Blood flow analysis by using the viscoelastic blood vessel model-based spectral element model

초록

It has been well recognized that the blood flow characteristics determine the wall shear stress and wall tension which are closely related to the cardiovascular diseases such as aneurysm and stenosis. Thus, it is very important to investigate the blood flow in blood vessels in an accurate and efficient way. Though the finite element method (FEM) is a powerful tool for complex systems, it is often inevitable to use the finer meshes to improve the FEM accuracy, which will in turn increase computational burden. In most blood flow analysis methods, the blood vessels have been represented by elastic tubes. However, to make the analysis results more realistic, the blood vessels should be represented by viscoelastic tubes. Thus, this paper develops a viscoelastic blood vessel model-based spectral element model for the blood flow analysis. To formulate the spectral element model, the time-domain governing equations are first transformed into the frequency-domain by using the DFT theory. The frequency-domain equations are then solved to obtain exact solutions, followed by the derivation of the frequency-dependent dynamic shape functions. The dynamic shape functions are then used to formulate the spectral element matrix (exact dynamic stiffness matrix). As the spectral element formulation is based on exact wave solutions, the inertia effects in a finite blood vessel element can be treated exactly. Thus, one-element model suffices to acquire the exact dynamic behaviour of a uniform finite blood vessel element, regardless of its length, which will drastically reduce the total degrees of freedom to be handled in the analysis. The spectral element model developed in this paper is numerically proved to provide extremely accurate and realistic results when compared with the solutions obtained by the conventional finite element model and the elastic blood vessel model-based spectral element model.