Fast Hyperelastic Deformation with Mooney-Rivilin Model for Surgical Simulation of Liver Deformation

Abstract

Surgical simulation based on virtual reality requires fast and accurate deforming models for interactive realism. In this paper, we propose a novel method to increase the computational efficiency of the convergence of nonlinear finite element methods encoding hyperelastic deformations. We propose to update a chosen partition of the tangential rigidity matrix instead of the whole matrix as is done in classical methods. This partition corresponds to the deformed area and its close neighbors. We keep constant the remaining elements of the rigidity matrix which are not in the partition. We initialize them before the iterative process with zero displacement. This initialization is justified by the fact that only the parts close to the deforming area undergoes large displacement. We prove experimentally that our method converges and allows us to substantially reduce the computational time when compared to classical solving.