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

Abstract

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.