Mathematical Model of Oxygen Transport in Tuberculosis Granulomas.
Tuberculosis (TB) is one of the world's most infectious diseases, accounting for
approximately 2 million deaths and 2 billion latent infections in 2009. Despite the
relative success of first-line anti-TB agents, multi-drug resistant strains of the TB
bacillus have become rampant, especially in impoverished nations. This is due in part to
the inability of chemotherapeutic agents to ... read morereach the TB bacilli trapped by the host
immune system within dense cellular masses known as granulomas, in the lungs. It is
argued here that granulomas are, in fact, morphologically similar to solid cancerous
tumors in that they both share high cell densities, evidence of mechanical stress,
abnormal vasculature, and oxygen-starved regions of hypoxia and necrosis where, in the
case of TB, the bacilli survive and lie in wait for the host immune system to be
compromised. Analogous to similar research in tumors, thus, this Thesis seeks to explore
transport limitations within TB granulomas, specifically to better understand how poor
oxygen delivery results in hypoxia and necrosis within these abnormal lesions. Chemical
engineering principles of transport and reaction were used to investigate oxygen
diffusion and cellular consumption within isothermal granuloma spheroids based on
Michaelis-Menten (MM) kinetics. An approximate analytical solution to the problem was
explored based on dividing the diffusion-limited region into two sub-regions: an outer
sub-region A where zero-order approximation of MM kinetics applies as the result of
adequate oxygen concentration, and an inner sub-region B of limited oxygen supply where
first-order approximation of MM kinetics is assumed, defining the hypoxic region. Cell
death ensues below a critical oxygen level that establishes the necrotic core, where the
TB bacteria repose. Based largely on a priori parameters, with the main exception of a
MM kinetic constant determined from the experimental minimum size of a granuloma with
the start of a necrotic core and an estimated oxygen effective diffusivity, the
resulting model is able to predict the emergence of hypoxia and necrosis in granulomas.
The theoretical sizes of the hypoxic and necrotic regions were found to be in good
agreement with experimental results from a rabbit model of TB, carried out at the
National Institutes of Health (NIH) as part of a collaboration with Massachusetts
General Hospital (MGH). Such quantitative understanding of transport limitations can
inform future TB treatment strategies that may, as in tumors, include adjunct
therapeutics that mitigate abnormal physiological traits in the granuloma structure and
microenvironment to facilitate oxygen, nutrient, and drug
Thesis (M.S.)--Tufts University, 2013.
Submitted to the Dept. of Chemical and Biological Engineering.
Advisor: Jerry Meldon.
Committee: Rakesh Jain, and Kyongbum Lee.
Keyword: Chemical engineering.read less