Derivation of closed-form expression for the cerebral circulation models.

Loops which occur due to anastomosing vascular networks, such as the circle of Willis, cannot be analyzed analytically using any of the published mathematical models. This paper presents the theoretical basis of a new model of the cerebral circulation loops which occur due to the circle of Willis. Equations of the model are presented and justified. The transmission line equations obtained from the linearized Navier-Stokes equations and the linearized dynamic deformation equations of the arterial wall are solved analytically to compute the hemodynamic parameters. A comparison of simulation result with experimental data shows that the agreement between experimental and theoretical results is satisfactory and more accurate than the numerical solution.