Dynamic Imaging With Multiple Resolutions Along Phase-Encode and Slice-Select Dimensions

Transcription

1 Magnetic Resonance in Medicine 45: (2001) Dynamic Imaging With Multiple Resolutions Along Phase-Encode and Slice-Select Dimensions Lawrence P. Panych, 1 * Lei Zhao, 1 Ferenc A. Jolesz, 1 and Robert V. Mulkern 2 An implementation is reported of an imaging method to obtain MUltiple Resolutions along Phase-encode and Slice-select dimensions (MURPS), which enables dynamic imaging of focal changes using a graded, multiresolution approach. MURPS allows one to trade spatial resolution in part of the volume for improved temporal resolution in dynamic imaging applications. A unique method of Hadamard slice encoding is used, enabling the varying of the phase encode and slice resolution while maintaining a constant effective TR throughout the entire 3-D volume. MURPS was implemented using a gradient-recalled echo sequence, and its utility was demonstrated for MR temperature monitoring. In this preliminary work, it has been shown that changes throughout a large volume can be effectively monitored in times that would normally only permit dynamic imaging in one or a very few slices. Magn Reson Med 45: , Wiley-Liss, Inc. Key words: dynamic multiresolution imaging; temperature monitoring; Hadamard encoding; spatially-selective RF excitation; non-fourier encoding; adaptive imaging Dynamic MRI methods for monitoring spatially localized changes usually involve reducing volume coverage to improve temporal resolution. This is a good tradeoff when changes are clearly limited to a small, well-defined volume of interest (VOI). However, in some applications, such as monitoring the progress of heating in focused ultrasound or interstitial laser surgery, this tradeoff is less than ideal because changes are not restricted to a well-defined volume. To achieve a reasonable temporal resolution, it then becomes necessary to monitor a relatively small VOI comprising very few slices where the dominant change is experienced. Changes may occur in other slices throughout the volume but, in the interests of temporal resolution, they may not be monitored. Here we propose a graded, multiresolution image acquisition as an alternative to the all or nothing approach. In a standard acquisition, the parameters affecting spatial resolution slice thickness and number of phase encodes are constant for all slice acquisitions. For example, if it is determined that 3-mm slices and 256 phase encodes are necessary to spatially resolve changes in one slice, the same parameters must be used for all slices, thereby limiting the volume that can be imaged. If, however, slice thickness and phase-encode resolution are varied within an acquisition, we reason that it will be possible to effectively monitor changes throughout a much larger volume without sacrificing temporal resolution. This depends, of course, on whether or not the requisite spatial resolution to resolve changes is also variable throughout the volume. For applications such as temperature mapping this is indeed the case. Sharp and rapid temperature changes occur close to the source of energy deposition; however, in regions distant from the source, the changes are slower and more spatially diffuse. In previous work, we and others have investigated multiresolution approaches based on non-fourier encoding with wavelets (1 9). In wavelet encoding, RF pulses were designed to excite spatial profiles shaped like wavelet functions. The special features of the wavelet transform make it particularly suitable for reconstructing images with spatially variable resolution, and this led us to propose adaptive imaging strategies based on multiresolution wavelet encoding (2). Our previous work with wavelets involved variation of resolution in a single RF select direction only. Other groups (10 14) have reported imaging methods that also involve expansions in terms of non-fourier basis functions with spatially variable resolution. In these methods, variable resolution is achieved through a nonuniform sampling of k-space in phase-encoding directions combined with a special reconstruction method that projects the selected Fourier basis set onto the non-fourier basis functions. We propose a method to obtain MUltiple Resolutions along Phase-encode and Slice-select dimensions (MURPS). In the MURPS approach, resolution parameters are constant within any single slice; however, both slice thickness and phase-encode resolution are varied for different slices. By reducing the number of phase encodes and increasing the slice thickness for some slices, we are able to directly trade reduced spatial resolution in some parts of the volume for an overall increase in either temporal resolution or volume coverage. Currently MURPS is being developed for MR temperature monitoring, but it also has potential for use with other applications, such as fmri and other dynamic contrast studies. 1 Department of Radiology, Brigham and Women s Hospital, Harvard Medical School, Boston, Massachusetts. 2 Department of Radiology, Children s Hospital, Harvard Medical School, Boston, Massachusetts. Presented in part at the 8th Annual Meeting of ISMRM, Denver, Grant sponsor: Whitaker Foundation; Grant number: TF ; Grant sponsor: NIH; Grant numbers: R29-CA70314; P01-CA67165; R01-NS *Correspondence to: Lawrence P. Panych, Ph.D., Department of Radiology, Brigham and Women s Hospital, 75 Francis Street, Boston, MA Received 2 October 2000; revised 3 January 2001; accepted 8 February Wiley-Liss, Inc. 940 METHODS Multiresolution Encoding Method Here we describe a MURPS implementation for acquiring seven slices, each with variable slice thickness and variable phase-encode resolution but with constant effective TR. The drawing at the top of Fig. 1 demonstrates the MURPS acquisition schematically, with each block in the drawing representing a view of a voxel in the slice-phase plane. The seven slices are arranged horizontally. For sim-

2 Dynamic Multiresolution Imaging 941 excited four times in the 12 TR periods. However, because reconstruction of the B slices requires two separate Hadamard encodes (B1 B2, B1 B2), only two phase encodes can be collected in the same time period in which slice A is phase encoded four times. The volume covered by the C slices is also excited four times in the 12 TR periods. Because reconstruction of the C slices requires four separate Hadamard encodes (C1 C2 C3 C4, C1 C2 C3 C4, C1 C2 C3 C4, and C1 C2 C3 C4), only one phase encode can be collected in the same time period in which slice A is phase encoded four times and the B slices are phase encoded twice. Note that with this scheme there is a relationship between the number of phase encodes and the Hadamard encoding factor. The reduction in the number of phase encodes is inversely proportional to the Hadamard encoding factor so that the product of the number of phase encodes and the Hadamard encoding factor is constant for all slices. For example, when the number of phase encodes acquired for a slice is one fourth of the full resolution case, then four slices are Hadamard encoded. Likewise if the number of phase encodes is reduced by half, the number of Hadamard-encoded slices is 2. This relationship is necessary in order to maintain a constant effective TR for all slices. There is no such restriction on the slice thickness. FIG. 1. The upper drawing is a schematic depiction of voxel sizes in the slice and phase-encoding directions for a seven-slice MURPS acquisition method. The lower drawing is of excitation profiles for the seven MURPS slices. The table lists resolution parameters for the seven-slice MURPS scheme used in brain imaging experiments. plicity, only a small number of voxels are shown in the phase-encoding direction (i.e., the vertical direction in the drawing). In the frequency-encoding direction (throughplane in Fig. 1) the resolution is constant for all slices. Ideal excitation profiles for the seven slices are shown below the drawing in Fig. 1. The table at the bottom of Fig. 1 lists parameters that were used in some of our experiments. In this example, a relatively thin (5-mm) center slice (labeled A) was acquired at full in-plane resolution. In an application such as the monitoring of heating by focused ultrasound, this slice should be placed so as to cover the location of maximum energy deposition. For two neighboring slices (B1 and B2), slice thicknesses were increased (to 10 mm) and phaseencode resolution was reduced by a factor of 2. For the outer four slices (C1, C2, C3, and C4), slice thicknesses were again varied and phase-encode resolution was reduced by another factor of 2. In the MURPS implementation described here, the B and C slices are separately Hadamard encoded (15 18) to enable a reduced number of phase encodes in the outer slices while still maintaining a fixed TR for all slices. Figure 2 shows the encoding scheme for the first 12 TR periods. After every three TR periods, the entire imaging volume (A, B, and C slices) is excited once; thus the effective TR throughout the volume is 3 TR. At the end of the 12 TR periods, as shown in Fig. 2, slice A has been excited four times and four phase encodes of the slice have been collected. The volume covered by the B slices has also been FIG. 2. Hadamard encoding profiles used for acquisition of data to reconstruct seven MURPS slices as shown in Fig. 1. From top to bottom, a different profile is used in succession on each of 12 successive TR periods. This sequence of profiles is used repeatedly for 3*N TR periods, where N is the number of phase encodes collected for slice A. The order of phase encoding is shown for the first 12 TR periods.

3 942 Panych et al. We are free to set slices to any convenient thickness. As shown in the table of Fig. 1, it is not even necessary to maintain constant slice thickness within a group of Hadamard-encoded slices (e.g., the C group). In MURPS, the signal-to-noise ratio (SNR) varies between slices according to slice thickness, number of phase encodes, and number of Hadamard encodes. The SNR in any slice with respect to slice A is equal to (S/ S A ) (HP A )/P, where S is the slice thickness, P is the number of phase encodes, and H is the number of Hadamard encodes. S A is the thickness of the slice A, and P A is the number of phase encodes for the slice. Since there is no Hadamard encoding of slice A, H A 1, and is not included in the equation. As discussed above, the product of the number of phase encodes and the Hadamard encoding factor is constant for all slices, so that P P A /H; thus, the relative SNR in any slice with respect to slice A is simply equal to H (S/S A ). A 2D spoiled gradient-echo (SPGR) sequence was modified for the MURPS implementation as follows. First, the sequence was altered so that a set of arbitrary RF pulses (as defined in external files) could be preloaded and then different RF pulses could be used for each excitation. Twelve pulses designed to excite the profiles shown in Fig. 2 were computed on a workstation and preloaded into the imager. Each of the 12 RF pulses (of 5.12-ms duration and 30 flip angle) was used in succession, with the sequence repeating after every 12 excitations. The imaging pulse sequence was further modified to execute a phase-encoding order, as denoted in Fig. 2, for the first 12 excitations. On each set of excitations, the phase-encoding order was simply equal to the order from the previous set of excitations plus {4,2,1,4,2,1,4,2,1,4,2,1}. The phase-encode ordering for each TR period was programmed directly in the pulse sequence, although it is also possible to read the order from an external file. Brain Imaging Experiments The seven-slice multiresolution MURPS acquisition scheme was implemented on our 1.5T Signa LX system (GE Medical Systems, Milwaukee, WI) and used to acquire a set of slices from a human volunteer after obtaining informed consent according to institutional review protocol. Seven slices of varying thickness and in-plane resolution were acquired in an interleaved fashion using the modified SPGR sequence (TR/TE, 30/8.6 ms). Slice A was acquired at full in-plane resolution ( acquisition matrix, 240-mm FOV) and at a thickness of 5 mm. The B slices were acquired at half the phase-encode resolution ( acquisition matrix) and the C slices were acquired at one fourth of the phase-encode resolution ( acquisition matrix). The B and C slices were two or three times the thickness of the center slice. As shown in the table of Fig. 1, with this scheme voxel volume increases in graded steps from 5 mm 3 in the center slice to 60 mm 3 in the outer slices. The total time for encoding the seven multiresolution slices is 3*N*TR, where N is the number of phase encodes collected for slice A (i.e., 256 in the brain imaging experiments). The total volume covered is 7.5 cm 24 cm 24 cm. To cover the same volume with 5-mm slices at the highest in-plane resolution would require 15*N*TR. Thus, the temporal resolution is increased fivefold over what it would be at full spatial resolution. Or, for the same temporal resolution, there is a fivefold increase in volume coverage with MURPS over a standard acquisition at constant full spatial resolution. A straightforward tradeoff is made, decreasing spatial resolution in some parts of the volume in order to increase either temporal resolution or volume coverage. Temperature Mapping Experiments MURPS was implemented on a Signa 1.5T LX system for dynamic temperature monitoring using the proton resonant shift method (19 21). A glass tube was inserted into the center of an orange and placed in the MRI system. A catheter with attached syringe was inserted into the glass tube so that hot water could be injected into the tube at the start of imaging. A doped water phantom was also placed within the imaged volume to monitor changes due to slow drift of the static magnetic field during the experiment. The method of acquisition was as described in the previous sections with resolution parameters as follows: Numbers of phase encodes in the A, B, and C slices, respectively, were 120, 60, and 30, and slice thicknesses were 80% of those used in the brain imaging experiments (i.e., 4 mm in the center slice, A, and 12 mm in the edge slices, C1 and C4). A dynamic series of images was acquired at the rate of one set of seven multiresolution slices every 12.6 s over a period of approximately 1 h. Each set of multiresolution slices was reconstructed and phase-difference images were computed by performing a complex division of the image set at each time point with the final image set in the dynamic series, then taking the phase of the result. For each voxel, a time series of 252 phase-difference values was obtained. These were then converted directly to temperature change given a reported shift in the proton resonance of approximately ppm per C of change (21). Prior to conversion from phase to temperature values, the phase was unwrapped using a library function in Matlab (The Mathworks, Natick, MA) that removes abrupt wraparound phase changes. The average phase was also measured in a VOI in the unheated doped-water phantom to separate phase changes due to heating from the background drift in phase due to static magnetic field changes. RESULTS Brain Imaging Experiments The upper part of Fig. 3 shows seven reconstructed axial brain slice images using MURPS. The variable resolution is evident across the volume with highest resolution (and lower SNR) in slice A and lowest resolution in slices C1 and C4. Note the uniform contrast behavior throughout the volume. The total volume covered in 23 s is 75 mm 240 mm 240 mm. At full resolution (5-mm 3 voxels) 115 s would be required to cover the same volume. The table at the bottom of Fig. 3 gives the theoretical and experimental SNR of the MURPS slices with respect to slice A. There is a relatively close agreement between the theoretical SNR values and those determined experimentally, thus validat-

4 Dynamic Multiresolution Imaging 943 FIG. 3. At top are seven brain slices acquired using the MURPS method. See Fig. 1 for a description of resolution parameters. The seven slices cover a volume of cm. The vertical is the frequency-encode direction, and the horizontal is the phase-encode direction. Below the MURPS set are images of virtual slices created from a reference set of 15 slices of 5-mm thickness and phase-encode resolution of 256, which cover the same total volume as the seven slices above. The virtual slices were created by averaging appropriate 5-mm slices to simulate the thicker slices, and by filtering the images in the phase-encode direction. The table below the images gives the theoretical and experimental SNR of each MURPS slice with respect to slice A. Relative SNR is equal to H (S/S A ) where S is the slice thickness, H is the Hadamard encoding factor, and S A is the thickness of slice A. ing our expression for the variation in SNR between MURPS-acquired slices. A reference set of 15 slices of 5-mm thickness covering the same volume as above was also acquired. Phaseencode resolution was 256 for this set. The slices were acquired sequentially with a TR of 90 ms so as to match the T 1 weighting of the multiresolution set (where the effective TR was ms). From this reference set of slices, virtual slices were created by averaging appropriate slices to simulate the thicker slices in the MURPS set, and then filtering the images in the phase-encode direction. As expected, the virtual set is very similar to the MURPS result except for a few understandable differences. Because the reference set was acquired sequentially, in-flowing spins were not saturated and blood vessels in the virtual image set appear bright. In MURPS, the entire volume is excited every three shots, minimizing the in-flow effect from vessels. Other minor contrast differences are likely due to slightly different flip angle settings in the two acquisitions. There is also a small but noticeable dark artifact in the frontal region of slice C4 in the MURPS result (Fig. 3, see arrow). We attribute this to susceptibility-induced losses in the slice direction due to the relatively large slice thickness. Note that it does not appear in the corresponding virtual slice because the image was created by averaging thinner slices. The left side of Fig. 4 shows mid-brain slices for axial, sagittal, and coronal orientations after an interpolated data set was created from the seven original MURPS slices. The interpolated slices were obtained using an interpolation function in Matlab. For comparison, we also created a comparable interpolated data set from the 15 reference slice images, and mid-brain slices for the three orientations are shown on the right of Fig. 4. The coronal slice on the left of Fig. 4 shows variable resolution in both the phase and slice directions, causing it to appear slightly more isotropically smoothed than the sagittal slice, which has variable resolution only in the slice direction. The dark streaks in the sagittal view on the left are due to thin horizontal features that are not broadened because the vertical is the frequency-encoded direction. However, the features are very poorly resolved in the slice direction, giving the streaked appearance. The central axial slice is, as expected, virtually identical with respect to resolution in the two sets. It should be noted that the interpolated images in Fig. 4 do not provide any information that does not also exist in Fig. 3. These interpolated data sets are presented only to demonstrate the tradeoffs that are made when using MURPS to increase temporal resolution or volume coverage. Temperature Mapping Experiments The left side of Fig. 5 shows three-plane views of an interpolated data set computed from seven magnitude multiresolution MURPS images of the phantom (orange with tube of hot water). Voxel sizes varied from 2 2

5 944 Panych et al. FIG. 4. Left: Mid-brain slices for axial, sagittal, and coronal orientations after creation of an interpolated data set from the MURPS slices shown at the top of Fig. 3. Right: Mid-brain slices for axial, sagittal, and coronal orientations after creation of an interpolated data set using 15 5-mm slices covering the same volume as the seven MURPS slices. 4 mm in the center slice to mm in the edge slices. Temperature-difference maps in three-plane views were computed and are also shown in Fig. 5 (right side). The temperature maps are obtained from phase-difference images using the linear relationship between the phase change (after unwrapping) and temperature change. The maps in Fig. 5 show the temperature difference at the beginning of the cooling period with respect to the baseline temperature at the end of the cooling period. As expected, the largest temperature change occurs close to the hot water tube. The images clearly demonstrate the ability of the multiresolution acquisition method to depict temperature change throughout a large, 3D volume. Figure 6 shows a segmented gray-scale representation of the temperature changes ocurring over a 30-min period along one column through the phantom in each of the FIG. 5. Left image set: Three-plane views of interpolated data set obtained from magnitude images of a phantom (orange with hot water tube inserted in center) acquired using the MURPS method. Right image set: Three-plane views of interpolated temperature difference maps for the period just after injection of hot water into the tube. The maps show the temperature change in C with respect to baseline temperature. White represents the hottest temperature, as shown on the scale at the far right.

6 Dynamic Multiresolution Imaging 945 FIG. 6. Evolution of heat over a 30-min period along one plane (8 cm wide) cutting through the phantom in all seven MURPS slices. The location of the plane is shown in the set of slice reference images on the right side of the figure. The maps are segmented into four temperature regions that are represented in the figure by successively lighter shades of gray (see color legend at bottom). White represents the hottest temperature region. seven MURPS slices. The maps are segmented into four regions of temperature change: [T 2 ], [2 T 4 ], [4 T 10 ], and [T 10 ], which are represented in the figure by successively lighter shades of gray, with white representing the highest temperature region. The position of the column in each slice is shown on the right in Fig. 6. The columns are displayed side by side for each time point so that the horizontal direction represents time and the vertical direction represents space. Figure 6 demonstrates temperature change with time in each of these slices along the column indicated in the right-hand panel. The figure demonstrates that, as expected, the time lag to reach peak temperature is a function of the slice distance from the hot water tube (which is located in slice A), and that temperature changes are more spatially and temporally diffuse in regions further away from the heat source. It should be noted that the data shown in Fig. 6 are only a small fraction of that available from the complete MURPS data set. DISCUSSION In this work we present MURPS, a multiresolution imaging scheme for dynamic imaging with variable slice thickness and phase-encode resolution. The MURPS method allows one to trade spatial resolution in part of the volume for improved temporal resolution or increased volume coverage in dynamic imaging applications. MURPS was implemented using a modified SPGR sequence, and its utility was demonstrated for MR temperature monitoring. In the preliminary work presented here, we have shown that temperature changes throughout a large volume can be effectively monitored in times that would normally only permit monitoring in one or a very few slices. The potential for the use of MURPS with other applications in which we have applied a multiresolution imaging approach, such as fmri (22), and in dynamic contrast studies (4), is currently under investigation.

7 946 Panych et al. The MURPS implementation described here uses Hadamard slice encoding, enabling the varying of the phaseencode resolution while maintaining constant effective TR. This is achieved when the product of the number of phase encodes and the Hadamard encoding factor is constant for all slices. Sequential, non-hadamard MURPS acquisitions are also possible (i.e., all phase encodes for one slice are acquired before acquisition of another slice begins). Therefore, constant effective TR can be achieved without Hadamard encoding, with the advantage that the temporal resolution of each slice acquisition can be varied along with spatial resolution. A fully sequential acquisition, however, is only time efficient for short TR applications, and SNR would suffer in regions of medium and long T 1. It is also possible to design a non-hadamard MURPS implementation that combines both sequential and interleaved acquisitions. For example, if N/4 phase encodes of slices [A,B1,C1] are followed by N/4 phase encodes of [A,B1,C2], followed in turn by N/4 phase encodes of [A,B2,C3] and, then, N/4 phase encodes of [A,B2,C4], we would achieve the same effective TR as Hadamard MURPS along with a variable number of phase encodes in the A, B, and C slices. The absence of Hadamard encoding in this scheme has the advantage of avoiding potential peak power problems and the need to design special RF pulses. These advantages, however, would have to be weighed against several disadvantages. SNR per unit time in Hadamard MURPS would be 100% and 40% higher, respectively, in the C and B slices compared to the non-hadamard implementation. Furthermore, in the non-hadamard MURPS acquisition, several extra dummy excitations would be needed to allow for signal equilibrium to be reached in the B and C slices. In addition, the temporal sampling window is not constant for all sets of slices, as it is for Hadamard MURPS. Hadamard encoding may introduce some constraints in terms of peak RF power. This was not a problem in our work, however, due to the fact that a gradient-echo sequence with relatively short TR was used, so flip angles in the range of 30 were sufficient. For spin-echo imaging, peak power constraints are more severe and the implications need to be investigated. Because of the flip angles used, we did not expect distortions in the Hadamard profiles due to nonlinear effects. When higher flip angles are used, however, special RF design methods must be employed with Hadamard MURPS to ensure that the desired profiles are excited (23). SNR varies considerably between MURPS slices due to the large variation in voxel sizes. In the implementation reported here, SNR in the central, high-resolution slice is the same as would be obtained in a normal high-resolution acquisition for an equivalent TR. In the MURPS acquisition, however, the SNR increases as one moves away from the central slice, and it is a full 12 times greater in the outer slices than in the central slice. Generally, because changes tend to become much smaller as one moves away from the focal VOI, an important advantage of MURPS is that it provides increasing SNR, which enables more accurate measures of the changes where they tend to be small. It should be noted that MURPS is not pulse-sequence dependent and, in principle, it is possible to implement it for any kind of sequence, including fast imaging approaches such as echo-planar imaging. Also, although we implemented MURPS using seven multiresolution slices, any number of variations is possible. It is not necessary, for example, to limit oneself to a single high-resolution slice located at the center of the imaged volume. Slices can be arranged in any fashion with one, two, or more highresolution slices mixed with other slices of varying thickness. Furthermore, it is not even necessary that slices be contiguous. Because RF pulses are designed off-line and read by the pulse sequence prior to scanning, it is easy to provide a flexible choice of slice thickness and location. We are currently investigating dynamically adaptive approaches in which such a choice is made on-line during a dynamic scan session (22). Finally, MURPS is compatible with other dynamic imaging methods that involve reconstructing information from a reduced number of phase encodes, thereby raising the possibility of hybrid approaches. For example, combining MURPS with keyhole approaches (24) involves a minimum of modifications simply replacing the appropriate data from a high-resolution static baseline dataset with the multiresolution dynamic data obtained in MURPS. Extended keyhole-type methods, such as time resolved imaging of contrast kinetics (TRICKS) (25,26), which segment k-space into regions with different update rates can also be combined with MURPS by redesigning the phase-encode acquisition scheme within individual slices. Constrained reconstruction methods, such as reduced-encoding imaging by generalized-series reconstruction (RIGR) (27 29) and related methods (30), use loworder phase encodes to reconstruct higher-resolution dynamic data based on assumptions about the dynamics, and can also be combined with MURPS to reconstruct data in the slices in which we have reduced phase encoding. More complex methods that involve nonuniform k-space sampling, such as locally focused MRI (11 14), are also compatible because MURPS does not require the use of any particular set of reduced phase encodes. Combining MURPS with locally focused MRI would enable variable resolution imaging within individual slices as well as between slices, further extending the multiresolution capability of both methods. ACKNOWLEDGMENTS The authors acknowledge Dr. Seung-Schik Yoo for his assistance with some of the experimental work, and Dr. Kullervo Hynynen and Nathan McDannold for the useful discussions on applications of the method for temperature mapping. REFERENCES 1. Panych LP, Jakab PD, Jolesz FA. An implementation of wavelet encoded MRI. J Magn Reson Imaging 1993;3: Panych LP, Jolesz FA. A dynamically adaptive imaging algorithm for wavelet encoded MRI. Magn Reson Med 1994;32: Panych LP, Zientara GP, Saiviroonporn P, Yoo S-S, Jolesz FA. Digital wavelet-encoded MRI: a new wavelet-encoding methodology. J Magn Reson Imaging 1998;8: Shimizu K, Panych LP, Mulkern RV, Yoo S-S, Schwartz RB, Kikinis R, Jolesz FA. 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