Teresa M Correia^{1}, Giulia Ginami^{1}, Radhouene Neji^{2}, Gastao Cruz^{1}, Rene Botnar^{1}, and Claudia Prieto^{1}

Conventionally, free-breathing whole-heart 3D coronary MR angiography (CMRA) uses navigator-gated acquisitions to reduce respiratory motion, by acquiring data only at a specific respiratory phase, which leads to prolonged scan times. Respiratory-resolved reconstruction approaches have been proposed to achieve 100% scan efficiency using mainly non-Cartesian acquisitions and exploiting sparsity in the respiratory dimension. Here, a robust framework for Cartesian imaging is proposed, which provides high-quality respiratory-resolved images by incorporating motion information from image navigators (iNAV) to increase the sparsity in the respiratory dimension. Furthermore, iNAV motion information is used to compensate for 2D translational motion within each respiratory phase.

3D CMRA data is acquired using a prototype golden-step
spiral-like Cartesian (CASPR) trajectory,^{8} which samples the k_{y}-k_{z}
plane with spiral interleaves on a Cartesian grid. Consecutive spirals are
separated by the golden-angle. A low-resolution 2D iNAV is acquired in every
heartbeat, before each spiral interleaf of the whole-heart 3D CMRA acquisition.
The 2D iNAVS are registered to a common respiratory position (end-expiration) to
estimate beat-to-beat 2D translational (right-left and superior-inferior: SI) motion.
The estimated SI motion is used to group the 3D CMRA data into five equally
populated respiratory bins. In XD-ORCCA, 2D translational motion correction within
each bin is performed in k-space before the reconstruction, thereby improving
image quality of each bin. During the reconstruction, intra-bin motion
corrected images are aligned to one respiratory position to increase sparsity
in the respiratory domain.

Each undersampled bin is reconstructed using: 1) XD-GRASP and 2) XD-ORCCA. The respiratory-resolved images were obtained by solving the following optimization problems: 1) $$$\hat{\rm{\bf{x}}}=\rm{arg} \min\limits_{x}\left\{ \frac{1}{2}\left\|\mathbf{E}\,\mathbf{x}\,-\mathbf{k}\right \|_2^2+\alpha\,\Psi_t(\mathbf{ x})\right\}$$$ and 2) $$$\hat{\rm{\mathbf{x}}}=\rm arg\min\limits_{x}\left\{\frac{1}{2}\left\|\bf E\,\mathbf{x}\,-\mathbf{b}\right\|_2^2+\alpha\,\Psi_t(\mathcal{R}\mathbf{x})+\beta\,\Psi_s(\mathbf{x})\right\}$$$, where $$$\bf{x}$$$ is the respiratory-resolved image series, $$$\bf{k}$$$ is the binned k-space data, $$$\bf{b}$$$ is the 2D translational corrected binned k-space data, $$$\Psi_{\rm s}$$$ is the 3D spatial TV function, $$$\alpha$$$ and $$$\beta$$$ are regularization parameters, $$$\mathcal{R}\mathbf{x}=T_{i}\mathbf{x}_i$$$ is the motion-corrected domain, where $$$T_i$$$ is the translation transform that maps the bin image $$$\mathbf{x}_i$$$ to the reference image $$$\mathbf{x}_1$$$ (end-expiration), and $$$\Psi_{\rm t}=\mathbf{x}_1-T_{i}\mathbf{x}_i$$$ is the 1D temporal TV function. The operator $$$\mathbf{E = AFS}$$$ incorporates the sampling matrix $$$\bf{A}$$$ for each bin, Fourier transform $$$\bf{F}$$$ and coils sensitivities $$$\bf{S}$$$. Additionally, a 3) XD-GRASP with intra-bin translational motion correction (TC) representative reconstruction was obtained, which consisted in solving 3) $$$\hat{\rm{\bf{x}}}=\rm{arg}\min\limits_{x}\left\{ \frac{1}{2}\left\|\mathbf{E} \,\mathbf{x}\,-\mathbf{b}\right \|_2^2+\alpha\,\Psi_t(\mathbf{ x})\right\}$$$. These problems were solved with the nonlinear conjugate gradient method.

*In-vivo* free-breathing experiments were performed on seven healthy subjects on a 1.5T scanner (Siemens Magnetom Aera) with 18-channel body and 32-channel spine coils. 3D CMRA bSSFP acquisitions were performed using the following parameters: coronal orientation, FOV=320x320x80-104mm^{3}, resolution=1x1x2mm^{3}, TR/TE=3.6/1.56ms, flip angle=90°, T_{2} preparation (40ms), SPIR-like fat saturation, subject specific mid-diastolic trigger delay, acquisition window ~100ms, 1 spiral interleaf per R-R interval, with acquisition time ~9-12min. For the 2D iNAV acquisition, 14 bSSFP startup echoes were used (same geometry).

1. Remetz M, Cleman M, Cabin H. Pulmonary and pleural complication of cardiac disease. Clinics in Chest Medicine 1989; 10:545-592.

2.
Feng L, Axel L, Chandarana H, *et al.* XD-GRASP:
Golden-angle radial MRI with reconstruction of extra motion-state dimension using
compressed sensing. MRM 2016; 75:775-788.

3.
Piccini D, Feng L, Bonanno G, *et al.* Four-dimensional respiratory motion-resolved
whole heart coronary MR angiography. MRM 2017; 77:1473-1484.

4.
Cruz G, Atkinson D, Buerger C, *et al.*
Accelerated motion corrected three-dimensional abdominal MRI using total
variation regularized SENSE reconstruction. MRM 2016, 75:1484-1498.

5.
Feng L, Chandarana H, Zhao T, *et al.* Golden-angle sparse liver imaging: radial or
Cartesian sampling?. ISMRM 2017; #1285.

6. Asif M, Hamilton L, Brummer, Romberg J. Motion-adaptive spatio-temporal regularization for accelerated dynamic MRI. MRM 2012; 70:800-812.

7.
Henningsson M, Koken P, Stehning S, *et al*.
Whole-heart coronary MR angiography with 2D self-navigated image
reconstruction. MRM 2012; 67:437-445.

8. Prieto C, Doneva M, Usman
M, *et al.* Highly efficient
respiratory motion compensated free-breathing coronary MRA using golden-step
Cartesian acquisition. JMRI 2015; 41:738-746.

Figure 1:
Reformatted
respiratory-resolved (5 bins) reconstructions obtained for one representative
subject using (top) XD-GRASP, (middle) XD-GRASP with intra-bin translational
motion correction (TC), (bottom) proposed XD-ORCCA. Each image shows the right
coronary artery (RCA) and the left anterior descending coronary artery (LAD),
and represents a different respiratory phase: from (left) end-expiration to
(right) end-inspiration. Including TC in XD-GRASP slightly improves the quality
of the respiratory-resolved images. XD-ORCCA improves considerably the visibility
and sharpness of both coronaries. XD-GRASP provides good quality end-expiration
images, which usually include less respiratory motion. However, the coronary
tree cannot be clearly visualized in near end-inspiration phases.

Figure 2: Fly-through coronal views showing the
end-expiration and end-inspiration respiratory bins obtained with XD-GRASP and
XD-ORCCA for a representative subject (same than figure 1). XD-GRASP provides
end-expiration images with sufficient quality to visualize the coronary
arteries, but end-inspiration images have low quality. XD-ORCCA can provide
very high quality end-expiration and end-inspiration images, allowing a clear
visualization of both coronary arteries.

Figure 3: Example of temporal sparsity achieved with
(left) XD-GRASP and (right) XD-ORCCA. The proposed XD-ORCCA increases the
sparsity in the respiratory dimension by incorporating translational motion
information into the sparsifying operator along the temporal dimension.

Figure 4: Reformatted
respiratory bin reconstructions obtained for two
representative subjects using XD-GRASP and proposed XD-ORCCA, showing the right
coronary artery (RCA) and left anterior descending coronary artery (LAD). The images
correspond to the bin that typically presents less respiratory motion
(end-expiration, phase 1) and the two bins with largest respiratory motion
(phase 4 and phase 5, end-inspiration). XD-GRASP provides end-expiration images
with good quality, allowing visualization of both coronary arteries. The
proposed XD-ORCCA improves the visibility and sharpness of the coronary tree
for all respiratory bins, particularly for those that have more motion (arrows).

Figure 5: Metrics
for 7 subjects for the XD-GRASP and XD-ORCCA approaches, for phase 1
(end-expiration) phase 4 and phase 5 (end-inspiration). Image
quality was assessed by measuring the (left) average vessel length, vessel
sharpness for (middle) the first 4 cm (right) and full length of the (top) RCA
and (bottom) LAD. Significant
differences (P<0.05) in vessel length and sharpness were observed between
XD-GRASP and XD-ORCCA for both coronaries. No significant differences were
found only in the sharpness of phase 1 images, for the full length of the RCA
(indicated by P=0.1). XD-ORCCA reduces the differences in image quality between
respiratory phase images.