Yuze Li^{1}, Chunyan Wu^{1}, Haikun Qi^{2}, Dongyue Si^{1}, Haiyan Ding^{1}, and Huijun Chen^{1}

^{1}Center for Biomedical Imaging Research, School of Medicine, Tsinghua University, Beijing, China, ^{2}School of Biomedical Engineering, ShanghaiTech University, Shanghai, China

A motion correction method for myocardial T1 mapping using Self-supervised Deep learning based Registration with contrAst seParation (SDRAP) was proposed. A sparse coding based method was firstly proposed to separate the contrast component from T1w images. Then, a self-supervised deep neural network was developed to register contrast separated images, followed by the signal fitting to generate motion corrected T1 maps. Models were trained and tested in 47 healthy volunteers using MOLLI sequence, and compared with Free Form Deformation method. Results showed the proposed method can achieve better performance in registration and T1 mapping with higher efficiency (7x acceleration).

In T1 mapping, high contrast variation and tissue signal nulling bring difficulties in motion correction. Therefore, separation of intensity contrast and tissue structure may help the following registration of T1w image series. The workflow of contrast separation is shown in Fig. 1.

Based on the sparse coding theory, ideal time intensity curves $$$p\in\mathbb{R}^{T\times2}$$$ of myocardium and blood pool can be coded using the dictionary $$$D$$$ and coefficient map $$$c$$$. $$$D\in\mathbb{R}^{T\times M}$$$ was a dictionary generated by the combination of $$$T$$$ frames of vectorized T1w image with totally $$$M$$$ voxels. Coefficient map $$$c\in\mathbb{R}^{M\times2}$$$ can be used to estimate the intensity contribution of the corresponding area. $$$c$$$ had two columns which denoted the two subspaces representing myocardium and blood pool.

Specifically, c can be solved by the following formula:

$$\hat{c}=argmin_{c}\frac{1}{2}\parallel p-Dc\parallel _2^2+λ\parallel c\parallel_{1}$$

when the coefficient map $$$c$$$ was obtained, the rescaled time intensity curve $$$r\in\mathbb{R}^{T\times2}$$$ was multiplied with $$$c$$$ pixel-by-pixel to generate the contrast variation components, and then subtracted from the original T1w images to form contrast separated images.

A self-supervised deep learning based

$$\hat{\theta}=argmin_{θ}\mathcal{L}_{sim}(f,R(m,G_{θ}(f,m)))+η\mathcal{L}_{smooth}(ψ)$$

where $$$\mathcal{L}_{sim}$$$ denoted a similarity measurement between the target image and warped image, $$$\mathcal{L}_{smooth}$$$ denoted a smoothness regularization, $$$\mathcal{R}$$$ denoted the wrap function that applied deformation field $$$\psi$$$ on the input image to obtain the spatial transformed image. $$$\psi$$$ was generated by a neural network $$$G_\theta$$$ parameterized with $$$\theta$$$. The hyperparameter $$$\eta$$$ was empirically set to 0.5. The DenseAttention U-Net

The whole framework is shown in Fig. 2. We tested two commonly used similarity matrixes which were Cross-Correlation (CC) and Mutual Information (MI). Two models that each combined one of the similarity loss functions were constructed, which were named as SDRAP-CC and SDRAP-MI.

A widely used registration method FFD (Free Form Deformation) was used as the compared method. Dice Similarity Coefficient (DSC) and Mean Boundary Error (MBE) were used as indicators to quantitatively evaluate the registration error on T1w images. Standard Deviation (SD) map of T1 quantification was used to evaluate the accuracy of T1 mapping.

An in-vivo cardiac datasets from MOLLI sequence with 47 healthy volunteers containg 921 images were recruited with institutional review board approval. MOLLI sequence was scanned with a 3T MR scanner (Achieva TX, Philips, The Netherlands). MOLLI protocol: TR=2.59 ms, TE=1.31 ms, FA=35

Quantitative results are shown in Table 1. The SDRAP-CC can achieve the highest DSC of 84.9±4.2% and the least MBE of 0.94±0.27mm, which was significantly better than uncorrected images (p = 0.011 for DSC and p = 0.003 for MBE). The proposed method was less than FFD that the former can process one slice with only 0.52s, achieving about 7x acceleration compared with FFD (3.7s/slice).

Fig. 4 shows SD maps of T1 mapping and the corresponding quantitative results. SD maps of uncorrected images and after FFD registration had overall higher value than those of SDRAP-MI and SDRAP-CC. In the analysis of blood pool and myocardium region, SDRAP-CC achieved the lowest mean SD of 35.6±18.7ms and 27.2±19.1ms among all methods.

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Fig. 1. Contrast Separation for T1w images. (A) Contrast separation based on sparse coding theory. (B) De-contrast images are generated by the original images minus contrast components.

Fig. 2. The framework of the proposed method

Fig. 3. Motion correction results for different methods on T1w images.

Table 1. Quantitative results for motion correction on T1w images.

Fig. 4. (A) SD maps of T1 mapping and (B) the corresponding quantitative comparisons.

DOI: https://doi.org/10.58530/2022/4121