Applying optimization algorithms to tuberculosis antibiotic treatment regimens

A systematic efficacy analysis of tuberculosis treatment with BPaL-containing regimens using a multiscale modeling approach

Tuberculosis (TB) is a life-threatening infectious disease. The standard treatment is up to 90% effective; however, it requires the administration of four antibiotics (isoniazid, rifampicin, pyrazinamide, and ethambutol [HRZE]) over long time periods. This harsh treatment process causes adherence issues for patients because of the long treatment times and a myriad of adverse effects. Therefore, the World Health Organization has focused goals of shortening standard treatment regimens for TB in their End TB Strategy efforts, which aim to reduce TB-related deaths by 95% by 2035. For this purpose, many novel and promising combination antibiotics are being explored that have recently been discovered, such as the bedaquiline, pretomanid, and linezolid (BPaL) regimen. As a result, testing the number of possible combinations with all possible novel regimens is beyond the limit of experimental resources. In this study, we present a unique framework that uses a primate granuloma modeling approach to screen many combination regimens that are currently under clinical and experimental exploration and assesses their efficacies to inform future studies. We tested well-studied regimens such as HRZE and BPaL to evaluate the validity and accuracy of our framework. We also simulated additional promising combination regimens that have not been sufficiently studied clinically or experimentally, and we provide a pipeline for regimen ranking based on their efficacies in granulomas. Furthermore, we showed a correlation between simulation rankings and new marmoset data rankings, providing evidence for the credibility of our framework. This framework can be adapted to any TB regimen and can rank any number of single or combination regimens.

Incorporating temporal information during feature engineering bolsters emulation of spatio-temporal emergence

MOTIVATION

Emergent biological dynamics derive from the evolution of lower-level spatial and temporal processes. A long-standing challenge for scientists and engineers is identifying simple low-level rules that give rise to complex higher-level dynamics. High-resolution biological data acquisition enables this identification and has evolved at a rapid pace for both experimental and computational approaches. Simultaneously harnessing the resolution and managing the expense of emerging technologies-e.g. live cell imaging, scRNAseq, agent-based models-requires a deeper understanding of how spatial and temporal axes impact biological systems. Effective emulation is a promising solution to manage the expense of increasingly complex high-resolution computational models. In this research, we focus on the emulation of a tumor microenvironment agent-based model to examine the relationship between spatial and temporal environment features, and emergent tumor properties.

RESULTS

Despite significant feature engineering, we find limited predictive capacity of tumor properties from initial system representations. However, incorporating temporal information derived from intermediate simulation states dramatically improves the predictive performance of machine learning models. We train a deep-learning emulator on intermediate simulation states and observe promising enhancements over emulators trained solely on initial conditions. Our results underscore the importance of incorporating temporal information in the evaluation of spatio-temporal emergent behavior. Nevertheless, the emulators exhibit inconsistent performance, suggesting that the underlying model characterizes unique cell populations dynamics that are not easily replaced.

AVAILABILITY AND IMPLEMENTATION

All source codes for the agent-based model, emulation, and analyses are publicly available at the corresponding DOIs: 10.5281/zenodo.10622155, 10.5281/zenodo.10611675, 10.5281/zenodo.10621244, respectively.

Mathematical model of oxygen, nutrient, and drug transport in tuberculosis granulomas

Physiological abnormalities in pulmonary granulomas-pathological hallmarks of tuberculosis (TB)-compromise the transport of oxygen, nutrients, and drugs. In prior studies, we demonstrated mathematically and experimentally that hypoxia and necrosis emerge in the granuloma microenvironment (GME) as a direct result of limited oxygen availability. Building on our initial model of avascular oxygen diffusion, here we explore additional aspects of oxygen transport, including the roles of granuloma vasculature, transcapillary transport, plasma dilution, and interstitial convection, followed by cellular metabolism. Approximate analytical solutions are provided for oxygen and glucose concentration, interstitial fluid velocity, interstitial fluid pressure, and the thickness of the convective zone. These predictions are in agreement with prior experimental results from rabbit TB granulomas and from rat carcinoma models, which share similar transport limitations. Additional drug delivery predictions for anti-TB-agents (rifampicin and clofazimine) strikingly match recent spatially-resolved experimental results from a mouse model of TB. Finally, an approach to improve molecular transport in granulomas by modulating interstitial hydraulic conductivity is tested in silico.

Optimizing Antimicrobial Treatment Schedules: Some Fundamental Analytical Results

This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC), which is equivalent to minimizing the cumulative dosage. We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the ideal concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the 'ideal' concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the 'ideal' concentration profile, using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the 'ideal' concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.

Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations

Although infectious disease dynamics are often analyzed at the macro-scale, increasing numbers of drug-resistant infections highlight the importance of within-host modeling that simultaneously solves across multiple scales to effectively respond to epidemics. We review multiscale modeling approaches for complex, interconnected biological systems and discuss critical steps involved in building, analyzing, and applying such models within the discipline of model credibility. We also present our two tools: CaliPro, for calibrating multiscale models (MSMs) to datasets, and tunable resolution, for fine- and coarse-graining sub-models while retaining insights. We include as an example our work simulating infection with Mycobacterium tuberculosis to demonstrate modeling choices and how predictions are made to generate new insights and test interventions. We discuss some of the current challenges of incorporating novel datasets, rigorously training computational biologists, and increasing the reach of MSMs. We also offer several promising future research directions of incorporating within-host dynamics into applications ranging from combinatorial treatment to epidemic response.

Optimizing tuberculosis treatment efficacy: Comparing the standard regimen with Moxifloxacin-containing regimens

Tuberculosis (TB) continues to be one of the deadliest infectious diseases in the world, causing ~1.5 million deaths every year. The World Health Organization initiated an End TB Strategy that aims to reduce TB-related deaths in 2035 by 95%. Recent research goals have focused on discovering more effective and more patient-friendly antibiotic drug regimens to increase patient compliance and decrease emergence of resistant TB. Moxifloxacin is one promising antibiotic that may improve the current standard regimen by shortening treatment time. Clinical trials and in vivo mouse studies suggest that regimens containing moxifloxacin have better bactericidal activity. However, testing every possible combination regimen with moxifloxacin either in vivo or clinically is not feasible due to experimental and clinical limitations. To identify better regimens more systematically, we simulated pharmacokinetics/pharmacodynamics of various regimens (with and without moxifloxacin) to evaluate efficacies, and then compared our predictions to both clinical trials and nonhuman primate studies performed herein. We used GranSim, our well-established hybrid agent-based model that simulates granuloma formation and antibiotic treatment, for this task. In addition, we established a multiple-objective optimization pipeline using GranSim to discover optimized regimens based on treatment objectives of interest, i.e., minimizing total drug dosage and lowering time needed to sterilize granulomas. Our approach can efficiently test many regimens and successfully identify optimal regimens to inform pre-clinical studies or clinical trials and ultimately accelerate the TB regimen discovery process.

A Credibility Assessment Plan for an In Silico Model that Predicts the Dose-Response Relationship of New Tuberculosis Treatments

Tuberculosis is one of the leading causes of death in several developing countries and a public health emergency of international concern. In Silico Trials can be used to support innovation in the context of drug development reducing the duration and the cost of the clinical experimentations, a particularly desirable goal for diseases such as tuberculosis. The agent-based Universal Immune System Simulator was used to develop an In Silico Trials environment that can predict the dose-response of new therapeutic vaccines against pulmonary tuberculosis, supporting the optimal design of clinical trials. But before such in silico methodology can be used in the evaluation of new treatments, it is mandatory to assess the credibility of this predictive model. This study presents a risk-informed credibility assessment plan inspired by the ASME V&V 40-2018 technical standard. Based on the selected context of use and regulatory impact of the technology, a detailed risk analysis is described together with the definition of all the verification and validation activities and related acceptability criteria. The work provides an example of the first steps required for the regulatory evaluation of an agent-based model used in the context of drug development.

Evolutionary optimisation of antibiotic dosing regimens for bacteria with different levels of resistance

Antimicrobial resistance is one of the biggest threats to global health, food security, and development. Antibiotic overuse and misuse are the main drivers for the emergence of resistance. It is crucial to optimise the use of existing antibiotics in order to improve medical outcomes, decrease toxicity and reduce the emergence of resistance. We formulate the design of antibiotic dosing regimens as an optimisation problem, and use an evolutionary algorithm suited to continuous optimisation (differential evolution) to solve it. Regimens are represented as vectors of real numbers encoding daily doses, which can vary across the treatment duration. A stochastic mathematical model of bacterial infections with tuneable resistance levels is used to evaluate the effectiveness of evolved regimens. The objective is to minimise the treatment failure rate, subject to a constraint on the maximum total antibiotic used. We consider simulations with different levels of bacterial resistance, two ways of administering the drug (orally and intravenously), as well as coinfections with two strains of bacteria. Our approach produced effective dosing regimens, with an average improvement in lowering the failure rate 30%, when compared with standard fixed-daily-dose regimens with the same total amount of antibiotic.

Research priorities towards precision antibiotic therapy to improve patient care

Antibiotic resistance presents an incessant threat to our drug armamentarium that necessitates novel approaches to therapy. Over the past several decades, investigation of pharmacokinetic and pharmacodynamic (PKPD) principles has substantially improved our understanding of the relationships between the antibiotic, pathogen, and infected patient. However, crucial gaps in our understanding of the pharmacology of antibacterials and their optimal use in the care of patients continue to exist; simply attaining antibiotic exposures that are considered adequate based on traditional targets can still result in treatment being unsuccessful and resistance proliferation for some infections. It is this salient paradox that points to key future directions for research in antibiotic therapeutics. This Personal View discusses six priority areas for antibiotic pharmacology research: (1) antibiotic-pathogen interactions, (2) antibiotic targets for combination therapy, (3) mechanistic models that describe the time-course of treatment response, (4) understanding and modelling of host response to infection, (5) personalised medicine through therapeutic drug management, and (6) application of these principles to support development of novel therapies. Innovative approaches that enhance our understanding of antibiotic pharmacology and facilitate more accurate predictions of treatment success, coupled with traditional pharmacology research, can be applied at the population level and to individual patients to improve outcomes.

The Use of Artificial Neural Networks to Forecast the Behavior of Agent-Based Models of Pathophysiology: An Example Utilizing an Agent-Based Model of Sepsis

Introduction: Disease states are being characterized at finer and finer levels of resolution via biomarker or gene expression profiles, while at the same time. Machine learning (ML) is increasingly used to analyze and potentially classify or predict the behavior of biological systems based on such characterization. As ML applications are extremely data-intensive, given the relative sparsity of biomedical data sets ML training of artificial neural networks (ANNs) often require the use of synthetic training data. Agent-based models (ABMs) that incorporate known biological mechanisms and their associated stochastic properties are a potential means of generating synthetic data. Herein we present an example of ML used to train an artificial neural network (ANN) as a surrogate system used to predict the time evolution of an ABM focusing on the clinical condition of sepsis. Methods: The disease trajectories for clinical sepsis, in terms of temporal cytokine and phenotypic dynamics, can be interpreted as a random dynamical system. The Innate Immune Response Agent-based Model (IIRABM) is a well-established model that utilizes known cellular and molecular rules to simulate disease trajectories corresponding to clinical sepsis. We have utilized two distinct neural network architectures, Long Short-Term Memory and Multi-Layer Perceptron, to take a time sequence of five measurements of eleven IIRABM simulated serum cytokine concentrations as input and to return both the future cytokine trajectories as well as an aggregate metric representing the patient's state of health. Results: The ANNs predicted model trajectories with the expected amount of error, due to stochasticity in the simulation, and recognizing that the mapping from a specific cytokine profile to a state-of-health is not unique. The Multi-Layer Perceptron neural network, generated predictions with a more accurate forecasted trajectory cone. Discussion: This work serves as a proof-of-concept for the use of ANNs to predict disease progression in sepsis as represented by an ABM. The findings demonstrate that multicellular systems with intrinsic stochasticity can be approximated with an ANN, but that forecasting a specific trajectory of the system requires sequential updating of the system state to provide a rolling forecast horizon.

A multi-scale pipeline linking drug transcriptomics with pharmacokinetics predicts in vivo interactions of tuberculosis drugs

Tuberculosis (TB) is the deadliest infectious disease worldwide. The design of new treatments for TB is hindered by the large number of candidate drugs, drug combinations, dosing choices, and complex pharmaco-kinetics/dynamics (PK/PD). Here we study the interplay of these factors in designing combination therapies by linking a machine-learning model, INDIGO-MTB, which predicts in vitro drug interactions using drug transcriptomics, with a multi-scale model of drug PK/PD and pathogen-immune interactions called GranSim. We calculate an in vivo drug interaction score (iDIS) from dynamics of drug diffusion, spatial distribution, and activity within lesions against various pathogen sub-populations. The iDIS of drug regimens evaluated against non-replicating bacteria significantly correlates with efficacy metrics from clinical trials. Our approach identifies mechanisms that can amplify synergistic or mitigate antagonistic drug interactions in vivo by modulating the relative distribution of drugs. Our mechanistic framework enables efficient evaluation of in vivo drug interactions and optimization of combination therapies.

Mathematical model and tool to explore shorter multi-drug therapy options for active pulmonary tuberculosis

Standard treatment for active tuberculosis (TB) requires drug treatment with at least four drugs over six months. Shorter-duration therapy would mean less need for strict adherence, and reduced risk of bacterial resistance. A system pharmacology model of TB infection, and drug therapy was developed and used to simulate the outcome of different drug therapy scenarios. The model incorporated human immune response, granuloma lesions, multi-drug antimicrobial chemotherapy, and bacterial resistance. A dynamic population pharmacokinetic/pharmacodynamic (PK/PD) simulation model including rifampin, isoniazid, pyrazinamide, and ethambutol was developed and parameters aligned with previous experimental data. Population therapy outcomes for simulations were found to be generally consistent with summary results from previous clinical trials, for a range of drug dose and duration scenarios. An online tool developed from this model is released as open source software. The TB simulation tool could support analysis of new therapy options, novel drug types, and combinations, incorporating factors such as patient adherence behavior.

A comprehensive in-silico model of pulmonary tuberculosis successfully predicted previous clinical trials and could simulate future therapeutics.

Optimising efficacy of antibiotics against systemic infection by varying dosage quantities and times

Mass production and use of antibiotics has led to the rise of resistant bacteria, a problem possibly exacerbated by inappropriate and non-optimal application. Antibiotic treatment often follows fixed-dose regimens, with a standard dose of antibiotic administered equally spaced in time. But are such fixed-dose regimens optimal or can alternative regimens be designed to increase efficacy? Yet, few mathematical models have aimed to identify optimal treatments based on biological data of infections inside a living host. In addition, assumptions to make the mathematical models analytically tractable limit the search space of possible treatment regimens (e.g. to fixed-dose treatments). Here, we aimed to address these limitations by using experiments in a Galleria mellonella (insect) model of bacterial infection to create a fully parametrised mathematical model of a systemic Vibrio infection. We successfully validated this model with biological experiments, including treatments unseen by the mathematical model. Then, by applying artificial intelligence, this model was used to determine optimal antibiotic dosage regimens to treat the host to maximise survival while minimising total antibiotic used. As expected, host survival increased as total quantity of antibiotic applied during the course of treatment increased. However, many of the optimal regimens tended to follow a large initial ‘loading’ dose followed by doses of incremental reductions in antibiotic quantity (dose ‘tapering’). Moreover, application of the entire antibiotic in a single dose at the start of treatment was never optimal, except when the total quantity of antibiotic was very low. Importantly, the range of optimal regimens identified was broad enough to allow the antibiotic prescriber to choose a regimen based on additional criteria or preferences. Our findings demonstrate the utility of an insect host to model antibiotic therapies in vivo and the approach lays a foundation for future regimen optimisation for patient and societal benefits.

Research into optimal antibiotic use to improve efficacy is far behind that of cancer care, where personalised treatment is common. The integration of mathematical models with biological observations offers hope to optimise antibiotic use, and in this present study an in vivo insect model of systemic Vibrio infection was used for the first time to determine critical model parameters for optimal antibiotic treatment. By this approach, the optimal regimens tended to result from a large initial ‘loading’ dose followed by subsequent doses of incremental reductions in antibiotic quantity (dose ‘tapering’). The approach and findings of this study opens a new avenue towards optimal application of our precious antibiotic arsenal and may lead to more effective treatment regimens for patients, thus reducing the health and economic burdens associated with bacterial infections. Importantly, it can be argued that until we understand how to use a single antibiotic optimally, it is unlikely we will identify optimal ways to use multiple antibiotics simultaneously.

Both Pharmacokinetic Variability and Granuloma Heterogeneity Impact the Ability of the First-Line Antibiotics to Sterilize Tuberculosis Granulomas

Tuberculosis (TB) remains as one of the world's deadliest infectious diseases despite the use of standardized antibiotic therapies. Recommended therapy for drug-susceptible TB is up to 6 months of antibiotics. Factors that contribute to lengthy regimens include antibiotic underexposure in lesions due to poor pharmacokinetics (PK) and complex granuloma compositions, but it is difficult to quantify how individual antibiotics are affected by these factors and to what extent these impact treatments. We use our next-generation multi-scale computational model to simulate granuloma formation and function together with antibiotic pharmacokinetics and pharmacodynamics, allowing us to predict conditions leading to granuloma sterilization. In this work, we focus on how PK variability, determined from human PK data, and granuloma heterogeneity each quantitatively impact granuloma sterilization. We focus on treatment with the standard regimen for TB of four first-line antibiotics: isoniazid, rifampin, ethambutol, and pyrazinamide. We find that low levels of antibiotic concentration due to naturally occurring PK variability and complex granulomas leads to longer granuloma sterilization times. Additionally, the ability of antibiotics to distribute in granulomas and kill different subpopulations of bacteria contributes to their specialization in the more efficacious combination therapy. These results can inform strategies to improve antibiotic therapy for TB.

Agent-based models of inflammation in translational systems biology: A decade later

Agent-based modeling is a rule-based, discrete-event, and spatially explicit computational modeling method that employs computational objects that instantiate the rules and interactions among the individual components ("agents") of system. Agent-based modeling is well suited to translating into a computational model the knowledge generated from basic science research, particularly with respect to translating across scales the mechanisms of cellular behavior into aggregated cell population dynamics manifesting at the tissue and organ level. This capacity has made agent-based modeling an integral method in translational systems biology (TSB), an approach that uses multiscale dynamic computational modeling to explicitly represent disease processes in a clinically relevant fashion. The initial work in the early 2000s using agent-based models (ABMs) in TSB focused on examining acute inflammation and its intersection with wound healing; the decade since has seen vast growth in both the application of agent-based modeling to a wide array of disease processes as well as methodological advancements in the use and analysis of ABM. This report presents an update on an earlier review of ABMs in TSB and presents examples of exciting progress in the modeling of various organs and diseases that involve inflammation. This review also describes developments that integrate the use of ABMs with cutting-edge technologies such as high-performance computing, machine learning, and artificial intelligence, with a view toward the future integration of these methodologies. This article is categorized under: Translational, Genomic, and Systems Medicine > Translational Medicine Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Models of Systems Properties and Processes > Organismal Models.

Global sensitivity analysis of biological multi-scale models

Mathematical models of biological systems need to both reflect and manage the inherent complexities of biological phenomena. Through their versatility and ability to capture behavior at multiple scales, multi-scale models offer a valuable approach. Due to the typically nonlinear and stochastic nature of multi-scale models as well as unknown parameter values, various types of uncertainty are present; thus, effective assessment and quantification of such uncertainty through sensitivity analysis is important. In this review, we discuss global sensitivity analysis in the context of multi-scale and multi-compartment models and highlight its value in model development and analysis. We present an overview of sensitivity analysis methods, approaches for extending such methods to a multi-scale setting, and examples of how sensitivity analysis can inform model reduction. Through schematics and references to past work, we aim to emphasize the advantages and usefulness of such techniques.

Emergence and selection of isoniazid and rifampin resistance in tuberculosis granulomas

Drug resistant tuberculosis is increasing world-wide. Resistance against isoniazid (INH), rifampicin (RIF), or both (multi-drug resistant TB, MDR-TB) is of particular concern, since INH and RIF form part of the standard regimen for TB disease. While it is known that suboptimal treatment can lead to resistance, it remains unclear how host immune responses and antibiotic dynamics within granulomas (sites of infection) affect emergence and selection of drug-resistant bacteria. We take a systems pharmacology approach to explore resistance dynamics within granulomas. We integrate spatio-temporal host immunity, INH and RIF dynamics, and bacterial dynamics (including fitness costs and compensatory mutations) in a computational framework. We simulate resistance emergence in the absence of treatment, as well as resistance selection during INH and/or RIF treatment. There are four main findings. First, in the absence of treatment, the percentage of granulomas containing resistant bacteria mirrors the non-monotonic bacterial dynamics within granulomas. Second, drug-resistant bacteria are less frequently found in non-replicating states in caseum, compared to drug-sensitive bacteria. Third, due to a steeper dose response curve and faster plasma clearance of INH compared to RIF, INH-resistant bacteria have a stronger influence on treatment outcomes than RIF-resistant bacteria. Finally, under combination therapy with INH and RIF, few MDR bacteria are able to significantly affect treatment outcomes. Overall, our approach allows drug-specific prediction of drug resistance emergence and selection in the complex granuloma context. Since our predictions are based on pre-clinical data, our approach can be implemented relatively early in the treatment development process, thereby enabling pro-active rather than reactive responses to emerging drug resistance for new drugs. Furthermore, this quantitative and drug-specific approach can help identify drug-specific properties that influence resistance and use this information to design treatment regimens that minimize resistance selection and expand the useful life-span of new antibiotics.