A Nonlinear Model for the Circle of Willis Based on Hemodynamics

A mathematical control model of blood flow through the circle of Willis was developed, within a nonlinear framework. Based on system´s viewpoint, the circle of Willis is fluid network system that is composed of four entrances and three communicating arteries. A nonlinear model is established for fluid network systems using lumped parameter approximations of incompressible Navier-Stokes equations and the graph theory of the circuit network, a nonlinear model is established for fluid network systems. This model provides the basis for the entire cerebral circulation network´s parameter computation, and survey, also provides treatment reference for branch blood flow and pressure control based on Willis control system.