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(Radiology. 2000;215:600-607.)
© RSNA, 2000

Technical Developments

Breath-Hold Three-dimensional Contrast-enhanced Coronary MR Angiography: Motion-matched k-Space Sampling for Reducing Cardiac Motion Effects1

Yi Wang, PhD, Priscilla A. Winchester, MD, Lawrence Yu, MD, Richard Watts, PhD, Guangliang Ding, PhD, Howard M. Lee, MD and Geoffrey W. Bergman, MD

1 From the Department of Radiology MR Research, Weill Medical College of Cornell University, 515 E 71st St, Suite S120, New York, NY 10021. From the 1998 RSNA scientific assembly. Received February 2, 1999; revision requested May 4; final revision received August 6; accepted August 30. Supported in part by research grants from the Whitaker Foundation, Epix Medical, and Berlex Laboratories. Address correspondence to Y.W. (e-mail: yiwang@mail.med.cornell.edu).


   Abstract
TOP
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
A view order that matches k-space sampling to cardiac motion within the acquisition window was developed for breath-hold three-dimensional contrast material–enhanced coronary magnetic resonance angiography. In vivo experiments in seven volunteers demonstrated that blurring was substantially reduced with this motion-matched view order as compared with the standard centric view order. Coronary arteries were well delineated.

Index terms: Coronary vessels, MR, 54.12142, 54.12143 • Magnetic resonance (MR), vascular studies, 54.121416, 54.12142


   Introduction
TOP
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Magnetic resonance (MR) imaging is a promising noninvasive technique for imaging of the coronary arteries, but its usefulness is limited by its variable image quality (1–23). Motion due to cardiac contraction and respiration is the primary cause of image quality degradation (1,3,10). Previous work on reducing motion effects in coronary MR angiography was focused on respiration effects (8–15,17–20,23). To date, to our knowledge, there is little work that addresses cardiac motion effects in coronary MR angiography.

In most coronary MR angiographic techniques, a 100–150-msec acquisition window is used in the cardiac cycle (4,7,15–23). There can be substantial cardiac motion within this period for many patients. The quiescent middiastolic period in the cardiac cycle depends on the patient pathophysiology and varies from 60 to 300 msec (24). The cardiac motion of coronary arteries can be complex, and corresponding effects in coronary MR angiography can be difficult to suppress. We propose a cardiac view ordering technique that reduces cardiac motion effects by matching k-space sampling with motion amplitude. In this study, we used a simple matching criterion that the center of k space, where the majority of MR signal resides, is sampled during the quiescent middiastolic period, and the edge of k space is sampled before and after middiastole.

Other limitations of current coronary MR angiography are the poor signal-to-noise ratio or long imaging time. Contrast agents that enhance the T1 of blood can be used to generate high and reliable vascular signal (25,26). Breath-hold three-dimensional (3D) coronary MR angiographic techniques have been reported recently with use of gadolinium-based contrast agents (27–31). Because the sum of quiescent middiastolic periods from all heartbeats in a breath hold is quite small (relative to the breath-hold duration), a 3D acquisition of an appropriate matrix that encompasses a major portion of the coronary tree with adequate spatial resolution requires data collection outside the quiescent middiastolic period (27–32). Unfortunately, this may lead to substantial cardiac motion artifacts. In this study, the motion-matched k-space sampling technique was applied to breath-hold 3D contrast material–enhanced coronary MR angiography to reduce cardiac motion effects. This article reports the feasibility of this motion-matched k-space sampling technique.


   Materials and Methods
TOP
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 Appendix
 References
 
It is known that the effects of motion introduced at the center of k space are much more severe than those of the same motion introduced at the edge of k space (33–35, Appendix). This is true for large objects such as the cardiac chambers with frequency spectra that consist primarily of low spatial frequencies. This is also true for small objects such as coronary arteries and stenoses with spatial frequency spectra (approximately sinc function) peaked at the center of k space. To minimize cardiac motion effects, acquisition of the center of k space at coronary MR angiography should be performed when cardiac motion is minimal. This forms the foundation of our motion-matched k-space sampling approach.

Cardiac Motion-matched k-Space Sampling
The following implementation of cardiac motion-matched k-space sampling was used in this preliminary study of 3D contrast-enhanced coronary MR angiography. In each heartbeat, data acquisition started at the edge of k space and moved toward the center of k space. The center of k space was sampled during middiastole where coronary motion is minimal. Then data acquisition moved back to the edge of k space at the later echoes. In this study, k space referred to the space spanned by ky (phase encoding) and kz (section encoding).

All points in k space to be sampled were sorted according to their frequency radius: kr = {surd}(ky2 + kz2) (36). This was implemented by generating a sequence {(ky, kz)} ordered according to ascending kr (37). Elements (ky, kz) with equal kr were ordered according to descending kz and ascending ky at each kz. View ordering was then achieved by accessing the index to this ordered sequence during data acquisition.

The group of points for the center of k space (the first 25% of points in the sequence) was acquired at middiastole. The remaining points for the edge of k space (the last 75% of points in the sequence) were partitioned into an odd-indexed group and an even-indexed group. The odd-indexed group was sampled in an edge-to-center order immediately before the center k-space acquisition, and the other group was sampled in a center-to-edge order immediately after the center k-space acquisition (Fig 1a).



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  		Figure 1a. Motion-matched k-space sampling for contrast-enhanced coronary MR angiography. (a) Schematic shows data acquisition (large gray box) starts at the edge of k space and moves toward the center of k space, which is acquired during middiastole where coronary motion is minimal, and then moves back to the edge of k space. Before data acquisition, disdaqs and fat saturation are used to condition spin. ECG = electrocardiography. (b) Graph depicts overview of motion-matched k-space sampling for a 3D acquisition with a 256 x 128 x 16 matrix. Data acquisition is completed in 32 heartbeats (a breath-hold length). Over the 32 heartbeats, the center of k space is acquired in an edge-center-edge manner, and the edge of k space is acquired in a sequential manner (Appendix).

 


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  		Figure 1b. Motion-matched k-space sampling for contrast-enhanced coronary MR angiography. (a) Schematic shows data acquisition (large gray box) starts at the edge of k space and moves toward the center of k space, which is acquired during middiastole where coronary motion is minimal, and then moves back to the edge of k space. Before data acquisition, disdaqs and fat saturation are used to condition spin. ECG = electrocardiography. (b) Graph depicts overview of motion-matched k-space sampling for a 3D acquisition with a 256 x 128 x 16 matrix. Data acquisition is completed in 32 heartbeats (a breath-hold length). Over the 32 heartbeats, the center of k space is acquired in an edge-center-edge manner, and the edge of k space is acquired in a sequential manner (Appendix).

 
The motion-matched k-space sampling for a 128 x 16 kykz matrix is summarized in Figure 1b. During the breath hold, the center of k space was sampled in an edge-center-edge manner, and the edge of k space was sampled in a sequential manner (Fig 1b). This was done to minimize effects of respiratory motion and variation in contrast material concentration that may occur during the breath hold and to ensure the center of k space was acquired when the contrast enhancement was maximal. We refer to the k-space sampling order outlined in Figure 1 as the "cardiac motion-matched" view order. The algorithm in C routine for generating this view order is detailed in the Appendix.

Imaging Parameters
Experiments were performed with a 1.5-T whole-body MR imager equipped with a fast gradient system (EchoSpeed Signa; GE Medical Systems, Milwaukee, Wis) that rises to 2.2 G/cm in 0.184 msec. A four-element receive-only phased-array surface coil (Torso Array [32-cm]; GE Medical Systems) was used for signal reception. The schematic of the coronary MR angiographic technique with motion-matched k-space sampling is shown in Figure 1.

For data acquisition, a 3D fast gradient-echo sequence was implemented with the capability of orienting sections in double-oblique directions, which allowed imaging of long segments of coronary arteries in a thin volume (9). Thirty disdaqs (executions of the pulse sequence with data acquisition disabled) and fat suppression were used before data acquisition to prepare spins into an equilibrium state (Fig 1a). Data acquisition of a 256 x 128 x 16 matrix was completed in 32 heartbeats. Sixty-four echoes were acquired in each heartbeat during diastole after the T wave on the electrocardiogram. The first echo was delayed from the electrocardiographic trigger by 500 msec for a 60–beats per minute heart rate, and the delay varied between 400 and 600 msec for heart rates between 75 and 45 beats per minute.

With a 24-cm field of view, 2-mm section thickness, 64-kHz receiver bandwidth, and 60% fractional echo, repetition time was 5.2 msec and echo time was 1.3 msec (5.2/1.3) for double-oblique orientation, which led to a 333-msec data acquisition period in each cardiac cycle (approximately one-third of the cardiac cycle for a heart rate of 60 beats per minute). A minimal phased Shinnar-Le-Roux radio-frequency pulse (1.6-msec duration and 7.232-kHz bandwidth) with a 25° flip angle (approximately the Ernst angle of enhanced blood) was used for data sampling.

Coronary MR angiography was performed with seven healthy volunteers (one woman and six men; age range, 25–34 years; mean age, 29 years; heart rate range, 50–70 beats per minute). The institutional review board approved this study, and all subjects provided informed consent. The imaging protocol consisted of (a) nonenhanced breath-hold two-dimensional (2D) coronary MR angiography to identify section orientation; (b) a timing acquisition to detect the arrival time after injection of a contrast material bolus in the ascending aorta, which was used to start 3D contrast-enhanced coronary MR angiography; and (c) breath-hold 3D contrast-enhanced coronary MR angiography with motion-matched k-space sampling.

The imaging parameters for breath-hold 2D coronary MR angiography were 9.5/2.3, 16 echoes per heartbeat, 5-mm section thickness, 16-kHz receiver bandwidth, 20° flip angle, centric view order, and 152-msec data acquisition duration in the cardiac cycle. The timing acquisition was performed with a 2D fast gradient-echo sequence (one frame per second) and 2–3 mL of gadodiamide (Omniscan; Nycomed Amersham, Princeton, NJ) injected at 1 mL/sec. Breath-hold 3D contrast-enhanced coronary MR angiography was performed with 20-25 mL of gadodiamide injected at 1 mL/sec. Data acquisition began when the contrast material bolus arrived at the ascending aorta. The imaging volume was oriented in the double-oblique plane (1,9,29). One volume that encompassed the atrioventricular groove (caudal left anterior oblique view) was used to image the right coronary artery and the left circumflex coronary artery. Another volume that encompassed the anterior interventricular groove (cranial left anterior oblique view) was used to image the left main coronary artery and the left anterior descending coronary artery (LAD). In two of the seven volunteers, two injections separated by 5-10 minutes were used to acquire the two volumes.

Evaluation of Cardiac Motion-matched View Order versus Standard Centric Order
In five of the seven volunteers, the effectiveness of motion-matched k-space sampling was evaluated by performing breath-hold 3D contrast-enhanced coronary MR angiography with both cardiac motion-matched and standard centric view orders. Two injections were separated by 10–15 minutes to minimize possible interference between injections.

With the standard centric view order, data are sampled in each heartbeat by starting from the center of k space and moving toward the edge of k space. This view order is commonly used in 3D coronary MR angiography (3,6,10,13,15,17,20–23,27-32). The cardiac motion-matched view order was acquired before the standard centric view order in three volunteers and after it in the other two volunteers. Three-dimensional contrast-enhanced coronary MR angiograms were viewed on a computer console with maximum intensity projection (MIP) and multiple planar reformatting. No image editing, such as manual removal of the chamber blood signal intensity, was used.

Both cardiac motion-matched and standard centric view-ordered 3D coronary MR images (both MIP and individual section images) were presented side by side to one radiologist (H.M.L.) and one physicist (Y.W.), who were experienced with coronary MR imaging. Both readers were blinded to the acquisition view order. The comparison results were quantified by means of consensus rating of the overall quality of the delineation of the coronary arteries, taking into account the sharpness of the coronary arteries. A relative scale was used in which one acquisition was interpreted as markedly better (++), modestly better (+), about the same (0), modestly worse (-), or markedly worse (--) than the other. The consensus score was reached in the following manner: First, two cases were scored by the two readers in joint session to calibrate their rating scale; then the other three cases were scored independently; and, finally, the independent scores were compared and their differences were resolved in a second joint session. The Wilcoxon paired sample signed rank test was performed on the ordinal scores to assess the statistical significance of the comparison evaluation (38).


   Results
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 Appendix
 References
 
Figure 2 demonstrates images of one section that contains the root of the right coronary artery and a cross section of the LAD from a double-oblique 3D volume (Fig 2a, nonenhanced; Fig 2b, contrast enhanced). The background signal was saturated by means of spin preparation; inflow effects still caused high ventricular signal in sections near the surface of the imaging volume. Contrast material provided strong vascular signal.



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  		Figure 2a. Subject 1. Caudal left anterior oblique (a) nonenhanced and (b) contrast-enhanced breath-hold 3D MR angiograms were obtained with motion-matched k-space sampling of identical sections that contain the root of the right coronary artery. In b, contrast material delineates the proximal right coronary artery (left arrow) and the proximal LAD (right arrow).

 


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  		Figure 2b. Subject 1. Caudal left anterior oblique (a) nonenhanced and (b) contrast-enhanced breath-hold 3D MR angiograms were obtained with motion-matched k-space sampling of identical sections that contain the root of the right coronary artery. In b, contrast material delineates the proximal right coronary artery (left arrow) and the proximal LAD (right arrow).

 
Findings in the comparison study are summarized in the Table. For subjects 1–3, the independent scores were the same for both readers. In all five cases, coronary arteries were substantially better depicted with the cardiac motion-matched view order than with the standard centric view order (P = .05, Wilcoxon test). There was only a slight difference in the background signal intensity between the two injections (average background region-of-interest ratio for the first and second injections, 0.9 [Table]). With both injections, background signal intensity (epicardial fat and myocardium next to the proximal coronary arteries) was substantially weak compared with blood signal intensity and was not a factor that affected detection of coronary arteries (Figs 2–5).


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  		Summary of Experiments to Compare Cardiac Motion-matched versus Standard Centric View Orders
 


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  		Figure 3a. Subject 2. Caudal left anterior oblique (a) centric and (b) cardiac motion-matched 3D contrast-enhanced MR angiograms of identical section show the right coronary artery (left arrow) and LAD (right arrow). Depiction in b was rated substantially better than that in a.

 


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  		Figure 3b. Subject 2. Caudal left anterior oblique (a) centric and (b) cardiac motion-matched 3D contrast-enhanced MR angiograms of identical section show the right coronary artery (left arrow) and LAD (right arrow). Depiction in b was rated substantially better than that in a.

 


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  		Figure 4a. Subject 5. Cranial left anterior oblique MIP images from (a) centric and (b) cardiac motion-matched 3D contrast-enhanced MR angiograms. The overall quality of the LAD (arrow) was rated substantially better in b than in a.

 


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  		Figure 4b. Subject 5. Cranial left anterior oblique MIP images from (a) centric and (b) cardiac motion-matched 3D contrast-enhanced MR angiograms. The overall quality of the LAD (arrow) was rated substantially better in b than in a.

 


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  		Figure 5a. Subject 4. Cranial left anterior oblique (a, b) reformatted and (c) MIP images from a breath-hold 3D contrast-enhanced MR angiogram show the left main coronary artery and LAD (arrow). In a and b, the left main coronary artery and segments of the LAD are well delineated. In c, the whole course of the proximal LAD is depicted.

 


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  		Figure 5b. Subject 4. Cranial left anterior oblique (a, b) reformatted and (c) MIP images from a breath-hold 3D contrast-enhanced MR angiogram show the left main coronary artery and LAD (arrow). In a and b, the left main coronary artery and segments of the LAD are well delineated. In c, the whole course of the proximal LAD is depicted.

 


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  		Figure 5c. Subject 4. Cranial left anterior oblique (a, b) reformatted and (c) MIP images from a breath-hold 3D contrast-enhanced MR angiogram show the left main coronary artery and LAD (arrow). In a and b, the left main coronary artery and segments of the LAD are well delineated. In c, the whole course of the proximal LAD is depicted.

 
The cardiac motion-matched view order was acquired after the standard centric view order in Figure 3 and before the standard centric view order in Figure 4. Figure 3 depicts images of sections at the same location. Blurring of the right coronary artery root and the LAD cross section was substantially reduced with the cardiac motion-matched view order (arrows in Fig 3b) as compared with that of the standard centric view order (arrows in Fig 3a). Note that the difference in the chamber blood depiction between cardiac motion-matched and standard centric view orders is smaller than the difference in the coronary artery depiction; this may be attributed to the large filling motion of chamber blood. Figure 4 depicts MIP images with identical projection angles. Blurring of the LAD was substantially reduced with the cardiac motion-matched view order (arrow in Fig 4b) as compared with that of the standard centric view order (arrow in Fig 4a). Note that the two nonidentical breath holds caused slight variation in background structures in Figure 4, but this is not a factor that contributed to the difference in the sharpness of the LAD in the two MIP images. The LAD segments were contiguously contained in both imaging volumes.

The cardiac motion-matched view-ordered acquisition demonstrated the proximal coronary arteries well in all seven cases. Figure 5 demonstrates another study of the left main coronary artery and LAD with breath-hold 3D contrast-enhanced coronary MR angiography. Images from the double-oblique volume (cranial left anterior oblique view) were reformatted to demonstrate the left main coronary artery (Fig 5a) and the LAD (Fig 5b). A longer segment of the LAD was depicted in an MIP image (Fig 5c).


   Discussion
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
Appendix
 References
 
Our preliminary results demonstrate that motion-matched k-space sampling can reduce cardiac motion effects at breath-hold 3D contrast-enhanced coronary MR angiography. Image contrast of coronary arteries is based on contrast enhancement, independent of flow effects that may cause image artifacts. Background tissues such as surrounding epicardial fat and myocardium are well suppressed. The coronary arteries can be viewed conveniently with MIP and multiplanar reformatting of the 3D data set.

In this study, we implemented a simple motion-matched k-space sampling. The center of k space was acquired when cardiac motion was minimal, and the edge of k space was acquired when cardiac motion had higher amplitude. In this manner, cardiac motion effects were displaced to the edge of k space, where there is much less signal, and corresponding motion effects on images were reduced as demonstrated in Figures 3 and 4. No matter what the size of an object, its spatial frequency spectrum always peaks at the center of k space. Therefore, our proposed motion-matched k-space sampling minimizes cardiac motion effects for all image structures whether large or small.

However, the residual motion at high spatial frequencies can adversely affect image quality. Such adverse effects are greater for structures with more high-frequency signal such as focal stenoses. Careful investigations will be required to quantify and minimize them. This motion-matched k-space sampling technique can be regarded as a generalization of the respiratory-ordered phase-encoding method, which reduces motion effects by smoothing respiratory motion over the phase-encoding direction (39–41). This study provides new information on the concept of smooth motion distribution in k space (Fig 6): There are multiple view orders that can be used to smooth motion in k space, the degree of motion blurring varies with view orders, and an optimal view order may be identified to minimize motion blurring.



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  		Figure 6. Simulation of motion effects in 2D coronary MR angiography performed in eight heartbeats (16 echoes per heartbeat). View orders from top to bottom: sequential, center edge, edge center edge (cardiac motion-matched), and edge center. Left column: Motion (displacement in x axis) distribution in ky space is estimated from a waveform obtained with cine coronary x-ray angiography. The motion range within the data acquisition window, d(ky), is 10 pixels. FOV = field of view. Right column: Corresponding y-axis PSF profiles, with full width at half maximum of 49, 15, 5, 15 pixels, respectively. PSF is substantially sharper with the edge-center-edge view order than with the others.

 
The motion-matched k-space sampling can be used to reduce cardiac motion effects in traditional nonenhanced coronary MR angiography, such as breath-hold 2D and navigator-gated 2D and 3D acquisitions (1–23). In these traditional coronary MR angiographic techniques, view ordering is required to minimize artifacts associated with the signal amplitude difference among echoes acquired in the readout window in the cardiac cycle. Centric view ordering is typically used to maximize signal at the center of k space by acquiring it at the beginning of the acquisition window when the spins are fresh. As demonstrated in this article, this centric view order can contain substantial cardiac motion effects. The diagnostic accuracy of these techniques has been inadequate not because of lack of signal-to-noise ratio but because of vessel blurring and other motion artifacts (20–23). The motion-matched k-space sampling strategy in this study may be adapted to reduce cardiac motion artifacts in these traditional coronary MR angiographic techniques.

In this preliminary work, the diastole estimation was based on electrocardiography in a manner similar to that in all work with coronary MR angiography (1–23). Electrocardiography is not a direct measurement of coronary motion, and the estimation for diastole is only a rough approximation. The inaccuracy of diastole estimation naturally affects the amount of cardiac motion in image data. The motion simulation outlined in the Appendix was repeated several times with different waveforms and different acquisition windows. The edge-center-edge view order (Fig 6) and the cardiac motion-matched view order in a 2D case consistently provided the sharpest point spread function (PSF), which suggests that the effectiveness of cardiac motion-matched view order is not affected by the inaccuracy of diastole estimation. We are currently developing an M-mode cardiac navigator echo method to provide a more precise MR estimation of cardiac motion and the rest period in the cardiac cycle.

We are also working to improve several aspects of this coronary MR angiographic technique to make it feasible for use with patients. In this preliminary implementation of motion matching, we referred to the k-space radius for view ordering and used an empiric definition of k-space center (25% of points). A better design for motion matching may be achieved by investigating the PSF for different motion distribution in k space, D(ky, kz), which is determined by the view ordering. This requires careful performance of the analysis outlined in the Appendix for the 3D case. An optimal D(ky, kz) and corresponding view order may be identified to provide the sharpest PSF. This preliminary pulse sequence took 32 heartbeats, which may be too long for patients. More efficient data acquisition methods such as spiral sampling are desired to shorten imaging time (42,43).

This study of motion-matched k-space sampling addressed cardiac motion in patients with a regular heartbeat. A different type of cardiac motion is arrhythmia. Image artifacts associated with signal intensity variations on standard electrocardiography-triggered MR images due to varying R-R interval did not occur with our contrast-enhanced coronary MR angiographic technique because spin equilibrium was established by means of disdaqs before data acquisition (Fig 1a). Cardiac motion artifacts could be the main potential problem of arrhythmia. In the case of atrial fibrillation, the cardiac cycle varies unpredictably, which causes serious artifacts on images acquired over multiple heartbeats. The duration of systole may be relatively constant for arrhythmia, and the middiastole corresponding to the shortest cycle may be used to acquire the k-space center. Atrial fibrillation occurs in only less than 10% of patients with acute myocardial infarction (44,45) and may not be a serious limitation for application of coronary MR angiography in patients in stable condition.

In summary, motion-matched k-space sampling reduces the imaging effects of cardiac motion during data acquisition and permits 3D coronary MR angiography to be performed in a breath hold. Coronary arteries are well depicted with this cardiac view-ordered breath-hold 3D contrast-enhanced MR angiographic technique.



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  		Figure 7. Energy disturbance functions of a digital coronary x-ray angiogram. Corresponding x-axis displacements are 3 and 7 pixels. Energy displacements are heavily peaked at k-space center (logarithmic scale). FOV = field of view.

 


   Appendix
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
References
 
Motion Analysis
Without loss of generality, we use the case of 2D imaging to illustrate that the effects of motion on MR images depend strongly on where motion occurs in k space. The same motion analysis can be performed for 3D imaging, but the mathematics is more complicated and the results are less comprehensible. In the case of 2D imaging, the cardiac motion-matched view order reduces to the simple edge-center-edge view order, which allows intuitive illustration of motion distribution in k space and corresponding PSF.

An energy disturbance function {delta}E can be used to characterize motion effects caused by a displacement d at view ky (33,34):

where Sd(kx, ky) is the MR signal with displacement d at k-space location (kx, ky), and S0(kx, ky) is the MR signal without motion. This energy disturbance function depends not only on the amount of displacement but also on the image signal intensity itself. MR images are always heavily weighted at the center of k space (35). This is true not only for large objects but also for small objects. For example, a single line has a spatial frequency spectrum of a sinc function that always peaks at the center of k space regardless of the line width. Consequently, the energy disturbance function is also heavily centered at the k-space center in the case of coronary angiography (Fig 7). Therefore, motion reduction methods must minimize motion at the center of k space.

Motion effects can be reduced by redistributing motion in k space by means of view ordering during data acquisition. This can be illustrated by means of the PSF associated with linear translation, with a Fourier transform of

Equation (A2) is derived from the Fourier properties that linear translation corresponds to a phase modulation, and the PSF is a multiplication function on signal intensity.

An example of a cardiac motion waveform and the corresponding PSF is illustrated in Figure 6. The motion waveform is exemplified by the craniocaudal displacement (along the x axis). Displacement of the coronary artery at a time point in data acquisition is estimated from a patient's coronary motion waveform obtained with breath-hold cine x-ray angiography (24). The motion distribution in k space, dx(ky), is determined by the view order of data acquisition (Fig 6, left column). The motion range was set to 10 pixels. The PSF is calculated from the Fourier transform of exp[ikxdx(ky)] (Eq [A2]). The magnitude profile of the PSF along the y axis is illustrated (Fig 6, right column) to demonstrate the degree of motion blurring associated with each view order.

The PSF for the sequential view order can be explained by means of the Fourier convolution theorem or the sampling theorem. The cyclic dx(ky) generates a cyclic k-space PSF, which can be regarded as a convolution of a basic pattern function F(ky) convoluting with a comb function with 32-point spacing

The corresponding PSF in x-y space is then the product of f(y) with a comb function of 8 (256/32) point spacing

which corresponds to sampling f(y) every 8 pixels as shown in Figure 6, right column.

The PSF for the standard centric (center-edge [ce]) view order has the same magnitude profile as that for the edge-center (ec) view order in this 2D case (Fig 6, right column):

The full width at half maximum was 15 pixels, 1.5 (15/10) times the motion range.

The PSF for the edge-center-edge view order, which is the cardiac motion-matched view order, has the sharpest profile. Its full width at half maximum is 5 pixels, half (5/10) of the motion range, or one-third (5/15) of the centric full width at half maximum. This is substantially sharper than all other view orders. Notice that the cardiac waveform is asymmetric or the flat part is not at the center of k space (Fig 6, left column), which accounts for possible error in the estimation of middiastole.

Algorithm in C Subroutine
In the exact algorithm in C subroutine for the motion-matched view order implemented in this study, let opslquant be the number of views along z (section) and rhnframes be the number of views along y (phase). Let kyz_ce[i], i {epsilon} [0, opslquant x rhnframes - 1], be the ascending integer array such that the frequency radius of view number ky = kyz_ce[i]/opslquant, kz = kyz_ce[i]%opslquant increases with index i as the ascending sequence described in Materials and Methods. Let nhbs be the number of heartbeats for the entire data acquisition and etl be the number of echoes acquired per heartbeat (nhbs x etl = opslquant x rhnframes). Let an integer array kyz_coro[i] be generated with the following subroutine:



   Footnotes
 
Abbreviations: LAD = left anterior descending coronary artery MIP = maximum intensity projection PSF = point spread function 2D = two-dimensional 3D = three-dimensional

Author contributions: Guarantor of integrity of entire study, Y.W.; study concepts and design, Y.W.; definition of intellectual content, Y.W.; literature research, Y.W.; clinical studies, Y.W., P.A.W., H.M.L., G.W.B.; experimental studies, Y.W., P.A.W., H.M.L.; data acquisition, Y.W., P.A.W., H.M.L., L.Y., R.W.; data analysis, Y.W., G.D.; statistical analysis, Y.W.; manuscript preparation, editing, and review, Y.W.


   References
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 

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