A mathematical model of cerebral blood flow chemical regulation--Part II: Reactivity of cerebral vascular bed.

In the present paper an original mathematical model of the chemical oxygen-dependent cerebral blood flow (CBF) regulation in the rat is proposed. Taking into account recent experimental works, the model assumes that oxygen acts on cerebral vessels through an indirect mechanism, mediated by the release of two metabolic substances (adenosine and H+) from tissue, and that any change in perivascular concentration of these substances affects the diameter of both the medium and small pial arteries as well as of intracerebral arterioles. The model is composed of several submodels, each closely related to a different physiological event. mathematical equations, which describe the reaction of the vasoactive portion of the cerebral vascular bed, are reported in detail and justified. The model permits the simulation of the role played by chemical factors in the control of CBF under many different physiological and pathological conditions in an attempt to clarify their relevance. Several events associated with an alteration in oxygen supply to tissue (auto-regulation to changes in arterial and venous pressure, reactive hyperemia following on cerebral ischemia, arterial hypoxia) have been simulated with the model. The results suggest that chemical factors, adenosine and H+, play a significant but not exclusive role in the regulation of the cerebral vascular bed. The action of other mechanisms (which are probably neurogenic) must be hypothesized to explain completely the CBF changes occurring in vivo.