Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma

A reaction-diffusion model to understand granulomas formation inside secondary lobule during tuberculosis infection

Mycobacterium tuberculosis (Mtb) is the causative agent for tuberculosis, the most extended infectious disease around the world. When Mtb enters inside the pulmonary alveolus it is rapidly phagocytosed by the alveolar macrophage. Although this controls the majority of inhaled microorganisms, in this case, Mtb survives inside the macrophage and multiplies. A posterior chemokine and cytokine cascade generated by the irruption of monocytes, neutrophils and posteriorly, by T-cells, does not necessarily stop the growth of the granuloma. Interestingly, the encapsulation process built by fibroblasts is able to surround the lesion and stop its growing. The success of this last process determines if the host enters in an asymptomatic latent state or continues into a life-threatening and infective active tuberculosis disease (TB). Understanding such dichotomic process is challenging, and computational modeling can bring new ideas. Thus, we have modeled the different stages of the infection, first in a single alveolus (a sac with a radius of 0.15 millimeters) and, second, inside a secondary lobule (a compartment of the lungs of around 3 cm³). We have employed stochastic reaction-diffusion equations to model the interactions among the cells and the diffusive transport to neighboring alveolus. The whole set of equations have successfully described the encapsulation process and determine that the size of the lesions depends on its position on the secondary lobule. We conclude that size and shape of the secondary lobule are the relevant variables to control the lesions, and, therefore, to avoid the evolution towards TB development. As lesions appear near to interlobular connective tissue they are easily controlled and their growth is drastically stopped, in this sense secondary lobules with a more flattened shape could control better the lesion.

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.