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.

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.

Individual-Based Modeling of Tuberculosis in a User-Friendly Interface: Understanding the Epidemiological Role of Population Heterogeneity in a City.

For millennia tuberculosis (TB) has shown a successful strategy to survive, making it one of the world's deadliest infectious diseases. This resilient behavior is based not only on remaining hidden in most of the infected population, but also by showing slow evolution in most sick people. The course of the disease within a population is highly related to its heterogeneity. Thus, classic epidemiological approaches with a top-down perspective have not succeeded in understanding its dynamics. In the past decade a few individual-based models were built, but most of them preserved a top-down view that makes it difficult to study a heterogeneous population. We propose an individual-based model developed with a bottom-up approach to studying the dynamics of pulmonary TB in a certain population, considered constant. Individuals may belong to the following classes: healthy, infected, sick, under treatment, and treated with a probability of relapse. Several variables and parameters account for their age, origin (native or immigrant), immunodeficiency, diabetes, and other risk factors (smoking and alcoholism). The time within each infection state is controlled, and sick individuals may show a cavitated disease or not that conditions infectiousness. It was implemented in NetLogo because it allows non-modelers to perform virtual experiments with a user-friendly interface. The simulation was conducted with data from Ciutat Vella, a district of Barcelona with an incidence of 67 TB cases per 100,000 inhabitants in 2013. Several virtual experiments were performed to relate the disease dynamics with the structure of the infected subpopulation (e.g., the distribution of infected times). Moreover, the short-term effect of health control policies on modifying that structure was studied. Results show that the characteristics of the population are crucial for the local epidemiology of TB. The developed user-friendly tool is ready to test control strategies of disease in any city in the short-term.

To achieve an earlier IFN-γ response is not sufficient to control Mycobacterium tuberculosis infection in mice.

The temporo-spatial relationship between the three organs (lung, spleen and lymph node) involved during the initial stages of Mycobacterium tuberculosis infection has been poorly studied. As such, we performed an experimental study to evaluate the bacillary load in each organ after aerosol or intravenous infection and developed a mathematical approach using the data obtained in order to extract conclusions. The results showed that higher bacillary doses result in an earlier IFN-γ response, that a certain bacillary load (BL) needs to be reached to trigger the IFN-γ response, and that control of the BL is not immediate after onset of the IFN-γ response, which might be a consequence of the spatial dimension. This study may have an important impact when it comes to designing new vaccine candidates as it suggests that triggering an earlier IFN-γ response might not guarantee good infection control, and therefore that additional properties should be considered for these candidates.

Evolution and role of corded cell aggregation in Mycobacterium tuberculosis cultures.

The aim of this study was to evaluate the evolution and role of corded cell aggregation in Mycobacterium tuberculosis cultures according to growth time and conditions. Thus, in standard culture using aerated 7H9 Middlebrook broth supplemented with 0.05% Tween 80, a dramatic CFU decrease was observed at the end of the exponential phase. This phase was followed by a stable stationary phase that led to dissociation between the optical density (O.D.) and CFU values, together with the formation of opaque colonies in solid culture. Further analysis revealed that this was due to cording. Scanning electron microscopy showed that cording led to the formation of very stable coiled structures and corded cell aggregations which proved impossible to disrupt by any of the physical means tested. Modulation of cording with a high but non-toxic concentration of Tween 80 led to a slower growth rate, avoidance of a sudden drop-off to the stationary phase, the formation of weaker cording structures and the absence of opaque colonies, together with a lower survival at later time-points. An innovative automated image analysis technique has been devised to characterize the cording process. This analysis has led to important practical consequences for the elaboration of M. tuberculosis inocula and suggests the importance of biofilm formation in survival of the bacilli in the extracellular milieu.

Effect of the haematocrit layer geometry on Plasmodium falciparum static thin-layer in vitro cultures.

BACKGROUND: In vitro cultivation of Plasmodium falciparum is usually carried out through the continuous preservation of infected erythrocytes deposited in static thin layers of settled haematocrit. This technique, called the candle-jar method, was first achieved by Trager and Jensen in 1976 and has undergone slight modifications since then. However, no systematic studies concerning the geometry of the haematocrit layer have been carried out. In this work, a thorough investigation of the effects of the geometric culturing conditions on the parasite's development is presented. METHODS: Several experimental trials exploring different settings have been carried out, covering haematocrit layer depths that ranged from 6 mm to 3 mm and separation between the walls of the culturing device that ranged from 7.5 mm to 9 mm. The obtained results have been analysed and compared to different system-level models and to an Individual-Based Model. CONCLUSION: In line with the results, a mechanism governing the propagation of the infection which limits it to the vicinity of the interface between the haematocrit layer and the culture medium is deduced, and the most appropriate configurations are proposed for further experimental assays.

Individual-based model and simulation of Plasmodium falciparum infected erythrocyte in vitro cultures.

Malaria is still one of the most fatal diseases in the world. Development of an effective treatment or vaccine requires the cultivation of the parasite that causes it: Plasmodium falciparum. Several methods for in vitro cultivation of P. falciparum infected erythrocytes have been successfully developed and described in the last 30 years. Some problems arising from the current harvests are the low parasitaemia and daily human supervision requirements. The lack of a suitable model for global culture behavior makes the assay of new methodologies a costly and tenuous task. In this paper we present a model and simulation tool for these systems. We use the INDividual DIScrete SIMulation protocol (INDISIM) to qualitatively reproduce the temporal evolution of the erythrocyte and merozoite populations. Whole system dynamics are inferred by setting the rules of behavior for each individual red blood cell, such as the nutrient uptake, metabolism and infection processes, as well as the properties and rules for the culture medium: composition, diffusion and external manipulation. We set the individual description parameters according to the values in published data, and allow population heterogeneity. Cells are arranged in a three-dimensional grid and the study is focused on the geometric constraints and physical design of experimental sets. Several published experimental cultures have been reproduced with computer simulations of this model, showing that the observed experimental behavior can be explained by means of individual interactions and statistical laws.

Individual-based modelling of bacterial cultures to study the microscopic causes of the lag phase.

The lag phase has been widely studied for years in an effort to contribute to the improvement of food safety. Many analytical models have been built and tested by several authors. The use of Individual-based Modelling (IbM) allows us to probe deeper into the behaviour of individual cells; it is a bridge between theories and experiments when needed. INDividual DIScrete SIMulation (INDISIM) has been developed and coded by our group as an IbM simulator and used to study bacterial growth, including the microscopic causes of the lag phase. First of all, the evolution of cellular masses, specifically the mean mass and biomass distribution, is shown to be a determining factor in the beginning of the exponential phase. Secondly, whenever there is a need for an enzyme synthesis, its rate has a direct effect on the lag duration. The variability of the lag phase with different factors is also studied. The known decrease of the lag phase with an increase in the temperature is also observed in the simulations. An initial study of the relationship between individual and collective lag phases is presented, as a complement to the studies already published. One important result is the variability of the individual lag times and generation times. It has also been found that the mean of the individual lags is greater than the population lag. This is the first in a series of studies of the lag phase that we are carrying out. Therefore, the present work addresses a generic system by making a simple set of assumptions.

INDISIM, an individual-based discrete simulation model to study bacterial cultures.

An individual-based model has been developed and designed to simulate the growth and behaviour of bacterial colonies. The simulator is called INDISIM, which stands for INDividual DIScrete SIMulations. INDISIM is discrete in space and time, and controls a group of bacterial cells at each time step, using a set of random, time-dependent variables for each bacterium. These variables are used to characterize its position in space, biomass, state in the cellular reproduction cycle as well as other individual properties. The space where the bacterial colony evolves is also discrete. A physical lattice is introduced, subject to the appropriate boundary conditions. The lattice is subdivided into spatial cells, also defined by a set of random, time-dependent variables. These variables may include concentrations of different types of particles, nutrients, reaction products and residual products. Random variables are used to characterize the individual bacterium and the individual particle, as well as the updating of individual rules. Thus, the simulations are stochastic rather than deterministic. The whole set of variables, those that characterize the bacterial population and the environment where they evolve, enables the simulator to study the behaviour of each microorganism-such as its motion, uptake, metabolism, and viability-according to given rules suited for the system under study. These rules require the input of only a few parameters. Once this information is inputted, INDISIM simulates the behaviour of the system providing insights into the global properties of the system from the assumptions made on the properties of the individual bacteria. The relation between microscopic and global properties of the bacterial colony is obtained by using statistical averaging. In this work INDISIM has been used to study (a) biomass distributions, (b) the relationship between the rate of growth of a bacterial colony and the nutrient concentration and temperature, and (c) metabolic oscillations in batch bacterial colonies. The simulation results are found to be in very good qualitative agreement with available experimental data, and provide useful insights into the mechanisms involved in each case.

Nonequilibrium dynamics in lattice ecosystems: Chaotic stability and dissipative structures.

A generalized coupled map lattice (CML) model of ecosystem dynamics is presented. We consider the spatiotemporal behavior of a prey-predator map, a model of host-parasitoid interactions, and two-species competition. The latter model can show phase separation of domains (Turing-like structures) even when chaos is present. We also use this CML model to explore the time evolution and structural properties of ecological networks built with a set of N competing species. The May-Wigner criterion is applied as a measure of stability, and some regularities in the stable networks observed are discussed.