ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2016

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 222

Novel Pharmacometric Methodsfor Informed Tuberculosis DrugDevelopment

OSKAR CLEWE

ISSN 1651-6192ISBN 978-91-554-9718-7urn:nbn:se:uu:diva-303872

Dissertation presented at Uppsala University to be publicly examined in B42, BMC,Husargatan 3, Uppsala, Friday, 25 November 2016 at 13:15 for the degree of Doctor ofPhilosophy (Faculty of Pharmacy). The examination will be conducted in English. Facultyexaminer: Professor Piet van der Graaf (Leiden Academic Centre for Drug Research, LeidenUniversity, The Netherlands).

AbstractClewe, O. 2016. Novel Pharmacometric Methods for Informed Tuberculosis DrugDevelopment. Digital Comprehensive Summaries of Uppsala Dissertations from the Facultyof Pharmacy 222. 70 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9718-7.

With approximately nine million new cases and the attributable cause of death of an estimatedtwo millions people every year there is an urgent need for new and effective drugs and treatmentregimens targeting tuberculosis. The tuberculosis drug development pathway is however notideal, containing non-predictive model systems and unanswered questions that may increase therisk of failure during late-phase drug development. The aim of this thesis was hence to developpharmacometric tools in order to optimize the development of new anti-tuberculosis drugs andtreatment regimens.

The General Pulmonary Distribution model was developed allowing for prediction of bothrate and extent of distribution from plasma to pulmonary tissue. A distribution characterizationthat is of high importance as most current used anti-tuberculosis drugs were introduced intoclinical use without considering the pharmacokinetic properties influencing drug distribution tothe site of action. The developed optimized bronchoalveolar lavage sampling design provides asimplistic but informative approach to gathering of the data needed to allow for a model basedcharacterization of both rate and extent of pulmonary distribution using as little as one sampleper subject. The developed Multistate Tuberculosis Pharmacometric model provides predictionsover time for a fast-, slow- and non-multiplying bacterial state with and without drug effect. TheMultistate Tuberculosis Pharmacometric model was further used to quantify the in vitro growthof different strains of Mycobacterium tuberculosis and the exposure-response relationships ofthree first line anti-tuberculosis drugs. The General Pharmacodynamic Interaction model wassuccessfully used to characterize the pharmacodynamic interactions of three first line anti-tuberculosis drugs, showing the possibility of distinguishing drug A’s interaction with drug Bfrom drug B’s interaction with drug A. The successful separation of all three drugs effect oneach other is a necessity for future work focusing on optimizing the selection of anti-tuberculosiscombination regimens.

With a focus on pharmacokinetics and pharmacodynamics, the work included in this thesisprovides multiple new methods and approaches that individually, but maybe more important thecombination of, has the potential to inform development of new but also to provide additionalinformation of the existing anti-tuberculosis drugs and drug regimen.

Keywords: pharmacokinetics, pharmacodynamics, PKPD, pharmacometric, nonlinear mixed-effects models, multistate tuberculosis pharmacometric model, general pharmacodynamicinteraction model, general pulmonary distribution model, tuberculosis, rifampicin, isoniazid,ethambutol

Oskar Clewe, Department of Pharmaceutical Biosciences, Box 591, Uppsala University,SE-75124 Uppsala, Sweden.

© Oskar Clewe 2016

ISSN 1651-6192ISBN 978-91-554-9718-7urn:nbn:se:uu:diva-303872 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-303872)

!

Things are only impossible until they're not

Jean-Luc Picard

Cover artwork: "Mycobacterium tuberculosis bacteria, the cause of TB" by NIAD, used under CC BY / Desaturated from original

List of Papers

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

I Clewe O, Goutelle S, Conte JE Jr, Simonsson USH. (2015) A

pharmacometric pulmonary model predicting the extent and rate of distribution from plasma to epithelial lining fluid and alveo-lar cells – using rifampicin as an example. Eur J Clin Pharma-col, 71(3):313-9

II Clewe O, Karlsson MO, Simonsson USH. (2015) Evaluation of optimized bronchoalveolar lavage sampling designs for charac-terization of pulmonary drug distribution. J Pharmacokinet Pharmacodyn, 42(6):699-708

III Clewe O, Aulin L, Hu Y, Coates AR, Simonsson USH. (2016) A multistate tuberculosis pharmacometric model: a framework for studying anti-tubercular drug effects in vitro. J Antimicrob Chemother, 71(4):964-74

IV Clewe O, Wicha SG, de Vogel C, de Steenwinkel JEM, Si-monsson USH. A model-informed pre-clinical approach for identification of exposure-response and pharmacodynamic in-teractions in early tuberculosis drug development. In manu-script.

Reprints were made with permission from the respective publishers.

List of Additional Papers

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

Wicha SG, Chen C, Clewe O, Simonsson USH. On perpetra-tors and victims: A general pharmacodynamic interaction mod-el identifies the protagonists in drug interaction studies. In manuscript.

Contents

Introduction ......................................................................................... 13 The need for improved tuberculosis therapy .................................. 13 Tuberculosis .................................................................................... 13 Treatment ........................................................................................ 14 Pharmacokinetics and pharmacodynamics ..................................... 16 Non-multiplying bacteria ................................................................ 18 Pharmacodynamic interactions ....................................................... 20 A deficient drug development pathway .......................................... 21 Model-informed drug development ................................................ 22 Modeling efforts within tuberculosis drug development ................ 24

Aims .................................................................................................... 26

Methods ............................................................................................... 27 Patient data ..................................................................................... 27 In vitro data ..................................................................................... 27

Bacteria ....................................................................................... 27 Natural growth assays ................................................................ 27 Time-kill assays .......................................................................... 28

General Pulmonary Distribution model .......................................... 29 Evaluation of bronchoalveolar lavage sampling designs ............... 29 The Multistate Tuberculosis Pharmacometric model ..................... 31 External validation of predicted bacterial numbers ........................ 32 In vitro antibacterial exposure-response relationships ................... 32 Isoniazid resistance ......................................................................... 33 Pharmacodynamic interaction assessment ...................................... 33 Software .......................................................................................... 35 Model development ........................................................................ 35

Results ................................................................................................. 36 General Pulmonary Distribution model .......................................... 36 Optimized sampling design for prediction of rate and extent of pulmonary distribution ................................................................... 38 The Multistate Tuberculosis Pharmacometric model ..................... 40 Exposure-response relationships .................................................... 44 Pharmacodynamic interactions ....................................................... 48

Discussion ........................................................................................... 53 General Pulmonary Distribution model .......................................... 53 A Multistate Tuberculosis Pharmacometric Model ........................ 54 Assessment of pharmacodynamic interactions ............................... 56

Conclusions ......................................................................................... 58

Populärvetenskaplig sammanfattning ................................................. 60

Acknowledgements ............................................................................. 62

References ........................................................................................... 63

Abbreviations

AC alveolar cells BAL bronchoalveolar lavage cfu colony-forming units CL clearance DDI drug-drug interaction dOFV delta OFV DOT directly observed therapy EBA early bactericidal activity EC50 concentration that gives 50% of Emax ELF epithelial lining fluid EMA European Medicines Agency Emax maximum effect EMB ethambutol FDA Food and Drug Administration FDC fixed-dose combination FO first order FOCE first order conditional estimation fu fraction unbound GPDI General Pharmacodynamic Interaction model HFS hollow fiber system IIV inter-individual variability INH isoniazid IOV inter-occasion variability k a rate constant ka absorption rate LOQ limit of quantification MDR-TB multidrug-resistant tuberculosis MIC minimum inhibitory concentration MTP Multistate Tuberculosis Pharmacometric model M. tuberculosis Mycobacterium tuberculosis NLME nonlinear mixed effect OD optimal design OFV objective function value PD pharmacodynamic PZA pyrazinamide RIF rifampicin

PK pharmacokinetic RSE residual standard error RMSE root mean square error RPF resuscitation-promoting factor SE standard error SSE stochastic simulation and estimation t time TB tuberculosis t1/2 half-life V distribution volume VPC visual predictive check pcVPC prediction corrected visual predictive check WT weight e epsilon, residual h eta, individual level random effect q theta, population fixed effect W omega, inter-individual variability covariance matrix S sigma, residual variability covariance matrix

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Introduction

The need for improved tuberculosis therapy Issued in the year 2000, the Cape Town Declaration of the Working Alliance for Tuberculosis (TB) Drug Development highlighted decades of absent progress and the dire need for regaining control of TB.1 With no real market incentive, fewer and fewer anti-tuberculosis drug programs had been kept active and thus, no new drugs were made available. Meanwhile, TB contin-ued to spread, claiming millions of victims each year. In 2012, signs of pro-gress were seen when the Food and Drug Administration (FDA) approved bedaquiline, the first new medicine aimed at TB in more than four decades.2 Following the approval of bedaquiline, in 2014 the European Medicines Agency (EMA) approved the drug delamanid, which was also aimed at drug-resistant TB.3 Despite the surge in research efforts following the drafting of the Cape Town declaration, TB is still a global health emergency. Annual TB statistics still include approximately nine million new cases and an esti-mated two million deaths.4 The needs for new drugs and to enhance existing treatments are thus still dire. Since the development of new drugs takes time and requires large investments, proper tools and strategies are required to decrease the risk of failure during late-phase drug development. This thesis focuses on the role of pharmacometric (PM) methods in optimizing the de-velopment of new anti-tuberculosis drugs and treatment regimens.

Tuberculosis Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis (M. tuberculosis). Pulmonary tuberculosis, the most common – but not ex-clusive – form of the disease, is an airborne contagion caused by inhalation of droplets spread by infected people. The inhaled bacteria make their way to the alveoli and distant airways where they proliferate and infiltrate tissue. Most people who are exposed to the bacteria are able to control the infection, but not get rid of it, via the immune response. The ability of the bacteria to survive in a non-active (latent), as opposed to an active multiplying form, is a trademark of the disease often referred to as latent TB infection (LTBI). Approximately 10% of people exposed to the bacteria develop an active disease, either immediately or at some point in their lifetime.4 Naturally, co-

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infection with human immunodeficiency virus (HIV) or an otherwise im-paired immune system increases susceptibility to the development of an active disease.4

Treatment Tuberculosis has historically been treated in various ways. For a long time, the only available way to deal with the disease was to isolate infected people in sanatoriums, providing them with fresh air and good nutrition. The first antibiotic with proven effectiveness against M. tuberculosis was streptomy-cin, purified from Streptomyces griseus.5 In 1946, streptomycin was the fo-cus of the first recorded randomized controlled clinical trial conducted by the TB Unit of the Medical Research Council in the United Kingdom.6 Although initially helpful, patients treated with streptomycin developed a resistance, which, unfortunately, severely limited the usefulness of streptomycin in treating TB patients. In 1949, a clinical study of para-aminosalicylic acid in combination with streptomycin was published and showed long-term effects in TB patients. From the mid-1950s, the combination of para-aminosalicylic acid, streptomycin and what was at that time the newly developed drug iso-niazid (INH), along with the Bacillus Calmette–Guérin (BCG) vaccine, re-duced mortality in the western world by almost 90%. However, the treatment duration was still long and efforts to reduce the length of treatment occupied researchers for decades. The introduction of rifampicin (RIF) in the 1970s resulted in a shortening of the treatment length to nine months, effectively cutting the treatment duration required at that time by 50%. Furthermore, when used in combination with pyrazinamide (PZA), another 3 months were eliminated. The current therapeutic regimen, which is used worldwide and recommended by the World Health Organization (WHO), lasts six months (short course) and consists of RIF, INH, ethambutol (EMB) and PZA.7 For drug-susceptible TB, under optimal conditions the short-course treatment regimen can achieve high cure rates,8 but in practice it is also associated with significant challenges, perhaps the most problematic of which is inadequate adherence to the treatment due to sheer length and adverse effects. The treatment regimen is complex at its core, consisting of two months of RIF, INH, EMB and PZA followed by an additional four months of RIF and INH (Figure 1).

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Figure 1. Standard treatment regimen for drug-susceptible tuberculosis The introduction of patient kits, which ensure the availability of a complete course of treatment, and fixed-dose combinations (FDC), which are formula-tions containing more than one of the anti-tuberculosis drugs, have com-prised two ways to address the problem of low adherence due to the com-plexity of the regimen. Supervised treatment in the form of directly observed therapy (DOT) is also a WHO-recommended component of a support pack-age that should address patients’ needs.7 Even though steps like these have been taken in order to reduce the complexity of the treatment regimen, im-plementation in developing countries, where the disease burden is the high-est, must be considered challenging. Naturally, as with all treatments, poor adherence due to adverse effects is an issue. Coping with potentially adverse effects for the required six months of treatment puts the most well-informed and motivated patient to the test. Consequently, alternative treatment regi-mens are naturally of great interest. A four-month regimen containing moxi-floxacin was recently evaluated, but unfortunately failed to exhibit non-inferiority (i.e., not worse than) compared with the standard six-month regi-men.8 Mycobacterium tuberculosis is often regarded as one of the oldest microbial threats and showcases an impressive ability to escape killing me-diated by both immune response and drug effects. The four different drugs comprising the treatment regimen all target different aspects and properties of the bacterial infection. Consequently, they are all needed for successfully curing the disease. Isoniazid is regarded as having the highest capacity to kill the bacteria of the four drugs and effectively reduces the bacterial load in the first days of treatment.9 This high early bacterial killing capacity is clearly demonstrated by having the highest early bactericidal activity (EBA) of the four drugs.10 Isoniazid is mainly metabolized in the liver by N-acetyltransferase (NAT-2), which shows genetic polymorphism resulting in classification of patients as either slow, intermediate or rapid metaboliz-ers.11,12 The relationship between clinical outcome and metabolic classifica-tion has been explored and patients with a rapid metabolic process have been

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suggested to have a higher risk of treatment failure.13,14 These patient also risk the emergence of resistance due to low exposure of INH.15 However, the clinical importance of INH monoresistance is a topic of debate.16–19 The function of INH is dependent on activation by the katG enzyme present in M. tuberculosis. Consequently, mutations in the katG enzyme risk rendering INH ineffective. Studies of in vitro INH time-kill curves with observed loss of INH effect have indicated both katG-related genetic and also efflux trans-porter-related phenotypic resistance.20,21 The impact of the observed in vitro resistance when extrapolating to clinical settings is unclear,22 partly because inclusion of EMB in the treatment regimen effectively reduces the risk of resistance development and loss of INH effect.23,24 The main function of RIF is to “sterilize” infected tissue by killing dormant persistent bacteria, which are thought to act as a pool of stagnant bacteria9 that could reinitiate infec-tion in favorable conditions. Resistance to both RIF and INH classifies the TB infection as a multi-drug resistant (MDR) disease for which the cure rate is low.4 RIF-resistance is considered a good marker of MDR in high-burden settings and has thus been prioritized over INH-resistance when developing susceptibility tests.25 Pyrazinamide also adds to the “sterilizing task”, but requires an acidic environment to be activated, which can be found in the pulmonary lesions formed during infection.26 The ability of PZA to kill a persister population of TB bacteria that was not effectively addressed before its introduction into the treatment regimen has made it a model prototype drug for targeting non-replicating persisters and, hence, an inspiration for efforts limited not only to TB, but for other persistent bacterial infections as well.27 The function of EMB is to prevent selection and or growth of drug-resistant bacteria during the early part of treatment, when bacterial drug sus-ceptibility is still unclear.28

Pharmacokinetics and pharmacodynamics During the revival of interest in TB drug development, the four-drug treat-ment regimen and the pharmacokinetic (PK) and pharmacodynamic (PD) properties of the drugs included have been re-evaluated. Because the drugs comprising the currently recommended TB treatment were developed before PK and PD were established components of drug development, there is a risk that important PKPD drug properties have been left unexplored and accord-ingly, a risk of suboptimal treatment efficacy. Research on this topic has resulted in questioning the clinical value of the widely recommended 600 mg dosing of RIF,29,30 resulting in the initiation of clinical studies evaluating the potential benefits and potential toxicity of increased doses of RIF.31 Fur-thermore, as the lengthy treatment duration is closely connected to the ina-bility of anti-tuberculosis drugs to clear tissue of nearly inactive or dormant bacteria that often reside in pulmonary lesions and in intracellular sites, the

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question of distribution properties has also been revisited. Characterization of distribution is fundamental for decisions on which tissue concentrations are most closely related to the observed effect. Hence, acquiring proper PKPD relationships based on plasma concentrations requires the plasma concentrations to actually reflect the concentrations that produce the ob-served effect. Slow distribution rates to the site of action pose a risk of intro-ducing displacements between plasma concentrations and the concentrations at the site of action and hence potentially skewing the PKPD relationship. Using a skewed PKPD relationship could thus result in sub-optimal dosing, for example. Skewed PKPD relationships could also be produced by the effect of differences in the fraction of unbound concentration in different in vitro and in vivo systems. Accounting for such differences is crucial for translational prediction efforts, where the site of action concentrations runs the risk of being different due to differences in the free fraction.

Due to the multitudes of tissues and cells found in the pulmonary tract, along with disease-induced changes (e.g. lesions), it can be challenging to characterize distribution properties. Different in vivo models have been sug-gested to represent human-like pathology, including the development of lesions.32,33 For these models, drug distribution has been quantified using different methods like high-performance liquid chromatography (HPLC) mass spectrometry and matrix assisted laser desorption/ionization (MALDI) mass spectrometry imaging,34 which provide valuable insight into the distri-bution properties of different anti-tuberculosis drugs. Quantifying drug con-centrations from pulmonary lesions, whether from humans or animals,35 naturally requires invasive or sacrificial sampling techniques. Semi-invasive sampling methods, such as bronchoalveolar lavage (BAL), do however ena-ble the quantification of drug concentrations from samples of the epithelial lining fluid (ELF) and alveolar cells (AC). Information on the extent of dis-tribution to extracellular and intracellular sites is often presented in compari-son to the plasma concentration.36 The accuracy and interpretation of measures involving ELF sampling have been raised and it is clear that link-ing concentrations quantified from such sampling procedures to clinical out-comes requires further investigation.37 However, it is not only important to assess whether sufficient concentrations are achieved, but also the rate at which distribution is carried out, on account of the simple fact that a slow distribution rate results in a different time of maximum concentration. This is illustrated in Figure 2, where a simulated plasma concentration is com-pared to simulated concentrations from various theoretical tissues exhibiting different distribution rates.

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Figure 2. Simulated tissue drug concentrations (solid lines) and plasma concentra-tion (dashed line) versus time after dose showing the impact of different distribution rates

Non-multiplying bacteria Rifampicin and PZA are often described as having sterilizing activity, which refers to the ability to kill bacteria responsible for post-treatment relapse. As previously discussed, this relapse is often attributed to the existence of dormant M. tuberculosis, representing bacteria that has very low metabolic activity.38 Dormant or non-multiplying bacteria are part of a simplified clas-sification that has been suggested to describe the cycle of M. tuberculosis growth.39 Although antibiotics are able to kill actively multiplying bacteria, they are extremely ineffective at killing these non-multiplying bacteria.40 The length of treatment required to achieve what is believed to be complete sterilization tells us something about the lack of effectiveness of the drugs currently used to combat non-multiplying bacteria. From a regulatory view-point, non-multiplying bacteria have been highlighted as important for eval-uating new drugs and their sterilizing activity against M. tuberculosis.41 This regulatory agency input is important, as historically, characterization of anti-tuberculosis drug activity has been performed using what is often referred to as logarithmic (log) bacterial cultures. In these types of cultures, most bacte-ria are in an active multiplying state, displaying an exponential or logarith-mic increase in the total bacterial number. The incorporation of assays that use stationary-phase bacterial cultures in the development of new drugs is regarded as an essential way to reduce the treatment duration, due to the

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possibility of evaluating the sought-after sterilizing effect.39 The difference between log and stationary-phase cultures comes down to the composition of the culture, with regards to the number of actively multiplying bacteria.42 Compared to log-phase cultures, as the name implies, stationary-phase cul-tures show no net growth. Stationary-phase cultures are commonly generated using various environmental control techniques, for example by regulating oxygen, nutrients or other growth-dependent factors. An example of bacteri-al growth from a hypoxia-driven in vitro system43 showcasing both a log and stationary phase is shown in Figure 3.

Figure 3. Example of the natural growth of M. tuberculosis as mean observed log10 colony-forming unit (cfu) versus time from a hypoxia-driven in vitro system. The bacterial culture is said to exist in a logarithmic state up until approximately 30 days (dashed line). After approximately 100 days (dashed line), the bacterial system is viewed as a stationary-phase system showing little net differences in the amount of bacteria.

Unfortunately, the use of stationary-phase cultures alone will not automati-cally allow for easy quantification of drug efficacy against dormant or non-multiplying bacteria. One major obstacle is that the measurement of colony-forming unit (cfu) counts only enables quantification of bacteria that will multiply on solid media. By definition, non-multiplying bacteria will not be captured using such assays. There is thus a gap between the continuum of growth states believed to exist in human hosts and what can be quantified using common cell-counting assays. Use of liquid-based assays, such as the Mycobacterial Growth Indicator Tube (MGIT) system, is suggested to repre-sent the potential to capture bacteria in more states than the use of solid me-dia-based assays.44 When it comes to growing bacteria and studying the ex-posure-response relationship of anti-tuberculosis drugs, another improve-

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ment is the Hollow Fiber System (HFS) TB model.45 This system was pio-neered as having the potential to mimic different PK concentration time-profiles found in humans, and mimicking different metabolic and physiolog-ical bacterial behaviors and states has recently been applied in TB research as an additional, complementary tool for the selection of dose and treatment regimens.46 The use of resuscitation-promoting factors (RPFs) has also of-fered a means of studying the presence of drug-persistent forms of M. tuber-culosis and the relationship between these bacterial forms and disease re-lapse in vivo.47

Pharmacodynamic interactions Due to the need for multiple drugs in TB treatment, there is a risk of drug-drug interactions (DDIs). Interactions can be both negative and positive in relation to treatment outcome. Pharmacokinetic interactions can lead to al-terations of concentration levels compared to monotherapy, and the conse-quent effect can often be attributed to dependencies of the same absorption, distribution or metabolic pathways. For TB, especially with the common concomitant therapy for HIV, this could lead to serious implications with regards to treatment outcome.48 Potential PK interactions for TB drugs when compared to PD interactions are quite extensively characterized and ac-counted for in drug development.49–52 A PD interaction is defined as an ef-fect that is more or less than the expected additivity, i.e. the sum of efficacy of the combined drugs in monotherapy. The two most commonly used crite-ria of additivity are Bliss Independence (BI)53 and Loewe Additivity (LA)54. The BI assumes that the effect of a drug at a certain concentration is inde-pendent of the presence of another drug and hence that the two drugs have different mechanisms of action.53,55 For two drugs, A and B, the Bliss non-interaction can be expressed as follows

!"# = !" + !# − !" ∙ !# (1)

where EAB is the fractional effect of the combination, and EA and EB are the individual effects of drugs A and B in combination. For drugs with a differ-ent maximum effect, the BI equation has been modified by normalising the effect of the more effective drug (EA) to 1 and the less effective one (EB) to the fraction of 1, i.e. EmaxB/EmaxA.

56 The LA defines a drug as non-interacting with itself and hence a fraction of the concentration of drug A, if potency is considered, can be replaced by drug B, leading to a similar effect as A alone. The LA criterion can be expressed as:

1 =)* + ,-

)*,-+

)+ * ,-

)+,- (2)

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where CA and CB are the concentration of drugs A and B, which individually gives rise to effect E, while CA(B) and CB(A) are the concentrations of drugs A and B which, in combination, produce the same effect E. Antagonism is indicated if the right-hand side of Equation 2 is >1 and synergy is suggested if it is <1. Limitations with the LA have been shown for certain scenarios involving drugs with different maximum effects.57 However, there is no def-inite answer to when which criterion is superior.55 The reason for the lack of characterization of anti-tuberculosis PD interactions could be attributed to multiple factors; the most probable reason is due to the limitations and use-fulness of the currently available methodologies. Graphical approaches, such as isobolograms,58 make interpretation of results difficult when the interac-tions are concentration-dependent. Model-based approaches using single59,60 or multiple-interaction parameters61 exist, but quantitative interpretation is difficult and in the case of single-interaction parameter usage, it might not reflect the whole response surface. Perhaps the most limiting factor from the viewpoint of anti-tuberculosis regimens is that most approaches are limited to interaction characterization of only two drugs.59,62 Classifying PD interac-tions with the terms antagonism and synergism is problematic to some ex-tent, as the definitions of the two differ somewhat based on the research area. In many microbiological-based studies, antagonism and synergism are de-fined as greater or less than a -2log drop in cfu compared to the effect ob-served during mono exposure. This definition makes less sense from a pharmacological viewpoint, where interactions are quantified on an effect-parameter level rather than through the total effect. Due to differences in the definitions, it can be difficult to compare characterized interactions. Never-theless, proper characterizations of PD interactions are crucial for the selec-tion of optimal combination regimens.

A deficient drug development pathway Regardless of the targeted disease, the development of new drugs requires enormous investments and vast amounts of time. Together with a high ob-served failure rate in late-phase drug development,63 this raises a concern for not only the drug industry, but also for patients, who are consequently de-nied proper treatment. A historical comparison of TB drug development is difficult due to sheer lack of development, but there is no doubt that the TB drug development pathway is lined with unanswered questions at all stag-es.64,65 This is perhaps made clearest by the fact that no new drugs targeting drug-susceptible TB have been approved for many years, and approval of the two most recent drugs targeting MDR-TB was accelerated based on data from phase II trials using surrogate endpoints that were likely to reflect clin-ical outcomes.66 Success in the clinical phase of drug development relies on the pre-clinical phase actually providing a proper selection of the most prom-

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ising drug candidates. Unfortunately, pre-clinical TB drug development re-search is represented by numerous old and new in vitro and in vivo systems in which unrepresentative growth conditions and non-human pathology are big obstacles. Deducing which pre-clinical assays are actually able to repro-duce the right PD properties of drugs and the conditions that the drugs must act under in the diseased host are crucial steps for establishing an effective drug development pathway for TB. Initiatives and projects, such as Pre-DiCT-TB and the Critical Path to TB Drug Regimens (CPTR), which focus on improving today’s deficient TB drug development pathway, constitute a new hope for improving not only the chances of transitioning the right drug candidates from the pre-clinical to clinical phase, but also establishing new regulatory approaches supporting innovative TB research – potentially providing findings that will help reduce the risk of late-phase drug develop-ment failure and meeting patients’ need for effective and manageable treat-ment.

Model-informed drug development Overcoming the gaps in TB drug development is a great challenge. As dis-cussed above, many of the shortcomings of the current anti-tuberculosis drugs and regimens can be traced back to a failure to properly characterize PKPD properties and relationships. In addition, the lack of effective new drugs targeting TB can be attributed to the reliance on non-predictive pre-clinical methods and the lack of integration of proper and applicable clinical biomarkers. There is thus a need for proper tools and strategies that can pro-vide a basis for informed decisions regarding improvements to the TB drug development pathway.

Pharmacometrics has been promoted as a methodology to rationalize and inform drug development through the application of mathematical and statis-tical methods for the characterization and prediction of PK and PD. In con-trast to the use of summary endpoints to describe PKPD relationships, PM models provide integration of the time-course of the relationships between exposure, effect and the underlying disease-specific mechanisms – thus providing valuable information for the evaluation of the rational use of exist-ing drug regimens and the development of new drugs.

When it comes to relating exposure and effect, the possibility of integrat-ing full-time course information as provided by PM models is superior to summary PD endpoints, such as minimum inhibitory concentration (MIC). The MIC is still the most widely used marker of antibiotic susceptibility, but it also has a number of disadvantages. Being a summary endpoint, it only reflects the activity at the time of the readout, telling us nothing about what has taken place regarding growth or kill before the readout.67 Use of the MIC in relation to drug PK through classification into a PK/PD index is often

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done to guide antibiotic dosage in vivo.68 The three commonly used indices include the fraction of the dosage interval in which the unbound concentra-tion is greater than the MIC (ƒT>MIC); the ratio of the total exposure of the unbound drug to the MIC (ƒAUC/MIC), and the ratio of maximum concen-tration of the unbound drug to the MIC (ƒCmax/MIC).69 However, the PK/PD indices incorporate the disadvantages of the MIC and add assumptions of appropriateness when extrapolating between different systems that could very well possess different PK.70

In PM research, one of the most common approaches for dealing with da-ta consisting of repeated measurements from different subjects is to pool all the data and estimate the population parameters by adjusting for correlations between the subject data. This approach is often referred to as population or non-linear mixed effects (NLME) modeling and can be used with both con-tinuous and categorical data. A NLME model can be broken down to fixed (population parameters) and random (variance in the population and between different subjects) effects. The random effects can then be divided into ex-plained variability and assigned to population parameters, most commonly as interindividual variability (IIV), interoccasion variability (IOV) and unex-plained variability, such as measurement errors, errors in data recording, model misspecification etc. The term “mixed effects” in NLME refers to the simultaneous handling of the fixed and random effects.

A description of the observation yij for an individual i at time tij is carried out by the function of the structural model f and residual error model func-tion h according to:

./0 = 1 2/0, 3 4, 5/, 6/, 7/ + ℎ 2/0, 3 4, 5/, 6/, 7/ , 9/0 (3)

in which g is a vector function of the population parameters (e.g. clearance) q, the vector of individual random effects hi, discrete design components (e.g. dose) ci and the vector of co-variate effects (e.g. weight) zi. The random effects ej and hi are expected to be normally distributed around zero, with a variance defined by the their respective co-variance matrix W and S. Finding the best model parameters for describing a set of observations is often car-ried out by maximum likelihood (ML) estimation. Simplified, ML estimation identifies the parameters that, within the boundaries of the model, maximize the probability of observing the data at hand.

The general goal of developing a PM model is to describe the set of ob-servations in the best way possible, and a distinction is often made between empirical and mechanistic modeling approaches. An empirical approach is generally viewed as less grounded in the pharmacological, biological and disease-specific processes. Mechanistic or semi-mechanistic approaches, however, strive to describe the data using prior knowledge about the drug and the biological system the approaches are to represent.

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As models are often developed not only to describe a set of data, but also to allow for predictions outside the observations, an approach based upon mechanistic pharmacological and biological process will be advantageous. However, fully mechanistic PM models are often too complex to allow for parameter estimation with a data-driven approach. Therefore, semi-mechanistic models representing mechanistic approaches that still allow for parameter estimation are often used. Previously, describing the relationship between PK and PD using semi-mechanistic approaches has successfully been done for antibiotics and bacteria in general.71–77

Modeling efforts within tuberculosis drug development Semi-mechanistic models describing the PK of all first-line anti-tuberculosis drugs have previously been developed.78–81 A proper description of the PD of anti-bacterial drugs requires taking the bacterial growth dynamics into ac-count. The simplest mechanism-based description of bacterial growth in-volves a single bacterial population that is capable of both growth and death.82,83 Previous efforts to describe the bacterial growth dynamics of M. tuberculosis have used exponential84,85 and bi-exponential86–89 models, the latter to describe the multiple visible growth states of M. tuberculosis and consequently to capture the biphasic bacterial elimination often observed in TB treatment.90

It has been suggested that effectively combating the development of re-sistance to antibiotics generally requires moving away from summary end-points such as the PK/PD indices.83 Efforts related to this notion include the exploration of INH resistance with PKPD models adapted from other anti-bacterial drugs.20

In recent years, the terms “systems pharmacology” and “quantitative sys-tems pharmacology” have gained popularity for emphasizing the application of biological processes to PKPD modeling. Linking TB-specific pathophysi-ological models91,92 with PKPD models of TB drugs has made it possible to take into account both drug effects and immune responses.93 In the TB field, physiologically based pharmacokinetic (PBPK) models that can be used to describe both whole-body or, in a lesser format, organ-specific PK have been used to describe, for example, drug distribution to the lungs94 and the effect of acetylator status on treatment outcome.14 Furthermore, the influence of patient adherence to therapy and of common retreatment regimens on treat-ment outcome have been described by describing the drug effects for differ-ent physiological locations of M. tuberculosis.95

It is clear that the use of more or less mechanistic PM models have pro-vided answers to some of the questions surrounding the historically deficient TB drug development pathway. However, some questions are still left unan-

25

swered and in order to provide simple and efficient treatment to the millions of people suffering from TB, these answers must be provided.

26

Aims

The aim of this thesis was to develop pharmacometric tools in order to optimize the development of new anti-tuberculosis drugs and treat-ment regimens. The specific aims were to: • Develop a non-drug-specific pharmacometric pulmonary model

that allows for predicting the rate and extent of distribution from plasma to epithelial lining fluid and alveolar cells for data from studies involving bronchoalveolar lavage sampling

• Develop and evaluate an optimized bronchoalveolar lavage sam-pling design that would allow for the characterization of both the rate and extent of distribution from plasma to pulmonary tissue

• Develop a pharmacometric template model that would facilitate pre-clinical studies of anti-tubercular drug effects on the different bacterial states of Mycobacterium tuberculosis

• Develop a model-informed pre-clinical approach for identification of exposure-response and characterization of pharmacodynamic interactions

27

Methods

Patient data Data from a previously published study96 was used for the PK analysis con-ducted in Paper I. The study population consisted of 40 adult subjects with-out TB, which included 10 women without acquired immunodeficiency syn-drome (AIDS), 10 men without AIDS, 10 women with AIDS, and 10 men with AIDS. The subjects received 600 mg RIF orally once a day for 5 days. Rifampicin plasma concentrations were measured on day 5 at approximately 2 and 4 hours post dose. Rifampicin concentrations in ELF and AC recov-ered by BAL were measured approximately 4 hours after administration of the last dose. Rifampicin concentrations were quantified by high-performance liquid chromatography and the urea dilution method was used to determine the concentration in ELF and AC.96

In accordance with the guidelines of the Institutional Review Board of the University of California, San Francisco, USA, written informed consent was obtained.

In vitro data Bacteria Two different genotypic strains of M. tuberculosis were used in papers III and IV. Mycobacterium tuberculosis H37Rv, a virulent strain common in laboratory research,97 was used in paper III. Mycobacterium tuberculosis Beijing 1585, a genotype of M. tuberculosis thought to be more closely as-sociated with MDR-TB,98,99 was used in paper IV.

Natural growth assays In paper III, M. tuberculosis strain H37Rv was grown in 7H9 medium sup-plemented with 10% albumin dextrose complex (ADC, Becton, Dickinson, UK) and containing 0.05% Tween 80 at 378C without disturbance for up to 200 days; 12 replicates were included. At different time points, the clumps of bacilli in each of a set of 10 mL cultures were broken up by vortexing with 2 mm diameter glass beads for 5 minutes, followed by sonication in a

28

water bath sonicator (Branson Ultrasonic, USA) for 5 minutes to obtain an evenly dispersed suspension of bacilli. Viability was estimated by plating a series of 10-fold dilutions of the cultures on 7H11 agar medium supplement-ed with oleic albumin dextrose complex (OADC, Becton, Dickinson, UK) and defined as cfu/mL.

In paper IV, M. tuberculosis genotype strain Beijing VN 2002-1585 (BE-1585) was cultured in Middlebrook 7H9 broth (Difco Laboratories, Detroit, MI, USA) supplemented with 10% oleic acid-albumin-dextrose-catalase enrichment (OADC; Baltimore Biological Laboratories, Baltimore, MD, USA), 0.5% glycerol (Scharlau Chemie SA, Sentmenat, Spain) and 0.02% Tween 20 (Sigma Chemical Co., St Louis, MO, USA), under shaking condi-tions at 96 rpm at 37°C. Vials with M. tuberculosis suspensions were stored at -80°C. Cultures on solid medium were grown on Middlebrook 7H10 agar (Difco), supplemented with 10% OADC and 0.5% glycerol for 28 days at 37°C with 5% CO2.

Time-kill assays Two different in vitro time-kill assays were used in papers III and IV.21,43 In paper III, log-phase M. tuberculosis H37Rv (grown to 4 days) was incubated with 0, 0.25, 0.5, 1, 2, 4, 8 and 16 mg/L RIF at 37°C with no replicates. Sta-tionary-phase cultures (grown to 100 days) were incubated with 0, 0.5, 1, 2, 4, 8, 16, 32 and 64 mg/L RIF at 37°C with two replicates. Viability of the cultures was determined by cfu counting at days 0, 2, 5, 10, 15, 20 and 30 after drug exposure for the log-phase cultures and at days 0, 3, 6, 10 and 14 after drug exposure for the stationary-phase cultures.

In paper IV, the concentration and time-dependent killing capacities of INH, RIF and EMB were studied by subjecting highly metabolically active (log-phase) M. tuberculosis cultures to anti-TB drugs at 4-fold increasing concentrations for 6 days at 37°C under shaking conditions at 96 rpm. The tested concentrations were based on the maximum free drug concentrations (fCmax) of the individual anti-TB drugs ranging from 4x fCmax to 1/1024x fCmax comprising a representative range of drug concentrations for studying in vitro drug activity. As for RIF, a concentration of 16x fCmax was added considering the high protein binding of this agent. To avoid drug carry-over to subculture plates, samples were centrifuged at 14000xg and subcultured onto solid medium. Plates were incubated for 28 days at 37°C with 5% CO2

to determine colony-forming units (cfu) counts. All experiments were per-formed in duplicates. In the combination experiments, the anti-TB drugs were tested using combinations of 4x, 1/16x and 1/1024x fCmax. In the dual combinations, INH was combined with RIF or EMB. Rifampicin was also combined with EMB. In the triple combination, INH and RIF were com-bined with EMB.

29

General Pulmonary Distribution model A previously published RIF plasma PK model that included an enzyme turn-over model accounting for RIF auto induction was used to describe RIF plasma PK.78 The impact of allometric scaling on apparent clearance and distribution volume was assessed by evaluating four different basic turn-over models: (1) no scaling; (2) allometric scaling using bodyweight as the size descriptor; (3) allometric scaling using normal fat mass (NFM) as the size descriptor, and (4) allometric scaling using fat free mass (FFM) as the size descriptor. The ELF and AC drug distribution was described using two com-partments: :)-;<:=

= >?@A ∙ B -;<CDEFGE

∙ "CDEFGEHCDEFGE

− I?@A 4

:)*J:=

= >") ∙ B *JCDEFGE

∙ "CDEFGEHCDEFGE

− I") 5

where C is concentration and kELF and kAC are the rate constants for the trans-fer of drug from the plasma to ELF or AC, respectively. RELF/plasma and RAC/plasma are the ELF/plasma and AC/plasma concentration ratios, respec-tively, at pseudo steady-state. Aplasma/Vplasma is the concentration of drug pre-dicted in the plasma compartment at time t, with Aplasma being the amount of drug in plasma and Vplasma being the apparent plasma volume of distribution. To derive the ratio of ELF and AC to unbound plasma concentrations, (RELF/unbound-plasma) and (RAC/unbound-plasma), respectively, RELF/plasma, and RAC/plasma were divided by free fraction of RIF in plasma.

Evaluation of bronchoalveolar lavage sampling designs For the development and evaluation of the optimized BAL sampling designs, a number of scenarios were constructed using the General Pulmonary Distri-bution model adapted from paper I, assuming two possible distribution char-acteristics: fast and slow. In the fast distribution scenario, the rate of distri-bution (k) between plasma and the pulmonary tract was 41.6 h-1, equivalent to an almost instantaneous distribution (1 minute) of drug from plasma to the pulmonary tract. In the second scenario, a slow (2-hour) distribution rate (k = 0.35 h-1) between plasma and the pulmonary tract was assumed. The study scenarios were varied with regards to samples taken per subject (1 or 2) and sample size (10, 20, 30 or 50 subjects). For the 1-sample-per-subject design, half of the study population was sampled at the early time point and the oth-er half at the late time point. In the evaluation of sampling designs, a RIF plasma PK model was used as an example of a drug plasma PK model.78 A

30

criterion for the sampling design was that a maximum of two samples was to be taken from the same individual within a 24-hour time-frame. Further-more, the approach assumed that the plasma concentration profile of the studied drug and the limit of quantification (LOQ) for the drug in the BAL sample were known. Typical plasma concentrations were simulated with the plasma PK model developed in paper I. Only one pulmonary submodel (Equation 6) was used for the evaluation of the optimized sampling design. :):== > ∙ B ∙ "CDEFGE

HCDEFGE− I 6

This one pulmonary compartment could represent the distribution from plasma to ELF, AC or both. Based on the simulated plasma concentration versus time profile, two time points for BAL sampling were selected. These two samples need to be taken at two time points where the plasma concentra-tion is the same, i.e. one sample in the rising part of the plasma concentration time profile, and one in the declining part of the plasma concentration time profile. In addition, the time points must be selected in order to maximize the likelihood that the BAL concentrations are above the BAL LOQ. The sam-pling time points chosen, based on the plasma concentration time profile and the BAL LOQ, were reevaluated based on correspondence between the plasma concentrations in the early and late samples, and the extent of pul-monary concentrations >BAL LOQ at the time of sampling. Based on this, an initial sampling time at 1 hour after dose was chosen. The late sample should be taken in the declining part of the time concentration profile, at a time point when the plasma concentration corresponds with (i.e. equals) the plasma concentration at the first sampling time point and is > the BAL LOQ. In this case, 13 hours was the corresponding time point with the 1 hour early sample.

1000 datasets were created for each distribution and sampling scenario using the Stochastic Simulation and Estimation (SSE) tool provided in the Perl speaks NONMEM (PsN) software.100 Estimations of k, R, residual error, and the IIV in R where applicable were carried out using the simulated pul-monary data. The plasma PK parameters including IIV estimates from the model developed in paper I were fixed, but the simulated plasma concentra-tions were retained in the model, i.e. a PPP&D approach.101 The evaluation of the sampling design was assessed by calculations of relative bias (%) and relative root mean square error (rRMSE) (%) in the parameter estimates according to:

BLMN2OPLQONR = 100 ∙ TU

VW=XY=Z[VX=Z[VX/ 7

BLMN2OPL\]]2^LN_R`aN\LL\\]\ = 100 ⋅ TU

VW=XY=Z[VX c

=Z[VXc/ 8

31

where esti represents the estimated typical population parameter value and truei represents the true typical population estimate for the parameter.

The Multistate Tuberculosis Pharmacometric model To enable a semi-mechanistic description of the in vitro antibacterial expo-sure on the different states of M. tuberculosis, characterization of the in vitro natural growth of the bacteria without drug effect as quantified by cfu count-ing was performed. The basis of the model development was a system with three differential equations (Equations 9-11), representing fast (F), slow (S) and non-multiplying (N) bacteria, for which different growth functions and transfer rates were evaluated. :A:== >d ∙ e + >fA ∙ g + >UA ∙ h − >Af ∙ e − >AU ∙ e 9

:f:== >Af ∙ e + >Uf ∙ h − >fA ∙ g − >fU ∙ g 10

:U:== >AU ∙ e + >fU ∙ g − >Uf ∙ h 11

As the cfu count reflects only the bacteria that are able to multiply on solid media, only the numbers in the fast and slow-multiplying states, as a sum, were part of the model prediction of the data. Furthermore, as the cfu count is a summary measure of total viable bacteria, the inoculum is the sum of the initial bacterial numbers in the fast-multiplying (F0) and slow-multiplying (S0) states. A model with estimation of both F0 and S0 was compared with models with either F0 or S0 fixed to 0, representing a situation in which all bacteria would be in the fast-multiplying or slow-multiplying state at the time of inoculum. The growth rates of the fast-multiplying and slow-multiplying bacteria were evaluated using different growth functions, includ-ing exponential, gompertz and logistic functions. In the simplest model structure, still involving the three bacterial states, bacterial movement be-tween the different states can be described via first-order linear rate con-stants relating to the transfer from one state to another. The transfer rate of fast-multiplying to slow-multiplying bacteria (kFS) was evaluated as a con-stant transfer rate and as a transfer rate that incorporated stimulation of trans-fer by the total number of bacteria in the fast, slow and non-multiplying states. Furthermore, time dependency in the fast-to-slow transfer was evalu-ated using a linear and an Emax and an exponential function. Initial runs re-vealed that the rate of transfer from N to F (kNF) was close to zero and was therefore assumed to be negligible and thus fixed to 0 in the model develop-ment.

32

To account for potential differences in the in vitro assays and experi-mental conditions, a reassessment of the growth and bacterial system param-eters was evaluated for significance when including additional natural growth data.

External validation of predicted bacterial numbers To provide an external and biological validation of the MTP model-predicted bacterial numbers in the fast and slow-multiplying bacterial state, data comprising the rate of protein synthesis over time were used.102 The protein synthesis was quantified by measuring the rate of incorporation of radiolabeled [35S]methionine into proteins of M. tuberculosis H37Rv from log-phase to stationary-phase growth. Sampling was conducted at 4, 10, 20, 30, 40, and 50 days. The incorporation of radiolabeled [35S]methionine into total proteins correlated as a percentage to the mean of the MTP model for natural growth predicted typical fast-multiplying bacterial number out of the predicted typical fast plus slow-multiplying bacterial number, i.e. 100×(F/F+S).

In vitro antibacterial exposure-response relationships The effects of in vitro drug exposure were evaluated as inhibition of growth and kill rates on each of the three bacterial states using linear functions, or-dinary Emax functions, and sigmoidal Emax functions. Inhibition of growth by the drug effect (Einhibition) was implemented in the differential equation sys-tem as a fractional inhibition, as exemplified for the fast-multiplying bacteri-al state (Equation 12), whereas the drug effect (Ekill) as a kill rate of the fast, slow and non-multiplying states was implemented as an additive bacterial killing-rate constant imposed by the drug, as exemplified for the slow-multiplying bacterial state (Equation 13). :A:== >d ∙ 1 − !/ij/k/=/li ∙ e + >fA ∙ g + >UA ∙ h − >Af ∙ e − >AU ∙ e

12

:f:== >Af ∙ e + >Uf ∙ h − >fA ∙ g − >fU ∙ g − !m/nn ∙ g 13

In paper III, evaluation of the drug effect was conducted by evaluating all possible combinations of effect functions on the three different bacterial states as either inhibition of growth or as a kill rate. The evaluation of all possible combinations of drug effect functions was followed by a step in which the identified functions were reduced to their simpler forms in order

33

to confirm the appropriateness of the final model. The complete evaluation of all possible combinations of effect functions and effect sites is cumber-some and prone to introduction of human errors. Therefore, a more efficient approach to the evaluation of the combination of drug effect functions and effect sites was used in paper IV.103 This evaluation involved a four-step approach in which an initial univariate analysis on each effect site was fol-lowed by a second and third step, in which combinations of all effect func-tions and sites were evaluated. The last step, using the identified functions and effect sites from step three, involved performing a backward elimination step on each effect site.

Isoniazid resistance In paper IV, the observed decrease in INH susceptibility during mono expo-sure was evaluated as an adaptive resistance, as a loss of active drug concen-tration and by the introduction of an additional bacterial state representing a drug-resistant sub-population. The adaptive resistance was evaluated using a function for development of resistance which was dependent on INH con-centrations (CINH), previously used to describe resistance by Pseudomonas aeruginosa to gentamicin.76 The adaptive resistance (ARon; Equation 14) was governed by the fraction of adaptive resistance relative to no resistance (ARoff; Equation 15). At the start of the experiment all bacteria were as-signed to the ARoff state.

:"opq:=

= >li ∙ IrUs ∙ tBluu − >luu ∙ tBli 14 :"opvv:=

= >luu ∙ tBli − >li ∙ tBluu 15

where >liand >luudescribe the rate of development of resistance and the rate of return to susceptibility, respectively. As no data was available sup-porting resistance reversal, koff was fixed to 0. The adaptive resistance was evaluated as affecting either the maximum effect (EMAX) or the potency (EC50) of the inhibition of growth and/or kill rates that were identified as describing the INH anti-bacterial effect in mono exposure.

Pharmacodynamic interaction assessment Assessment of in vitro PD interactions between drugs was carried out using the General Pharmacodynamic Interaction (GPDI) model implemented into the BI additivity criterion.104 The assessment was performed in steps, the first of which was evaluation of interactions in duo combinations. During

34

this step, the drug effects identified in mono exposure were fixed. Thereaf-ter, the combination of three drugs was evaluated using fixed estimates of the parameters related to natural growth and the mono and duo-combination data. The final step comprised an attempt to estimate all parameters simulta-neously. To account for differences in the maximum effect (Emax), and ac-cording to the BI criterion, scaling of each individual drug Emax from mono exposure by the largest predicted Emax was performed.56 If a slope parameter was identified in the evaluation of the effect from mono exposure, the BI additivity was approximated by effect addition with scaling by Emax, i.e. !"# = !" + !#due to the minor contribution of !" ∙ !# at concentrations well below the EC50 when slope models were identified. An example of the combined effect of EAB with potential PD interactions between two drugs (A and B) that display drug effects described by an Emax model is given in Equa-tion 16, while an example of two drugs (C and D) described by an Emax and linear model, respectively, is given in Equation 17

! =?GEw*∙)*

?)xy*∙ Tz{|}+,*∙J+-Jxy+,*∙J+

∙)*+

?GEw+∙)+

?)xy+∙ Tz{|}*,+∙J*-Jxy*,+∙J*

∙)+ 16

! =?GEwJ∙)J

?)xyJ∙ Tz{|}~,J∙J~-Jxy~,J∙J~

∙)J+ m~

Tz{|}J,~∙JJ-JxyJ,~∙JJ

∙ I� 17

where CA, CB, CC, CD are the respective concentrations of drugs A, B, C and D. The maximum fractional change of the respective PD parameter due to interaction between drugs A, B and C, D is reflected by the interaction pa-rameters ÄhÅ",#, ÄhÅ#," and ÄhÅ),�, ÄhÅ�,) . For an interaction term applied to EC50 an INT parameter estimated value of zero suggests no interaction; a positive value suggests an increased EC50 and a negative value suggests a decreased EC50. As a range of drug concentrations was studied in this work, the possibility of a non-linear interaction relationship across the concentra-tion range existed. This was evaluated using the parameters !IÇÉ",#,

!IÇÉ#,", !IÇÉ),�and !IÇÉ�,)which reflected the concentration of drugs A, B, C and D at which 50% of the maximum fractional increase was predicted. As a starting point, the least complex GPDI model was used, in which ÄhÅ",# = ÄhÅ#,", !IÇÉ",# = !IÇÉ"and !IÇÉ#," = !IÇÉ#, where !IÇÉ"and

!IÇÉ#where the EC50 values of drug A and B are fixed to estimates obtained only from data of mono exposure. The estimate of separate INT and interac-tion EC50 parameters was then evaluated for statistical significance. Reduc-

tion of the interaction term 1 + rUÑ*,+∙)*?)xy*,+∙)*

to an on/off function 1 +

ÄhÅ",# was also evaluated. After the evaluation of the PD interaction of duo combinations, the triple drug combination was assessed. The possibilities of

35

a non-additive interaction of the combination of drugs RIF+INH and EMB, INH+EMB and RIF and RIF+EMB and INH were evaluated by adding a modulator term (ÄhÅ",#|)) to the interaction term identified for the duo combinations (Equation 18).

! =?GEw*∙)*

?)xy*∙ Tz{|}+,*∙J+-Jxy+,*∙J+

∙)*+

?GEw+∙)+

?)xy+∙ Tz{|}*,+∙ áà

{|}*,+|J∙JJ-Jxy*,+|J∙JJ

∙J*

-Jxy*,+∙J*∙)+

18

Software All data analysis was performed using the software NONMEM (versions 7.2, 7.3; Icon Development Solutions, Ellicott City, USA, http://www.iconplc.com/technology/products/nonmem),105 using the first-order conditional estimation method with interaction (FOCE INTER) or Laplace. R (R Foundation for Statistical Computing, http://www.R-project.org)106 was used for data management and Xpose (Department of Pharmaceutical Biosciences, Uppsala University, Sweden, http://xpose.sourceforge.net) was used for graphical assessment of results.107 PsN (Department of Pharmaceutical Biosciences, Uppsala University, Swe-den, http://psn.sourceforge.net)100 was used for running models and generat-ing VPCs and pcVPCs. Numerical model comparison and a run record were used and maintained with the software Pirana (Pirana Software & Consult-ing, Denekamp, The Netherlands, http://www.pirana-software.com).108

Model development

Model evaluation was done using goodness-of-fit (GOF) plots, precision in parameters, objective function values (OFVs), scientific plausibility, visual predictive checks (VPC) and prediction-corrected visual predictive checks (pcVPC). The OFV given by NONMEM, which approximates 2 log(likelihood) of the data, given the model, was used in likelihood-ratio testing (LRT) to compare nested models. The difference in OFV (dOFV) is approximately c2 distributed and dependent on the significance level and degrees of free- dom. Analysis was conducted using a significance level of 0.05, which corresponds to a critical dOFV of 3.84 for 1 degree of freedom.

36

Results

General Pulmonary Distribution model A schematic representation of the final General Pulmonary Distribution model is shown in Figure 4.

Figure 4. Schematic representation of the final rifampicin (RIF) lung and plasma pharmacometric submodels. Drug is transferred via a number of transit absorption compartments to the absorption compartment and further via the rate constant ka to the central plasma compartment. Rifampicin autoinduction was modeled with an enzyme turnover model in which the RIF plasma concentrations increased the en-zyme production rate (kENZ), which in turn increased the enzyme pool in a non-linear fashion by means of an Emax-model. Cp is the RIF plasma concentration and Emax is the maximal autoinduction of CL/F. EC50 is the RIF concentration resulting in 50% of the maximal autoinduction of CL/F. The ELF and AC drug distribution submod-els were described using two parameters for each submodel. The rate of distribution of drug from plasma to ELF and AC was captured by two distribution rate constants, kELF and kAC, respectively. The extent of distribution to ELF and AC was described by unbound ELF/plasma concentration ratio (RELF/unbound-plasma) and unbound AC/plasma concentration ratio (RAC/unbound-plasma).

37

The final model included allometric scaling using FFM. This model had a 22-point lower OFV compared to a model without scaling. Models with allometric scaling using NFM and body weight had an OFV drop of 22 and 18, respectively, compared to the model without scaling. Scaling with FFM and NFM had the same OFV value. However, the former was selected due to fewer parameters compared to a model with NFM scaling. To mimic an al-most instantaneous distribution from plasma to the lungs, the rate constants for the transfer of drug from the plasma to ELF or AC, kELF and kAC, respec-tively, were fixed to an equivalent of an equilibration half-life of about 1 minute (instantaneous). The final model predicted the plasma, AC, and ELF data well. The RELF/plasma and RAC/plasma were predicted to be 0.26 and 1.1, respectively. When adjusting for free fraction of 20% in plasma, the un-bound RELF/unbound-plasma and RAC/unbound-plasma ratios were predicted to be 1.28 and 5.5, respectively. Interestingly, when the RELF/plasma and RAC/plasma were not corrected for unbound fraction in plasma, the model predicted the expo-sure in ELF to be lower than in plasma, whereas the reverse was seen when accounting for the protein binding in plasma. The parameter estimates of the final model are shown in Table 1.

Table 1. Parameter estimates and relative standard errors of the final General Pulmonary Distribution model

Parameter Estimate (95% CI) Relative standard error (%)

TV(CL/F)STD (L×h-1) 3.85 (2.26-8.68) 3.1 TV(Vc/F)STD (L) 76.6 (60.85-88.83) 2.7 MTT (h) 0.71a N 1a Emax 1.04a EC50 (mgL-1) 0.0705a kENZ (h-1) 0.0036a kELF (h

-1) 41.58a RELF/plasma 0.26 (0.21-0.31) 4.3 RELF/unbound-plasma 1.28b kAC (h

-1) 41.58a RAC/plasma 1.1 (0.92-1.35) 6.2 RAC/unbound-plasma 5.5c IIVCL/F (%) 88.8 (9.43-106.77) 24.2 Plasma proportional error (%) 35.2 (25.11-45.42) 3.6 ELF proportional error (%) 40.7 (30.26-54.76) 2.9 AC proportional error (%) 37.1 (22.95-46.91) 7.3 aFixed parameter, b,cCalculated post estimation

38

Optimized sampling design for prediction of rate and extent of pulmonary distribution The simulated plasma profile, using the plasma PK model from paper I, along with the chosen sampling time points of 1 and 13 hours are shown in Figure 5.

Figure 5. Simulated typical plasma concentrations versus time after a single 600 mg oral dose (black solid line) based on final estimates from the population pharmaco-kinetic model. The grey dashed line represents the limit of quantification (LOQ), 0.05 mg/L, of rifampicin in bronchoalveolar lavage (BAL) fluid (epithelial fluid or alveolar cells). The identified optimized rifampicin BAL sampling time points are marked on the x-axis and were 1 and 13 hours post dose. The sampling time points should be as early and as late as possible within the study time-frame and were se-lected from the simulated plasma concentration time profile based on correspond-ence in plasma concentrations: plasma concentrations ≥ LOQ in BAL fluid and max-imizing BAL fluid concentrations ≥ LOQ in BAL fluid assuming a slow distribution.

For the fast pulmonary distribution scenarios using a 1-sample-per-subject design, both rRMSE and relative bias decreased for the parameter estimates of R and the residual error with increasing sample size. A slight increase in relative bias was observed for the R parameter. The evaluation using the same distribution rate (fast) but with 2 samples per subject showed similar trends, but with an overall lower relative bias and rRMSE in the parameter estimates for the different study population sizes compared to the 1-sample-per-subject scenarios. The scenarios with a fast distribution that included estimation of IIV in the R parameter showed similar trends as the scenarios

39

without IIV, but with slightly larger rRMSE and bias in the R and residual error parameters.

The result from the slow distribution scenarios and the 1-sample-per-subject designs showed an overall decrease in rRMSE for the parameter estimates with an increasing number of subjects. Relative bias for the k and R parameter estimates, however, increased with increased study population sizes. For these scenarios, estimation of the rate parameter k was possible in contrast to the fast distribution scenarios, and included in the evaluation. The rRMSE and relative bias for the 1 and 2-sample-per-subject slow distribution scenarios were of similar magnitude with slightly smaller rRMSE for the 2-sample-per-subject design. The scenarios with a slow distribution that in-cluded estimation of IIV in the R parameter showed similar trends as the scenarios without IIV, but with slightly larger rRMSE and bias in the R and residual error parameters. The results from the evaluation of the different scenarios are shown in Figure 6.

40

Figure 6. Results from the evaluation using the different distribution scenarios. Relative root mean square error (rRMSE) (left) and relative bias (right) in the esti-mate of the bronchoalveolar lavage (BAL) fluid/plasma concentration distribution ratio (R) and the residual error for the scenarios for A. fast distribution and 1 sample per subject, B. fast distribution and 2 samples per subject, C. slow distribution and 1 sample per subject, D. slow distribution and 2 sample per subject, E. fast distribution and 2 samples per subject including interindividual variability in the R parameter, F. slow distribution and 2 samples per subject including interindividual variability in the R parameter. The different sample sizes are given in different grey shades.

The Multistate Tuberculosis Pharmacometric model The final Multistate Tuberculosis Pharmacometric (MTP) model described the 200-day in vitro growth of M. tuberculosis utilizing a fast, a slow and a non-multiplying state (Figure 7).

41

Figure 7. The multistate tuberculosis pharmacometric model. F, fast-multiplying state; S, slow-multiplying state; N, non-multiplying state; kG, growth rate of the fast-multiplying state bacteria; kFS, time-dependent linear rate parameter describing transfer from fast to slow-multiplying state; kSF, first-order transfer rate between slow and fast-multiplying states; kFN, first-order transfer rate between fast and non-multiplying states; kSN, first-order transfer rate between slow and non-multiplying states; kNS, first-order transfer rate between non-multiplying and slow-multiplying states.

Estimation of the initial bacterial numbers F0 and S0 resulted in a significant decrease in OFV when compared with fixing either F0 or S0 to 0. Growth of the fast-multiplying bacteria, kG, was best described by a gompertz function. Addition of any of the growth functions to the slow-multiplying state did not result in any significant improvement in the OFV. The rate of transfer be-tween the fast and slow-multiplying states, kFS, was best described with a time-dependent linear function, which described the data better than any of the other functions evaluated. A VPC of the final MTP model is shown in Figure 8. In Figure 11 in the panel entitled natural growth, the predicted bacterial numbers in the different states over time are shown as a mean of the 12 replicates of the 200-day in vitro natural growth data.

!42

Figure 8. Visual predictive check-plot of the final multistate tuberculosis pharma-cometric model using H37Rv M. tuberculosis in vitro without drug (natural growth). Open circles are observed log10 cfu data; the solid line is the median of the ob-served data and the dashed lines are the 5th and 95th percentiles of the observed data. The top and bottom shaded areas are the 95% CIs for the 5th and 95th percen-tiles of simulated data. The middle shaded area is the 95% CI for the median of the simulated data.

The external validation of the final model describing the natural growth showed a strong correlation (R2 =0.98) between the rate of incorporation of radiolabeled methionine into proteins by the bacteria and, as a percentage, the mean of the natural growth model predicted typical fast-multiplying bac-terial number out of the predicted typical fast plus slow-multiplying bacterial number, i.e. 100!(F/F+S). The final estimates of the MTP model can be found in Table 2.

43

Table 2. Parameter estimates of the final Multistate Tuberculosis Pharmacometric model applied to cfu data from rifampicin log and stationary-phase M. tuberculosis H37Rv cultures

Parameter Estimate RSE (%)

käã (days-1) 0.206 1

kåç (days-1) 0.897·10-6 1.2

kéç (days-1) 0.186 4.3

kéå (days-1) 0.0145 4.9

kçé (days-1) 0.123·10-2 2.7

kåé@/iè

(days-2) 0.166·10-2 1.6

FÉ (mL-1) 4.1 2.9

SÉ (mL-1) 9770 2.4

Bìãî (mL-1) 242·106 4.5

ωF0 (%) 473.3

5.9

kG, growth rate of the fast-multiplying state bacteria; kFN, first-order transfer rate between fast and non-multiplying state; kSN, first-order transfer rate between slow and non-multiplying state; kSF first-order transfer rate between slow and fast-multiplying state; kNS, first-order transfer rate between non and slow-multiplying state; F0 initial fast-multiplying state bacterial number; S0 initial slow-multiplying state bacterial number; Bmax, system-carrying capacity; ωF0, variability in F0 ex-pressed as coefficient of variation; RSE, relative standard error reported on the ap-proximate standard deviation scale.

agrowth=F·kG ·log(Bmax/F+S+N)

bkFS = kFSLin

44

Exposure-response relationships Proper characterization of the exposure-response relationship relies on a solid description of the growth characteristics without drug effect. Differ-ences in start inoculum and experimental conditions, for example, can influ-ence the natural growth time-course, making addition and joint analysis of data from different experiments cumbersome. Thus, differences in the bacte-rial system parameters, such as growth and start inoculum, must be evaluat-ed. Therefore, for the natural growth data associated with the drug exposure assays, the MTP model was initially applied in evaluations estimating the growth rate, the initial fast and slow-multiplying bacterial number and the maximum system-carrying capacity. This resulted in the use of experiment-specific growth parameters for the log and stationary-phase systems in paper III (Table 3). The same approach was applied in paper IV when evaluating differences between the estimates from the original MTP model (paper III) and those estimated using the M. tuberculosis B1585 associated natural growth data (Table 3).

Table 3. Parameter estimates from different natural growth assays

Parameter Estimate RSE (%)

käï (days-1) 0.102 12.5

FÉï (mL-1) 674·103 39.2

Bìãîk (mL-1) 1410·106 0.8

>dñ (days-1) 0.796 5

eÉñ (mL-1) 209·103 17

gÉñ (mL-1) 324·103 12

a Log-phase cultures (paper III) b Stationary-phase cultures (paper III) c M. tuberculosis B1585 Log-phase cultures (paper IV)

45

In paper III, the RIF effect on the bacterial system was linked to the MTP model by including a RIF pharmacokinetic model (Figure 9). The RIF phar-macokinetic model consisted of one compartment accounting for RIF in vitro PK.

Figure 9. Schematic illustration of the Multistate Tuberculosis Pharmacometric model with inclusion of rifampicin pharmacokinetics (drug model). CRIF, rifampicin (RIF) concentration; F, fast-multiplying state; S, slow-multiplying state; N, non-multiplying state; kG, growth rate of the fast-multiplying state bacteria; kFS, time-dependent linear rate parameter describing transfer from fast to slow-multiplying state; kSF, first-order transfer rate between slow and fast-multiplying states; kFN, first-order transfer rate between fast and non-multiplying states; kSN, first-order transfer rate between slow and non-multiplying states; kNS, first-order transfer rate between non-multiplying and slow-multiplying states; FGk, linear drug-induced inhibition of fast-multiplying state growth; FDEmax , maximum achievable drug-induced fast-multiplying state kill rate; FDEC50 , concentration at 50% of FDEmax ; SDEmax , maximum achievable drug-induced slow-multiplying state kill rate; SDEC50, concentration at 50% of SDEmax ; NDk, non-multiplying state kill rate.

The effect of RIF on the different bacterial states was initially evaluated separately for the log-phase and stationary-phase cultures, where applicable, as either an inhibition of growth or a kill rate. A simultaneous evaluation using the log-phase and the stationary-phase data was also performed and the final simultaneous fit model included inhibition of fast-multiplying bacterial growth, kill rate of the fast-multiplying bacteria, kill rate of the slow-multiplying bacilli and kill rate of the non-multiplying bacilli. The final dif-ferential equations system of the MTP model with inclusion of RIF exposure response on log and stationary-phase cultures was as follows:

46

:A:== e ∙ >d ∙ M]3

#GEwAzfzU

∙ 1 − eóm ∙ IorA + >fA ∙ g + >UA ∙ h − >Af ∙

e − >AU ∙ e −A�-GEw∙)ò{<A�-Jxyz)ò{<

∙ e 19

:f:== >Af ∙ e + >Uf ∙ h − >fU ∙ g − >fA ∙ g −

f�-GEw∙)ò{<f�-Jxyz)ò{<

∙ g 20

:U:== >fU ∙ g + >AU ∙ e − >UA ∙ h − >Uf ∙ h − hôm ∙ h 21

A prediction-corrected VPC (pcVPC) of the final MTP model is shown in Figure 10.

Figure 10. Prediction-corrected visual predictive check for the final Multistate Tu-berculosis Pharmacometric model using log (left panel) and stationary-phase (right panel) H37Rv M. tuberculosis in vitro and different static rifampicin concentrations. Open circles are prediction-corrected observed log-phase log10 cfu data after differ-ent static rifampicin concentrations; the solid line is the median of the observed data and the dashed lines are the 5th and 95th percentiles of the observed data. The top and bottom shaded areas are the 95% CIs for the 5th and 95th percentiles of simulat-ed data. The middle shaded area is the 95% CI for the median of the simulated data. The black solid line in the lower plot is the median of data below the LOQ. The shaded area in the lower plot is the 95% CI for the simulated LOQ data.

The final effect parameterization differed from the model describing only the log-phase culture data, which did not support inclusion of a kill rate in the non-multiplying state. The predicted reduction in log10 cfu after 14 days and at 0.5 mg/L was 2.2 and 0.8 in the log-phase and stationary-phase systems, respectively. Figure 11 shows the model-predicted change in bacterial num-bers over time after RIF exposure in both the log and stationary-phase cul-tures.

47

Figure 11. Model-predicted typical M. tuberculosis bacterial numbers in the fast, slow and non-multiplying states without drug (natural growth) and after different static rifampicin (RIF) concentrations in log and stationary-phase cultures. In paper IV, the drug effects from mono exposure of RIF, INH and EMB were initially separately evaluated using the MTP model. Rifampicin was found to exert an effect as inhibition of growth of F and as kill of the F, S and N bacteria sub-states. Isoniazid and EMB were found to exert a kill ef-fect on both the F and S bacteria sub-states. Rifampicin displayed the small-est EC50 (0.003 mg·L-1) on the kill of F-state bacteria while the smallest EC50 for INH (0.03 mg·L-1) was found on the S state bacteria. For EMB an Emax function could only be supported on the kill of the state bacteria, hence only one EC50 value (0.86 mg·L-1) could be estimated. The observed decrease in INH susceptibility was best described as an adaptive resistance using an exposure-driven inhibition of the INH effect on the kill of F and S-multiplying state bacteria.

The rate of resistance development to INH, kon, was estimated to 0.0206 ^ö ∙^3YT ∙ õNú. Visual predictive check-plots of the observed log10 cfu versus time after mono exposure of RIF, INH and EMB using the final combined MTP is shown in Figure 12.

!48

Figure 12. Visual predictive check (VPC) of observed log10 colony-forming unit (cfu) versus time after different combination exposure of rifampicin (RIF), isoniazid (INH) and ethambutol (EMB) using the final combined Multistate Tuberculosis Pharmacometric (MTP) model. The blue shaded area is the 95% confidence interval for the median of the simulated data. The exposure level is given after the drug ab-breviation in each figure sub-title. Filled circles are observed log10 cfu data and the solid line is the median of the observed data.

Pharmacodynamic interactions The potential PD interactions for the combinations of RIF, INH and EMB in paper IV were assessed using the GPDI model. Figure 13 shows a schematic illustration of the MTP model linked to the GPDI model showing the drug effects from mono exposure and the identified PD interactions from combi-nation exposure of RIF, INH and EMB.

49

Figure 13. Schematic illustration of the final Multistate Tuberculosis Pharmacomet-ric model linked to the General Pharmacodynamic Interaction model. CRIF, rifampic-in concentration; CINH, isoniazid concentration; CEMB, ethambutol concentration; AROFF and ARON, states describing the development of adaptive resistance to INH; kON, rate of resistance development; F, fast-multiplying bacterial state; S, slow-multiplying bacterial state; N, non-multiplying bacterial state; kG, growth rate of the fast-multiplying state bacteria; kFS, time-dependent linear rate parameter describing transfer from fast to slow-multiplying bacterial state; kSF, first-order transfer rate between slow and fast-multiplying bacterial state; kFN, first-order transfer rate be-tween fast and non-multiplying bacterial state; kSN, first-order transfer rate between slow and non-multiplying bacterial state; kNS, first-order transfer rate between non-multiplying and slow-multiplying bacterial state; FG, drug effect as inhibition of fast-multiplying bacterial state bacterial growth; FD, drug effect as kill of fast-multiplying bacterial state bacteria; SD, drug effect as kill of slow-multiplying bac-terial state bacteria; ND, drug effect as kill of non-multiplying bacterial state bacte-ria. The pharmacodynamic interactions are displayed as – and + symbols, indicating decrease or increase in the EC50s identified in mono exposure.

All three drugs were found to interact at the level of killing of the F sub-state, as displayed in Equation 22-24. Ethambutol decreased the EC50 of RIF (66%) whereas RIF decreased the EC50 of INH (68%). Ethambutol EC50 decreased in the presence of RIF (99%) whereas it unchanged in the pres-ence of INH.

!orAA� = ?GEwò{<<~ ∙)ò{<

?)xyò{<<~ ∙ Tz

{|}{|ù,ò{<<~ ∙J{|ù

-Jxy{|ù<~ ∙J{|ù

∙ TzrUÑ-û+,ò{<<~ ∙)ò{<

22

where ÄhÅrUs,orAA� is the maximal fractional change in RIF EC50 due to an interaction by INH, !IÇÉrUs

A� is the EC50 of INH identified in mono exposure and ÄhÅ?ü#,orAA� is the maximal fractional change in RIF EC50 due to an in-teraction by EMB.

50

!rUsA� = ?GEw{|ù<~ ∙){|ù†{|ù

<~

?)xy{|ù<~ †{|ù

<~∙ Tz

{|}ò{<,{|ù<~ ∙Jò{<

-Jxyò{<<~ ∙Jò{<

∙ Tz{|}-û+,{|ù

<~ ∙J-û+-Jxy-û+

<~ ∙J-û+∙){|ù

†{|ù<~

23

where ÄhÅorA,rUsA� is the maximal fractional change in INH EC50 due to an interaction by INH, !IÇÉorA

A� is the EC50 of RIF identified in mono exposure , ÄhÅ?ü#,rUsA� is the maximal fractional change in INH EC50 due to an interac-tion by EMB and !IÇÉ?ü#

A� is the EC50 of EMB identified in mono exposure.

!?ü#A� = ?GEw-û+<~ ∙)-û+

?)xy-û+<~ ∙ Tz

{|}{|ù,-û+<~ ∙J{|ù

-Jxy{|ù<~ ∙J{|ù

∙ Tz{|}ò{<,-û+

<~ ∙Jò{<-Jxyò{<

<~ ∙Jò{<∙)-û+

24

where ÄhÅrUs,?ü#A� is the maximal fractional change in EMB EC50 due to an interaction by INH, !IÇÉrUs

A� is the EC50 of INH identified in mono exposure, ÄhÅorA,?ü#A� is the maximal fractional change in EMB EC50 due to an interac-tion by RIF and !IÇÉorA

A� is the EC50 of RIF identified in mono exposure. In addition to the interactions found on the F state, all three drugs were found to interact at the level of killing of the S sub-state as displayed in equations 25-27. Ethambutol increased the EC50 of RIF (171%) whereas RIF increased the EC50 of INH (153%). Ethambutol EC50 decreased in the presence of RIF (479%) and in the absence of INH (91%). The effect due to the combination of RIF and INH was also found to be decreased (67%) by the inclusion of EMB.

!orAf� = ?GEwò{<°~ ∙)ò{<

?)xyò{<°~ ∙ Tz

{|}{|ù,ò{<°~ ∙J{|ù

-Jxy{|ù°~ ∙J{|ù

∙ TzrUÑ-û+,ò{<°~ ∙)ò{<

25

where ÄhÅrUs,orAf� is the maximal fractional change in RIF EC50 due to an

interaction by INH, !IÇÉrUsf� is the EC50 of INH identified in mono exposure

and ÄhÅ?ü#,orAf� is the maximal fractional change in RIF EC50 due to an in-teraction by EMB. !rUsf� =

?GEw{|ù°~ ∙){|ù†{|ù

°~

?)xy{|ù°~ †{|ù

<~∙ Tz

{|}ò{<,{|ù°~ ∙ áà{|}ò{<,{|ù|-û+ ∙Jò{<

-Jxyò{<°~ ∙Jò{<

∙ TzrUÑ-û+,{|ù°~ ∙){|ù

†{|ù°~

26 where ÄhÅorA,rUsf� is the maximal fractional change in INH EC50 due to an interaction by INH, !IÇÉorA

f� is the EC50 of RIF identified in mono exposure, ÄhÅ?ü#,rUsf� is the maximal fractional change in INH EC50 due to an interac-

tion by EMB, !IÇÉ?ü#f� is the EC50 of EMB identified in mono exposure and

51

ÄhÅorA,rUs|?ü# is the modulator term describing EMB’s effect on ÄhÅorA,rUsf� .

!?ü#f� = m-û+°~

TzrUÑ{|ù,-û+°~ ∙){|ù ∙ Tz

{|}ò{<,-û+°~ ∙Jò{<

-Jxyò{<°~ ∙Jò{<

27

where ÄhÅrUs,?ü#f� is the maximal fractional change in EMB EC50 due to an interaction by INH, ÄhÅorA,?ü#f� is the maximal fractional change in EMB

EC50 due to an interaction by RIF and !IÇÉorAf� is the EC50 of RIF identified

in mono exposure. Visual predictive check-plots of the observed log10 cfu versus time after different combination exposure of RIF, INH and EMB us-ing the final combined MTP and GPDI model are shown in Figure 14.

!

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. Vis

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e af

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ri

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Gen

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53

Discussion

General Pulmonary Distribution model When assessing the distribution of drug from plasma to pulmonary tissue, as in this case, it is not only important to correctly describe the pulmonary dis-tribution, but also to strive to describe the plasma PK properties of the drug as accurately as possible. Failure to capture the plasma PK properties of the drug will not only bias the description of the plasma concentrations of the drug, but also the relationship of drug concentrations in plasma and the pul-monary tract. It is thus equally important to develop a plasma PK submodel as the submodel relating to the pulmonary concentrations that is as true as possible. The General Pulmonary Distribution model represents a non-drug-specific approach and can be applied to any drug as long as the plasma PK submodel is optimized for the particular drug. Although providing an easy approach for proper prediction of extent and rate, the General Pulmonary Distribution model cannot capture saturable processes in the distribution. In order to describe such processes additional model elements accounting satu-rable processes must be added.

Invasive sampling methods such as the BAL technique make repeated sampling from the same subject more problematic compared to repeated sampling using a non-invasive method. Consequently, many studies involv-ing BAL sampling have too few samples per subject to allow for a traditional compartmental approach for describing the entire time-course of drug distri-bution from plasma to ELF and AC. The General Pulmonary Distribution model circumvents this issue by using an extent and rate parameter to de-scribe distribution. The concentration ratios estimated by the General Pul-monary Distribution model describe the extent of distribution and are a good indication of the potential of the studied drug to reach the site of action and have an effect at the extracellular and intracellular sites in the lung. The rate of distribution to ELF and AC from plasma was captured in the model by the rate constants kELF and kAC. However, due to the lack of information in the data where only one sample was obtained from the subjects the rate of distri-bution could not be estimated; rather, an instantaneous distribution from plasma to ELF and AC was assumed. Although this study design allowed for estimation of the extent of distribution, the true rate of distribution could have been obtained using a more informative sampling design. The opti-mized BAL sampling design presented in paper II is an example of a sam-

54

pling design that enables characterization of the rate and extent of the pul-monary distribution for both quickly and slowly equilibrating drugs. The sampling design involves sampling at only 2 time points, one early and one late, and can be performed with only 1 sample per subject in accordance with how most BAL studies are performed. The time of sampling for the two samples is determined based on usage of the drug-specific plasma PK model and must exhibit correspondence with the early and late samples regarding plasma concentration. The early sample should be as early as possible from the ascending part of the concentration time profile to maximize the chance of capturing fast distribution rates from plasma to the pulmonary tract. How-ever, one must consider that slow distribution might require taking the first BAL sample at a later time point in order to reduce the risk of pulmonary concentrations <LOQ. The late sample should be taken at the descending part of the concentration time profile when the plasma concentration is simi-lar to the sample from the ascending part. In summary, deciding when to sample is carried out in three steps:

1. A plasma concentration versus time profile is simulated with the

drug-specific plasma PK model 2. Pulmonary BAL concentrations are simulated using the general

pulmonary model and an assumed slow distribution rate (if the distribution is truly perfusion-limited, i.e. fast, this assumption will not impact the bias and precision of PK estimates as shown in this work)

3. One early and one late BAL sampling time points are identified using the simulated plasma and BAL concentrations versus the time profiles and BAL LOQ. The two BAL sampling time points should be taken when the plasma concentration is the same and when the BAL samples are >BAL LOQ

The approach is further applicable to situations in which little is known re-garding the pulmonary distribution properties and relies only on pre-characterized plasma PK and LOQ of the BAL technique.

A Multistate Tuberculosis Pharmacometric Model The MTP model consists of three different bacterial states representing fast, slow and non-multiplying bacteria. A two sub-state model without the non-multiplying state resulted in a much poorer fit compared with the final MTP model for describing the natural growth of M. tuberculosis in a hypoxia-driven in vitro system. In in vitro systems, slow or non-multiplying states of M. tuberculosis are thought to be induced by hypoxia.38 In the in vitro hy-poxia system, the bacteria slowly adapt to the microaerophilic and eventually

55

anaerobic conditions. Fully adapted, the bacterial culture is said to exist in a stationary phase in which protein synthesis is switched off.109 However, the dormant stationary-phase bacteria can reinitiate growth in response to favor-able changes in the environment. The ability of re-initiation has been shown to exist in vitro, in vivo and in sputum using methods involving RPFs.110–116 As the cfu count reflects only the bacteria that are able to multiply on solid media, the number in the fast and slow-multiplying states, as a sum, were part of the model prediction of the data. However, the non-multiplying state influences the predictions. As the clinical relevance of these non-culturable bacteria is undoubtedly large, it is naturally of great interest to be able to quantify drug effect on this type of bacteria. As judged based on the VPC, the final MTP model was able to capture the observed changes in cfu over time very well. The data used for external validation of the bacterial numbers predicted by the MTP model indicated that the protein synthesis in M. tuber-culosis is, not surprisingly, high during log-phase growth and gradually de-creased with the establishment of a stationary-phase culture. The strong cor-relation in the external validation (R2 =0.98) speaks highly in favor of the prediction provided by the model of both the fast and the slow-multiplying bacterial numbers over time, as incorporation should be driven mainly by the fast-multiplying bacteria, which are predicted by the model to make up the majority of bacteria in log-phase cultures. The MTP model was further used to describe in vitro natural growth data associated with both pure log and stationary-phase cultures (paper III) as well as natural growth from other M. tuberculosis genotypes (paper IV).

The exposure-response relationship of RIF using log and stationary-phase bacteria was described in paper III. The RIF effect was included as inhibition of the growth function of the fast-multiplying state and as a kill rate of the fast, slow and non-multiplying states. It is important to keep in mind that the effect parameterization of any drug will be dependent on the data, i.e. whether the bacterial culture is in log or stationary phase. Naturally, a drug effect that is studied with bacteria from a log-phase culture will have more information on the effect carried out on the fast-multiplying state bacteria, as these types of bacteria comprise the majority of a log-phase culture. Re-versed, a stationary-phase culture will provide more information on the drug effect on slow and non-multiplying bacteria as the ratio of the bacterial states have shifted in favour of slow and non-multiplying bacteria. However, a drug effect will still be carried out on each of the bacterial states regardless of which phase the culture is in. In paper IV, the effects of mono-exposure of RIF, INH and EMB on log-phase cultures of M. tuberculosis B1585 were described using the same approach as in paper III. For this data, RIF was found to exert an effect in similar ways to the effect found in paper III. INH was found to exert an effect as a kill rate on both the fast and slow-multiplying states. Others have discussed and explored the cause of the ob-served decrease in susceptibility to INH in vitro and in vivo. The adaptive

56

resistance included in the final model is an empirical approach that is at-tributable to both genotypic and phenotypic resistance mechanisms that have been suggested to exist in vitro.20,21 In the model, INH stimulates an adaptive resistance pool which in turn inhibits the drug efficacy on the F and S sub-bacterial states. This is in line with previous experimental findings suggest-ing presence of efflux transporter related phenotypic INH resistance in vitro.21

The MTP model and the possibility of quantifying exposure-response re-lationships on different types of bacterial states provide a platform for study-ing anti-tuberculosis drugs in different pre-clinical settings as well as the groundwork for human translational efforts. Examples of this include the successful application of the MTP model for studying anti-tuberculosis drug exposure-response relationships in a chronic TB mouse model and for simu-lation and predictions in a clinical setting.103,117 Translational efforts include the successful application of the MTP model and the quantified in vitro ex-posure-response relationships for translational predictions to HFS, in vivo and clinical studies for determination of EBA.118

Assessment of pharmacodynamic interactions Proper characterization of PD interactions is crucial for the selection of drug combinations in early drug development. In paper IV, the interactions be-tween three first-line anti-tuberculosis drugs were assessed using the MTP model linked to the GPDI model implemented into BI additivity criterion. The decision to use the BI criterion was based on the fact that the three drugs present the possibility of independent action due to different action mecha-nisms. In addition, the three drugs displayed different maximal effects which invalidates the assessment of pure LA. For bacterial infection, a theoretical maximum effect can be reached already with mono exposure as bacteria can only be killed once. When drugs are used in combinations and assuming an additive total effect (i.e. no interaction), this can thus lead to a large discrep-ancy between predictions using drug effects quantified from mono exposure and the observed drug effect of the combination regimen. There is also a possibility of concentration-dependent interactions, i.e. that different concen-trations result in different degrees or even classification of interactions. The GPDI-model quantifies interactions on effect parameter level, in this case EC50, as either an increased or decreased EC50 depending on the deviation from a pure additive effect combination. This means that the quantified in-teractions are describing pharmacological interactions rather than interac-tions viewed as deviations from adding the effect of drugs in mono exposure. However, in order to predict the impact of the interaction on the biomarker level and to judge if the PD interaction is synergistic or antagonistic at a biomarker level, simulations need to be done. This was demonstrated in Fig-

57

ure 14 where the grey shaded area reflects the predictions of using only the MTP model, i.e. ignoring the pharmacodynamic interactions as estimated by the final GPDI model and only assuming expected additivity of the drug effects from mono exposure. The predictions from this additivity model showed that for most duo and trio combinations, a lower effect was achieved than predicted from a model assuming only additivity (grey area) i.e. antag-onism on a biomarker level. However, the drug effect of the combinations was higher than for any of the drugs alone, at highest exposure and last stud-ied time point, apart from adding EMB to INH in duo combination which did not result in an increased effect compared to monotherapy of INH alone. Similar, the addition of EMB to the duo combination of INH+RIF did not result in an increased effect, at highest exposure and last studied time point, compared to duo combination of INH and RIF. The impact of PD interac-tions on the biomarker level would have not been possible to judge by only inspection of the change in EC50, where 3 out of 13 PD interactions lead to decreased EC50´s. The quantified time and concentration dependency of the PD interactions is made possible by the inclusion of the whole time-course of the kill-curve in the MTP-GPDI approach, as opposed to only using a summary endpoint. From many perspectives, it is not reasonable to charac-terize PD interactions in an in vivo or clinical setting. For TB, where the standard treatment regimen includes four different drugs, the sheer amount of combinations and concentrations that need to be studied in order to pro-vide a proper identification of multidimensional PD interactions is too great to make anything but an in vitro setting the ethical and practical choice. Providing that the PD interactions identified in vitro are predictive of the in vivo and clinical PD interactions, this enables simulation of drug combina-tion exposure-response relationships in order to optimize the dosage of treatment regimens.

58

Conclusions

In many ways, tuberculosis has been left out of the evolution of modern drug development, largely due to the lack of market incentives motivating drug companies to keep active drug programs running. Unfortunately, this prob-lem is not specific to TB, but is also the reality for treatment of many other diseases relying on antibiotics. However, in the case of TB, the major issue is not primarily the development of resistance and consequent loss of drug effect. When properly implemented, the current anti-tuberculosis treatment regimen has a high cure rate and a low rate of resistance development. In-stead, one of the biggest problems is that curing a patient requires such a vast amount of time on treatment that the regimen is rendered impractical and thus not optimal. Some causes of the need for such a long treatment duration include the lack of effect on dormant bacteria and the poorly characterized PK and PD properties of single as well as combinations of anti-tuberculosis drugs. Since the introduction of the currently used anti-tuberculosis drugs, the significance and understanding of PK and PD for developing effective drugs and drug regimens has improved. The overall aim of this thesis was to provide modern tools and methods allowing for informed drug development with regards to quantification of PK and PD of new and existing drugs and drug regimens. Pharmacometric models have previously been used for such efforts in other therapeutic areas and are today an widely implemented and by regulatory agencies accepted part of drug development. The work in this thesis provides multiple new methods and approaches that have the potential to inform the development of new, but also to provide additional information on the existing anti-tuberculosis drugs and drug regimens. The General Pul-monary Distribution model allowing for the prediction of both rate and ex-tent of distribution from plasma to pulmonary tissue is extremely important, as most anti-tuberculosis drugs used today were introduced into clinical use without considering the PK properties influencing drug distribution to the site of action. The modeling approach can be used to guide drug developers toward decisions regarding the appropriateness of using plasma as a marker of concentrations at the site of action. The General Pulmonary Distribution model is non-drug-specific and can be used to describe distribution not only to ELF and AC, but to any type of pulmonary tissue. The model is especially advantageous when dealing with data from sampling techniques that only allow for sparse sampling. The optimized BAL sampling design developed in paper II provides a simplistic but informative approach to gathering the

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data needed to allow for model-based characterization of both rate and extent of pulmonary tissue distribution, as exemplified for RIF in paper I – a distri-bution characterization that is crucial for a proper description of the expo-sure-response relationships of drugs with slow distribution between plasma and the pulmonary tract. Evaluation of the optimized sampling design re-vealed that it allows for estimates of both the rate and extent of pulmonary distribution with adequate parameter precision using only one sample per subject and relatively small total sampling sizes. The MTP model presented in paper III provides predictions over time for a fast, slow and non-multiplying bacterial state with and without drug effect. The possibility of quantifying the drug effect on non-multiplying M. tuberculosis bacteria is hugely important, as targeting both multiplying and non-multiplying bacteri-al populations is regarded as an essential way to shorten treatment duration and slow the emergence of drug resistance. The MTP model has been used to characterize the effect of RIF on both log and stationary-phase bacterial cultures, effectively quantifying the difference in exposure-response between these types of bacterial systems, supporting the importance of incorporation of stationary-phase bacterial cultures in TB drug development programs. The MTP model has also been used to quantify the growth of different strains of M. tuberculosis and the effect of three first-line anti-tuberculosis drugs – a quantification that clearly shows the dissimilarity in effect on the different M. tuberculosis growth states among the three drugs. The MTP model con-stitutes an important foundation, providing a basis from which to make in-formed decisions about the selection of new anti-tuberculosis drugs with asserted effects against non-multiplying bacteria. Outside the scope of this thesis, but building on its results, the MTP model has been used for RIF clinical trial simulations and predictions by taking into account clinical PK and PD properties.103

The characterization of PD drug interactions using the GPDI model al-lows for distinguishing drug A’s interaction with drug B from drug B’s in-teraction with drug A, which is a necessity in the selection of anti-tuberculosis combination regimens. The interactions of RIF, INH and EMB were characterized for a broad response surface with quantification of inter-pretable interaction parameters. Differences in how the three drugs affected each other were revealed, with most of the interactions identified as leading to decreased potency compared to mono exposure.

The methods and approaches presented in this thesis provide multiple tools that individually, but more importantly, in combination represent the possibility of truly model-informed anti-tuberculosis drug development.

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Populärvetenskaplig sammanfattning

Tuberkulos är en infektionssjukdom som årligen orsakar miljontals dödsfall. Behandling av tuberkulos sker genom användandet av fyra olika läkemedel under en tidsperiod av minst sex månader. Den långa behandlingstiden krävs för att fullständigt döda de bakterier som existerar i ett sovande stadie. Miss-lyckande i att döda alla dessa sovande bakterier har kopplats samman med återfall i sjukdomen. Behovet av den långa behandlingstiden innebär att be-handlingen om än effektiv är svårt att genomföra. Svårigheterna ökar givet-vis också i de länder som saknar tillgång till den typ av sjukvård och allmän-standard som existerar i Sverige. Utvecklingen av nya och förbättrade former av läkemedel mot tuberkulos har länge varit obefintlig. De läkemedel som idag används utvecklades innan 1970-talet och de potentiella skillnader som existerar mellan dåtida och nutida metoder och krav vid utvecklingen av läkemedel kan givetvis medföra att behandlingen ej är optimal. Sedan år 2000 så har en ökning i intresset för utvecklingen och förbättringen av läke-medel mot tuberkulos skett. År 2012 godkändes bedakilin, vilket var det första nya läkemedlet mot tuberkulos på över 40 år. Ökningen till trots så existerar dock fortfarande ett behov av nya och förbättrade former av läke-medel mot tuberkulos. Denna avhandling fokuserar på användandet av far-makometriska metoder för att besvara frågeställningar kring och etablera ett effektivt och välgrundat utvecklande av nya och förbättrande av existerande läkemedel mot tuberkulos. Farmakometri är en vetenskap som grundar sig i användandet av matematiska modeller för att beskriva farmakologiska, bio-logiska, fysiologiska och sjukdomsspecifika processer och system. En mo-dell som väl beskriver ett skeende kan sedan användas för att förutsäga hur detta skeende påverkas av olika faktorer kopplade till användandet av läke-medel. Ett exempel på detta kan vara hur samtidigt intag av föda påverkar upptaget av läkemedlet från magtarmkanalen eller i om skillnader i läkeme-delseffekt föreligger mellan personer med olika etnicitet. Modeller utveck-lade för att beskriva skeenden i så kallade in vitro eller provrörsbaserade försök kan exempelvis, genom att ta hänsyn till humanspecifika faktorer, användas för att prediktera effekter av läkemedel i människor. Modellerna i denna avhandling berör bland annat beskrivningar av hur läkemedel fördelas i lungvävnad. Användning av läkemedelskoncentrationer uppmätta i lung-vävnad kan för vissa läkemedel ge bättre information om det samband som existerar mellan koncentration och effekt jämfört med användning av läke-medelskoncentrationer uppmätta i blodet. Vidare så har en modell, beskri-

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vande de olika stadier av aktivitet som tuberkulosbakterier kan existera i, utvecklats. Denna modellen, kallad ”The Multistate Tuberculosis Phar-macometric model”, beskriver hur läkemedel påverkar inte bara aktiva men också de bakterier som existerar i en vilande eller inaktiv form. Beskrivande av läkemedelseffekt på dessa vilande bakterieformer är en mycket viktig del i utvecklingen av nya läkemedel med en eftersträvad kortare behandlingstid än vad som idag är möjlig. Dagens behandling av tuberkulos kräver, som ovan nämnt, att upp till fyra olika läkemedel tas samtidigt. I och med att de alla har som mål att döda bakterier så existerar risken att de vid samtidig användning kan ha mindre total effekt än vad som observeras vid använd-ning var för sig. I vissa fall kan också den totala effekten av två läkemedel vara större vid samtidig intag än när tagna var för sig. För att beskriva detta så har modeller utvecklats och används för att beskriva de potentiella skill-nader i effekt som föreligger när läkemedel tas tillsammans jämfört med när de tas var för sig.

Alla modellerna presenterade i denna avhandling har potentialen att bidra med viktig information till utvecklingen av nya, men också till förbättringen av existerande tuberkulosläkemedel. Som helhet visar avhandlingen effektivt på nyttan av användandet av farmakometriska metoder för att bedriva den typ av välinformerad och effektiv läkemedelsutveckling som i slutändan gagnar patienter över hela världen på största och bästa sätt.

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Acknowledgements

The research presented in this thesis was conducted at the Department of Pharmaceutical Bioscience at Uppsala University. The work was funded by the Swedish Research Council (grant number 521-2011-3432) and the Innovative Medicines Initiative Joint Undertaking (grant agreements number 115337) for the PreDiCT-TB consortium, resources of which are com-posed of financial contributions from the European Union’s Seventh Frame-work Programme (FP7/2007-2013) and in-kind contributions from EFPIA companies. Generous travel grants from Anna-Maria Lundin’s Fund at Smålands Nation and Apotekarsociteten made it possible to attend and present findings at several international conferences. Ulrika, I am very thankful that I was given the opportunity to have you as my main supervisor. You have been a tremendous source of knowledge, experience, support and positiveness, not limited to only research and sci-ence. Thank you for keeping me challenged but always indisputably sup-ported! Mats, my co-supervisor. Thank you for letting me be a part of your fantastic research group and for sharing your endless knowledge and enthusiasm for the sciences of pharmacometrics. I am ever thankful for the support and friendship of Team TB; Elin, Chunli, Robin and Sebastian.

My collaborators and co-authors, specially Anthony, Corné, Gerjo, Jurriaan, Linda, Sylvain and Yanmin, for making this thesis possible.

I would also like to thank all PhD-students, post-docs, administrators, teach-ers, past and present who have contributed to the kind and inspirational at-mosphere at the department. Special thanks to Oskar A, Sofia, Anders K, Jörgen (“ner i bocken och mosa!”) and my past and present office-mates, Waqas, Ana and Erik.

My family, both Clewe and Thomée-Dahlén, and friends.

Emma, the light that never goes out. I love you so much!

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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 222

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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