Extended Kalman Filter Nonlinear Finite Element Method for Nonlinear Soft Tissue Deformation

•This paper formulates mechanical deformation of biological tissues as nonlinear filtering for dynamic estimation of mechanical deformation behaviours of biological tissues;•Tissue mechanical deformation is discretised in the spatial and temporal domains by the nonlinear finite element method (NFEM) and central difference integration scheme, respectively, to construct the nonlinear state-space equations for dynamic filtering;•An extended Kalman filter (EKF) is developed to dynamically estimate mechanical deformations of biological tissues•The proposed EKF-NFEM conquers the NFEM limitation of expensive computations and still preserves a reliable level of accuracy as the NFEM. Background and Objective: Soft tissue modelling is crucial to surgery simulation. This paper introduces an innovative approach to realistic simulation of nonlinear deformation behaviours of biological soft tissues in real time. Methods: This approach combines the traditional nonlinear finite-element method (NFEM) and nonlinear Kalman filtering to address both physical fidelity and real-time performance for soft tissue modelling. It defines tissue mechanical deformation as a nonlinear filtering process for dynamic estimation of nonlinear deformation behaviours of biological tissues. Tissue mechanical deformation is discretized in space using NFEM in accordance with nonlinear elastic theory and in time using the central difference scheme to establish the nonlinear state-space models for dynamic filtering. Results: An extended Kalman filter is established to dynamically estimate nonlinear mechanical deformation of biological tissues. Interactive deformation of biological soft tissues with haptic feedback is accomplished as well for surgery simulation. Conclusions: The proposed approach conquers the NFEM limitation of step computation but without trading off the modelling accuracy. It not only has a similar level of accuracy as NFEM, but also meets the real-time requirement for soft tissue modelling.