# Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans

arXiv: https://arxiv.org/abs/2311.16536 · HTML: https://mlsanity.com/paper/2311.16536/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 68 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation](https://mlsanity.com/paper/2012.02681/) (2020)
- [Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2107.00940/) (2021)
- [Multi-Loss Weighting with Coefficient of Variations](https://mlsanity.com/paper/2009.01717/) (2020)
- [Predictive Digital Twin for Optimizing Patient-Specific Radiotherapy Regimens under Uncertainty in High-Grade Gliomas](https://mlsanity.com/paper/2308.12429/) (2023)
- [Neural parameters estimation for brain tumor growth modeling](https://mlsanity.com/paper/1907.00973/) (2019)
- [Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect](https://mlsanity.com/paper/2006.09932/) (2020)
- [Ensemble inversion for brain tumor growth models with mass effect](https://mlsanity.com/paper/2106.06016/) (2021)
- [Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data](https://mlsanity.com/paper/2308.14925/) (2023)
- [Image-Driven Biophysical Tumor Growth Model Calibration](https://mlsanity.com/paper/1907.07774/) (2019)
- [A for-loop is all you need. For solving the inverse problem in the case of personalized tumor growth modeling](https://mlsanity.com/paper/2205.04550/) (2022)

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

- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)
- [Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization](https://mlsanity.com/paper/2409.20409/) (2024)
- [BiLO: Bilevel Local Operator Learning for PDE Inverse Problems](https://mlsanity.com/paper/2404.17789/) (2024)
- [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)
- [A Family of Adaptive Activation Functions for Mitigating Failure Modes in Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.18328/) (2026)

## Abstract (arXiv)

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion PDE model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse domain method is employed to handle the complex brain geometry within the PINN framework. Our method is validated both on synthetic and patient datasets, and shows promise for real-time parametric inference in the clinical setting for personalized GBM treatment.