Heat conduction-based methodology for nonlinear soft tissue deformation

Modelling of interactions of soft tissues with surgical tools is a fundamental issue in interactive surgical simulation. This paper presents a new methodology for modelling of nonlinear characteristics of soft tissue deformation for interactive surgical simulation. The proposed methodology formulates soft tissue deformation as a process of energy propagation; the mechanical load applied to soft tissues to cause deformation is treated as the equivalent thermal energy according to the conservation law of energy and further distributed among masses of soft tissues in the manner of heat conduction. Heat conduction of mechanical load and non-rigid mechanics of motion are combined to conduct soft tissue deformation. To obtain real-time computational performance, cellular neural networks are developed for both propagation of mechanical load and non-rigid mechanical dynamics, leading to novel neural network models embedded with deformation mechanics and physical dynamics for interactive soft tissue simulation. Real-time force interaction is also achieved with an integration of a haptic device via force input, soft tissue deformation, and force feedback. Simulations and experimental results demonstrate the proposed methodology exhibits the typical mechanical behaviour of soft tissues and accepts nonlinear soft tissue deformation. It can also accommodate isotropic and homogeneous, anisotropic, and heterogeneous materials by a simple modification of thermal conductivity values of mass points.