Mathematical Model of Oxygen Transport in Tuberculosis Granulomas II: Transvascular and Interstitial Convection, Diffusion, and Reaction

Abstract Physiological abnormalities in pulmonary granulomas – pathological hallmarks of tuberculosis (TB) – compromise the transport of oxygen, nutrients, and drugs. In prior studies, we demonstrated mathematically and experimentally that hypoxia and necrosis emerge in the granuloma microenvironment (GME) as a direct result of limited oxygen availability. Building on our initial model of avascular oxygen diffusion, here we explore additional aspects of oxygen transport, including the roles of granuloma vasculature, transcapillary transport, plasma dilution, and interstitial convection, followed by cellular metabolism. Approximate analytical solutions are provided for oxygen and glucose concentration, interstitial fluid velocity, interstitial fluid pressure, and the thickness of the convective zone. These predictions are in agreement with prior experimental results from rabbit TB granulomas and from rat carcinoma models, which share similar transport limitations. Additional drug delivery predictions for anti-TB-agents (rifampicin and clofazimine) strikingly match recent spatially-resolved experimental results from a mouse model of TB. Finally, an approach to improve molecular transport in granulomas by modulating interstitial hydraulic conductivity is tested in silico.