Nonlinear elastic model for image registration and soft tissue simulation based on piecewise St. Venant-Kirchhoff material approximation

摘要

Linear elastic model widely applied for simulation of soft tissue deformations in biomedical imaging applications is basically limited to the range of small deformations and rotations. Thus, computation of large deformations and rotations using linear elastic approximation and its derivatives is associated with substantial error. More realistic modeling of mechanical behavior of soft tissue requires handling of different types of nonlinearities. This paper presents a framework for more accurate modeling of deformable structures based on the St. Venant-Kirchhoff law with the nonlinear Green-Lagrange strain tensor and variable material constants, which considers both material and geometric nonlinearities. We derive the governing partial differential equation of nonlinear elasticity, which represents consistent extension of the Lame-Navier PDE of linear elasticity, and describe two alternative numerical schemes for solving this nonlinear PDE via the Newton's and fixed point method, respectively. The results of our comparative studies demonstrate the advantages of nonlinear elastic model for accurate computing of large deformations and rotations in comparison to the linear elastic approximation.