A finite-element simulation of pulsatile flow in flexible tubes
The relationship between pulsatile pressure and pulsatile flow is an essential element in the understanding of blood flow in large arteries. The study of this relationship and the various factors that affect it is therefore of great physiological significance, both for normal arterial flow and for the case of arterial disease where partial occlusion of a major artery may reduce blood perfusion to the distal vascular beds. The purpose of this study is to investigate blood flow through normal healthy arteries and arteries containing localized constrictions (stenoses) by the use of mathematical models;The mathematical models used in the study are based on one-dimensional flow equations. The model of the unobstructed tube includes two equations which are derived from a consideration of conservation of mass and momentum, and a third equation of state which relates the cross-sectional area to the pressure. The momentum equation is linearized and two different models for the equation of state, one based on a linear relationship and the other on a quadractic polynomial relationship between the cross-sectional area and pressure, are considered. The model for the obstructed tube is based on the same basic equations but expanded to include an empirical relationship between pressure drop and flow across a stenosis. The resulting partial differential equations are solved numerically using the finite-element method;The mathematical models and numerical solutions are validated by comparing calculated and experimental results. The experimental results are obtained from a hydraulic laboratory system which includes a pulsatile pump, a flexible tube test-section, and a peripheral resistance. The stenosis is simulated with a rigid plug of hollowed cylindrical shape inserted into the tube, and the fluid used is physiological saline at room temperature. Pressures and flows are recorded simultaneously at the inlet and outlet of the tube using strain-gage pressure transducers and electromagnetic flowmeters with cannula probes;The solutions predicted from the unobstructed tube model are compared with experimental data for a variety of boundary conditions and frequencies of oscillation. In general, the waveforms predicted from the linear model are in good agreement with the experimental results. Use of the nonlinear model improved the agreement between the calculated and experimental results. The model for the flow in the obstructed tube is validated by comparing calculated and experimental results for a variety of stenosis severities, locations of stenosis, and frequencies of oscillation. In general, this model also satisfactorily predicts the pressure and the flow waveforms. With the validated model, the effects of a developing stenosis on the flow waveform are investigated. It is found that changes in percent stenosis progressively alter the shape and consequently the harmonic composition of the flow waveform.