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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 (PO2)) 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 PO2 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 PO2 in blood capillary (Pbc) greater than PO2 in interstitial fluid (Pf), that is, for Pbc > Pf, a decrease (approaching zero value) followed by a gradual increase for Pbc < Pf and a constant like behavior for Pbc = Pf. 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.

Mathematical modelling of oxygen transport in biological tissues played a great role and provides optimal results for advanced biomedical and biophysical research. Conventionally, oxygen is administered to hypoxic patients through pul- monary route. A mathematical model has been proposed to establish an alternative route for oxygen supply, whereby oxygen is administered directly into the target tis- sue bypassing the lung compartment. Our study aims at evaluating the feasibility of the novel approach using compartment modelling. The model is represented by a system of first order ordinary differential equations and their solution by Cramer’s rule and Laplace transform method. The concentration profiles of oxygen through pulmonary and intravenous routes were estimated in the arterial blood and tissue compartments at different flow rates; and with respect to initial oxygen concen- tration in the lung compartment and in the injected solution. Our results are in agreement with those arrived at by Lin Gui and Jing Liu (2006) [4]. The method offers a promising alternative to the conventional approach for clinical rescue of hypoxic patients, more so in emergency situations.

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