A real time finite element based tissue simulation method incorporating nonlinear elastic behavior

Abstract

This paper presents a new finite element simulation approach for surgical simulators. Based on the solution of the algebraic equations derived from a nonlinear elastic model, we propose a real time simulation rule based on the implicit relation between the displacements of contacted and free nodes. This rule is an analytic expression in the linear case, and an approximation of the implicit relation in the non-linear case. We also remove some of the restrictions on flexibility exhibited by previous linear and nonlinear approaches. In the linear case, real time reconfiguration of the contacted nodes and the boundary constraints is realized using the simulation rule, while in the nonlinear case, a similar result is obtained by employing affine mapping.

These methods allow nonlinear material properties to be applied to real time tissue simulation, with an efficiency comparable to that of the tensor matrix method for linear elastic models.

Keywords:

• Surgical simulation
• Finite element method
• Nonlinear elasticity
• Tissue modeling