Physiological flow waveform in a rigid elliptical vessel.

A procedure to model the velocity and wall shear stress for a physiological flow in a non-cylindrical vessel is presented. The work describes how a vessel with an elliptical cross section may be used to represent flow in compressed or partially occluded arteries and veins. The procedure was applied to produce a simulation of a physiological flow in a straight rigid vessel with a slightly elliptical cross section (ellipticity, epsilon = 0.8). Fourier analysis was performed on a physiological flow waveform. Flow in the common carotid artery was satisfactorily represented (Pearson correlation coefficient, r > 95%) with a series of five harmonic terms. Expressions involving a linear combination of ordinary and modified Mathieu functions were used to describe the velocity and wall shear stress for each harmonic. An outline of the procedure, and the expressions, which were used to compute the characteristic Mathieu numbers and coefficients is illustrated with their behaviour at the fundamental and Nyquist frequencies. Superposition of the individual contributions to the velocity and wall shear stress allowed the calculation of the overall properties of the flow.