PULSATILE FLOW IN TUBES OF ELLIPTIC GROSS SECTIONS

The compression of blood vessels by surrounding tissue is an important problem in hemodynamics, most prominently in studies relating to the heart. In this study we consider a long tube of elliptic cross section as an idealization of the geometry of a compressed blood vessel. An e xact solution of the governing equations for pulsatile flow in a tube of elliptic cross section involves Mathieu functions which are conside rably more difficult to evaluate than the Bessel functions in the case of a circular cross section. Results for the velocity field, flow rat e and wall shear stress are obtained for different Values of the pulsa tion frequency and ellipticity, with emphasis on how the effects of fr equency and ellipticity combine to determine the Bow characteristics. It is found that in general the effects of ellipticity are minor when frequency is low but become highly significant as the frequency increa ses. More specifically, the velocity profile along the major axis of t he elliptic cross section develops sharp double peaks. the flow rate i s reduced in approximately the same proportion as in the case of circu lar cross section. and the point of maximum shear on the tube wail mig rates away from the minor axis where it is located in steady Bow. (C) 1998 Biomedical Engineering Society. [S0090-6964(98)01105-9].