ZeinebZH / TumorNetSolvers

Efficient Deep Learning-based Forward Solvers for Brain Tumor Growth Models

TumorNetSolvers: A Deep Learning Framework for Personalized PDE-Based Tumor Growth Modeling

TumorNetSolvers is an adaptive deep learning framework designed for efficient personalization of PDE-based tumor growth models, focused on simulating and predicting tumor evolution. Built on the powerful nnU-Net framework, it leverages state-of-the-art neural architectures to address both forward and inverse tumor modeling problems.

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Table of Contents

1. Overview
2. Core Concepts
3. Model Architectures
4. Usage
5. Installation
6. Contributing
7. License
8. References

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Overview

TumorNetSolvers provides a flexible and efficient solution for simulating tumor growth in 3D using Partial Differential Equations (PDEs), specifically the Fisher-Kolmogorov equation. It personalizes the model for individual patients by inferring tumor growth parameters (diffusion coefficient, growth rate, initial location) from MRI scans or similar medical images.

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Forward Problem

• Input: A 3D medical image (e.g., brain tissue segmentations) and tumor parameters (growth rate, diffusion coefficient, tumor location).
• Output: A 3D simulation of tumor corresponding to the given anatomy and tumor parameters.

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Inverse Problem

Given a high-performing differentiable forward model, we "freeze" the model and optimize its parameters based on a target tumor simulation.

• Input: A target tumor simulation (e.g., MRI-based 3D tumor image).
• Goal: Infer the underlying tumor parameters (e.g., growth rate, diffusion coefficient, tumor location) by adjusting these input parameters to match the target simulation.

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Core Concepts

1. PDE-Based Tumor Growth Modeling

TumorNetSolvers is trained on the Fisher-Kolmogorov equation to model brain tumor cell dynamics over time and space:

$$ \frac{\partial c}{\partial t} = \nabla \cdot (D \nabla c) + \rho c(1 - c) $$

Where:

• ( c(x, t) ) is the tumor cell concentration,
• ( D ) is the diffusion coefficient,
• ( \rho ) is the growth rate,
• ( \nabla \cdot (D \nabla c) ) is the diffusion term,
• ( \rho c(1 - c) ) models logistic growth, limiting ( c ) as it approaches 1.

TumorNetSolvers uses deep learning to approximate this PDE's solutions but can, in theory, adapt to different PDE-based models.

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2. Deep Learning Surrogate Models

Neural networks approximate the PDE solution, mapping inputs (image + parameters) to outputs (simulation).

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3. Built on nnU-Net

The framework builds upon nnU-Net's self-configuring capabilities, adapting it for conditioned image-to-image regression tasks.

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Model Architectures

TumorNetSolvers includes three key models:

1. TumorSurrogate (Baseline)

   • A 3D CNN that integrates anatomy info and tumor metadata for conditioned tumor simulation.

2. Modified nnU-Net

   • An adapted version of the powerful self-configuring nnU-Net framework for tumor growth simulation using conditioned inputs.

3. 3D Vision Transformer (ViT)

   • A transformer-based model incorporating tumor metadata as additional input tokens in the embedding space.

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Usage

For detailed usage, refer to the scripts in the scripts directory or follow the instructions below:

1. Forward Problem
   Run the script running_inference.py with the necessary inputs (3D medical image, tumor parameters) to generate tumor simulations.

2. Inverse Problem
   Run the script predict_tumor_params.py to infer tumor parameters by optimizing against a target tumor simulation.

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Installation

To get started with TumorNetSolvers, install it directly from GitHub by following these steps:

1. Clone the repository:

   git clone https://github.com/ZeinebZH/tumornetsolvers.git
   cd tumornetsolvers

2. Install the required dependencies and the package:

   pip install -r requirements.txt
   pip install .

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Contributing

We welcome contributions to TumorNetSolvers!

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License

This project is licensed under the MIT License and incorporates code from nnU-Net, licensed under Apache 2.0. Both licenses apply and must be respected. See the LICENSE file for details.

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References

1. Weidner J, et al. Rapid Personalization of PDE-Based Tumor Growth Using a Differentiable Forward Model. Medical Imaging with Deep Learning, 2024. DOI
2. Ezhov I, et al. Geometry-aware Neural Solver for Fast Bayesian Calibration of Brain Tumor Models. IEEE Transactions on Medical Imaging, 2021;41(5):1269–78. DOI
3. Isensee F, et al. nnU-Net: A Self-configuring Method for Deep Learning-based Biomedical Image Segmentation. Nature Methods, 2021;18(2):203–11. DOI
4. Lin K, Heckel R. Vision Transformers Enable Fast and Robust Accelerated MRI. International Conference on Medical Imaging with Deep Learning, 2022. DOI