Explicit finite difference method to estimate oxygen concentration in biological tissues under variable oxygen tension in capillaries. Issue 2 (26th October 2020) - Lone, Ahsan Ul Haq; Khanday, M. A.; Mubarak, Saqib
Abstract : A mathematical model based on radial reaction‐diffusion equation has been formulated. An explicit formula of finite difference method based on the forward‐time central‐space (FTCS) scheme has been applied to solve the initial‐boundary‐value problem. The main purpose of this study is to estimate the concentration profiles of oxygen at the biological tissues under variable oxygen tension (oxygen partial pressure ( PO 2 )) in capillaries. The results obtained illustrate the variation of oxygen concentration in biological tissues with respect to temporal and spatial parameters. The results have shown a remarkable change in response to variation in PO 2 in the blood capillary relative to that in the interstitial fluid. It has been observed, at fixed values of time period, oxygen concentration as a function of radial distance shows a decrease for PO 2 in blood capillary ( P bc ) greater than PO 2 in interstitial fluid ( P f ), that is, for P bc  >  P f, a decrease (approaching zero value) followed by a gradual increase for P bc  <  P f and a constant like behavior for P bc  =  P f . The values estimated in this study may help medical scientists to understand conditions under which hypoxia and other respiratory ailments occur to the biological tissues.