Incorporating vessel taper and compliance properties in Navier-Stokes based blood flow models

A popular and useful technique used to model blood flow in cardiovascular simulations is to divide each blood vessel into a series of segments, each with its own lumped resistance, inertance, and compliance parameters. The values of these parameters are usually obtained through a simplification of the Navier-Stokes equations for fluid flow. However, the simplification often ignores the nonlinear and convective terms of the equations, resulting in errors in the parameter values, especially in the value found for resistance per unit length. We report a new method for the calculation of vessel resistance per unit length which takes into account the effects of vessel taper and wall compliance. It is shown that these effects can be addressed by the addition of two time-varying terms to the calculation of resistance per unit length. One term, due to vessel taper, is proportional to volumetric flow rate Q. The other term, due to vessel compliance, is proportional to delta p/delta t. These variables are readily available in computer simulations of blood flow in lumped parameter systems. Using data for the descending aorta, the new parameter values, when averaged over a cardiac cycle, compare favorably with results in the literature.