A modeling study of blood flow and oxygen transport in the circle of Willis

A computer model for simulating pressure, flow propagation and oxygen transport in the circle of Willis is developed. The model is based on one-dimensional nonlinear equations of pulsatile fluid flow in an elastic tube and oxygen transport equation. The two-step Lax-Wendroff method was employed in the discretization of momentum and continuity equation, the upwind scheme was used in the discretization of the oxygen transport equation. Results reveal that the oxygen concentration fluctuates following the pulsative blood flow, but its range is extremely small. Moreover, due to the influence of the artery wall, the oxygen concentration gradually decreases along the direction of flow.