BMapEst: Estimation of Brain Tissue Probability Maps using a Differentiable MRI Simulator

TL;DR

This work introduces BMapEst, a physics-informed framework that estimates voxel-wise brain tissue probability maps (GM, WM, CSF) from $T_1$/$T_2$ MRI without requiring training data. It leverages a differentiable MRI simulator, MR-zero, to map tissue probabilities to $qT_1$, $qT_2$, and $PD$ maps, generates forward MRI data for given clinical sequences, and backpropagates the $L_2$ loss to recover the maps. Evaluated on 20 BrainWeb subjects with multi-contrast FLASH variants, BMapEst achieves high PSNR/SSIM and CSF Dice, outperforming a supervised U-Net baseline and clustering methods, particularly when multiple contrasts are used. The approach demonstrates the power of physics-based priors to solve ill-posed inverse problems in MRI, enabling adaptable tissue-map estimation across sequences without data-driven training, and suggests directions for sequence optimization and probabilistic extensions.

Abstract

Reconstructing digital brain phantoms in the form of voxel-based, multi-channeled tissue probability maps for individual subjects is essential for capturing brain anatomical variability, understanding neurological diseases, as well as for testing image processing methods. We demonstrate the first framework that estimates brain tissue probability maps (Grey Matter - GM, White Matter - WM, and Cerebrospinal fluid - CSF) with the help of a Physics-based differentiable MRI simulator that models the magnetization signal at each voxel in the volume. Given an observed $T_1$/$T_2$-weighted MRI scan, the corresponding clinical MRI sequence, and the MRI differentiable simulator, we estimate the simulator's input probability maps by back-propagating the L2 loss between the simulator's output and the $T_1$/$T_2$-weighted scan. This approach has the significant advantage of not relying on any training data and instead uses the strong inductive bias of the MRI simulator. We tested the model on 20 scans from the BrainWeb database and demonstrated a highly accurate reconstruction of GM, WM, and CSF. Our source code is available online: https://github.com/BioMedAI-UCSC/BMapEst.

Figures (15)

• Figure 1: Optimization pipeline: The CSF, GM, and WM probability maps are converted into q$T_1$, q$T_2$, and PD maps using known $T_1$ and $T_2$ relaxation times. These maps are input into the MR-zero simulator to generate K-space measurements, and the image is reconstructed via Inverse Fourier Transform $I$. The L2 loss is computed against a real MRI and backpropagated to the probability maps.
• Figure 1: Dice score, PSNR, and SSIM comparisons for a combination of MRI clinical sequences. Except for the first row, all the experiments use 4 contrasts per sequence. † represents the baseline configuration. Our method is compared against two baselines: U-Net and BCEFCM. Note:BCEFCM can only take a single contrast as input.
• Figure 2: From the left are CSF, GM, and WM. The first row shows the raw tissue probability maps for subject 42 in the BrainWeb dataset. The second row shows the estimated probability maps using our baseline configuration. The third row shows the ill-posed estimation using the single contrast from the $T_1$ inversion recovery sequence.
• Figure 3: The first row shows the raw tissue probability maps for subject 42 in the BrainWeb dataset. The second row shows the checkerboard pattern enclosed in a red-marked region while optimizing 19 linear coefficients instead of using probability maps directly.
• Figure 4: From the left are CSF, GM, and WM. The first row shows the ground truth probability maps for subject 20 of BrainWeb. The second row shows the estimated map using our baseline method. The third and fourth row shows the inferred probability maps using U-Net and BCEFCM.