Mathematical Analysis of Hemodynamic Pulse Wave In Human Fluid-Structure Interaction

Abstract

Mathematical study of human pulse wave was studied with the view to gaining an insight into physiological situations. Fluid –Structure interaction (FSI) in blood flow is associated with pressure pulse wave arising from ventricular ejection. Solution of the coupled system of nonlinear PDEs that arose from the FSI was sought in order to determine pressure. Further study on pressure pulse waves showed that the Korteweg-de Vries (KdV) equations hold well for the propagation of nonlinear arterial pulse wave. Solutions of the KdV equation by means of the hyperbolic tangent (tanh) method and the bilinear method each yielded solitons. The solitons describe the peaking and steepening characteristics of solitary wave phenomena. The morphologies of the waves were studied in relation to the length occupied by the waves (which corresponds to length of arterial segment and stature) and the left ventricular ejection time (LVET). The study showed that both stature and LVET are independent descriptors of cardio-vascular state.