On the other hand, model-based methods are a set of registration techniques that treat images as a deformable volume--a notion first introduced by Broit [1981]--to better allow for presenting elastic and plastic deformations.

Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element method (FEM) is a proven technique to effectively approximate soft tissue deformation through biomechanical formulations, their degree of success boils down to a trade-off between accuracy and speed. To circumvent this problem, the most recent works in this domain have proposed leveraging data-driven models obtained by training various machine learning algorithms---e.g., random forests, artificial neural networks (ANNs)---with the results of finite element analysis (FEA) to speed up tissue deformation approximations by prediction. These methods, however, do not account for the structure of the finite element (FE) mesh during training that provides information on node connectivities as well as the distance between them, which can aid with approximating tissue deformation based on the proximity of force load points with the rest of the mesh nodes. Therefore, this work proposes a novel framework, PhysGNN, a data-driven model that approximates the solution of the FEM by leveraging graph neural networks (GNNs), which are capable of accounting for the mesh structural information and inductive learning over unstructured grids and complex topological structures. Empirically, we demonstrate that the proposed architecture, PhysGNN, promises accurate and fast soft tissue deformation approximations, and is competitive with the state-of-the-art (SOTA) algorithms while promising enhanced computational feasibility, therefore suitable for neurosurgical settings.

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.

The FE simulations in our study were carried out on quad-core Intel i7 @ 2.9 GHz CPU, while The summary table below compares our results with a few similar studies based on empirical grounds. Mesh Maximum Displacement in the Dataset(s) (mm) Mean Absolute Position Error (mm) Mean Euclidean Error (mm) % of Euclidean Error Below 1 mm Average of Maximum Euclidean Error per Simulation (mm) Tonutti et al. [2017] 1087 -- 0.191 0.18 -- --

This task, however, poses a challenge.

Soft tissue simulation in virtual environments is becoming increasingly important for medical applications. However, the high deformability of soft tissue poses significant challenges. Existing methods rely on segmentation, meshing and estimation of stiffness properties of tissues. In addition, the integration of haptic feedback requires precise force estimation to enable a more immersive experience. We introduce a novel data-driven model, a conditional graph neural network (cGNN) to tackle this complexity. Our model takes surface points and the location of applied forces, and is specifically designed to predict the deformation of the points and the forces exerted on them. We trained our model on experimentally collected surface tracking data of a soft tissue phantom and used transfer learning to overcome the data scarcity by initially training it with mass-spring simulations and fine-tuning it with the experimental data. This approach improves the generalisation capability of the model and enables accurate predictions of tissue deformations and corresponding interaction forces. The results demonstrate that the model can predict deformations with a distance error of 0.35$\pm$0.03 mm for deformations up to 30 mm and the force with an absolute error of 0.37$\pm$0.05 N for forces up to 7.5 N. Our data-driven approach presents a promising solution to the intricate challenge of simulating soft tissues within virtual environments. Beyond its applicability in medical simulations, this approach holds the potential to benefit various fields where realistic soft tissue simulations are required.

Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element method (FEM) is a proven technique to effectively approximate soft tissue deformation through biomechanical formulations, their degree of success boils down to a trade-off between accuracy and speed. To circumvent this problem, the most recent works in this domain have proposed leveraging data-driven models obtained by training various machine learning algorithms---e.g., random forests, artificial neural networks (ANNs)---with the results of finite element analysis (FEA) to speed up tissue deformation approximations by prediction. These methods, however, do not account for the structure of the finite element (FE) mesh during training that provides information on node connectivities as well as the distance between them, which can aid with approximating tissue deformation based on the proximity of force load points with the rest of the mesh nodes. Therefore, this work proposes a novel framework, PhysGNN, a data-driven model that approximates the solution of the FEM by leveraging graph neural networks (GNNs), which are capable of accounting for the mesh structural information and inductive learning over unstructured grids and complex topological structures.

In various applications, such as virtual reality and gaming, simulating the deformation of soft tissues in the human body during interactions with external objects is essential. Traditionally, Finite Element Methods (FEM) have been employed for this purpose, but they tend to be slow and resource-intensive. In this paper, we propose a unified representation of human body shape and soft tissue with a data-driven simulator of non-rigid deformations. This approach enables rapid simulation of realistic interactions. Our method builds upon the SMPL model, which generates human body shapes considering rigid transformations. We extend SMPL by incorporating a soft tissue layer and an intuitive representation of external forces applied to the body during object interactions. Specifically, we mapped the 3D body shape and soft tissue and applied external forces to 2D UV maps. Leveraging a UNET architecture designed for 2D data, our approach achieves high-accuracy inference in real time. Our experiment shows that our method achieves plausible deformation of the soft tissue layer, even for unseen scenarios.

Data augmentation (DA) is a key factor in medical image analysis, such as in prostate cancer (PCa) detection on magnetic resonance images. State-of-the-art computer-aided diagnosis systems still rely on simplistic spatial transformations to preserve the pathological label post transformation. However, such augmentations do not substantially increase the organ as well as tumor shape variability in the training set, limiting the model's ability to generalize to unseen cases with more diverse localized soft-tissue deformations. We propose a new anatomy-informed transformation that leverages information from adjacent organs to simulate typical physiological deformations of the prostate and generates unique lesion shapes without altering their label. Due to its lightweight computational requirements, it can be easily integrated into common DA frameworks. We demonstrate the effectiveness of our augmentation on a dataset of 774 biopsy-confirmed examinations, by evaluating a state-of-the-art method for PCa detection with different augmentation settings.

Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element method (FEM) is a proven technique to effectively approximate soft tissue deformation through biomechanical formulations, their degree of success boils down to a trade-off between accuracy and speed. To circumvent this problem, the most recent works in this domain have proposed leveraging data-driven models obtained by training various machine learning algorithms -- e.g., random forests, artificial neural networks (ANNs) -- with the results of finite element analysis (FEA) to speed up tissue deformation approximations by prediction. These methods, however, do not account for the structure of the finite element (FE) mesh during training that provides information on node connectivities as well as the distance between them, which can aid with approximating tissue deformation based on the proximity of force load points with the rest of the mesh nodes. Therefore, this work proposes a novel framework, PhysGNN, a data-driven model that approximates the solution of the FEM by leveraging graph neural networks (GNNs), which are capable of accounting for the mesh structural information and inductive learning over unstructured grids and complex topological structures. Empirically, we demonstrate that the proposed architecture, PhysGNN, promises accurate and fast soft tissue deformation approximations, and is competitive with the state-of-the-art (SOTA) algorithms while promising enhanced computational feasibility, therefore suitable for neurosurgical settings.