Introduction

MRI is sensitive to motion, and subject motion during brain MRI has been problematic in clinical practice. Generally, motion causes artifacts manifesting as ghosting, blurring, geometric distortion or decreased signal-to-noise ratio (SNR)¹. Study showed that both motion-free time and average displacement of scanning object were highly correlated with brain image quality². Severe motion may result in non-diagnostic image in clinical scans, which result in repeated scans and additional cost.
Several methods have been proposed for motion correction of the brain. One type of methods utilizes the self-navigation property of radial acquisition, and use the analysis of projection moment to detect motion^3-5. However, the detection of both translational and rotational parameters using single coil is not robust to noise. Projection moment analysis in 3D radial MRI was able to detect motion occurrence, but failed to get specific rigid-body motion parameters with stationary multichannel coils.
In this study, we proposed a generalized rigid-body motion correction method using 3D radial acquisition and projection moment analysis. The motion pattern can be continuous, and the calculation is relatively fast that it can be easily implemented in clinical scans. The preliminary results demonstrate that the proposed method is a powerful tool for motion correction in the brain.

Methods

Motion Estimation and Correction
The center-of-mass (COM) of an image is the ratio of its first and zeroth moments⁴. In 3D radial acquisition, the projection of COM of an object onto a radial spoke (P) is:
$$P=\frac{\int r\left(F^{-1}s\right)dr}{\int\left(F^{-1}s\right)dr}\tag{1}$$
where s is the k-space data of a spoke, F^-1 is 1D inverse Fourier transform operator, and r is the radius vector along spoke direction. Let $$$v=\left(v_x,v_y,v_z\right)^T$$$ denote a unit vector pointing at spoke direction, and the relationship of P and COM can be expressed as⁵:
$$\left(\begin{array}{c}P_1 \\P_2 \\\vdots \\P_n\end{array}\right)=\left(\begin{array}{ccc}v_{1,x} & v_{1,y} & v_{1,z} \\v_{2,x} & v_{2,y} & v_{2,z} \\\vdots & \vdots & \vdots \\v_{n,x} & v_{n,y} & v_{n,z}\end{array}\right)\left(\begin{array}{c}\operatorname{COM}_x \\\operatorname{COM}_y \\\operatorname{COM}_z\end{array}\right)\tag{2}$$
where n is the number of spokes involved in the calculation. P can be calculated after 1D inverse Fourier transform of k-space data. By introducing variable forgetting-factor recursive least-squares (VFF-RLS) algorithm⁶, the above least-squares problem can be extended to recursively estimate subject COM with a nominal temporal resolution of one TR.
To estimate rigid-body object displacement directly from k-space data, we first assume that a flexible coil is used that it moves with the head. For translational motion estimation, a PCA-based coil compression is performed that its first virtual coil contains information which is an overall representation of object position, as shown in Figure 1. By calculating the evolution of COM in this virtual coil using VFF-RLS, the translational motion can be estimated and the original k-space data is aligned accordingly for translation correction. After this operation, the COM of each coil was calculated using VFF-RLS separately, as shown in Figure 2(A). Rotational parameters can be calculated using a least-squares estimation between sets of vectors acquired at different time (Figure 2(B))⁷.
Experiments
One healthy subject was scanned using a 3D radial sequence with multi-dimensional golden-means trajectory⁸ with two flexible coils (totally 20 channels) on a 3T MRI scanner (uMR790, United Imaging Healthcare, Ltd., Shanghai, China). Written consent was obtained before scan. The scanning parameters were: FOV = 240×240×240 mm³, matrix = 240x240x240, flip angle = 17°, TR = 7.1 ms, TE = 3 ms, bandwidth = 250 Hz/pixel, spoke number = 90,000. The total scan time was 10.65 min. Two scans were made. In one scan the volunteer was asked to remain still, while in the other scan he was told to perform some random movements.
A simulation was made that a sinusoidal periodic motion was added to the motion-free k-space data to create motion-corrupted image. The proposed method was applied, and the motion corrected image was compared with original image. It was then tested on k-space data with real motion.

Results

Simulation showed that for continuous motion, the proposed method successfully eliminated motion artifacts (Figure 3). Motion artifacts in prospective motion-corrupted scan were also eliminated with the cost of slightly-reduced SNR (Figure 4). The estimated motion pattern in prospective motion-corrupted scan is shown in Figure 5, which consists of a large-scale fast motion and a small-scale random position change, which successfully mimics head motion pattern commonly seen in clinical scans⁹.

Discussion and Conclusion

Preliminary results have demonstrated that the proposed method is an easy, robust, and time-efficient tool for motion correction in brain MRI. The prerequisite is that a flexible coil attached to the head needs to be used rather than a stationary coil, which may require a specialized coil design.

Acknowledgements

This work was supported by the Shanghai Science and Technology Commission Explorer Program under Grant 22TS1400300.

References

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