185 190 0.0 0.5 1.0 1.5 2.0 Eta CL vs Weight [kg] 55 60 65 70 75 80 85 0.0 0.5 1.0 1.5 2.0 Eta CL vs Age [yr] 20 22 24 26 28 30 32 0.0 0.5 1.0 1.5 2.0

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133 Figure 7 15 Probability of target attainment rates of ceftobiprole for 90% of population (solid line) based on 1000 Monte Carlo simulation following 2 hour intravenous infusion ceftobiprole. Dark and light grapy bars were simulated based on time of drug concentration above MIC 25% and 50% of dosing interval. Four doses and three MIC profile s were simulated. Figure 7 16 Probability of target attainment rates of ceftobiprole for 90% of population (solid line) based on 1000 Monte Carlo simulation following 1 hour intravenous infusion ceftobiprole. Dark and light grapy bars were simulated based on time of drug concentration above MIC 25% and 50% of dosing interval. Two doses and three MIC profiles were simulated. Plasma Muscle Adipose % Population Achived Target 0 20 40 60 80 100 Plasma Muscle Adipose % Population Achived Target 0 20 40 60 80 100 Plasma Muscle Adipose % Population Achived Target 0 20 40 60 80 100 MIC = 1 g/ mL MIC = 2 g/ mL MIC = 4 g/ mL a = 500 mg b = 400 mg c = 300 mg d = 250 mgabcd T> MIC 25% of Dosing Interval T> MIC 50% of Dosing Interval Plasma Muscle Adipose % Population Achived Target 0 20 40 60 80 100 Plasma Muscle Adipose % Population Achived Target 0 20 40 60 80 100 Plasma Muscle Adipose % Population Achived Target 0 20 40 60 80 100 MIC = 2 g/ mL MIC = 4 g/ mL a = 500 mg b = 400 mg MIC = 1 g/ mL a b T> MIC 25% of Dosing Interval T> MIC 50% of Dosing Interval

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134 Figure 7 1 7 Integration of ceftobiprole pharmacokinetics described by the PBPK model with the Compensatory Mutation PD model for resistance evaluations S kd R kc kc Rfit kd ksH(C(t)) ksH(C(t)) + + PBPK Pharmacodynamic

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135 Figure 7 1 8 Simulation of ceftobiprole pharmacodynamic profiles: MRSA in tissues without the emergence of drug resistance. Figure 7 19 Simulation of ceftobiprole pharmacodynamic profiles: MRSA in subcutaneous adipose tissue without the emergence of drug resistance after various doses and inoculation levels Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 Plasma Effect Muscle Effect S.C. Adipose Tissue Effect Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 4 CFU/mL 5 CFU/mL 6 CFU/mL 7 CFU/mL 8 CFU/mL 9 CFU/mL Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 200 mg 300 mg 400 mg 500 mg

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136 Figure 7 20 Simulation of ceftobiprole pharmacodynamic profiles: MRSA with the emergence of drug resistance. Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 Plasma Effect Muscle Effect S.C. Adipose Tissue Effect Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 200 mg 300 mg 400 mg 500 mg 10% Reduction in Drug Effect in S.C. Adipose Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 4 CFU/mL 5 CFU/mL 6 CFU/mL 7 CFU/mL 8 CFU/mL 9 CFU/mL 10% Reduction in Drug Effect in Tissues Time (hr) 0 4 8 12 16 20 24Log CFU/mL 0 2 4 6 8 10 12 14 10% 20% 30% 40% 50% Various degree of reduction in S.C. Adipose 10% Reduction in Drug Effect in S.C. Adipose

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137 CHAPTER 8 CONCLUSIONS The emergence of antimicrobial resistance poses a critical challenge to public health. The current practice to treat microbes is less than optimal. Relying on single MIC data to define clinical dos e disregards the adaptive nature of microbial response, which leads to fostering of drug resistance microbes over time. In order to overcome antimicrobial resistance, the time course relationships of drug and microbial behavior must first be delineated. In this dissertation, the development of novel mechanism based PKPD models was described using new molecular and genetic findings. The resulting mathematical models provide insight into the complex PKPD relationships necessary to optimize antimicrobial tr eatments. Within recent years, several hypotheses claim to explain the main mechanisms of antimicrobial resistance were published. The two most well accepted hypotheses are the dormant and compensatory mutation hypotheses. Dormant hypothesis describes the ability of microbes to induce a dormant phenotypic variant upon sensing environmental challenge. It does so by upregulating endogenous toxins to temporarily disable DNA replications and translations. Since antimicrobial agents only target dividing cells, the dormant microbes safely escape drug killings. Once the environment improves (decreased drug concentration), microbes can upregulate antitoxins to reinitiate microbial cell divisions. The Compensatory Mutation hypothesis on the other hand proposes a genetic variant model. When microbes undergo random mutations to develop drug resistance characteristics, a fitness cost is imposed on the new strain. In order to be a clinically relevant strain, these mutated strains need c ompensatory mutations to restore microbial

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138 fitness. These new strains would be able to grow at the same rate as the susceptible strains but with increased MICs. Mathematical models describing each of the new hypotheses independently and in combination a s well as a common literature model were developed to using extensive in vitro dynamic kill -curve data. Each model fitted control, suboptimal and lethal doses of ciprofloxacin against E. coli (totaling 11 dose groups) simultaneously. The models describin g each resistance hypothesis underwent rigorous testing in order to select the best model to describe the kill -cuves. The model selection criteria consisted of performance in terms of (1) having fewest possible parameters to describe the hypotheses (2) bo otstrap statistics of 1000 new dataset (3) visual predictive check of 1000 simulation (4) observe versus predicted plots (5) agreement of model fitting with ADAPT II versus median, mean and 90% confidence interval of bootstrap statistics with NONMEM VI (6) subcompartmental profile evaluation (7) multiple dose simulation (8) literature comparisons and (9) inhouse kill -curve experimental data. After thorough evaluations of these models, the Compensatory Mutation Model best describes the dynamics of antimic robial resistance. The model was used to simulate anticipated results prior to the laboratory work which helped guide the study design of new multiple dose experiments. The first experiment confirmed the absence of pre-resistance strains of a clinical is olate of P. aeruginosa to ciprofloxacin. This information supports the development of a new model capturing the emergence of resistance, rather than using the literature model where a small percentage of resistance strain was included to model the suscept ible and resistance population independently. The dynamic kill -curve evaluated the changing unbound drug

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139 concentration versus microbial response over time. The MIC during and post antimicrobial treatments were evaluated. The dynamic kill -curve of P. aer uginosa confirmed the model prediction of loss of drug effects after the second exposure of 200 mg ciprofloxacin at 12 hours. The MIC increased several folds within six hours of ciprofloxacin dose and remain significantly high throughout the treatment per iod. The post antimicrobial effects indicated that despite the overall return to the predose MIC level three days after drug exposure, the microbial population was not homogenous; the E-strip test revealed that visible individual colonies were growing th roughout the high ciprofloxacin concentration zone, indicating a wide range of MIC distribution formed post ciprofloxacin treatment. Once P. aeruginosa developed resistance to ciprofloxacin, a three-fold drug dose increase was still inadequate to induce significant killing effects, supporting the highly adaptive nature of microbial response. In this stage, it would be necessary to switch to a new treatment with different mechanism of actions. However, our findings revealed that arbitrarily switching to a new class of antimicrobial agent does not guarantee successful outcome due to cross -resistance potential. The first alternative drug (ceftriaxone) used to treat the emerged resistance strain was ineffective. This was further confirmed by susceptibility analysis with microscan that the particular clinical isolate of P. aeruginosa was intermediate resistance to ceftriaxone prior to ciprofloxacin treatment and was advanced to full resistance after ciprofloxacin treatment. The microscan analysis of drug susceptibility across a large panel of antimicrobial agents revealed that mainly the aminoglycosides retained their drug effects after ciprofloxacin exposure. This ability to suppress ciprofloxacinresistant strains was confirmed in

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140 another dynamic kill -cur ve study using gentamicin. The drug-induced resistance lactam, aztreonam, was also capable of inducing emergence of resistance. The exact mechanisms of resistance development in such a timely f ashion warrant further investigations. The in vitro PKPD and dynamic MIC profiles revealed important drugmicrobe relationships. However, the translational interpretation needs to consider the lack of immune system involvement. The immune system may pl ay an important role in eradicating the bacteria infection from the system 147, thereby creating a temporal differences in the emergence of resistance in clinical settings. From statistics we know that antimicrobial drug effects reduce over time. However, the ability to predict this clinical observation remains a challenge in this field. Nonetheless, understanding th ese PKPD relationships is crucial to achieving the ultimate goal of predicting clinical resistance. It confirms the inadequate traditional dosing approach of using exposure MIC relationship where the PKPD depends on a single PD time point. It would be ne cessary to consider the adaptive nature of microbes over the course of antimicrobial treatment to optimize effective dosing strategies against emerged resistance populations. While exposureMIC dosing approaches still provide useful pharmacology guideline s, incorporation of a resistance emergence component would be informative. To integrate a resistance emergence model to a clinical scenario, a novel population physiologically based PK model for ceftobiprole against MRSA was developed as the PK input for P D simulations. The population PBPK model estimated the partition coefficients of drugs to relevant tissue sites, plasma clearance and inter and intrasubject variabilities which are important for clinical predictions. Monte Carlo

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141 simulations were used to predict target attainment rate with and without ceftobiprole resistance development. The PBPK model combined with the mechanism based PD model for resistance further provided insights into different scenarios of pharmacodynamic profiles at tissue sites The PBPK model reaffirmed that 500 mg ceftobiprole infused intravenously over 1 or 2 hours is sufficient to achieve the more frequent dosing or higher dose levels of ceft obiprole. In conclusion, the dynamics of microbes in response to drug treatments are extremely complex, involving the drug, microbes, and host. Currently, the best system to study drugmicrobes relationship is to use in vitro dynamic kill -curve models. T he immune system may potentiate the killings of drug actions and prolong the regrowth time of resistance strains. One of the most important findings that disregards the traditional exposureMIC approach is that the MIC is not stationary during the treatment period. In order to ensure successful treatment over time, the dosing strategy should consider susceptible and the newly emerged populations. The findings presented in this dissertation serve as a foundation to further explore the emergence of antimi crobial resistance. Specifically for P. aeruginosa, it would be informative to evaluate the doseand inoculation dependency on the emergence resistance. It is possible that a higher initial dose of ciprofloxacin (i.e. 600 mg starting dose instead of 200 mg) may reduce the development of resistance. The current study only tested the emergence of resistance at a low clinical dose. Evaluation of a range of initial inoculation concentrations (4 to 9 CFU/mL) will further characterize the adaptive nature of microbes. In summary, the mechanism based PKPD model improved the

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142 understanding of antimicrobial resistance and was used to explore new dosing strategies for the resistant populations. The clinical utilities of the resistance model were presented for a n ovel population PBPK model of ceftobiprole against MRSA.

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155 BIOGRAPHICAL SKETCH Benjamin M Wu received his b achelor s degree in m olecular c ellular d evelopmental b iology from University of California of Satan Cruz with Honors in thesis research in e nvironmental t oxicology. P ost b achelor s he started out working as a biochemist at Stanford Research Institute where he was awarded as an Honorary Member of the United States Medical Regimen by Surgeon Ronald Blank for his contribution work on the Gulf War Syndrome. He then worked at Chiron Corporation and Genentech Inc. in the clinical pharmacokinetic/pharmacodynamic department for over five years running clinical and nonclinical studies, analyzing data, writing reports and support ing fili ngs of protein therapeutics. A bioengineered drug for psoriasis (efalizumab) he was heavily involved in at Genentech was approved by the FDA in 2003. Benjamin received his m aster s from University of Buffalo and joined Dr. Hartmut Derendorfs lab for the PhD work on mathematical modeling of antimicrobial resistance. He received his doctor of philosophy in p harmaceutics in December 2010.