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Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization
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Proposes a physics-regularized, particle-on-grid discretization that soft-constrains learned tumor cell and brain tissue fields to reaction-diffusion-advection and neo-Hookean elasticity PDEs, improving glioblastoma radiotherapy target coverage of recurrence.
Problem
Estimating the full spatial distribution of low-concentration glioblastoma tumor cells (invisible on MRI) for radiotherapy planning, given limited patient data and unknown initial conditions, while avoiding overly rigid physics models.
Approach
Discrete PDE residuals for tumor growth and tissue elasticity are computed on a dynamic Lagrangian particle mesh projected to Eulerian grids, and used as soft regularization (not hard constraints) alongside imaging data losses; the method also jointly infers the initial healthy brain anatomy.
Key results
- Recurrence coverage (any segmentation): 74.7% for the proposed method vs 72.9% static grid (GliODIL) and 70.0% Standard Plan.
- Recurrence coverage (enhancing core): 89.9% vs 89.0% static grid and 87.3% Standard Plan; Wilcoxon p=0.00082 vs Standard Plan for enhancing core.
- On synthetic single-focal data with full inputs, RMSE 0.3% vs 3.3% for static grid baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed soft-physics method instead of Static Grid Discretization | Radiotherapy planning · Recurrence (Any) | Recurrence Coverage [%]: 72.9 ± 3.5 -> 74.7 ± 3.1 | Helped |
| Use the proposed soft-physics method instead of Static Grid Discretization | Radiotherapy planning · Recurrence (Enhancing Core) | Recurrence Coverage [%]: 89.0 ± 3.3 -> 89.9 ± 2.7 | Helped |
| Add physics constraints to the data-driven neural network | NN (Unconstrained) · Recurrence (Any) | Recurrence Coverage [%]: 59.0 ± 4.3 -> 70.4 ± 3.7 | Helped |
| Add physics constraints to the data-driven neural network | NN (Unconstrained) · Recurrence (Enhancing Core) | Recurrence Coverage [%]: 66.8 ± 4.9 -> 84.3 ± 3.3 | Helped |
| Infer the initial anatomy instead of fixing it to an average brain (ablation) | Ours · Recurrence (Any) | Recurrence Coverage [%]: 73.4 ± 3.2 -> 74.7 ± 3.1 | Helped |
| Infer the initial anatomy instead of fixing it to an average brain (ablation) | Ours · Recurrence (Enhancing Core) | Recurrence Coverage [%]: 89.3 ± 2.9 -> 89.9 ± 2.7 | Helped |
| Include imaging data reconstruction losses (ablation) | Ours · Recurrence (Any) | Coverage [%]: 60.5 ± 4.9 -> 74.7 ± 3.1 | Helped |
| Include edema and metabolic-map losses (ablation) | Ours · Recurrence (Any) | Coverage [%]: 63.5 ± 4.0 -> 74.7 ± 3.1 | Helped |
| Include the initial Gaussian tumor-distribution loss (ablation) | Ours · Recurrence (Any) | Coverage [%]: 70.0 ± 3.8 -> 74.7 ± 3.1 | Helped |
| Include tumor-growth physics regularization (ablation) | Ours · Recurrence (Any) | Coverage [%]: 70.9 ± 3.8 -> 74.7 ± 3.1 | Helped |
| Include tissue-elasticity physics regularization (ablation) | Ours · Recurrence (Any) | Coverage [%]: 71.9 ± 3.8 -> 74.7 ± 3.1 | Helped |
| Include the healthy-anatomy symmetry loss (ablation) | Ours · Recurrence (Any) | Coverage [%]: 72.8 ± 3.9 -> 74.7 ± 3.1 | Helped |
Surprising findings
- Physics-constrained neural network slightly outperforms the Standard Plan on any-recurrence coverage only modestly, while unconstrained NN drops to 59.0%.
- Enhancing-core recurrence coverage gains are small because many methods reach 100% coverage near pre-operative segmentations.
Limitations
- Multi-resolution convergence assumes the problem can be represented at lower resolutions; may not apply to PDEs with narrow-phase interfaces.
- Assumes large deformations do not cause material rupture; Lagrangian scheme may not handle this without modification.
- Large mean uncertainty in per-patient recurrence coverage; gains over baselines are small relative to standard errors.
Experimental setup
Datasets: publicly available 58-patient glioblastoma dataset with preoperative MRI, FET-PET and follow-up MRI synthetic tumor dataset (100 patients) generated by finite difference solver
Benchmarks: 58-patient glioblastoma recurrence dataset (recurrence coverage, any and enhancing core) synthetic tumor RMSE
Metrics: recurrence coverage [%] IoU RMSE Wilcoxon signed-rank p-value
Baselines: Standard Plan (1.5 cm margin) Static Grid Discretization (GliODIL) Numerical Physics Simulations NN (Unconstrained) NN (Physics-Constrained)
Builds on: ODIL PINNs GliODIL reaction-diffusion-advection tumor growth model Neo-Hookean hyperelasticity
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- Incomplete Multi-modal Brain Tumor Segmentation via Learnable Sorting State Space Model (CVPR 2025 · similarity 0.82)
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