Mathematical analysis of oxygen and carbon dioxide exchange in the human capillary and tissue system.

Human body has a great ability to maintain homeostasis and the respiratory system plays a pivotal role in physiological processes. In this paper, a mathematical model of oxygen and carbon dioxide transport in the human body through capillary and tissue system has been formulated. The model is given by four ordinary differential equations for the oxygen and carbon dioxide transport, two equations for the capillary and other two for the tissue. An analytic approach based on Taylor's series method has been presented in this paper to obtain a computable approximate solution of the differential equation to model the oxygen and carbon dioxide diffusion in a spherical tissue. The concentration profiles at the capillary and tissue regions has been estimated in relation with partial pressure as the main driving force. The results are in agreement with the literature data those arrived at by Whiteley et al. (2005). The results obtained may help bio-medical sciences to deal with hypoxia and other respiratory ailments faced by the people living at high altitudes. Moreover, facilitated diffusion due to haemoglobin has been presented.