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Myocardial Tissue Tracking with Two-dimensional Cine Displacement-encoded MR Imaging: Development and Initial Evaluation¹

¹ From the Departments of Radiology (D.K., W.D.G., C.M.K., F.H.E.), Biomedical Engineering (D.K., W.D.G., F.H.E.), and Internal Medicine (C.M.K.) and the Cardiovascular Research Center (W.D.G., C.M.K., F.H.E.), University of Virginia Health System, Rm 1175, MR-4 Bldg, 409 Lane Rd, Charlottesville, VA 22908. Received September 23, 2002; revision requested November 26; final revision received August 8, 2003; accepted September 8. Supported in part by Siemens Medical Solutions, the University of Virginia Fund for Excellence in Science and Technology, and National Institutes of Health grant 5T32 HL07284. Address correspondence to F.H.E. (e-mail: fhe6b@virginia.edu).

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

 
A breath-hold two-dimensional cine magnetic resonance (MR) pulse sequence based on displacement encoding with stimulated echoes (DENSE) for quantitative myocardial motion tracking was developed and evaluated. In the sequence, complementary spatial modulation of magnetization was used for time-independent artifact suppression, and echo-planar imaging was used for rapid data sampling. Twelve healthy volunteers underwent cine DENSE MR imaging, and six of them also underwent conventional MR imaging myocardial tagging. The circumferential shortening component of strain (E_cc) was measured on cine DENSE MR images and conventional tagged MR images. With complementary spatial modulation of magnetization, 10% or less of the total cine DENSE MR image energy was attributed to an artifact-generating echo during systolic imaging. Two-dimensional intramyocardial displacement and strain were measured at cine DENSE MR imaging with spatial resolution and temporal resolution of 2.7 x 2.7 mm and 60 msec, respectively. E_cc measured at cine DENSE MR imaging correlated well with that measured at conventional MR imaging tagging (slope = 0.88, intercept = 0.00, R = 0.87).

© RSNA, 2004

Index terms: Heart, function • Heart, MR, 511.121412, 511.12144 • Myocardium, MR, 511.121412, 511.12144

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

 
The imaging of myocardial function plays a central role in the evaluation of cardiac disease. Function at rest may be abnormal as a result of one of the spectrum of ischemic heart diseases (ischemia, infarction, hibernation) or of cardiomyopathy from other causes. During stress testing, new or worsening wall motion abnormalities are indicative of functionally significant coronary artery stenoses (1). In addition, wall motion imaging to detect regional contractile reserve is an accurate measure of myocardial viability, and the results can help guide coronary revascularization therapy (2).

Most clinical modalities used to image myocardial function evaluate passive wall motion (ventriculography) or wall thickening (echocardiography, gated single photon emission computed tomography, or cine magnetic resonance [MR] imaging). MR imaging also allows quantitative measurement of regional intramyocardial motion and, subsequently, strain, which can be more sensitive to wall motion abnormalities than is wall thickening (3). The two most widely used MR imaging methods for the quantification of intramyocardial wall motion are myocardial tagging (4,5) and velocity-encoded imaging (6,7). Each technique has advantages and disadvantages.

The primary disadvantage of tagging is the reduced spatial resolution of strain relative to the image spatial resolution. In tagging, after the displaced tag lines are detected (8), the displacement field can be estimated and intramyocardial strain can be computed in a variety of ways (9). With this approach, although strain may be interpolated to any desired spatial resolution, the fundamental spatial resolution of strain is nominally determined by the distance between the tag lines, which is typically several pixels. Tag detection has an additional disadvantage in that it typically requires substantial manual intervention and is therefore a time-consuming task. Harmonic phase analysis will likely obviate tag detection (10–12), but the spatial resolution of the resultant strain maps will not necessarily improve. The spatial resolution of strain maps obtained from tagged images after harmonic phase analysis is determined by the k-space filter of the analysis; in practice with single–breath-hold acquisitions, the resolution has been relatively poor (13).

In contrast to the spatial resolution with tagging, that with velocity-encoded MR imaging provides pixelwise velocity data and direct extraction of velocity values from a phase-contrast MR image. A disadvantage of velocity-encoded imaging, however, is that instantaneous velocity rather than displacement is measured. This complicates the tracking of tissue displacement over time (14) and the computation of intramyocardial strain (15).

MR imaging with displacement encoding with stimulated echoes (DENSE) offers many of the advantages of both myocardial tagging and velocity-encoded imaging (16–18). As with tagging, DENSE MR imaging involves spatial modulation of magnetization to position encode the magnetization at end diastole and to subsequently image tissue displacement relative to the end-diastolic position later in the cardiac cycle. Similar to velocity-encoded images, phase-reconstructed images are obtained at DENSE MR imaging to achieve pixelwise spatial resolution and direct extraction of motion data (in this case, displacement rather than velocity). To date, however, data acquisition in single–breath-hold DENSE MR imaging has been limited to only one cardiac phase. The purpose of this study was to develop a high-spatial-resolution breath-hold cine DENSE MR imaging technique to sample two-dimensional (2D) displacement-encoded images at multiple phases of the cardiac cycle and to evaluate the technique in healthy volunteers.

	Materials and Methods

TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

 
Pulse Sequence and Image Reconstruction
We (D.K., F.H.E.) developed a breath-hold 2D cine DENSE MR imaging pulse sequence that is similar to breath-hold 2D cine myocardial tagging (19). The background theory for cine DENSE MR imaging is explained in the Appendix. To account for the need to encode displacement in two orthogonal directions, to perform complementary acquisitions for suppression of T1 relaxation artifacts, and to acquire background phase reference data in each direction, six cine data sets were acquired at single–breath-hold 2D cine DENSE MR imaging. Accordingly, we employed a hybrid fast gradient-echo echo-planar imaging pulse sequence (20,21) (Fig 1) to acquire individual cine data sets in three heartbeats. Six cine data sets were then acquired in succession as follows. For displacement encoding in one direction, the phase reference data set was acquired first, and then the two complementary displacement-encoded data sets were acquired. Next, radiofrequency pulses and data acquisition were suspended for one heartbeat to reduce interference between displacement-encoding pulses in orthogonal directions. After the delay, the readout and phase-encoding directions were swapped, and three cine data sets were acquired in the orthogonal direction in the same manner as was used in the original direction.

View larger version (21K): [in this window] [in a new window] [Download PPT slide]   Figure 1.  Pulse sequence timing diagram for cine DENSE MR imaging. Immediately following an electrocardiographic (ECG) trigger, the 1:1 spatial modulation of magnetization displacement-encoding pulses are emitted. A segmented fast gradient-echo echo-planar MR imaging sequence modified to include the DENSE unencoding gradient is used to rapidly sample the displacement-encoded longitudinal magnetization at multiple cardiac phases. For phase-corrected 2D displacement encoding with complementary spatial modulation of magnetization-based artifact suppression, six cine data sets are acquired in a single breath hold. GRO = readout gradient, Rf = radiofrequency.

View larger version (25K): [in this window] [in a new window] [Download PPT slide]   Figure 2.  Schematic demonstrates the computation of 2D displacement maps from raw data obtained with cine DENSE MR imaging. Complementary data are subtracted to suppress the T1 relaxation echo, and a small circular filter is applied to remove residual signal. After 2D inverse Fourier transformation (2DIFT), phase correction and phase unwrapping are performed, followed by computation of one-dimensional displacement values. Vector addition of orthogonal one-dimensional displacement values yields a 2D displacement map. Phase ref. = phase reference.

Imaging parameters for cine DENSE MR imaging included repetition time msec/echo time msec of 12/5, section thickness of 8 mm, field of view of 350 x 350 mm, matrix of 128 (readout) x 60 (phase encode), partial Fourier acquisition in the phase-encode direction with 35 lines acquired with k_y 0 and 25 lines acquired with k_y < 0 [where k_y is the spatial frequency in the phase-encoding direction], flip angle of 15°, receiver bandwidth of 888 Hz/pixel, and echo train length of six. Also, the number of phase-encode lines acquired per cardiac phase per heartbeat was 30, which led to temporal resolution of 60 msec. Image reconstruction was performed with a 128 x 128 matrix by means of zero filling in the phase-encode direction. Displacement encoding was performed in the readout direction by using hard 90° radiofrequency pulses and a gradient pulse that achieved k_e = 0.35 cycles per pixel (where k_e is the spatial frequency produced by the displacement-encoding gradient pulse applied during the displacement-encoding module) for the first six volunteers and k_e = 0.28 cycles per pixel for the latter six volunteers. For conventional tagging, MR imaging parameters included 8.57/3.8, field of view of 360 x 293 mm, matrix of 256 x 168, phase-encode lines per cardiac phase per heartbeat of seven, flip angle of 15°, receiver bandwidth of 200 Hz/pixel, temporal resolution of 60 msec, tag spacing of 7 mm, and partial Fourier factor of 0.75.

Evaluation of Artifact Suppression
An important component of the breath-hold cine DENSE MR imaging sequence is the use of complementary acquisitions to achieve multiphase artifact suppression. Accordingly, one author (D.K.) evaluated the effectiveness of this artifact suppression technique by measuring the percentage of total image energy that came from the T1 relaxation echo. For each multiphase data set, the artifact-suppressed DENSE MR imaging k space was computed, and the percentage of energy due to the T1 relaxation echo was estimated. Specifically, since the displacement-encoded echo was centered at k_x = 0 cycles per pixel and the T1 relaxation echo was centered at k_x = +0.35 cycles per pixel (where k_x is the spatial frequency in the frequency-encoding direction), the energy attributed to the T1 relaxation echo was estimated to be the energy in all raw data columns above and including k_x = +0.22 cycles per pixel.

Displacement and Strain Analysis
For cine DENSE MR images, segmentation of the left ventricular myocardium was performed manually by one author (D.K.), a 2D phase-unwrapping algorithm was applied to the pixels of the left ventricular myocardium, and the pixel phase was then converted to one-dimensional displacement, according to Equation (A8). The 2D displacement of each pixel was computed by means of vector addition of the two orthogonal one-dimensionally displacement-encoded data sets. Regional Lagrangian strain E was computed by means of isoparametric formulation with quadrilateral elements (22). Each quadrilateral element was a square 4-pixel neighborhood of myocardium where the final position of each element of myocardium is known (the pixel location), and the initial 2D position of each pixel is measured. After diagonalization of E, the directions of the first and second principal strains and the corresponding eigenvalues are found. Relative to the center of mass of the left ventricle, the circumferential shortening component E_cc and the radial thickening component E_rr were computed by means of projection of E into the appropriate directions.

Strain analysis of the conventionally tagged MR images was performed by one author (D.K.) with the Findtags software program (8). Mean values of transmural E_cc measured at multiple cardiac phases in the septum and anterior, lateral, and inferior walls with cine DENSE MR imaging and conventional tagging were compared by means of linear regression that was forced to go through the (0,0) point. Bland-Altman analysis was also used to compare transmural E_cc measured with cine DENSE MR imaging with that measured with conventional tagging.

	Results

TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

 
Artifact Suppression with Complementary Spatial Modulation of Magnetization
While essentially complete artifact suppression with complementary spatial modulation of magnetization can be achieved in a phantom (Appendix), we achieved good but less than complete artifact suppression on breath-hold MR images obtained in volunteers with our protocol. Typical in vivo artifact suppression is shown in Figure 3, where k-space data and magnitude-reconstructed images are shown for two complementary displacement-encoded data sets (Fig 3, A, E) and (Fig 3, B, F), complementary spatial modulation of magnetization subtraction data (Fig 3, C, G), and subtraction data with the additional circular k-space filter (Fig 3, D, H). In this example, the percentage of total image energy that came from the T1 relaxation echo was estimated to be 8%. In the corresponding magnitude-reconstructed image, the amplitude modulation is fairly well suppressed. By removing the residual energy with the k-space filter, the corresponding amplitude modulation is essentially completely suppressed.

View larger version (82K): [in this window] [in a new window] [Download PPT slide]   Figure 3.  The k-space data and magnitude-reconstructed images from various data sets. A, E, Displacement-encoded MR images. B, F, Complementary displacement-encoded MR images. C, G, Complementary spatial modulation of magnetization subtraction MR images. D, H, Subtraction images obtained with additional circular k-space filter. Percentage of total image energy that came from the T1 relaxation echo in the subtraction data was 8% before application of the circular filter.

View larger version (20K): [in this window] [in a new window] [Download PPT slide]   Figure 4.  Plot shows mean percentage of total image energy that came from the T1 relaxation echo as a function of cardiac phase in six healthy volunteers. Mean percentage was approximately 2% in initial cardiac phases and increased to approximately 30% in the last phase. At end systole, mean percentage was 10%.

View larger version (187K): [in this window] [in a new window] [Download PPT slide]   Figure 5.  Cine magnitude-reconstructed DENSE MR images obtained in a 32-year-old male volunteer. A-I, Multiphase images cover approximately two-thirds of the cardiac cycle. Ventricular blood appears black and myocardium appears bright.

View larger version (56K): [in this window] [in a new window] [Download PPT slide]   Figure 6.  Two-dimensional cine displacement maps correspond to images in Figure 5. A-I, Tail of each displacement vector indicates the 2D position of that element of myocardium at end diastole when the displacement encoding occurred.

View larger version (50K): [in this window] [in a new window] [Download PPT slide]   Figure 7.  Cine Ecc maps correspond to the displacement maps in Figure 6. A-I, Maps illustrate the temporal development of Ecc across approximately two-thirds of the cardiac cycle. Ecc progresses from approximately zero (blue-green) early in the cardiac cycle to around -0.2 (darker blue) at end systole and returns toward zero later in the cardiac cycle.

View larger version (50K): [in this window] [in a new window] [Download PPT slide]   Figure 8.  Cine Err maps correspond to the displacement maps in Figure 6. A-I, Maps illustrate the temporal development of Err across approximately two-thirds of the cardiac cycle. Err progresses from approximately zero (blue-green) early in the cardiac cycle to around 0.45 (orange) at end systole and returns toward zero later in the cardiac cycle.

View larger version (50K): [in this window] [in a new window] [Download PPT slide]   Figure 9.  Plots of Ecc and Err versus time in various segments of the myocardium. A, B, Septal segments. C, D, Anterior segments. E, F, Lateral segments. G, H, Inferior segments. Data are mean values from midventricular DENSE MR images obtained in six healthy volunteers. Consistent with previous data from myocardial tagging studies, Err increases through systole and reaches a maximum end-systolic value of around 0.45, while Ecc decreases through systole and reaches a minimum end-systolic value of around -0.20.

View larger version (28K): [in this window] [in a new window] [Download PPT slide]   Figure 10.  Maps obtained with cine DENSE MR imaging in a 32-year-old male volunteer. A, End-systolic displacement map. B, Ecc map. High spatial resolution of pulse sequence captures the transmural increase in function from the subepicardium (lighter blue) to the subendocardium (darker blue).

View larger version (39K): [in this window] [in a new window] [Download PPT slide]   Figure 11.  Scatterplot shows correlation of transmural Ecc measured with cine DENSE MR imaging and that measured with conventional myocardial tagging at multiple cardiac phases and in different wall segments. Good linear correlation was found, with a slope of 0.88 and R = 0.87.

View larger version (29K): [in this window] [in a new window] [Download PPT slide]   Figure 12.  Bland-Altman plot shows good agreement between transmural Ecc measurements obtained with cine DENSE MR imaging and those obtained with conventional myocardial tagging.

	Discussion

TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

The breath-hold cine DENSE MR imaging sequence encompasses some aspects of previously described DENSE MR imaging sequences (16,17) and harmonic phase analysis MR imaging sequences (10,11). Most important, cine DENSE MR imaging retains the noncine DENSE imaging conventions of centering the displacement-encoded echo at k_x = 0 and shifting or suppressing other extraneous echoes with the goal of sampling the uncorrupted displacement-encoded echo with high spatial resolution. However, because the echo centered at k_x = k_e was not completely suppressed after subtraction of complementary data sets, our cine DENSE MR imaging sequence includes a harmonic phase analysis–like approach with application of a k-space filter to eliminate the residual echo. Our future work will be directed toward development of better signal suppression and elimination of the filter.

In postprocessing, cine DENSE MR imaging is more like DENSE MR imaging than harmonic phase analysis because displacement is computed for each individual pixel and strain is computed in 4-pixel neighborhoods. Unlike with previously reported DENSE MR imaging sequences, we did not adhere to the exact pulse sequence timing that strictly defines stimulated echoes. In our sequence, the time between the radiofrequency pulses in the 1:1 spatial modulation of magnetization module was shorter than the echo time in the fast gradient-echo echo-planar imaging module. We did not, however, observe any obvious adverse effects from this deviation, such as severe sensitivity to signal loss caused by intravoxel dephasing. Finally, the use of complementary spatial modulation of magnetization for artifact suppression was first used in the context of harmonic phase analysis imaging (30). However, the authors of that study did not develop single–breath-hold MR imaging.

While we achieved an acceptable signal-to-noise ratio with a fast gradient-echo echo-planar MR imaging sequence to sample the displacement-encoded echo at multiple cardiac phases, previous authors (17) reported insufficient signal-to-noise ratio with this approach for DENSE MR imaging at a single cardiac phase. Subsequently, the meta-DENSE MR imaging pulse sequence was developed on the basis of fast spin-echo MR imaging (18). The 90° excitation pulse used in fast spin-echo MR imaging undoubtedly creates more signal than does the 15° excitation pulse used in fast gradient-echo echo-planar MR imaging and produces excellent single-phase DENSE MR images. However, this approach is incompatible with multiphase breath-hold DENSE MR imaging as developed in the current study. The discrepancy in signal-to-noise ratios with fast gradient-echo echo-planar MR imaging may potentially be explained by other implementation differences. In the previous implementation of fast gradient-echo echo-planar MR imaging, additional and larger gradient pulses were used. Specifically, large crusher gradients were applied in the section-select direction for artifact suppression; this may have caused signal loss due to intravoxel dephasing (31). Also, the gradient area used for displacement encoding was approximately 4.5 times greater, which may have been an additional source of intravoxel dephasing. Ideally, it would be desirable to achieve both higher signal-to-noise ratio and multiphase imaging. Toward this aim, our future work will include development of a true fast imaging with steady-state precession sequence (32) to sample the displacement-encoded echo.

The mathematic description of cine DENSE MR imaging developed in the Appendix assumes that residual transverse magnetization does not contribute to theacquired signal. This assumption is justified in the context of this study because our pulse sequence employed radiofrequency spoiling, which effectively eliminated these magnetization components. When sampling the displacement-encoded magnetization with sequences that reuse transverse magnetization, such as fast spin-echo or true fast imaging with steady-state precession, it is important to unencode the phase of the transverse magnetization before subsequent application of radiofrequency pulses to avoid phase errors (18). Our mathematic description would need to be modified to apply to these cases.

For each myocardial pixel of each cine DENSE MR image, the 2D in-plane displacement of the tissue in that pixel relative to its position at end diastole is measured. Since the through-plane component of displacement is not currently measured, the in-plane displacement measured at different cardiac phases may come from different tissue. This limitation is common to techniques that neglect through-plane motion, including 2D myocardial tagging and 2D velocity-encoded MR imaging.

In Figure 11, which compares E_cc measured with cine DENSE MR imaging and that measured with conventional myocardial tagging, two clumps of data are observed around the values (0.0, 0.0) and (-0.15, -0.15). This may be explained by the fact that the data were acquired during the end-diastolic to end-systolic period of the cardiac cycle. More specifically, the first two cardiac phases were acquired around end diastole and typically had E_cc values near zero, which led to the small clump of data around the values (0.0, 0.0). During early systole and midsystole, E_cc values changed with each sampled cardiac phase, which led to sparser sampling of the intermediate E_cc values. At end systole, E_cc remained near -0.15 for two to four acquired phases, which led to the larger clump of data observed around the value (-0.15, -0.15).

With the exception of fewer data points in our study, the results of linear correlation and Bland-Altman analyses are very similar to those obtained by Garot et al (13) with harmonic phase analysis. Other differences between our data and theirs are that the clumps seen in Figure 11 do not appear in their data, and the range is greater in their data. The lack of clumps in their data is probably a result of inclusion of patients after infarction, which would provide more intermediate E_cc values. The range in their data was greater because the data were obtained in volunteers during dobutamine stress and at rest.

There are numerous potential applications of the cine DENSE MR imaging pulse sequence used in the current study. Use of this technique with parameters modified to achieve higher temporal resolution may allow performance of MR imaging during dobutamine stress testing (13,33,34) with high-spatial-resolution on-the-fly strain mapping. Also, cine DENSE MR imaging may be useful in the study of postinfarct contractile function, particularly in the setting of nontransmural infarction where the ability to distinguish subepicardial from subendocardial strain is important. Finally, high-spatial-resolution strain mapping may provide a means for assessment of the results of therapies intended to improve contractile function, such as those delivered by means of direct myocardial injection.

	APPENDIX

TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

 
In DENSE MR imaging, it is known that in addition to the displacement-encoded stimulated echo, an artifact-generating echo due to T1 relaxation also appears in the readout window and needs to be suppressed (18). One issue that complicates multiphase DENSE MR imaging is suppression of this artifact-generating echo at multiple time points. We developed a mathematic description of DENSE MR imaging and used it to show how complementary acquisitions (35), which have recently been used for improved harmonic phase analysis imaging (30), can be employed to isolate the displacement-encoded stimulated echo independent of time. This approach can be used to develop a breath-hold cine DENSE MR imaging pulse sequence.

DENSE MR imaging has been described previously in terms of stimulated echoes (18), but for the purpose of developing a complementary artifact-suppression method, we analyzed DENSE MR images from the perspective of 1:1 spatial modulation of magnetization. In DENSE MR imaging, encoding pulses are emitted immediately after an electrocardiographic trigger (Fig 1). Since the displacement-encoding pulses are identical to those for 1:1 spatial modulation of magnetization, the longitudinal magnetization after displacement encoding is cosine modulated as a function of position according to the following equation:

where M_z is the longitudinal magnetization, M is the value of M_z just prior to application of the displacement-encoding pulses, and x is position. To separate different MR imaging echoes, Equation (A1) can be rewritten in the Eulerian form of cos(k_ex) as the following equation:

Equations (A1) and (A2) describe the spatially encoded longitudinal magnetization immediately after the electrocardiographic trigger pulse, which is nominally at end diastole. Later, at subsequent time points in the cardiac cycle, the stored longitudinal magnetization is sampled after application of a radiofrequency pulse and generation of transverse magnetization. However, T1 relaxation occurs during the intervening time, which leads to a time-dependent artifact-generating echo. The time dependence of M_z can be derived by means of application of the empiric Bloch equation, which governs longitudinal magnetization, to Equation (A1) to obtain the following equation:

where M₀ is the thermal equilibrium value of the longitudinal magnetization. Next, at multiple phases during the cardiac cycle, a radiofrequency pulse is applied to create transverse magnetization and, in DENSE but not 1:1 spatial modulation of magnetization techniques, an unencoding gradient pulse with an area equal to that of the initial displacement-encoding gradient pulse is applied just prior to signal readout. In Figure 1, the unencoding gradient pulse and the readout prephaser pulses are combined into a single gradient pulse that preceeds the readout gradient. These events modify Equation (A3), such that

where M_xy is the transverse magnetization after the excitation pulse, is the flip angle of the excitation pulse, and x is the tissue displacement that occurred from end diastole to the current time t. By applying the Eulerian form of cosine specified in Equation (A2) to Equation (A4) and by rearranging terms, we obtain

Equation (A5) contains three distinct terms, or echoes, that are summed together: (a) the desired DENSE echo (stimulated echo) whose phase is directly proportional to the tissue displacement x, (b) one artifact-generating echo whose phase is additionally modulated by a factor of 2 k_ex, and (c) a second artifact-generating echo that arises from T1 relaxation and whose phase is additionally modulated by a factor of k_ex. Ideally with DENSE MR imaging, an image is reconstructed that depicts the phase of the first echo, which is encoded for tissue displacement, while the artifact-generating echoes are completely eliminated.

While Equation (A5) describes the desired and artifact-generating echoes in DENSE MR imaging, it is instructive to examine the corresponding DENSE k space wherein these echoes can be easily visualized. First, we note that since Equation (A5) is composed of three simple exponential functions of k_x, the DENSE k space has three distinct echoes centered at k = 0, k = k_e, and k = 2 k_e. With the DENSE unencoding gradient, these echoes are shifted by the amount k_e relative to the conventional 1:1 spatial modulation of magnetization k space, which has echoes centered at k = -k_e, k = 0, and k = k_e. Experimental data from a stationary phantom are shown in Figure A1, which illustrates the three k-space echoes obtained with 1:1 spatial modulation of magnetization and the three shifted k-space echoes obtained with DENSE MR imaging. In Figure A1, A and B, the value of k_e is 0.17 cycle per pixel, and all three echoes appear in the readout window for both 1:1 spatial modulation of magnetization and DENSE MR imaging, which leads to cosine-modulated magnitude-reconstructed images (Fig A1, E, F). By increasing the value of k_e to 0.35 cycle per pixel in DENSE MR imaging, the first artifact-generating echo can be encoded at a spatial frequency that is higher than that detected during data sampling and therefore does not contribute to the signal. The value of k_e should not be further increased so that the second artifact-generating echo is spatially encoded beyond the detectable value, however, because this leads to substantial signal loss when the contracting heart is imaged (31).

View larger version (65K): [in this window] [in a new window] [Download PPT slide]   Figure A1.  The k-space images and corresponding magnitude-reconstructed MR images obtained in a phantom demonstrate the progression from the 1:1 spatial modulation of magnetization method to the DENSE method with artifact suppression. A, E, These 1:1 spatial modulation of magnetization MR images were obtained with three echoes centered at k = -ke, k = 0, and k = ke, which leads to an amplitude-modulated magnitude-reconstructed MR image. B, F, These DENSE MR images were obtained with ke = 0.17 cycle per pixel and without suppression of the T1 relaxation echo. The three echoes in the 1:1 spatial modulation of magnetization method were shifted and are now centered at k = 0, k = ke, and k = 2 ke, which leads to the magnitude-reconstructed image in F being identical to that in E. C, G, These DENSE MR images were obtained with ke = 0.35 cycles per pixel and without suppression of the T1 relaxation echo. One artifact-generating echo is centered at k = 2 ke and has a spatial frequency greater than spatial frequencies detected during data sampling, which leads to a different amplitude-modulated magnitude-reconstructed image. D, H, DENSE MR images were obtained with ke = 0.35 cycle per pixel and suppression of the T1 relaxation echo with complementary spatial modulation of magnetization. The remaining displacement-encoded echo is centered at k = 0, which leads to a magnitude-reconstructed image that is not amplitude modulated and a phase-reconstructed image where the pixel phase is proportional to tissue displacement (Eq [A8]).

and

where M¹_xy and M²_xy are the transverse magnetization values for the two complementary DENSE acquisitions. In addition, in Equations (A6) and (A7), we assumed that k_e is large enough to encode the first artifact-generating echo with a spatial frequency outside the detected range. By acquiring and subtracting these two data sets, we obtain

where M^c_xy is M¹_xy - M²_xy . M^c_xy (x, t) represents the isolated displacement-encoded stimulated echo (ie, an echo whose phase is proportional to the tissue displacement and that does not contain artifact-generating terms at any time t).

	ACKNOWLEDGMENTS

 
We thank Daniel B. Ennis, BS, for helpful discussions regarding strain analysis of cine DENSE MR imaging data. We thank Michael A. Guttman, MS, and Elliot R. McVeigh, PhD, for providing the Findtags analysis program.

	FOOTNOTES

 
² Current address: Department of Radiology, New York University School Of Medicine, New York, NY

See also the editorial by Buonocore in this issue.

Abbreviations: DENSE = displacement encoding with stimulated echoes, E = regional Lagrangian strain, 2D = two-dimensional

Author contributions: Guarantor of integrity of entire study, F.H.E.; study concepts and design, all authors; literature research, all authors; experimental studies, D.K., F.H.E., W.D.G.; data acquisition and analysis/interpretation, all authors; statistical analysis, D.K., F.H.E.; manuscript preparation and definition of intellectual content, all authors; manuscript editing, D.K., C.M.K., F.H.E.; manuscript revision/review and final version approval, all authors

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TOP ABSTRACT INTRODUCTION Materials and Methods Results Discussion APPENDIX REFERENCES

 

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