Pulsatile flow of blood with periodic body acceleration

Abstract

Pulsatile flow of blood through a rigid tube has been studied under the influence of body acceleration. With the help of finite Hankel and Laplace transforms, analytic expressions for axial velocity, fluid acceleration, wall shear and instantaneous volume flow rate have been obtained. It is of interest to note that these solutions can be used for all the feasible values of pulsatile and body acceleration Reynolds numbers Re p and Re b. This is in contrast with the existing results where different approximate solutions have to be used for different ranges of Re p and Re b. Using physiological data, the following qualitative and quantitative results have been obtained. The amplitude of the instantaneous volume flow rate, for flows with body acceleration, decreases shaprly as the tube radius decreases (from aorta to arteriole). This variation of amplitude is very slow for flows with no body acceleration. Another interesting result is the maximum of the axial velocity and fluid acceleration shifts from the tube axis to the vicinity of the tube wall as the tube diameter increases. The variation of the amplitude of wall shear with tube diameter (aorta to coronary) is less for flows with body acceleration than that of flows with no body acceleration. The phase lag between pressure gradient and flow rate changes sharply with tube diameter in narrow tubes, it varies asymptotically in wide tubes. The obtained results are qualitatively in good agreement with existing theoretical observations. Quantitatively, they differ from the other theoretical results (19 to 3000%). The difference in the results of the analyses decreases as the tube diameter increases (arteriole to aorta).