A global mathematical model of the cerebral circulation in man
Authors:
Mokhtar Zagzoule and Jean-Pierre Marc-Vergnes
Affiliation:
* Laboratoire de Mécaniqué, Groupe de rhéologie, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex, France
† LHEC-INSERM U.230, Chu Purpan, 31059, Toulouse Cedex, France
Abstract:
A mathematical model of the cerebral circulation has been formulated. It was based on non-linear equations of pulsatile fluid flow in distensible conduits and applied to a network simulating the entire cerebral vasculature, from the carotid and vertebral arteries to the sinuses and the jugular veins. The quasilinear hyperbolic system of equations was numerically solved using the two-step Lax-Wendroff scheme. The model's results were in good agreement with pressure and flow data recorded in humans during rest. The model was also applied to the study of autoregulation during arterial hypotension. A close relationship between cerebral blood flow (CBF) and capillary pressure was obtained. At arterial pressure of 80 mmHg, the vasodilation of the pial arteries was unable to maintain CBF at its control value. At the lower limit of autoregulation (60 mm Hg), CBF was maintained with a 25% increase of zero transmural pressure diameter of nearly the whole arterial network.