Transformer-based rapid dictionary generation for navigator-gated free-breathing cardiac joint T1-T2 mapping

Background: Joint cardiac T₁–T₂ mapping techniques such as PARMANav¹ use subject-specific extended phase graph (EPG)² dictionaries that can take 30 min to compute per map, limiting clinical throughput. Deep learning can be used to massively accelerate dictionary generation,³ but existing solutions struggle to handle the large delays caused by navigator rejections and ECG trigger detection failures (“skipped heartbeats”). We therefore developed a Transformer model⁴ to directly predict EPG signal evolutions from the acquisition timing, and hypothesize that this network matches the original EPG simulated dictionaries more closely than previously proposed networks.

Methods: PARMANav is a navigator-gated joint T₁-T₂ mapping sequence that uses 25 ECG-triggered images. To rapidly generate the dictionaries, we used an encoder-decoder Transformer model with 6 layers (700 674 trainable parameters) (Figure 1). Intervals were obtained from N=42 participants (56±15y, 8F); after augmentation through interval shuffling, the training data consisted of 7 million EPG-simulated signals. The model architecture and hyperparameters (learning rate, depth, width, dropout, L₂ penalty) were tuned using Optuna⁵ and Adam⁶. Similar data was used to train a previously described fully connected Multilayer Perceptron (MLP)³.

Dictionary bias was measured in the ISMRM/NIST⁷ phantom through Bland-Altman analysis between the EPG-, Transformer-, and MLP- generated dictionary T₁ and T₂ values.

On an independent test set comprising 1120 maps (pre- and post-contrast) from 138 patients (51F, 66±15y ), the mean absolute percentage error (MAPE = 1/n ∑_iⁿ |Ti-Ti|/T_i where Ti is the reference EPG value and T_i is the predicted value of the n-sized dictionary) of each dictionary was calculated for T₁ and T₂. Spearman correlations were calculated between MAPE and the total number of skipped heartbeats. Bland-Altman analysis was performed for the blood pool and myocardial T₁-T₂ values. Inference time was recorded.

Results: On a CPU, the Transformer dictionary inference time was ~10 seconds, a more than 150‑fold speedup compared to the EPG dictionary generation. The bias between the dictionaries in the phantom was very small (≤1.81ms, Figure 2). Across all test subjects, the MAPE for T₁ and T₂ were 0.49%±0.51% and 0.66%±0.58%, respectively for the Transformer and 2.32%±1.91% and 3.50%±2.32% for the MLP. The correlation between the T₁&T₂ MAPE and the ECG skips were 0.22 and 0.10, lower than the MLP dictionary at 0.27 and 0.39 (p < 0.003 for all, Figure 2). In vivo mapping showed minimal differences between EPG and the Transformer maps (Figure 3).

Conclusion: The Transformer model not only achieves negligible bias relative to the EPG‑based methods, but also runs over 150 times faster and handles skipped heartbeats more robustly than the MLP, enabling free‑breathing cardiac T₁–T₂ mapping in clinical practice.

Figure 1: Diagram of training and testing pipeline. MSE = mean square error, MAPE = mean average percentage error, EPG = extended phase graph, TF = transformer.
Figure 2: Values of the spin echo reference and the models in the phantom compared to the EPG, alongside the Bland-Altman plot using the Transformer model dictionary, and the maps of the scanned phantom. For T2, values larger than 120 were omitted.
Figure 3. A Histograms of T1 and T2 MAPE across all test patients, comparing the dictionaries for the Transformer and the baseline MLP model. Bin size 0.06. B Average MAPE per number of total skips (due to navigator rejection or ECG trigger detection failure) during the scan, for both models, bin size 5. C Exemplary comparison of maps created with the PARMANav EPG dictionary and the PARMANav Transformer dictionary. D Difference plot (Transformer Model - EPG). The maps are visually identical.