continuous update with random encoding (cure): a new strategy for dynamic imaging

Continuous Update with Random Encoding (CURE): A New Strategy for Dynamic Imaging Todd Parish, Xiaoping Hu

Although dynamic imaging is presently used for various applications, it is still limited by the temporal resolution. In this paper, we present a new technique that uses a random phase- encoding strategy to facilitate faster and smoother update of images and to improve the temporal resolution in dynamic studies. The technique was implemented on a conventional clinical scanner and demonstrated with various in vivo studies. Technical details, simulations, and experimental results are described. Images from experimental studies indicate that the new technique is robust in generating dynamic images and can be potentially utilized for clinical applications. Key words: dynamic imaging; real-time imaging; interventional MRI; MR fluoroscopy.

INTRODUCTION

Since its inception in 1973 (l), magnetic resonance imaging (MRI) has evolved into a widely used clinical and research tool. Nevertheless, new developments of MRI are still emerging. Of particular interest is the development of ultrafast imaging techniques that can be used for dynamic applications such as monitoring interventional procedures, visualizing organ movement, and studying the passage and uptake of contrast agents. While still in its infancy, interventional MRI has generated substantial interest and is currently an area of active research (2, 3). MRI is potentially advantageous for such a task, because it provides excellent soft tissue contrast and flow sensi- tivity, and it is free of radiation hazards. However, despite many technical advances, the imaging acquisition speed is still a limiting factor in interventional MRI. Contrast agent studies have been utilized to differentiate tumors (4 ,5) , to derive blood volume and perfusion maps of the brain (6, i’), and to derive the perfusion of the heart (8). While these studies have met with substantial suc- cess, they can be improved with increased temporal resolution.

An attempt toward dynamic imaging was made by Riederer et al. in their development of fluoroscopic imaging (9). In their approach, fluoroscopic imaging was implemented on a standard clinical imager using special reconstruction and display hardware and was achieved

at the expense of reduced spatial resolution. With such a system, the image update time was dictated by the repetition time and the matrix size in the phase-encoding dimension. Others have utilized echo planar imaging (EPI) techniques, such as spiral imaging (10) and seg- mented EPI (l l- lz), to acquire the image data more rapidly. These techniques have potentially high temporal resolution. However, they require more advanced hardware and may suffer from artifacts specific to EPI. In addition, the image update time is still limited by the acquisition of a minimum set of data needed for each image.

On conventional scanners where the data acquisition speed is limited by hardware, a number of techniques have been developed to reduce the amount of time needed to acquire data for each new image. For example, the k-space substitution or the keyhole technique was proposed to accelerate dynamic imaging (13-14). The keyhole method provides a way to improve the temporal resolution at the expense of reduced spatial resolution of the dynamic information (15). In addition, its image update speed is still limited by the time needed to acquire the data in the keyhole. Recently, a variable field of view technique was developed based on the assumption that the dynamic information can be captured in a reduced field of view (16); the technique works well when its assumption is valid but may not be applicable in general. Another approach is the data sharing technique, which uses the same high k-space lines for neighboring images (1 7); because the technique is based on using a regularly ordered phase-encoding table, the image update speed is also limited.

In this paper, we present a new technique that samples the k-space in a pseudo-random manner to facilitate faster and smoother updating of images and to improve the temporal resolution in dynamic studies. The technique was investigated with simulations, implemented on a conventional clinical scanner and demonstrated with various in vivo studies. In the Results section, the images from these studies are presented. These images indicate that the new technique is robust in generating dynamic images and can be potentially utilized for clinical applications.

MRM 3Ck326-336 (1995) From the Department of Radiology and Center for Magnetic Resonance Research, University of Minnesota Medical School, Minneapolis. Address correspondence to: Xiaoping Hu, Department of Radiology, Box 292, UMHC, 420 Delaware Street SE, Minneapolis, MN 55455. Received April 27, 1994; revised November 14, 1994; accepted November 14, 1994. This work is supported in part by the National Institute of Health (grant RR 08079).

Copyright 0 1995 by Williams 8 Wilkins All rights of reproduction in any form reserved.

0740-3194/95 $3.00

METHODS

Most existing implementations of dynamic imaging continuously acquire phase-encoded lines and slide a window along the acquired data stream to select data for the reconstruction of images (e.g., 18). The difference between our technique and the others lies in the choice of the phase-encoding table and the data selection criteria. In a conventional approach, the k-space is sampled in an

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A New Strategy for Dynamic Imaging 327

orderly and repetitive fashion (e.g., the repetition of a linear phase encode table or the repetition of the table needed for the keyhole data). In the reconstruction, if the window is moved by an interval smaller than the duration of the table, the k-space data are updated in a non- uniform fashion and the low k-space lines are usually not changed. The former leads to periodic fluctuations in image intensity and the latter limits the temporal resolution to the time needed for updating the low k-space data.

To alleviate these problems, our approach uses a new phase-encoding strategy (see Fig. I), in which the phase- encoding steps are traversed randomly and the low k- space lines are visited more frequently. The randomization of phase-encoding steps ensures that the k-space is updated uniformly, thereby reducing the image-to-image fluctuations. With the low k-space lines traversed more frequently, the images can be updated more rapidly as the images are determined to a large extent by the low k-space lines.

This sampling scheme was implemented on a 1.5 T Siemens SP63 Magnetom scanner (Siemens Medical Sys- tems Inc, Iselin, NJ). Ideally, a random table with as many elements as required for the whole imaging session should be used. However, because the clinical system does not support the real time storage of such an ex- tended phase-encoding array, the table is approximated by the repetition of a finite unit random table. Despite the periodicity introduced by the repetition of the finite random table, this implementation is virtually equivalent to a completely random table.

A unit random table was constructed by randomizing the elements in a conventional table and adding more low k-space lines (see Fig. 1). In the current implementation, starting from a random table of 64 phase-encoding steps, we added 18 extra steps, making a total of 82 steps.

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The additional lines included 4 zero phase encode lines, 3 pairs of lines, 2 pairs of ?2 lines, 1 pair of 2 3 lines, and 1 pair of 2 4 lines. These lines were uniformly spaced throughout the unit table. This approach reduces the average spacing of the low k-space lines substantially relative to the total number of lines in the unit phase- encode table despite a slight increase in the unit table size. For example, the average spacing between the zero lines is 16 in the unit random table of 82 lines. Therefore, for each time the reconstruction window shifts by 16 lines, it will encounter, on the average, a new zero phase- encode line.

To elucidate the properties of the random sampling technique and compare it with the linear update approach (g), two simulation studies were conducted. With no loss of generality, the simulations were performed in the dimension along the phase-encoding direction. Both assumed a TR of 6.5 ms. The first study simulated a I D box moving at 10 cm/s over a field of view (FOV) of 20 cm and the second simulated dynamic contrast changes in a stationary I D box by varying the signal intensity (see Fig. 3b for details). k-Space data were computed based on the simulated object at each TR and images were updated at intervals of 10 TRs. Images were obtained with both CURE and the linear updating approach; ideal images were also calculated for comparison.

Using the same models, simulations were also performed to compare CURE with the keyhole method. To illustrate the difference between the two techniques, images of the moving box were updated at intervals of 10 TRs and 5 TRs, respectively. For the dynamic contrast simulation, images were updated with an interval of 10 TRs .

The imaging sequence used for data acquisition was an ultrafast gradient echo sequence with no magnetization

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FIG. 4. Results from the comparison between CURE and the keyhole technique with the simulation study of the moving box. (a) Profiles at a representative time obtained by the two techniques with an interimage delay of 10 TRs, and the true profile. (b) Locations of the moving box estimated by CURE and the keyhole approach plotted against image number and compared to the ideal locations. (c) RMS error in the simulated profiles obtained from the two techniques plotted versus image number. (d) Same as (a) with an interimage delay of 5 TRs. (e) Same as (b) with an interimage delay of 5 TRs. (9 Same as (a) with an interimage delay of 5 TRs.

preparation. In the experimental studies, we used a TR of 4.5-6.5 ms, a TE of 2.4 ms, a flip angle of 8-10', a slice thickness of 10 mm and a matrix of 128 x 64. During the data acquisition, a low flip angle gradient echo was re- peated over and over again for a duration of the whole session. Each repetition covered a different phase-encoding step as specified by the unit random table and this table was cycled through a plurality of times during the experiment. With the continued excitation, a steady state

of the longitudinal magnetization was reached. Conse- quently, the images generated are predominantly T, weighted and exhibit time-of-flight contrasts in the ves- sels and the blood pool of the heart.

In principle, the image reconstruction can be implemented in real time with proper computer hardware and software (18). However, in this work, the reconstruction was done off-line to illustrate the feasibility of the ran-

330 Parrish, Hu

dom sampling technique. Ignoring the frequency-encoding dimension, the acquired data can be put in a 1D data stream. To reconstruct an image at a given time, appro- priate data are selected within a window along the stream; the size of the window is identical to that of the unit table and its center is the temporal location of the desired image. The data selection is carried out as follows. Starting from the center of the window, the algo- rithm searches outward for the desired phase-encoding lines until the matrix is filled. When a low k-space line is encountered more than once, the one that is closest to the center of the window is used while the others are dis- carded. Images at other times are reconstructed in a sim- ilar manner. In principle, the time shift between images can be any multiple of the TR.

Studies of the abdomen during breathing, the knee during movement, and cardiac motion were conducted on normal volunteers (with informed consent and IRE3 approval) using a body coil. In the abdominal study, the volunteer was instructed to breath normally and a coronal slice with a field of view (FOV) of 40 X 40 cm through the liver was imaged. In the cardiac study, a 25 cm X 25 cm short axis view of the heart was imaged continuously with no EKG triggering. The knee study was performed on a sagittal slice through the knee with a FOV of 20 cm X

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20 cm while the subject moved his lower leg. The TR used for these studies were 4.5 ms for the abdomen and knee studies and 6.5 ms for the heart study. For each study, imaging data were acquired continuously for ap- proximately 30 sec.

In addition to the volunteers, dogs were also imaged using a body Helmholtz coil. Two different studies were conducted. The first study imaged the heart of an arrhythmic dog. During arrhythmia, the blood pool became stagnant and saturation caused its intensity to decrease. This effect was demonstrated by the time course of the signal in the left ventricle. The second study monitored the signal changes of the heart with a bolus injection of 0.1 mM polylysine (Schering AG, Berlin, Germany). The time courses of the left ventricle and the myocardium, respectively, were determined and plotted to illustrate the passage of the contrast agent.

RESULTS Simulations of CURE versus the Linear Update Approach

The results from the simulation of the moving box are presented in Fig. 2. In panel (a), a representative profile of the object is illustrated. Comparison of the reconstructed profiles to the ideal one indicates that the ran-

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FIG. 5. Simulation results of the study of the fixed box with varying intensity comparing CURE and the keyhole technique. (a) Representative profiles reconstructed using the two techniques plotted and compared to the ideal profile. (b) Plot of the intensity of the center of the box obtained with CURE and the keyhole technique, compared with the ideal intensity variation. (c) RMS error of simulated profiles obtained from the two techniques plotted versus image number.


dom approach provides a better depiction of the main features (e.g., location) of the moving object but is degraded by errors throughout the FOV. In contrast, the profile obtained with the linear approach tends to mis- represent the location of the box yet exhibits fewer artifacts elsewhere. To demonstrate this further, we estimated the location of the box in each image by calculating the center of mass of the reconstructed profile. The estimated location is plotted against true location in Fig. 2b; the location estimated by CURE is in good agreement with the true location while that estimated from the linear approach deviates from the true location substantially in a pseudo-periodic fashion. Panel (b) also indicates that the performance of CURE is consistent in time while that of the linear approach varies dramati- cally. This observation is further supported in panel (c) where the root-mean-square (RMS) errors in the reconstructed profiles are plotted against image number. It is evident that errors in the random approach are generally smaller than those from the linear update, with little temporal variation.

Figure 3 shows the results from the simulation study of the fixed box with dynamic contrast changes. Panel (a) presents profiles obtained at one representative time; the reconstructed profiles are compared with the corresponding ideal profile. The profile obtained by CURE follows the ideal profile closely while that from the linear approach does not. In panel (b), the intensity of the central pixel in the simulated box is plotted against image number and compared with the ideal intensity. The intensity change obtained by CURE agrees with the ideal intensity, while that obtained with the linear update approach exhibits a staircase like variation. The “time courses” of the RMS error are plotted in panel (c), which indicates that errors in CURE are generally less than

those in the linear approach and do not oscillate from time to time.

Some insights of CURE can be inferred from the above simulation results. By updating the low k-space data more frequently, CURE is able to capture the main features of the dynamic information at the expense of increased errors elsewhere. In addition, the randomization of the phase-encoding steps virtually eliminated the temporal fluctuation of the errors in the images. The two studies described above represent two diversely different cases of dynamic imaging. In the first study, the low k-space variation is not substantial (for example, the zero k-space line is constant), therefore the advantage of CURE is not as remarkable as that exhibited in the second study where the low k-space data vary significantly.

Simulations of CURE versus the Keyhole Technique

Results from the simulated moving box are presented in Fig. 4. Panels (a-c) illustrate the results obtained when the images were updated every 10 TRs. At this updating speed, the keyhole technique performs better because it captures most of the energy of the moving object within the 10-line keyhole. When the images are updated every 5 TRs (panels d-f), the performance of CURE is un- changed while that of the keyhole technique is substantially degraded. This is particularly evident in the RMS error plot (panel 0.

The box with dynamic contrast was simulated with an interimage delay of 10 TRs. The results are shown in Fig. 5. As illustrated by the representative profiles in Fig. 5a, CURE is able to provide a good estimation of the true profile and the keyhole technique only generates a low resolution version of it. The intensity of the center of the box in the CURE images tracks the true intensity very

FIG. 6. A subset of coronal images of the abdomen during normal breathing of a volunteer. The image set begins at full inhalation and covers exhalation. The series shows how the liver and other organs moved during the exhalation portion of the respiratory cycle.

332 Parrish. Hi1

closely: in contrast, the corresponding intensity in the keyhole images deviates from the ideal one substantially (Fig. 5b). In Fig. 5c, the RMS error plot also validates that CURE outperforms the keyhole technique in this simulation.

The results of the above comparison revealed some interesting properties of the two techniques. By updating the low k-space lines in the keyhole from image to image, the keyhole technique allows the most current representation of the low k-space lines, and it outperforms CURE when these lines capture most of the object variation. In cases when the low k-space lines in the keyhole are no longer adequate to describe the object variation, its performance becomes worse than that of CURE as indicated in Figs. 4d-4f and Fig. 5. By randomizing the phase- encoding steps in CURE, it is possible to update the images at any multiple of the TR, and the image quality is

FIG. 7. Images from the study during lower leg movement. The volunteer was prone while flexing the lower leg at his own pace, during the image acquisition. This series consists of a subset of images separated in time by 20 TRs (90 ms). The motion of the knee and the lower leg is clearly depicted; however, two of the images exhibited noticeable motion artifacts.

not dependent on the updating interval as shown in Fig. 4. This continuous updating capability of CURE is clearly demonstrated in the simulation. However, i t is important to note that each updated image represents a temporal average.

In Vivo Studies

Consecutive images, 20 TRs (90 ms) apart, were reconstructed from the abdominal study. A total of 330 images were obtained. When viewed i n a cine mode, these images depicted the continuous movement of the liver and other organs. In Fig. 6, we present a subset of images from the study. The respiration related motion is clearly rep- resented by these images despite slight motion artifacts in some images.

In Figure 7, we present a series of images demonstrat-

FIG. 8. Short axis images of a normal human heart. This series corresponds to a single cardiac cycle and the images are separated by 10 TRs (65 ms). Note that during systole the heart was moving rapidly and artifacts arose. Nevertheless, the cardiac motion can be visualized in most of the cardiac cycle.

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b FIG. 9. (a) Short axis heart images, separated by 6 TRs (45 ms), of an arrhythmic dog. The images in the first row correspond to a normal beat and the rest corresponds to a sinus arrhythmia. The hypokinesia in both ventricles during arrhythmia is evident. The blood pool also darkens due to progressive saturation of stagnant blood. (b) Time course of the left ventricle. The data points are separated by 10 TRs (45 mS). It is apparent that a decrease of the signal in the ventricle accompanied the missing beats. In this plot, three missing beats are illustrated.

334 Parrish, Hu

ing the kinetics of the knee during the lower leg movement. These images are separated by 20 TRs (or 90 ms) in time. The motion of the knee and the lower leg was captured with minor artifacts and a smooth transition from image to image. When the complete set of the reconstructed images are viewed in a cine loop, the motion of the knee and the lower leg is readily visualized.

From the experiment on the normal human heart, consecutive images were reconstructed at an interval of 10 TRs (65 ms). In Fig. 8, we illustrate a subset of the short axis images. The cardiac motion is reasonably visualized despite some motion artifacts near systole (images marked by letter S). In this case, the effective temporal resolution was not sufficient to “freeze” the heart motion during systole. Nevertheless, the continuous motion depicted by these images throughout most of the cardiac cycle indicates that the random sampling technique provides a good vehicle for visualizing cardiac motion in real time. Furthermore, despite the use of continuous excitation and acquisition, there is adequate contrast between the blood pool and the myocardium, allowing for good discrimination of the two.

In the arrhythmic dog, short axis heart images during a normal beat followed by a missing beat are presented in Fig. 9a. A close examination of the images confirmed that the motion of the heart stopped during the missing beat. As a result, the intensity in the blood pool was reduced by progressive saturation of the stagnant blood. This reduction is visible in the images and more evident in the time course of the left ventricle intensity as shown in Fig. 9b (the oscillation of the signal was due to the heartbeat).

For the contrast agent study, images of the dog heart were reconstructed at an inter-image spacing of 10 TRs (45 ms). Selected images are presented in Fig. 10 to illustrate different stages of the passage of the contrast agent. Images A and B are baseline images obtained be- fore the injection of contrast agent. Images C-D occurred with the contrast agent in the right ventricle; consequently, the right ventricle was enhanced. In images E-G, the left ventricle is enhanced by the contrast agent. Fi- nally, images H-K exhibit the contrast enhancement in the myocardium. These signal changes are better visualized with time courses of the left ventricle and the myocardium as shown in Fig. 11. The gradual change of the signal variation is due to the contrast agent while the rapid oscillations arise from cardiac motion. The latter may be removed retrospectively by selecting (resam- pling) images corresponding to a specific point of the cardiac cycle for perfusion analysis. The advantage of a nontriggered technique is that the image intensity is not adversely affected by an irregular heart rate, which results in TR variations in triggered techniques.

DISCUSSION

We have described a new strategy for dynamic imaging and demonstrated it with an ultrafast gradient echo sequence. As a general sampling strategy, it can be implemented with other sequences such as spin-echo or conventional gradient-echo sequences for faster and smoother image update. Several applications of the technique are described in this paper. Its full potential re-

FIG. 10. A subset of images, separated by 20 TRs (90 ms), obtained from the contrast agent study. These images correspond to baseline (A-B), right ventricular enhancement (C-D), left ventricular enhancement (E-G), and myocardial enhancement (H-K).

mains to be further explored and assessed. As the technique does not require any special gradient hardware, it can be readily implemented on conventional scanners. Due to constraints of the clinical system used for this work, actual real time implementation was not achieved. However, with proper modification of the sequence control and image reconstruction hardware and software, it will be straightforward to accomplish. With a real time implementation, the user will be able to continuously monitor images, have real time control of the slice posi- tion and orientation and have the ability to track a cath- eter or dynamically examine the heart from various ori- entations. The technique can thus be utilized for interventional MRI. It is well suited for such applications, because it provides fast updating of images and smooth representation of motion.

The cardiac studies described here are clinically important because they generated dynamic images without EKG triggering, allowing one to visualize the heart motion during individual cardiac cycles. These studies are likely to play an important role in visualizing abnormal heart beats, in assessing the hemodynamics of the heart within an individual cardiac cycle and in first pass studies of contrast agents. With the ultrafast gradient echo implementation, the contrast between the muscle and blood pool is ideal for visualizing the heart.

The general goal in choosing the oversampling scheme for the low k-space lines is to achieve the most efficient


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FIG. 11. Time course of the left ventricle and t h e myocardium of the images shown in Fig. 10.

updating of the low k-space lines with a marginal increase in overall acquisition time. Without a priori knowledge of the signal distribution in the k-space, the solution to the optimal oversampling scheme is not straightforward. The ad hoc scheme described here was chosen to approximate a typical low k-space signal distribution. In this work we have not conducted a thorough theoretical or experimental investigation of this issue. However, related work by others (20-21) has suggested that an optimal choice may be determined based on the principal features of the image. It is interesting to note that the singular value decomposition (SVD) method described in reference (21) uses a rather different approach in data acquisition and a comparison between CURE and the SVD based method may be hitful.

Although the new strategy facilitates faster and smoother image updating in dynamic studies, it is still limited by the length of the sliding window, resulting in some drawbacks. First, the effective temporal resolution is limited by the matrix size despite the fact that it is improved by the random sampling scheme. In addition, the finite window size also leads to motion artifacts when the imaged organ moves substantially in the window. Both problems are slightly exacerbated by the additional length of the unit table due to the extra low k-space lines and can be reduced with more advanced hardware. Unfortunately, the temporal resolution cannot be precisely specified as it depends on the spatial fre-

quency content of the changes in the image as well as the specific table used. While the exact manifestation of the artifacts depends on the motion and the phase-encoding order for the window, the artifacts generally appear as noisy fluctuations or ghosts. An illustration of the artifact is seen in the simulation results and in several images in Fig. 10 where the systolic motion was not adequately captured. It is also interesting to note that, with the random phase encode table, the ghosting due to periodic motion may be reduced because it destroys the periodicity of the motion as previously pointed out (19).

Finally we would like to discuss the temporal correlation of noise. For any technique that shares the data in the reconstruction of temporally adjacent images, the noise is also shared. Consequently, the noise in adjacent images are correlated; with the repetition of a unit random table as used in the current implementation of CURE, this correlation results in a temporally pseudo- periodic fluctuation (with the period equal to the length of the unit table) in the images. If the measured data are very noisy, this fluctuation can potentially introduce ar- tifactual signal changes and limit the utility of the technique in quantitative studies such as perfusion.

CONCLUSION

We have developed and demonstrated a new strategy that greatly facilitates dynamic MRI studies and can be po-

336 Parrish. Hu

tentially used for real time imaging. Simulation studies showed that the technique was better than the linear approach in depicting dynamic information and there was little temporal variation of the noise. Comparison with the keyhole method indicated that CURE was advantageous in certain applications. On a scanner with conventional gradient hardware, pseudo-real time images were obtained. With more advanced hardware, motion artifacts will be reduced and the new technique will be more robust. The technique was shown to have a wide variety of potential applications, particularly in cardiac imaging and possibly in interventional studies. More sys- tematic studies are needed to fully establish its clinical utility.

ACKNOWLEDGMENTS

The authors thank Drs. Norbert Wilke and Arthur Still- man for helpful discussions.

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continuous update with random encoding (cure): a new strategy for dynamic imaging

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