A mathematical model of cerebral blood flow chemical regulation. I. Diffusion processes

A mathematical model which describes the production and diffusion of vasoactive chemical factors involved in oxygen-dependent cerebral blood flow (CBF) regulation in the rat is presented. Partial differential equations describing the relations between input and output variables have been replaced with simpler ordinary differential equations by using mathematical approximations of the hyperbolic functions in the Laplace transform domain. The model is composed of two submodels. In the first, oxygen transport from capillary blood to cerebral tissue is analyzed to link changes in mean tissue oxygen pressure with CBF and arterial oxygen concentration changes. The second submodel contains equations describing the production of vasoactive metabolites by cerebral parenchyma, due to a lack of oxygen and their diffusion towards pial perivascular space. The equations have been used to simulate the time dynamics of mean tissue P/sub O2/, perivascular adenosine concentration, and perivascular pH following changes in CBF. The simulation shows that the time delay introduced by diffusion processes is negligible compared with the other time constants of the system under study.<>