Incorporating residual stresses in multi-layer vascular wall models: A comparative study of pure mechanical simulations and hemodynamic responses

Abstract

In numerical simulations of vascular mechanical properties, the incorporation of layer-specific residual stresses and the contribution of anisotropic fibers are often neglected. Additionally, simulating hemodynamic fluid-structure interaction (FSI) that simultaneously accounts for the coupled dynamics of myocardium, blood vessels, and blood presents significant challenges. The objective of this study is to develop a multi-layer constitutive model of the vascular wall that incorporates specific residual stresses and to evaluate the influence of these residual stresses, as well as the number of vascular wall layers, on the outcomes of pure mechanical simulations. Furthermore, a multi-layer, fully coupled FSI analysis method that considers residual stresses is proposed to more accurately reproduce the hemodynamic response of the vascular wall. A multi-layer constitutive model of the vascular wall, which incorporates layer-specific residual stresses, was first established based on the Holzapfel-Gasser-Ogden strain energy function. Biaxial tensile curves were obtained through experimental measurements of two porcine artery samples. The modified Fourier decomposition (MFD) algorithm was employed to fit the experimental data, yielding key constitutive parameters for the multi-layer vascular wall model. These fitted parameters were subsequently utilized to perform pure mechanical simulations of the multi-layer vascular wall. The results demonstrated that the multi-layer vascular model, which accounts for layer-specific residual stresses, effectively captured the mechanical response of blood vessels, with deviations from experimental curves ranging from 2% to 3%. Finally, four FSI simulations were conducted based on two simplified vascular models. The fully coupled FSI framework was implemented using a specialized mesh partitioning technique and governing equations. Comparative analysis indicated that, compared to non-fully coupled FSI methods, the multi-layer, fully coupled FSI approach that incorporates residual stresses provides a superior methodology for analyzing the hemodynamic response of the vascular wall.