4648

A Dictionary Matching-Based Motion Correction Method for Cardiac Multi-Parametric Mapping

Haiyang Chen¹, Yixin Emu¹, Zhuo Chen¹, Juan Gao¹, and Chenxi Hu¹
¹Shanghai Jiao Tong University, Shanghai, China

Synopsis

Keywords: Motion Correction, Motion Correction, multi-parametric mapping

Motivation: Motion correction (MoCo) for cardiac parametric mapping can be challenging due to the dynamic signal variations. Traditional model-based methods need an analytical model, which is often unavailable for multi-parametric mapping applications.

Goal(s): To propose a model-free dictionary matching-based MoCo method for cardiac multi-parametric mapping.

Approach: The method alternates between dictionary matching and image registration. In vivo validation was performed in 10 healthy subjects for cardiac joint T1 and T2 mapping with controlled breathing.

Results: Compared with non-MoCo, the proposed method significantly reduced inter-image misalignment and improved the quality of the T1 and T2 maps.

Impact: The proposed MoCo method can be applied to any quantitative MRI application with a signal dictionary, which includes both single-parametric and multi-parametric mapping.

Introduction

Retrospective motion correction (MoCo) is imperative for accurate cardiac parametric mapping^1,2. However, the image contrast variations pose a significant challenge to image-based MoCo methods^1,3–9, which solely rely on image registration algorithms to estimate the motion. Model-based methods^10–13 use physical models to synthesize images of similar contrasts as the acquired images, transforming the original multi-contrast registration problem into a single-contrast registration problem, which is easier to solve. However, current model-based methods need an analytical signal model for image synthesis, which is often absent for multi-parametric mapping^14–16. Here we propose a model-free dictionary matching-based MoCo method for cardiac multi-parametric mapping. We validated the method for cardiac Multimapping¹⁶ in 10 healthy subjects with controlled breathing.

Methods

Theory
Let $$$\mathbf{D}$$$ be the dictionary, with each unit-length entry (column) $$$\mathbf{d}_{\mathrm{n}}$$$ corresponding to a simulated signal determined by tissue and imaging parameters. We formulate the proposed method as an optimization problem
$$\min _{\boldsymbol{\alpha}, \boldsymbol{\theta}} \sum_{\mathbf{r}}\|\mathbf{M}(\mathbf{y}, \mathbf{r}, \boldsymbol{\theta})-\mathbf{D} \boldsymbol{\alpha}(\mathbf{r})\|_{2}^{2}+\lambda \mathrm{R}(\boldsymbol{\theta}) \text { s.t. }\|\boldsymbol{\alpha}(\mathbf{r})\|_{0} \leq 1 \text {, }\tag{1}$$
where $$$\mathbf{r}$$$ is the spatial coordinate, $$$\mathbf{y}$$$ the acquired image signal, $$$\boldsymbol{\alpha}$$$ the sparse code, $$$\mathbf{M}$$$ the deformation operator, $$$\boldsymbol{\theta}$$$ the deformation parameters, $$$\mathrm{R}$$$ the spatial regularization term, and $$$\lambda$$$ the regularization coefficient. We solve the problem by alternating minimization with two steps.

Step 1: By fixing $$$\boldsymbol{\theta}$$$, we obtain a dictionary matching subproblem. The optimal sparse code $$$\boldsymbol{\alpha}^{*}(\mathbf{r})$$$ is computed by finding the entry that best matches the deformed image signal $$$\mathbf{M}(\mathbf{y}, \mathbf{r}, \boldsymbol{\theta})$$$ based on the inner product:
$$\left[\boldsymbol{\alpha}^{*}(\mathbf{r})\right]_{\mathrm{n}}=\left\{\begin{array}{l}\left\langle\mathbf{M}(\mathbf{y}, \mathbf{r}, \boldsymbol{\theta}), \mathbf{d}_{\mathrm{n}}\right\rangle, \text { for } \mathrm{n}=\underset{\mathrm{m}}{\arg \max }\left\langle\mathbf{M}(\mathbf{y}, \mathbf{r}, \boldsymbol{\theta}), \mathbf{d}_{\mathrm{m}}\right\rangle, \\0, \text { otherwise, }\end{array}\right.\tag{2}$$
where $$$\left[\boldsymbol{\alpha}^{*}(\mathbf{r})\right]_{\mathrm{n}}$$$ is the $$$\mathrm{n}$$$-th component of $$$\boldsymbol{\alpha}^{*}(\mathbf{r})$$$. The constructed synthetic images $$$\mathbf{D} \boldsymbol{\alpha}^{*}(\mathbf{r})$$$ are motion-free and have consistent contrasts with the acquired images.

Step 2: By fixing $$$\boldsymbol{\alpha}$$$, we obtain an image registration subproblem, i.e., registering the acquired images $$$\mathbf{y}(\mathbf{r})$$$ to the synthetic images $$$\mathbf{D} \boldsymbol{\alpha}(\mathbf{r})$$$. We used the free-form deformations and bending energy as the deformation model and spatial regularization term, respectively¹⁷. $$$\boldsymbol{\theta}$$$ was the collection of control point meshes for all images. We implemented a gradient descent algorithm to solve the subproblem.

As illustrated in Figure 1, the proposed methods alternately construct motion-free synthetic images by dictionary matching and register the acquired images to the synthetic images until convergence. The motion-corrected parametric maps are generated by the last dictionary matching.

Experiments
The institutional review board approved the study. We performed cardiac Multimapping¹⁶ over 10 healthy subjects in a 3T scanner (uMR 790, United Imaging Healthcare, Shanghai, China) after obtaining written informed consent from each subject. For each subject, we acquired 3 short-axis slices in both controlled-breathing and breath-hold states. We constructed the dictionary for each scan using the extended phase graph (EPG)¹⁸ for ranges of T1, T2, and B1¹⁶. To evaluate the MoCo performance, we measured the mean contour distances (MCD) of the epicardium and endocardium between each pair of images from the image sequence. Two readers qualitatively evaluated the quality of the reconstructed T1 and T2 maps using a 5-point scale.

Results

Figure 2 shows the multi-contrast images of one representative subject without and with our MoCo method. The method considerably reduced the motion, especially in the left ventricular region. Figure 3 shows the parametric maps of the same subject in Figure 2 before and after MoCo. Without MoCo, the reconstructed T1 and T2 maps exhibited relatively severe motion artifacts (white arrows). Our MoCo method considerably improved the mapping quality, which was similar to that of the breath-hold scan. Figure 4 shows comparisons of average epicardial and endocardial MCDs between reconstructions of the non-MoCo, MoCo, and breath-hold datasets. For both epicardial and endocardial contours, the motion-corrected images exhibited significantly lower MCDs than the uncorrected images. The breath-hold images achieved the lowest MCDs. Figure 5 shows the result of qualitative comparisons. After MoCo, the proportion of maps with poor or fair qualities substantially declined (T1: 3% vs 37%; T2: 10% vs 46%), while that of excellent qualities substantially increased (T1: 60% vs 10%; T2: 53% vs 3%). Based on the Wilcoxon signed-rank test, the proposed method significantly improved the rating scores for both T1 and T2 maps.

Discussion and Conclusions

We developed a model-free dictionary matching-based MoCo method for cardiac multi-parametric mapping. The preliminary results showed that the method reduced the respiratory motion and significantly improved the mapping quality relative to non-MoCo in the presence of controlled breathing. In principle, the method can be applied to any MRI application where a dictionary of the signal is available. Future investigations will focus on the use of deep learning-based registration methods to further improve the MoCo quality.

Acknowledgements

No acknowledgements found.

References

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Figures

Figure 1. A schematic of the proposed method when applied to the task of cardiac joint T1 and T2 mapping. After dictionary generation, the method alternately performs dictionary matching and image registration until it converges. The parametric maps generated by the last dictionary matching are motion-corrected. (HB: heartbeat)

Figure 2. The reconstructed multi-contrast images of one subject before and after MoCo. The proposed method reduced the respiratory motion, generating a better alignment of the left ventricular myocardium over different images.

Figure 3. The T1 and T2 maps of the same subject in Figure 2 before and after MoCo. The left panel shows the T1 maps, while the right panel shows the T2 maps. The white arrows indicate the motion artifacts in the absence of MoCo. The artifacts were not found in the maps reconstructed with MoCo. The maps with MoCo well agreed with those with breath-hold.

Figure 4. Comparisons of average epicardial and endocardial MCDs between images reconstructed from non-MoCo, MoCo, and breath-hold scans. Error bars indicate standard deviations. For each subject, only MCD of the mid-ventricular slice was used. MoCo significantly reduced the MCD compared with non-MoCo (P＜0.001), indicating an improvement of alignment between images acquired in different heartbeats. However, residual motion was still present compared with breath-hold scans.

Figure 5. (A) Distribution of the qualitative scores over 30 slices (3 slices × 10 subjects). After MoCo, the proportion of maps with poor or fair qualities (1 ≤ score ≤ 3) substantially declined (T1: 3% vs 37%; T2: 10% vs 46%), while that of excellent qualities (4＜score ≤ 5) substantially increased (T1: 60% vs 10%; T2: 53% vs 3%). (B) Mean and standard deviation of the qualitative scores. The proposed method significantly improved the quality of the maps compared with non-MoCo. However, there were still small but significant differences between MoCo and breath-hold results.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

4648

DOI: https://doi.org/10.58530/2024/4648