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.