Soft Tissue Behaviour Estimation in Small Deformations

The core of a medical simulator in applications such as diagnosis and palpation simulation rely on the realistic mechanical modelling of the manipulated soft tissue. The traditional Finite Element Method is the most accurate physical approach to simulate soft tissue behaviour but suffers from extended computational time due to the complexity of the tissue models. This paper presents a novel computational method that employs the computationally fast Kalman filter to speeding up the traditional FEM without sacrificing its accuracy. The Newmark-β temporal discretization method is used to formulate the FE equilibrium equation in state-space representation. Given the real-time displacement measurements from the manipulated tissue, the proposed KF-FEM was able to estimate the system state variable, ie displacement, in near real-time performance as perceived by humans. Simulations of the indentation operation on a pig liver shows that the proposed method achieves a response frequency of more than 25 Hz. In addition, it is demonstrated that the proposed method was able to filter more than 90% of the noise in the displacement measurements. It is concluded that the proposed KF-FEM utilizes the strength of the traditional FEM in terms of accuracy and achieves a real-time computational performance by incorporating direct measurements from the manipulated tissue. Furthermore, adoption of the Kalman filter allows to optimally reduce the noise level involved in measurements. The method allows to achieve highly accurate tissue response model in real-time loading.