Simulation of Blood Pressure Wave Propagation in a Vessel by One-Dimensional Model

Abstract

The patterns of blood pressure wave propagation and their variations may convey useful information for clinical diagnosis of cardiovascular diseases. This study aims to construct a mathematical model for the vascular system and simulate behavior of blood pressure waves. The model entails a set of governing equations regarding conservation of mass and momentum applied to the vessel. The integral proximal and distal boundary conditions for the model are given in the form of partial differential equations. The model parameters include the length, radius, thickness and elasticity of vessels, blood density and other properties. The model allows investigation of the propagation of blood pressure waves under different physiological and pathological states. Typical pathological states like vessel stiffening, peripheral vessel stenosis and arteriosclerosis are simulated. The model reproduces essential properties of blood pressure wave propagation in a vessel including the forwarding, reflected and dicrotic components on the blood pressure wave. With initial values of the parameters, the model output reaches a steady state in 5-10s. The simulation results show that in the case of peripheral vessel stenosis, the reflected wave shifts forwards and the amplitude of the dicrotic wave is elevated relative to the control. The blood pressure wave transit time is shortened for the simulated arteriosclerosis. These results generally agree with physiological and pathological features of vessels observed in clinical practice. In conclusion, the validity of the developed model in simulating physiological and pathological variations of the blood pressure wave propagation indicates that a one-dimensional cardiovascular model is appropriate and efficient to simulate pressure wave propagation characteristics, may reveal the relevant hemodynamic properties, and offers a good compromise between accuracy and computational cost.