Integration of the Circle of Willis into Avolio's model of the arterial haemodynamics

Operations on the open heart require perfusion of the body by a heart-lung machine. A sufficient perfusion of vital organs is essential and has to be guaranteed also for patients with severe stenoses of the carotid arteries. Models of the arterial system offer the opportunity to simulate arterial flow and pressure in organs that cannot be accessed by direct measurement. They can support surgical planning and provide real-time information during the operation itself. In 1980 A. P. Avolio published a 1D model of the arterial haemodynamics. It consists of a branching system of 128 arterial segments which represent short elastic tubes. Avolio's model assumes a tree-like structure of the arterial system. However this is not appropriate for the brain: The anterior and posterior communicating arteries are missing in this approach. The Circle of Willis becomes important in case of an asymmetric perfusion of the brain. In this paper we show how this redundant structure can be integrated into Avolio's model using a state-space representation. Simulation results demonstrate significant differences between Avolio's model and our model if a carotid artery is stenosed.