Accurate Tissue Deformation Modeling Using a Kalman Filter and ADMM-Based Projective Dynamics

In low-dose-rate permanent-seed (LDR-PS) implant brachytherapy, it is crucial to predict the movement of internal target points (planned radioactive seed locations) under the effect of external forces. Accurate prediction of the target locations is critical for precise seed implantation, as inaccurate seed implantation diminishes the effectiveness of radiotherapy. Therefore, developing a model to simulate tissue dynamics is necessary. All physics-based tissue models have model-reality mismatches due to unmodeled dynamics, a problem which should be addressed. In this work, we propose the KF-ADMM method as a solution, which compensates for a portion of unmodeled dynamic terms existing in the alternating direction method of multipliers (ADMM)-based projective dynamics (PD) tissue simulator through Kalman filtering. This method provides accurate predictions of the location of inner tissue points with an error of around 0.8 mm. Experiments on a breast tissue phantom are performed to evaluate the efficacy of the proposed approach. According to the results, the accuracy of tissue deformation is enhanced by $52 \%$ on average, and the convergence rate is accelerated compared to an ADMM-based PD tissue simulator.