# Biophysics Informed Pathological Regularisation for Brain Tumour Segmentation

arXiv: https://arxiv.org/abs/2403.09136 · HTML: https://mlsanity.com/paper/2403.09136/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [3D MRI brain tumor segmentation using autoencoder regularization](https://mlsanity.com/paper/1810.11654/) (2018)
- [Recurrent Residual Convolutional Neural Network based on U-Net (R2U-Net) for Medical Image Segmentation](https://mlsanity.com/paper/1802.06955/) (2018)
- [Better Aggregation in Test-Time Augmentation](https://mlsanity.com/paper/2011.11156/) (2020)
- [PC-SwinMorph: Patch Representation for Unsupervised Medical Image Registration and Segmentation](https://mlsanity.com/paper/2203.05684/) (2022)

## Built on by (most cited first, 7 of 7)

- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups](https://mlsanity.com/paper/2410.02698/) (2024)
- [Enhancing Fourier Neural Operators with Local Spatial Features](https://mlsanity.com/paper/2503.17797/) (2025)
- [Brain Foundation Models with Hypergraph Dynamic Adapter for Brain Disease Analysis](https://mlsanity.com/paper/2505.00627/) (2025)
- [Symplectic Neural Flows for Modeling and Discovery](https://mlsanity.com/paper/2412.16787/) (2024)
- [Multi-modal MRI Translation via Evidential Regression and Distribution Calibration](https://mlsanity.com/paper/2407.07372/) (2024)
- [Generalized Lie Symmetries in Physics-Informed Neural Operators](https://mlsanity.com/paper/2502.00373/) (2025)

## Abstract (arXiv)

Recent advances in deep learning have significantly improved brain tumour segmentation techniques; however, the results still lack confidence and robustness as they solely consider image data without biophysical priors or pathological information. Integrating biophysics-informed regularisation is one effective way to change this situation, as it provides an prior regularisation for automated end-to-end learning. In this paper, we propose a novel approach that designs brain tumour growth Partial Differential Equation (PDE) models as a regularisation with deep learning, operational with any network model. Our method introduces tumour growth PDE models directly into the segmentation process, improving accuracy and robustness, especially in data-scarce scenarios. This system estimates tumour cell density using a periodic activation function. By effectively integrating this estimation with biophysical models, we achieve better capture of tumour characteristics. This approach not only aligns the segmentation closer to actual biological behaviour but also strengthens the model's performance under limited data conditions. We demonstrate the effectiveness of our framework through extensive experiments on the BraTS 2023 dataset, showcasing significant improvements in both precision and reliability of tumour segmentation.