Domain-Agnostic Stroke Lesion Segmentation Using Physics-Constrained Synthetic Data

qATLAS fits an nnU-Net [14] that predicts four qMRI maps (PD, $R_{1}$, $R_{2}^{*}$, MT) from a single MPRAGE^***Estimating $R_{2}^{*}$ from one T1 is ill-posed; errors mainly affect simulated T2w/FLAIR.. Training used 51 subjects (22 healthy, 29 stroke; 80/20 split) with 3D-EPI ground-truth maps from hMRI [22]. Thus any routine MPRAGE can be converted to qMRI and fed to our physics-based simulator.

Diverse MPRAGE images were simulated using NiTorch with parameters: $T_{R}\sim\mathcal{U}(1.9,2.5)$ s, $T_{I}\sim\mathcal{U}(0.6,1.2)$ s, $T_{E}\sim\mathcal{U}(2,4)$ ms, $\alpha\sim\mathcal{U}(5^{\circ},12^{\circ})$, and $B_{0}\sim\mathcal{U}(0.3,7)$ T.

Data Augmentation: We applied standard augmentations (elastic/affine deformations, bias field, Gibbs ringing, Rician noise, and random cropping to $192^{3}$ voxels) using MONAI [7]. Figure 1 illustrates examples of the augmented training data.

Model Architecture and Training: Our U-Net comprises five encoder stages (channels: 24, 48, 96, 192, 384), each with two residual units, using GELU activations [13], instance normalisation [23], linear upsampling, and 0.1 dropout. The network outputs four channels corresponding to PD, $R_{1}$, $R_{2}^{*}$, and MT. To enforce positivity, PD, $R_{1}$, and $R_{2}^{*}$ are computed as the exponential of their raw outputs, while MT is computed as 100 times the sigmoid of its raw output.

Training was performed over 200,000 iterations (batch size 1) using AdamW (lr=$10^{-4}$, $\beta_{1}=0.9$, $\beta_{2}=0.999$, weight decay=0.01). An initial 20,000 iterations used L2 loss; thereafter, we employed a combined loss $L=\text{L1}(y,\hat{y})+\text{L2}(y,\hat{y})+\text{L1}(\nabla y,\nabla\hat{y})+\text{L2}(\nabla y,\nabla\hat{y})$ augmented by a perceptual LPIPS loss [27] (weight 0.1) using features from a pretrained Med3D encoder [9].

Figure 2 displays examples of predicted qMRI maps from input MPRAGE images in the ATLAS dataset [16].

Simulation of MRI Sequences: We used the estimated qMRI maps from the ATLAS dataset to simulate diverse MRI sequences via a physics-based generative model (see Section 2.3), thereby creating the qATLAS dataset for segmentation training.

The qSynth method generates synthetic qMRI maps directly from segmentation labels using label-conditioned Gaussian Mixture Models (GMMs). We first define prior distributions for each qMRI parameter (PD, $R_{1}$, $R_{2}^{*}$, MT) for different tissue types (gray matter, white matter, cerebrospinal fluid, and lesions). These priors are estimated from the population used in qATLAS (for anatomy or pathology where real data is not available, it is feasible that parameters could be estimated based on values reported in literature). For each voxel in a segmentation label, the corresponding qMRI parameters are sampled from the appropriate prior, thereby producing a synthetic qMRI map that reflects realistic tissue properties. Healthy tissue maps are obtained using the Multibrain SPM toolbox [5], and lesion masks are generated by overlaying random binary lesion maps onto these healthy tissue maps (see [8] for further details).

Simulation of MRI Sequences: The synthetic qMRI maps are then used with our physics-based generative model (Section 2.3) to simulate diverse MRI sequences, resulting in the qSynth dataset for training an alternative segmentation model.

Both qATLAS and qSynth use a physics-based generative model to simulate realistic MRI images from qMRI parameter maps via standard signal equations. We simulate several common MRI sequences, including Fast Spin-Echo (FSE), Gradient-Echo (GRE), Fluid-Attenuated Inversion Recovery (FLAIR), and Magnetisation-Prepared Rapid Gradient Echo (MPRAGE).

For example, the FSE signal is computed as:

where $B_{1}$ is the receive field strength, PD is the proton density, $R_{1}$ and $R_{2}\ (\approx R2^{*})$ are the relaxation rates, and $T_{R}$ and $T_{E}$ are the repetition and echo times, respectively. Similar equations are used for GRE, FLAIR, and MPRAGE sequences.

Acquisition parameters (e.g., $T_{R}$, $T_{E}$, $T_{I}$, $T_{X}$, $T_{D}$, and $\alpha$) were sampled from physically plausible distributions; please refer to our code repository^†††https://github.com/liamchalcroft/qsynth for the complete sampling details.

To mimic realistic MRI data, we add Rician noise by perturbing the simulated signal $S_{\text{MRI}}$ with independent Gaussian noise on the real and imaginary components:

All simulations and noise additions were implemented using the NiTorch library^‡‡‡https://github.com/balbasty/nitorch. Additional augmentations - such as elastic deformations, bias field variations, axis flips, Gaussian noise, low-resolution reslicing, and random cropping to $192\times 192\times 192$ voxels - were applied using MONAI [7].

We trained nnUNet-based segmentation models [14] on four settings: (i) real MPRAGE images from the ATLAS dataset (baseline), (ii) the qATLAS dataset (from MPRAGE-derived qMRI maps), (iii) a synthetic data model using the public Synth method [8], and (iv) the qSynth method. The qSynth method differs from Synth in that Synth directly samples the random tissue intensities, while qSynth uses intensity priors to first synthesise qMRI parameter maps, which may then be used to generate realistic tissue intensities via random variations of real forward models. For Synth and qSynth, we additionally evaluated models trained on a mixture of synthetic and real ATLAS images.

Model Architecture and Training Details: All models use PReLU activations [12] with one residual unit per block. The qATLAS model performs binary segmentation (background vs. stroke lesion), while the qSynth model predicts additional healthy tissue classes (gray matter, white matter, GM/WM partial volume, and cerebrospinal fluid). Baseline and qATLAS models were trained on the ATLAS dataset (N=419/105/131 train/validation/test), whereas Synth and qSynth models used ATLAS lesion labels combined with healthy tissue labels from OASIS-3 (N=2579/100 train/validation) as detailed in [8].

All models were optimised using a combined Dice and cross-entropy loss with the AdamW optimiser [19] (lr=$10^{-4}$, $\beta_{1}=0.9$, $\beta_{2}=0.999$, weight decay=0.01) and a learning rate scheduler $\eta_{n}=\eta_{0}\,(1-\frac{n}{N})^{0.9}$. Training was run for 700,000 iterations with a batch size of 1.