A major challenge in whole-heart coronary MR angiography (CMRA) is image quality degradation due to respiratory motion. Free-breathing “pencil-beam” navigator-gated acquisitions are commonly used to minimize respiratory motion. However, this approach only compensates for translational motion in the superior-inferior (SI) direction and leads to prolonged acquisition times, since only a portion of the acquired data is used for reconstruction (referred to as scan efficiency). Several approaches have been introduced recently to achieve 100% scan efficiency and correct for more complex motion in fully sampled acquisitions.^1-4 These approaches usually correct for beat-to-beat translational motion based on image navigators (iNAV) or correct for bin-to-bin affine motion estimating the motion from the data itself. Here we propose a combined 2D beat-to-beat translational and 3D bin-to-bin non-rigid motion correction approach, combined with undersampling acquisition to further reduce the scan time. A generalized matrix formalism with total variation regularization (GM-TV) is used to perform the non-rigid correction directly in the reconstruction.^5,6 The proposed GM-TV method was tested on 3 healthy subjects and compared against a conventional 6mm navigator-gated and tracked acquisition.

Undersampled 3D CMRA is acquired using a golden-step spiral-like Cartesian (CASPR) trajectory,⁴ which samples the k_y-k_z plane with spiral interleaves on a Cartesian grid. Consecutive spirals are separated by the golden-angle θ_G=111.25°. A 2D golden radial (GR) iNAV is acquired at every heartbeat interleaved with each segment of the whole-heart 3D CMRA scan (Fig1.a). 2D iNAVs are reconstructed using non-uniform FFT and registered to a common respiratory position to estimate 2D translational (SI and right-left: RL) beat-to-beat motion (Fig1.b). The SI dimension of this motion is used to group the 3D CMRA data into different respiratory bins (Fig1.c) and 2D translational motion for each bin is performed. Each highly undersampled bin is reconstructed with soft-gated total variation regularized SENSE (SENSE-TV)⁶ and 3D non-rigid motion is estimated via image registration (Fig1.d). The estimated bin-to-bin non-rigid motion fields are incorporated into an undersampled motion compensated reconstruction using the GM-TV method (Fig1.e), given by:

$$\hat{I}=\textrm{arg}\,\textrm{min}_I\left\{\frac{1}{2} \left\| EI-K \right\|^2 + \lambda \, TV\right\}\,\textrm{with}\,\,E=\sum_b A_bFSU_b,$$

where $$$\hat{I}$$$ is the reconstructed non-rigid motion corrected image, $$$K$$$ is the translational corrected k-space data, $$$\lambda$$$ is the regularization parameter, $$$TV$$$ represents the 3D spatial total variation function, $$$A_b$$$ is the sampling matrix corresponding to bin $$$b$$$, $$$F$$$ is the Fourier transform, $$$S$$$ are the coil sensitivities and $$$U_b$$$ are the non-rigid motion fields. This problem is solved using a nonlinear conjugate gradient method. A similar cost function, without bin-to-bin motion information, is used to reconstruct images $$$\hat{I}_b$$$ for each bin from binned data $$$K_b$$$:$$$\hat{I}_b=\textrm{arg}\,\textrm{min}_{I_b}\left\{\frac{1}{2}\left\| EI_b - K_b \right\|^2+\lambda\,TV\right\}\, \textrm{with} \,\,E=A_bFS$$$.

In-vivo free-breathing experiments were performed on three healthy subjects on a 1.5T Philips scanner using a 32-channel receiver coil. Acquisitions were performed using undersampled 2D GR iNAV (gradient echo, 4x4mm in-plane resolution, 25mm slice thickness, 300x300 FOV, TR/TE = 3.6/1.5ms, flip angle = 5°, 24 radial profiles) interleaved with segmented 3D b-SSFP CASPR acquisition. Relevant scan parameters for 3D CASPR are: FOV = 300x300x100mm, resolution = 1x1x2mm, TR/TE = 5.3/2.6ms, flip angle = 70°, T2 preparation (T = 50ms), fat saturation (SPIR), subject specific mid-diastolic trigger delay, acquisition window ~120ms, 1 spiral-like interleaf per R-R interval, 3x and 4x undersampling with corresponding acquisition times of 3.5min ± 0.4 and 2.4min ± 0.2. Three bins with undersampling factors of 9x and 12x (for the 3x and 4x datasets, respectively) were reconstructed to estimate non-rigid respiratory motion with end-expiration as reference position. A fully sampled 6mm navigator-gated and tracked acquisition was performed with the same trajectory and identical parameters for comparison. The nominal acquisition time of the navigator-gated acquisition was of 10.6min ± 1.4.

Reformatted images obtained with the fully sampled navigator-gated and proposed GM-TV approaches are shown in Fig.2 for two healthy subjects, along with motion corrupted SENSE-TV 3x and 4x undersampled reconstructions. Significant motion blurring is observed in the non-corrected SENSE-TV images. The proposed methodology provides reconstructions from 3x and 4x undersampled data of comparable quality to those achieved with the navigator-gated scan. The navigator efficiency for the gated scan was 66%±4 compared to ~100% for the proposed approach (respiratory outliers were not included in reconstructions).A motion compensated reconstruction framework for accelerated 3D CMRA has been proposed. High-temporal resolution (beat-to-beat) translational motion is estimated from 2D iNAV images and 3D non-rigid motion is estimated from undersampled high-resolution 3D CMRA data. Non-rigid motion is incorporated into a generalized matrix formalism with total variation regularization reconstruction to obtain images of comparable quality to gated scans, enabling acquisitions to be performed about 5 times faster.