Spectral element modeling and analysis of the blood flows in viscoelastic vessels

As the cardiovascular diseases are closely related to the blood flow characteristics such as blood flow rates and pressures in vessels, accurate prediction of the blood flow characteristics in an efficient way has been an important research issue. In this paper, one-dimensional (1D) nonlinear spectral element model is developed by using the variational approach for the blood flows in the vessels with slowly varying cross-sections. The mechanical behavior of the vessel walls is represented by the Kelvin viscoelastic model. The nonlinear spectral element model is formulated by using the frequency-dependent dynamic shape functions which are derived from the free wave solutions to the frequency-domain governing differential equations. The direct iterative method based on an alternating frequency-time method is used to obtain frequency-domain or time-domain solutions from the nonlinear spectral element model. The nonlinear spectral element model is applied to an example artery and its high accuracy is validated by comparing with the solutions obtained by the conventional finite element method. In addition, the effects of the viscoelasticity of artery wall and the nonlinear fluid terms on the blood flow characteristics in the example artery are investigated.