The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees

Abstract

Patient specific geometrical data on human coronary arteries can be reliably obtained multislice computer tomography (MSCT) imaging. MSCT cannot provide hemodynamic variables, and the outflow through the side branches must be estimated. The impact of two different models to determine flow through the side branches on the wall shear stress (WSS) distribution in patient specific geometries is evaluated. Murray's law predicts that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power. The empirical model is based on flow measurements performed by Doriot et al. (2000) in angiographically normal coronary arteries. The fit based on these measurements showed that the flow ratio through the side branches can best be described with a power of 2.27. The experimental data imply that Murray's law underestimates the flow through the side branches. We applied the two models to study the WSS distribution in 6 coronary artery trees. Under steady flow conditions, the average WSS between the side branches differed significantly for the two models: the average WSS was 8% higher for Murray's law and the relative difference ranged from -5% to +27%. These differences scale with the difference in flow rate. Near the bifurcations, the differences in WSS were more pronounced: the size of the low WSS regions was significantly larger when applying the empirical model (13%), ranging from -12% to +68%. Predicting outflow based on Murray's law underestimates the flow through the side branches. Especially near side branches, the regions where atherosclerotic plaques preferentially develop, the differences are significant and application of Murray's law underestimates the size of the low WSS region.

Computational fluid dynamic simulations of image-based stented coronary bifurcation models

“…The coefficients of this equation were obtained by van der Giessen and co-workers fitting the data of blood flow of 18 human coronary bifurcations [24] by means of a nonlinear regression analysis. From these data, the blood flow and diameter for each coronary branch were calculated assuming a parabolic flow profile and circular vessel area [23]. Applying equation (2.1), an average flow rate of 42.2 ml min 21 was calculated for case A and 45.1 ml min 21 for case B.…”

“…Applying equation (2.1), an average flow rate of 42.2 ml min 21 was calculated for case A and 45.1 ml min 21 for case B. The same measurements [24] were used by van der Giessen et al [23] to derive the relation between the diameter ratio of two daughter branches and the flow ratio through the branches:…”

“…On the top right, the shape of the flow waveform which was applied at the inlet section of the models is shown. The flow curve amplitude was scaled on inlet diameters of each case to obtain the average flow rate calculated through the relations by van der Giessen et al [23]. (Online version in colour.…”

Imaging Techniques for the Assessment of Coronary Arteries in Diabetic Patients Undergoing PCI with Bioresorbable Vascular Scaffolds

“…13 Caro et al were the first who described the evidence regarding endothelial shear stress in the localization of atherosclerosis about 40 years ago. The clinical significance of atherosclerotic plaques is mostly dependent on the formation and development of atherosclerosis and on the vascular remodeling response.…”

“…MSCT can provide the geometrical data necessary to calculate wall shear stress near bifurcations. 13 …”