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Biophysics Informed Pathological Regularisation for Brain Tumour Segmentation

Lipei Zhang, Yanqi Cheng, Lihao Liu, Carola-Bibiane Schönlieb, Angelica I Aviles-Rivero

TL;DR

This paper proposes a novel approach that designs brain tumour growth Partial Differential Equation (PDE) models as a regularisation with deep learning, operational with any network model, and demonstrates the effectiveness of this framework through extensive experiments on the BraTS 2023 dataset.

Abstract

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.

Biophysics Informed Pathological Regularisation for Brain Tumour Segmentation

TL;DR

This paper proposes a novel approach that designs brain tumour growth Partial Differential Equation (PDE) models as a regularisation with deep learning, operational with any network model, and demonstrates the effectiveness of this framework through extensive experiments on the BraTS 2023 dataset.

Abstract

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.
Paper Structure (14 sections, 8 equations, 4 figures, 1 table)

This paper contains 14 sections, 8 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Proposed Method
  3. Brain tumour segmentation.
  4. Biophysics-informed optimisation.
  5. Tumour cell density estimator.
  6. Calculation of biophysics-informed regularisation.
  7. Experiment
  8. Datasets.
  9. Main experimental Details and compared methods.
  10. Evaluation Metrics.
  11. Results and Discussion.
  12. Conclusion
  13. Acknowledgments.
  14. Disclosure of Interests.

Figures (4)

  • Figure 1: The Biophysics-informed optimisation for segmentation. A. Main structure for brain tumour segmentation. B. Tumour cell density estimator (the flattened feature map will be concatenated with assumed time matrix T). C. Calculation of PDE loss. D. Calculation of boundary loss.
  • Figure 2: (a) shows the impact of activation functions and boundary conditions on the biophysics-informed UNet performance on Dice score. (b)-(d) shows comparisons of UNet, with and without the biophysics-informed module with mean on Dice score over the 3 regions. (b) explores performance variations using two or three modalities, (c) presents comparisons on different training set sizes, (d) compares different loss combinations.
  • Figure 3: MRI tumour segmentation comparison: All enhanced by biophysics-informed regularisation. The GD-enhancing tumour (ET), the peritumoral edematous tissue (ED), and the necrotic tumour core (NCR). The WT combines red, blue, and green; the TC merges green and blue; and the ET is represented by red.
  • Figure 4: Localisation in Brain Tumour Segmentation: The images compare the UNet with its biophysics-informed version using GradCAM, revealing more precise tumour localisation. The ground truth scan is shown first, followed by GradCAM visualisations of last encoder and decoder layers, with and without biophysics-informed regularisation.