Real-time integrated modeling of soft tissue deformation and stress based on deep learning.

Objective. Accurately and in real-time simulating soft tissue deformation and visualizing stress distribution are crucial for advancing surgical simulators closer to real surgical environments. The concept of using neural networks to accelerate the finite element method has emerged as a powerful approach for real-time physical modeling of soft tissues due to its excellent performance. However, existing models primarily focus on deformation modeling, neglecting the important guiding role of soft tissue stress field modeling in surgical training. Moreover, when modeling multiple physical fields, the vast differences in data distribution between these fields can cause a model to become biased toward features with larger scales if they are simply concatenated and fed into the network for training. This paper aims to address the issue of missing stress rendering in surgical simulators by developing a neural network-based real-time multi-physics modeling framework for soft tissues.Approach. By compactly encoding the nonlinear relationship between soft tissue boundary conditions and physical fields, the method accelerates the computation of deformation and stress fields. The feature scales of the physical fields are balanced usingZ-Score normalization, which mitigates the problem of large-scale features dominating the model training.Main results. We validated the effectiveness of our method on three-dimensional models of a cantilever beam, liver, spleen, and kidney. Experiments demonstrate that our method achieves an excellent balance between efficiency and accuracy. Compared to traditional methods, it offers a 1000-fold or even 10 000-fold improvement in efficiency with only around a 1% loss in accuracy.Significance. The proposed model effectively predicts the displacement and stress distribution of soft tissue, offering the potential to enhance surgical simulators with the capability to render multiple physical properties.