Soft tissue deformation estimation by spatio-temporal Kalman filter finite element method

Soft tissue modeling plays an important role in the development of surgical training simulators as well as in robot-assisted minimally invasive surgeries. It has been known that while the traditional Finite Element Method (FEM) promises the accurate modeling of soft tissue deformation, it still suffers from a slow computational process.

This paper presents a Kalman filter finite element method to model soft tissue deformation in real time without sacrificing the traditional FEM accuracy.

The proposed method employs the FEM equilibrium equation and formulates it as a filtering process to estimate soft tissue behavior using real-time measurement data. The model is temporally discretized using the Newmark method and further formulated as the system state equation.

Simulation results demonstrate that the computational time of KF-FEM is approximately 10 times shorter than the traditional FEM and it is still as accurate as the traditional FEM. The normalized root-mean-square error of the proposed KF-FEM in reference to the traditional FEM is computed as 0.0116.

It is concluded that the proposed method significantly improves the computational performance of the traditional FEM without sacrificing FEM accuracy. The proposed method also filters noises involved in system state and measurement data.