# Conditional Graph Neural Network for Predicting Soft Tissue Deformation and Forces

arXiv: https://arxiv.org/abs/2507.05315 · HTML: https://mlsanity.com/paper/2507.05315/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [A survey on Deep Learning Advances on Different 3D Data Representations](https://mlsanity.com/paper/1808.01462/) (2018)
- [PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery](https://mlsanity.com/paper/2109.04352/) (2021)
- [Learning Soft Tissue Behavior of Organs for Surgical Navigation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.00722/) (2019)

## Built on by (most cited first, 1 of 1)

- [Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry](https://mlsanity.com/paper/2608.20967/) (2026)

## Abstract (arXiv)

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±0.03 mm for deformations up to 30 mm and the force with an absolute error of 0.37±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.