Magnetic resonance parameter mapping using model-guided self-supervised deep learning

Abstract

Purpose: To develop a model-guided self-supervised deep learning MRI reconstruction framework called reference-free latent map extraction (RELAX) for rapid quantitative MR parameter mapping.

Methods: Two physical models are incorporated for network training in RELAX, including the inherent MR imaging model and a quantitative model that is used to fit parameters in quantitative MRI. By enforcing these physical model constraints, RELAX eliminates the need for full sampled reference data sets that are required in standard supervised learning. Meanwhile, RELAX also enables direct reconstruction of corresponding MR parameter maps from undersampled k-space. Generic sparsity constraints used in conventional iterative reconstruction, such as the total variation constraint, can be additionally included in the RELAX framework to improve reconstruction quality. The performance of RELAX was tested for accelerated T₁ and T₂ mapping in both simulated and actually acquired MRI data sets and was compared with supervised learning and conventional constrained reconstruction for suppressing noise and/or undersampling-induced artifacts.

Results: In the simulated data sets, RELAX generated good T₁ /T₂ maps in the presence of noise and/or undersampling artifacts, comparable to artifact/noise-free ground truth. The inclusion of a spatial total variation constraint helps improve image quality. For the in vivo T₁ /T₂ mapping data sets, RELAX achieved superior reconstruction quality compared with conventional iterative reconstruction, and similar reconstruction performance to supervised deep learning reconstruction.

Conclusion: This work has demonstrated the initial feasibility of rapid quantitative MR parameter mapping based on self-supervised deep learning. The RELAX framework may also be further extended to other quantitative MRI applications by incorporating corresponding quantitative imaging models.

Keywords: MR parameter mapping; deep learning; latent map; model-based reconstruction; rapid MRI; self-supervised learning.

Figure 1:

The schematic demonstration of the CNN framework implementing RELAX. A cyclic workflow was constructed to enforce self-supervised learning. The physics models and additional constraints can be incorporated into the framework to guide the learning of CNN mapping function to extract the latent image parameter maps from undersampled images. The labels follow the description in the main text.

Figure 2:

Representative T1 maps estimated using RELAX in one simulated brain dataset at three different experiment conditions, respectively. RELAX successfully suppressed the noises at 5% noise level (NL) and removed the undersampling artifacts at R=5 through self-supervised deep learning reconstruction, providing image quality that is comparable to the noise/artifact-free ground truth (G.T.) T1 map. The NLLS was applied to zero-filling reconstructed images at R=5.

Figure 3:

Representative T2 maps estimated using RELAX in one simulated brain dataset at three different experiment conditions, respectively. RELAX successfully suppressed the noises at 5% noise level (NL) and removed the undersampling artifacts at R=5 through self-supervised deep learning reconstruction, providing image quality that is comparable to the noise/artifact-free ground truth (G.T.) T2 map. The NLLS was applied to zero-filling reconstructed images at R=5.

Figure 4:

Examples showing the influence of the weighting parameter (for spatial TV constraint) on reconstructed parameter maps.

Figure 5:

Examples showing the performance of RELAX in different noise levels. RELAX generated acceptable T1 or T2 parameters at different noise conditions due to the inherent noise suppression in CNN training and the additional spatial TV constraint.

Figure 6:

Two representative slices of T1 maps estimated from different reconstruction methods for a testing knee dataset at R=5. The RELAX reconstruction generated T1 maps with image quality that is comparable to the reference T1 maps obtained from fully sampled images.

Figure 7:

Comparison of T1 maps generated from different reconstruction methods for another testing knee dataset at R=5. The deep learning-based methods, including both MANTIS and RELAX, removed most of the artifacts and showed a similar reconstruction performance, which outperformed conventional constrained reconstruction k-t SLR. The absolute error maps were amplified by five times for display purposes to show the method difference.

Figure 8:

Two representative slices of T2 maps estimated from different reconstruction methods for a testing knee dataset at R=5. RELAX generated T2 maps with successful suppression of image artifacts and noise compared to the reference T2 maps obtained from fully sampled images. There was noticeable noise suppression but a slight image blurring in the bone and muscle in the T2 maps generated from RELAX. To better highlight cartilage contrast, the same example with an adjusted color window was also provided in the Supporting Information Figure S4.

Figure 9:

Comparison of T2 maps generated from different reconstruction methods for another testing knee dataset at R=5. Both MANTIS and RELAX provided nearly artifact-free T2 maps and presented similar reconstruction performance. The absolute error map for each reconstructed T2 map indicated better reconstruction accuracy for both MANTIS and RELAX in comparison to k-t SLR. The absolute error maps were amplified by five times for display purposes to show the method difference.