Abstract
Computational investigations of blood flow require validation using analytical solutions and in vitro and in vivo experimental methods. Analytical solutions to the Navier-Stokes equations are possible in only a few select cases with very special geometry and boundary conditions. Fortunately, a canonical solution for pulsatile flow does exist: the Womersley solution for fully developed pulsatile flow in a straight circular cylinder. This analytical solution is essential in assessing the accuracy of numerical methods and examining such important issues as spatial and temporal discretization errors. In vitro experimental investigations can be used to validate computational solutions for blood flow in rigid and deformable models of complex geometries. Detailed information on velocity fields can be obtained using Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV). Although analytical and in vitro experimental methods are extremely important tools for validating numerical solutions, ultimately in vivo measurements, utilizing ultrasound or magnetic resonance imaging, must be utilized for validating predictions made with numerical methods.
Computational solutions for blood flow in a straight cylindrical vessels are validated using Womersley’s analytic solution. Computational solutions for flow in a model of an end-to-side anastomosis are validated by comparing predicted velocity profiles with those obtained by Loth (1993) using LDA. Magnetic resonance imaging of blood flow in the aorta was performed during dynamic exercise conditions to investigate whether numerically predicted changes in infrarenal blood flow are observed in vivo.
