Abstract
The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation method can be used for the analytical solution. In the paper, the simplified nonlinear problem for the semi-infinite vessel with constant properties is solved analytically, and the solutions for different models are compared. The effects of the flattening of the velocity profile and hematocrit value on the deviation from the Newtonian model are investigated.
Highlights
The one-dimensional (1D) models are used for the simulation of blood flow in large vascular systems, where the application of 2D and 3D models leads to computational difficulties [1,2,3,4]
(2) It is demonstrated that in the case of large arteries, small parameters are observed in the models, so the perturbation method can be used for the analytical solution of model problems
For the models, where the hematocrit is taken into account, the deviation from the Newtonian solution increases with the increase of hematocrit value at all considered velocity profiles
Summary
The one-dimensional (1D) models are used for the simulation of blood flow in large vascular systems, where the application of 2D and 3D models leads to computational difficulties [1,2,3,4]. In most works devoted to 1D models of blood flow, the non-Newtonian properties are ignored. The non-Newtonian 1D models of blood flow, obtained by the averaging of Navier–Stokes equations on the vessel cross-section, are presented. Where U(t, z) is the mean velocity, R(t, z) is the vessel radius and s is the dimensionless velocity profile As it is demonstrated in [6,7], system (2) after the averaging is reduced to the following form:. According to the existence of the cellular part, the flattened velocity profile is typical for the blood [50] Such profiles are obtained in 2D and 3D simulations of blood flow, based on the non-Newtonian models in [9,18,31,32]. The value of α, corresponding to (7), is computed as:
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