Accelerated and Accurate Myocardial T1 Mapping with PENGUIN: Combining Deep Learning with Extended Phase Graph Modeling

Accelerated and Accurate Myocardial T1 Mapping with PENGUIN: Combining Deep Learning with Extended Phase Graph Modeling Catarina N. Carvalho1,2, Andreia S. Gaspar 1, Rita G. Nunes 1, and Teresa Correia2,3 1Institute for Systems and Robotics - Lisboa and Department of Bioengineering, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal; 2Center of Marine Sciences (CCMAR), Faro, Portugal; 3School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom Synopsis Motivation: Myocardial T1 mapping sequences typically require multiple breath-hold scans, leading to limited spatial resolution, patient discomfort and motion artifacts. Moreover, mapping is generally accomplished through three-parameter exponential tting, which may compromise the accuracy of the estimation due to the model’s simplicity. Goal(s): Improve T1 mapping estimation accuracy, while also reducing acquisition and reconstruction times. Approach: We propose a physics-informed deep learning network to obtain myocardial T1 maps directly from undersampled k-space following the Extended Phase Graph formulation. Results: Our method is able to estimate T1 maps for acceleration factors 4 and 8× with minimal error. Impact: We propose a novel physics-based deep learning method that performs accelerated myocardial T1 mapping directly from undersampled kspace acquisitions considering the Extended Phase Graph formulation, greatly improving the accuracy of the estimated T1 values while shortening acquisition/reconstruction times. Introduction Model-based Deep Learning (DL) has become increasingly popular for accelerated MRI reconstruction and quantitative mapping. DL architectures that perform quantitative mapping directly from accelerated k-space have been proposed for T1 and T2 mapping in various anatomical regions1–3. However, all of these approaches assume exponential recovery for T1 and T2 mapping, simplifying the relaxation dynamics. A more accurate way of modeling the signal is to consider the Extended Phase Graph (EPG) formulation ; however, this can be very resource-consuming, especially in the4 case of cardiac T1 mapping, where simulated signals must consider the subjects’ heart rate (HR). Here, we propose modifying our PhasE Graph sigNal and Gradients QUantitative Inference machiNe (PENGUIN)5, initially proposed for brain T2 mapping, to accelerate myocardial T1 mapping, whilst considering the EPG formulation. Compared to our previous implementation, this work has the following novelties: (a) quantitative mapping is now performed directly from undersampled k-space, instead of from reconstructed images; (b) signal intensity curves are now simulated not only for a range of T1 values, but also for a range of regular HR values, resulting in a comprehensive dictionary which moves the resource burden away from the inference stage and into the preprocessing stage. Methods PENGUIN combines a Recurrent Inference Machine6 with a dictionary of EPG simulated signal evolution curves that provides the network with a pre-calculated signal model, alleviating the computational burden during inference. In this work, PENGUIN aims to learn a maximum a posteriori estimator by unrolling the optimization process with a forward model given by: 𝑑 =𝑈𝐹𝐸(𝑇1) + 𝑁𝑜𝑖𝑠𝑒 where d is the acquired (undersampled) k-space data, U is the undersampling operator, F is the Fourier Transform, and E is the EPG formulation that produces a signal intensity 4D image (3D image sampled at multiple inversion times) given a T1 value. PENGUIN performs J = 2 inference steps to obtain J estimates of the T1 maps, which contribute to the loss function used to optimize the network: 𝐿 = 1 𝐽+1∑10−𝐽−𝑗+2 𝐽𝐿1 (𝑇1,𝑇1 ) 𝐽 𝑗=0 , where L1 is the L1-norm loss, evaluated in the myocardium. PENGUIN follows the architecture in Figure 1. Networks were trained in an NVIDIA Quadro RTX 8000 GPU, ADAM optimizer, learning rate=1e-4, 300 epochs, considering C = 64 and C = 256 channels for acceleration factors 4 and 8, respectively. Data were obtained from MICCAI’s 2023 CMR reconstruction challenge 7. T1 mapping was conducted following a MOLLI sequence which acquired 9 images (4-(1)-3-(1)-2), short axis (SA) view only, FOV=360×307 mm2 , spatial resolution=1.4×1.4 mm , slice thickness=5.0 mm, TR=2.67 ms, TE=1.13 ms, partial Fourier=7/8, and GRAPPA factor =2, on a 3T MAGNETOM Vida Siemens scanner. We considered only the single coil, fully-sampled dataset and slices 1-4; subjects #001-#100 were used for training, #101- #110 for validation, and #111-#120 for testing. K-space data were undersampled retrospectively, following a radial k-t sampling trajectory with golden angle increments. EPG-based simulations were implemented for the protocol described above, HR sampled from 28 to 102 bpm, T1=0:1:2000 ms, T2=50 ms and used to build a dictionary of complex T1-weighted signal intensity curves for varying HRs. Ground-truth T1 maps (GT) were obtained by performing a pattern recognition approach over the reconstructed, fully sampled signal intensity images, through dot product matching. In addition, we also performed a three-parameter exponential fitting8 over the reconstructed images to illustrate the di erences between exponential and EPG-based estimation. Zero-filled (ZF) and Compressed Sensing (CS) reconstructions were performed to compare with PENGUIN. The CS approach consisted in a wavelet-based CS algorithm to reconstruct the images. The pattern recognition approach described above was employed to obtain the corresponding ZF and CS T1 maps. Maps were evaluated through the relative error and the mean structural similarity index measurement (MSSIM) with respect to the GT values. Results Figures 2 and 3 illustrate the estimated maps with ZF, CS and PENGUIN for distinct test subjects, slices, and acceleration factors. T1 maps estimated with PENGUIN achieved mean relative errors of 10.1±11.0% and 15.9±15.4%, and mean MSSIM scores of 0.999±0.001 and 0.998±0.001, for accelerations 4 and 8×, respectively (Figure 4). Figure 5 depicts the AHA segmentation analysis on all estimated T1 maps. PENGUIN requires only 1.49s and 0.41Gb of RAM to infer a T1 map. Conclusions & Discussion We successfully modied PENGUIN to perform myocardial T1 mapping directly from undersampled k-space with improved accuracy when compared to three-parameter exponential-based tting. Moreover, PENGUIN is less resource-consuming than CS-based inference, since the computational burden is moved to the preprocessing stage. In the future, we will incorporate sensitivity information from multiple coils (parallel imaging) into the signal model to allow larger acceleration rates, and build the dictionaries considering an additional range of T2 values for increased accuracy. Acknowledgements This work was supported by: NVIDIA GPU hardware grant; “la Caixa” Foundation and FCT, I.P [LCF/PR/HR22/00533]; FCT (SFRH/BD/120006/2016, PTDC/EMD/EMD/29686/2017; UIDP/50009/2020), Programa Operacional Regional de Lisboa 2020 (LISBOA-01-0145-FEDER-029686), LARSyS funding (DOI: 10.54499/LA/P/0083/2020,10.54499/UIDP/50009/2020,10.54499/UIDB/50009/2020. This research was supported by FCT through projects UIDB/04326/2020 (DOI:10.54499/UIDB/04326/2020), UIDP/04326/2020 (DOI:10.54499/UIDP/04326/2020) and LA/P/0101/2020 (DOI:10.54499/LA/ P/0101/2020). References 1. Liu F, Kijowski R, Feng L, El Fakhri G. High-performance rapid MR parameter mapping using modelbased deep adversarial learning. Magn ResonImaging. 2020;74:152-160. doi:10.1016/j.mri.2020.09.0212. 2. Liu F, Kijowski R, El Fakhri G, Feng L. Magnetic resonance parameter mapping using model-guided selfsupervised deep learning. Magn ResonMed. 2021;85(6):3211-3226. doi:10.1002/mrm.286593. 3. 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T1-mapping in the heart: accuracy and precision. J Cardiovasc Magn Reson. 2014;16(1):2. doi:10.1186/1532-429X-16-2 Figures Fig 1. PENGUIN architecture drawn for inference step j. At each inference step, the estimate of the T1 maps p^j is given to the dictionary to obtain the signal-intensity and corresponding derivative attributed to each T1 value in the map. With these, the gradient of the negative log-likelihood of the model ∇Lj is calculated, concatenated to p^j and given as input to the network, which outputs the incremental update to the estimated maps. The network uses two memory vectors hj to learn the optimization process. Fig 2. T1 maps estimated with the dierent methods applied to 5 distinct test subjects (rows), with dierent HRs and acceleration factor 4×; from left to right: ground-truth (GT), Exponential Fitting, zero-lled (ZF), compressed-sensing (CS), and PENGUIN. The dierent slices are shown in each frame of the animation. Fig 3. Ground-truth (GT) and estimated T1 maps with zero-lled (ZF), compressed-sensing (CS) and PENGUIN methods for 1 representative subject, HR=64 bpm, for acceleration factors 4 (top) and 8× (bottom). Fig 4. Violin plots of the (a) T1 relative errors and (b) MSSIM scores obtained with zero-lled (ZF), compressed-sensing (CS) and PENGUIN, for acceleration factors 4 and 8×. A two-factor ANOVA and pairwise-test was carried out to identify statistically signicant dierences between methods, indicated by * (pvalue<0.05) and *** (p-value<0.001). Fig 5. Segmental distribution of (a) mean T1 values and (b) standard deviation according to the AHA 16segment model, for 2 representative subjects and acceleration 4×. PENGUIN provides results that are in good agreement with the ground-truth (GT) T1 values, despite the lower variation within each segment.