Numerical Simulation of Blood Flow in an Anatomically-Accurate Cerebral Venous Tree

Although many blood flow models have been constructed for cerebral arterial trees, few models have been reported for their venous counterparts. In this paper, we present a computational model for an anatomically accurate cerebral venous tree which was created from a computed tomography angiography (CTA) image. The topology of the tree containing 42 veins was constructed with 1-D cubic-Hermite finite element mesh. The model was formulated using the reduced Navier-Stokes equations together with an empirical constitutive equation for the vessel wall which takes both distended and compressed states of the wall into account. A robust bifurcation model was also incorporated into the model to evaluate flow across branches. Furthermore, a set of hierarchal inflow pressure boundary conditions were prescribed to close the system of equations. Some assumptions were made to simplify the numerical treatment, e.g., the external pressure was considered as uniform across the venous tree, and a vein was either distended or partially collapsed but not both. Using such a scheme we were able to evaluate the blood flow over several cardiac cycles for the large venous tree. The predicted results from the model were compared with ultrasonic measurements acquired at several sites of the venous tree and agreements have been reached either qualitatively (flow waveform shape) or quantitatively (flow velocity magnitude). We then discuss the significance of this venous model, its potential applications, and also present numerical experiments pertinent to limitations of the proposed model.