# PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery

arXiv: https://arxiv.org/abs/2109.04352 · HTML: https://mlsanity.com/paper/2109.04352/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 68 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Learning Soft Tissue Behavior of Organs for Surgical Navigation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.00722/) (2019)
- [Deformable Models for Surgical Simulation: A Survey](https://mlsanity.com/paper/1909.03363/) (2019)
- [Suite of Meshless Algorithms for Accurate Computation of Soft Tissue Deformation for Surgical Simulation](https://mlsanity.com/paper/1903.04760/) (2019)
- [Biomechanical modeling and computer simulation of the brain during neurosurgery](https://mlsanity.com/paper/1904.01192/) (2019)

## Built on by (most cited first, 22 of 22)

- [Enhancing Mechanical Metamodels with a Generative Model-Based Augmented Training Dataset](https://mlsanity.com/paper/2203.04183/) (2022)
- [Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2311.07548/) (2023)
- [Physics-Encoded Graph Neural Networks for Deformation Prediction under Contact](https://mlsanity.com/paper/2402.03466/) (2024)
- [PhysRFANet: Physics-Guided Neural Network for Real-Time Prediction of Thermal Effect During Radiofrequency Ablation Treatment](https://mlsanity.com/paper/2312.13947/) (2023)
- [RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.08367/) (2024)
- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [Domain-informed graph neural networks: a quantum chemistry case study](https://mlsanity.com/paper/2208.11934/) (2022)
- [Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks](https://mlsanity.com/paper/2201.10122/) (2022)
- [Physics-Informed Graph Learning](https://mlsanity.com/paper/2202.10679/) (2022)
- [Body Fat Estimation from Surface Meshes using Graph Neural Networks](https://mlsanity.com/paper/2308.02493/) (2023)
- [Feature Mapping in Physics-Informed Neural Networks (PINNs)](https://mlsanity.com/paper/2402.06955/) (2024)
- [FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2506.11398/) (2025)
- [Graph Neural Networks for modelling breast biomechanical compression](https://mlsanity.com/paper/2411.06596/) (2024)
- [Neural-Augmented Kelvinlet for Real-Time Soft Tissue Deformation Modeling](https://mlsanity.com/paper/2506.08043/) (2025)
- [Conditional Graph Neural Network for Predicting Soft Tissue Deformation and Forces](https://mlsanity.com/paper/2507.05315/) (2025)
- [Unveiling the Unseen Potential of Graph Learning through MLPs: Effective Graph Learners Using Propagation-Embracing MLPs](https://mlsanity.com/paper/2311.11759/) (2023)
- [STMPL: Human Soft-Tissue Simulation](https://mlsanity.com/paper/2403.08344/) (2024)
- [MIXPINN: Mixed-Material Simulations by Physics-Informed Neural Network](https://mlsanity.com/paper/2503.13123/) (2025)
- [Real-time prediction of breast cancer sites using deformation-aware graph neural network](https://mlsanity.com/paper/2511.13082/) (2025)
- [Long-Term Alzheimers Disease Prediction: A Novel Image Generation Method Using Temporal Parameter Estimation with Normal Inverse Gamma Distribution on Uneven Time Series](https://mlsanity.com/paper/2511.21057/) (2025)
- [Autoregressive deep learning for real-time simulation of soft tissue dynamics during virtual neurosurgery](https://mlsanity.com/paper/2601.13676/) (2026)
- [Data-driven registration and modeling of brain deformation for image-guided neurosurgery](https://mlsanity.com/paper/2602.10155/) (2026)

## Abstract (arXiv)

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.