Finite element based dynamic modelling of soft tissue deformation

Physically realistic modelling of deformable biological tissues is critical for medical applications such as palpation and disease diagnosis, surgical simulation, surgical procedure planning, and robot assisted minimally invasive surgery. These applications require modelling of tool-tissue interactions with both physical fidelity and runtime computational efficiency. Nevertheless, given the difficulty in achieving the two paradoxical requirements, modelling of mechanical tissue deformation remains a research challenge. The finite element method can be typically used for modelling soft tissue deformation with highly physical realism. However, it suffers from expensive computation, unable to meet the requirement of real-time simulation. The Kalman filter is a popular method to online estimate unknown system state variables. This method conducts the state estimation in the form of feedback control, where system state variables are estimated using their measurements as feedback. It can achieve the accuracy of minimum mean-square error with a small computational load.

This thesis proposed novel methods by combining the finite element method with the Kalman filter for real-time and accurate modelling of soft tissue deformation in both linear and nonlinear analysis. The novelty of those methods is that soft tissue deformation is formulated as a filtering identification process to online estimate soft tissue deformation from the local measurement of displacement. For constructing the discrete system state equation for filtering estimation, soft tissue deformation is discretised based on elastic theory in the space domain by FEM and is further discretised in the time domain by using implicit or explicit time integration to solve the dynamic equilibrium equation of finite element method deformation modelling. Subsequently, a Kalman filter is developed for online estimation and analysis of soft tissue deformation according to the local measurement of displacement. Interactive tool-tissue interaction with haptic feedback is also achieved for surgery simulation. The presented methods significantly improve the computational performance of the traditional finite element method, but still maintains a similar level of accuracy. It not only achieves real-time performance, but also exhibits similar deformation behaviours as the traditional finite element method.