Neural network modelling of soft tissue deformation for surgical simulation

•A new neural network methodology for modelling of soft tissue deformation for real-time, realistic, and stable surgical simulation.•Two CNN models are developed to carry out soft tissue deformation via (i) neural propagation and (ii) dynamics by combining bioelectric energy propagation of soft tissues with mechanical deformation dynamics.•The proposed methodology not only satisfies the real-time requirement of surgical simulation but also achieves the physical behaviours of soft tissue deformation. Further, it also achieves stable model dynamics for soft tissue simulation, but with similar computational efficiency to the explicit time integration.•Simulation and experimental results demonstrate that the proposed method exhibits nonlinear force-displacement relationship and the associated nonlinear deformation behaviours of soft tissues. Further, the proposed method can accommodate not only homogeneous but also anisotropic and heterogeneous materials by simple modification of electrical conductivity values of mass points. This paper presents a new neural network methodology for modelling of soft tissue deformation for surgical simulation. The proposed methodology formulates soft tissue deformation and its dynamics as the neural propagation and dynamics of cellular neural networks for real-time, realistic, and stable simulation of soft tissue deformation. It develops two cellular neural network models; based on the bioelectric propagation of biological tissues and principles of continuum mechanics, one cellular neural network model is developed for propagation and distribution of mechanical load in soft tissues; based on non-rigid mechanics of motion in continuum mechanics, the other cellular neural network model is developed for governing model dynamics of soft tissue deformation. The proposed methodology not only has computational advantage due to the collective and simultaneous activities of neural cells to satisfy the real-time computational requirement of surgical simulation, but also it achieves physical realism of soft tissue deformation according to the bioelectric propagation manner of mechanical load via dynamic neural activities. Furthermore, the proposed methodology also provides stable model dynamics for soft tissue deformation via the nonlinear property of the cellular neural network. Interactive soft tissue deformation with haptic feedback is achieved via a haptic device. Simulations and experimental results show the proposed methodology exhi