Several studies have demonstrated that three dimensional (3D) affine transformations can be used to accurately model the deformation of the heart throughout the respiratory cycle [1-3]. Applying such a model to coronary MR angiography (CMRA) acquisitions could allow for image acquisitions throughout the whole respiratory cycle, and subsequently allow shortening the scan time compared with end-expiration gated acquisitions which are still the most commonly used approach. The currently used methods typically employ a linear rigid body translational motion model to correct for foot-head (FH) motion, only accepting image data which has been acquired during end-expiration . This often leads to a prolonged scan time and residual respiratory motion in some subjects. The motion measurement is typically performed using a 1D navigator (1D-NAV) positioned on the right hemi-diaphragm and requires a correction factor that relates diaphragm to heart motion, which is usually assumed to be 0.6 . Subject specific factors have been shown to improve motion correction [6, 7]. One method to incorporate 3D affine motion correction involves acquiring low-resolution 3D single-shot images in a pre-scan, using image registration and interpolation to create affine states for any 1D-NAV position in the respiratory cycle . The transformations are then applied in the following CMRA scan, resulting in significantly higher scan efficiency but similar image quality , however this method is unable to account for any differences in respiratory pattern between the calibration scan and the CMRA scan. Another approach uses the image data itself, and with a scan efficiency of 100% creating under-sampled radial images for different respiratory bins from end-expiration to end-inspiration . As a 3D radial trajectory is used, the centre of k-space is sampled for all bins, however, k-space may be unevenly under-sampled depending on the distribution of the acquired profiles in the respective bins. Despite the undersampling, image quality was found to be sufficient to generate a 3D affine transformation for each bin with respect to the end-expiratory bin. After the transformations have been applied all bins are combined to produce high-resolution CMRA image, which shows similar image quality as images acquired with the previously mentioned standard approach with 6-mm gating window. The drawback of this approach is that radial trajectories intrinsically have a lower signal-to-noise ratio compared with Cartesian trajectories  and susceptibility to errors of the density compensation function .
In this work, we propose a respiratory motion correction strategy with 100% gating efficiency for Cartesian whole-heart CMRA. This is accomplished by encoding the startup profiles of a balanced steady-state free precession sequence to build fully sampled 3D navigator (3D-NAV) images for different bins, where each bin represents a state in the respiratory cycle. Compared with previous work where low-resolution 2D navigator images were acquired using the startup profiles in a beat-to-beat fashion , the binning mechanism allows for the acquisition of 3D images at different motion states with higher resolution. By means of image registration 3D affine transformations can be computed between the end-expiratory 3D-NAV image and all other 3D-NAV images. The calculated 3D transformations are subsequently applied to the respective CMRA acquisitions which have been similarly assigned to different respiratory bins.
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In this work, a novel respiratory motion correction approach for whole-heart CMRA was implemented and evaluated. The proposed method with 100% gating efficiency performs equally well compared with the commonly used diaphragmatic navigator with a gating window of 7 mm and slice tracking factor of 0.6. On average, the method leads to a reduction in scan time by a factor of two in healthy subjects with the previously mentioned imaging parameters, compared with the 7-mm respiratory gated scans. By incorporating parallel imaging with an acceleration factor of 2  the whole-heart acquisition could reasonably be performed in 4–5 min with the proposed method without compromising image quality compared with a gated coronary artery scan.
The simulation experiment demonstrated that a minimum of 10–15 shots are necessary, per respiratory bin, to ensure that reliable 3D affine motion estimation is obtained from the 3D-NAV. In this work, all data were used (i.e., 100% respiratory efficiency), however, image quality may be improved by re-acquiring data which has been acquired in a respiratory bin containing less than 15 shots. Two of seven volunteers had end inspiratory bins which contained less than 15 shots. Nevertheless, 15 shots correspond to approximately 3% of the total amount of data, and with the proposed strategy, would contain mainly high-resolution data. Therefore, this data could potentially be rejected without causing significant undersampling artefacts. A further option could be to discard data from bins with insufficient 3D-NAV accuracy and estimate the gaps in k-space using compressed sensing reconstruction [18, 19].
Compared with other recently developed motion compensation methods which achieve 100% gating efficiency using either radial acquisition and affine correction  or Cartesian acquisition and non-rigid correction , the proposed method uses a Cartesian trajectory with 1D translational intra-bin and 3D affine inter-bin correction. The intra-bin correction is performed on a beat-to-beat basis to minimize respiratory motion artefacts within each bin and is particularly important for Cartesian k-space trajectories which are more sensitive to motion than radial or spiral trajectories. Compared with the approach proposed by Bhat et al.  where the undersampled radial image acquisitions at different respiratory bins are used to estimate the respiratory motion, here we use fully sampled Cartesian 3D-NAV images for this purpose. 3D respiratory motion transformations could be robustly and accurately estimated with a relatively small amount of data in each bin and independently of the breathing pattern, as demonstrated in the simulation experiment. Furthermore, because a Cartesian acquisition was used, a fast inverse Fourier transform reconstruction, in conjunction with affine motion correction, could be applied and thus the post-processing was not computationally expensive and could be performed on a standard workstation in approximately 5 min using MATLAB. In addition, the proposed method did not add any complexity or modification to the CMRA image acquisition because the 3D-NAV images were generated from the startup profiles. In the current implementation, the diaphragmatic 1D-NAV is still necessary to prospectively bin the 3D-NAV and CMRA acquisition, and also for the 1D translational intra-bin correction. Therefore, the respiratory binning mechanism is susceptible to errors due to any hysteresis between the heart and diaphragm during inspiration and expiration. A potential solution to this problem could be to utilize a respiratory navigator that measures the motion directly on the heart [21-23], which would also circumvent the need for a subject specific tracking factor for the 1D intra-bin correction. The use of prospective binning results in different 3D-NAV spatial resolution for each bin depending on the breathing pattern of the examined subject. The 3D-NAV resolution is always directly proportional to the amount of CMRA data in each bin, therefore, even with different breathing patterns this will result in higher 3D-NAV resolution and subsequently better motion correction for bins with a larger amount of data. However, respiratory drift may cause significant non-rigid deformation within a certain respiratory bin, which the inter-bin affine correction would be unable to compensate for and this is a limitation of the proposed approach.
A further limitation of the proposed motion correction approach is that the data acquisition is performed with a spiral-like phase encoding trajectory, which is typically not used for CMRA acquisitions. Although it can be exploited to ensure that the 3D-NAV images are fully sampled, and that bin 1 of the high-resolution CMRA data is acquired in end-expiration, it has the adverse effect of reducing the effect of the pre-pulses, particularly the fat suppression due to the fast T1 recovery of the fat signal. Cartesian CMRA acquisitions often use a low–high phase encoding scheme whereby the center of k-space, which contains most of the image contrast information, is acquired early in the 100–130 ms data acquisition window and the outer part of k-space is acquired at the end of the acquisition window. In contrast, with the spiral like phase encoding trajectory used here, the center or outer part of k-space will be acquired throughout the whole acquisition window depending on the respiratory position. However, this unconventional phase encoding scheme is more robust toward respiratory motion because the center of k-space is acquired during end-expiration, which is the most quiescent respiratory phase. Therefore, even without gating and without correction the resulting measurements for RCA and LAD vessel sharpness and LAD vessel length were not statistically different from the case of 1D-NAV motion correction and 7-mm gating.
In conclusion, 3D affine respiratory motion transformations can be extracted from 3D-NAV image acquisitions and applied to un-gated whole-heart CMRA scans, which reduces the scan time by a factor of approximately two compared with 7-mm gated scans, without compromising image quality.