Zihao Chen^{1,2}, Hsu-Lei Lee^{1}, Xianglun Mao^{1}, Tianle Cao^{1,2}, Yibin Xie^{1}, Debiao Li^{1,2}, and Anthony Christodoulou^{1,2}

^{1}Biomedical Imaging Research Institute, Cedars-Sinai Medical Center, Los Angeles, CA, United States, ^{2}Department of Bioengineering, University of California, Los Angeles, Los Angeles, CA, United States

CMR multitasking is promising for quantitative cardiac imaging, and can achieve fast three-slice quantification when combined with simultaneous multi-slice (SMS) acquisition. However, slow non-Cartesian iterative reconstruction is a barrier to clinical adoption. Deep learning can accelerate reconstruction, but the SMS training data are currently limited. Here we propose a data-consistent deep subspace transfer learning strategy that trains on single-slice T1 CMR multitasking data but is applied to SMS-encoded T1 CMR multitasking image reconstruction. The proposed strategy is >40x faster than the conventional SMS reconstruction, resulting in an equally better image quality and comparably precise T1 as in single-slice reconstruction.

In CMR multitasking, a dynamic image is represented as a low-rank tensor $$$\mathcal{X}$$$ decomposed into a spatial factor matrix $$$\mathbf{U}$$$ and a low-rank temporal factor tensor $$$\it{\Phi}$$$ according to $$$\mathcal{X}=\it{\Phi}\times_\mathrm{1}\mathbf{U}$$$.

Here $$$\mathbf{b}$$$ is the acquired data, $$$\mathbf{F}_{\mathrm{NU}}$$$ is the non-uniform Fourier transform, $$$\mathbf{S}$$$ applies sensitivity maps, $$$\mathit\Omega$$$ is the k-t space undersampling operator, and $$$R$$$ is a regularization functional such as a wavelet sparsity penalty. Conventionally, Eq. (1) is solved by slow iterative methods.

where the network has been trained on iterative solutions to Eq. (1). Here, we also add a gradient descent DC layer

$$E_\mathit{\Phi}(\mathbf{Y})=\mathit\Omega\left(\mathit\Phi\times_{1}\mathbf{F}_{\mathrm{NU}}\mathbf{Y}\right)\tag{4}$$

where $$$\alpha$$$ is the step-size, $$$E_\mathit{\Phi}$$$ is the encoding matrix for each channel, and $$$\mathbf{P}$$$ is the preconditioner.

Figure 2 shows spatial factor NRMSE in the testing sets. For both SMS and single-slice data, the CNN block significantly reduced NRMSE (p<0.001) versus $$$\mathbf{U}_{\mathrm{0}}$$$, and the DC layer further reduced NRMSE (p<0.001) versus $$$\mathbf{U}_{\mathrm{cnn}}$$$. NRMSE of $$$\mathbf{U}_{\mathrm{cnn}}$$$ was not significantly different for SMS versus single-slice data (p=0.75); nor was the NRMSE of $$$\mathbf{U}_{\mathrm{dc}}$$$ for SMS versus single-slice (p=0.85).

Figure 3 shows the PSNR, SSIM and NRMSE of reconstructed dynamic images. Again, the CNN improved the initial guess, and the DC layer further improved the reconstruction, for both SMS and single-slice data.

Figure 4 shows an example testing slice comparing deep learning and iteratively-reconstructed SMS images and T1 maps. Visual quality is consistent with the results in Figure 3. Figure 5 shows the Bland-Altman plots for average T1 values in the left-ventricular myocardium, for both SMS and single-slice testing data. SMS T1 values show a small (–34ms) but statistically significant bias (p=0.002) between deep learning and iterative reconstructions, but comparable precision (limits-of-agreement=±55ms) as the single-slice T1 results (limits-of-agreement=±49ms).

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Figure 1. Network architecture of the proposed method.

Figure 2. NRMSE over spatial factor U among the testing set for both SMS data and single-slice data. Values in brackets are standard deviations. Best results are bolded.

Figure 3. Quantitative image metrics over reconstructed dynamic images among the testing set for both SMS data and single-slice data. Each bar is averaged over all the 2D frames, and error bar represents the corresponding standard deviation. Each image slice contains 20 cardiac frames, so there are 240 frames for SMS data and 300 frames for single-slice data.

Figure 4. An example slice of testing SMS image reconstructed from *U*_{0}, *U*_{cnn}, *U*_{dc} and iteratively reconstructed reference. (a) T1-weighted images in dark blood contrast with its corresponding error maps. (b) T1 maps with its corresponding error maps.

Figure 5. Bland-Altman plots for SMS and single-slice T1 testing results. Average T1 values in the left-ventricular myocardium are shown.

DOI: https://doi.org/10.58530/2022/1763