AWPAUNet: An advanced surrogate for real-time simultaneous modeling of multiple mechanical fields of soft tissues

Real-time mechanical modeling of soft tissues using deep learning has long been a research hotspot in surgical simulation. Current studies predominantly focus on scenarios where soft tissues are subjected to external concentrated forces, which fail to align with the complex spatial displacement interaction strategies inherent to surgical simulations. Moreover, while deformation prediction has received significant attention, the indispensable role of multiple mechanical fields information in accurate surgical simulations is often overlooked. Achieving precise and synchronized modeling of multiple mechanical fields remains a major challenge due to the significant differences in their magnitudes. To address these issues, this paper presents a UNet-based surrogate model for real-time simultaneous prediction of soft tissue behavior under spatial displacement interactions, the Adaptive Weighted Parallel Attention UNet (AWPAUNet). The proposed model incorporates a parallel attention module to enhance feature extraction in mechanically sensitive regions and an adaptive weighting strategy to balance the joint learning of mechanical fields with different numerical scales. This effectively addresses the instability in synchronized modeling of multiple mechanical fields caused by larger-scale mechanical fields dominating the training process. Extensive experiments across multiple modeling objects demonstrate that AWPAUNet is an efficient and accurate surrogate for real-time synchronized modeling of multiple mechanical fields of soft tissues. It may support surgical simulation and related medical-assistance applications by enabling real-time, accurate prediction of deformation, stress, and reaction force information.