Accurate and efficient modeling of soft-tissue interactions is fundamental for advancing surgical simulation, surgical robotics, and model-based surgical automation. To achieve real-time latency, classical Finite Element Method (FEM) solvers are often replaced with neural approximations; however, naively training such models in a fully data-driven manner without incorporating physical priors frequently leads to poor generalization and physically implausible predictions. We present a novel physics-informed neural simulation framework that enables real-time prediction of soft-tissue deformations under complex single- and multi-grasper interactions. Our approach integrates Kelvinlet-based analytical priors with large-scale FEM data, capturing both linear and nonlinear tissue responses. This hybrid design improves predictive accuracy and physical plausibility across diverse neural architectures while maintaining the low-latency performance required for interactive applications. We validate our method on challenging surgical manipulation tasks involving standard laparoscopic grasping tools, demonstrating substantial improvements in deformation fidelity and temporal stability over existing baselines. These results establish Kelvinlet-augmented learning as a principled and computationally efficient paradigm for real-time, physics-aware soft-tissue simulation in surgical AI.

In image-guided liver surgery, the initial rigid alignment between preoperative and intraoperative data, often represented as point clouds, is crucial for providing sub-surface information from preoperative CT/MRI images to the surgeon during the procedure. Currently, this alignment is typically performed using semi-automatic methods, which, while effective to some extent, are prone to errors that demand manual correction. Alternatively, correspondence-based point cloud registration methods further offer a promising fully automatic solution. However, they may struggle in scenarios with limited intraoperative surface visibility, a common challenge in liver surgery, particularly in laparoscopic procedures, which we refer to as complete-to-partial ambiguity. We first illustrate this ambiguity by evaluating the performance of state-of-the-art learning-based point cloud registration methods on our carefully constructed in silico and in vitro datasets. Then, we propose a patches-to-partial matching strategy as a plug-and-play module to resolve the ambiguity, which can be seamlessly integrated into learning-based registration methods without disrupting their end-to-end structure. This approach effectively improves registration performance, especially in low-visibility conditions, reducing registration errors to 6.7 mm ($-$29%) in silico and 12.5 mm ($-$40%) in vitro, compared to state-of-the-art performance achieved by Lepard of 9.5 mm and 20.7 mm, respectively. The constructed benchmark and the proposed module establish a solid foundation for advancing applications of point cloud correspondence-based registration methods in image-guided liver surgery. Our code and datasets will be released at https://github.com/zixinyang9109/P2P.

Image-guided surgery collocates patient-specific data with the physical environment to facilitate surgical decision making. Unfortunately, these guidance systems commonly become compromised by intraoperative soft-tissue deformations. Nonrigid image-to-physical registration methods have been proposed to compensate for deformations, but clinical utility requires compatibility of these techniques with data sparsity and temporal constraints in the operating room. While finite element models can be effective in sparse data scenarios, computation time remains a limitation to widespread deployment. This paper proposes a registration algorithm that uses regularized Kelvinlets, which are analytical solutions to linear elasticity in an infinite domain, to overcome these barriers. This algorithm is demonstrated and compared to finite element-based registration on two datasets: a phantom liver deformation dataset and an in vivo breast deformation dataset. The regularized Kelvinlets algorithm resulted in a significant reduction in computation time compared to the finite element method. Accuracy as evaluated by target registration error was comparable between methods. Average target registration errors were 4.6 ± 1.0 and 3.2 ± 0.8 mm on the liver dataset and 5.4 ± 1.4 and 6.4 ± 1.5 mm on the breast dataset for the regularized Kelvinlets and finite element method, respectively. Limitations of regularized Kelvinlets include the lack of organ-specific geometry and the assumptions of linear elasticity and infinitesimal strain. Despite limitations, this work demonstrates the generalizability of regularized Kelvinlets registration on two soft-tissue elastic organs. This method may improve and accelerate registration for image-guided surgery, and it shows the potential of using regularized Kelvinlets on medical imaging data.

Image-guided intervention for soft tissue organs depends on the accuracy of deformable registration methods to achieve effective results. While registration techniques based on elastic theory are prevalent, no methods yet exist that can prospectively estimate registration uncertainty to regulate sources and mitigate consequences of localization error in deforming organs. This paper introduces registration uncertainty metrics based on dispersion of strain energy from boundary constraints to predict the proportion of target registration error (TRE) remaining after nonrigid elastic registration. These uncertainty metrics depend on the spatial distribution of intraoperative constraints provided to registration with relation to patient-specific organ geometry. Predictive linear and bivariate gamma models are fit and cross-validated using an existing dataset of 6291 simulated registration examples, plus 699 novel simulated registrations withheld for independent validation. Average uncertainty and average proportion of TRE remaining after elastic registration are strongly correlated ( r = 0.78 ), with mean absolute difference in predicted TRE equivalent to 0.9 ± 0.6 mm (cross-validation) and 0.9 ± 0.5 mm (independent validation). Spatial uncertainty maps also permit localized TRE estimates accurate to an equivalent of 3.0 ± 3.1 mm (cross-validation) and 1.6 ± 1.2 mm (independent validation). Additional clinical evaluation of vascular features yields localized TRE estimates accurate to 3.4 ± 3.2 mm. This work formalizes a lower bound for the inherent uncertainty of nonrigid elastic registrations given coverage of intraoperative data constraints, and demonstrates a relation to TRE that can be predictively leveraged to inform data collection and provide a measure of registration confidence for elastic methods.

During image guided liver surgery, soft tissue deformation can cause considerable error when attempting to achieve accurate localization of the surgical anatomy through image-to-physical registration. In this paper, a linearized iterative boundary reconstruction technique is proposed to account for these deformations. The approach leverages a superposed formulation of boundary conditions to rapidly and accurately estimate the deformation applied to a preoperative model of the organ given sparse intraoperative data of surface and subsurface features. With this method, tracked intraoperative ultrasound (iUS) is investigated as a potential data source for augmenting registration accuracy beyond the capacity of conventional organ surface registration. In an expansive simulated dataset, features including vessel contours, vessel centerlines, and the posterior liver surface are extracted from iUS planes. Registration accuracy is compared across increasing data density to establish how iUS can be best employed to improve target registration error (TRE). From a baseline average TRE of 11.4 ± 2.2 mm using sparse surface data only, incorporating additional sparse features from three iUS planes improved average TRE to 6.4 ± 1.0 mm. Furthermore, increasing the sparse coverage to 16 tracked iUS planes improved average TRE to 3.9 ± 0.7 mm, exceeding the accuracy of registration based on complete surface data available with more cumbersome intraoperative CT without contrast. Additionally, the approach was applied to three clinical cases where on average error improved 67% over rigid registration and 56% over deformable surface registration when incorporating additional features from one independent tracked iUS plane.

In open image-guided liver surgery (IGLS), a sparse representation of the intraoperative organ surface can be acquired to drive image-to-physical registration. We hypothesize that uncharacterized error induced by variation in the collection patterns of organ surface data limits the accuracy and robustness of an IGLS registration. Clinical validation of such registration methods is challenged due to the difficulty in obtaining data representative of the true state of organ deformation. We propose a novel human-to-phantom validation framework that transforms surface collection patterns from in vivo IGLS procedures (n = 13) onto a well-characterized hepatic deformation phantom for the purpose of validating surface-driven, volumetric nonrigid registration methods. An important feature of the approach is that it centers on combining workflow-realistic data acquisition and surgical deformations that are appropriate in behavior and magnitude. Using the approach, we investigate volumetric target registration error (TRE) with both current rigid IGLS and our improved nonrigid registration methods. Additionally, we introduce a spatial data resampling approach to mitigate the workflow-sensitive sampling problem. Using our human-to-phantom approach, TRE after routine rigid registration was 10.9 ± 0.6 mm with a signed closest point distance associated with residual surface fit in the range of ±10 mm, highly representative of open liver resections. After applying our novel resampling strategy and improved deformation correction method, TRE was reduced by 51%, i.e., a TRE of 5.3 ± 0.5 mm. This paper reported herein realizes a novel tractable approach for the validation of image-to-physical registration methods and demonstrates promising results for our correction method.