# 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 python -m venv .venv 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 $$\text{cost}_2(\varphi, A) = \frac{\text{mean}(|B_1^+|)}{\text{std}(|B_1^+|)} - \lambda\max_{x\in subject}\text{SAR}(x)$$ 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 ## Data You can download the data from [Google Drive](https://drive.google.com/drive/folders/17yIm9Pjc1QsyB-fAGvf5FCk9AmqIDXUW?usp=drive_link) Place the data directory in the main directory of the project. It should look something like this: ```plaintext 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. ## 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# hackathonMAGNET