Numerical modeling of compensation mechanisms for peripheral arterial stenoses.

The goal of this paper is to develop a numerical model for physiological mechanisms that help to compensate reduced blood flow caused by a peripheral arterial stenosis. Thereby we restrict ourselves to the following compensation mechanisms: Metabolic regulation and arteriogenesis, i.e., growth of pre-existing collateral arteries. Our model is based on dimensionally reduced differential equations to simulate large time periods with low computational cost. As a test scenario, we consider a stenosis located in the right posterior tibial artery of a human. We study its impact on blood supply for different narrowing degrees by the help of numerical simulations. Moreover, the efficiency of the above compensation mechanisms is examined. Our results reveal that even a complete occlusion of this artery exhibiting a cross-section area of 0.442cm(2) can be compensated at rest, if metabolic regulation is combined with collateral arteries whose total cross-section area accounts for 8.14% of the occluded artery.

The influence of an unilateral carotid artery stenosis on brain oxygenation.

We study the impact of varying degrees of unilateral stenoses of an carotid artery on pulsatile blood flow and oxygen transport from the heart to the brain. For the numerical simulation a model reduction approach is used involving non-linear 1-D transport equation systems, linear 1-D transport equations and 0-D models. The haemodynamic effects of vessels beyond the outflow boundaries of the 1-D models are accounted for using a 0-D lumped three element windkessel model. At the cerebral outflow boundaries the 0-D windkessel model is extended by metabolic autoregulation, based on the cerebral oxygen supply. Additionally lumped parameter models are applied to incorporate the impact of the carotid stenosis. Our model suggests that for a severe unilateral stenosis in the right carotid artery the partial pressure of oxygen in the brain area at risk can only be restored, if the corresponding cerebral resistance is significantly decreased and if the circle of Willis (CoW) is complete.