# Deformable Models for Surgical Simulation: A Survey

arXiv: https://arxiv.org/abs/1909.03363 · HTML: https://mlsanity.com/paper/1909.03363/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2019.

## Built on by (most cited first, 6 of 6)

- [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)
- [Boundary Constraint-free Biomechanical Model-Based Surface Matching for Intraoperative Liver Deformation Correction](https://mlsanity.com/paper/2403.09964/) (2024)
- [SAW: Toward a Surgical Action World Model via Controllable and Scalable Video Generation](https://mlsanity.com/paper/2603.13024/) (2026)
- [Enhancing Mechanical Metamodels with a Generative Model-Based Augmented Training Dataset](https://mlsanity.com/paper/2203.04183/) (2022)
- [NVIDIA Cosmos-H-Dreams: Real-Time Generative Physics Simulation for Surgical Robotics](https://mlsanity.com/paper/2608.24199/) (2026)
- [Autoregressive deep learning for real-time simulation of soft tissue dynamics during virtual neurosurgery](https://mlsanity.com/paper/2601.13676/) (2026)

## Abstract (arXiv)

This paper presents a survey of the state-of-the-art deformable models studied in the literature concerning soft tissue deformable modeling for interactive surgical simulation. It first introduces the challenges of surgical simulation, followed by discussions and analyses on the deformable models, which are classified into three categories: the heuristic modeling methodology, continuum-mechanical methodology, and other methodologies. It also examines linear and nonlinear deformable modeling, model internal forces, and numerical time integrations, together with modeling of soft tissue anisotropy, viscoelasticity, and compressibility. Finally, various issues in the existing deformable models are discussed to outline the remaining challenges of deformable models in surgical simulation.