Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models

Mathematical investigation of aetiology and pathogenesis of atherosclerosis in human arteries

“…However, they have modelled blood flow in the artery to be a flow between two parallel plates which is a common approximation employed for axisymmetric flows since it is mathematically convenient to avoid the cumbersome integration and differentiation of modified Bessel functions with complex arguments while calculating the HWPs and simply replace them with those of hyperbolic functions. In this present work, we extend the above work (Gayathri and Shailendhra, 2014) to the case of pulsatile blood flow through an artery of uniform circular cross section with rigid porous walls. Indeed, Loudon and Tordesillas (1998) envisaged that a simple blood flow model through parallel plate channel can predict qualitatively the same results which are obtained through a model of blood flow through a tube of uniform circular cross section although quantitatively there may be significant differences in the results.…”

“…where 0 A is the constant amplitude of pressure gradient and 1 A is the amplitude of pulsatile component giving rise to the systolic and diastolic pressure, where 2 f ω π = is the pulse frequency and 1.2 Hz f = is the heart frequency. For detailed literature of Burton's model, one can refer to the work of Gayathri and Shailendhra (2014).…”

“…In this context, Gayathri and Shailendhra (2014) investigated the pulsatile blood flow in three human arteries, brachial, femoral and pulmonary, and carried out a very exhaustive comparative study of Burton's and McDonald's model for pressure gradient and established the superiority of McDonald's model over the commonly employed Burton's model in capturing the pulsatile nature of blood flow. They disproved the common hypothesis in the cardiovascular literature that the low WSS and high OSI co-locate although both may contribute to the pathogenesis of atherosclerosis.…”

“…However, to the best of our knowledge, no work is reported in the literature to estimate the quantitative differences in the hemodynamic factors in the mathematical modelling of pulsatile blood flow through parallel plate channel and through a circular tube. Hence, one of the main objectives (Objective I) of this article is to compare the present work with the work of Gayathri and Shailendhra (2014) on pulsatile blood flow though parallel plate channel and provide a measure on the quantitative differences in hemodynamic factors such as velocity of blood in lumen and WSS.…”

“…Accordingly, the arteries considered here are large-sized arteries such as brachial and femoral artery from systemic circulation, pulmonary artery from pulmonary circulation and coronary artery from coronary circulation. Gayathri and Shailendhra (2014) concluded that it is enough to use Saffman slip condition instead of the well-known BJ condition as the order of magnitude of the Darcy velocity in the porous wall is very less compared to that of slip velocity at the wall. Hence, in this article, Saffman slip condition as well as no-slip condition has been employed as the lumen-wall interface condition.…”