Simulations of pulsatile blood flow in tapered S-shaped in-plane and out-of-plane coronary arteries

Abstract

Ischaemic heart disease has been the leading cause of death in Australia for the past 10 years. Included in this category are angina, blocked arteries and heart attacks. This paper presents a modelling study of the precursors to artery blockage, namely coronary artery disease, or narrowing of the coronary arteries, based on geometrical considerations. It is believed that wall shear stress is a key initiating factor in coronary artery disease, especially low wall shear stress. Wall shear stress is caused by the blood flowing along the walls of the artery and in regions of low wall shear stress the flow is relatively slow compared to that in other parts of the artery. In these slow flow regions, there is enhanced opportunity for molecules carried in the blood (for example low density lipoprotiens (LDL)) to diffuse out of the blood and into the artery wall. Long term exposure to this diffusive process results in thickening of the artery wall and, hence, narrowing of the available area for blood flow within the artery. Of major concern are regions of the coronary arteries which demonstrate consistently low wall shear stress over the cardiac cycle. The complex flow patterns observed in coronary arteries are believed to be related to the pulsatile nature of the flow, the rheological properties of the blood and the geometry of the arteries, including branching, bifurcation and curvature. Possible factors that may cause differences in the coronaries compared with other arteries in the body are the particular character of the coronary inlet velocity waveform and the fact that coronary velocities are lower than most of the other arteries, which, with their smaller diameters, leads to lower Reynolds numbers. Other factors may be their tortuous nature, which includes out-of-plane bends. The combination of the complicated three dimensional structure of the coronary arteries and the complex flow patterns makes it difficult to isolate factors affecting wall shear stress (WSS) distributions along the artery walls. Here, as a way to simplify the complications, we present a series of transient simulations to model blood flow in tapered, threedimensional, in-plane and out-of-plane, S-shaped coronary arteries. The simulations are performed by solving the three dimensional Navier-Stokes and continuity equations which govern fluid flow. It is also assumed that blood behaves as an incompressible Newtonian fluid. In each of the arteries, for the majority of the cycle (that is, during forward flow), “high”WSS is found on the outside of each bend and (relative to this) “low”WSS on the inside of the bend. Within each of these low stress regions a point of consistently low WSS (that is, low throughout the entire cardiac cycle) can be identified. In addition, the tapered arteries considered here also show a region of consistently low WSS in the proximal region of the artery, where the majority of plaques are found in the coronary arteries. Such points are not observed in constant radius artery models. In every case these points of consistently low WSS appear to be related to the planar geometry of the artery only and not to the form of the inlet waveform used or whether the curvature is in-plane or out-of-plane. The identification of a region of consistently low wall shear stress in the straight inlet (proximal) region in the model with tapered arteries (and not in the model with constant radius arteries) fits with postmortem findings. It then follows that this region of low WSS in realistic coronary arteries is due, in part, to the overall taper in the artery and not only to the local curvature variation. It is concluded that, to realistically model coronary arteries, it is necessary to include taper and also out-of-plane bends.