Finite element modeling of the Circle of Willis from magnetic resonance data

This paper presents a methodology to construct realistic patient-specific computational fluid dynamics models of the circle of Willis (CoW) using magnetic resonance angiography (MRA) data. Anatomical models are reconstructed from MRA images using tubular deformable models along each arterial segment and a surface-merging algorithm. The resulting models are smoothed and used to generate finite element (FE) grids. The incompressible Navier-Stokes equations are solved using a stabilized FE formulation. Physiologic flow conditions are derived from phase-contrast MR velocity measurements. The methodology was tested on image data of a normal volunteer. A pulsatile flow solution was obtained. Measured flow rates were prescribed in the internal carotid arteries, vertebral arteries, middle cerebral arteries and anterior cerebral arteries. Pressure boundary conditions were imposed in the posterior cerebral arteries. Visualizations of the complex flow patterns and wall shear stress distributions were produced. Potential applications of these FE models include: study the role of the communicating arteries during arterial occlusions and after endovsascular interventions, calculate transport of drugs, evaluate accuracy of 1D flow models, and evaluate vascular bed models used to impose boundary conditions when flow data is unavailable or incomplete.