ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2013

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 170

Pharmacokinetic andPharmacodynamic Modeling

AMI FAZLIN SYED MOHAMED

ISSN 1651-6192ISBN 978-91-554-8568-9urn:nbn:se:uu:diva-188306

of Antibiotics and Bacterial Drug Resistance

Dissertation presented at Uppsala University to be publicly examined in B41, UppsalaBiomedical Center, Husargatan 3, Uppsala, Friday, February 8, 2013 at 09:15 for thedegree of Doctor of Philosophy (Faculty of Pharmacy). The examination will be conductedin English.

AbstractSyed Mohamed, A. F. 2013. Pharmacokinetic and Pharmacodynamic Modeling of Antibioticsand Bacterial Drug Resistance. Acta Universitatis Upsaliensis. Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty of Pharmacy 170. 77 pp. Uppsala.ISBN 978-91-554-8568-9.

Exposure to antibiotics is an important factor influencing the development of bacterialresistance. In an era where very few new antibiotics are being developed, a strategy for thedevelopment of optimal dosing regimen and combination treatment that reduces the rate ofresistance development and overcome existing resistance is of utmost importance. In addition,the optimal dosing in subpopulations is often not fully elucidated. The aim of this thesis wasto develop pharmacokinetic (PK) and pharmacokinetic-pharmacodynamic (PKPD) models thatcharacterize the interaction of antibiotics with bacterial growth, killing and resistance over time,and can be applied to guide optimization of dosing regimens that enhance the efficacy of mono-and combination antibiotic therapy.

A mechanism-based PKPD model that incorporates the growth, killing kinetics and adaptiveresistance development in Escherichia coli against gentamicin was developed based on in vitrotime-kill curve data. After some adaptations, the model was successfully applied for similar dataon colistin and meropenem alone, and in combination, on one wild type and one meropenem-resistant strain of Pseudomonas aeruginosa.

The developed population PK model for colistin and its prodrug colistin methanesulfonate(CMS) in combination with the PKPD model showed the benefits for applying a loading dosefor this drug. Simulations predicted the variability in bacteria kill to be larger between dosingoccasions than between patients. A flat-fixed loading dose followed by an 8 or 12 hourlymaintenance dose with infusion duration of up to 2 hours was shown to result in satisfactorybacterial kill under these conditions.

Pharmacometric models that characterize the time-course of drug concentrations, bacterialgrowth, antibacterial killing and resistance development were successfully developed.Predictions illustrated how PKPD models based on in vitro data can be utilized to guidedevelopment of antibiotic dosing, with examples advocating regimens that (i) promote bacterialkilling and reduce risk for toxicity in preterm and term newborn infants receiving gentamicin, (ii)achieve a fast initial bacterial killing and reduced resistance development of colistin in criticallyill patients by application of a loading dose, and (iii) overcome existing meropenem resistanceby combining colistin and meropenem

Keywords: Pharmacometrics, pharmacokinetics, pharmacodynamics, modeling, antibiotics,resistance, combination, Gram-negative bacteria, gentamicin, colistin, meropenem, newborninfants, critically ill patients

Ami Fazlin Syed Mohamed, Uppsala University, Department of Pharmaceutical Biosciences,Box 591, SE-751 24 Uppsala, Sweden.

© Ami Fazlin Syed Mohamed 2013

ISSN 1651-6192ISBN 978-91-554-8568-9urn:nbn:se:uu:diva-188306 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-188306)

It is not the destination,but the journey.

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Mohamed, A.F., Nielsen, E.I., Cars,O., Friberg, L.E. (2012)

Pharmacokinetic-Pharmacodynamic Model for Gentamicin and Its Adaptive Resistance with Predictions of Dosing Schedules in Newborn Infants. Antimicrob. Agents Chemother, 56(1):179-188.

II Mohamed, A.F., Karaikos, I., Plachouras, D., Karvanen, M., Pontikis, K., Jansson, B., Papadomichelakis, E., Antoniadou, A., Giamarellou, H., Armaganidis, A., Cars,O., Friberg, L.E. (2012) Application of a Loading Dose of Colistin Methanesul-fonate in Critically Ill Patients: Population Pharmacokinetics, Protein Binding, and Prediction of Bacterial Kill. Antimicrob. Agents Chemother, 56(8):4241-4249.

III Mohamed, A.F., Cars,O., Friberg, L.E. A Pharmacokinetic-

Pharmacodynamic Model Developed for Colistin on Pseudo-monas aeruginosa in vitro with Evaluation of Population PK Variability in Simulated Bacterial Killing. (In manuscript)

IV Mohamed, A.F., Karvanen, M., Cars,O., Friberg, L.E. Interac-

tion of Colistin and Meropenem on a Wild-type and a Resistant strain of Pseudomonas aeruginosa in vitro as Quantified in a Mechanism-based Model. (In manuscript)

Reprints were made with permission from the respective publishers.

Contents

Introduction ................................................................................................... 11 Bacterial resistance ................................................................................... 12 Pharmacometrics ...................................................................................... 13

PK models of antibiotics ...................................................................... 14 PKPD models of antibiotics ................................................................. 15

Model-based development of dosing regimens ........................................ 17 Gentamicin in newborn infants ............................................................ 17 Colistin and meropenem in critically ill patients ................................. 18

Aims .............................................................................................................. 20

Materials and Methods .................................................................................. 21 In vitro data .............................................................................................. 21

Bacteria and Media .............................................................................. 22 Antibiotics ........................................................................................... 22 In vitro time-kill experiments .............................................................. 23

Clinical study............................................................................................ 24 Patients ................................................................................................. 24 Analytical method ................................................................................ 25

Model development .................................................................................. 25 PKPD Model (Paper I, III, IV) ............................................................ 25 Population PK model (Paper II) .......................................................... 29 Model selection and evaluation ........................................................... 29

Plasma protein binding of colistin (Paper II) ........................................... 30 Simulations ............................................................................................... 30

Assessment of patient population variability (Paper III) ..................... 30 Comparison of dosing algorithm (Paper III) ........................................ 31 Predictions of gentamicin dosing regimens for newborn infants (Paper I) ............................................................................................... 32 Predictions of colistin dosing regimens for critically ill patients (Paper II) .............................................................................................. 32 Predictions of colistin and meropenem combination dosing regimens for critically ill patients (Paper IV) ...................................... 32

Software ................................................................................................... 33

Results ........................................................................................................... 34 Measured colistin concentrations ............................................................. 34

Mechanism-based PKPD Models ............................................................. 34 Time-kill curve experiments for gentamicin ....................................... 36 Mechanism-based PKPD model for gentamicin .................................. 37 Mechanism-based model for colistin ................................................... 40 Mechanism-based model for colistin and meropenem combination ... 41

Population PK of colistin in critically ill patients .................................... 43 Patients and colistin concentration ...................................................... 43 Population PK model ........................................................................... 44 Plasma protein binding of colistin ....................................................... 45

Simulations for assessment of variability ................................................. 46 Simulations for comparison of dosing algorithm ................................ 48

Dosage regimen for specific populations ................................................. 50 Gentamicin in newborn infants ............................................................ 50 Colistin in critically ill patients ............................................................ 50 Colistin and meropenem combination in critically ill patients ............ 52

Discussion ..................................................................................................... 54 Mechanism-based PKPD Model .............................................................. 54 Population PK model for colistin ............................................................. 56 Dosing regimen for specific population ................................................... 57

Conclusion .................................................................................................... 59

Future perspectives ....................................................................................... 61

Acknowledgements ....................................................................................... 63

References ..................................................................................................... 66

Abbreviations

AUC Area under the curve Bmax Bacterial count at stationary phase BP Breakpoint, the lowest total number of bacteria required for

the transfer rate constant from the sensitive (S) to the resting (R) compartment being > 0

C Drug concentration CFU Colony-forming unit CI Confidence interval CL Clearance CLCMS CMS clearance CLCol Clearance of formed colistin CMS Colistin methanesulfonate Cmax/MIC a ratio of peak plasma concentration to minimum inhibitory

concentration CrCL Creatinine clearance Con50 the drug concentration that results in 50% of konmax EC50 Drug concentration producing 50% of Emax Emax Maximum achievable effect Emax(0) Maximal achievable effect when no adaptive resistance has

been developed EU European Union GNB Gram negative bacteria ICU Intensive Care Unit IIV Interindividual variability Int Parameter describing drug interaction IOV Interoccasion variability kdrug the maximum bacterial killing of the antibiotic

kdrugkill the maximal achievable rate constant of bacterial killing. ke Rate constant for drug elimination kgrowth Rate constant for multiplication of bacteria koff Rate constant for reversal of adaptive resistance kon Rate constant for development of adaptive resistance konmax Rate constant for maximal achievable transfer of the hypo-

thetical amount to the resistance compartment in the presence of drug

kRS Rate constant for transformation from R to S kSR Rate constant for transformation from S to R L2 Level-two data item in NONMEM

LLP Log-likelihood profiling LOD Limit of detection MIC Minimum inhibitory concentration MDR Multi-drug resistant MU Million units OFV Objective function value PI Prediction interval PK Pharmacokinetics PKPD Pharmacokinetic-Pharmacodynamic PsN Pearl-speaks-NONMEM QCMS CMS intercompartmental clearance R Resting, drug-insensitive bacterial population RESdynamic Residual error (on ln-scale) for dynamic experiments Re50 Relative amount in ReON needed to reduce Emax(0) by 50% REOFF Compartment for resistance being off REON Compartment for resistance being on RESstatic Residual error (on ln-scale) for static experiments RRES Replicate residual error (on ln-scale) S Growing, drug-sensitive bacterial population V1CMS Volume of distribution for the central compartment of CMS V2CMS Volume of distribution in peripheral compartment of CMS VCol Volume of distribution for formed colistin VPC Visual predictive check WT Body-weight β Hill factor for the development of resistance γ Sigmoicidity factor characterizing the steepness of the con-

centration effect relationship δ Hill factor for drug concentration influencing rate constant for

the development of adaptive resistance in presence of colistin (kon)

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Introduction

The discovery of antibiotics was an important milestone in the history of medicine. Apart from the obvious use in treating infections with reduction in morbidity and mortality, antibiotics have also made a major contribution in advancing other parts of medical care namely organ transplantation, open surgery, and support for immunocompromised patients including those with HIV and on cancer chemotherapy (3, 26).

It is well known that exposure to antibiotics is the most important factor influencing the development of bacterial resistance. Differences in the use and misuse of antibiotics have contributed to different degrees and types of bacterial resistance among regions and countries. The effect of bacterial resistance on health is prolonged illness and a higher risk to develop compli-cations which may lead to increased morbidity and mortality. The economic impact includes loss of income and escalated cost of treatment as there is an increased number of days of hospitalization, consultation, diagnostics and antibiotics treatment (93). In 2007, the estimated numbers of infections with resistant Gram-negative bacteria (GNB) in EU were 193,300 with 18,200 deaths. There was also 1,375,000 extra hospital days compared to the hospi-tal days of patients infected by antibiotic-susceptible isolates of the same bacteria (37, 93). From these numbers, carbapenem resistant Pseudomonas aeruginosa caused 141,900 infections with 10,200 deaths and 809,000 extra hospital days (37, 93). This illustrated that Pseudomonas aeruginosa resis-tance is a major threat to human health as it caused the majority of the resis-tant GNB infections.

Bacterial resistance is a growing problem and its seriousness is amplified by the fact that during the last years the number of antibiotics being devel-oped and brought to the market has been declining. Most pharmaceutical industries are not keen on developing antibiotics as there is less monetary gain because the treatment is for a short period and there is a high possibility of the antibiotic having a short lifespan due to development of resistance (26).

In view of the limited treatment options it is imperative that the available antibiotics are used appropriately for the right indication (i.e. sensitive or-ganism, appropriate antibiotics spectrum) with the optimal dosing regimen (i.e. size of dose, dosing interval, duration, tolerable side effects). Model-based methods can be a powerful tool to extract information from datasets and quantitatively describe the antibiotics disposition, effects and toxicity.

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Model-based methods are increasingly used in drug development to exploit better ways to utilize the ‘precious’ few antibiotics left in an optimal way (58). Pharmacokinetic (PK) models describe the concentration-time profile of a given dose which is dependent on the how the body absorbs, distributes, metabolizes and eliminates the drug. Pharmacodynamic (PD) models de-scribe the relationship between the drug concentration and therapeutic and/or toxic effects of the drug. The advantage of using these mathematical models (PK, PD, PKPD models) is that apart from using the information on the stud-ied population, it is also possible to predict dosing strategies on new indi-viduals in other settings than the one studied. This is especially important in vulnerable subpopulations, for example newborn infants and critically ill patients.

Bacterial resistance Opportunistic GNB frequently cause nosocomial infections, i.e. hospital-acquired infections like ventilator-assisted pneumonia, in patients in inten-sive care units (ICU) and burns units, and in immunocompromised and cys-tic fibrosis patients. Antibiotics for treatment of infections due to GNB in-clude beta-lactams, fluroquinolones, aminoglycosides, and polymyxins. Ex-posures to these antibiotics can however give rise to multi-drug resistant (MDR) GNB infections, which are associated with high mortality with few therapeutic options. Examples of GNB with relatively high frequency of MDR are Acinetobacter baumannii, Klebsiella spp., and Pseudomonas aeruginosa.

Bacterial resistance is the development of tolerance to antibiotics to which the bacteria once were susceptible. Genetic resistance is where susceptible bacteria mutate or acquire resistant genes by horizontal transfer (89). Genetic resistance is usually non-reversible and the degree of resistance can be de-termined as an increase in the minimum inhibition concentration (MIC) al-though initially mutations are associated with a fitness cost.

Another type of resistance is adaptive resistance (a phenotypic resistance) which is a reversible refractoriness to the antibiotic action and has been re-ported for the aminoglycosides, polymyxins and fluoroquinolone groups of antibiotics (5, 6, 30, 31, 42, 96). Adaptive resistance is a pharmacodynamic (PD) process that has been demonstrated by in vitro and in vivo studies. The resistance emerges already at the initiation of therapy, is enhanced by higher exposures, and augmented by consecutive doses if administered before the bacteria return to their susceptible stage (12). The time to full recovery of the susceptibility is typically longer for the higher doses (5).

There are multiple mechanisms of resistance for Pseudomonas aerugi-nosa which are often present simultaneously. Examples of resistance mecha-nisms are production of enzymes which destroys the antibiotics structure

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rendering them useless (eg beta-lactamases), over-expression of efflux pumps, decreased expression of porins, or mutations in antibiotic targets (21).

As bacterial resistance impact significantly on the efficacy of antibiotic treatment, developing strategies to overcome and prevent resistance is of utmost importance. A few different strategies have been investigated to pre-vent or reduce the emergence of bacterial resistance. Among these strategies are antibiotic surveillance, antibiotic cycling, reducing unnecessary use of antibiotics (eg in animal husbandry, not prescribing antibiotics for viral in-fections), reducing the duration of therapy and prophylaxis, optimization of antibiotic therapy and combination therapy (76, 93). Antibiotic surveillance is important to detect MDR bacteria, to monitor the epidemiologic trends and to measure the effect of intervention programs (76).

The optimization of dosing strategies of single antibiotics is of high rele-vance for drugs such as colistin and gentamicin where the most advanta-geous treatment schedule is not fully elucidated. There is however limited information on PKPD-relationships from patients, but an advantage with the field of antibiotics is that much PKPD information can be gained from in vitro experiments This is especially important in the development of drug combinations where the impact of many different concentration-time profiles are of interest to study. Combination therapy should be a priority for the future in considering the potential benefits of overcoming existing resistance and preventing emergence of resistance (70).

In order to optimize single and combination dosing regimens, a powerful method for analyzing the data is pharmacometrics where PKPD models are developed that can be utilized for predictions and simulations

Pharmacometrics Pharmacometrics, a science of quantitative pharmacology, has been defined as, “the science of developing and applying mathematical and statistical methods to characterize, understand and predict a drug’s pharmacokinetic, pharmacodynamic and biomarker-outcomes behaviour” (38). The value of pharmacometrics has increasingly become recognized over the last few dec-ades and is now frequently being applied within all larger pharmaceutical companies and by many academic research groups studying PK and PKPD relationships. Models that have the capacity to be used for translation from preclinical (in vitro and/or animal studies) to patients can be very valuable for exploring drug effects at an early drug development stage.

All data can be analyzed simultaneously in non-linear mixed effect or population modeling. Models typically consist of a structural part (described by fixed effects parameters) and a statistical part (described by random ef-fects parameters) (19). The fixed effects describe a typical individual in a

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population by linear and/or nonlinear functions while the random effects quantifies the unexplained variability between individuals (interindividual variability, IIV), between (dosing) occasions (interoccasion variability, IOV (54)) and residual variability. These various types of variability can be dif-ferentiated by the mixed effects approach.

The difference between a parameter value for ‘an individual’ and ‘the typical individual’ is described by ‘eta’ and the variance of the eta values in the population is the value estimated. Residual variability is typically quanti-fied as an additive error, a proportional error or a combination of the two (54). In population analyses individual factors (covariates) are searched for to explain the variability. Examples of common covariates are weight, age, sex, and creatinine clearance.

Model evaluation can be conducted by internal validation, by comparing model predictions with the same data as was used in model development, and/or external validation where a new set of data is tested on the model. The first method can for example be applied by simulation-based diagnostics such as visual predictive checks (VPCs) and methods for investigating the confidence intervals (CI) of the parameters such as bootstrap and log-likelihood profiling. In external validation the appropriateness of the model in predicting new studies or experiments, with the same or a different design, is assessed.

PK models of antibiotics PK models characterize the relationship between the drug dose and plasma concentration. Typically the PK is modeled first to characterize the concen-tration versus time profile. Thereafter the concentration-effect relationships to desired effects and side-effects are investigated in PKPD models.

To understand the drug disposition of antibiotics used clinically, it is im-portant to establish PK models which are built on concentration-time data in patients. Different subpopulations of patients often show different PK pro-files. For example, compared with healthy subjects, critically ill patients often have higher volume of distribution, reduced renal clearance, reduced blood flow to certain organs, changes in protein binding, and possible altera-tion in the pH (20). For newborns, especially in preterm babies, differences when compared to adults are due to factors such as lower weight, immaturity of hepatic enzymes, and immaturity of the kidneys (8). The resultant concen-tration-time profiles will thereby be affected and an adjustment in the dosing regimen may be needed for adequate exposure.

Population PK model for colistin It is important to have a good PK model to understand the concentration-time profile in the population of interest. One interesting antibiotic is colistin (polymyxin E), a cationic polypeptide, used clinically in the late 1950s but

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later shelved in the early 1970s mainly due to reports of its nephrotoxicity and the availability of easier to use and less toxic antibiotics (40, 61, 77). Recent studies indicate that the toxicity of colistin may have been exagger-ated and that the use of colistin in combination with other antibiotics may lead to additive or synergistic antibacterial effects (39, 62).

The inactive prodrug colistin methanesulfonate (CMS) is now being used as a last resort treatment for MDR infections in severely ill patients. How-ever, the dosing regimen of CMS has not been established according to to-day’s rigorous drug development procedures and there has been a dearth of information on PK data of colistin and CMS. Recent developments of novel methods to quantify colistin and CMS (51, 60) have enabled the PK of colistin to be characterized, but the optimal dosing strategy is still being searched for. It has been demonstrated that colistin has a long half-life in critically ill patients (around 14 hours) (82). Following a dose regimen of 240 mg every 8 hours, it takes approximately 12 to 48 hours after initiation of CMS treatment to reach a total colistin concentration of 2 mg/L (82). It is likely that a low initial concentration would be suboptimal in killing the bac-teria (14), especially in critically ill patients where an immediate effect is important (47, 83). Sub-therapeutic concentrations may also favor resistance development (62). Therefore, it has been suggested that a loading dose should be given (82). In addition, the degree of protein binding of colistin in humans is unknown.

PKPD models of antibiotics PKPD models are developed to summarize the relationship between the drug dose, plasma concentration, drug effect and side effects. Traditionally PK/PD indices are being applied to develop dosing regimens of antibiotics. PK/PD indices describe the relationship between a summary measurement of pharmacokinetic exposure of the antibiotics and a summary measurement of the antibiotic effect on the bacteria. The three commonly applied PK/PD indices are: (i) the ratio of the highest unbound concentration to the MIC (fCmax/MIC), (ii) the ratio of the area under the unbound concentration-time curve to the MIC (fAUC/MIC), and (iii) the percentage of a 24 h time period that the unbound concentration exceeds the MIC (fT>MIC) (71). The indices are identified by performing a large number of in vitro or animal studies with different dosing schedules to search for the index that best describes the relationship to the effect, e.g. the bacteria kill at 24 h (34, 88). There are however rarely, a PK/PD index that describes the PKPD-relationship perfectly and they are often correlated. The applications of summary variables also throw away the information on the time-course of effect, and thereby limit the possibilities to perform predictions on evaluat-ing the impact of different dosing regimens.

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PKPD models from in vitro time kill studies Much information on bacterial growth and antibiotic killing effects can be gained from in vitro time-kill curve experiments. In these experiments, the drug effect on the bacteria can be tested against single or combinations of antibiotics, with repeated measurements over time. The bacteria can be ex-posed to antibiotics at a constant concentration or at concentration profiles that mimic different PK profiles and dosing regimens (65). The experiments are relat ively easy to perform with flexibility in the study design. The results are not affected by factors that can produce variability in in vivo stud-ies, such as immune defense, disease burden and drug disposition. The number of bacteria can be quantified at frequent time points to al low for a detailed PD characterization of the time course of the effect.

The generated data can support development of PKPD models. A mecha-nism-based PKPD model (75) that considers the co-existence of sensitive and resting bacteria with different susceptibility to antibacterial agents has earlier been developed. The model has compartments for drug-susceptible, growing bacteria (S) and insusceptible, resting bacteria (R) with first order rate constants for growth (kgrowth) and natural death (kdeath). All bacteria were here assumed to be in the growing stage (S) at the start of the experiments. The bacteria transfer into a resting stage (R), with the rate constant kSR, when the total bacterial content in the system increase. Eventually the bacterial count approach a stationary phase where the total bacterial population is no longer increasing. In the resting stage, there is no bacterial growth but the bacteria are assumed to have the same natural death rate (kdeath) as bacteria in the growing stage (75). The model can however not predict the emergence of resistance, but the mechanistic nature may allow for further expansion to incorporate resistance.

The emergence of bacterial resistance has been modeled as pre-existing bacterial subpopulations with different susceptibility to antibiotics (22, 66), an adaptation factor (87) and emergence of new resistance In the model where subpopulations are assumed to preexist, the resistant population is selected under antibiotic exposure. The different subpopulations have differ-ent values of Ec50 or Emax and there is a fitness cost associated with the resis-tance, so that the resistant subpopulation has a slower growth rate than the other subpopulations(52, 66).

In the adaptation factor model, resistance is assumed to develop over time. For example, the adaptive resistance observed for Pseudomonas aeruginosa and Acinetobacter baumanii exposed to constant gentamicin concentrations has been modeled as an increase in EC50 with time and drug concentration (87). This model predicts a continuous development of resis-tance as it is dependent on time, prohibiting the bacteria to revert to the ini-tial susceptibility when gentamicin exposure diminishes.

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The sequential mutation model assumed that irreversible resistance devel-ops during the experiment. The first mutation would occur at a certain muta-tion rate and the bacteria would become a resistant non-growing subpopula-tion. A second mutation is assumed to occur at the same mutation rate and the bacteria have now become resistant growing bacteria(95).

Model-based development of dosing regimens It is important to ensure that the appropriate dosing regimens of antibiotics are utilized in all subpopulations of patients infected by bacteria. As PK characteristics differ between patient groups, the dose and dosing interval found appropriate for one patient group may not be suitable for another. As indicated above, modeling and simulation is a useful tool in developing dos-ing strategies and to explore the impact of differences in PK.

Mechanism-based PKPD-models may be used to simulate both previously investigated and untested dosing strategies, when combined with a PK model developed from patient data. This approach may be preferable over the use of PK/PD indices in the development of dosing guidelines as the full time-course of the killing effects for different dosing regimens in different patient populations may be predicted. In the predictions it is important to consider that it is the unbound drug that is free and available to act on the bacteria, i.e. the plasma protein binding needs to be accounted for in such predictions. Furthermore, unspecific binding and degradation during the experimental time needs to be considered in model development for accurate description of PKPD-relationships.

Gentamicin in newborn infants The administration of the aminoglycoside gentamicin has changed from three times daily dosing to an extended dosing interval of 24 hours for adults (72). The change has primarily been due to that gentamicin has been sug-gested to have a concentration dependent bacterial killing along with the main side effect, nephrotoxicity. The changed practice has also been based on gentamicin’s post-antibiotic effect and the presence of adaptive or pheno-typic resistance (4). Based on studies in vitro, and in patients, a ratio of peak plasma concentration to minimum inhibitory concentration (Cmax/MIC) higher than 8-10 mg/L has been indicated to be important for maximal bacte-rial kill (18, 57, 69). Nephrotoxicity has been suggested to be related to trough levels above 1-2 mg/L (7, 11, 29). These criteria do not, however consider changes in the concentration-effect relationships over time, which happens in the case of adaptive resistance. Gentamicin is popular as treatment or prophylactic treatment for con-firmed or suspected Escherichia coli infections in preterm or term newborn

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infants (79). In newborn infants dosing intervals of 24, 36 or 48 hours are frequently used (13, 59, 72, 84). The optimal dosing schedule is however not known, and there is a need for therapeutic drug monitoring of gentamicin in this population (32, 33, 50, 85). An appropriate a priori dosing would assist in ensuring that a therapeutic level is achieved faster with reduced frequency of monitoring (78). In a prospective study of preterm and term newborn in-fants, a three-compartment PK model with body weight, gestational age (GA) and post-natal age (PNA) as covariates for gentamicin was described (74). Based on the developed PK model, a dosing regimen of 4.5 – 5 mg/kg was suggested for preterm infants while a standard regimen of 4 mg/kg was found suitable for term infants.

The influence of the dosing regimens on the emergence of adaptive resis-tance has however not been well understood, and the development of dosing regimens should also consider that aspect. A PKPD model that incorporates adaptive resistance would provide valuable input to understanding which dosing interval would be most appropriate as a duration that is too long would allow surviving bacteria to markedly grow before the next dose.

Colistin and meropenem in critically ill patients For multi-resistant P.aeruginosa, colistin is considered as the last resort therapy and as mentioned above, some efforts have recently been conducted to optimize its dosing regimen (14, 16, 24, 44, 67). Both PK and PKPD-studies have been performed, but the effects of bacteria kill following clini-cally relevant dosing regimens have not been studied.

Since there is an increased threat of resistance development when using colistin as monotherapy (81), combination treatment may be preferred (14, 35, 94). Combination treatments can broaden the spectrum of antibiotic ac-tivity, enhance the activity by synergistic effects, and prevent resistance de-velopment. This may be achieved by penetrating cells and tissues not reached by single antibiotic treatment, and by inhibiting or overcoming cer-tain mechanisms of resistance such as, toxin or enzyme production (46). However, the potential adverse consequences like increased drug toxicities, antagonism, increased risk to multidrug resistance or increased drug-drug interaction should also be considered (46).

Reported combination regimens for colistin include imipenem (15), doripenem (35), meropenem (41, 80, 86) and rifampicin (45). In vitro studies have found the combination of colistin and meropenem to produce indiffer-ent (90), additive (90) or synergistic (80, 86) effects against different P.aeruginosa strains. In a retrospective clinical study, patients with P.aeruginosa infections who received colistin and meropenem in combina-tion did not have a significant difference in infection cure rate compared to those who received colistin as monotherapy (41). These results illustrate that it is crucial to optimize the dosing regimen in order to maximize the antibiot-

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ics efficacy, to minimize the toxicity and to overcome and prevent the devel-opment of resistance.

The variables that may be of interest to study in the optimization of a dos-ing regimen are dose size, including a loading dose, dosing frequency, infu-sion length and possibilities for individualization based on covariates and drug concentration ton measurements (therapeutic monitoring, TDM). For drug combinations also the relative dose size and the relevance of bacteria type is of interest. Most of these variables can be studied by simulating the outcome based on developed PK and PKPD variables.

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Aims

The general aim of this thesis was to develop pharmacokinetic (PK) and pharmacokinetic-pharmacodynamic (PKPD) models, which characterizes the interaction of antibiotics with bacterial growth, killing and resistance, and can be applied to guide optimization of dosing regimens that enhance the efficacy of mono- and combination antibiotic therapy. The specific aims were: • To develop mechanism-based PKPD models that can characterize the

time course of bacterial killing and emergence of resistance as observed in in vitro time-kill curve experiments for different antibiotics: gen-tamicin, colistin and meropenem.

• To develop a mechanism-based model that characterizes the interaction between meropenem and colistin.

• To investigate the impact of a loading dose and covariates on the PK of

colistin, and its prodrug CMS, in critically ill patients, and to quantify the unexplained interindividual variability (IIV) and interoccasion vari-ability (IOV).

• To perform simulations of different dosing regimens and dosing algo-

rithms to evaluate the effect of IIV and IOV in PK of CMS and colistin on the time-course of bacterial killing.

• To conduct predictions based on developed PK and PKPD models, and

information on protein binding, that can be used to suggest effective dos-ing regimens for the antibiotics either as single drugs or in combination.

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Materials and Methods

The methods in this thesis were conducted in the following steps: i. data collection by in vitro time kill experiments or collected in a clinical study, ii. developing models based on the data, iii. model validation with visual pre-dictive checks and external data and, iv. predictions of dose and simulations of combination experiments (Fig. 1).

Fig. 1. Summary of the methods.

In vitro data There were 2 types of experiments that were conducted on several bacterial strains and antibiotics, i. static and ii. dynamic in vitro time-kill experiments.

Predictions & Simulations

Model validationVisual Predictive Check (VPC)

External data validation

Model developmentPKPD models PK model

Data generationIn vitro time-kill experiments Clinical study

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Bacteria and Media

The types of bacteria that were used in the experiments were Escherichia coli ATCC (American Type Culture Collection) 25922, Pseudomonas aeruginosa ATCC 27853 and Pseudomonas aeruginosa L0603761, a clinical isolate at the Uppsala Academic Hospital (UAH)(56).

The bacteria were stored in -80°C and grown on 5% horse blood agar plates (Columbia agar base, Acumedia Manufactures Inc., Baltimore, Mary-land, USA) at 37°C. Six hours prior to the experiments the bacteria were incubated in Mueller Hinton (MH) broth (Difco, USA) supplemented with Ca2+/Mg2+ (MH Ca2+/Mg2+) at 37°C to achieve bacteria concentrations in the inoculums of approximately 109 CFU/ml which were diluted to 106 CFU/ml.

Antibiotics The three antibiotics used in the experiments were gentamicin (Sigma-Aldrich, Schnelldorf, Germany), colistin sulphate (Sigma Aldrich, Schnell-dorf, Germany) and meropenem trihydrate (AstraZeneca, Södertälje, Swe-den). Prior to each experiment, fresh stock solutions were prepared by dis-solving the antibiotics in sterile distilled water to a concentration of 10,000 to 12,000 mg/L and further diluted to the intended concentration in series of dilutions.

The minimum inhibitory concentration (MIC) of gentamicin for E.coli was 2.0 mg/L as determined by using the macrodilution method, according to the guidelines of the Clinical and Laboratory Standards. The MIC for meropenem was determined at 0.2 mg/L for P.aeruginosa ATCC 27853 and at 16 mg/L for P.aeruginosa L0603761. For colistin, the MIC values were 1 mg/L and 1.5 mg/L for the two strains, respectively. The MICs were deter-mined by the E-test method according to the instructions of the manufacturer Biomerieux (Marcy-l’Etoile, Rhone, France).

Antibiotics concentrations The gentamicin concentration were measured at 0, 6, 12 and 24 hours and analyzed by fluorescence polarization immunoassay (TDx, Abbot Laborato-ries, Chicago, IL, USA). Actual colistin concentrations were measured at 0, 8 and 24 hours with a previously established analytical method utilizing liquid chromatography-tandem mass spectrometry (51) to evaluate potential colistin degradation and binding to material during the experiments. The rate constant of colistin loss (kd) was calculated between the measurement time-points using log-linear regression. The measured concentrations and the kd values were used to derive a predicted colistin concentration at any time point during the experiment and these predictive concentrations were driving

23

the PKPD-model. Meropenem was measured at 0, 8 and 24 hours by a bio-logical measurement method (64).

In vitro time-kill experiments A starting inoculum of bacteria of approximately 106 CFU/ml was added in each culture vessel filled with culture media. Antibiotics were then added to the tube to achieve a range of different starting concentrations, both under and over MIC as listed in Table 1. The tubes were incubated in a temperature regulated-room at 35°C (for gentamicin) or 37°C (for colistin and mero-penem). Samples were taken frequently, diluted serially and cultivated on two to four agar plates. The blood agar plates were similarly incubated at 35°C (for gentamicin) or 37°C and the number of colonies was counted manually after 18 to 24 hours. For each concentration, the experiments were conducted in two or three replicates at different occasions. At each occasion, a growth control experiment was conducted where no antibiotics was added. The limit of detection (LOD) was 10 CFU/ml.

Static time-kill experiments In static time-kill experiments, the concentrations of the antibiotics were intended to be constant throughout the duration of the experiments. All ex-periments were conducted in 10 ml polyprophylene tubes with a total vol-ume of 4 ml. There were two types of experimental set-ups, single antibiotic (gentamicin, colistin or meropenem) and combination antibiotics (colistin and meropenem) studies. The starting concentrations were as listed in Table 1.

Table 1.Summary of all time-kill experiments

Bacteria Antibiotic Time-kill experiment

Starting concentration (mg/L) Paper

E.coli ATCC 25922

Gentamicin Static 0.125, 0.25,0.5,1,2,4,16 I Dynamic 1, 2, 3.9,8Repeated 2 (6h, 12h) , 3.9 (24h),8(24h)

P.aeruginosa ATCC 27853

Colistin Static 0.042, 0.19, 0.3, 0.77, 2.12, 4.3, 12 III, IV

Meropenem Static 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2 IV Colistin + Static 0.43, 0.21, 0.47 IV Meropenem 0.05, 0.1, 0.2P.aeruginosa L0603761

Colistin Static 0.081, 0.25, 0.96, 2.7, 5.1, 11, 24 III, IV

Meropenem Static 4, 8, 16, 32, 64, 128, 256 IV Colistin + Static 0.67, 1.47, 1.7, 7.7, 3.5 IV Meropenem 16, 32Note: Colistin concentrations reported are the measured initial concentrations. The simulated half-lives for the two-compartment kinetics used in the dynamic experiments for gentamicin correspond to neonatal values and were 0.33 h-1 for the first phase and 0.037 h-1 for the second

24

phase corresponding flow rates in the in vitro kinetic system of 37 and 4 L/h (as calculated for a typical PK parameters in a preterm infant of 1 kg).

Dynamic time-kill curve experiments For gentamicin, the experiments with dynamic concentration-time profiles were conducted in an in vitro kinetic system (65) consisting of an open bot-tom glass flask with a magnetic stirrer for homogeneous mixing. The flask was attached to a base but separated by two filters that functioned to main-tain the bacteria in the flask. A pump (P-500; Pharmacia Biotech, Uppsala, Sweden) was connected to the base and this device pumped media out from the flask to a sink-vessel. The flask has two arms, in one of the arms there was a silicone membrane for repeated sampling and the other arm was used to transport fresh media to the flask to dilute the drug concentration.

Combination in-vitro experiments For the combination experiments, both meropenem and colistin were used at concentrations based on predictions from the PKPD model developed (in step v above). The combinations that were chosen were those predicted to have bacterial killing but that would not fall below the limit of detection (LOD) and where regrowth may occur in the end of the experiment. For ATCC27853, the four chosen intended concentrations to study in combina-tion were (i) 0.25 mg/L and 0.1 mg/L,(ii) 0.25 mg/L and 0.2 mg/L, (iii) 0.5 mg/L and 0.05 mg/L, and, (iv) 0.5 mg/Land 0.1 mg/L, of colistin and mero-penem, respectively. For L0603761 the concentrations were (i) 1 mg/L and 32 mg/L, (ii) 2 mg/L and 16 mg/L, (iii) 8 mg/L and 16 mg/L, and (iv) 4 mg/L and 32 mg/L.

Clinical study A prospective PK study was conducted at the Critical Care Unit of Attikon University General Hospital, Athens, Greece from July 2009 to January 2010. Ethics approval was obtained from the Ethics Committee of the hospi-tal (Registration no. 7/30-07-09.).

Patients Critically ill patients who met the inclusion criteria: (i) age 18 or above and (ii) receiving colistin for suspected or proven multi-drug resistant GNB infection were enrolled. Patients receiving continuous venovenous hemo-diafiltration as renal replacement therapy were excluded. Informed consent was obtained from all patients enrolled in the study. For each patient, de-tailed information was collected on the first day of colistin administration: gender, age, body weight (actual and ideal), serum creatinine, serum albu-

25

min, hemoglobin, hematocrit levels, and APACHE II (Acute physiology and chronic health evaluation II) score. Serum creatinine was measured on day 1, 7, 14 and 21 and creatinine clearance was calculated according to the Cock-roft-Gault formula(25).

A loading dose of CMS (Colistin, Norma, Greece) was administered at 480mg (6 million units (MU)); approximately 180 mg of colistin base activ-ity (CBA)) with subsequent maintenance doses of 80 - 240 mg of CMS (1 to 3 MU; 30 – 90 mg CBA) every 8 hours. CMS was dissolved in 100 ml of normal saline (same volume for all dose sizes) and administered as intrave-nous infusions over 15 minutes.

Serial venous blood collection was conducted for the loading dose and the 8th dose. For all patients the samples were taken immediately prior to the start of the 15 minute infusion and at 15, 30, 60, 120, 240 and 465 minutes after the end of the infusion.

Analytical method

Plasma CMS and colistin concentrations were determined by a previously established method. Plasma concentrations of colistin A and colistin B were determined with the liquid chromatography-tandem mass spectrometry method (51) while CMS concentrations were determined from the difference of measured colistin concentrations in samples pre and post hydrolysis (60), accounting for the difference in molecular weight (molar masses are, on average, 1743 g/mol for CMS and 1163 g/mol for colistin). The limit of quantification of the method for 100 µl of plasma was 0.019 mg/L for colistin A and 0.010 mg/L for colistin B. The coefficient of variation (CV) for the method was 6.2%. Seven CMS standards ranging from 0.12 to 18.45 mg/L were analyzed and the intra-day CV was between 6.2 and 8.8% (n=6). Inter-day CV ranged from 6.7 to 7.9% based on single analysis of the stan-dards on 8 different days.

Model development PKPD Model (Paper I, III, IV) Bacterial system A previously developed mechanism-based model for antibiotics (75) formed the basis for the model development but was expanded to evaluate different functions describing the adaptive resistance development (Fig. 2). The model has compartments for drug-susceptible, growing bacteria (S) and insuscep-tible, resting bacteria (R) with first order rate constants for growth (kgrowth) and natural death (kdeath). The relationship in the absence of antibiotics can be described by the equations below:

26

dS/dt = kgrowth · S - kdeath · S - kSR · S + kRS · R (i) dR/dt = kSR · S - kdeath · R - kRS · R (ii)

All bacteria were here assumed to be in the growing stage (S) at the start

of the experiments. The bacteria transfer into a resting stage (R), with the rate constant kSR that increase with an increased number of total bacterial content in the system. In the absence of antibiotics, the bacterial count even-tually approaches a stationary phase where the total bacterial population is no longer increasing. In the resting stage, there is no bacterial growth but the bacteria are assumed to have the same natural death rate (kdeath) as bacteria in the growing stage. In all models developed here, kdeath was fixed to 0.179 h-1, the value obtained in the model described by Nielsen et al. (75), as there was limited information on this parameter in the current experiments and fixing the parameter stabilized the model.

A proportionality constant is calculated from the difference between the rate constant of growth (kgrowth) and the rate constant of death (kdeath) divided by the maximum number of bacteria in the stationary phase (Bmax). The proportionality constant times the total number of bacteria in the system (S+R) provides the transfer rate constant kSR. As in Nielsen et al. (75), the experimental data did not support a transfer from the resting to the growing bacterial stage (kRS=0) as there was minimal improvement in the model fit when allowing the rate constant kRS to be estimated. In Paper I, to be able to predict the pronounced bacterial killing observed following high gentamicin exposures, kSR was set to be zero at low bacterial counts and, the transfer from the sensitive stage into the resting stage only occurred when the total bacterial content in the system exceeded an estimated breakpoint value (BP).

Drug effect The drug effect on bacterial killing (kdrug) was evaluated to be a linear (γ=1) or a power function (γ≠1), by the estimated parameter Slope (Equation iii), or a basic (γ=1) or sigmoid (γ≠1) Emax function (Equation iv). kdrug at time 0 is the maximal achievable rate constant of bacterial killing at the start of the experiments and no resistance has developed. The ‘drug’ in kdrug refers to gentamicin, colistin or meropenem. The drug affected only the bacteria in the growing susceptible stage (S). kdrug = Slope · Cγ (iii) (Paper III, IV) kdrug = (Emax · C

γ)/( EC50γ + Cγ) (iv) (Paper I, III, IV)

Reduction of drug effect In Paper I, the presence of gentamicin-initiated adaptive resistance resulted in a reduction of Emax from its initial value Emax(0). The amount of reduction was determined by the fraction of the amount in ReON and the estimated

27

value describing when Emax was reduced to 50% (Re50) (Equation v which was incorporated into Equation vii). Emax(0) represents the maximal achiev-able rate constant of bacterial killing when no adaptive resistance has devel-oped while Re50 is the antibiotic concentration that results in 50% of Emax(0).

kdrugkill = kdrug · (1-(ReON / (ReON + Re50) (v) (Paper I) kdrugkill = kdrug · (1- ReON

β) (vi) (Paper III, IV) dS/dt = kgrowth · S – (kdeath + kdrugkill)· S - kSR · S (vii) (Paper I, III, IV)

The actual kill rate constant (kdrugkill) after the exposure-driven resistance

development (ReON) has been considered (Equations v and vi), was incorpo-rated into Equation i as described in Equation vii. At time 0, i.e. when no resistance has developed (ReON=0), kdrugkill is the maximal achievable rate constant of bacterial killing. β is the Hill factor for describing the relation-ship between ReON and the reduction in drug effect.

Resistance development Resistance development was described by a model where a hypothetical amount (ranging between 0 and 1) in the resistance compartment (ReON) acted on Emax or Slope to result in a reduction of kdrug from their initial values (Equations iii or iv), as described in Equation v or vi. The degrees of reduc-tion in Emax or Slope were determined by the fraction of the amount that had shifted from the compartment representing resistance being off (ReOFF, set to 1 at the start of the experiments), to the compartment with resistance being on (ReON, set to 0 at the start of the experiments) (Equations xi - xii). kon and koff describe the rate of development and reversal of adaptive resistance, respectively (Equations viii-x). Gentamicin concentration was proportionally affecting the rate constant (kon(G)) driving the transfer from ReOFF to ReON (Equation viii) while kon for colistin (kon(C)) was dependent on the concentra-tion by a sigmoidal Emax function where konmax is the maximum rate constant for transfer of the hypothetical amount to the resistance compartment in the presence of colistin and Con50 the colistin concentration that results in 50% of konmax (Equation vii). δ is the Hill factor for kon(C). For the meropenem ex-periments there was no significance dependence on drug concentration and kon (kon(M)) was best fitted by a drug-independent constant upon introduction of meropenem. The development and reversal of resistance are described in Equations xi-xii with the specific drug represented as x. Since no reversal of resistance was evident for meropenem, koff(M) was fixed to 0 in the final model.

kon(G) = kon(G) · C (viii) (Paper I) kon(C) = konmax · C

δ / (Cδ+ Con50δ) (ix) (Paper III, IV)

kon(M) = kon(M) (x) (Paper IV) dReOFF(x)/dt= koff(x) · ReON(x) - kon(x) · ReOFF(x) (xi) (Paper I, III, IV)

28

dReON(x) /dt = kon(x) · ReOFF(x) - koff(x) · ReON(x) (xii) (Paper I, III, IV)

Combined model The structural components from the best model for colistin and meropenem alone were transferred to a combined code and applied simultaneously on both single drug data in a combined model. The bacteria-specific parameters were constrained to be the same for both antibiotics and for each of the strains. kgrowth and kSR were allowed to be strain-specific, while Bmax was estimated to be the same value irrespective of bacterial strain or antibiotic.

This model was evaluated with a visual predictive check (VPC) and an external time-kill data from previous experiments performed on the same bacteria strains where colistin and meropenem, alone and in combination, had been studied in a kinetic system with dynamic concentrations (56). The time-kill curve experiments were conducted for 8 hours and had concentra-tion-time profiles with peak concentrations of 50 mg/L for meropenem and 0.5 mg/L for colistin with half-lives of 1 and 4 hours, respectively. Drug concentrations had previously been determined to be as intended in this ex-perimental system. An additive interaction for the antibiotics was assumed and the model was run without re-estimation.

The parameters obtained from the combined model were used to perform the predictions and the total bacterial killing was assumed to be dependent on the additive effects of the two kill rate constants (kdrugkill(C) and kdrugkill(M)) acting on the sensitive bacteria by the rate constant ktotalkill (equation xiii).

After prediction of the observed combination experiments, parameter val-ues were allowed to be reestimated and the significance for estimating a drug interaction parameter (Int) was tested (equation xiv). An Int value of zero suggests no interaction (kill as expected by adding the two rate constants), a positive value suggests synergy (more kill than expected) and a negative value suggest antagonism (less kill than expected). Int was estimated sepa-rately for each bacterial strain.

ktotalkill = kdrugkill(C) + kdrugkill(M) (xiii) (Paper IV) ktotalkill = kdrugkill(C) + kdrugkill(M) + Int · kdrugkill(C) · kdrugkill(M) (xiv)(Paper IV)

Model for random effects and data below LOD An additive residual error on the natural logarithmic scale was estimated for all experiments. In the analysis, there was generally more than one observa-tion per sampling time point and experiment included as all plates with de-tectable number of bacteria were analyzed. In order to avoid bias that can occur due to correlations between replicate samples, the residual error was estimated as two components: one consistent difference common for all rep-licates at the same time-point and experiment (RE) and one replicate-specific difference (RRE) (54). For time-points where all dilutions had bacterial

29

counts below the LOD, the probability for the observation to be below LOD was estimated using the M3 method for handling data below LOD (1, 10).

Population PK model (Paper II) All log-transformed PK data were modeled simultaneously with the data from the previous study (160-240 mg (2-3 MU) every 8 hours in 18 patients from the same hospital; a similar sampling design with a total of 267 sam-ples at two occasions) where the initial PK model was developed (82). Con-centrations in molar units were used in the modeling to account for one molecule of CMS that is hydrolyzed into one molecule of colistin.

Structural and Random-effects model The structural model from the previous study with two CMS compartments and one colistin compartment was reevaluated with different combinations of one, two and three compartments, as well as linear and non-linear elimi-nation pathways. The typical parameter values were estimated along with random effects described by IIV, IOV and residual errors. Correlation be-tween individual parameters was also investigated. The residual error was modeled by using an additive, a proportional, or a combined additive and proportional error model.

Covariate model Covariate model building was performed in a stepwise fashion with forward inclusion and backward deletion. As CMS is partially eliminated renally and previous population PK analyses have reported CrCl as a significant covari-ate for CMS and/or colistin (27, 44), CrCl and serum creatinine were ex-plored more extensively, including modeling CrCl as a time varying covari-ate (92). The unit for CrCl was in L/h in the modeling and observed CrCl values above 7.8 L/h (130 ml/min) were capped at 7.8 L/h.

Model selection and evaluation Model performance was assessed by evaluation of diagnostic plots and the objective function value (OFV). In order to discriminate between nested models, the difference in OFV (-2 log likelihood) was used. The more com-plex model was selected when the reduction in OFV was at least 10.83 (cor-responding to a P value <0.001 for 1 degree of freedom). Clinical relevance and reduction in IIV were also requirements for covariate inclusion in Paper II. The models were evaluated by VPC (55) in which a total of 500-1000 replicates were simulated by using the original dataset as a template. In Pa-per II, the prediction-corrected VPC was utilized to account for that some patients received a different dose (17). For Paper II, a bootstrap (500 sam-

30

ples) was performed to obtain the confidence interval of the parameters while log-likelihood profiling was used for Paper I, III and IV.

Plasma protein binding of colistin (Paper II) The unbound fraction (fu) of colistin was measured by equilibrium dialysis. Fresh human plasma (EDTA) from healthy volunteers was spiked with colistin purchased from Sigma Chemicals (St. Louis, USA) to concentrations of 0.25, 1, 4, 8, 16 and 24 mg/L. Plasma (0.5 ml) was dialyzed across a semi permeable membrane (Spectra/Por 4, cutoff 12-14000 Da) against an equal volume of phosphate buffer pH 7.4 containing sodium chloride. Triplicate samples were incubated during 24 hours at 37°C. At sampling, the buffer was mixed with an equal volume of blank plasma to avoid unspecific bind-ing of colistin to the tube material and thereby avoiding falsely low buffer concentrations. Colistin A and B were determined in both plasma and buffer with the same analytical method as described above. The protein binding was also determined after adding α1-acid glycoprotein (AAG) to plasma. In addition, the protein binding in each of the patients in Paper II and the pre-vious (82) study was determined in thawed samples by addition of colistin to pre-treatment samples (n=9), pre-treatment samples mixed with post-treatment samples (n=18) or post-treatment samples (n=3) to result in total combined concentrations of colistin A and colistin B of 0.8-5.6 mg/L in the equilibrium dialysis.

Simulations The PK models of specific antibiotics and the developed PKPD models were combined to predict the antibiotics concentration-time profile and the resul-tant bacterial kill for typical patients from different groups of subpopula-tions. In the simulations, a start inoculum, i.e. the average values of all starting inocula in the conducted experiments, of 4.83 · 105 CFU/ml (for gentamicin) and 4.5 · 105 CFU/ml (for colistin and combination antibiotics) were as-sumed. The simulated medians and 5th and 95th percentiles for CMS concen-tration, colistin concentration and bacterial killing were computed at fre-quent time-points during 36 hours. Assessment of patient population variability (Paper III) The final parameter estimates from the colistin PKPD model for the ATCC27853 strain and the developed PK model for CMS and colistin in critically ill patients was used to simulate the drug concentration and bacte-

31

ria-time profiles, including IIV and/or IOV. CMS loading doses of 480, 720 and 960 mg (6, 9 or 12 MU respectively) followed by maintenance of 360 mg (4.5 MU) every 12 hours, administered as 15-min infusions, were evalu-ated after inclusion of both IIV and IOV, or IIV only or IOV only. The IIV and IOV values were simulated for three different scenarios: i. all variability terms included as in the developed PK model (68), ii. variability for CMS or colistin only, and iii. variability for CLCMS or CLCol only. For each scenario and dosing schedule, 1000 patients were simulated. Comparisons of the vari-ability (the 90% prediction interval) were made for the measured variables colistin concentration and log bacterial count. The percentage of simulated patients who achieved 3-log bacterial killing at a certain time point (eg 12 hours) was also computed.

Comparison of dosing algorithm (Paper III) In order to evaluate the performance of different dosing schedules, the PKPD model for the ATCC strain was combined with PK models without covariates, and, with covariates (weight on V1CMS or CrCL on CLCMS) to generate new individuals by stochastic simulations(68) (44). When covariate relationships were included in the simulation, the relationships were (44): V1CMS = 11.5· (Weight/60) CLTCMS = CrCL · 0.0613 + 1.90

One thousand simulations were conducted in each scenario to predict the time-courses of colistin concentration and bacterial killing: i. the impact of different CrCL values in patients (30, 70 and 120 ml/min) for patients with the same weight, ii. the influence of the time interval between the loading dose and start time of maintenance dosing (12 versus 24 hours), iii. the influ-ence of infusion duration (15 minutes, 30 minutes and 2 hours infusion) and iv. the impact of different patient weights (50, 70, 90 and 120 kg) given they have the same CrCL values. For each scenario, two dosing algorithms were compared:

A. Flat-fixed CMS dosing: 720 mg loading dose then 360 mg maintenance

dose every 12 hours (q12h) to all patients and B. CMS dosing calculated by previously developed algorithms (44):

• Loading dose (mg) = colistin Css,ave target (mg/L) X 2.0 X weight (kg)

• Daily maintenance dose (mg) = colistin Css,ave target (mg/L) X (1.5 X CrCL (ml/min) + 30)

[Note: *Css,ave target (average steady state plasma concentration) was set at 1.5 mg/L to obtain similar colistin Css as for a maintenance dose of 360 mg q12h]

32

Predictions of gentamicin dosing regimens for newborn infants (Paper I) Gentamicin concentration-time profiles and E. coli counts were predicted based on the final PKPD model for four typical newborn infants with gesta-tional ages (GA) of 25, 29, 34 and 40 weeks and birth weights (WT) of 778, 1200, 2710 and 3500 gram, respectively. The typical ages and weights were selected based on the same gentamicin study from which the 3-compartment PK model was chosen to drive the bacterial killing in the predictions (74). The treatments were assumed to start on the day of birth and included doses of 2–7 mg/kg administered at dosing intervals ranging between 8 and 48 hours as 5-minutes infusions.

Predictions of colistin dosing regimens for critically ill patients (Paper II) The PK model developed was combined with the PKPD model for colistin. In the predictions of Pseudomonas aeruginosa ATCC27853 killing for a typical patient following different dosing regimens, the predicted plasma concentration of total colistin and unbound concentrations of CA and CB were computed from the predicted total concentrations based on the relation-ships identified for fu and CA and CB. The total concentration of unbound colistin (i.e. the sum of unbound CA and unbound CB) was driving the bac-teria kill, assuming CA and CB were the active components possessing simi-lar potency. CMS was administered as intravenous infusion over 15 minutes for prediction of dosing schedules with:

i. 240 mg every 8 hours (no loading dose) ii. a loading dose of CMS of 480, 720 and 960 mg of with subse-

quent maintenance doses of 240 mg every 8 hours or 360 mg every 12 hours.

iii. dosing intervals of 8, 12, and 24 hours between the loading and maintenance doses.

iv. individuals who had the lowest and highest measured colistin concentrations at 4 hours after the administration of the loading dose.

Predictions of colistin and meropenem combination dosing regimens for critically ill patients (Paper IV) Total and unbound colistin concentration-time profiles, unbound meropenem concentration-time profiles and P.aeruginosa counts for L0603761 strain were predicted for a typical patient based on colistin and meropenem (28) PK models developed for critically ill patients and the final combined PKPD model including interaction that was developed in this thesis. For mero-

33

penem, the PK was based on a 90 kg patient with creatinine clearance of 70 ml/min. Clearance was 13 L/h, central volume was 21.5 L, intercompartmen-tal clearance was 10.5 L/h and the peripheral volume was 16.2 L (28).

The dosing schedules evaluated consisted of CMS loading doses of 480 mg, 720 mg or 960 mg followed by maintenance dosing of 360 mg every 12 hours administered as 15 minutes infusion, in combination with meropenem doses of 500, 1000 or 2000 mg every 8 hour administered as 3 hour infu-sions.

Software Data analysis was conducted using the first-order conditional estimation method with interaction and ADVAN5 (Paper II) and ADVAN9 (Paper I, III and IV) within the population analysis software NONMEM 7 (Icon Devel-opment Solutions, Ellicott City, MD). NONMEM was also used to predict the antibiotics concentrations versus time and bacterial count versus time profiles. The Xpose program (version 4) (53) and R (version 2.10, www.r-project.org) were used for dataset review and graphical evaluation. Simula-tions and calculations for VPC, execution of stepwise covariate model (SCM) building and bootstrap were performed using the Perl speaks NON-MEM (PsN) toolkit (63). The relationships between fu and the total plasma concentration for CA and CB in Paper II were obtained with nonlinear least-square regression using Microsoft Excel Solver (48).

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Results

Measured colistin concentrations The measured initial colistin concentrations in the experiments were 8.3-83% lower than intended, except for the concentration of 24 mg/L that was measured to be the same as the intended concentration. The loss was larger the lower the concentration, and there was also a progressive decline in colistin concentration with time, likely due to unspecific binding of colistin to material and possible degradation during the experiments. The application of actual colistin concentrations was important in the characterization of the concentration-effect relationship.

Mechanism-based PKPD Models A mechanism-based PKPD model was developed to describe bacterial growth, killing and resistance development in in- vitro bacterial cultures for three different antibiotics; gentamicin, colistin and meropenem. A sche-matic illustration of the final model for each antibiotic is shown in Fig. 2.

Gentamicin killing effect on E.coli and colistin effect on the wild-type strain of P.aeruginosa were best described by basic Emax models. The colistin effect on L0603761 was a linear function as estimation of a more complex model did not improve the fit. The effect of meropenem on both P.aeruginosa strains was best described by sigmoid Emax models. The differ-ence between the antibiotics in the functions describing relationship between ReON and reduction in drug kill rate constant, and kon are also shown in Table 2. The functions for colistin and meropenem were maintained in the com-bined model for colistin and meropenem. An overview of the drug-dependent model functions are summarized in Table 2.

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Fig. 2. Schematic illustration of the final PKPD model. The bacteria are either in a proliferating and drug susceptible compartment (S) or in a resting and drug-insusceptible compartment (R). The bacteria multiply with a first-order rate constant in the susceptible compartment (kgrowth) and the bacteria in both compartments are affected by a first-order natural death rate (kdeath). The total bacterial content in the system (S + R) stimulates the transfer from the proliferating stage into the resting stage (kSR) with increasing total number of bacteria in the system, or for gentamicin, when the number of bacteria is above an estimated value. The concentration in the central compartment, with a first-order elimination rate (ke), was driving the killing of the bacteria. Adaptive resistance was described by a hypothetical amount transfer-ing with a rate constant (kon) to a compartment of adaptive resistance/resistance (REON) stimulated by the the antibiotic concentration. koff characterized the return to susceptibility. The degree of REON resulted in a reduction of the maximum bacterial killing of the antibiotic (kdrug). Subscript (x) represents the different antibiotics.

Table 2. Summary of functions for drug effect, reduction of drug effect due to resis-tance development and rate constants for resistance development (kon) for the differ-ent antibiotics models.

Antibiotic Bacteria Drug effect

Reduction of drug effect due to resistance devel-opment

kon koff

Gentamicin E.coli Basic Emax

kdrug · (1-(ReON / (ReON + Re50)

Conc dependent Fixed to 50

Colistin P.aeruginosa ATCC27853

Basic Emax

kdrug · (1- ReONβ) Conc dependent

sigmoid Emax

Slope

P.aeruginosa PL0603761

Slope kdrug · (1- ReONβ) Conc dependent

sigmoid Emax Slope

Meropenem P.aeruginosa ATCC27853

Sigmoid Emax

kdrug · (1- ReON) Conc indepen-dent

Fixed to 0

P.aeruginosa PL0603761

Sigmoid Emax

kdrug · (1- ReON) Conc indepen-dent

Fixed to 0

S(x)

C(x) R(x)

kdeath

kSR(x)

kgrowth(x)

kdeath

ke(x)

ReON(x)

+

+

kon(x)

koff(x)

kdrug(x)

S+R

Pharmacokinetics Resistance development Bacterial system

+

NReReOFF(x)

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Time-kill curve experiments for gentamicin Time-kill curves for typical gentamicin experiments are shown in Fig. 3. No or low gentamicin exposures resulted initially in exponential growth but at high inocula the growth rate reduced to approach a maximum bacterial count of approximately 109 CFU/ml. In the static experiments (Fig. 3A) regrowth occurred for concentrations of 0.5, 1 and 2 mg/L while the bacterial count remained below the LOD at 4 and 16 mg/L. In the experiments where the bacteria was grown for 12 hours before adding the antibiotic, an antibacterial effect was seen only for the highest concentration of 16 mg/L. In all dynamic experiments with single doses administered at time 0 (Fig. 3B) regrowth occurred. There was consistently a limited bacterial killing with subsequent doses of the same size, indicating development of resistance (Figs. 3C and 3D).

37

Fig. 3. Typical time-kill curves for E. coli exposed to gentamicin. A, static time-kill curve experiments with concentrations ranging between 0 to 16 mg/L; B, dynamic time-kill curve experiments with four single doses (Cmax= 2.0, 3.9, 7.8 or 16 mg/L); C, dynamic time-kill curve experiments with repeated dosing (Cmax= 7.8 or 16 mg/L) administered at 24 hours interval. D, dynamic time-kill curve experiments with repeated dosing (Cmax=3.9 mg/L) with a single second dose at 6 hours or at 12 hours interval. In C, some experiments with Cmax of 16 mg/L showed bacterial regrowth at approximately 12 hours (black dash-dotted line) while others had bacterial counts that stayed below limit of detection throughout the experiment (grey dash-dotted line). Arrows indicate the time of dose administration. Grey arrow in D indicates the second dose at 6 hours. Bacterial counts below limit of detection are plotted as 10 CFU/ml.

Mechanism-based PKPD model for gentamicin As expected, the original semi-mechanistic PKPD model (75) could not de-scribe the gentamicin data well due to the development of adaptive resis-tance and the model was expanded as described above. As indicated by the VPCs, the model described the observed data well for both static and dy-namic experiments, while for the experiments where the bacteria was al-

0 6 12 18 240

2

4

6

8

10

0 mg/L0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L16 mg/L

0 6 12 18 24 30 36 42 480

2

4

6

8

10Cmax = 7.8 mg/ L τ = 24hCmax = 16 mg/L τ = 24hCmax = 16 mg/L τ = 24h

E.co

li co

unt (

Log 10

CFU

/ml)

Time (h)

A

C0 6 12 18 24 30 36 42 48

Cmax = 2.0 mg/LCmax = 3.9 mg/LCmax = 7.8 mg/LCmax = 16 mg/L

0 6 12 18 24 30 36 42 48

Cmax = 3.9 mg/L τ = 6hCmax = 3.9 mg/L τ = 12h

B

D

38

lowed to grow 12 hours prior to addition of gentamicin (Fig. 4C), the model over predicted the antibacterial effect at 2 and 4 mg/L.

The estimated parameters of the final model for gentamicin were listed in Table 3. Gentamicin had a fast bactericidal effect with a maximum killing rate constant (Emax(0)) of 51 h-1 and an EC50 of 9.85 mg/L. The growth rate constant was estimated at 2.00 h-1. kon was estimated at 0.0426 Lmg-1h-1 while there was limited information in the data on the half-life for the bacte-ria to return to the susceptible state after developing adaptive resistance (ln2/koff). This parameter was therefore fixed to 50 hours as lower half-lives resulted in an increased OFV. The estimated value of Re50 indicated that the maximum Emax inhibition by the adaptive resistance mechanism was 90% as the maximum amount possible in ReON is1 (1/(1+0.113) = 0.90).

39

02468

10

0 6 12 18 24

0 mg/L

0 6 12 18 24

0.125 mg/L

0 6 12 18 24

0.25 mg/L

0 6 12 18 24

0.5 mg/L02468

101 mg/L 2 mg/L 4 mg/L 16 mg/L

02468

10

0 12 24 36 48

2.0 mg/L

0 12 24 36 48

3.9 mg/L

0 12 24 36 48

3.9 mg/L τ12h

0 12 24 36 48

3.9 mg/L τ 6h02468

107.8 mg/L 7.8 mg/L τ24h 16 mg/L 16 mg/L τ24h

02468

10

0 6 12 18 24 30 36

0 mg/L

0 6 12 18 24 30 36

1 mg/L

0 6 12 18 24 30 36

2 mg/L

0 6 12 18 24 30 36

4 mg/L02468

1016 mg/L

Obs

erve

d an

d m

odel

pre

dict

ed b

acte

rial c

ount

(log

10 C

FU/m

l)

Time (h)

A

B

C

40

Fig. 4. Visual predictive checks for the final model of gentamicin with observed bacterial counts (o), as well as the median (−) and the 80% prediction interval (--) of the simulated data. A, growth controls and experiments with static gentamicin con-centrations; B, dynamic experiments using single and repeated dosing regimens (for 3.9 mg/L τ6h, only one additional dose was administered); C, experiments with static gentamicin concentrations added after a 12 hour period of bacterial growth.

Table 3. Population parameter estimates for the final gentamicin and colistin model. The 95% confidence intervals (CI) were obtained from log-likelihood profiling.

Parameter Gentamicin E.coli

Colistin P.aeruginosa ATCC27853

Colistin P.aeruginosa

L0603761 kgrowth (h

-1) 2.00 (1.89 – 2.27) 0.919 (0.800 – 1.05) 0.813 (0.733 – 0.893)

kdeath(h-1) 0.179 (fix)

BP (CFU/ml) 2.09 x 106

(1.01 – 3.32 x 106)- -

Bmax (CFU/ml) 8.26 x 108

(6.18 – 11.10 x 108)2.19 x 108 (1.07 x 108 – 3.97 x 108)

Emax(0) (h-1) 51.0 (44.6 – 61.6) 282 (129 - 298) -

EC50 (mg/L) 9.93 (8.45 – 12.1) 1.16 (0.735 – 1.85) -Slope (mg/L) 15.9

(1.59 – 25.6) Re50 0.113

(0.0983 – 0.146)- -

β - 0.0208 (0.00461 – 0.363) kkon(G) (L/mgh ) 0.0426

(0.0376 – 0.0478)- -

konmax (L/mgh) 0.824 (0.557 – 1.27) 4.76 (1.94 – 14.3) Con50 2.61 (1.30 – 8.18) 105 (25 – 243) δ 0.791 (0.605 – 0.982)koff (h

-1) 0.0139 (fix) 0.0911 (0.0714– 0.112)RESstatic 1.69 (1.52 – 1.83) 1.36 (1.24 – 1.48)RESdynamic 2.80 (2.56 – 2.98)RRES 0.618 (0.59 – 0.649) 4.75 (4.30 – 4.96)

Mechanism-based model for colistin The model structure of the PKPD model for gentamicin described above could fairly well describe the effect of colistin when all parameters were allowed to be reestimated, although to arrive at the final model adaptions were made as described in Table 2. For example, the function in how the amount in ReON inhibits kcol (through Emax) was simplified to a direct rela-tionship as described in Equation v, and the transfer from ReOFF to ReON was described by a sigmoid Emax-relationship for kon (Equation viii). A reversal of resistance could be estimated by a first order rate constant, koff. The parame-ter estimates of the final model are listed in Table 3.

41

Fig. 5. Visual predictive checks for the final combined model on single drugs with observed bacterial counts (o), as well as the median (−) and the 80% prediction interval (--) of the simulated data. The plots include growth controls and experi-ments with static colistin (C) and meropenem (M) concentrations for I, wild-type P.aeruginosa (ATCC27853) with meropenem; II, meropenem resistant P.aeruginosa, (L0603761) with meropenem; III, wild-type P.aeruginosa (ATCC27853) with colistin; and IV, meropenem resistant P.aeruginosa, (L0603761) with colistin.

Mechanism-based model for colistin and meropenem combination The parameters estimated from the model based on the combined single-drug and combination experiment data are listed in Table 4. The parameters differed somewhat compared to when the colistin data was modeled alone (Table 3). For meropenem and ATCC27853 the maximal killing rate con-stant Emax was lower than for colistin. For L060376, Emax was lower (2.06 h-1) and EC50 considerably higher (11.1 mg/L) than for ATCC27853 (Table 4), consistent with the clinical isolate being meropenem resistant. There was no indication of reversibility of the resistance for meropenem and therefore koff

was fixed to 0. VPCs showed the adequacy of the model for both bacteria strains (Fig. 6).

The inclusion of an interaction parameter to describe the combined killing effect of meropenem and colistin resulted in a drop in OFV of 170 units for ATCC27853. For L0603761 the drop in the OFV was 27 units when interac-tion was allowed. The interaction factor for ATCC27853 was -0.842 and indicated a less than expected effect and thereby an antagonistic effect ac-cording to the definition. Visually, the experiments indicated no benefit of

Time (h)

Obs

erve

d an

d m

odel

pre

dict

ed b

acte

rial c

ount

(log

10 C

FU/m

l)2468

10M 0 mg/L M 0.05 mg/L M 0.1 mg/L M 0.2 mg/L M 0.4 mg/L M 0.8 mg/L M 1.6 mg/L M 3.2 mg/L

2468

10M 0 mg/L M 4 mg/L M 8 mg/L M 16 mg/L M 32 mg/L M 64 mg/L M 128 mg/L M 256 mg/L

2468

10C 0 mg/L C 0.042 mg/L C 0.19 mg/L C 0.3 mg/L C 0.77 mg/L C 2.12 mg/L C 4.3 mg/L C 12 mg/L

2468

10C 0 mg/L C 0.081 mg/L C 0.25 mg/L C 0.96 mg/L C 2.7 mg/L C 5.1 mg/L C 11 mg/L C 24 mg/L

6 1218 240 6 1218 240 6 1218 240 6 1218 240 6 1218 240 6 1218 240 6 1218 240 6 1218 240

I. Wild type ATCC27853with Meropenem

II. Resistant L0603761with Meropenem

III. Wild type ATCC27853with Colistin

IV. Resistant L0603761with Colistin

42

adding colistin for this meropenem sensitive strain (Fig. 6). For L0603761 the interaction factor was estimated to 0.408, indicating a synergistic effect.

Table 4. Population parameter estimates for the final colistin and meropenem com-bination model. The 95% confidence intervals (CI) were obtained from log-likelihood profiling.

Parameter Combined model with interaction (data with combined experiments)

Colistin Meropenem

ATCC 27853

L0603761 ATCC 27853

L0603761

kgrowth (h-1)

1.10 (1.02 – 1.19)

0.899 (0.827-0.979)

1.10 (1.02 – 1.19)

0.899 (0.827-0.979)

kdeath (h-1)

0.179 (fix)

Bmax (CFU/ml) 7.06 x 107

(4.90 – 10.4 x 107)Emax (h-1)

498 (206 -599)

- 3.86 (3.33 – 4.79)

2.06 (1.85 – 2.27)

EC50 (mg/L) 0.31 (0.223 – 0.58)

11.1 (9.44-13.0)

Slope (L/mgh)

- 21.8 (5.95 – 39.6)

- -

γ - - 0.934 (0.712 – 1.18)

1.84 (1.33-2.63)

kkon(M) (h-1) - - 0.113

(0.0964-0.132)0.0794 (0.0652 –

0.0956) β 0.0173

(0.0101 – 0.0679)- -

konmax (L/mgh) 0.967 (0.585-1.68)

2.15 (1.38 – 3.46)

- -

Con50 (mg/L) 3.73 (2.30 – 6.65)

16.9 (11.7 – 29.2)

- -

δ 1.21 (1.06 – 1.21)

koff

(h-1) 0.107

(0.0844-0.131)0 (fix)

RES 1.61 (1.54-1.70)

RRES 0.456 (0.438 – 0.475)

Int - 0.842 (-0.962 - -0.743)

0.408 (0.224 – 0.655)

-0. 842 (-0.962 – -0.743)

0.408 (0.224 – 0.655)

43

Fig. 6. VPCs based on the final model for colistin and meropenem with bacteria-specific parameters shared for the two drugs and allowing drug interaction for I. P.aeruginosa (ATCC27853) andmeropenem resistant P.aeruginosa, (L0603761) (two bottom rows). The plots show observed bacterial counts (o), the median (−) and the 80% prediction interval (--) of simulated data. Colistin (C) and meropenem (M) concentrations indicated are the initial concentrations.

Population PK of colistin in critically ill patients Patients and colistin concentration There were 10 patients (6 males, 4 females) enrolled in the study. The mean age was 55.4 years (age range, 32 to 88 years). Colistin concentrations were on average 1.34 mg/L (range 0.374 – 2.59 mg/L) at 8 h following the loading dose of 480 mg of CMS.

Time (h)

Obs

erve

d an

d m

odel

pre

dict

ed b

acte

rial c

ount

(log

10 C

FU/m

l)

2468

100 mg/L M 0.2 mg/L C 0.43 mg/L C 0.21; M 0.1 mg/L

2468

10C 0.22; M 0.2 mg/L C 0.48; M 0.05 mg/L C 0.47; M 0.1 mg/L C0.20;M0.1(1h)mg/L

2468

100 mg/L M 32 mg/L C 1.47 mg/L C 0.67; M 32 mg/L

2468

10

0 6 12 18 24

C 1.7; M 16 mg/L

0 6 12 18 24

C 7.7; M 16 mg/L

0 6 12 18 24

C 3.5; M 32 mg/L

0 6 12 18 24

C 3.5; M 32(1h)mg/L

I. Wild typeATCC27853

II. ResistantL0603761

44

Population PK model A model with two compartments for CMS and one compartment for colistin was sufficient to describe the data (OFV 77 units lower than for a one com-partment model). Parameter estimates are presented in Table 5. IIV was sig-nificant for CMS clearance (CLCMS), colistin clearance (CLcol), intercom-partmental clearance for CMS (Q) and in the residual error of CMS. Inclu-sion of covariance between CLCMS and CLcol improved the OFV further (27 units) and as the correlation was estimated to 100%, the magnitude of the variability for CLcol was scaled from the estimated variability in CLCMS with a factor estimated to 1.8. IOV was significant for CLCMS, the peripheral vol-ume of distribution of CMS (V2), CLcol and the volume of distribution of formed colistin (Vcol). For a typical individual, the half-lives of the two phases of CMS were 0.026 and 2.2 hours respectively, and the half-life of colistin was 18.5 hours. No covariate relationship met the pre-defined statis-tical criteria.

The prediction-corrected visual predictive check (pcVPC) showed that the final PK model without covariates explained the observed data well (Fig. 7). The bootstrap indicated that all parameters were estimated with reasonable uncertainty, except for Q where uncertainty was large (90% CI: 92 – 640 L/h) (Table 5).

Fig. 7. Visual predictive check of the final model stratified for the studied dosing occasions. Shown are the median (-) of prediction-corrected observed concentrations

1st dose

Pred

−cor

r Con

centr

ation

(μmo

l/liter

)

0.01

0.1

1

10

0 2 4 6 8

CMS

0 2 4 6 8

Colis tin

24 26 28 30

CMS

24 26 28 30

Colis tin

Tim e (h o u rs a fte r s ta r t o f s tu d y)Pred

−cor

r Con

centr

ation

(μmo

l/liter

)

0.01

0.1

1

10

40 42 44 48

CMS

40 42 44 48

Colis tin

Tim e (h o u rs a fte r s ta r t o f s tu d y)

1

56 58 60 62

CMS

56 58 60 62

Colis tin

4th dose

8th dose

32

6452

45

(o) and the 95% confidence intervals of the medians of prediction-corrected simu-lated concentrations (grey area).

Table 5. Estimated population pharmacokinetic parameters of CMS and colistin for the final model based on the combined data from the current and previous (82) studies.

Parameter (unit)

CMS Colistin

Typical value

IIV IOV Typical value

IIV IOV

CL (L/h) 13.1 (11.6-15.1)

42 (21-42.3)

30 (21– 31)

8.2 (6.0 -11.2)

*76 (52-76.1)

48 (34-51)

V1 (L) 11.8 (7.6 -12.5)

- - 218 (192-252)

- 48 (34-51)

Q (L/h) 206 (93-641)

111 (52-197)

- - - -

V2 (L) 28.4 (22.4- 33.5)

- 59 (51-85)

- - -

Additive residual error (µmol/L)

0.071 (0.063-0.25)

- - 0.044 (0.018-0.053)

- -

Proportio-nal error (%)

0.23 (0.12-0.27)

52 (31 -61)

- 0.082 (0.065 -0.12)

- -

Plasma protein binding of colistin The unbound fraction of colistin A (fuA), and consequently the fu based on total colistin concentration (CA+CB), was concentration dependent whereas fu of colistin B (fuB) was constant (average of 43%) across the evaluated concentrations from the plasma of healthy volunteers (Fig. 3). A non-linear equation was fitted to the data for colistin A.

fuA (%) = 31.2 · CA/(0.094 + CA)

CA is the total concentration of colistin A in mg/L. The predicted fu was 15% for total colistin concentrations (CA + CB) of 0.01 mg/L and 34% for 2.5 mg/L.

There was no obvious difference in the plasma binding in the critically ill patients and the healthy volunteers over the studied concentration range (Fig. 7). It should however be noted that fu is dependent on the ratio of colistin A and colistin B. There was no evident change in protein binding when adding AAG to plasma.

46

Fig. 8. Unbound fraction of colistin A and colistin B in healthy volunteers (left), and total colistin in healthy volunteers and patients (right), versus the end dialysis total plasma concentration of colistin A, colistin B and total colistin in the equilibrium dialysis study. The solid lines represent the fits obtained by non-linear least-squares regression for colistin A (R2=97%) and total colistin for healthy volunteers (R2=91%). The fit for colistin B is a horizontal line at y = 0.43.

Simulations for assessment of variability The simulations showed that the variability in concentration arising from IOV was higher than the variability arising from IIV and also when propa-gated to variability in bacterial counts (Fig 10 A-C). For a loading dose of 480 mg, 50% of the patients were predicted to achieve a 3-log bacterial kill-ing at 24 hours, while for a 960 mg loading dose the majority of the patients will have sufficient exposure for a 3-log bacterial killing. The IIV and IOV in CMS parameters resulted in relatively low variability in the colistin con-centration and bacterial killing profiles (Fig 10D) compared to IIV and IOV in colistin parameters (Fig 10E). The IIV for CMS resulted in lower colistin variability than IOV in CMS, and the same was found for colistin when only variability in colistin parameters were included in the simulations.

Total plasma colistin concentration(mg/liter)0.01 0.03 0.1 0.2 0.4 0.81 2 3 5 8 13

Total (A+B) healthy volunteersTotal (A+B) patients

Plasma colistin concentration (mg/liter)0.01 0.03 0.1 0.2 0.4 0.81 2 3 5 8 13

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Colistin AColistin B

Unbo

undf

racti

onof

colis

tin

47

Fig. 9. Comparison of the variability in 1000 simulated patients for unbound colistin concentrations (upper row for each scenario) and for P. aeruginosa count (lower row for each scenario) when including IIV only (left column), IOV only (middle column) and IIV and IOV (right column). Three different loading doses were evaluated; A. 480 mg, B. 720 mg and C. 960 mg followed in all scenarios by a maintenance dose of 360 mg 12 hourly. Variability in only CMS parameters (D) was simulated for the loading dose of 720 mg (9MU). The solid line is the 50th percentile with the dashed lines representing the 5th and 95th percentiles. Grey dotted lines represent the starting bacteria inocula of 4.5x105 CFU/ml (top line), the 3-log kill (middle line) and 10 CFU/ml (bottom line).

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

0

2

4

6

8

10

0

2

4

6

8

10

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

03

0

2

4

6

8

10

63

0

2

4

6

8

10

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

0

2

4

6

8

10

0

2

4

6

8

10

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

0

2

4

6

8

10

0

2

4

6

8

10

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

0

2

4

6

8

10

0

2

4

6

8

10

A. Variability for both CMS and colistin. 480 mg (6 MU) loading dose then 360 mg (4.5 MU) q12h

B. Variability for both CMS and colistin. 720 mg (9 MU) loading dose then 360 mg (4.5 MU) q12h

C.Variability for both CMS and colistin. 960 mg (12 MU) loading dose then 360mg (4.5 MU) q12h

D. Variability for CMS only. 720 mg (9 MU) loading dose then 360 mg (4.5 MU) q12h

E. Variability for colistin only. 720 mg (9 MU) loading dose then 360 mg (4.5 MU) q12h

IIV only IOV only IIV + IOV

Time (h)

0 6 241812 30 36 0 6 241812 30 36 0 6 241812 30 36

02

4

6

8

10

0

0.5

1

1.5

2

Colis

tin un

boun

d co

nc (m

g/L)

02

4

6

8

10

0

0.5

1

1.5

2

Bacte

rial c

ount

(log 10

CFU

/ml))

Colis

tin un

boun

d co

nc (m

g/L)

02

4

6

8

10

0

0.5

1

1.5

2

Bacte

rial c

ount

(log 10

CFU

/ml))

Colis

tin un

boun

d co

nc (m

g/L)

02

4

6

8

10

0

0.5

1

1.5

2

Bacte

rial c

ount

(log 10

CFU

/ml))

Colis

tin un

boun

d co

nc (m

g/L)

02

4

6

8

10

0

0.5

1

1.5

2

Bacte

rial c

ount

(log 10

CFU

/ml))

Colis

tin un

boun

d co

nc (m

g/L)

Bacte

rial c

ount

(log 10

CFU

/ml))

48

Simulations for comparison of dosing algorithm For the model including a CrCL-CMS relationship (Fig 10A, right panel), the log-bacterial killing was higher for patients with reduced renal function (CrCL of 30 ml/min) compared to those with CrCL of 120 ml/min (3.0 vs. 2.2) at 12 hours for a flat-fixed loading dose. A 24 hour interval between the loading and initiation of maintenance dosing resulted in a tendency for re-growth of bacteria at 18 hours for all loading doses tested (Fig 10B). The CMS peak concentrations during maintenance dosing reduced with infusion duration but there seemed to be no important differences in bacterial killing between the evaluated infusion lengths (Fig 10C). Weight as a covariate on V1 had limited impact on the CMS peak concentration and the colistin con-centrations for both the model with and without weight as a covariate (Fig 10D). Importantly, a weight-based loading dose resulted in 2.7 less log-bacterial killing at 24 hours for a 50 kg compared with a 90 kg patient (Fig 10D).

49

Fig. 10. Simulated medians of CMS concentration (top panel), colistin unbound concentration (middle panel) and bacterial killing (lower panel) for a model not including covariate relationships (left) and a model including a covariate (right). In scenarios A and B CrCL on CMSCL was the included covariate in the model predic-tions. In Scenario D body weight on CMSV1 was the included covariate. For scenario C only the results without inclusion of covariates are shown. In scenarios A, B and C, a flat-fixed dose or the calculated doses for a WT-based loading dose or a CrCL-maintenance dose were simulated for different body weights and CrCL values as indicated in the legend. In D, the patients were assumed to receive a flat-fixed load-ing and maintenance dose, or, a calculated loading dose for weights of 50, 70, 90 or 120 kg and a maintenance dose based on a CrCL of 70 ml/min. CrCL for the flat-fixed dosing was 84 ml/min and the weight was 70 kg. In the bottom panels (bacte-rial count), the grey dotted lines represent starting bacteria inoculum of 4.5x105 CFU/ml (top line), 3-log kill (middle line) and 10 CFU/ml (bottom line).

0 6 12 18 24 30 36 0 6 12 18 24 30 36 0 6 12 18 24 30 36 0 6 12 18 24 30 36 0 6 12 18 24 30 36

0 6 12 18 24 30 36 0 6 12 18 24 30 36 0 6 12 18 24 30 36 0 6 12 18 24 30 36

Bact

eria

coun

t (lo

g 10 C

FU/m

l)Co

listin

unb

ound

co

nc (m

g/L)

CMS

conc

(mg/

L)

0

2

4

6

0

0.5

1.00

10

20

3025

15

5

0

2

4

6

0

0.5

1.0

10

20

3025

15

Model with no covariate Model with CrCl on CMSCL

A. Maintenance dose at 12 hours ● Model with no covariate

B. Maintenance dose at 24 hours

15 min 30 minC. Infusion duration

Model with no covariate Model with weight on V1D. Different weight

2 h

05

Time (h)

720 mg load & 360 mg q12h (flat-fixed)400 mg load & 270 mg q12h (WT50)560 mg load & 270 mg q12h (WT70)720 mg load & 270 mg q12h (WT90)960 mg load & 270 mg q12h (WT120)

720 mg load & 360 mg q12h (flat-fixed)560 mg load & 150 mg q12h (CRCL30)560 mg load & 270 mg q12h (CRCL70)560 mg load & 420 mg q12h (CRCL120)

Legend for A.B and C Legend for D

12

12 12 12 12

12 12 12

Bact

eria

coun

t (lo

g 10 C

FU/m

l)Co

listin

unb

ound

co

nc (m

g/L)

CMS

conc

(mg/

L) Model with CrCl on CMSCL

0 6 12 18 24 30 36

0 6 12 18 24 30 36

50

Dosage regimen for specific populations Gentamicin in newborn infants In Fig. 11, the time courses of gentamicin concentrations and bacterial counts following several commonly used dosing schedules in neonates are predicted. The higher initial doses produced more bacterial killing during the first 24 hours. The extreme preterm newborn infant achieved lower peak concentrations than the more mature infants but had nevertheless higher overall bacterial killing because of the lower clearance and consequently larger AUC. The model predicted however bacterial regrowth for all three dosing schedules. No major advantage of a fractionated schedule over 36 hours was found when a single dose of 6 mg/kg was compared to fraction-ated schedules with the same total dose.

Fig. 11. Model predictions of gentamicin concentration (top) and E. coli count (bot-tom) for four typical newborn infants with varying gestational ages (GA) for three commonly used dosing schedules in neonates. Grey dotted lines represents a gen-tamicin concentration of 2 and 10 mg/L (top) or a bacterial count of 4.83x105 CFU/ml (starting inocula) and 1 CFU/ml (bottom).

Colistin in critically ill patients In Fig. 12A, for the individual with the typical population value, the pre-dicted time courses of total and unbound colistin concentrations and bacte-rial counts following a maintenance dose of 240 mg every 8 hours or 360 mg every 12 hours and loading doses of 480, 720 and 960 mg are shown. It was predicted that it takes approximately 12.5 hours to achieve a 3-log kill of the wild-type P.aeruginosa following a loading dose of 480 mg, compared to a dose of 240 mg where it did not reach 3-log kill at all. For loading doses of 720 mg and 960 mg, the times to 3-log kill decreased further and were esti-mated to 6.5 and 5 hours, respectively.

The predictions of bacteria kill following increased dosing intervals (Figs. 12D-F) show that the interval can be extended without a pronounced bacteria regrowth. For the 960 mg loading dose with subsequent 240 mg maintenance

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dose, the wild-type bacterial count stayed below 10 CFU/ml after 16 and 18 hours for the time intervals of 12 and 24 hours, respectively. The 960 mg loading dose with subsequent 360 mg maintenance dose achieved a similar kill for the same time interval. Also for the lower loading doses the time interval to the next dose could be expanded to 12 hours without a notable bacteria regrowth, although the 240 mg and 480 mg loading doses did not result in a bacterial count lower than 10 CFU/ml at any time point.

For the patient with the lowest measured colistin concentration only the highest loading dose, 960 mg, achieved a 3-log kill (Fig. 12B). As expected, for the observed patient with the highest measured colistin concentrations, the predicted bacterial kill occurred faster and the 240 mg dose achieved a 3-log kill at approximately 9 hours (Fig. 12C).

The non-linear binding was predicted to have an impact on the initial bac-teria kill as for a loading dose of 720mg, the non-linear fu predicted a 3 log bacterial kill at 6.5 hours, while if fu would be constant and 34%, a 3-log kill would be achieved 1 hour earlier, i.e. at 5.5 h.

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Fig. 12. Model predictions of colistin concentration (upper panels) with bacterial counts for a wild-type P.aeruginosa strain (lower panels) for three individuals with typical population values (A, D, E and F), lowest measured colistin concentration (B) and highest measured colistin concentration (C). The three individuals (A-C) received an initial 480 mg, 720 mg or 960 mg as loading dose followed by mainte-nance doses of 240 mg 8 hourly after first 8 hours (the commonly used 240 mg 8 hourly dosing is also shown). This is followed by model predictions for a typical individual receiving the loading doses followed by maintenance doses starting at different dosing intervals D. 240 mg 8 hourly after first 12 hours, E. 240 mg 8 hourly after first 24 hours and F. 360 mg 12 hourly. All doses were given as 15 minute infusions. In the top panels, the black lines represent unbound colistin con-centration and the grey lines represent total colistin concentration. In the lower pan-els, the grey dashed lines represent the bacterial count at initiation of therapy, the bacterial count for 3-log kill and the bacterial count below the limit of detection at 10 CFU/ml.

Colistin and meropenem combination in critically ill patients The possibility to overcome meropenem-resistance for L0603761 with clini-cally achievable doses of colistin and meropenem was predicted based on the final model with interaction between the two drugs. Fig. 13 shows predicted time courses for the total and unbound colistin concentrations (first row) for CMS loading doses of 480 mg, 720 mg or 960 mg followed by maintenance of 360 mg every 12 hours and the predicted meropenem concentration-time profiles (second row from top) following administration of 500, 1000 or 2000 mg every 8 hours. Unbound colistin concentration increased during the 24 hours and with a maximum unbound concentration of 0.65 mg/L for the highest dose (960 mg) (Fig. 13, first row). For this dose, L0603761 grew without net bacteria kill when only colistin was present (Fig. 13, third row). There was some bacterial killing for meropenem 2000 mg alone (Fig. 13, fourth row).

When combining the two drugs, not even the highest loading dose of CMS resulted in a 3-log kill when the meropenem dose was 500 mg or 1000 mg 8 hourly (Figs. 13A and 13B). For a meropenem dose of 2000 mg (Fig. 13C), a 3-log kill was achieved at 6, 9 and 11 hours for CMS loading doses of 480 mg, 720 mg and 960 mg respectively. A shorter infusion rate for meropenem of 1 hour did not result in any obvious difference in the bacterial killing (results not shown).

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Fig. 13. Model prediction of total and unbound colistin concentrations (1st row), meropenem concentration (2nd row), bacterial killing by colistin only (3rd row), bac-terial killing by meropenem only (4th row) and bacterial killing by colistin and mer-openem combination (5th row) for a typical patient. CMS doses of 480, 720 and 960 loading doses followed by 360 mg every 12 hours in combination with A. mero-penem 500 mg every 8 hours, B. meropenem 1000 mg every 8 hours and C. mero-penem 2000 mg every 8 hours. CMS and meropenem doses were given as 15-min and 3-hour infusions respectively. In the first row, the black lines represent the un-bound colistin concentration and the grey lines represent the total colistin concentra-tion. In the third, fourth and fifth row, the grey lines represent the bacterial count at initiation of therapy, the bacterial count for 3-log-unit kill, and the bacterial count below the limit of detection at 10 CFU/ml.

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Discussion

Mechanism-based PKPD Model In this thesis, mechanism-based PKPD models were developed based on in vitro time-kill curves experimental data to describe the growth, killing and adaptive resistance development for different antibiotics. A previous model with two bacterial stages representing growing susceptible bacteria and rest-ing nonsusceptible bacterial compartments (75) was extended to incorporate extra compartments to describe adaptive resistance.

Different antibiotics displayed different functions of affecting different GNB kill in the susceptible compartment. The drug effect here represented the maximum rate of bacteria killing upon introduction of the antibiotics into the infectious environment. In Paper I, gentamicin displayed a basic Emax function for the drug effect on E.coli. The PKPD model for colistin in Paper III could well characterize the observed time courses of bacterial killing where colistin’s effect on the wild strain of P.aeruginosa (ATCC27853) was best described by a sigmoid Emax function but for colistin on L0603761, a linear function was sufficient to describe the data. The effects of meropenem in Paper IV were sigmoid Emax for both strains of P.aeruginosa.

The models described the development of adaptive resistance which caused reduction of the drug effect. In Paper I, E.coli was exposed to gen-tamicin in both static and dynamic time-kill experiments. The raw data showed a fast kill with regrowth. The dynamic experiments enabled multiple doses to be administered which further illustrated the effect of adaptive resis-tance where the subsequent doses produced less bacterial kill than the initial dose. The antibacterial effect of subsequent administration of gentamicin will depend on the fraction predicted in the adaptive resistant stage. In Paper III, colistin-driven adaptive resistance was characterized for a wide range of concentration-time profiles for both strains of P.aeruginosa. The model maintained a similar structure for the adaptive resistance as for gentamicin on E.coli but the degree of adaptive resistance characterized by ReON directly affected the rate constant of drug effect. Similar to gentamicin’s effect, the introduction of colistin into the in-vitro environment caused a fast rate of bacterial killing and triggering the development of adaptive resistance, which resulted in a graded reduction in the drug effect and thereby a reduced capacity to kill the bacteria.

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Adaptive resistance was found to be reversible and was predicted to re-turn to the original degree of susceptibility once the antibiotics diminish. There was however limited information on reversal of adaptive resistance in the gentamicin data and this was fixed at 50 h. Even though the colistin ex-periments were set up as a static study where the antibiotic concentrations were intended to be constant throughout the experiment, colistin concentra-tions declined with time as evidenced from the measured concentration at 0, 8 and 24 hours. The decreasing colistin concentrations may have contributed to that, as it was here possible to estimate koff, despite the lack of dynamic experiments. Estimation of koff also allowed the degree of adaptive resistance to achieve equilibrium. The half-life for the bacteria to return to the suscep-tible state after developing adaptive resistance (ln2/koff) was estimated to 7.6 hours for both strains. For meropenem, in Paper IV, a reversal of adap-tive resistance was not supported by the data and koff was fixed to 0.

The regrowth observed in the colistin, meropenem and gentamicin ex-periments was assumed to only be due to adaptive resistance. When mutants are emerging during the experiment, the developed model structure may also be applicable. In those cases koff would be set to zero. In presence of pre-existing subpopulations of resistant mutants, a model with different growth rates and/or sensitivity to drug exposure for two types of bacteria can explain the regrowth observed at the end of experiments (23, 24, 66).

The final PKPD model developed for the combination of colistin and meropenem illustrated the interaction between the two antibiotics, and could well characterize the observed time courses of bacterial killing. The interac-tion effect of the combination was greater than adding the two rate constants for L0603761, supporting a synergistic effect for that strain. For the wild-type there seemed however to be a less than expected effect since the inter-action term was negative, indicating an indifferent or antagonistic effect. The definition of synergism and antagonism are not clear and it may be more relevant to relate the combined effect to “killing activity”(43). Another way to define the interaction is to investigate how much bacterial killing different concentrations achieve, e.g.in log bacterial killing. To be additive, there should be 1 to 2 log10 CFU/ml additional kill compared to the most effective of the two drugs when studied alone in the same concentration as in the combination, while synergy is defined as ≥ 2 log10 CFU/ml additional bacte-rial killing(15). In the current study, when colistin was added to meropenem (Fig 6II, C 0.67: M 32 and C 3.5: M 32), the resulting bacterial killing was more than 2 log-kill from 12 hours onwards when compared to meropenem 32 mg/L alone (Fig 6II, M 32), i.e. also corresponding to the log-kill defini-tion of synergy. Also when meropenem was lower, at 16 mg/L, the addition of colistin resulted in 2-log kill.

Mechanistically, colistin works by changing the permeability of the outer membrane of the cell wall and meropenem requires entrance into the cyto-plasmic space to acytylate the penicillin binding proteins in order to interfere

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with the formation of peptidoglycan in the cell wall. In the combination for the resistant strain, it could be postulated that colistin could have interfered with the outer membrane that allowed entrance for meropenem to act inside the bacteria. In the current study it was demonstrated that meropenem ad-ministered in combination with colistin achieved significant bacterial killing for the meropenem-resistant strain to warrant the use of the combination.

A strain-dependent type of interaction for meropenem and colistin in combination has been shown previously (80, 90). Mechanistically, each an-tibiotic would have worked with its respective mechanism of action but in reality the two drugs may have competed for the kill or possibly, the pres-ence of one drug could have blocked the action of the other. Based on the results in Paper IV there is limited benefit, if any, of combination therapy for a sensitive strain.

Population PK model for colistin A loading dose of 480 mg CMS was successfully administered to criti-

cally ill patients in Paper II. The total concentrations of CMS and colistin were as expected for drugs with linear PK, in that the total concentrations doubled compared to the previous study where the starting dose of CMS was 240 mg. The previously developed PK model, consisting of two compart-ments for CMS and one compartment for colistin (82), could well describe all data in this study with similar parameter estimates. The lack of statisti-cally significant covariate relationships in the analysis may be because of the relatively small number of patients and/or the lack of urine data to support the relationship.

In the simulations, IOV was shown to impose a larger overall variability than IIV (Fig. 9). The large variability in bacterial killing appeared to pri-marily be caused by IOV in formation of colistin and/or colistin clearance and volume of distribution. These simulations suggest that a target concen-tration dosing, where the dose to be administered is calculated using an algo-rithm based on covariates (e.g. weight, CrCL), may overemphasize the value of individual dose adjustments. In the presence of a large IOV and/or a co-variate that changes over time, covariate-based dose adjustment may be less useful to control variability (9, 49), and a flat-fixed dosing may be a more simple alternative.

A weight-based loading dose was shown to result in much lower bacte-rial killing in low weight patients compared to what was obtained in patients weighing 70 kg or more (Figs 10A and 10D). This is not surprising as V1CMS has very limited impact on the time-course of the active drug, colistin. A patient’s CrCL value is however influencing the degree of bacterial killing already during the loading dose, with a larger bacterial killing the lower the CrCL, given that a CLCMS-CrCL relationship exists. This is also reflected in

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the maintenance dose where a CrCL-based dosing resulted in more similar profiles when the covariate relationship is assumed to be true and included in the model for predictions of typical patients (Figs 10A and 10B). The predic-tions also showed that infusion duration of up to 2 hours can be recom-mended based on the current simulations (Fig 10C) as the bacterial killing profiles were similar for a 15 min, a 30 min and a 2 hour infusion. There appeared to be some benefit in increasing the bacterial killing by introducing the maintenance dose before 24 hours after the loading dose (Figs. 10A and 10B).

Dosing regimen for specific population Today, PK and PD information based on PK/PD indices developed from preclinical data are applied to suggest dosing regimens for drug development of antibiotics. PK/PD indices have been suggested to result in similar values in animals and patients (2), and may be adequately predicted from mecha-nism-based PKPD models developed from in vitro data (73). As PK/PD indices do not provide information on the time-course of effect, their appli-cation is limited for evaluation of differences in the initial bacterial killing rate by different dosing regimens. Furthermore, the optimal type and magni-tude of the PK/PD index depends on the PK, and PK may vary between dif-ferent population of patients (73). In this thesis, the concept of using PK and PKPD models for antibiotics as a tool in the search for improved dosing regimens in different subpopulations was suggested and explored.

Previously, the dosing of gentamicin in neonates was empirically based on a therapeutic target of peak concentrations of >8-10 mg/L (1 h post-infusion) and trough concentrations of <1-2 mg/L. Based on this criteria and based on PK information only (74), it was shown that a standard gentamicin dosage of 4 mg/kg was regarded as being suboptimal in preterm neonates. In Paper I, predictions of different dosing schedules for preterm and term neo-nates were conducted from the combinations of a 3-compartments PK model of gentamicin (74) with the developed PKPD-model. The predictions showed that despite the peak concentration being lower in the extreme pre-term newborn infant, there was higher bacterial killing than in the term new-born infant. However, a 24 hour dosing interval with trough concentrations < 2 mg/L is not achievable in the extreme preterm infant and an extended dosing interval (36-48 hours) is therefore justified. This suggested that the target concentrations needed to be reevaluated.

The predictions for colistin’s effect on bacterial killing in critically ill pa-tients based on the PK model developed in Paper II and the PKPD model for colistin showed that a loading dose lead to more rapid clearance of bacteria than a standard dose of 240 mg (Fig. 12). The effect of non-linear colistin binding to plasma proteins where lower colistin concentrations had a lower

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fu and a higher colistin concentration had a higher fu was found, with bind-ing fractions similar to what has been observed in neutropenic mice (36). As a consequence of the difference in protein binding for colistin A and colistin B, the unbound colistin concentrations more than doubled, when the initial dose was doubled from 240 mg to 480 mg, leading to an even more efficient bacteria kill from higher doses. This paper illustrated the importance of util-izing a loading dose of CMS as a rapid bacterial kill will likely mean a faster resolution of the infection in a seriously ill patient. In Paper III, the effect of bacterial kill for different individuals with the lowest and highest concentra-tion of colistin concentrations demonstrated that the IIV was a contributing factor to the drug effect.

As monotherapy, both colistin and meropenem had limited activity against L0603761 but in Paper IV it was demonstrated that meropenem in combination with colistin could enhance the antibiotic activity for this strain, and the interaction was quantified. In predictions of bacterial killing by the combination, the highest dose of CMS (loading dose 960 mg followed by 360 mg every 12 hours) and meropenem (2000 mg every 8 hours) were needed to achieve 3-log kill at 6 hours for a typical patient (Fig. 13). The optimal relative dosing of meropenem and colistin in combination could be further searched for by application of the model developed in Paper IV.

The limitations for the predictions of the dosing schedules in the papers were the absence of the effect of the immune system, the lack of concentra-tion-toxicity relationship and the lack of IIV in the predictions. It should also be considered that the amount of bacterial killing obtained in a specific pa-tient will also depend on many factors, such as site of infection, bacteria strain and inocula size. Further information on side-effects especially on the combinations of antibiotics would be desirable, before performing clinical evaluation of proposed dosing regimens.

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Conclusion

In this thesis, PK and PKPD models describing the time-courses of antibiotic drug concentration, killing and emergence of resistance for different strains of Gram negative bacteria were developed, evaluated and applied to predict and thereby guide improvement of dosing regimens. The performed studies established relationships on dose-concentration of colistin in critically ill patients, and for several antibiotics on concentration-effect and concentra-tion-resistance development based on in vitro time-kill curve experiments. The predictions illustrated how PKPD-models characterizing the time-courses of antibiotic drug effects can be applied to describe the influence on bacterial kill of a loading dose, covariate-based dosing, the infusion duration and the dosing interval.

The mechanism-based PKPD model developed for gentamicin’s effect on E.coli characterized the growth, killing and adaptive resistance development as observed in static and dynamic in vitro time-kill curve experiments. The compartments for growing and resting bacteria, with a function allowing the maximal bacterial kill to reduce upon increasing gentamicin exposure, char-acterized both the fast bactericidal effect and the adaptive resistance to gen-tamicin.

The PKPD model for gentamicin was, after some modifications, success-fully applied for colistin and meropenem to describe the effect and regrowth for both wild-type and resistant P. aeruginosa in single drug and combina-tion experiments. In the combination model for colistin and meropenem, the estimated interaction term between the killing effects for the two drugs in combination identified no benefit of combining the two drugs for the sensi-tive strain and a higher than expected (synergistic) effect for the resistant strain.

A population PK model for colistin in critically ill patients receiving a loading dose strengthened a previous model based on data from PK studies without loading dose. A two-compartment model for CMS and one-compartment model for colistin best described the PK and confirmed a long half-life (18.5 hours) for colistin. There was no statistically significant co-variate identified in this population of patients. The unbound fraction of colistin in human plasma was determined to be 26 - 41% at clinically used concentrations and colistin A was shown to be concentration-dependent. The variability in PK for CMS and colistin was shown to translate into a pro-nounced IOV in bacterial killing which was found to be higher than the vari-

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ability arising from IIV. A flat-fixed loading dose was demonstrated to result in less variability than an algorithm based on weight.

The developed PKPD model was successfully combined with previously developed PK models on gentamicin and meropenem and the developed PK model here on CMS and colistin to predict drug concentrations and bacteria kill of different dosing schedules in simulated subpopulations (newborn in-fants for gentamicin and critically ill patients for single colistin and combi-nation of colistin and meropenem). For gentamicin, the overall higher drug exposure (AUC) for a given dose administered on a per kg basis in preterm newborn infants resulted in a higher total bacterial kill compared with a term newborn infant, even if the gentamicin peak concentration was lower. Pre-dictions from the PKPD model suggest that it would be of interest to clini-cally evaluate an extended dosing interval (>24 hours) in the extreme pre-term infants. This study supports that adaptive resistance of gentamicin plays a role in the efficacy of gentamicin and will affect the choice of optimal dos-age. For single colistin dosing, the studied loading dose of 480 mg (6MU) for the prodrug CMS was shown to increase the initial bacterial killing com-pared to the standard regimen with an initial dose of 240 mg. Based on the predictions, a loading dose of 480 – 720 mg is recommended in critically ill patients. For the resistant P. aeruginosa strain, the study supports that a high dose combination therapy of colistin and meropenem is needed to overcome the resistance, despite the presence of synergism.

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Future perspectives

PK and PKPD-relationships have been considered for several decades in the development of dosing regimens for antibiotics. More recent advances in modeling and simulation methodologies allow however for improved char-acterization of the relationships, including the description of the full time-course of bacterial killing. Predictions and simulations of clinically relevant dosing regimens based on mechanism-based PKPD models, developed from preclinical data, will likely become more frequently applied in the infection area in the near future. Translating preclinical outcomes to clinical outcomes by models reduces the need for extensive testing in patients and thereby cre-ate possibilities to speed up drug development in this area where the need for new approaches is accelerating due to antibiotic drug resistance.

Colistin has become increasingly applied, most frequently in combination with other antibiotics, to overcome resistance to Gram negative bacteria. The advances in the understanding of its PK and PKPD relationships during the last years are of interest to further evaluate clinically. Randomized clinical trials for combination of colistin with other antibiotics are being planned and carried out: for example a randomized study evaluating colistin alone (720 mg with 360 mg maintenance dose) versus colistin and meropenem (2 g q8h) in combination against carbapenem-resistant bacteria (AIDA, http://www.aida-project.eu). Other combination studies being conducted are the colistin and imipenem, as well as colistin and fosfomycin as treatment of MDR A.baumanii, and colistin and rifampicin against MDR A.baumanii, (91).

The mechanism-based PKPD models developed for the antibiotics in this thesis were based on 24-h in vitro studies that were performed without the involvement of the immune system. At best the models are therefore mim-icking a worst-case scenario of an immunocompromised patient. A future improvement of the quantitative accuracy of the predictions may be achieved by investigating an interaction with the immune system. A model consider-ing the immune system may provide a more accurate scenario of the actual situation in the body. Predictions of the dosing regimens (dose size, dosing interval and infusion duration) based on a 24-48 hours in vitro time-kill ex-periment do likely not allow prediction of treatment duration. Experiments in systems like the hollow fiber would allow a longer experimental period that would span days or weeks which would also allow more flexibility of dosing regimens designs. This would allow the treatment duration to be discerned.

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Combination treatments will be of high importance to overcome and pre-vent antibiotic drug resistance. In other infectious diseases such as tubercu-losis and HIV, combination treatment is already standard. The search for combination regimens with high killing activity is however tedious. Model-ing and simulation is an excellent technique to study a wide range of dose combinations in silico, based on relatively few preclinical experiments. In this thesis, it was shown that the combination of colistin and meropenem could overcome meropenem-resistance for P.aeruginosa. However, the combination did not provide an advantage over monotherapy in the kill of the wild-type strain of P.aeruginosa. It is however not clear if a prolonged combination treatment would reduce the emergence of resistance, or lead to overuse of antibiotic that may predispose the bacteria to develop resistance. Long-term studies of combination regimens would therefore also be of inter-est.

Antibiotic dosing regimens are today often optimized for a more general population. Models that consider the full time-course of concentration and bacterial killing can be a step forward in developing more optimal dosing for subpopulations of patients, especially where there are limited possibilities to study outcomes clinically. Examples of other subpopulations or situations than those studied in this thesis that need to be considered are patients with infections in specific tissues, cavities or organs that are either not well per-fused by the blood vessels (for example joint infection, bone infections, ab-scess) or areas separated by membrane barriers (like the brain or meninges). These are infections that would also benefit from an improved dosing regi-men.

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Acknowledgements

This work presented in this thesis was carried out at the Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University. I am grateful to the Ministry of Health Malaysia (MSD) for the study leave and scholarship that provided me the opportunity to study in Sweden and Swedish Cancer foundation for the financial support during my studies. It is with my most sincere gratitude that I thank everyone who has contrib-uted to the thesis and to those who have been providing great support during this period. “Why Sweden?”, a common question that I have encountered. I guess it was not so surprising as I come from a country where the sun shines 365 days a year. The answer to that was the answer given by Alison Thomson, “There are two places you can go. One is in France and you don’t speak French. Go to Sweden!”. That was the start of the journey years ago. Lena Friberg, my main supervisor, for taking me under your wings not only in a foreign land but also what was an initially a foreign pharmacometrics world. Thank you for having the eternal patience with my snail pace, for always pushing me, for reading the manuscripts, for always having the ques-tions (and answers) to the whys and hows and for always having an open door. Thank you, the simplest of words but a vast ocean of gratitude from me. My co-supervisor, Otto Cars, for the support and enthusiasm on why we have to do something about the resistant bacteria. For taking the time in your busy schedule to read and provide insights to the manuscripts. My other co-supervisor, Mats Karlsson, for always having questions and suggestions for the projects. Thank you for accepting me into a dynamic group that I am sure will continue to flourish. The antibiotic group, Bettan for always being there and answering the sim-plest question even during the time when you’re awaiting for the delivery of you bundle of joy. David, Anders and Salim, for the discussions, questions,

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ever ready assistance whenever requested and the times when we just hang around. The microbiology lab especially Matti for providing me with the background, support and assistance in the colistin studies. Juliana for teach-ing me how to shake the house down for the experiments and literally being on-call when the experiments were conducted. Pernilla for suffering with me when we had to face the dynamic leaking. Of course, Brit who forever would have time to explain the intricacies of measuring CMS and colistin and the protein binding. And to Jonathan, my exxjob, thank you for the work. To all my co-authors, Bettan, Matti and those from Athens. Thank you. To my past & present roommates. Elodie, for always being at hand with the R scripts or whatever scripts or answering all the questions that I had and Åsa who would always lend me when an ear when I really wanted to kill the bacteria or when I can’t seem to get another plot exactly correct and it was really my sleigh that caught you that time. Camille, thank you for the support and we can always go and chase another typhoon. To the ones that have been with me during this journey, my past and present colleagues in the department. I have always enjoyed the diverse subjects that was presented and discussed during the PM meeting and seminars as it dem-onstrated that the width and depth of this field are limitless. I also learned a lot about the November months, the joy of candlelit fika, the delicious cakes and buns, Lucia at Sala mines, watching those skating on frozen lakes, sled-ding with zero intention of causing body harm to your colleagues, sista April, midsummer day, berry picking in the forest, fun dissertations, traips-ing around Europe due to a certain volcano and the summers that always managed to wipe off the memory of winter coldness. To Andy, Kajsa and Ron, for the fantastic softwares and Magnus who have been a great help with the computer programs and shaping up the papers. Of course, the Sweden experience would not have been completed without Mona & Duen, Linda & Rahim, Ipin & Ja, Zikri & Saz, Mimi & Ahmad, Syeling, Aiko & Boon, Qory, Nana, Ejant & Rumaizi, Shahrin & Yan, Wan & Poje, Farizah & Shahril, Fara & Mezan, Shima & Kamarul, Maya, Jihah, Nor, Ailin, Jesmin & Shan. To be home no matter how far we were. Kirsten and Åke for acclimatizing me to your warm home and Muscot and your wonderful girls, dinners, fikas, walk on the frozen lakes, traditional Swedish Christmas and snow shoveling! I could not have done this if it is not for the continuous support and the will-ingness of Dr. Zakiah Ismail and of course the Director of IMR, Dr. Shahnaz

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Murad. I am one of those lucky ones. To the Information Unit and Globin-Med team, past, present and future, thank you for shouldering on. To the iron ladies in my life; Wan Cu, for forever worrying about me and the continuous supply of Malaysian delicacies, handbags and dresses, for hold-ing the fort and resolving all the issues back home. Anim, Minah Ruhana, K.Murni, Emiliea and Dierdre, I thank you for the friendships that transcend time, space and distance. For my 5 brothers and 2 sisters (Nyah, Abang, Adik, Pidah, Ando, Cik Tam and Mat Ila!) and the sisters and brothers I attained by default (Teh, Etong, Sofi, Ika and Jaja), thank you for keeping me on my toes and for calling at wee hours to ensure that I have a reminder that you still think of me. Thank you for taking care of Mama in my absence. To Mama, thank you for keeping me company on the bus every morning and to my late father, you were never far. Have heart, tempat jatuh lagikan dikenang, inikan pula tempat membeku!! Tack så mycket Uppsala för en minnesvärd 4 år.

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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 170

Editor: The Dean of the Faculty of Pharmacy

A doctoral dissertation from the Faculty of Pharmacy, UppsalaUniversity, is usually a summary of a number of papers. A fewcopies of the complete dissertation are kept at major Swedishresearch libraries, while the summary alone is distributedinternationally through the series Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty ofPharmacy.

Distribution: publications.uu.seurn:nbn:se:uu:diva-188306

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2013