# Neural parameters estimation for brain tumor growth modeling

arXiv: https://arxiv.org/abs/1907.00973 · HTML: https://mlsanity.com/paper/1907.00973/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 11 of 11)

- [Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling](https://mlsanity.com/paper/2111.04090/) (2021)
- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [Treatment-aware Diffusion Probabilistic Model for Longitudinal MRI Generation and Diffuse Glioma Growth Prediction](https://mlsanity.com/paper/2309.05406/) (2023)
- [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)
- [Generalized Wasserstein Dice Loss, Test-time Augmentation, and Transformers for the BraTS 2021 challenge](https://mlsanity.com/paper/2112.13054/) (2021)
- [Mechanistic Learning with Guided Diffusion Models to Predict Spatio-Temporal Brain Tumor Growth](https://mlsanity.com/paper/2509.09610/) (2025)
- [PREDICT-GBM: A multi-center platform to advance personalized glioblastoma radiotherapy planning](https://mlsanity.com/paper/2509.13360/) (2025)
- [Semi-Implicit Neural Solver for Time-dependent Partial Differential Equations](https://mlsanity.com/paper/2109.01467/) (2021)
- [Evaluating glioma growth predictions as a forward ranking problem](https://mlsanity.com/paper/2103.11651/) (2021)
- [SEDNet: Shallow Encoder-Decoder Network for Brain Tumor Segmentation](https://mlsanity.com/paper/2401.13403/) (2024)

## Abstract (arXiv)

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the physiological processes that govern the growth of the tumor are considered. To personalize the model, i.e. find a relevant set of parameters, with respect to the tumor dynamics of a particular patient, the model is informed from empirical data, e.g., medical images obtained from diagnostic modalities, such as magnetic-resonance imaging. Existing model-observation coupling schemes require a large number of forward integrations of the biophysical model and rely on simplifying assumption on the functional form, linking the output of the model with the image information. In this work, we propose a learning-based technique for the estimation of tumor growth model parameters from medical scans. The technique allows for explicit evaluation of the posterior distribution of the parameters by sequentially training a mixture-density network, relaxing the constraint on the functional form and reducing the number of samples necessary to propagate through the forward model for the estimation. We test the method on synthetic and real scans of rats injected with brain tumors to calibrate the model and to predict tumor progression.