The mathematical modeling in biomechanical aspects of circulatory system

Abstract

Cardiovascular function is characterized by, among other factors, a number of newlinebiomechanical indices and parameters. In the field of biomechanics, Researchers are newlineinvolving, engineering mathematical modeling and scientific computing. The newlineimportance of mathematical modeling for physiological understanding, diagnostics, newlineprosthesis development, patient selection and medical planning is indicated and newlinediscussed in the present work. Blood system functions are very important for most newlineprocesses in human organism. One of its primary functions is matter transport among newlinedifferent parts of the organism including tissue supplying with oxygen, carbon dioxide newlineexcretion, drug propagation etc. These processes are affected when any abnormalities newlineor diseases like atherosclerosis, loss of blood, anatomical abnormalities, are present in newlinethe arteries or veins. The stenosis is the cause of the beginning of the atherosclerosis. newlinePresence of stenosis effects the various flow parameters such as resistance to flow, newlineflow rate, and wall shear stress. Because of this there are so many researchers, works in newlinethis field. In 1980, Shukla et.al [133] examined the effects of stenosis on the resistance newlineto flow and on the wall shear stress in an artery by assuming blood as a power-law and newlineCasson s fluid. In 1979 Young [178] has pointed out that the variations of the newlineresistance to flow and the wall shear stress with the axial distance are physiologically newlineimportant quantities. In 2010 Shaw et al., [131] have obtained the theoretical results for newlinethe velocity profiles, pressure drop, wall shear stress and separation phenomenon for newlinespecific geometries for Newtonian model of blood. In 2012, Cito et al., [22] have newlinediscussed the visualization and measurement of capillary-driven blood flow using newlinespectral domain optical coherence tomography. On the basis of blood constituents, newlinevarious types of blood flow models are developed assuming it as single phase newlineNewtonian or non-Newtonian fluid. In a series of papers, [27, 33, 39, 45] they have newlineinvestigated that the probl