Stability of the bicarbonate system in the blood

In this paper, we describe a mathematical model about the reaction–diffusion kinetics of bicarbonate system, which it plays a key role in regulating blood pH. It is very important to know the determinants of blood pH in both experimental and theoretical studies, in order to help to investigate the hidden mechanism of acid–base disorders in the clinical setting. We explore the dynamics of the bicarbonate system under the closed condition. This condition yields that the total amount of carbon dioxide is conserved and the difference in concentrations between anions and cations is conserved. For the stability of the model, we hypothesize that the amount of initial concentrations perturbed around an equilibrium point is less than a certain constant depending on a rate constant. With an application of Liapunovʹs method, we prove that the model in the form of reaction–diffusion system is globally stable under the hypothesis. We also provide the blood pH profile, which is computed in our model with the experimentally observed rate constants.