XD-GRASP: Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing

Abstract

Purpose: To develop a novel framework for free-breathing MRI called XD-GRASP, which sorts dynamic data into extra motion-state dimensions using the self-navigation properties of radial imaging and reconstructs the multidimensional dataset using compressed sensing.

Methods: Radial k-space data are continuously acquired using the golden-angle sampling scheme and sorted into multiple motion-states based on respiratory and/or cardiac motion signals derived directly from the data. The resulting undersampled multidimensional dataset is reconstructed using a compressed sensing approach that exploits sparsity along the new dynamic dimensions. The performance of XD-GRASP is demonstrated for free-breathing three-dimensional (3D) abdominal imaging, two-dimensional (2D) cardiac cine imaging and 3D dynamic contrast-enhanced (DCE) MRI of the liver, comparing against reconstructions without motion sorting in both healthy volunteers and patients.

Results: XD-GRASP separates respiratory motion from cardiac motion in cardiac imaging, and respiratory motion from contrast enhancement in liver DCE-MRI, which improves image quality and reduces motion-blurring artifacts.

Conclusion: XD-GRASP represents a new use of sparsity for motion compensation and a novel way to handle motions in the context of a continuous acquisition paradigm. Instead of removing or correcting motion, extra motion-state dimensions are reconstructed, which improves image quality and also offers new physiological information of potential clinical value.

Keywords: compressed sensing; free-breathing; golden-angle; motion compensation; radial sampling.

Fig. 1

Schematic illustration of the XD-GRASP method. a: Continuously acquired radial k-space data are sorted into respiratory states from expiration (top) to inspiration (bottom), using a respiratory motion signal extracted directly from the data. Different colors indicate different motion states. The number of spokes grouped in each motion state is the same. b: Approximately uniform coverage of k-space, with distinct sampling patterns in each respiratory motion state, is achieved using the golden-angle acquisition scheme. c: Data sorting removes blurring and clearly resolves respiratory motion, at the expense of introducing undersampling artifacts. The purple dashed line shows the distinct respiratory motion states after data sorting. d: Sparsity is exploited along the extra dimension to remove aliasing artifacts due to undersampling.

Fig. 2

XD-GRASP motion estimation and data sorting for cardiac cine imaging. a: 2D golden-angle radial trajectory. Motion signals are estimated from the central k-space position of each radial line (gray dot). b,c: Estimation of cardiac and respiratory motion signals using information from multiple coils. The signals with the highest peaks in the frequency range of 0.1–0.5 Hz and 0.5–2.5 Hz are automatically selected for respiratory and cardiac motion signals, respectively. d: Conventional iGRASP sorting of cardiac phases, given by grouping consecutive spokes in each frame. e: XD-GRASP sorting, in which all the cardiac cycles are concatenated into an expanded dataset with one cardiac dimension (t_C) and an extra respiratory dimension (t_R), so that sparsity along t_C and t_R can be exploited in the multidimensional compressed sensing reconstruction.

Fig. 3

XD-GRASP motion estimation and data sorting for DCE-MRI imaging. a: 3D stack-of-stars radial trajectory with golden-angle rotation, where all spokes along k_z for a given rotation angle are acquired before rotating the sampling direction to the next angle. b: A 1D Fourier transform along the series of k-space central points of each slice is performed to obtain a projection profile of the entire volume for each angle and all the projection profiles from all coils are concatenated into a large 2D matrix, followed by principal component analysis (PCA) along the z+coil dimension. c,d: The principal component with the highest peak in the frequency range of 0.1–0.5 Hz is selected to represent respiratory motion. e–g: Contrast-enhancement effect is approximately removed by estimating and subtracting the envelope of the composite signal. h,i: Processed respiratory motion signals are shown superimposed on the z-projection profiles for normal breathing (left) and heavy breathing (right), demonstrating reliable motion estimation.

Fig. 4

Conventional NUFFT reconstruction without respiratory sorting (motion average) and XD-GRASP reconstruction with six respiratory states for datasets acquired in transverse, coronal and sagittal orientations. XD-GRASP significantly reduces motion-blurring, as indicated by the white arrows.

Fig. 5

XD-GRASP reconstruction results for four representative respiratory sparsity regularization parameters (λ₂) in cardiac imaging and liver DCE-MRI. Usage of a sparsity constraint along the extra respiratory-state dimension improved the removal of under-sampling artifacts, when compared with the nonregularized case (λ₂=0). Very low values of λ₂ resulted in residual aliasing artifacts, while very high values introduced blurring. A λ₂ of 0.01 in cardiac cine imaging and 0.015 in liver DCE-MRI provided a good tradeoff between residual aliasing artifacts and temporal fidelity.

Fig. 6

Comparison of XD-GRASP against the standard breathhold approach used in routine clinical studies (i.e., with retrospective ECG-gating) at end-diastolic and end-systolic cardiac phases in the volunteer scans. XD-GRASP provided similar performance to the routine clinical breathhold method.

Fig. 7

a: XD-GRASP provides access to respiratory motion information for each cardiac phase, where respiratory-related motion of the interventricular septum, especially at diastolic cardiac phases (top row) can be seen, indicating left–right ventricular interaction during respiration. Gray arrows indicate different respiratory motion states. b: Comparison of XD-GRASP reconstruction exploiting sparsity along two dynamic dimensions (right-hand column) with iGRASP reconstruction exploiting sparsity along a single dynamic dimension only (left-hand column), using the same data set acquired during free-breathing.

Fig. 8

a: Comparison of XD-GRASP and the standard breathhold approach with retrospective ECG-gating for the patients. Conventional breathhold scans achieved good image quality in a patient with normal sinus rhythm, but it produced poor image quality for patients with arrhythmias. XD-GRASP achieved consistent image quality by separating the cardiac cycles with arrhythmia. b: In the patient with 2nd degree AV block, the arrhythmic cardiac cycles were further sorted for a separate XD-GRASP reconstruction to provide additional physiological information. c: Corresponding cardiac motion signals for three patients with varying length of the cardiac cycle indicated by gray arrows.

Fig. 9

Comparison of iGRASP with XD-GRASP in both aortic (AO) and portal-venous (PV) enhancement phases in two representative partitions each from two volunteer datasets. XD-GRASP improved delineation of the liver and vessels with enhanced vessel-tissue contrast.

Fig. 10

Comparison of iGRASP with XD-GRASP in a total of five representative partitions from two volunteers and one patient. Volunteer 4 was asked to breathe deeply. XD-GRASP achieved superior overall image quality, with reduced motion-blurring. The white arrow indicates a suspected liver lesion, which was better delineated in XD-GRASP.