A population model capturing dynamics of tuberculosis granulomas predicts host infection outcomes

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.

The transmission mechanism theory of disease dynamics: Its aims, assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process. Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history, dating back to over a century now, that knowledge has not yet been formalized into a scientific theory. In this article, we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system, disease dynamics is determined by transmission as the main dynamic disease process. Therefore, the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now. The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims, assumptions and limitations.

An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis

Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steady-state transitions can be the occurrence of transcritical and saddle-node bifurcations, which are induced by slowly changing parameters. Transcritical bifurcation, occurring when the basic reproduction number equals to one, determines whether the infection clears or spreads. Saddle-node bifurcation is the key mechanism to create and destroy steady states. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyses on transcritical bifurcation conditions and saddle-node bifurcation conditions. The sensitivity analysis results suggest that the macrophage apoptosis rate is the most significant factor affecting the transition in disease outcomes. This result agrees with the discovery that the programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interplay. Sensitivity analysis narrows down the parameters of interest, but cannot answer how these parameters influence the model outcomes. To do this, we employ bifurcation analysis and numerical simulation to unfold various disease outcomes induced by the variation of macrophage apoptosis rate. Our findings support the hypothesis that the regulation mechanism of macrophage apoptosis affects the host immunity against tuberculosis infection and tuberculosis virulence. Moreover, our mathematical results suggest that new treatments and/or vaccines that regulate macrophage apoptosis in combination with weakening bacillary viability and/or promoting adaptive immunity could have therapeutic value.

Modelling the dynamics of tuberculosis lesions in a virtual lung: Role of the bronchial tree in endogenous reinfection

Tuberculosis (TB) is an infectious disease that still causes more than 1.5 million deaths annually. The World Health Organization estimates that around 30% of the world's population is latently infected. However, the mechanisms responsible for 10% of this reserve (i.e., of the latently infected population) developing an active disease are not fully understood, yet. The dynamic hypothesis suggests that endogenous reinfection has an important role in maintaining latent infection. In order to examine this hypothesis for falsifiability, an agent-based model of growth, merging, and proliferation of TB lesions was implemented in a computational bronchial tree, built with an iterative algorithm for the generation of bronchial bifurcations and tubes applied inside a virtual 3D pulmonary surface. The computational model was fed and parameterized with computed tomography (CT) experimental data from 5 latently infected minipigs. First, we used CT images to reconstruct the virtual pulmonary surfaces where bronchial trees are built. Then, CT data about TB lesion' size and location to each minipig were used in the parameterization process. The model's outcome provides spatial and size distributions of TB lesions that successfully reproduced experimental data, thus reinforcing the role of the bronchial tree as the spatial structure triggering endogenous reinfection. A sensitivity analysis of the model shows that the final number of lesions is strongly related with the endogenous reinfection frequency and maximum growth rate of the lesions, while their mean diameter mainly depends on the spatial spreading of new lesions and the maximum radius. Finally, the model was used as an in silico experimental platform to explore the transition from latent infection to active disease, identifying two main triggering factors: a high inflammatory response and the combination of a moderate inflammatory response with a small breathing amplitude.

Linking Individual Natural History to Population Outcomes in Tuberculosis

Background

Substantial individual heterogeneity exists in the clinical manifestations and duration of active tuberculosis. We sought to link the individual-level characteristics of tuberculosis disease to observed population-level outcomes.

Methods

We developed an individual-based, stochastic model of tuberculosis disease in a hypothetical cohort of patients with smear-positive tuberculosis. We conceptualized the disease process as consisting of 2 states—progression and recovery—including transitions between the 2. We then used a Bayesian process to calibrate the model to clinical data from the prechemotherapy era, thus identifying the rates of progression and recovery (and probabilities of transition) consistent with observed population-level clinical outcomes.

Results

Observed outcomes are consistent with slow rates of disease progression (median doubling time: 84 days, 95% uncertainty range 62–104) and a low, but nonzero, probability of transition from disease progression to recovery (median 16% per year, 95% uncertainty range 11%–21%). Other individual-level dynamics were less influential in determining observed outcomes.

Conclusions

This simplified model identifies individual-level dynamics—including a long doubling time and low probability of immune recovery—that recapitulate population-level clinical outcomes of untreated tuberculosis patients. This framework may facilitate better understanding of the population-level impact of interventions acting at the individual host level.

A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment

Tuberculosis (TB) is an ancient and deadly disease characterized by complex host-pathogen dynamics playing out over multiple time and length scales and physiological compartments. Computational modeling can be used to integrate various types of experimental data and suggest new hypotheses, mechanisms, and therapeutic approaches to TB. Here, we offer a first-time comprehensive review of work on within-host TB models that describe the immune response of the host to infection, including the formation of lung granulomas. The models include systems of ordinary and partial differential equations and agent-based models as well as hybrid and multi-scale models that are combinations of these. Many aspects of M. tuberculosis infection, including host dynamics in the lung (typical site of infection for TB), granuloma formation, roles of cytokine and chemokine dynamics, and bacterial nutrient availability have been explored. Finally, we survey applications of these within-host models to TB therapy and prevention and suggest future directions to impact this global disease.

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

Optimization and Control of Agent-Based Models in Biology: A Perspective

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Understanding the pathophysiology of the human TB lung granuloma using in vitro granuloma models

Tuberculosis remains a major human health threat that infects one in three individuals worldwide. Infection with Mycobacterium tuberculosis is a standoff between host and bacteria in the formation of a granuloma. This review will introduce a variety of bacterial and host factors that impact individual granuloma fates. The authors describe advances in the development of in vitro granuloma models, current evidence surrounding infection and granuloma development, and the applicability of existing in vitro models in the study of human disease. In vitro models of infection help improve our understanding of pathophysiology and allow for the discovery of other potential models of study.

Computational immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.

Local Inflammation, Dissemination and Coalescence of Lesions Are Key for the Progression toward Active Tuberculosis: The Bubble Model

The evolution of a tuberculosis (TB) infection toward active disease is driven by a combination of factors mostly related to the host response. The equilibrium between control of the bacillary load and the pathology generated is crucial as regards preventing the growth and proliferation of TB lesions. In addition, some experimental evidence suggests an important role of both local endogenous reinfection and the coalescence of neighboring lesions. Herein we propose a mathematical model that captures the essence of these factors by defining three hypotheses: (i) lesions grow logistically due to the inflammatory reaction; (ii) new lesions can appear as a result of extracellular bacilli or infected macrophages that escape from older lesions; and (iii) lesions can merge when they are close enough. This model was implemented in Matlab to simulate the dynamics of several lesions in a 3D space. It was also fitted to available microscopy data from infected C3HeB/FeJ mice, an animal model of active TB that reacts against Mycobacterium tuberculosis with an exaggerated inflammatory response. The results of the simulations show the dynamics observed experimentally, namely an initial increase in the number of lesions followed by fluctuations, and an exponential increase in the mean area of the lesions. In addition, further analysis of experimental and simulation results show a strong coincidence of the area distributions of lesions at day 21, thereby highlighting the consistency of the model. Three simulation series removing each one of the hypothesis corroborate their essential role in the dynamics observed. These results demonstrate that three local factors, namely an exaggerated inflammatory response, an endogenous reinfection, and a coalescence of lesions, are needed in order to progress toward active TB. The failure of one of these factors stops induction of the disease. This mathematical model may be used as a basis for developing strategies to stop the progression of infection toward disease in human lungs.