ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2017

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 231

Pharmacokinetic-Pharmacodynamic Evaluationsand Experimental DesignRecommendations for PreclinicalStudies of Anti-tuberculosis Drugs

CHUNLI CHEN

ISSN 1651-6192ISBN 978-91-554-9877-1urn:nbn:se:uu:diva-318845

Dissertation presented at Uppsala University to be publicly examined in B/B42,Biomedicinskt Centrum, Husargatan 3, Uppsala, Friday, 19 May 2017 at 13:15 for thedegree of Doctor of Philosophy (Faculty of Pharmacy). The examination will be conductedin English. Faculty examiner: Professor Bernd Meibohm (Department of PharmaceuticalSciences, University of Tennessee Health Science Center, Memphis, TN, USA).

AbstractChen, C. 2017. Pharmacokinetic-Pharmacodynamic Evaluations and Experimental DesignRecommendations for Preclinical Studies of Anti-tuberculosis Drugs. Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty of Pharmacy 231. 58 pp. Uppsala: ActaUniversitatis Upsaliensis. ISBN 978-91-554-9877-1.

Tuberculosis is an ancient infectious disease and a leading cause of death globally. Preclinicalresearch is important for defining drugs and regimens which should be carried forward to humanstudies. This thesis aims to characterize the population pharmacokinetics and exposure-responserelationships of anti-tubercular drugs alone and in combinations, and to suggest experimentaldesigns for preclinical settings.

The population pharmacokinetics of rifampicin, isoniazid, ethambutol and pyrazinamidewere described for the first time in two mouse models. This allowed for linking thepopulation pharmacokinetic model to the Multistate Tuberculosis Pharmacometric (MTP)model for biomarker response, which was used to characterize exposure-response relationshipsin monotherapy. Pharmacodynamic interactions in combination therapies were quantitativelydescribed by linking the MTP model to the General Pharmacodynamic Interaction (GPDI)model, which provided estimates of single drug effects together with a quantitative model-based evaluation framework for evaluation of pharmacodynamic interactions among drugs incombinations. Synergism (more than expected additivity) was characterized between rifampicinand ethambutol, while antagonism (less than expected additivity) was characterized betweenrifampicin and isoniazid in combination therapies.

The new single-dose pharmacokinetic design with enrichened individual sampling wasmore informative than the original design, in which only one sample was taken from eachmouse in the pharmacokinetic studies. The new oral zipper design allows for informativepharmacokinetic sampling in a multiple-dose administration scenario for characterizingpharmacokinetic-pharmacodynamic relationships, with similar or lower bias and imprecisionin parameter estimates and with a decreased total number of animals required by up to 7-fold compared to the original design. The optimized design for assessing pharmacodynamicinteractions in the combination therapies, which was based on EC20, EC50 and EC80 ofthe single drug, provided lower bias and imprecision than a conventional reduced four-by-four microdilution checkerboard design at the same total number of samples required, whichfollowed the 3Rs of animal welfare.

In summary, in this thesis the population pharmacokinetic-pharmacodynamic models offirst-line drugs in mice were characterized through linking each population pharmacokineticmodel to the MTP model. Pharmacodynamic interactions were quantitatively illustrated by theMTP-GPDI model. Lastly, experimental designs were optimized and recommended to bothpharmacokinetic and pharmacodynamic studies for preclinical settings.

Keywords: tuberculosis, pharmacokinetics, pharmacodynamics, pharmacometrics, theMultistate Tuberculosis Pharmacometric model, the General Pharmacodynamic Interactionmodel, optimized design, rifampicin, isoniazid, ethambutol, pyrazinamide

Chunli Chen, Department of Pharmaceutical Biosciences, Box 591, Uppsala University,SE-75124 Uppsala, Sweden.

© Chunli Chen 2017

ISSN 1651-6192ISBN 978-91-554-9877-1urn:nbn:se:uu:diva-318845 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-318845)

To Hongxiu and Hongge

致我的母亲与舅舅

List of Papers

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

I Chen C, Ortega F, Alameda L, Ferrer S, Simonsson USH.

(2016) Population pharmacokinetics, optimised design and sample size determination for rifampicin, isoniazid, ethambu-tol and pyrazinamide in the mouse. Eur. J. Pharm. Sci. 93:319-333

II Chen C, Ortega F, Rullas J, Alameda L, Angulo-Barturen I, Ferrer S, Simonsson USH. (2017) The multistate tuberculosis pharmacometric model – a semi-mechanistic pharmacokinetic-pharmacodynamic model for studying drug effects in an acute tuberculosis mouse model. J. Pharmacokinet. Pharmacodyn. 44(2):133–141

III Chen C, Wicha SG, de Knegt GJ, Ortega F, Alameda L, Sousa V, de Steenwinkel JEM, Simonsson USH. Assessing pharmacodynamic interactions in mice using the multistate tu-berculosis pharmacometric and general pharmacodynamic in-teraction models. [submitted]

IV Chen C*, Wicha SG*, Nordgren R, Simonsson USH. Compar-isons of analysis methods for assessment of pharmacodynamic interactions including design recommendations. [in manu-script]

Reprints were made with permission from the respective publishers.

*The authors contributed equally to this work

List of Additional Paper

In addition to the appended papers, Chunli Chen has been a co-author of the publication listed below.

Wicha SG, Chen C, Clewe O, Simonsson USH. On perpetrators and victims: A general pharmacodynamic interaction model identifies the protagonists in drug interaction studies. [submitted]

Contents

Introduction ................................................................................................... 13 Tuberculosis ............................................................................................. 13 Treatment of drug-susceptible tuberculosis ............................................. 13 Experimental models for tuberculosis drug development ........................ 15 

In vivo experimental models ................................................................ 15 The Three Rs ....................................................................................... 16 

Pharmacokinetics and pharmacodynamics ............................................... 17 Colony-forming unit ............................................................................ 17 The Multistate Tuberculosis Pharmacometric model .......................... 18 Pharmacodynamic drug-drug interactions ........................................... 19 The General Pharmacodynamic Interaction model ............................. 20 

Pharmacometrics ...................................................................................... 21 Naïve pooling ...................................................................................... 22 Nonlinear mixed-effects models .......................................................... 22 Maximum likelihood estimation method and objective function value ..................................................................................................... 23 

Aims .............................................................................................................. 24 

Methods ........................................................................................................ 25 In vivo pharmacokinetic data (paper I and III) ......................................... 25 In vivo pharmacodynamic data (paper II and III) ..................................... 26 Simulated in vitro pharmacodynamic data (paper IV) ............................. 26 Pharmacokinetic modeling (paper I and II) .............................................. 27 Pharmacodynamic modeling (paper II and III) ........................................ 28 

The Multistate Tuberculosis Pharmacometric model .......................... 28 The General Pharmacodynamic Interaction model ............................. 28 

Optimized design recommendations (paper I and IV) ............................. 29 Design for pharmacokinetic studies ..................................................... 29 Design for assessing pharmacodynamic interactions .......................... 30 

Software and modeling evaluation ........................................................... 30 

Results ........................................................................................................... 32 Population pharmacokinetics of first-line drugs (paper I and II) ............. 32 Pharmacokinetics-Pharmacodynamics of first-line drugs (paper II, III and IV) ..................................................................................................... 34 

Monotherapy in a C57BL/6 mouse model ........................................... 34 

Combination therapy in a BALB/c mouse model ................................ 35 Comparison of pharmacodynamic interaction models ........................ 37 

Optimized design recommendations (paper I and IV) ............................. 41 Design for pharmacokinetic studies ..................................................... 41 Design for assessing pharmacodynamic interactions .......................... 43 

Discussion ..................................................................................................... 45 Population pharmacokinetics of first-line drugs ...................................... 45 Pharmacodynamics of first-line drugs in monotherapy and combinations ............................................................................................ 45 Optimized experimental design recommendations .................................. 48 

Conclusions ................................................................................................... 50 

Acknowledgments......................................................................................... 52 

References ..................................................................................................... 55 

Abbreviations

BCG Bacillus Calmette-Guerin CFU colony forming units CL clearance DOT directly observed therapy EC50 concentration that gives 50% of EMAX EMAX maximum effect EMB ethambutol GPDI General Pharmacodynamic Interaction model IGRA Interferon-Gamma Release Assay IIV inter-individual variability INH isoniazid IOV inter-occasion variability IV intravenous k a rate constant ka absorption rate ke elimination rate LLOQ low limit of quantification MDR-TB multi-drug-resistant tuberculosis MGIT Mycobacterial Growth Indicator Tube MTP Multistate Tuberculosis Pharmacometric model M. tuberculosis Mycobacterium tuberculosis NLME nonlinear mixed effect OFV objective function value PD pharmacodynamics PK pharmacokinetics PO oral administration PZA pyrazinamide Q inter-compartmental rate rBias relative bias RIF rifampicin RSE relative standard error rRMSE relative root mean square error SE standard error SS steady state SSE stochastic simulation and estimation t Time

TB tuberculosis Tlag lag time V volume of distribution VPC visual predictive check pcVPC prediction-corrected visual predictive check WHO World Health Organization

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Introduction

Tuberculosis Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuber-culosis (M. tuberculosis), which are curved rod-shaped Mycobacteria, and were discovered by the German scientist Robert Koch in 1882. Under wet conditions, Mycobacterium tuberculosis can survive for several months. It can survive even longer time and can be culturable under dry conditions.1 Mycobacterium tuberculosis usually affects the lungs, which is called pul-monary TB, but also affects other organs (extra-pulmonary TB). The symp-toms of pulmonary TB include sub-febrile temperature, fever, coughing, night sweating and fatigue. The infection often transmits through direct or close contact with contagious patients with active TB. Inhalation of infected droplets containing M. tuberculosis can penetrate into and infect the lungs of healthy humans. The risk of dissemination of infection is eliminated if pa-tients are treated with anti-tubercular drugs and isolated from healthy people in time.

In 2015, approximately 1.8 million people died from TB, according to a World Health Organization (WHO) report published in 2016, and 10.4 mil-lion new cases were reported world-wide.2 Developing countries have a higher burden of TB than other countries. The Bacillus Calmette-Guerin (BCG), a live attenuated strain of Mycobacterium bovis, has existed for 80 years and is one of the most widely used vaccines, for instance in China and India, against TB, TB meningitis and miliary TB in children.3 To diagnose TB, a tuberculin skin test is normally conducted as the first step, but there are limitations, for instance, previous BCG vaccination will lead to a false-positive reaction from tuberculin skin test. Additional investigations should be conducted and will provide further information on the infection, including Interferon-Gamma Release Assay (IGRA), clinical symptoms, chest radio-graph and diagnostic microbiology.

Treatment of drug-susceptible tuberculosis The first-line drug treatment for drug-susceptible TB consists of a two-month initial phase of daily dosing of a four-drug combination, including rifampicin (RIF), isoniazid (INH), ethambutol (EMB) and pyrazinamide

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(PZA), followed by a four-month continuation phase of both RIF and INH, shown in Table 1.4 Rifampicin was discovered in 1965 and is known to in-hibit the bacterial DNA-dependent RNA polymerase,5 which makes RIF active to both multiplying and non-multiplying bacteria. Isoniazid is a pro-drug that is activated by the mycobacterial catalase-peroxidase KatG, gener-ating an isonicotinoyl acyl radical6, which make the production of mycolic acid in the bacterial cell wall be inhibited by INH7. The synthesis of arabino-galactan can be inhibited rapidly when exposure to EMB.8 Ethambutol is a bacteriostatic agent against multiplying bacteria, but has a limited effect on non-multiplying bacteria.9 The main role of EMB is to prevent development of drug resistance, such as INH. Nowadays, strains of M. tuberculosis that are resistant to relative cheap first-line anti-tubercular drugs, makes treating drug-susceptible TB even more difficult and expensive. Pyrazinamide plays an important role in shortening the treatment period of drug-susceptible TB from the previous 9 months to the current 6 months of the standard short-term regimen, because it kills a subpopulation of bacteria in an acidic pH environment in the lesions that other drugs do not kill.10

The standard 6-month regimen against drug-susceptible TB is effective with approximately 5% of relapse. Without treatment, mortality is high. However, due to the development of drug resistance, a 6-month treatment regimen results in a high risk of low patient adherence, as well as disease relapse in patients. If TB patients do not take the medication regularly or follow the doctor’s prescriptions, the treatment may not be successful and result in relapse, because a small number of M. tuberculosis still survives within the body in such situations, will eventually be active, which will make patients become sick again and the worst-case scenario would be that patients are resistant to all first-line anti-tubercular drugs. Therefore, WHO recommends that all contagious TB patients should be under observation while receiving treatment, called directly observed therapy (DOT), aiming to make sure high patient adherence. Fluoroquinolones, including moxifloxacin, levofloxacin and ofloxacin, are second-line drugs used to treat multi-drug-resistant TB (MDR-TB). Secondary injectable drugs, including amikacin, kanamycin and capreomycin are also used to treat MDR-TB. Compared to drug-susceptible TB, a much longer treatment period, normally more than a year, and higher costs are needed to treat MDR-TB.11

Recent phase III clinical trials have recently been conducted aiming to re-duce the treatment duration of drug-susceptible TB in 9 countries, unfortu-nately they were failed to show noninferiorty.12–14 The aim of those clinical trials was to determine whether a fluoroquinolones-containing regimen could reduce the treatment period for drug-susceptible TB from 6 months to 4 months or even shorter. However, results of those trials were insufficient to show that the regimen can be shorten by 2 months, mainly due to high re-lapse rates under clinical trial conditions. Therefore, new drugs and/or new

15

combinations with existing drugs are highly needed to shorten the current duration of therapy.

Table 1. Standard short-term treatment of drug-susceptible tuberculosis

Standard short-term treatment 2-month initial phase 4-month continuation phase

Rifampicin Isoniazid Ethambutol -Pyrazinamide -

Experimental models for tuberculosis drug development In preclinical setting, a variety of experimental models have been used for the study and development of anti-tubercular drugs, because of the host specificity of M. tuberculosis and the ethical restrictions, which might limit for TB studies in humans.15 However, there is no preclinical model that can completely mimic TB in humans. Most of experimental models are useful from one or more aspects, but they have their own limitations too, such as lacking the ability to account for the host-pathogen interactions. No matter what preclinical model or biomarker is chosen in preclinical experiments, it is not realistic to provide all information of every aspects of human TB.15

In vivo experimental models Guinea pig Robert Koch used guinea pigs to gain understanding about the establish M. tuberculosis. Since then, guinea pigs have been widely used, mainly because of their high susceptibility to infections by different experimental strains of M. tuberculosis. Immunological and physiological characteristics of guinea pig are similar to those in human beings16, which make guinea pigs being considered as the closest model to mimic the pathological process of TB in humans17. In addition, primary pulmonary lesions after infection with a small number of M. tuberculosis can be detected in guinea pigs.18 Nowadays, guinea pigs are usually used to test the potency of vaccines against TB,19 and the efficacy of anti-tubercular drugs.20

Rabbit The rabbit model for TB is known as its similarities to TB in humans and it is relative resistance to infection with M. tuberculosis. This characteristic may allow rabbits to recover in the following 4 to 6 months from low dose infection, just as infections in human can be hampered or slowed by the im-mune system.21 M. tuberculosis-infected rabbits develop pulmonary granu-

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lomas and occasionally cavities, which are histologically similar to what can be found in humans.22

Zebrafish The long-term survival of M. tuberculosis in granulomas is the hallmark of TB in human, which also can be found similar in zebrafish. M. tuberculosis could survive in zebrafish embryos under laboratory environments, as a re-sults, infection of zebrafish embryos is suitable for the first screening phase during new anti-tubercular drug development.23,24

Mouse Mouse model can be purchased and housing with low costs, which is the main advantages of using mouse model. The ability of an anti-tubercular drug to kill M. tuberculosis in the lungs can be designed and measured by using mouse models with proper experimental designs. One major difference in mice is that mice have a less complex bronchial tree and lymphatics com-pared to human beings, due to its size.17 There are several types of inbred mouse models, including the C57BL/6 mouse, gamma interferon-disrupted (GKO) mouse and BALB/c mouse etc. The GKO mouse can be used to test the immune response in mice, since it has an impaired immune system, but it is also more expensive compared to other mouse model. Under similar ex-perimental conditions, the adaptive immune response in wild C57BL/6 mice does not impair growth of M. tuberculosis, since the growth rate is the same in both the wild type of C57BL/6 mouse and the gamma interferon-disrupted GKO mouse.25 After aerosol infection, the BALB/c mouse and C57BL/6 mouse have a similar response to treatment with first-line anti-tubercular drugs, whereas after intravenously infection, a delayed response and higher relapse rate is shown in both types of mice, which means the ways of infec-tion also matters.26,27 Recently the C3HeB/Fej mouse has attracted interest by researchers, because after low-dose aerosol infection with experimental strains of M. tuberculosis, the C3HeB/Fej mouse develops a more human-like pathology, such as caseating granulomas and cavities, compared to other commonly used experimental mouse models.28 In general, mice serve as valuable tools for quantifying drug exposure-response relationships and ide-ally predicting response at certain dose levels of anti-tubercular drugs in humans.

The Three Rs In 1959, W.M.S. Russell and R.L. Burch first described the Three Rs (3Rs), which are Replacement, Reduction and Refinement.29 The aim of the 3Rs is to improve experimental animals’ welfare, to allow researchers to care for animals and to limit the number of animals used to the minimum during experiments. Replacement refers to methods which avoid or replace the use

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of animals, and has not been fully achieved by current techniques in preclin-ical settings, which makes more focus on reduction and refinement.30 Reduc-tion refers to methods that minimize the number of animals used in each experiment and refinement refers to methods that minimize animal suffering and improve animal welfare during experimental procedure. Reducing the number of animals used in the laboratory setting can be done with a popula-tion approach analysis, which has the significant advantage and ability of pooling data from different animals, experiments and/or trials via model-based prediction and simulation. Obtaining sufficient information and data is impossible only from clinical trials due to ethical and practical reasons. It has to be accompanied with basic information from preclinical studies, main-ly by means of extrapolation from animal experiments.31 Then optimized experimental designs can be suggested and recommended by using a phar-macometric analysis, in order to maximize the information animals provide and minimize the usages of experimental animals.

Pharmacokinetics and pharmacodynamics Pharmacokinetics (PK) is the study of describing the time course of a drug concentration in different body compartments, such as blood, plasma, brain, lungs and other tissue etc. In short, PK describes what the body does to the drug, including absorption, distribution, metabolism and excretion. Pharma-codynamics is the study of describing the time course of the biological ef-fects of a drug, the mechanism of actions, the relationships of the effects to drug exposure (drug concentration, dose or area under the curve of PK). In short, PD describes what the drug does to the body. In preclinical studies of TB, the most commonly used biomarkers include CFU on solid agar plate and time-to-positivity in liquid media using Mycobacterial Growth Indicator Tube (MGIT). Understanding of drug absorption, distribution and elimina-tion (PK), its relation to e.g. CFU and MGIT (PD), and the underlying math-ematical and statistical functions comprise fundamental aspects of PK-PD modeling and analysis, shown in Figure 1.

Colony-forming unit Colony-forming unit is a common used biomarker for bacterial infections and it is the individual colonies of M. tuberculosis on a surface of a solid agar plate for TB. In order to get CFU counts, taking animal experiments as an example, after sacrificing M. tuberculosis-infected mice, the lungs are removed, placed in tubes and homogenized. Samples of homogenized lungs are diluted and spread over the surface on the agar plate. After 3 to 4 weeks of incubation under suitable conditions, depending on the strains of M. tu-berculosis used, the actual number of multiplying bacteria per lungs

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(CFU/lungs) or per sample volume (CFU/mL) is obtained. The CFU assay is widely used and easy to perform in the laboratory. However, the limitation of the CFU assay is that only microbiologically viable bacteria could be counted. Non-culturable or non-multiplying bacteria could not be captured by the CFU assay, which would be problematic in a clinical setting, since those types of bacteria are difficult to diagnose and more difficult to kill by anti-tubercular drugs, and are the main reason of treatment failure. In general, to get a general idea of a time-kill curve of the bacterial natural growth (without treatment) and the kill capacity with anti-tubercular drugs treatment over a time period in experiments can be informed by CFU assay.

Figure 1. Typical plots for pharmacokinetics, pharmacodynamics and pharmacoki-netic-pharmacodynamic relationship of a hypothetical anti-tubercular drug.

The Multistate Tuberculosis Pharmacometric model The Multistate Tuberculosis Pharmacometric (MTP) model was first devel-oped by Oskar Clewe using in vitro data and consists of fast-multiplying (F), slow-multiplying (S) and non-multiplying (N) bacteria, as shown in Figure 2.32 The MTP model is a semi-mechanistic PK-PD model for studying both bacterial natural growth (without treatment) and the exposure-response rela-tionship of anti-tubercular drugs. The MTP model has been successfully implemented for clinical data, in order to estimate the drug efficacy of hu-

19

man early bacterial activity and clinical trial simulations.33 The MTP model includes first-order bacterial transfer rate from slow- to fast-multiplying bacteria (kSF), first-order bacterial transfer rate from slow- to non-multiplying bacteria (kSN), first-order bacterial transfer rate from non- to slow-multiplying bacteria (kNS), first-order bacterial transfer rate from fast- to non-multiplying bacteria (kFN), and linearly time-dependent transfer rate from fast- to slow-multiplying bacteria (kFS). The growth of fast-multiplying bacteria in the MTP model is described by the growth rate kG. In the MTP model, there is no natural death rate, due to evidence in vitro showing that the majority of bacilli entered a viable but non-culturable state on solid me-dia.34 Therefore, Both fast- and slow-multiplying bacteria resemble CFU, but not non-multiplying bacteria. There is also no element characterizing im-mune response, as the MTP model was developed using in vitro time-kill data, which lacking an immune system. But the MTP model could be ex-tended by introducing an extra component to account for the immune re-sponse if necessary.

Figure 2. Schematic illustration of the Multistate Tuberculosis Pharmacometric model consisting of fast- (F), slow- (S) and non-multiplying (N) bacterial compart-ments. The bacterial system was described using the growth rate (kG) of the fast-multiplying bacteria, a time-dependent linear rate parameter , the transfer rate from fast- to slow-multiplying bacterial states (kFS), the first-order transfer rate from slow- to fast-multiplying bacterial states (kSF), the first-order transfer rate from fast- to non-multiplying bacterial states (kFN), the first-order transfer rate from slow- to non-multiplying bacterial states (kSN) and the first-order transfer rate from non- to slow-multiplying bacterial states (kNS).

Pharmacodynamic drug-drug interactions Pharmacodynamic drug-drug interactions occur in the combination therapies against TB, cancer etc.35 The PK interactions between anti-tubercular drugs in combination are described in mice before,36,37 but with less of a focus on drug-drug PD interactions, although these may also contribute to therapeutic

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failure or success in the disease need to be treat by the combination therapy. Two classes of PD interactions are synergy and antagonism, which are equivalent to increased or decreased effects compared to expected additivity of single drugs effect quantified in the monotherapy. The definition of addi-tivity is not trivial and mainly three competing criteria are used for defining additivity, including pure effect summation (Equation 1)38, Bliss Independ-ence (Equation 2)39 and Loewe Additivity (Equation 3)40. The current meth-ods, for instance the Greco model based on Loewe additivity41, the Empirical Bliss Independence-based model, assessing antagonism and synergy are based on the single additivity criterion, single interaction parameter and can-not assess asymmetric interactions31,42–44.

Equation 1 Equation 2

where EAB is the fractional effect of the combination of Drug A and Drug B; and EA and EB are the single Drug A effect and Drug B effect in monothera-py, respectively. Bliss Independence and pure effect summation could be applied to drugs with the same, but also differing maximum effects.

1 ,

,

,

, Equation 3

where CA,E and CB,E are the concentration of Drug A and Drug B, each alone stimulating the same effect E. CA(B),E and CB(A),E are the concentration of Drug A in the combination with Drug B and the concentration of Drug B with Drug A, stimulating the same effect E. Conceptually, parts of the con-centration of Drug A can be replicable by the Drug B resulting in the same effect E. Therefore, Loewe Additivity can only be applied if Drug A and B stimulating the same maximum effect E, as Loewe Additivity is not defined for drugs with different maximum effect.45

The General Pharmacodynamic Interaction model The General Pharmacodynamic Interaction (GPDI) model46 can be used with different additivity criteria, including most commonly used Bliss Independ-ence, Loewe Additivity and pure effect summation, which makes the GPDI model an appealing approach for studying and comparing various underlying additivity criteria.46 The GPDI model allows for the characterization and quantification of PD interactions of both symmetric and asymmetric syner-gistic or antagonistic interactions. Asymmetric PD interaction is concentra-tion-dependent, i.e. the interaction changes in magnitude depending on the concentration of the perpetrator and victim drug, shown as Equation 4 and 5 of each single drug effect in combination of Drug A and Drug B. The GPDI model has already been successfully applied to data from high-throughput screening experiments.46

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,

, , ,

Equation 4

,

, , ,

Equation 5

where INTAB and INTBA characterize the maximum fractional change of the respective PD parameters, here EC50. An estimated value of zero of INTAB or INTBA suggested no interaction. A positive value suggested a decrease in drug potency, whereas a value between -1 and 0 suggested an increase in drug potency caused by interactions between the two drugs. EC50INT,AB and EC50INT,BA represent the interaction potencies. HINT,A and HINT,B represent the interaction sigmoidicities. Depending on if the interplay between perpetrator and victim, additive, synergistic, antagonistic or asymmetric interactions are quantifiable. In the asymmetric case, the observed synergism, additivity or antagonism depends on the concentration-ratio of Drug A and Drug B.

Pharmacometrics Pharmacometrics is the emerging science by using mathematical models to quantify drug exposure-response relationships and disease progression, in order to aid and assess new drug development.47,48 Pharmacometricians, who are experts in pharmacometrics, must have a good understanding and knowledge about the data which a model was built on and the assumptions were made during the development of the model. Pharmacometric model describe the relationships between drug exposure and response for desired effects and adverse effects and the relationships between the biomarkers, for instance CFU in TB drug development, and preclinical and clinical outcomes, and disease progression can also be illustrated by the model.49 Models can describe and characterize the existing data, and to simulate new data based on the existing model with reasonable assumptions. In TB drug development, no established link between the biomarkers and the clinical endpoints, e.g. relapse, is available, which makes it more difficult to predict successful combination regimens to treat TB. Pharmacometrics could fill in this gap and assist in the interpretation and give optimized design recommendations of both preclinical experiments and clinical trials, in order to inform drug

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development with respect to new anti-tubercular drugs, regimen and/or new combinations with existing drugs, which are highly needed.

Naïve pooling The naïve pooling is an approach that focusing simply on the typical pa-rameters, normally mean or median of the data, that characterize the struc-tural model whilst ignoring the variability of typical parameters within the population. It is based on the assumption that all data are from the single or same experimental individual/subject. With that, obvious drawback to use naïve pooling approach includes, for example, it ignores subject variability and only estimates the typical profile in, for example, PK.50 The naïve pool-ing approach is normally used when only one observation is taken from each individual, which is most often the case in animal experiments, and as a re-sult, only residual errors can be derived from the data and no inter-individual variability (IIV) is estimated.

Nonlinear mixed-effects models Nonlinear Mixed-effects (NLME) modeling is often used to characterize PK and PD e.g. exposure-response relationships, in both preclinical and clinical work. Structural model, statistical model, and covariate model are three types of the NLME models.47,48 The structural model describes the general tendency of the data, such as a one or two-compartmental PK model. The parameters of structural model are fixed-effect parameters, which represent the typical value of the population. The statistical model includes random-effect parameters, which represent the variability of the fixed-effect parame-ters. Using the NLME approach, within individual variability (residual error, Equation 6), IIV and inter-occasion variability51 (IOV, Equation 7) are ex-plained using statistical parameters. The covariate model describes how co-variates, for instance, experimental subject-specific variables, can be mod-eled and linked to population parameters, and those parameter-covariate relationships can be used to e.g. facilitate dose adjustment in clinical trials. The NLME model can be described as follow:

, , , , , , , , Equation 6

Where yi,j,k is the jth observation of the ith individual at occasion k. f(…) is the individual prediction described by either a linear or non-linear function with independent variables xi,j,k and parameter vectors i,k at occasion k. εi,j,k is residual error for observation j for individual i at occasion k, which is as-sumed to be normally distributed with a mean of zero and an estimated vari-ance of σ2. The element of i,k is modeled as follow:

, ∙ ŋ Equation 7

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where θi,k is the value of the parameter in individual i at occasion k, θ is the typical value of the parameter in a population and ŋi is the normally distrib-uted IIV with a mean of zero and a variance of ω2. κk is the normally distrib-uted IOV with a mean of zero and a variance of П2.

Maximum likelihood estimation method and objective function value Maximum likelihood parameter estimation corresponds to the parameter values that maximize the likelihood of the parameters in the model given to the observed data obtained from experiments. In some software, such as NONMEM®, minimizing the extended least squares objective function val-ues (OFV) is used during the estimation process, which corresponds to max-imizing the likelihood. The OFV is proportional to minus two times the loga-rithm likelihood of the data given by the model.52 Therefore, minimizing the OFV in NONMEM is equivalent to maximizing the likelihood, which means the lower the OFV is, the better the model fits the data.

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Aims

The general aim of the thesis was to evaluate the pharmacokinetics and pharmacodynamics of anti-tubercular drugs in mice and to give experimental design recommendations for preclinical studies.

The specific aims were:

To evaluate pharmacokinetics of first-line anti-tubercular drugs To describe pharmacodynamics in mice using monotherapy To assess pharmacodynamic interactions in mice using combination

therapies To give experimental design recommendations for both pharmacokinetic

and pharmacodynamic studies for preclinical settings

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Methods

In vivo pharmacokinetic data (paper I and III) In population PK studies in healthy mice, C57BL/6 mice (8-10 weeks old, Harlan Laboratories) were divided into four groups with similar average weights (18.8 g) and each group was administered RIF, INH, EMB or PZA in solution via oral gavage (20 mL·kg-1) or intravenous (IV) bolus injection (10 mL·kg-1). Rifampicin was given as a single IV dose (12 mg·kg-1), a sin-gle oral dose (1, 3, 10, 30 or 100 mg·kg-1) or multiple oral doses (10 mg·kg-

1·day-1) for three days. Isoniazid was given as a single IV dose (10 mg·kg-1), a single oral dose (0.2, 0.5, 1, 5 or 25 mg·kg-1) or multiple oral doses (25 mg·kg-1·day-1) for three days. Ethambutol was given as a single IV dose (16 mg·kg-1) or a single oral dose (10, 30, 100, 300 or 1000 mg·kg-1, there was no multiple-dose regimen for EMB). Pyrazinamide was given as a single IV dose (25 mg·kg-1), a single oral dose (15, 25, 50, 150, 400 or 1000 mg·kg-1) or multiple oral doses (150 mg·kg-1·day-1) for four days. All mice received treatment in the fed state.

In population PK studies in M. tuberculosis-infected mice, PK infor-mation was obtained from BALB/c mice. One blood sample per mouse was drawn from infected mice (n=49) receiving 4-week treatment with RIF (5, 10 or 20 mg·kg-1), INH (12.5, 25 and 50 mg·kg-1), EMB (50, 100 and 200 mg·kg-1) or PZA (75, 150 and 300 mg·kg-1) at 1, 4 and 8 hours after the last dose with 3 mice per time point. Mice receiving 75 mg·kg-1 of PZA in monotherapy only contributed CFU data and not PK data, since the mice did not survive beyond 1 week with treatments of PZA or EMB. To support the population PK model development for RIF, drug concentrations from the sparsely sampled M. tuberculosis-infected mice were combined with a sec-ond PK study in healthy BALB/c mice (n=18).53 Healthy mice were adminis-tered 10 and 160 mg·kg-1 of RIF for 5 days a week for 3 weeks and the PK was obtained at 0.08, 0.25, 0.5, 0.75, 1.5, 3 and 6 hours after the last dose (one sample per mouse).

Drug plasma samples from infected mice were frozen at -80 and pro-cessed by protein precipitation with organic solvents plus filtration. Samples were then analyzed by ultra-performance liquid chromatography tandem mass-spectrometry for quantification of each drug at GlaxoSmithKline. Ri-fampicin, quantified in plasma samples from healthy mice, was measured by

26

protein precipitation, followed by high-performance liquid chromatography with ultraviolet detection.54

In vivo pharmacodynamic data (paper II and III) In the M. tuberculosis-infected mouse study using monotherapy with RIF only, sixty C57BL/6 mice were anaesthetized with 3% isoflurane (IsoVet®, B.Braun, Piramal Healthcare, Maharashtra, India) and intubated with a metal probe (catalogue number 27134, Unimed SA, Lausanne, Switzerland). Infec-tion was initiated by intratracheal instillation of M. tuberculosis H37Rv. The inoculum (105 CFU per mouse suspended in 50 µl of phosphate-buffered saline) was put into the probe and delivered through forced inhalation with a syringe on Day 0. Twenty-five mice received RIF (Sigma-Aldrich) 1, 2.83, 8.88, 26.4 or 98 mg·kg-1 orally once daily for 8 days from Day 1 after infec-tion and samples were taken after sacrificing mice on Day 9 after infection. An additional twenty mice were given 30 mg·kg-1 RIF orally once daily for up to 8 days. Five of these were sacrificed on each of Days 2, 3, 4 and 9 after infection. Fifteen mice received no treatment (natural growth group) and were sacrificed on Days 1, 9 and 18 (five mice on each occasion).

In the M. tuberculosis-infected BALB/c mouse study using mono and combination therapies, all treatment started 14 days after infection. Mono-therapy of RIF at dose levels of 5, 10 and 20 mg·kg-1 (R5, R10 and R20), INH of 12.5, 25 and 50 mg·kg-1 (H12.5, H25 and H50), EMB of 50, 100 and 200 mg·kg-1 (E50, E100 and E200) or PZA of 75, 150 and 300 mg·kg-1 (Z75, Z150 and Z300) were orally administered daily for 5 days per week via oral gavage, lasting for 4 weeks.53 The CFU counts were assessed in monotherapy after 1, 2 and 4 weeks of treatment with RIF or INH, using 9 mice per time point, including 3 mice per dose level. The CFU counts were only obtained from 6 mice after 1 week of treatment of EMB and PZA, since mice did not survive beyond 1 week with treatments of EMB and PZA. Fixed doses were used in combination therapies, including R10, H25, E100 and Z150. Combination thera-pies (R10H25, R10H25Z150 and R10H25Z150E100) lasted up to 24 weeks. The CFU counts were assessed in drug combinations after 1, 2, 4, 8, 12 and 24 weeks of treatment with 3 mice at each occasion. Bacterial natural growth (no treatment) data was collected at 1, 3, 7, 14 and 21 days after infection.

Simulated in vitro pharmacodynamic data (paper IV) Two different designs based on the conventional microdilution checkerboard technique of two hypothetical anti-tubercular drugs, Drug A and Drug B, were used. A conventional rich study design with a ten-by-ten checkerboard, including 1 scenario of natural growth (no treatment), 9 scenarios of mono-

27

therapy with each single drug and 81 scenarios of combinations, was em-ployed based on 2-fold increasing static in vitro concentrations, ranging from 0.25 mg·L-1 to 64 mg·L-1 for Drug A and Drug B with a daily sample to 14 days after treatment (Figure 3). A conventional reduced study design with a four-by-four checkerboard, including 1 scenario of natural growth (no treat-ment), 3 scenarios of monotherapy with each single drug and 9 scenarios of combinations was employed with 8-fold increasing concentration, including 0, 8 mg·L-1, 16 mg·L-1 and 64 mg·L-1 for Drug A and Drug B and with daily sampling to 14 days. Drugs were assumed to be added 4 days after start of infection and lasted for 14 days.

Figure 3. Illustration of the combinations of concentrations of Drugs A and B in the a) conventional rich design, b) conventional reduced design and c) newly proposed optimized design with EC20, EC50 and EC80 of each drug.

Pharmacokinetic modeling (paper I and II) All the PK samples for each drug (obtained using the original sampling de-signs) were modeled simultaneously using a NLME approach. Initially, one- and two-compartmental PK models, with first-order absorption and elimina-tion, were evaluated. For PZA, a three-compartmental model was also evalu-ated due to data-driven observations. Dose dependence and time dependence were also tested for RIF, INH and PZA PK. Only dose dependence was evaluated for EMB since no PK information was available from multiple-dose oral administrations in healthy C57BL/6 mice. The IIV and IOV were evaluated on all fixed effects using log-normal distribution.51 In order to link

28

to the PD model, a population pharmacokinetic parameter approach was used as input.55

Pharmacodynamic modeling (paper II and III) The Multistate Tuberculosis Pharmacometric model The MTP model was simultaneously fitted to all observed CFU (log trans-formation on both sides) versus time data. The MTP model consists of a series of differential equations representing fast-multiplying (F), slow-multiplying (S) and non-multiplying (N) bacterial states (Figure 2), with first-order linear rate to represent the transfers between states.

The estimates of transfer rates were taken from fitting the MTP model to in vitro data with the same bacterial strain,32 except for the time-dependent transfer from fast- to slow-multiplying bacteria (kFS), which was re-estimated using EMAX and linear functions with respect to time in this study (Equations 8 and 9). Re-estimation of kFS as well as the other transfer rates, one at a time, were compared to fixing the parameter to the in vitro estimate.32

Equation 8

Equation 9

where t is time; KFSlin is the linear increase in kFS with time; KFSsig is the initial transfer rate from F to S; tMAX is the time to reach the highest value of kFS; and t50 is 50% of tMAX. The growth in CFU in untreated animals was explored using exponential and Gompertz growth functions. All parameters associated with the natural growth (kG, kFS, kSF, kFN, kSN, kNS) were fixed during the esti-mation of drug effects. The anti-tubercular drug effects were evaluated for each possible mechanism in the model, i.e. inhibition of the growth of fast-multiplying bacteria and stimulation of the death of fast-, slow- and non-multiplying bacteria. Different exposure-response relationships were evalu-ated for each possible mechanism, such as linear models, EMAX models, and sigmoidal EMAX models.

The General Pharmacodynamic Interaction model Bliss Independence39 (i.e. EAB=EA+EB-EA×EB) was used as an additivity criterion for the GPDI model46, since Loewe Additivity40 cannot handle dif-ferences in EMAX of a single drug. A scaling approach was used to account for differences in EMAX between drugs in which the drug effects were scaled relative to the highest EMAX.56 Bliss Independence was simplified to EAB=EA+EB due to the minor contribution of EA×EB at concentrations well below the EC50 in cases when slope models were identified. Hence, the drug

29

effects of Drugs A and B can be expressed as in Equations 4 and 5. In three- and four-drug combinations, interaction parameters identified in previous combinations were fixed. In the full GPDI model, all parameters were esti-mated simultaneously.

However, due to the fact that few exposure levels were included in the combination therapy data in the study, a joint INTAB was estimated (INTAB =INTBA) and EC50INT was set to a very low value of 1x10-8, which reduced the EMAX function of the interaction model to an On/Off effect. Equation 10 shows an example of a reduced GPDI model for the evaluation of a joint effect of Drugs A and B when the exposure-response relationship was de-fined using a slope model, and On/Off interaction with a joint interaction term INTAB:

Equation 10

where kA and kB are linear effects of Drug A and Drug B identified in mono-therapy.

Optimized design recommendations (paper I and IV) Design for pharmacokinetic studies A stochastic simulation and estimation (SSE) approach was used for the developed population PK models for each of the four drugs in order to opti-mize the sampling designs and to decrease the number of animals required. Different sampling schemes and numbers of mice were evaluated for each drug with the aim of reducing the total number of animals required while retaining at least the same relative imprecision (rRMSE) and relative bias (rBias) in the fixed and random effects parameters. The new designs for each drug were optimized for both single-dose and multiple-dose experiments with the PK data obtained on one occasion (the multiple-dose designs used single-dose IV design plus single-dose oral design at steady-state). For the single-dose designs, the number of samples per animal was increased to eight, which was judged to be practical and ethically justified, and other scenarios explored included extending the sampling period to 24 hours post-dose, varying the total number of animals used and varying the sampling time points. The zipper design allowed the sampling scheme within each animal to be reduced in the multiple-dose administrations compared with the new single-dose design and three or four samples per animal were evaluated, but samples from at least one animal were also collected at each of the other optimal sampling time points identified in the evaluation of the single-dose design for each drug. Since the auto-induction of RIF in the PK model was described using a separate clearance (CL) value only on Day 3 rather than

30

for the full course of RIF auto-induction, the multiple-dose oral zipper de-sign only included simulation of the PK following a single dose but with the zippered PK sampling scheme. As such, the RIF CL on Day 3 was not esti-mated in the SSE. Because the half-lives of RIF, INH, EMB and PZA were short, the PK for multiple-dose experiments were obtained following a single dose, mimicking a PK occasion at any time during a PKPD experiment. The last samples for the new designs for each drug and route of administration were dependent on the low limit of quantification (LLOQ) for the observed data used for building population PK models of each drug.

Design for assessing pharmacodynamic interactions An optimized design for the evaluation of PD interactions of drug combina-tions based on exposure levels at 0, EC20, EC50 and EC80 of each single drug was proposed in this study. The rationale behind this optimized design was to better capture changes in the potencies (EC50) of each drug, using information from the exposure-response relationships of each drug in mono-therapy. The optimized design included 1 scenario of natural growth (no treatment), 3 scenarios of monotherapy with each single drug and 9 scenari-os of combinations. Sampling time points for the optimized design are the same as the conventional rich and reduced study design (Figure 3). All treatments started 4 days after infection and lasted for 14 days with daily treatment.

Software and modeling evaluation All data analysis was done using the software NONMEM (version 7.3; Icon Development Solution, Ellicott City, Maryland, United States, [http://www.iconplc.com/technology/products/nonmem]) using the first-order conditional estimation method.52 Model evaluation and selection were based on the OFV with a decrease of 3.84 considered statistically significant (p<0.05, χ2 distribution) for nested models and one degree of freedom. In addition, goodness-of-fit plots, parameter precision, predictive performance assessed using visual predictive check (VPC),57 prediction-corrected visual predictive check (pcVPC)58 and scientific plausibility were used for model selection. In both VPC and pcVPC, 1000 replicates were simulated based on the model and 5th, median and 95th percentiles were used in conjunction with the corresponding data to assess model performance using Perl-speaks-NONMEM (PsN) (version 4.2.0; Department of Pharmaceutical Bioscienc-es, Uppsala University, Uppsala, Sweden; [http://psn.sourceforge.net]).57 R package Xpose (version 4.4.1; Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden; [http://xpose.sourceforge.net]) was used for visualization of results and data management. The run record was

31

produced with Pirana software (version 2.7; Pirana software and consulting, San Francisco, United States; [http://www.pirana-software.com]).59 The M3 method in NONMEM was used to handle data below the LLOQ.60,61 Propor-tional, combined proportional and additive error models for PK data and an additive error model on log scale for PD data were evaluated to describe residual unexplained variability.

One thousand replicates were simulated for each design, and each simu-lated dataset was analyzed using the final models, which were also used for the simulations. The designs were assessed by estimating rBias (Equation 11), rRMSE (Equation 12) and correct classification rate (Equation 13) of interaction parameters.

100% ∑ Equation 11

100% ∑ Equation 12

100%

Equation 13

where estimationi denotes the estimated parameter i value; truei is the true parameter i value used in the initial simulations and N is the number of simu-lations for each set of truei (N = 1000).

32

Results

Population pharmacokinetics of first-line drugs (paper I and II) In healthy C57BL/6 mice, the final population PK parameter estimates for RIF, INH, EMB and PZA are presented in Table 2. A one-compartmental model with first-order absorption and elimination provided the best fit for the RIF PK data. The volume of distribution at the lowest dose of RIF (Vlowest

dose) was significantly higher than at higher doses (V). Neither a nonlinear nor a linear relationship describing the change in V with dose was supported by the data. Due to auto-induction of RIF, CL on Day 3 (132 mL·h-1·kg-1) was statistically significantly higher than that on Days 1 and 2 (79.3 mL·h-1·kg-1). The bioavailability was estimated as 65.6%. The IIV of the absorption rate constant (ka), V/Vlowest dose and CL were estimated as 55.6%, 21.8% and 15.9%, respectively. The data did not support inclusion of IOV in any of the PK parameters.

In the M. tuberculosis-infected BALB/c mouse, rifampicin apparent CL treated for 4 weeks was quantified three times higher than in healthy mice treated for 3 weeks.

Isoniazid blood PK was best described using a one-compartmental model with dose-dependent V and CL. The CL decreased with increasing dose lev-els from 0.2 mg·kg-1. The volume of distribution at a dose of 0.2 mg·kg-1 (Vlowest dose) was 1.8-fold lower than the V at higher doses. The IIV of CL was estimated as 14.6%. The bioavailability of INH was estimated as 84.3%.

Ethambutol blood PK was described well by a two-compartmental model with an absorption lag time (Tlag) of 3.6 minutes and a bioavailability of 64%. The volumes of distribution of the central and peripheral compartments (V and V2) were 2180 mL·kg-1 and 4910 mL·kg-1, respectively. The IIV was not estimated in the PK of EMB because of the very sparse original design using only one sample per mouse.

Pyrazinamide blood PK was best described using a two-compartmental model. The PZA CL was statistically lower at the highest PZA (CLhighest dose) than that at lower doses. The IIV of CL and the inter-compartmental rate (Q) were estimated to 27.8% and 118.7%, respectively, in the final PZA PK model. The bioavailability of PZA was estimated to 55.9%.

Tab

le 2

. Fin

al p

harm

acok

inet

ic p

aram

eter

est

imat

es f

or r

ifam

pici

n (R

IF),

ison

iazi

d (I

NH

), e

tham

buto

l (E

MB

) an

d py

razi

nam

ide

(PZ

A)

in

mic

e, b

ased

on

bloo

d co

ncen

trat

ions

and

the

orig

inal

sam

plin

g de

sign

s.

Par

amet

ers

RIF

IN

H

EM

B

PZ

A

Typ

ical

va

lue

RS

E (

%)

Typ

ical

va

lue

RS

E (

%)

Typ

ical

va

lue

RS

E (

%)

Typ

ical

va

lue

RS

E (

%)

k a (

h-1)

1.02

15

.2

12.6

12

.1

0.86

9 9.

9 2.

84

11.2

C

L (

mL·h

-1·k

g-1)

79.3

11

.4

855

8.4

2560

5.

9 51

5 5.

3 V

(m

L·k

g-1)

1250

4.

3 98

9 4.

2 21

80

12.8

53

2

5.8

Q

(m

L·h

-1·k

g-1)

- -

- -

1760

13

.5

55.9

8

V2

(mL·k

g-1)

- -

- -

4910

7.

6 70

9 18

.9

Bio

avai

labi

lity

(%)

65.6

6.

4 84

.3

4.9

64.0

6.

7 43

.8

23.5

T

lag

(h-1

) -

- -

- 0.

0577

11

.1

- -

Vlo

wes

t dos

e(m

L·k

g-1)

2280

8.

4 43

7 13

-

- -

- C

Lhi

ghes

t dos

e (m

L·h

-1·k

g-1)

- -

- -

- -

95

17.1

C

LM

AX

(%)

- -

75.2

26

.7

- -

- -

CL

50 (µ

g·kg

-1)

- -

1750

0

69.7

-

- -

- C

L a

t Day

3 (

mL·h

-1·k

g-1)

132

9.5

- -

- -

- -

IIV

in C

L (

%)

15.9

23

.3

14.6

16

.6

- -

27.8

14

.7

IIV

in k

a (%

) 55

.6

22

- -

- -

- -

IIV

in V

(%

) 21

.8

23.6

-

- -

- -

- II

V in

Q (

%)

- -

- -

- -

118.

7 19

.5

IOV

in F

(%

)

15

.6

20.8

34

Pharmacokinetics-Pharmacodynamics of first-line drugs (paper II, III and IV) Monotherapy in a C57BL/6 mouse model In the MTP model, bacterial transfer rates, except kFS, were fixed to esti-mates obtained for the same bacterial strain in vitro. Re-estimating the trans-fer rate from F to S (kFS) as a linear function with time provided a decrease in OFV of 7.3 points, compared to fixing the parameter to the in vitro estimate. Re-estimation of the other transfer rates between states did not provide a reduction in OFV and was therefore fixed to in vitro estimates. The final model included an exponential growth function for M. tuberculosis with an exponential growth rate kG. The initial number (inoculum) of fast-multiplying bacteria in untreated mice (F0

†) differed, compared to those in the RIF-treated groups (F0). The data did not support inclusion of any inocu-lum of slow- or non-multiplying bacteria and these were therefore set to zero in the final model.

The final MTP model, shown in Figure 4, included statistically significant and separate RIF effects on inhibition of the growth of fast-multiplying bac-teria ( ; Equation 14), stimulation of the death of fast-multiplying bacteria ( ; Equation 15) and stimulation of the death of slow-multiplying bacteria ( ; Equation 16). An RIF effect on non-multiplying bacteria was tested but was not statistically significant and was therefore not included in the final model.

Equation 14

Equation 15

Equation 16

where FGIMAX is the maximal achievable fractional RIF-induced inhibition of fast-multiplying bacterial growth rate; FDEMAX is the maximal achievable RIF-induced stimulation of fast-multiplying bacterial death rate; FGIC50 and FDEC50 are the RIF concentrations at 50% of FGIMAX and FDEMAX, respectively; SDk is the second-order slow-multiplying bacterial death rate; γ is a sig-moidicity parameter; and CRIF is the RIF blood concentration. The final dif-ferential equation system for fast-multiplying bacteria (F; Equation 17), slow-multiplying bacteria (S; Equation 18), and non-multiplying bacteria (N; Equation 19) changing over time was as follow:

1 ∙

Equation 17

Equation 18

Equation 19

35

where F, S and N represent fast-, slow- and non-multiplying bacteria, respec-tively. The transfer rates between bacterial states are given by kFS, kSF, kFN, kSN and kNS, as shown in Figure 4.

Figure 4. Rifampicin drug effects in an M. tuberculosis-infected C57BL/6 mouse model using the MTP model approach linked to the population pharmacokinetic model in a healthy C57BL/6 mouse model.

Combination therapy in a BALB/c mouse model In Figure 5, by using BALB/c mice, the final MTP model included RIF mono drug effects on inhibition of the growth of fast-multiplying bacteria, stimulation of the death of fast-, slow- and non-multiplying bacteria, as well as INH mono drug effects as stimulation of the death of both fast- and slow-multiplying bacteria. Isoniazid effect on stimulation of the death of non-multiplying bacteria was identified only in the combination of R10H25Z150 using a linear function, which was not identifiable in INH monotherapy and R10H25 combination therapy. Mono drug effects of EMB and PZA could not be quantified, due to a lack of longitudinal CFU data.

By linking the MTP model to the GPDI model, RIF and INH decreased their respective potencies on joint stimulation of the death of slow- ( ) and non-multiplying bacteria ( ). and were estimated to 4.49 and 0.32, respectively, which can be interpreted as a 4.49-fold or 0.32-fold decrease in the potency of RIF and INH, respectively. This potency shift leads to 0.86 log10 CFU/lungs higher CFU at 28 days after treatment com-pared to the expected additivity of the two drugs based on monotherapy alone, i.e. PD antagonism was observed on the biomarker level. Figure 6 illustrates simulations from the final MTP-GPDI model and revealed that antagonistic interactions between RIF and INH. Figure 7 shows the VPCs of

36

the final MTP-GPDI model in a BALB/c mouse using different mono and combination therapies.

Figure 5. Schematic illustration of the final population pharmacokinetic models and the final Multistate Tuberculosis Pharmacometric (MTP) model consisting of fast- (F), slow- (S) and non-multiplying (N) bacteria linked to the General Pharmacody-namic Interaction (GPDI) model for the combination therapies.

Rifampicin and EMB increased their potencies ( =-0.15) as estimat-ed by the GPDI model. These PD interactions led to 2.84 log10 CFU/lungs lower CFU compared to expected additivity between four drugs. The data did not support any PD interaction between EMB and PZA. The differential equation system for F (Equation 20), S (Equation 21) and N (Equation 22) for the final MTP-GPDI model was as follow:

Equation 20

Equation 21

Equation 22

where FG and FD are the inhibition of the growth and stimulation of the death of fast-multiplying bacteria, and SD and ND are the stimulation of the death of slow- and non-multiplying bacteria. Detailed differential equations of FG, FD, SD and ND are shown in Figure 5.

37

Figure 6. Predicted log10 CFU/lungs in numbers and log10 CFU/lungs deviation from expected additivity (in shaded areas) for rifampicin and isoniazid in different combinations at 28 days after treatment. White areas in the figure show expected additivity, whereas blue shaded areas show higher log10 CFU/lungs (antagonism) than expected additivity and orange shaded areas show lower log10 CFU/lungs (synergism) than expected additivity.

Comparison of pharmacodynamic interaction models The true interactions on a parameter level (EC50) in the GPDI model of the simulated combinations are displayed in Figure 8 as % shift of EC50A or EC50B. Figure 8 displays the result from estimating the Greco model using the Loewe Additivity-based MTP-GPDI model. In each plot of Figure 8, four sectors are shown as true antagonistic interactions on a parameter level (i.e. both EC50 values shifted > 0%), true synergistic interaction (i.e. both EC50 values shifted < 0%), true asymmetric interaction (i.e. one EC50 value shifted > 0% and the other EC50 value shifted < 0%) and additivity (i.e. both EC50 values shifted 0%). The estimated interactions on a parameter level from the Greco model are color-coded, i.e. antagonism (ANT in red), syner-gy (SYN in green) and no interaction (ADD in blue) as quantified by the single interaction parameter.

38

Figure 7. Visual Predictive Check of the final Multistate Tuberculosis Pharmaco-metric (MTP) model linked to the General Pharmacodynamic Interaction (GPDI) model applied to colony forming unit (CFU) data from a tuberculosis-infected ex-perimental mouse model without treatment (natural growth) and with different drug treatments.

In the conventional rich design, the Empirical Bliss model and the Greco model correctly captured antagonism and synergy. In situations with asym-metric interactions, however, conventional models only estimated symmetric antagonism (ANT in red), symmetric synergy (SYN in green) and defined additivity (ADD in blue) and were intrinsically unable to estimate asymmet-ric interactions, because of only one parameter estimated. In addition, the obtained classification in the asymmetric region of the interaction space was apparently dependent on both the maximum effect and the potency of the interaction from Drug A and B. It was difficult to foresee whether an interac-tion would lead to synergy, antagonism or no interaction in the asymmetric sector, shown as Figure 9.

F

igur

e 8.

Cla

ssif

icat

ion

by th

e G

reco

mod

el b

ased

on

Loe

we

Add

itivi

ty u

sing

the

conv

entio

nal r

ich

desi

gn (

left

) or

the

conv

entio

nal r

educ

ed

desi

gn (

righ

t). T

he c

olor

of

each

dot

indi

cate

s th

e cl

assi

fica

tion

of th

e ph

arm

acod

ynam

ic in

tera

ctio

n by

the

Gre

co m

odel

: Loe

we

Add

itivi

ty

(AD

D in

blu

e), a

ntag

onis

m (

AN

T in

red

) an

d sy

nerg

y (S

YN

in g

reen

). T

he tr

ue c

lass

ific

atio

n is

giv

en b

y th

e fo

ur d

iffe

rent

sec

tors

in e

ach

plot

: the

upp

er r

ight

sec

tor

show

s A

NT

, the

low

er le

ft s

ecto

r sh

ows

SY

N a

nd th

e up

per

left

and

low

er r

ight

sec

tors

sho

w a

sym

met

ric

inte

rac-

tion

(A

NT

+SY

N).

F

igur

e 9.

Pre

dict

ed l

og10

CFU

/mL

in

num

bers

and

log

10 C

FU

/mL

dev

iatio

n fr

om L

oew

e A

dditi

vity

(in

sha

ded

area

s) f

or h

ypot

hetic

al d

rug

A

and

drug

B i

n di

ffer

ent

com

bina

tions

at

7 da

ys a

fter

tre

atm

ent.

Plo

ts 1

), 2

), 3

) re

pres

ent

corr

espo

ndin

g se

lect

ed p

oint

1-e

stim

ated

syn

ergy

, 2-

esti

mat

ed a

ddit

ivit

y, 3

-est

imat

ed a

ntag

onis

m b

y th

e G

reco

Mod

el in

Fig

ure

8. I

n ea

ch p

lot,

conc

entr

atio

ns o

f dr

ug A

and

dru

g B

are

sho

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Similar patterns of interaction classification were observed in the conven-tional reduced design in the scenario with differing EMAX between Drug A and B as well. In the scenarios with the same EMAX for Drug A and B, most of the estimations from the conventional models were not statistically signif-icant to estimate and therefore defined additivity was estimated and indicat-ed by the blue color coding dots, regardless of which PD interactions were simulated from the MTP-GPDI model.

Optimized design recommendations (paper I and IV) Design for pharmacokinetic studies A sample was taken at 24 hours in the new single-dose oral and IV designs for RIF and INH, since the rRMSE values for some parameters were lower than those without a 24-hour sample. For the new single-dose oral design for PZA, the last sampling time was 4 hours post-dose, since most of the obser-vations from the new simulated data were below the LLOQ after the lower doses at 4 hours post-dose. The sampling time points for the investigated drugs and designs, and the predicted log concentrations, are shown in Figure 10 (only RIF). The PK sampling times after PZA oral and IV administrations ended at 4 and 8 hours post-dose, respectively. Due to the short half-life of EMB, the 24-hour sample was deleted from the original design. The sam-pling time points for the single-dose designs were assessed after evaluation of the last sample taken for each drug. Several time points were omitted from the original designs for each drug in order to limit the designs to up to 8 samples from each mouse, covering the whole experimental period up to the last sampling time point. For the new single-dose IV and oral designs, the sampling time points of 0.25, 0.75 and 4 hours post-dose were deleted from the original RIF design; those of 1.5, 3 and 8 hours post-dose were deleted from the original INH design, and those of 1.5, 3 and 24 hours post-dose were deleted from the original EMB design. In the new designs for PZA, the 3-hour post-dose sampling time point was omitted from the origi-nal single-dose IV design and samples taken at 8 and 24 hours post-dose were excluded from the single-dose oral design. A new sampling time point was added at 0.08 hours post-dose for the single-dose oral design and multi-ple-dose oral zipper design, and another at 1.5 hours post-dose was added to the oral zipper design. For new single-dose designs of RIF, INH and EMB, the sampling time points were identical for the IV and oral studies. The total number of animals required for the new optimized single-dose designs were 24, 24, 33 and 33 for RIF, EMB, INH and PZA, respectively. For RIF, INH and EMB, numbers of animals required for the new single-dose designs were up to 7-fold lower than that in the original designs. The number of animals

42

required for PZA only decreased by 31% because the original sampling de-sign already included more than one sample per mouse.

Figure 10. Predicted log blood concentrations versus time based on the final popula-tion pharmacokinetic models after single-dose intravenous (IV) or single-dose oral (PO) or PO steadystate (SS) administrations of A) rifampicin, B) isoniazid, C) eth-ambutol and D) pyrazinamide. The sampling time points in the new designs for single-dose administrations are indicated by * in each plot. For the multiple-dose oral zipper designs, half of the animals were sampled according to ¤ in black and the other half according to ¤ in grey.

The multiple-dose oral zipper designs were based on the sampling time points that had been optimized for the new single-dose oral designs for RIF, INH, EMB and PZA. However, only four samples per mouse were required for the zipper designs, compared to eight for the single-dose designs. The re-estimation of data in the SSE for the zipper design analysis used PK infor-mation from the single-dose IV and single-dose oral experiments in order to include information about bioavailability and to use the richer sampling from the single-dose IV experiment. The total numbers of animals required for the new optimized multiple-dose oral zipper designs were 30, 30, 30 and 36 for RIF, EMB, INH and PZA, respectively. For RIF, INH and EMB, these num-bers were almost 5-fold lower in the oral zipper designs than those in the original designs, which included up to 186 animals for each drug. The re-quired number of animals for PZA was similar to that in the original design because more than one sample per mouse was also taken in the original de-sign. The rBias and rRMSE for each parameter, based on the oral zipper

43

designs (which included the new single-dose IV design and eight samples per animal), were at least as low as those from the new single-dose design for each drug. As shown in Figure 11 (only RIF), the rBias and rRMSE for each parameter in the new designs for each drug, i.e. the oral zipper design with four samples per animal for multiple-dose oral administration and the single-dose IV or oral design with up to eight samples per animal, were simi-lar or lower than those for the original designs, except for the rBias in IIV for the CL of PZA, which was 2% higher in the zipper design than in the original design. The rBias in the INH CL50 was also 6% and 3% higher in the new single-dose and zipper designs than in the original design.

Design for assessing pharmacodynamic interactions The suitability of using conventional rich and reduced designs to support estimation of parameters from the GPDI model was assessed using SSE for 1000 combinations of the two hypothetical Drugs A and B. In addition, the correct interaction classification rate was calculated for the GPDI models, as well as for the Empiric Bliss Independence and the Greco model for compar-ison. Regardless of the underling additivity criterion, the rBias and rRMSE of the conventional rich design were lowest overall. The conventional re-duced design was the least informative design for estimating GPDI parame-ters, as seen from the highest rBias, up to 7.56% and highest rRMSE, up to 78.9%. The optimized design based on EC20, EC50 and EC80 of the respec-tive single drugs resulted in lower rBias and lower rRMSE than the reduced design at the same sample size. The rRMSE of the optimized designs was up to 1.6-fold lower than those in the reduced design.

The reduced design was shown to be inferior to the rich and optimized designs for correctly detecting synergies; the rich and optimized designs provided similarly high correct classification rates of >93.5%, including the asymmetric type of interaction. In contrast, the conventional models could not classify the asymmetric interactions at all, shown as a 0% correct classi-fication rate. However, ‘pure’ antagonism or synergy were also correctly classified by the Empiric Bliss Independence and the Greco model in >97.5% of the scenarios. .

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45

Discussion

Population pharmacokinetics of first-line drugs Dose-dependent PK was identified for RIF, INH and PZA in the healthy C57BL/6 mice in this work. The Vlowest dose for RIF was higher than the V for the other doses. The Vlowest dose for INH was lower than for the other doses. Dose-dependent CL was identified for both INH and PZA. The mechanisms behind the dose-dependent PK identified using the healthy mice in this work remain unknown.

In the M. tuberculosis-infected BALB/c mouse model, we included PK information from healthy C57BL/6 mice to describe the sparse data. To our knowledge, for the first time, our modeling approach quantified that appar-ent CL of RIF in M. tuberculosis-infected mice treated for 4 weeks is three times higher than that in healthy mice treated for 3 weeks. This is most likely due to auto-induction of RIF. The observed systemic exposure after a single dose may be different from that after multiple-dose administration if the compound has the potential to induce or inhibit CL or absorption mecha-nisms, leading to dose- or time-dependent PK. In humans, RIF is a known inducer of cytochrome P45062 and P-glycoprotein through activation of the nuclear pregnane X receptor,63 which causes potential for drug-drug PK in-teractions. Full steady-state RIF auto-induction in humans is reached after 40 days of oral dosage.64 In the study using healthy C57BL/6 mice, CL of RIF on Day 3 was predicted to be 66.4% higher than on Days 1 and 2, which indicates that RIF is auto-induced not only in humans, but also in mice. However, a more mechanistic model estimating the enzyme turn-over could not be quantified because of the short PK sampling period. It is important to note that humans may differ from animals with regard to expression catalytic activities of drug metabolizing enzymes. For instance, cytochrome P450 2B was not detectable in the human intestine,65 but was expressed in the mouse intestine.66

Pharmacodynamics of first-line drugs in monotherapy and combinations Rifampicin is effective against both replicating and non-replicating bacteria, because it targets essential and central DNA machinery.67 It is thought to

46

inhibit the bacterial DNA-dependent RNA polymerase.5 In the final MTP model using RIF monotherapy in the C57BL/6 mouse model in paper II, RIF significantly inhibited the growth of fast-multiplying bacteria and stimulated the death of fast- and slow-multiplying bacteria. Two separate exposure-response relationships were identified for the RIF effect on the stimulation of the death of fast- and slow-multiplying bacteria described as non-linear and linear relationships, respectively. The final model did not include a RIF ef-fect on non-multiplying bacteria as it was not statistically significant. This was possibly due to the fact that non-multiplying bacteria was a minority segment of the total bacterial burden in this acute C57BL/6 mouse model. The MTP model did not include any immune response element as it was based on in vitro time-kill experiments lacking an immune system. However, an immune response may occur in an in vivo system such as that represented by the mouse. The MTP model could be extended to include immune re-sponse components. However, it was not considered necessary for this study, where the acute C57BL/6 mouse model was used, since the adaptive im-mune response under similar experimental conditions did not impair the growth of M. tuberculosis during the assay period.25 As such, there was no effect of the immune system on the CFU versus time relationship in this study. Although animal models are not expected to always predict drug ex-posure in humans, they serve as valuable tools for quantifying exposure-response relationships and ideally predict the response at certain dose levels in humans.

In the combination therapies using a BALB/c mouse model in paper III, this study quantified for the first time the observed in vivo PD interactions in combination therapies by using the MTP-GPDI model.46 Both Bliss Inde-pendence and Loewe Additivity are compatible with the GPDI model, which makes the GPDI model approach more flexible than the other approaches. As our studies emphasized the GPDI model is not limited to two drugs in combination therapies. A property of the GPDI approach is that asymmetric interactions can be quantified, i.e. a different effect of Drug A on Drug B and vice versa. In our study, asymmetric interactions were not characterized, due to the single-dose level of each drug in the combination therapy, which led to the assumption of an On/Off effect only estimating INTAB, instead of an EMAX function. In R10H25Z150, INH was shown to stimulate the death of non-multiplying bacteria as well, which was not identified in monotherapy. There are some implications to consider when interpreting INH effect on the non-multiplying bacterial state. Due to the different length of the exposure-response experiments, i.e. 4-week mono drug treatments versus 24-week combination treatments, the composition of the bacterial burden was quite different, with a much higher number of non-multiplying bacteria in the 24-week experiment compared to the 4-week experiment. However, INH effect on the non-multiplying bacteria was not identified in R10H25 either, but sole-ly in the presence of PZA in the triple-drug combination, even though there

47

was no PZA effect identified from monotherapy. Still, because of the lack of data on INH mono effects at later time points, we could not clearly distin-guish whether PZA triggered the INH effect on non-multiplying bacterial state or whether this was an effect of INH alone. This aspect of our work underscores the importance of defining the same setting of experiments for drug efficacy evaluation in monotherapy and in assessing PD interactions in combinations. In the report from Grosset et al.,36 the combination of RIF and INH was bactericidal to a similar magnitude as the combination of RIF, INH and PZA, but both of those two combinations were less effective than the one combining RIF and PZA. They concluded that there was antagonism between INH and the combination of RIF and PZA in mice. Later studies by Almeida et al.68 reported that the antagonism between INH and the combina-tion of RIF and PZA was dependent on the dose of INH. Increasing the dose of INH alone resulted in a better antimicrobial effect. Conversely, increasing the dose of INH in the combination of RIF and PZA resulted in a lower an-timicrobial effect. Our model-based approach matches these observations, but surpasses these results by providing quantitative measures to describe PD interactions, i.e. our model predicted a 0.86 log10 CFU/lungs higher bac-terial load compared to an expected additivity in R10H25. An antagonistic interaction (less effect than expected additivity) between INH and RIF was found in this thesis, which is consistent with the clinical early bactericidal activity data from Day 0 to Day 14 reported by Jindani et al.69 A synergistic interaction was identified between RIF and EMB in this work. However, mono effect and interactions arising from EMB could not be differentiated using the data, since there was no longitudinal CFU data from mice receiv-ing EMB alone.

The term ‘asymmetric interaction’ was introduced earlier and summarizes concentration-dependent synergistic and antagonistic behavior of interacting drugs, which can only be quantified with the GPDI model approach.46 The GPDI concept was developed using 200-drug combination experiments em-anating from a high-throughput screening investigation and up to 38% of the observed interactions were asymmetric.46 Hence, the asymmetric interaction type might represent an important and relevant class of PD interactions that conventional model-based approaches, including the evaluated Empirical Bliss model and the Greco model, cannot intrinsically evaluate. In paper IV, we explored how conventional models compare to the GPDI model in an assessment of the PD interactions of anti-tubercular drugs on a parameter level. Thereafter, different scenarios based on EMAX and EC50 for hypothet-ical Drugs A and B were created and mimicked realistic situations. While there was in a good agreement overall between the conventional models and the GPDI models for ‘pure’ synergy and antagonism, the conventional mod-els were not able to classify the asymmetric interactions correctly and there was no clear pattern of what conventional models would classify in the asymmetric region of the PD interaction space. Hence, conventional models

48

may provide erratic classification results in these scenarios and may likely lead to wrong decisions on the nature of a PD interaction, which may harm decision-making in a drug development program. Moreover, the convention-al models are tied to a single additivity criterion. For instance, the Empirical Bliss model is based on Bliss Independence and the Greco model is based on Loewe Additivity, whereas the GPDI model is compatible with various addi-tivity criteria, including both of the latter criteria. The advantage of compati-bility with different additivity criteria is that no assumption about additivity has to be made and several criteria can be evaluated. In addition, INTAB and INTBA characterized the maximum fractional change of the respective PD parameters from a single drug, e.g. EC50 of a single drug. Hence, the inter-action parameters of the GPDI model are interpretable, which is not possible when conventional models are applied.

Optimized experimental design recommendations Traditionally in population PK studies, PK are determined in satellite exper-iments and the data are then used as fixed PK input in PK-PD models for TB.70 The design would, of course, be more informative if the PK and PD are obtained in the same animal. With such a design in mind, the oral zipper design was developed, which obtains the PK of the drug after one dose in a multiple-dose experiment. In this design, only four samples are taken per animal but all the samples from all the animals are zipped together to cover the entire sampling period. Similarly, for the multiple-dose oral zipper de-sign, changing the sampling design from one sample per animal to four sam-ples per animal decreased the number of animals required by up to 5-fold. For new compounds, the lessons learned from this work are the advantages of using serial sampling instead of single sample designs. However, if the PK is not known for a new compound, there is no standard sampling series that can fit for drugs with both short and long half-lives. We therefore sug-gest that a small pilot experiment is done with a zipper design where the samples are taken in order to collect some information. Based on the infor-mation from the initial work, the design can be optimized as done in this study. This is also in agreement with the learning-confirming paradigm.71

For PD studies, our study focused on the performance of the MTP-GPDI model under different experimental designs. In addition to conventionally used checkerboard designs, termed rich and reduced design in paper IV, an optimized design was proposed, which was based on EC20, EC50 and EC80 of each drug defined in the monotherapy. The rich design was based on the ten-by-ten microdilution checkerboard design, resulting in a labor-intensive set of 81 scenarios of two-drug combination experiments. The reduced de-sign was a small version of the rich design and spanned the same concentra-tion range as the rich design, but with a four-by-four checkerboard at lower

49

granularity than the rich design yielding 9 scenarios of two-drug combina-tion experiments. The proposed optimized design, based on 0, EC20, EC50 and EC80 of each drug also resulted in 9 scenarios of two-drug combination experiments. However, our analysis demonstrated that the optimized design was much more informative than the reduced design and enabled estimates of both the GPDI interaction parameters INTAB and INTBA at lower rBias and lower rRMSE compared to the conventional reduced design. Notably, rBias was even 0.25-fold lower in the optimized design than in the conventional rich design. Our study reflected a very wide range of potential interacting drugs with varied EMAX from 1 to 5 day-1, EC50 from 0.1 to 64 mg/L and hill factor from 1 to 2 for each single drug.72 In addition to the superior rBias and rRMSE estimates for the optimized design, the classification rate was also very close to the rich design and even >93.5% for the asymmetric interaction type that was not possible to identify with the conventional PD interaction models at all. The optimized design proposed in this study thus provides more information on PD interactions than the conventional reduced design.

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Conclusions

In summary, in this thesis the population PK-PD models of first-line drugs for drug-susceptible TB were characterized through linking each population PK model to the MTP model. In addition, PD interactions in the combination therapies were quantitatively illustrated by linking the MTP model to the GPDI model. More importantly, experimental designs were optimized and recommended to both PK and PD studies.

The population PK model of RIF, INH, EMB and PZA were, for the first

time, described in both the C57BL/6 mouse model and the BALB/c mouse model. These models were later used for linking PK to PD and to optimize the designs using simulations.

The MTP model described the changes in CFU over time well in M. tuberculosis-infected C57BL/6 and BALB/c mouse models. Rifampicin treatment effects on different bacterial states were characterized in both mouse models. Isoniazid treatment effects were characterized in the BALB/c mouse model. Future work needs to explore the predictive val-ue of these models for predicting response in humans.

Using the MTP model together with the GPDI model provided estimates

of single drug effects and a quantitative model-based evaluation frame-work for PD interactions among anti-tubercular drugs in the TB drug development. In the M. tuberculosis-infected BALB/c mice, the MTP-GPDI model could describe CFU data from untreated mice or mice treated with RIF, INH, EMB and PZA, as well as an assessment of an-tagonistic interactions between RIF and INH, and synergistic interac-tions between RIF and EMB using a model-based approach. The MTP-GPDI model approach is suggested to be used for selection of drug com-binations for Phase 2b evaluation during the development of anti-tubercular drugs.

The new single-dose PK design with enrichened individual sampling

was more informative than the original design in which only one sample was taken from each mouse in the PK studies. The proposed oral zipper design allows informative PK sampling in a multiple-dose administra-

51

tion scenario for characterizing PK-PD relationships, with similar or lower biases and imprecisions in parameter estimates, and decreased the total number of animals required by up to 7-fold compared to the origi-nal design.

The GPDI model, which provides model-based estimates of PD interac-

tions given as symmetric and asymmetric % shift of PD parameters of single drug effects, is compatible with different additivity criteria and has been shown to be advantageous to other conventional models, espe-cially for characterizing asymmetric interactions. The optimized design for assessing PD interactions, which was based on EC20, EC50 and EC80 of the single drugs, provided lower bias and lower imprecision than a conventional reduced four-by-four checkerboard study design at the same total number of samples required.

52

Acknowledgments

The research works presented in the thesis were conducted in the Pharma-cometric Research Group at the Department of Pharmaceutical Bioscienc-es at Uppsala University. The research works leading to these results re-ceived funding from the Innovative Medicines Initiative Joint Undertaking under grant agreement n°115337, resources comprising financial contribu-tions from the European Union’s Seventh Framework Programme (FP7/2007-2013), EFPIA companies’ in-kind contributions, and Chinese Scholarship Council (CSC). With financing from Anna-Maria Lundin’s Fund at Smålands Nation and Apotekarsociteten, I had opportunities to at-tend project-related courses and present results at national and international conferences.

After a long, intensive, joyful and informative period from October 29, 2011, which is the day I first arrived in Sweden and started the journey of my PhD studies, so many people have inspired me and contributed directly or indi-rectly to this thesis who I wish to thank, especially:

Ulrika Simonsson, my main supervisor, for your endless patience, outstand-ing expertise and care. I have learned so much from you and I feel so happy and fortunate to be your student. I am grateful for all the support you have granted me, and while I may not remember every story about special days you have told me, I will definitely remember what an excellent supervisor you are.

My deputy supervisors: Mats Karlsson, your endless energy and brilliant approach to thinking and sharing have inspired me; and Sebastian Wicha, for allowing me to enjoy the German approach to science. Thank you for every discussion and for your ways of explaining things to me. I have al-ready started drawing in order to understand and take notes like you do.

All my colleagues in the PreDiCT-TB consortium, especially Fatima Or-tega, Joaquin Rullas-Trincado, Santiago Ferrer and Inigo Angulo-Barturen at GlaxoSmithKline in Tres Contos and Gerjo J. de Knegt and Jurriaan E.M. de Steenwinkel in Erasmus MC at University Medical Cen-tre Rotterdam.

53

TB group, Elin Svensson, Oskar Clewe, Robin Svensson and Lenaig Tanneau, you are my closest colleagues; it is my great honor to be one of the members of the best TB research group, to work and to discuss with you all, and to have such a wonderful time traveling to conferences with you.

Lena, Margareta, Andy, Mia, Siv, Elisabet, Martin, Elodie, Irena, Kris-tin, Sebastian U, Thomas and Joakim, for providing such a pleasant work-ing environment; and Paolo, for your valuable input on my work.

To all the past and present postdocs in the PM and tPKPD group, Ron, for Pirana support; Vijay, Miriam, Tina, Chayan and Yasunori for all the great parties; Waqas and Anna, for the wonderful time in Stockholm; Winn, for good times on discussion around Asian topics; Elke, for talking to me when I was down and for the delicious bacon roll recipe; Eva, my stretching teacher, you are awesome and almost “killed” me; Margreke, for being so nice and easy to talk to; Philippe, for all the jokes that made me happy.

To all the past and present students in the PM and tPKPD group; Sofia, for accompanying me when I was in the hospital for pain from kidney stones and for keeping me active during my early days in Sweden; Anders K, the 3-hour long translation of risk 1 was so helpful for me, and I am grateful for all of our discussions; Åsa, because of you, I’ve started to like cats; Jesmin and Siti, for preparing soup, birthday cakes and being good friends; Irene P, for your friendship and for inviting me to Patras University – we are travel buddies forever; Anne-Gaëlle, my longest-term office-mate, for your kind-ness for taking care of my bike – I’m sorry for sleeping when you visited and make you waiting outside; Brenden, my kettlebell teacher, for pushing me so hard at the gym; Henrik, for encouraging me while I prepared for my driver’s license, even though, I still didn’t get one; Oskar A and Annika, for your numerous translations from Swedish to English; Emilie and Sreenath, my short-term office-mate with whom I had a wonderful time, please do me one more favor and take care of all the plants; João, Flavia and Erik, let’s keep the badminton tradition alive in this group; Gunnar, you spotted the error in my work at the last stage and almost gave me a heart attack – that was a real lesson learned; Benjamin, for all your awesome tips and help on R, which made my plotting easier; Camille, Salim, David and Ana, for all the information on preparation of animal courses and thesis production; Ari, for being so nice to talk to; Steve and Eric, for all the photos taken at special events and occasions, so many of which are such valuable reminders of the colorful life within our group; Ida and Marina, for all the fun times during fika breaks; Mustafa, for statistics discussions during UPSS; Gustaf, for all the talks on the press and news about Sweden; Nebojsa, for being so cool in the specs, I will never forget the roles; Anders T, for the fun time during World Cup and showing an interest in China.

54

Svetlana, for all the girl talk, enjoying Chinese food together, and the lovely roses – please remember our future travel plans in Asia, and I’ll definitely try the sushi place you recommended; Kajsa and Richard, your kind and professional help on PsN and techniques are truly invaluable not only to me, but also to the entire group.

Marina, Karin, Ulrica and Elisabet J, your support in administration, course registration and taking care of expenses and insurance allowed me to concentrate on my research; Magnus, Jerker and Tobias, for your IT sup-port; Agneta, for your support in ordinary life in the group and for format-ting the manuscripts into this thesis.

My Chinese friends, Rui, for saving me when I was kicked out by my land-lords and for offering to help me get rid of bedbugs – I enjoyed every chat, fika, lunch and dinner with you; Zhongren, for helping me prepare for the PhD journey in Sweden; Xiaomei, for the fun times while you visited UU; Chenhui, for your help with my silly questions; Chenyan, for proofreading my article; Shijun, for providing me lunch, tips and information; Yang, for the discussions and fika at Starbuck, let’s continue in the future.

My uncle, Hongge Zhu，我亲爱的舅舅-朱洪革：从高中，大学，研究生，出国攻读博士学位，我跨出的每一步，都是舅舅在默默地引领。尤其在瑞典攻读博士期间，在生活中和学业上，舅舅每一句关爱的话语，都是我前进的动力和方向；在我彷徨时，都是舅舅像明灯一样为我指路；在我远离父母家人时，也是舅舅代我照顾每一位家庭成员，让我没有后顾之忧。舅舅于公是一家公司的领导，于私是我们大家庭的定海神针，舅舅有多个角色，多个身份，而我则奉舅舅为我的偶像。感谢舅舅为我，为这个大家庭付出的一切。小粉丝爱您，我的舅舅！

My grandfather, Zengze Chen，我亲爱的爷爷-陈增泽：我爱您且想念您！向爷爷汇报，您的孙女博士毕业啦！

My mother, Hongxiu Zhu and my father, Yongchao Chen, 我亲爱的妈咪-朱洪秀和我亲爱的爸爸-陈永超：谢谢您们把我带到这个缤纷的世界，谢谢您们支持我的每一个决定；请爸爸妈咪放心，我在瑞典的每一分钟都在享受这个正确而无悔的决定；不知从何时起，我已经对妈咪爸爸非常信任，无比依赖。我希望我的妈咪爸爸可以健康快乐幸福地享受每一天的阳光与我的微笑。妈咪爸爸：谢谢您们那么无私地爱着我，守护着我，我爱您们! 亲亲我的妈咪！

55

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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. (Prior to January, 2005, the series was publishedunder the title “Comprehensive Summaries of UppsalaDissertations from the Faculty of Pharmacy”.)

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