Efficient finite element hyperelasticity solver for blood vessel simulations

Abstract

The blood vessels play a key role in the human circulatory system. As a tremendous amount of efforts have been devoted to develop mathematical models for investigating the elastic behaviors of human blood vessels, high performance numerical algorithms aiming at solving these models have attracted attention. In this work, we present an efficient finite element solver for an elastodynamic model which is commonly used for simulating soft tissues under external pressure loadings. In particular, the elastic material is assumed to satisfy the Saint–Venant–Kirchhoff law, the governing equation is spatially discretized by a finite element method, and a fully implicit backward difference method is used for the temporal discretization. The resulting nonlinear system is then solved by a Newton–Krylov–Schwarz method. It is the first time to apply the Newton–Krylov–Schwarz method to the Saint–Venant–Kirchhoff model for a patient-specific blood vessel. Numerical tests verify the efficiency of the proposed method and demonstrate its capability for bioengineering applications.