# Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization

arXiv: https://arxiv.org/abs/2409.20409 · HTML: https://mlsanity.com/paper/2409.20409/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 30 Sep 2024.

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

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks](https://mlsanity.com/paper/2310.09528/) (2023)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations](https://mlsanity.com/paper/2205.09332/) (2022)
- [Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans and Bayesian Inference](https://mlsanity.com/paper/1807.00499/) (2018)
- [Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling](https://mlsanity.com/paper/2111.04090/) (2021)
- [Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models](https://mlsanity.com/paper/2312.09787/) (2023)
- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)
- [Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans](https://mlsanity.com/paper/2311.16536/) (2023)
- [Continuous-Time Deep Glioma Growth Models](https://mlsanity.com/paper/2106.12917/) (2021)
- [Ensemble inversion for brain tumor growth models with mass effect](https://mlsanity.com/paper/2106.06016/) (2021)
- [Flow reconstruction by multiresolution optimization of a discrete loss with automatic differentiation](https://mlsanity.com/paper/2303.04679/) (2023)
- [Physics-aware deep learning framework for linear elasticity](https://mlsanity.com/paper/2302.09668/) (2023)

## Built on by (most cited first, 9 of 9)

- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation](https://mlsanity.com/paper/2507.17019/) (2025)
- [PREDICT-GBM: A multi-center platform to advance personalized glioblastoma radiotherapy planning](https://mlsanity.com/paper/2509.13360/) (2025)
- [A Lightweight Optimization Framework for Estimating 3D Brain Tumor Infiltration](https://mlsanity.com/paper/2412.13811/) (2024)
- [Efficient Deep Learning-based Forward Solvers for Brain Tumor Growth Models](https://mlsanity.com/paper/2501.08226/) (2025)
- [Bayesian Inference for PDE-based Inverse Problems using the Optimization of a Discrete Loss](https://mlsanity.com/paper/2510.15664/) (2025)
- [A Biophysically-Conditioned Generative Framework for 3D Brain Tumor MRI Synthesis](https://mlsanity.com/paper/2510.09365/) (2025)
- [Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory](https://mlsanity.com/paper/2606.28630/) (2026)

## Abstract (arXiv)

Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient's anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.