Reduced modelling of blood flow in the cerebral circulation:: Coupling 1-D, 0-D and cerebral auto-regulation models

Pulsatile blood flow in the cerebral circulation is simulated using a nonlinear, one-dimensional model of the arterial haemodynamics coupled in the time domain with lumped parameter and flow auto-regulation models of the perfusion of the microcirculation. A linear analysis of the coupling shows that a resistance equal to the characteristic impedance of the blood vessel is required at the inflow of a terminal windkessel model to avoid the generation of non-physiological wave reflections. The cerebral model suggests that the worst anatomical variation of the circle of Willis in terms of restoring normal cerebral flows after a sudden carotid occlusion is a circle without the first segment of the contralateral anterior cerebral artery. Copyright (C) 2007 John Wiley & Sons, Ltd.