Energy balance method for modelling of soft tissue deformation

Abstract

This paper presents a novel methodology for modelling of soft tissue deformation, from the standpoint of work–energy balance based on the law of conservation of energy. The work done by an external force is always balanced against the strain energy due to the internal force of the object. A position-based incremental approach is established, in which the work–energy balance is achieved via an iterative position increment process for the new equilibrium state of the object. The position-based incremental approach is further combined with non-rigid mechanics of motion to govern the dynamics of soft tissue deformation. The proposed method employs nonlinear geometric and material formulations to account for the nonlinear soft tissue deformation. Soft tissue material properties can be accommodated by specifying strain energy density functions. Integration with a haptic device is also achieved for soft tissue deformation with haptic feedback for surgical simulation. Experimental results demonstrate that the deformations by the proposed method are in good agreement with those by a commercial package of finite element analysis. Isotropic and anisotropic deformations, as well as soft tissue viscoelastic behaviours, can be accommodated by the proposed methodology via strain energy density functions.