Computational studies of blood flow at arterial branches in relation to the localisation of atherosclerosis

Abstract

Atherosclerotic lesions are non-uniformly distributed at arterial bends and branch sites, suggesting an important role for haemodynamic factors, particularly wall shear stress (WSS), in their development. Using computational flow simulations in idealised and anatomically realistic models of aortic branches, this thesis investigates the role of haemodynamics in the localisation of atherosclerosis. The pattern of atherosclerotic lesions is different between species and ages. Such differences have been most completely documented for the origins of intercostal arteries within the descending thoracic aorta. The first part of the thesis deals with the analysis of wall shear stresses and flow field near the wall in the vicinity of model intercostal branch ostia using high-order spectral/hp element methods. An idealised model of an intercostal artery emerging perpendicularly from the thoracic aorta was developed, initially, to study effects of Reynolds number and flow division under steady flow conditions. Patterns of flow and WSS were strikingly dependent on these haemodynamic parameters. Incorporation of more realistic geometrical features had only minor effects. The WSS distribution in an anatomically correct geometry of a pair of intercostal arteries resembled in character the pattern seen in the idealised geometry. Under unsteady and non-reversing flow conditions, the effect of pulsatility was small. However, significantly different patterns were generated for reversing aortic near-wall flow and reversing side branch flow. The work was extended to study the wall shear stress distribution within the aortic arch and proximal branches of mice, in comparison to that of men. Mice are increasingly used as models to study atherosclerosis and it has been shown that, in knockout mice lacking the low density lipoprotein receptor and apolipoprotein E, lesions develop in vivo at the proximal wall of the entrance to the brachiocephalic artery. Three aortic arch geometries from wild-type mice were reconstructed from MRI images using in-house and commercial software, and the WSS distribution was calculated under steady flow conditions to establish the mouse haemodynamic environment and mouse-to-mouse variability. Approximated human aortic arch geometries were further considered to enable comparison of the flow and WSS fields with that of mice. The haemodynamic environment of the aortic arch varied between the two species. The overall distribution of wall shear stress was more heterogeneous in the human aortic arch than in the mouse arch, although some features were similar. Intraspecies differences in mice were small and influenced primarily by the detailed anatomical geometry and the Reynolds number. A number of simplifications were made in the above flow analyses, and clearly, relaxing these assumptions would increase complexity. Nonetheless, this thesis demonstrates the fundamental features of flow, which underlie the disparate patterns of WSS in different species and/or ages, for simplified cases, and the results are expected to be relevant to more complex ones. Aspects of the observed WSS patterns in the simplified model of intercostal artery correlate with, and may explain, some of the lesion patterns in human, rabbit and mouse aortas. WSS distributions in the aortic arch of wild-type mice associate with lesion locations seen in diseased mice.