Mathematical investigation of aetiology and pathogenesis of atherosclerosis in human arteries

Abstract

To understand the role of medically significant hemodynamic wall parameters in the pathogenesis of vascular diseases, pulsatile blood flow in large human arteries of systemic, pulmonary and coronary circulation is investigated by mathematical modelling. To be medically realistic, the pressure gradient waveforms reported in the cardiology literature for the arteries considered are digitised and developed in Fourier series (McDonald's model). Three objectives of the article are to (i) compare qualitatively and quantitatively the pulsatile blood flow between the parallel plate and circular geometry, (ii) compare the hemodynamic wall parameters in the three major circulations mentioned above to gain new medical or physiological insights and (iii) understand if slip at the wall has significant influence on the hemodynamic wall parameters. Our model is reliable since the results obtained here through exact solutions are in great agreement with those reported in the medical literature. New insights gained from our study, documented here for the first time in the hemodynamic literature, are as follows: parallel plate geometry approximation is not reliable quantitatively; larger the radius (Womersley number), larger is the value of relative residence time and hence, higher the probability for vascular diseases; none of the commonly employed interface conditions are suitable for the hemodynamic studies. Comparing our results with earlier studies, we recommend that future research should focus on developing an interface condition exclusively for haemodynamics. We support the recent understanding that low wall shear stress and high oscillatory shear index need not co-locate. We have rendered new physiological insight for this result.