Computational modelling and analysis of haemodynamics in a simple model of aortic stenosis

In a study motivated by considerations associated with heart murmurs and cardiac auscultation, numerical simulations are used to analyse the haemodynamics in a simple model of an aorta with an aortic stenosis. The aorta is modelled as a curved pipe with a $180^{\circ }$ turn, and three different stenoses with area reductions of 50 %, 62.5 % and 75 % are examined. A uniform steady inlet velocity with a Reynolds number of 2000 is used for all of the cases and direct numerical simulation is employed to resolve the dynamics of the flow. The poststenotic flow is dominated by the jet that originates from the stenosis as well as the secondary flow induced by the curvature, and both contribute significantly to the flow turbulence. On the anterior surface of the modelled aorta, the location with maximum pressure fluctuation, which may be considered as the source location for the murmurs, is found to be located around $60^{\circ }$ along the aortic arch, and this location is relatively insensitive to the severity of the stenosis. For all three cases, this high-intensity wall pressure fluctuation includes contributions from both the jet and the secondary flow. Spectral analysis shows that for all three stenoses, the Strouhal number of the vortex shedding of the jet shear layer is close to 0.93, which is higher than the shedding frequency of a corresponding free jet or a jet confined in a straight pipe. This frequency also appears in the pressure spectra at the location postulated as the source of the murmurs, in the form of a ‘break frequency.’ The implications of these findings for cardiac auscultation-based diagnosis of aortic stenosis are also discussed.