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Plots showing solution curves in the center compartment of the 5×5 metapopulation lattice, for parameter values that lead to latency. All parameter values are the baseline values shown in Table 3.2 (hence, α 20 = 0.03).
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![Table 1 . Kinetic parameter estimates from [35]](profile/David-Gammack-2/publication/43048359/figure/tbl1/AS:601690143195142@1520465517268/Kinetic-parameter-estimates-from-35_Q320.jpg)
The immune response to Mycobacterium tuberculosis infection (Mtb) is the formation of unique lesions, called granulomas. How well these granulomas form and function is a key issue that might explain why individuals experience different disease outcomes. The spatial structures of these granulomas are not well understood. In this paper, we use a meta...
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Citations
... For example, the model by Segovia-Juarez et al. showed that a slower bacterial growth rate within infected cells is worse for the host [141]. Bacterial replication and decay rates as well as other model components identified distinct pathological states including early clearance, granuloma formation, and persistent infection [68,140,150,152,160,165,166,172,179,188]. ...
Lung inflammation may occur due to viral and bacterial infections, structural damage, or inhalation of dangerous particles. These injuries may be quickly resolved by the immune system, treated effectively through various interventions, become chronic problems, or lead to death. Mathematical modeling has been used to understand immune system dynamics during a number of pulmonary infections and injuries, identify key mechanisms, and provide important insights into new treatments. In this review, we present long-accepted modeling techniques and novel strategies for simulating various lung injuries to highlight the usefulness of mathematical modeling in addressing these life-threatening conditions. Advances in computational power have allowed for a diverse collection of models ranging from those using only Boolean operatorsto complex hybrid multi-scale models, each specifically designed to address relevant biological questions. To illustrate the findings from these mathematical approaches, we present detailed examples, summarize results, and consider future directions from modeling influenza, pneumonia, COVID-19, tuberculosis, anthrax, and other non-infectious injuries.
... Due to the important role of the host adaptive immune response on impacting treatment effect, various mathematical models have been developed to describe bacterial infection and the resulting immunological responses in animal models of TB (71,73,81,83,(95)(96)(97)(98). The enormous amount of data from mouse models of TB has provided great advantages in modeling the bacterial infection and the underlying development of immune responses. ...
Tuberculosis (TB) kills more people than any other infectious disease. Challenges for developing better treatments include the complex pathology due to within-host immune dynamics, interpatient variability in disease severity and drug pharmacokinetics-pharmacodynamics (PK-PD), and the growing emergence of resistance. Model-informed drug development using quantitative and translational pharmacology has become increasingly recognized as a method capable of drug prioritization and regimen optimization to efficiently progress compounds through TB drug development phases. In this review, we examine translational models and tools, including plasma PK scaling, site-of-disease lesion PK, host-immune and bacteria interplay, combination PK-PD models of multidrug regimens, resistance formation, and integration of data across nonclinical and clinical phases. We propose a workflow that integrates these tools with computational platforms to identify drug combinations that have the potential to accelerate sterilization, reduce relapse rates, and limit the emergence of resistance.
Expected final online publication date for the Annual Review of Pharmacology and Toxicology, Volume 61 is January 8, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... A mathematical model based on the human immune response to MTB in the lung which incorporates macrophages and lymphocyte interaction was earlier developed by Marino and Kirscher [18] . The present paper builds on this work as well as other works on mycobacteria infection [19][20][21][22][23][24] . However, most of these models of tuberculosis infection do not concentrate on the switching time (the time activated macrophages surpasses infected macrophages) with a few works like [25,26] etc. doing so. ...
... We will refer to the set of such equations in (18)(19)(20) as the infected subsystem. As a rule that exist, the first step is to linearize the infected subsystem about the bacteria-free steady state. ...
The use of mathematical tools to study biological processes is of necessity in determining the effects of these biological processes occurring at different levels. In this paper, we study the immune system's response to infection with the bacteria Mycobacterium tuberculosis (the causative agent of tuberculosis). The response by the immune system is either global (lymph node, thymus, and blood) or local (at the site of infection). The response by the immune system against tuberculosis (TB) at the site of infection leads to the formation of spherical structures which comprised of cells, bacteria, and effector molecules known as granuloma. We developed a deterministic model capturing the dynamics of the immune system, macrophages, cytokines and bacteria. The hallmark of Mycobacterium tuberculosis (MTB) infection in the early stages requires a strong protective cell-mediated naive T cells differentiation which is characterised by antigen-specific interferon gamma (IFN-γ). The host immune response is believed to be regulated by the interleukin-10 cytokine by playing the critical role of orchestrating the T helper1 and T helper2 dominance during disease progression. The basic reproduction number is computed and a stability analysis of the equilibrium points is also performed. Through the computation of the reproduction number, we predict disease progression scenario including the latency state. The occurrence of latent infection is shown to depend on a number of effector function and the bacterial load for R0<1. The model predicts that endemically there is no steady state behaviour; rather it depicts the existence of MTB to be a continuous process progressing over a differing time period. Simulations of the model predict the time at which the activated macrophages overcome the infected macrophages (switching time) and observed that the activation rate (ω) correlates negatively with it. The efficacy of potential host-directed therapies was determined by the use of the model.
... These are particularly used in epidemiology (Arino and van den Driessche 2006;Hickson et al. 2012), where the species represent individuals in different states of disease or susceptibility and have been used to show that greater understanding of the differentials within the global population can allow researchers to understand and better control the dynamics of global infections (Helbing et al. 2014) and how spatial heterogeneities in aspects like contact rates, vaccination uptake and demographics can alter the effectiveness of intervention programs to prevent disease transmission (Wang et al. 2016). Ganguli et al. (2005) use this approach in modelling the formation of a single TB lesion, with a grid of compartments modelling a small portion of alveolar tissue, each of which contains a variety of species including bacteria and various immune cells. Their metapopulation model incorporates spatial heterogeneity by restricting the interactions between agents of the system to only those in the same spatial compartment, with some agents able to move between compartments. ...
Tuberculosis (TB) is an ancient disease that, although curable, still accounts for over 1 million deaths worldwide. Shortening treatment time is an important area of research but is hampered by the lack of models that mimic the full range of human pathology. TB shows distinct localisations during different stages of infection, the reasons for which are poorly understood. Greater understanding of how heterogeneity within the human lung influences disease progression may hold the key to improving treatment efficiency and reducing treatment times.
In this work, we present a novel in silico software model which uses a networked metapopulation incorporating both spatial heterogeneity and dissemination possibilities to simulate a TB infection over the whole lung and associated lymphatics. The entire population of bacteria and immune cells is split into a network of patches: members interact within patches and are able to move between them. Patches and edges of the lung network include their own environmental attributes which influence the dynamics of interactions between the members of the subpopulations of the patches and the translocation of members along edges.
In this work, we detail the initial findings of a whole-organ model that incorporates distinct spatial heterogeneity features which are not present in standard differential equation approaches to tuberculosis modelling. We show that the inclusion of heterogeneity within the lung landscape when modelling TB disease progression has significant outcomes on the bacterial load present: a greater differential of oxygen, perfusion and ventilation between the apices and the basal regions of the lungs creates micro-environments at the apex that are more preferential for bacteria, due to increased oxygen availability and reduced immune activity, leading to a greater overall bacterial load present once latency is established.
These findings suggest that further whole-organ modelling incorporating more sophisticated heterogeneities within the environment and complex lung topologies will provide more insight into the environments in which TB bacteria persist and thus help develop new treatments which are factored towards these environmental conditions.
Electronic supplementary material
The online version of this article (10.1007/s41109-018-0091-2) contains supplementary material, which is available to authorized users.
... In many such models, however, individual-level temporal dynamics and pathological processes (such as disease onset, progression, cure, and death) are simplified as population-level rates or probabilities. In contrast, within-host models can help disentangle individual-level dynamics of M. tuberculosis replication, host immune cell responses, cytokine signaling, pathology, and bacterial metapopulations [11][12][13][14][15]. Most within-host models of tuberculosis have uncertain applicability to human epidemics, however, as they draw on biological observations of experimental animal infection that have important dissimilarities with key aspects of human disease-including long-term asymptomatic latency, spontaneous self-resolution, and heterogeneity in disease outcome [16]. ...
... While these conceptual phases of progression and recovery are simplifications of the complex pathophysiology of tuberculosis infection [21], they are analogous to experimentally observable dynamics of bacterial replication and immune responses in vivo [7]. Unlike biological within-host models of tuberculosis [11][12][13][14]22], this model does not attempt to capture the complex and diverse immunological and pathophysiological mechanisms that influence clinical outcomes in any given individual. Rather, for simplicity and ease of understanding, we use "disease burden" as a mathematical benchmark that is likely associated with clinical outcomes (eg, individuals who develop a higher burden may experience more severe symptoms, increased risk of mortality, and other pathological characteristics such as increased infectiousness) [18,23,24]. ...
Background:
Substantial individual heterogeneity exists in the clinical manifestations and duration of active tuberculosis. We sought to link the individual-level characteristics of TB disease to observed population-level outcomes.
Methods:
We developed an individual-based, stochastic model of TB disease in a hypothetical cohort of patients with smear-positive TB. We conceptualized the disease process as consisting of two states - progression and recovery - including transitions between the two. We then used a Bayesian process to calibrate the model to clinical data from the pre-chemotherapy 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 TB patients. This framework may facilitate better understanding of the population-level impact of interventions acting at the individual host level.
... The first spatial model of granulomas developed was an agent-based model (ABM) [64,69]; formation of the granuloma was an emergent behavior in the model. PDE models [58,68,71] and other formulations such as metapopulation models [70] were also used and compared [146]. One model examined early events in mice, including neutrophils and the role they play in granuloma formation [66], while others examined the role of the bacterial burst size on granulomas [67]. ...
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.
... By combining both of these analysis tools [55][56][57][58], we guide our understanding as to how and what extent variability in model mechanisms captured by parameter values can affect infection outcomes in an ordered fashion. We have successfully used this approach in our previous studies, both equation-based (i.e., ordinary, partial and delay differential equation systems), as well as agent-based model settings [24,25,[59][60][61]. ...
Results:
The model was calibrated using experimental data from the lungs and blood of NHPs. The addition of DCs allowed us to investigate in greater detail mechanisms of recruitment, trafficking and antigen presentation and their role in tuberculosis infection.
Conclusion:
The main conclusion of this study is that early events after Mtb infection are critical to establishing a timely and effective response. Manipulating CD8+ and CD4+ T cell proliferation rates, as well as DC migration early on during infection can determine the difference between bacterial clearance vs. uncontrolled bacterial growth and dissemination.
... Mathematical and computational models have been used to predict the granulomatous response in TB infection based on experimental observations and the available information about the disease [110][111][112][113][114][115][116][117]. Mathematical models are inexpensive and allow investigators to test a variety of new hypotheses and incorporate a number of complex parameters without the cost and time issues encountered in wet laboratory experiments. ...
... For example, differential equation (DE) based models describe a relationship between numbers of cells and concentrations of molecules and their rates of change in the granuloma and time [113][114]117]. In contrast to DE based models, individual based models, or agentbased models (ABMs), are rule-based models that capture the events occurring in the immune systems (e.g., immune cells, bacteria, environmental factors) using a 2D grid representing a section of lung tissue [110,[115][116]. Although these models have been useful in answering complex questions, they are highly dependent on the parameters chosen, and require previous observations in different systems to extrapolate the results. ...
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.
... These methods can be used to better explore hypothesized mechanisms, generate and test new hypotheses, run virtual (in silico) experiments, interpret data, motivate particular experiments, and suggest new drug targets. A series of mathematical and computational models have been developed to investigate the host response to M. tuberculosis infection [45][46][47][48][49][50][51][52][53][54][55][56][57] . In particular, model-based analysis of the formation and function of a TB granuloma contributes to understanding the mechanisms that control the immune response to M. tuberculosis [ 45-49, 51, 57 ] . ...
The pathologic hallmark of tuberculosis is the granuloma. A granuloma is a multifaceted cellular structure that serves to focus the host immune response, contain infection and pathology, and provide a niche for the bacillus to persist within the host. Granulomas form in response to Mycobacterium tuberculosis infection, and if a granuloma is capable of inhibiting or killing most of the M. tuberculosis present, humans develop a clinically latent infection. However, if a granuloma is impaired in function, infection progresses, granulomas enlarge, and bacteria seed new granulomas; this results in progressive pathology and disease, i.e., active tuberculosis. In clinical latency, immunologic perturbation at the level of the granuloma can result in reactivation of infection. In humans, there are a variety of granuloma types, even within the lungs of a single host.
The roles and interactions of various cells (macrophages, T cells, B cells, and neutrophils) and molecules (cytokines, chemokines, and effector molecules) within a granuloma are complex and challenging to address by experimental methods alone. Computational approaches, in particular agent-based modeling, can be used to dissect the temporal and spatial aspects of granuloma formation and function. Here we explain how a systems biology approach can integrate experimental and computational work to address critical questions necessary to understanding granulomas and contribute to the development and testing of strategies for prevention and treatment.
... In silico models do not share the same experimental limits of in vivo models and allow more direct control on multiple experimental conditions. Computational and mathematical models of the cellular response to granulomatous infection have been developed previously in the context of tuberculosis3132333435, sarcoidosis [36] and leishmaniasis [37], but they generally account only for a limited number of leukocyte populations. For example, a recent study used a coloured Petri net approach to model the innate macrophage granuloma that forms during infection of zebrafish with Mycobacterium [38]. ...
Author Summary
Granulomatous inflammation is a common feature of chronic infectious and non-infectious disease. In the parasitic disease visceral leishmaniasis, the formation of granulomas in the liver is a hallmark of effective cellular immunity and host resistance to infection. Conventional experimental models, however, have inherent limitations in their capacity to assess the dynamics of this complex inflammatory response and in their ability to discriminate the local contribution of different immune cells and mediators to the outcome of infection. To overcome these limitations and to provide a future platform for evaluating how novel drugs might be used to improve host resistance, we have developed a computational model of the Leishmania granuloma. Using this model, we show that conventional measures of parasite load potentially mask an underlying heterogeneity in the ability of individual granulomas to control parasite number. In addition, we have used our model to provide novel insights into the relative importance of IL-10 production by different immune cells found within the granuloma microenvironment. Our model thus provides a complementary tool to increase understanding of granulomatous inflammation in this and other important human diseases.
