Mathematical model of oxygen, nutrient, and drug transport in Tuberculosis Granulomas

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. Treatment failure in infectious diseases such as tuberculosis is often the result of inadequate drug delivery to the site of infection. In the case of tuberculosis, that site is most commonly a pulmonary granuloma-an abnormal mass of immune cells that forms in the lung in response to the body's attempt to confine and constrain the infection-causing bacteria. Within the granuloma interior, blood vessels are non-functional or absent, and the tissue is dense and fibrous. These physiological abnormalities hinder not only drug delivery, but also oxygen and nutrient availability to the immune cells fighting off the infection. Here, we mathematically examine the basis and scope of the poor delivery of oxygen, glucose, and tuberculosis-fighting drugs in granulomas. Our simulations agree with experimental results from animal models of this disease and reveal potential strategies to overcome physiological barriers to drug delivery in granulomas.