Modeling Granulomas in Response to Infection in the Lung

Alveolar macrophages play a large role in the innate immune response of the lung. However, when these highly immune-regulatory cells are unable to eradicate pathogens, the adaptive immune system, which includes activated macrophages and lymphocytes, particularly T cells, is called upon to control the pathogens. This collection of immune cells surrounds, isolates and quarantines the pathogen, forming a small tissue structure called a granuloma for intracellular pathogens like Mycobacterium tuberculosis (Mtb). In the present work we develop a mathematical model of the dynamics of a granuloma by a system of partial differential equations. The 'strength' of the adaptive immune response to infection in the lung is represented by a parameter a, the flux rate by which T cells and M1 macrophages that immigrated from the lymph nodes enter into the granuloma through its boundary. The parameter a is negatively correlated with the 'switching time', namely, the time it takes for the number of M1 type macrophages to surpass the number of infected, M2 type alveolar macrophages. Simulations of the model show that as a increases the radius of the granuloma and bacterial load in the granuloma both decrease. The model is used to determine the efficacy of potential host-directed therapies in terms of the parameter a, suggesting that, with fixed dosing level, an infected individual with a stronger immune response will receive greater benefits in terms of reducing the bacterial load.