Hemodynamic analysis of the Pulsatile Flow in Tubes of Bipolar Cross Sections

Abstract

Pulsatile flow through compressed or defective blood vessels is a topic of fundamental importance in hemodynamics, particularly in cardiovascular research. This study examines flow dynamics within a tube with a bipolar cross section, possibly representing the geometry of bicuspid aortic valves (BAV), aortic bifurcations, and the aortic arch regions where non-uniform vessel shapes significantly influence hemodynamic behavior. An analytical solution is derived for the governing equations of pulsatile and poiseuille flow in a bipolar cross-sectional tube. The analysis focuses on the velocity field, flow rate, and wall shear stress (WSS) across different pulsation frequencies and geometric parameters, highlighting how these factors interact to shape flow characteristics. At low frequencies, the velocity profile remains smooth, with gradual acceleration and deceleration phases. In contrast, at higher frequencies, oscillatory effects become more pronounced, and the peak volume flow, initially occurring near ${\omega}t=0$ and ${\omega}t$=${\pi}$, shifts toward an earlier phase in the cycle ${\omega}t=0$ to ${\omega}t={\pi}/2)$ before stabilizing at very high frequencies. Shear stress behavior also exhibits frequency-dependent variations. At low frequencies, the fluid responds smoothly to pressure gradients, producing a shear stress distribution similar to steady flow. However, as frequency increases, inertial and unsteady effects introduce phase lags, leading to more complex shear stress patterns. These findings provide valuable insights into the interplay between vessel geometry and pulsatile forces, with implications for understanding disease progression and refining diagnostic models in cardiovascular medicine.