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1 All authors: MRI Research Laboratory, Department of Diagnostic Radiology, Mayo Clinic, 200 First St., S.W., Rochester, MN 55905.
Received June 2, 2000;
accepted after revision July 28, 2000.
Supported in part by National Institutes of Health grants CA51124 and
AG16574.
Abstract
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MATERIALS AND METHODS. Ten consecutive volunteers were imaged with an unenhanced gradient-recalled echo three-dimensional time-of-flight MR angiography sequence of the circle of Willis. Each volunteer was asked to rotate approximately 2° after completion of one third and one half of the acquisition in the axial, sagittal, and oblique planes (45° to the axial and sagittal planes). A single static data set was also acquired for each volunteer. Unprocessed and autocorrected maximum-intensity-projection images were reviewed as blinded image pairs by six radiologists and were compared on a five-point image quality scale.
RESULTS. Mean improvement in image quality after autocorrection was 1.4 (p < 0.0001), 1.1 (p < 0.0001), and 0.2 (p = 0.003) observer points (maximum value, 2.0), respectively, for examinations corrupted by motion in the axial, oblique, and sagittal planes. All three axes had statistically significant improvement in image quality compared with the uncorrected images. Changes in image quality after the application of the autocorrection algorithm to static angiogram data were not statistically significant (mean change in score = -0.13 points; p = 0.29).
CONCLUSION. Autocorrection can reduce artifacts in motion-corrupted MR angiography of the circle of Willis without distorting motion-free examinations.
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A number of approaches for addressing such motions have been described. Navigator-based adaptive motion correction [2] has been shown to be useful in numerous applications, including diffusion [3], cardiac [4], musculoskeletal [5], and functional imaging [6]. However, a disadvantage of navigator techniques is the need for a special pulse sequence that may prolong scanning time or place assumptions on the direction of motion. Recently, a new class of algorithms has been shown to correct for both translation-and rotation-induced artifacts [7,8]. This retrospective technique, known as autocorrection, does not require a special pulse sequence and uses an image metric to measure changes in image quality induced by applying iterative phase correction estimates to the k-space data.
The reliability of this technique for reducing motion-induced artifacts in MR imaging remains largely unknown. However, an evaluation of autocorrection in high-resolution musculoskeletal imaging of the shoulder has shown that improvements in image quality are comparable to those achieved with navigator-based adaptive motion correction techniques [8]. In that study, a relatively simple motion model was used by considering only motion only along the image phase-encoding axis and ignoring any effects of rotation. Autocorrection of rotational motion in head imaging has also been reported [9], but that work focused on improving image quality in single-slice images in two volunteers and two patients, and no improvement was reported for the patient examinations. In applying this method to MR angiography, the challenge is to improve image quality in larger data sets (3D versus two-dimensional) with complex motion (rotation and translation) and lower signal-to-noise ratio values than other MR imaging examinations.
We evaluated autocorrection in high-resolution MR imaging of the cerebral arteries. Specifically, we developed two hypotheses: autocorrection can improve the quality of 3D time-of-flight MR angiography maximum-intensity-projection (MIP) images that have been degraded by motion; and autocorrection will not adversely affect images that have not been degraded by motion. The purpose of this study was to evaluate both of these hypotheses.
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Static- and motion-corrupted data sets were performed on 10 volunteers who gave verbal consent before imaging. Volunteers were recruited by canvassing healthy personnel from our research group. The first 10 persons to volunteer were then scanned in consecutive order. For each volunteer, approximately 2° of rotation in the axial, sagittal, and oblique (aligned 45° between the axial and sagittal) planes was introduced after acquisition of one third and one half of the total k-space data. The axial plane of rotation was defined as the plane comprising the anterior-posterior and right-left physical axes of the magnet. Similarly, the anterior-posterior and superior-inferior magnet axes defined the sagittal plane. To define the oblique plane, the axial plane was rotated 45° in a counterclockwise direction about the anterior-posterior axis of the magnet. The magnitude of rotation was chosen to be consistent with rotations measured in in vivo head imaging examinations [10, 11]. These rotations did not explore the full range of typical patient motions that may occur in vivo. Instead, the rotations were chosen to represent situations in which rotations produced moderate and severe motion artifacts that were consistent with rotation angles that have been previously reported [10, 11]. The situation of slow continuous motion throughout the scanning was not explored because of the difficulty in reproducing similar motion among the volunteers. No attempt was made to determine the sensitivity of the autocorrection technique to the amplitude of motion corruption (one third and one half of k-space). Instead, these data were combined to provide a more clinically realistic—that is, heterogeneous—representation of the effect of motion-induced artifacts. Precision and subject-to-subject uniformity of deliberate rotations were ensured by the use of a bite block apparatus attached to the head coil. This device limited the amount of rotation and minimized out-of-plane rotation. Each volunteer was audibly prompted to rotate his or her head at the two predefined data acquisition times.
Before our autocorrection algorithm could process the MR angiography data, these data were first reformatted. Reformatting involved zero padding in kx and ky so that the number of complex data points along both axes was 256. In the frequency-encoding direction, the echo was shifted so its center was located at the center of the data window (kx = 128). No attempt was made to perform a homodyne reconstruction of the partial echo data. Artifacts arising from the acquisition of the partial echo were ignored.
Autocorrection of 3D Time-of-Flight MR Angiography Data
Frequency of motion.—For continuous motion in three
dimensions, autocorrection must estimate an individual phase correction factor
for each view and direction of motion. For motion along all three axes, a
total of 3 x Ny x Nz (where Ny and Nz are the number of
phase-encoding steps along the y- and z-axes, respectively)
phase factors must be estimated. Because of the iterative nature of
autocorrection, this large number of phase factors would make the algorithm
computationally excessive. To address this problem, we made two assumptions:
first, that continuous motion does not occur during acquisition of 3D
time-of-flight MR angiography data; and second, that motion along the kz axis
is minimal for each ky phase-encoding step. In a sense, we created a
second, pseudo phase-encoding axis (nominally, kz) in which only view-to-view
motion is present and intraview motion is absent. For the clinical acquisition
parameters used in this study, this assumption is invalid when the patient
moves along the z-axis in an interval of less than 1.4 sec. We
considered this to be clinically unlikely because patients with such large
frequency of motion would not be imaged without some method of restraint or
sedation or both. This simplifying assumption allows a single phase correction
term, equal to the slope of the phase correction ramp, to be applied to all kz
terms for a fixed kx and ky value. Thus, for each kx, ky pair, a single term,
rather than Nz terms, needs to be determined by the autocorrection
algorithm.
Small-angle rotations.—Fourier theory states that rotation
in image space produces an equal rotation of the k-space data
[12]. However, if the angle of
rotation is small and the region of interest is far enough from the fulcrum of
rotation, then rotation of an object in this region can be broken into
equivalent translations along the two in-plane axes. This relationship is
valid as long as the approximation of sin
= , where is the
angle of rotation, holds. In 3D time-of-flight MR angiography data, we apply
this approximation to our corrupted data so that instead of regridding the
k-space data, we apply a translational motion model with linear phase
correction factors to correct for `equivalent' linear translations. For 3D
time-of-flight MR angiography of the circle of Willis, the fulcrum of rotation
is considered to be posterior to the vessels of interest (i.e., the anterior
circle of Willis).
Measurement and subsequent reduction of motion artifacts by the autocorrection algorithm were performed over a region anterior to this fulcrum. An MIP was generated from the 3D MR angiography data and included only the anterior cerebral arteries, extending posteriorly to include the basilar artery tip and the posterior cerebral artery (Fig. 1). The region included the entire field of view along the ky phase-encoding axis (left-right).
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Autocorrection.—In a manner similar to our previously described two-dimensional autocorrection algorithm [8], autocorrection of 3D time-of-flight data was performed by dividing k-space into blocks of Ny/2 x Nz views, starting at +kymax. In the case in views which motion occurs along all three physical axes, separate phase rotation corrections are estimated for each k-space axis, starting with kx, then ky, and finally kz. Each phase correction is determined by searching a range of phase slopes, centered at kx, ky, and kz = 0, corresponding to physical displacements between -20 to +20 pixels along the x- and y-axes and -10 to +10 pixels along the z-axis, respectively. Once a phase term for each axis has been calculated, the next block of views is selected, and the process is repeated until all views have been processed. The block size is decreased by a factor of 2 and the process repeated until a block size of 2 x Nz is autocorrected. Because of the computational burden of correcting for motion along all three axes, autocorrection of motion along all three axes was performed only when volunteers were asked to rotate in an oblique plane. Rotations in the axial and sagittal planes were corrected by estimating phase correction factors along the kx-ky or the kx-kz axes, respectively.
Quantification of motion artifacts by the autocorrection algorithm was performed using two methods. Both approaches used the entropy of the gradient image metric [13]. In the first method, the metric was calculated over all axial slices and then summed. In the second approach, the metric was calculated on an axial MIP image generated from the 3D data. Measurement of the metric over the MIP image is computationally faster than measuring the metric over all slices and then summing the value, but the efficacy of the autocorrection algorithm in MR angiography using the two metric measures remains untested. Autocorrection using the metric summed over all slices in the 3D data was designated autocorrection method 1, and the MIP-derived metric measure was designated method 2. Only axial corrupted and static image data sets were processed with autocorrection metric methods 1 and 2, whereas all data sets were processed with autocorrection method 2.
Image Analysis
To determine if regional autocorrection of motion-corrupted MR angiography
data improved image quality, a blinded observer study was conducted. The
uncorrected and autocorrected MIP images were presented simultaneously to each
observer. The order of the motion-corrupted and autocorrected images was
randomized to ensure a blinded comparison. Special attention was given to the
randomization of these images (we designated them images A and B,
respectively). Randomization involved being sure that the uncorrected image
was displayed as image A 50% of the time to ensure that any bias in the
selection process was removed. The order in which the motion-corrupted images
(one third and one half k-space motion) were presented was similarly
randomized.
Six radiologists experienced in reviewing MR angiography studies of the circle of Willis were asked to grade the two images by ranking the quality of image A relative to that of image B. Quality was defined as the visually perceived sharpness and contrast of the circle of Willis vessels. Image pairs were displayed on a computer workstation, and a rating scale of -2 through +2 was used in which -2 indicated image A significantly worse than image B;-1, A worse than B; 0, A and B equivalent; +1, A better than B; and +2, A significantly better than B. For each plane of motion, the data sets corrupted after acquisition of one third and one half the data were combined to provide a range of motion-induced artifacts. For each volunteer, a total of 10 image pairs were generated. These consisted of four axial (one third and one half motion-corrupted processed with algorithms autocorrection method 1 and autocorrection method 2), two sagittal, two oblique corrupted, and two static (processed with autocorrection method 1 and autocorrection method 2) MIP image pairs. Each observer reviewed a total of 100 image pairs (10 volunteers x 10 image pairs per volunteer). Because this technique of motion correction is not an exact solution, only the region of the anterior circle of Willis over which the image metric was calculated was displayed. Regions of the MIP outside the metric calculation zone were zeroed. The kappa statistic was calculated to determine interobserver agreement. The six observers' scores were averaged and a one-sample t test was performed. To determine the sensitivity of the autocorrection algorithm to the plane of motion, a one-way repeated measures analysis of variance of the data was also performed.
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Table 1 summarizes the t test data for the three axes of motion and the two metric techniques, autocorrection method 1 and autocorrection method 2. For all planes of motion, statistically significant improvements in image quality were observed when autocorrection was performed. Motion in either the axial or the oblique plane showed the largest improvement in image quality, with mean differences of 1.4 and 1.1 (on a scale of 2.0) observer units for the axial and oblique planes, respectively. Autocorrection of sagittal plane motion produced statistically significant improvements in image quality, but with the lowest mean change in observer score (0.22 points). No statistically significant difference between static and autocorrected static images was reported in this study for both metric measures, autocorrection method 1 (mean = 0.07, p = 0.31), and autocorrection method 2 (mean = -0.13, p = 0.29). Figure 2A,2B is an example of the application of autocorrection to static MR angiography data. In the uncorrected image (Fig. 2A), no detectable motion artifacts are observed. The autocorrected image (Fig. 2B) is of similar image quality as the uncorrected image, indicating that the autocorrection algorithm did not introduce spurious image artifacts.
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Figures 3A,3B,3C,3D,3E,4A,4B,5A,5B show corrupted and autocorrected circle of Willis MIP images corrupted with motion in the axial, sagittal, and oblique planes, respectively. In each image set, the motion-corrupted image is figure part A and the autocorrected is figure part B. Both horizontal and diagonal arrows indicate how motion can induce a decrease in signal intensity and an increase in blurring in both the anterior and the middle cerebral arteries. In all autocorrected images, an improvement in the quality of the anterior circle of Willis images can be observed. As quantified in the mean change in observer scores, the greatest improvement in image quality was in cases in which axial or oblique motion was present. However, significant improvements in image quality were also observed in examinations corrupted by motion in the sagittal plane (Fig. 4A,4B), particularly in the small branching vessel of the middle cerebral artery (diagonal arrow) and distal branches of the middle cerebral artery in the sylvian fissure (horizontal arrow).
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Table 2 summarizes the repeated measures analysis of variance results. The improvement in image quality after autocorrection for motion in the axial plane using the MIP-based metric, autocorrection method 2, when compared with the image-based metric, autocorrection method 1, was nearly significant (p = 0.080). However, as seen in Table 1, the MIP-based metric resulted in a larger mean improvement in score (1.4 observer units versus 0.80) compared with the image-based metric. No difference was seen in the improvement in image quality after autocorrection with the MIP-based metric when motion occurred in the axial and oblique planes (p = 0.27). However, improvements in image quality after autocorrection for motion in the axial and sagittal planes were better than those achieved when motion was in the sagittal plane (p < 0.0001). This may be because motion in an oblique plane produces a considerable amount of image artifact in the axial plane that is quantified in the axial MIP metric.
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A potential limitation of this technique is the long computation time (several hours on a 550-MHz Pentium III PC [Gateway 2000, Sioux City, SD]) of the algorithm and the restriction of the motion model to small rotations. Although the computation requirements of this technique are great because of the 3D data and the number of degrees of freedom over which motion can occur, we believe that processing time can be decreased significantly. This assumption is strengthened by our initial experience with autocorrection of shoulder MR data, which has shown that computation time of this algorithm can be reduced from approximately 20 min [8] to less than 1 sec per image (Manduca A et al., presented at the International Society for Magnetic Resonance in Medicine, April 2000). Specific improvements that could be implemented immediately to decrease computation time include performing autocorrection on a faster computer system, using a multiprocessor array processor, and optimizing the autocorrection computer code. Initial tests in our laboratory of the shoulder autocorrection algorithm [8] on a PC (550-MHz Pentium III) and Octane workstation (Silicone Graphics, Mountain View, CA) have realized a 6.4-fold decrease in computation time. We expect similar improvements when applied to the circle of Willis data. A dedicated array processor can also be used to perform the numerous fast Fourier transforms required by the autocorrection algorithm rapidly and in parallel, further reducing computation time. Finally, reorganization of the way in which the algorithm processes the data so that the operator has the ability to review and stop the autocorrection process if image quality shows no further improvements, could also reduce processing time. Initial experiments with smaller data sets and angles of rotation up to 6° have shown that this linear model can still be used to improve image quality. Thus, it is feasible that with the use of existing computer hardware and optimized software, autocorrection can be applied to 3D time-of-flight MR angiography with computation times that are clinically acceptable (minutes instead of hours).
We did not test the diagnostic accuracy of the technique. Instead, our goal was to break down a complex problem (can motion reduction schemes improve diagnostic accuracy?) into its constituent components (autocorrection as a method for reducing motion artifacts) and address these components. The use of a relative scale for rating images improved the statistical power of the study compared with using a five-point forced choice diagnostic or nondiagnostic absolute scale. The use of healthy volunteers with consistent motion records precluded any disorders in the data sets and was not representative of the true distribution of motion records seen in a large patient population. To accurately test the diagnostic accuracy of the autocorrection technique will require evaluating a large clinical series corrupted by motion and comparing results with an external gold standard.
Because our algorithm does not provide an exact solution to the problem of rotation—that is, the k-space data are not regridded—the autocorrection algorithm disorts regions of the image proximal to the fulcrum of motion. However, autocorrection of several contiguous subvolumes can be performed with the final image composed of the sum of these regions. Figures 3C,3D,3E show such an approach. Figure 3C shows the larger field of view of the uncorrected MIP image in Figure 3A, and Figure 3D shows the larger field of view of the image shown in Figure 3B. In Figure 3D, image quality has been degraded by ghosting of the distal branches of the middle cerebral and posterior cerebral arteries, which were external to the metric calculation region, whereas the anterior cerebral arteries have been corrected. Figure 3E shows the composite MIP image generated by autocorrection of Figure 3A with nine separate, contiguous regions of 256 x 20 pixels. In the composite image, all regions of the image have few remaining artifacts introduced either by rotation or by the autocorrection algorithm.
This initial study shows that significant improvements in rotation-induced artifacts in 3D time-of-flight MR angiography of the circle of Willis can be achieved with an autocorrection method. Further refinement and clinical evaluation of this technique are required.
Acknowledgments
We thank Ken Persons for his assistance in setting up the image review and
analysis system and Peter O'Brien for statistical assistance.
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