Registration of Deformed Tissue: A GNN-VAE Approach With Data Assimilation for Sim-to-Real Transfer

In image-guided surgery, deformation of soft tissues can cause substantial errors in targeting internal targets, since deformation can affect the translation of preoperative image-based surgical plans during surgery. Having a realistic tissue deformation simulator could enhance the accuracy of internal targets localization by giving an accurate estimation of the deformation applied to a preoperative model of the organ. A key challenge is to address the sim-to-real gap between the simulator and the actual intraoperative behavior of the tissue. The sim-to-real transfer challenge is addressed by formulating the problem as a probabilistic inference over a low-dimensional representation of deformed objects. The proposed method utilizes a generative variational autoencoder structure based on graph neural networks (GNN-VAE) to generate a probabilistic low-dimensional representation of the outputs of a physics-based simulator. To match simulation data to real data, the resultant low-dimensional distribution (i.e., prior distribution) is updated iteratively using an ensemble smoother with multiple data assimilation. The advantages of the proposed method are first, it only uses simulation data for training the GNN-VAE, and no retraining of GNN-VAE is required intraoperatively, second, it does not require estimating the mechanical properties of the tissue it is simulating, and third, is able to work with any physic-based simulator. The proposed framework was verified both in experimental and simulation studies and showed it can reduce the registration error in tissue deformation.