Radial spoke energy for self-navigated motion detection and position-ordered dynamic musculoskeletal MRI

TL;DR

This work introduces spoke energy as a self-navigated, hardware-free motion sensing metric for 3D radial MRI, exploiting the Fourier Slice and Parseval theorems to link spoke energy with motion-induced changes in object-coil alignment. It enhances robustness with a sliding-window sum and fuses multi-coil data using the second PCA component (2ndPCA) to yield a unified, motion-sensitive signal. Beyond traditional motion detection, the approach enables position-based spoke sorting to produce motion-resolved 4D dynamic MRI of the ankle and knee under continuous movement, improving anatomical clarity and reducing artifacts. The method offers real-time motion detection and realistic dynamic imaging without sequence modification or additional hardware, with demonstrated improvements in head-motion correction and musculoskeletal dynamic imaging. This has potential to broaden motion-aware MRI in clinical workflows and dynamic joint assessment.

Abstract

Motion remains a key challenge in MRI, as both involuntary (e.g., head motion) and voluntary (e.g., joint motion) movement can degrade image quality or provide opportunities for dynamic assessment. Existing motion sensing methods, such as external tracking or navigator sequences, often require additional hardware, increase SAR, or demand sequence modification, which limits clinical flexibility. We propose a computationally efficient, self-navigated motion sensing technique based on spoke energy derived from 3D radial k-space data. Using the Fourier Slice and Parseval's theorems, spoke energy captures object-coil alignment and can be computed without altering the sequence. A sliding window summation improves robustness, and a second principal component analysis (2ndPCA) strategy yields a unified motion-sensitive signal. Beyond conventional head motion correction, we demonstrate the novel application of this method in enhancing dynamic 4D MRI of the ankle and knee under a continuous movement protocol. By sorting spokes based on position rather than time, we achieve motion-resolved reconstructions with improved anatomical clarity. This approach enables real-time motion detection and supports broader adoption of motion-aware dynamic MRI.

Figures (8)

• Figure 1: Illustration of the relationship between sliding-window-summed spoke energy (a) and individual spoke energy (b). In panel (b), the spoke energy during the motion duration $M$ is highlighted in bold, which starts at $i_1$ and ends at $i_2$, i.e., $i_2-i_1=M-1$. For demonstration purposes, four windows are marked with dashed rectangles of different colors (green, blue, red, and yellow). The green dashed rectangle represents the first window, the blue rectangle indicates the last window before the motion event, the red rectangle marks the first window encompassing motion spokes, and the yellow rectangle corresponds to the first window after the motion event. Their respective window-summed spoke energies are indicated on the curve in panel (a) using the same colors. The window length $L$ equals the number of spokes in a shot. Within a shot, spoke energy may vary in a specific pattern due to relaxation effects and other factors, even when the subject is stationary. During a motion event lasting $M$, the window-summed spoke energy is affected for a duration of $L+M$ (represented by the interval between the blue and yellow dots). This relationship demonstrates the interplay between motion events and the dynamics of window-summed spoke energy.
• Figure 2: Motion sensing of simulated head motion data using a sliding shot-length window. Six motion events are injected in the simulated data, which begin at spoke indices [10000,14000,20000,24000,30000,40000] and end at [10000, 15000, 20000, 25000, 30000, 40000], respectively. (a1–a3) display the curves of the CoM coordinates in the x, y, and z directions, respectively, with different colors representing individual coil signals. (a4) shows a composite curve generated by combining all CoM signals using 2ndPCA in (a1–a3) to facilitate motion tracking. The CoM is calculated from the spokes within the sliding window using Least-Squares minimization, with a total computation time of 1 hour and 34 minutes. (b1) presents the sliding window-sum spoke energy curves, and (b2) shows a 2ndPCA combined curve from all signals in (b1) for simplified motion tracking. The total calculation time for sliding window-sum spoke energy is under 1 second. Red and blue dashed vertical lines indicate the ideal starting [9552, 13552, 19552, 23552, 29552, 39552] and ending [10001, 15001, 20001, 25001, 30001, 40001] of the motion events in the axis of sliding window index, respectively.
• Figure 3: Results of head motion sensing and registration in Head Data 1. (a) Sliding window-summed spoke energy plot with a window length of 448 spokes, where each coil is represented by a differently colored line. (b) Normalized 2ndPCA combined signal derived from all coil signals in panel (a), providing an intuitive visualization of motion. (c) Difference of the normalized 2ndPCA combined signal, used for motion detection. Peaks in the plot indicate severe motion events, dividing the data into 7 stationary states separated by 6 peaks. The signal intensity has been normalized, and a threshold of 0.1 is applied to retrieve the starting and ending indices of the peak bandwidths as [6543, 12778, 19123, 25847, 32053, 38317] and [7158, 13421, 19711, 26401, 32655, 38959], respectively. Using these indices, 7 spoke subsets corresponding to the 7 stationary states are identified, with starting indices [1, 7157, 13420, 19710, 26400, 32654, 38958] and ending indices [6991, 13226, 19571, 26295, 32501, 38765, 44800]. These subsets are used for subsequent registration-based flexible (flex)-spoke-length motion correction, while spokes outside the 7 subsets are discarded due to severe motion corruption. (d1–d5) Reconstructed axial images from motion-corrupted data without correction (NoMoCo), no-motion data (NoMo), motion-corrected data using 20-shot Motion Correction (20-shot MoCo), 10-shot Motion Correction (10-shot MoCo), and flexible-spoke-length Motion Correction (flex-spoke MoCo). (e1–e5) Reconstructed sagittal images following the same sequence as in (d1–d5). In both (d1–d5) and (e1–e5), red arrows highlight specific anatomical structures to aid visual comparison. Additionally, Spectral Entropy (SE), Average Edge Strength (AES), and Structural Similarity Index Measure (SSIM) values are provided for quantitative evaluation.
• Figure 4: Results of head motion sensing and registration in Head Data 2. (a) Sliding window-summed spoke energy plot with a window length of 448 spokes, where each coil is represented by a differently colored line. (b) Normalized 2ndPCA combined signal derived from all coil signals in panel (a), providing an intuitive visualization of motion. (c) Difference of the normalized 2ndPCA combined signal, used for motion detection. Peaks in the plot indicate severe motion events, separating the data into 14 stationary states divided by 13 peaks. The signal intensity has been normalized, and a threshold of 0.1 is applied to identify 14 spoke subsets corresponding to stationary states according to \ref{['prop1']}, with starting indices [1, 14766, 15994, 17091, 18724, 21198, 24251, 26271, 28748, 30778, 33364, 36228, 37712, 41426] and ending indices [14767, 15995, 17092, 18725, 21199, 24252, 26272, 28749, 30779, 33365, 36229, 37713, 41427, 44800]. These subsets are used for subsequent registration-based flexible (flex)-spoke-length motion correction, while spokes outside the 14 subsets are discarded due to severe motion corruption. (d1–d5) Reconstructed axial images from motion-corrupted data without correction (NoMoCo), no-motion data (NoMo), motion-corrected data using 20-shot Motion Correction (20-shot MoCo), 10-shot Motion Correction (10-shot MoCo), and flexible-spoke-length Motion Correction (flex-spoke MoCo). (e1–e5) Reconstructed sagittal images following the same sequence as in (d1–d5). In both (d1–d5) and (e1–e5), red arrows highlight specific anatomical structures to aid visual comparison. Additionally, Spectral Entropy (SE), Average Edge Strength (AES), and Structural Similarity Index Measure (SSIM) values are provided for quantitative evaluation.
• Figure 5: Analysis of stepwise moving ankle data using spoke energy. (a) Reconstructed image from all 44,800 spokes. (b) Sliding window-summed spoke energy with a window length of 448 spokes, where signals from all 18 coils are represented in different colors. (c) The normalized 2ndPCA combined signal derived from the signals in panel (b) for intuitive motion observation. (d) The difference of the normalized 2ndPCA combined signal, used for motion detection. Peaks in this plot indicate significant motion events, separating the data into 5 stationary states divided by 4 peaks. The signal intensity has been normalized. A threshold of 0.1 is applied to determine the starting and ending indices of the peak bandwidths, identified as [7029, 16476, 25864, 35368] and [9792, 19068, 27275, 37732], respectively, which are used to determine the spoke indices for each stationary state. (e1–e5) Reconstructed images corresponding to the 5 stationary states using the identified spoke subsets according to proposition \ref{['prop1']}, with starting and ending spoke indices [1, 9791, 19067, 27274, 37731] and [7477, 16924, 26312, 35816, 44800], respectively.

Theorems & Definitions (1)

• Proposition 1