A Motion Assessment Method for Reference Stack Selection in Fetal Brain MRI Reconstruction Based on Tensor Rank Approximation

Question

1. What is the proposed motion assessment (MA) method for optimal performance in a fully automated fetal brain processing pipeline?

2. What is the relationship between matrix rank and inter-slice motion?

3. What is the purpose of SVD-RSS method?

4. What is CP decomposition?

Accepted Answer

The proposed motion assessment (MA) method for optimal performance in a fully automated fetal brain processing pipeline is the CANDECOMP/PARAFAC decomposition method. This method factorizes a 3D stack into low-rank and sparse components to extract its motion information. It is compared with an improved version of Kainz's method, which performs SVD on re-sliced images along all three axes to mitigate the loss of spatial information due to stack flattening. The CANDECOMP/PARAFAC decomposition method is hypothesized to be sensitive to motion by utilizing motion information in 3D and relatively unbiased to stacks in different orientations at baseline through interpolating stacks into isotropic volumes. The performance of different MA methods is evaluated by simulating linearly increasing and random motions onto motion-free fetal brain volumes and testing the correlation between proposed motion indicators and the simulated motions.

Accepted Answer

The relationship between matrix rank and inter-slice motion is crucial in understanding the lowrankness of data. In the context of fetal motion assessment, matrix rank refers to the number of linearly independent rows or columns in a matrix. A lower rank indicates that the data can be represented by a smaller number of basis vectors, which implies that the motion between slices is more constrained. This constraint is essential for accurately capturing the fetal motion patterns and reducing noise in the data. By analyzing the matrix rank, researchers can gain insights into the underlying motion patterns and develop more effective algorithms for motion assessment. The principle of matrix rank and its relationship with inter-slice motion is discussed in Section 2.1.1 of the provided text, where the concept is explained in detail and its significance in the context of fetal motion assessment is highlighted.

Accepted Answer

The SVD-RSS method aims to achieve low-rank approximation of a 2D matrix by selecting the first minimum singular vectors and values. It minimizes bias between stacks acquired in different orientations by interpolating the input stack into an isotropic volume. The method reslices the volume into 2D stacks along x/y/z axes and performs SVD on the three sets of re-sliced images. This approach provides complementary motion information and balances accuracy and efficiency by selecting five singular values and vectors to reconstruct a rank-5 approximate matrix. The relative error between the original and approximate matrices is used as a motion indicator (MI), considering through-plane motion and effective area of corresponding slices.

Accepted Answer

CP decomposition is a tensor decomposition method that factorizes a tensor into a sum of rank-one tensors. It can be considered as a higher-order principal component analysis method. Given a tensor Rxx with slices, the approximate tensor can be written as EQUATION, where represents the outer product of the vector. , , , are factor matrices containing a combination of factor vectors. The rank of a tensor is defined as the minimal number of rank-one tensors whose sum is equivalent to the original tensor. MI is defined as the relative error between the original tensor and the approximate tensor containing rank-one tensors. In the proposed CP-based method, input stacks are interpolated into an isotropic volume to minimize the influence of different resolutions before CP decomposition. Altogether, 110 high-resolution 3D volumes were reconstructed successfully for further experiments.

Accepted Answer

Fetal brain motion is parameterized using 3D rigid transformation with 6 Degrees of Freedom (6-DoF). The motion is presented in the Euler-Cartesian space, utilizing a rotation matrix based on three rotation parameters (, , ) and a translation component (, , ). The transformation parameters can be represented as a 4x4 matrix, as shown in Equation Transformation parameters for adjacent slices are considered as a temporal sequence, and a motion trajectory is generated to represent continuous motion. Slices are sampled from the corresponding position of the transformed volumes (36). Two types of motion, linearly increasing and random, are generated as specified in the following sections.

Accepted Answer

In the study, large and small degrees of motion were simulated to test the sensitivity of different MA methods. The first group had a large motion with a rotation of 5 degrees and translation of 1 mm between adjacent slices, based on the average degree of motion observed in motion-corrupted stacks. The second group had a smaller motion with a rotation of 2 degrees and translation of 0.4 mm between adjacent slices. Supplementary Figure S2 illustrates examples of motion-corrupted stacks with large and small motions. To further analyze the impact of motion degrees, the rotation between adjacent slices was varied from 0 to 5 degrees at an interval of 0.5 degrees, and in-plane translation was varied from 0 to 2 mm at an interval of 0.2 mm. This allowed for a comprehensive evaluation of the MA methods' sensitivity to different motion degrees, providing valuable insights into their performance in real-world scenarios.

Accepted Answer

Pseudorandom motion trajectories were simulated using a control-point scheme based on a random walk model. Control points were generated with specific uniform distributions, and the speed and direction between neighboring points represented fetal motion. Smoothing cubic splines were then used to fit the motion trajectory. The trajectory was split into first and second halves for odd and even slices, with local variation determined by uniform distributions and a global offset set to twice the local variation. The maximum absolute values were limited to 25deg and 5mm to avoid unrealistic fetal motion. This process is demonstrated in Figure 2, showing a 34-week fetal brain data with interleaved random motions in three stacks simultaneously.

Accepted Answer

The proposed evaluation metrics for motion detection are the Relative Motion Indicator (RMI) and Baseline Motion Indicator (BMI). RMI measures the sensitivity of motion detection by calculating the ratio of Motion Indicators (MIs) before and after adding motion. It reflects the effectiveness of motion detection. On the other hand, BMI evaluates the degree of bias towards slice orientation by comparing MIs between different orientations in the absence of added motion, such as the coronal and sagittal stacks with respect to the axial stack. Additionally, the success rate of selecting the correct reference stack with the minimum motion is assessed. These metrics help in evaluating the performance of different methods in detecting and handling motion in reconstructed volumes.

Accepted Answer

The optimal rank for SVD-RSS is 5. The rank selection experiment showed that the RMI first increased with rank and reached its maximum of 1.2481 at rank 5. The computational time had no significant changes with rank, making 5 the optimal rank for low-rank approximation. This balance between accuracy and efficiency was chosen based on the results of the experiment.

Accepted Answer

In the large-motion group, the proposed CP method outperformed the other two methods with the highest RMI of 1.52, 1.59, and 1.51 for axial, coronal, and sagittal stacks, respectively. Paired t-test demonstrated significant differences (P<10^-4) between three methods in all axes. CP achieved a 100% success rate in determining the minimum motion stacks, while SVD-FS provided success rates of 98%, 74%, and 96% for axial, coronal, and sagittal orientations, respectively. The CP method retained a 100% success rate for axial and sagittal stacks and successfully estimated 96% cases for coronal stacks. The lower success rate in coronal orientation was likely due to the lower effective volume in coronal stacks, which increased the MI and overestimation of motion. Overall, CP showed higher sensitivity and better performance compared to SVD-RSS and SVD-FS in large motion.

Accepted Answer

CP showed the highest success rate of 100% in identifying the correct reference stack among all 110 cases, compared to SVD-RSS and SVD-FS with success rates of 83.4% and 69.7%, respectively. This indicates that CP was more effective in simulating random motion resembling real-world situations, making it a superior method for this task. The success rate along different axes also showed notable differences, with sagittal stacks having the highest success rate in SVD-FS. Overall, CP outperformed other methods in terms of success rate and reconstruction quality, as evidenced by the highest SSIM of 0.9840 and the lowest NRMSE of 0.1508, as well as fewer outliers compared to SVD-FS and the default pipeline.

Accepted Answer

The proposed CP decomposition-based method for determining the degree of motion in fetal brain MRI involves interpolating stacks into volumes to reduce structural bias among different orientations and then calculating the low-rank component to obtain motion information. This method shares the same core idea as SVD-RSS, both of which interpolate stacks into volumes to reduce structural bias and then calculate the low-rank component. The CP method provides a computationally efficient way for direct 3D factorization. Experiments on linear and random motion demonstrated the advantages of treating the stack as a whole using CP decomposition, which gave higher motion sensitivity, success rate, and reconstruction quality compared to the two SVD-based methods. Additionally, CP also achieved lower computational time compared to SVD-FS. However, there are limitations in this work, such as the use of simulated motions and the influence of other image attributes on evaluation metrics. Interpolation during volume-to-volume registration may also reduce the sensitivity of motion detection.

A Motion Assessment Method for Reference Stack Selection in Fetal Brain MRI Reconstruction Based on Tensor Rank Approximation

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Most frequently asked questions

1. What is the proposed motion assessment (MA) method for optimal performance in a fully automated fetal brain processing pipeline?

2. What is the relationship between matrix rank and inter-slice motion?

3. What is the purpose of SVD-RSS method?

4. What is CP decomposition?

5. How is fetal brain motion parameterized in 3D rigid transformation?

6. How did varying motion degrees affect the sensitivity of different MA methods?

7. How were pseudorandom motion trajectories simulated?

8. What are the proposed evaluation metrics for motion detection?

9. What is the optimal rank for SVD-RSS?

10. How does CP method compare to SVD-RSS and SVD-FS in large motion?

11. How did CP perform in identifying correct reference stacks?

12. What is the proposed CP decomposition-based method for determining the degree of motion in fetal brain MRI?

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