A nonlinear mathematical model of blood flow in a constricted artery experiencing body acceleration

A nonlinear mathematical model is developed analytically to study the flow characteristics of blood through an artery in the presence of multistenoses when it is subjected to whole body acceleration. An appropriate shape of the time-dependent multistenoses which are overlapped in the realm of the formation of arterial narrowing caused by atheroma is constructed mathematically. The artery is simulated as a flexible cylindrical tube containing a nonhomogeneous Newtonian fluid with variable viscosity characterising blood, having a narrowed portion forming multistenoses in its lumen. To update resemblance to the in vivo situation, the viscosity of blood is taken to be a function of hematocrit in such a way that it varies radially more near the central region where most blood cells are aggregated and less towards the arterial wall, a cell-free region, and thus, the nonhomogeneity of blood is accounted for. The unsteady flow mechanism in the multistenosed artery is subjected to a pulsatile pressure gradient arising from the normal functioning of the heart as also the body acceleration. The present analysis bears the potential to calculate the flow-field with low computational complexity by using the appropriate boundary conditions. Finally, the extensive quantitative analysis helps estimating the significant effects of the severity of the multistenoses, the external body acceleration together with the vessel wall distensibility and nonhomogeneity of the flowing blood on the unsteady flow characteristics in order to justify the applicability of the present model.