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Keywords:

  • respiratory motion correction;
  • whole-heart CMRA;
  • 3D affine transform;
  • phase reordering

Abstract

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

Purpose

Robust motion correction is necessary to minimize respiratory motion artefacts in coronary MR angiography (CMRA). The state-of-the-art method uses a 1D feet-head translational motion correction approach, and data acquisition is limited to a small window in the respiratory cycle, which prolongs the scan by a factor of 2–3. The purpose of this work was to implement 3D affine motion correction for Cartesian whole-heart CMRA using a 3D navigator (3D-NAV) to allow for data acquisition throughout the whole respiratory cycle.

Methods

3D affine transformations for different respiratory states (bins) were estimated by using 3D-NAV image acquisitions which were acquired during the startup profiles of a steady-state free precession sequence. The calculated 3D affine transformations were applied to the corresponding high-resolution Cartesian image acquisition which had been similarly binned, to correct for respiratory motion between bins.

Results

Quantitative and qualitative comparisons showed no statistical difference between images acquired with the proposed method and the reference method using a diaphragmatic navigator with a narrow gating window.

Conclusion

We demonstrate that 3D-NAV and 3D affine correction can be used to acquire Cartesian whole-heart 3D coronary artery images with 100% scan efficiency with similar image quality as with the state-of-the-art gated and corrected method with approximately 50% scan efficiency. Magn Reson Med 71:173–181, 2014. © 2013 Wiley Periodicals, Inc.

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 [4]. 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 [5]. 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 [8]. The transformations are then applied in the following CMRA scan, resulting in significantly higher scan efficiency but similar image quality [9], 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 [10]. 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 [11] and susceptibility to errors of the density compensation function [12].

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 [13], 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.

METHODS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

3D Navigator Image and Coronary MRA Phase Ordering

In total five respiratory bins were prospectively defined by the 1D-NAV, where bin one contained data acquired in end-expiration and bin five data in end-inspiration. Bin one to four were evenly spaced, each comprising 5-mm diaphragmatic motion, while the fifth bin contained the remaining end-inspiratory breathing positions. For every respiratory bin a fully sampled low-resolution 3D-NAV image and a high resolution but under-sampled CMRA image was acquired using Cartesian k-space sampling. 3D-NAV image data was generated from the startup profiles of the high-resolution 3D balanced steady-state free precession sequence. Both 3D-NAV and CMRA were acquired with a Cartesian “spiral like” k-space trajectory in phase and slice encoding directions. Because startup profiles were used to generate the navigator images, the 3D-NAV acquisition had the same imaging parameters, such as field-of-view (FOV), flip angle, echo time (TE) and repetition time (TR) as the high-resolution CMRA acquisition. The only difference between the 3D-NAV and CMRA acquisitions was the k-space phase ordering. The phase encoding order of the 3D-NAV acquisition used a low–high phase encoding order, acquiring the centre of k-space at the start and increasing the phase encoding steps in a spiral like fashion in subsequent shots for each respiratory bin as shown in Figure 1. To ensure that the centre of k-space contained as little respiratory motion as possible, the same approach was utilized for the CMRA acquisition of bin, one which was defined at end-expiration. All other CMRA bins (bin 2–5) were acquired with a similar but reversed (high-low) phase encoding order and with the phase encoding steps incremented irrespective of the bin position (bin 2–5). All 3D-NAVs were reconstructed to the same spatial resolution as the CMRA data using zero-padding. Figure 2 illustrates the k-space sampling strategy both for the 3D-NAV and CMRA acquisition depending on the respiratory bin and by pixel-wise combination of the CMRA data from all bins the fully sampled, high-resolution dataset was reconstructed.

image

Figure 1. Cartesian trajectory used for the 3D-NAV and end-expiratory 3D CMRA bin, with spiral-like phase encoding steps (ky, kz). The first k-space shot is acquired in the center of k-space (highest signal intensity). Subsequent shots sample higher k-space data on a spiral trajectory (correspondingly lower signal intensity) also indicated by the dotted spiral arrow. For CMRA bin 2–5, a similar but reversed spiral like k-space trajectory was used.

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image

Figure 2. Schematics of 3D-NAV and CMRA acquisition. The distribution of the data in the respiratory cycle, as measured by the diaphragmatic 1D-NAV, (a) from end-expiration (bin 1) to end-inspiration (bin 5) defines amount of data in each bin. The k-space maps (ky−kz) of the 3D-NAV (b) and CMRA (d) acquisitions show how the k-space ordering differs between the two acquisitions. 3D-NAV is always fully sampled, as the reconstructed images show (c), however, the resolution of the acquisition depends on the amount of data in the bin. CMRA bin 1 is acquired with a similar strategy to ensure that the centre of k-space is acquired in the most quiescent respiratory phase, and CMRA bin 2–5 are used to acquire the high-resolution data. By summing all the CMRA bins, the high-resolution (uncorrected) dataset is generated.

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1D Translational Intra-Bin and 3D Affine Inter-Bin Motion Correction

Before 3D affine correction was performed, the 3D-NAV and CMRA images in the different respiratory bins were corrected with an intra-bin translational correction in FH direction using a subject specific tracking factor. This intra-bin correction was performed to minimize the distribution of the profiles within each 5 mm window. k-space profiles for 3D-NAV and CMRA images were retrospectively registered to a reference point in each bin. The reference point within each bin was selected as the average 1D-NAV position in that bin. Translational correction was performed in FH (readout) direction using the 1D-NAV positions, which allowed calculating a linear phase modulation which was applied to the acquired k-space samples, shifting them to their respective reference points (Fig. 3). A subject specific correction factor was calculated using the 3D-NAV acquisitions which traverse the centre of k-space (i.e., the first shot of each bin—3D-NAV0) and their corresponding 1D-NAV positions. For this purpose, translational FH motion was measured from the 3D-NAV0 images using a template matching algorithm, with the template manually defined covering the base of the heart. 3D-NAV0 from bin 1 was defined as the reference to which the 3D-NAV0 images from the other bins were registered. Figure 3 gives a schematic overview of the translational FH motion correction procedure.

image

Figure 3. Schematics of the translational FH correction procedure for the intra-bin motion. The 3D-NAV acquisition containing the central profile (3D-NAV0) was used to extract FH motion which was correlated with the associated 1D-NAV acquisitions using linear regression. The slope of the line was then defined as the subject specific correction factor. Acquired 1D-NAV values for each bin was used, together with the subject specific factor, to retrospectively correct for the FH motion within each bin. This effectively reduces the FH distribution of respiratory positions within a bin to a single point. Only uncorrected and corrected 3D-NAV images are shown here, however, the same correction was performed for the CMRA images as well. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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A 3D affine transformation is a 12 parameter model which describes rotation, scaling, shear, and translation in three dimensions. The 3D affine transformation A can be written as

  • display math(1)

which maps the 3D coordinate X to X′ as

  • display math(2)

The affine transformation parameters for the inter-bin correction were calculated using a MATLAB implementation of the image-based registration algorithm described by Rueckert et al. [14] using cross correlation as similarity measure and cubic interpolation. The 3D affine motion correction was applied in image space, similar to that described by Bhat et al. [10], with the main difference being that in our implementation fully sampled Cartesian low-resolution 3D-NAV images were used to generate the affine transformations. 3D-NAV images from bin 2–5 were registered to the end-expiratory bin 1, and the resulting transformations were applied to the corresponding CMRA images. Finally, the transformed CMRA images from the different bins were combined by a pixel-wise summation to generate a final high-resolution CMRA image. Figure 4 shows a schematic overview of the acquisition and post processing steps of the 3D-NAV and CMRA acquisition.

image

Figure 4. Schematics of the image acquisition and post processing procedures. The bins are prospectively defined by the diaphragmatic 1D-NAV during the data acquisition. The 1D-NAV values are used together with the subject specific tracking factor to perform 1D translational intra-bin motion correction in feet-head (FH) direction. Each bin and coil is reconstructed using an inverse fast Fourier transform (IFFT). The 3D-NAV images are used to calculate affine 3D transformations by registering 3D-NAV bin 2–5 to bin 1. The calculated 3D affine transformations are thereafter applied to the corresponding CMRA bins, and the motion corrected image is acquired by a pixel-wise summation of all bins and coils. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Simulations

The accuracy of the proposed motion correction approach is largely related to the spatial resolution of the navigators at each respiratory bin. If there is only a small amount of data in a certain respiratory bin, the 3D-NAV acquisition will have a relatively low spatial resolution, and accurate respiratory transformations may be difficult to calculate for such a bin. To evaluate the robustness of the proposed approach for respiratory motion estimation with different amounts of data per bin, a simulation experiment was performed. In the simulations, we used a high-resolution dataset acquired with a 7-mm gating window and a FH tracking factor of 0.6, which was defined as the motion free reference image. The resolution of the reference image was constant during the simulation experiment, however, the resolution of the target image (i.e., equivalent to 3D-NAV) was adjusted to investigate the effect of navigator resolution on the motion measurement accuracy. To simulate respiratory motion, two different 3D affine motion transformations from end-expiration to end-inspiration (as measured by the affine registration in two healthy subjects, described in the previous section) were applied to the target image. The 3D affine transformations ArefX had the following values:

  • display math
  • display math

The target image was generated from the same data as the reference but had a lowered spatial resolution. This was done by successively reducing the resolution of the target dataset in a reversed fashion to how the 3D-NAV images were acquired (i.e., reversed spiral like trajectory in phase and slice encoding direction). For the in vivo experiments 10 startup profiles were acquired per shot and contributed to the 3D-NAV data, therefore, we subtracted 10 k-space lines from the target image per iteration in the simulations. The simulation procedure consisted of the following steps: (i) successive downsampling of the target image spatial resolution, (ii) application of 3D affine transformation, ArefX, to target image, (iii) 3D affine image registration of target to reference image, yielding the estimated 3D affine motion ÂrefX, (iv) application of ArefX to reference image, yielding I, (v) application of ÂrefX to the reference image, yielding Î, and (vi) calculating the normalized cross-correlation (NCC) between I and Î. The simulation procedure is illustrated in Figure 5.

image

Figure 5. Schematics of the simulation experiments. First, a high resolution, motion free, reference image (REF) was downsampled by successively removing high-resolution data in a reversed fashion to how the 3D-NAV was sampled. Second, a 3D affine transformation ArefX was applied to the downsampled image to generate the target (TAR) image. The TAR was registered back to the REF to estimate the 3D affine transformation ÂrefX. The difference between ArefX and ÂrefX is proportional to the downsampling of the REF image. To parameterize this difference, the NCC was calculated between REF which had been transformed by ArefX and REF transformed by ÂrefX.

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In Vivo Experiments

Seven healthy adult subjects (27±7 years) were scanned on a Philips 1.5 T Achieva scanner (Philips Healthcare, Best, NL). All volunteers provided written consent before undergoing MRI and the study was approved by the institutional review board. Balanced steady-state free precession imaging parameters for the volunteer experiments included FOV=280 × 280 × 90–120 mm, voxel size=1 × 1 × 2 mm, TE/TR=4.6/2.3 ms, flip angle=70° and coronal orientation. A five element cardiac coil array was used for signal detection. For every volunteer one CMRA dataset was acquired with the proposed correction method and one with a 1D-NAV with 7 mm gating and a tracking factor of 0.6. As motion correction was performed retrospectively for the dataset acquired with 100% gating efficiency, it was also reconstructed with no motion correction for comparison. Before the CMRA scan, a subject specific trigger delay and acquisition window was defined for the mid-diastolic rest period from a 2D cine acquisition. Ten startup profiles were used for all whole-heart coronary scans, and for the proposed motion correction approach these acquired profiles contributed to the 3D-NAV data. For the CMRA acquisition, approximately 20–28 profiles were acquired in every shot depending on the subject specific duration of the mid-diastolic rest period. All reconstructed images were reformatted and visualized with dedicated post processing software [15]. Vessel sharpness and vessel length was measured for the right coronary artery (RCA) and left anterior descending artery of all reconstructed datasets. The differences of the quantitative measurements were tested for statistical significance with a paired student t-test using a P threshold of 0.05. A visual score was given for the RCA and LAD of each dataset using a four-point scale: 1—poor, 2—fair, 3—acceptable, and 4—excellent coronary vessel delineation [16]. The images were graded by an expert observer and all images were anonymized and randomized before the review process. A Wilcoxon signed-rank test was used to test the qualitative measurements for statistical significance, with a P threshold of 0.05.

RESULTS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

Simulations

The NCC between a high-resolution dataset transformed with reference 3D affine transformations and estimated 3D affine transformations, as a function of the number of shots used to estimate the 3D affine transformation, is shown in Figure 6. The results in Figure 6 are average values for two different 3D affine transformations. A high NCC (>0.85) was observed when more than 15 shots were employed for the motion estimation. At least 40 shots were necessary to ensure a NCC of more than 0.95.

image

Figure 6. NCC between images transformed with 3D affine reference motion and estimated motion, as a function of the number of shots in the image from which the estimated 3D affine motion was calculated.

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Coronary MRA

All in vivo scans were completed successfully and respiratory motion corrected angiograms were generated using the proposed technique. Table 1 shows statistics from the seven healthy subject scans, including scan time for the 7-mm gated scans and the un-gated scans, navigator gating efficiency for the gated scans and the calculated FH correction factors for diaphragmatic motion correction. Averaged 12 parameter 3D affine matrices, ±standard deviation, are shown in Table 2 for respiratory bin 2–5 (bin 1 was the identity matrix). The respiratory gated scans resulted in approximately 2-fold increased scan time, compared with the scans acquired without gating. Figure 7 shows reformatted CMRA images of the RCA and LAD from four healthy subjects using either the 1D-NAV with a 7-mm gating window and slice tracking (Fig. 7 top row), the proposed 1D translational intra-bin+3D affine inter-bin motion correction with no gating (Fig. 7 middle row), and no correction and no gating (Fig. 7 bottom row). The results of the vessel sharpness, vessel length, and visual score are shown in Figure 8, where a statistically significant result (P<0.05) is denoted by *. Both LAD vessel sharpness, vessel length and visual score were significantly increased after applying the proposed motion correction procedure compared with the un-gated and uncorrected data, whereas only vessel length was increased for the RCA for the comparison of corrected versus uncorrected for the un-gated scans. For the comparison of the 7-mm gated scan and 1D-NAV, FH motion correction versus un-gated and uncorrected scan statistically significant differences were found for the vessel length of the RCA and visual score of the LAD. However, no statistically significant differences were found for the 7-mm gated scan and the un-gated scan using the proposed method for respiratory motion correction.

image

Figure 7. Example images of the RCA and left anterior descending artery from four healthy volunteers using 7-mm gated reference and slice tracking with the 1D-NAV, 1D translational intra-bin correction and 3D affine inter-bin motion correction without respiratory gating using the proposed approach (1D+3D MC), or no gating and no correction (NC). NE=navigator efficiency.

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image

Figure 8. Quantitative and qualitative results from the healthy volunteer study. Statistically significant differences (P<0.05) are denoted by *. 1D-NAV=respiratory gating (7-mm window) and motion correction in FH using diaphragmatic 1D-NAV; 1D+3D MC=1D translational and 3D affine correction without respiratory gating; NC=no motion correction and no gating.

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Table 1. Scan Statistics for the Seven Healthy Subjects (S1–7)
 7-mm gatingNo gating
 Scan time (s)NAV efficiency (%)Scan time (s)Correction factor
S1621684330.64
S21386375680.38
S31059525130.55
S41234495640.71
S5863504680.46
S61360436310.61
S71130495340.53
AVG±STD1093±27549±10530±660.55±0.11
Table 2. Twelve Parameter 3D Affine Transformations for Respiratory Bins 2–5 (Bin 1 Was the Identity Matrix) for the Seven Healthy Volunteers, Reported as Average±Standard Deviation
 3D rotation, scaling and shear3D translation
  1. The nine 3D rotational, scaling, and shearing values for each bin correspond to the nine affine coefficients A00-33 in Eq. (1), while the 3D translation values correspond to the affine coefficients Tx, Ty, and Tz, respectively in Eq. (1).

Bin 2 (n=7)1.022±0.005−0.003±0.005−0.051±0.0113.106±0.327
0.000±0.0040.993±0.004−0.006±0.0040.219±0.634
0.000±0.0010.002±0.0031.005±0.0020.222±0.242
Bin 3 (n=7)1.037±0.010−0.005±0.010−0.085±0.0265.345±0.220
−0.004±0.0050.989±0.004−0.009±0.0120.355±0.716
0.001±0.0020.003±0.0041.006±0.0030.312±0.355
Bin 4 (n=6)1.039±0.016−0.007±0.011−0.116±0.0307.040±0.204
−0.006±0.0080.975±0.012−0.101±0.0120.962±0.842
0.003±0.0060.004±0.0021.007±0.0010.708±0.196
Bin 5 (n=5)1.042±0.014−0.006±0.013−0.119±0.03510.05±0.413
−0.006±0.0100.971±0.014−0.131±0.0191.051±0.952
0.004±0.0050.006±0.0041.009±0.0031.066±0.429

DISCUSSION

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

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 [17] 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 [10] or Cartesian acquisition and non-rigid correction [20], 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. [10] 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.

REFERENCES

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES