A Mathematical Model for the Elimination of Carbon Monoxide in Humans

Carboxyhaemoglobin (COHb) build-up in the blood as a result of exposures to carbon monoxide (CO) affects human beings. It is important to eliminate CO from the blood for treatment and health safety. A mathematical model is proposed to compute COHb level in the blood as a function of post-exposure time as CO is eliminated. The model takes into account molecular diffusion, facilitated diffusion, convection, non-equilibrium kinetics of CO with haemoglobin and the important physiological parameters, such as ventilation rate, blood flow rate and the total volume of blood in the body. Endogeneous production of CO in the body is included in the formulation. The resulting coupled system of non-linear partial differential equations with physiologically relevant initial, entrance and boundary conditions is solved numerically. Hb levels computed from our model agree with those measured experimentally (Pace et al., 1950; Peterson & Stewart, 1970). The half-life of COHb, i.e. the time required for the blood COHb to decrease from the initial level to its half-value is computed. The half-life values of COHb computed from our model are in good agreement with those based on experimental data collected under different physiological conditions (Pace et al., 1950). Also, the results predicted from our model give better approximation to the experimental values than the CFK equation (Coburn et al., 1965). It is found that the rate of elimination of CO increases with the increase of inspired PO2 and ventilation rate.