Hackathon

Spring School on Physics Informed Machine Learning for Medical Sciences

Welcome to the Hackathon accompanying the 2025 Spring School on Physics Informed Machine Learning for Medical Sciences.

This repo will serve you as a starting point for solving the task described below.

Getting Started

To setup the environment, fork this repository (or create a new one using this repository as a template) and clone the repository.

In the new repository create a new environment and install all requirements by running the following commands:

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Problem setting

You are given a complex 3D object sitting inside an array of 8 dipoles, positioned radially around the object as seen in Figure 1.

Figure 1: Coil and object positions.

The domain is a simulated MRI environment with electric $E$ and magnetic $H$ field already calculated at each point using the CST studio suite and exported at a voxel size of 4mm. The contribution of each dipole $i$ is calculated and stored separately $E_i, H_i$, and the total fields are the sum of the contributions of each dipole $E = \sum_{i=1}^8 E_i$ and $H = \sum_{i=1}^8 H_i$.

Additionally, the object mask and various physical properties (electrical conductivity, magnetic permittivity and density) are also available as seen in Figure 2.

Figure 2: Example simulation with physical features and distribution of electric and magnetic fields.

When the phase and amplitude for a specific dipole $i$ is changed to $\varphi$ and $A_i$ respectively, the resulting contribution of this dipole can then be calculated as $$ \hat{E_i} = A_i e^{i\varphi} E_i\ \hat{H_i} = A_i e^{i\varphi} H_i $$

This can significantly change the overall distribution of the fields and in result, the distribution of the SAR and the $B_1^+$ field (which directly corresponds to what the MRI scanner can register). See Figure 3 for an example.

Figure 2: Example distribution of Fields, SAR and the $B_1^+$ field for two different coil configurations.

Task description

Your task is to optimize the phase and amplitude of the coils (coil configuration) with respect to a specified cost function (e.g. $B_1$ homogeneity, minimal peak SAR etc.).

For the purposes of this task we consider two cost functions:

B1 Homogeneity

Given the $B_1^+$ Field calculated as $B_x + i*B_y$ we consider the cost function:

$$\text{cost}_1(\varphi, A) = \frac{\text{mean}(|B_1^+|)}{\text{std}(|B_1^+|)}$$

This cost function maximizes the mean strength of the $B_1^+ Field$, while simultaneously minimizing the variability of the field within the subject. The task is to maximize this cost function.

B1 Homogeneity with SAR constraint

Additionally, we also consider the cost function which maximizes the $B_1^+$ Homogeneity, while also minimizing the peak SAR. The cost function is given by

$$\text{cost}_2(\varphi, A) = \frac{\text{mean}(|B_1^+|)}{\text{std}(|B_1^+|)} + \lambda \frac{\text{min}(|B_1^+|)}{\sqrt{\text{max}(SAR)}}$$

Where $\lambda$ is an additional weighting factor and $\text{SAR}(x)$ is the Specific Absorption Rate at a certain point in space given by:

$$\text{SAR}(x) = \frac{|E(x)|^2\cdot\sigma(x)}{\rho(x)}$$

with $\sigma(x)$-electric conductivity and $\rho(x)$-mass density. During evaluation a weighting factor of $\lambda=100$ will be used.

Data

You can download the data from Google Drive

Place the data directory in the main directory of the project. It should look something like this:

project/ 
├── ...
├── data/
│ ├── simulations/
│ │ ├── sim1.h5     
│ │ ├── sim2.h5     
│ │ └── ...     
│ └── antenna/
│ │ └── antenna.h5     
└── ...

Evaluation

All teams will be asked to submit their solutions as a git repository. In the git repository the main.py should be modified (only) to include the optimization algorithm developed by the team. The evaluation.py script should not be changed at all.

Each submission will be evaluated on a previously unseen set of simulations, with both cost functions specified in the task. The optimization algorithm should run within 5 Minutes after which the program execution will timeout and the solution will be disqualified.

For the second cost function a weighting factor of $\lambda = 100$ will be used during evaluation.

Ideas where to go from here

• Implement parallel processing during optimization
• Speed up the calculation of phase-shifted fields
• Run pytorch (or other DL software) to use gradient descent for local optimization
• Try out different global optimization algorithms