2D cine DENSE with low encoding frequencies accurately quantifies cardiac mechanics with improved image characteristics

This protocol was approved by the local Institutional Review Board of the University of Kentucky. Ten healthy subjects (50 % female, age 27 ± 9) with no history of cardiovascular disease and ten subjects with a history of myocardial infarction or congestive heart failure (40 % female, age 57 ± 6) consented for the study. A 3 T Siemens (Erlangen, Germany) Tim Trio with a 6-element chest and 24-element spine coil was used to acquire mid-ventricular short-axis 2D cine DENSE images with the following parameters: 6 spiral interleaves, 1 average, 360 × 360 mm² field of view, 128 × 128 reconstruction matrix, 2.8 × 2.8 mm² pixel size, 8 mm slice thickness, 1.08 ms/17 ms TE/TR, constant 20° flip angle. Two spirals were acquired per heartbeat which yielded a temporal resolution of 34 ms. View sharing was used to achieve 17 ms between reconstructed cardiac frames. Simple encoding was used to measure in-plane displacements while through-plane dephasing of 0.08 cycles/mm and CSPAMM were used for echo suppression [3, 7, 11]. To remove effects due to variable breath-hold position, the acquisitions were performed with respiratory navigator gating and an acceptance window of ±3 mm.

In each subject, the same mid-ventricular short-axis slice was acquired five times with different values of in-plane k_e: 0.02, 0.04, 0.06, 0.08, and 0.10 cycles/mm. The 0.10 cycles/mm acquisition was repeated during the same imaging session to assess inter-test reproducibility.

Myocardial strain and twist were derived from the DENSE images using custom software written in MATLAB (The Mathworks Inc, Natick, MA). The post-processing steps for each cine DENSE slice included manual segmentation of the left ventricular myocardium and semi-automated phase unwrapping to obtain the 2D Eulerian displacements within each cardiac frame [10]. Following the unwrapping, spatial smoothing and temporal fitting of displacements (10^th order polynomial) were performed to obtain smooth trajectories for all tissue points beginning at end-diastole and continuing through systole into much of diastole [10]. Radial strain, circumferential strain, and twist were calculated from the resulting displacement fields for each cardiac frame [14].

Radial and circumferential strains were quantified with the 2D Lagrangian finite strain tensor in six circumferential segments throughout the cardiac cycle. Radial strain was defined as positive for thickening while circumferential strain was negative for shortening. To report peak global strains, the curves from the six segments were averaged into a single global curve from which the peak was selected. Twist was quantified in the same segments and was defined as the angle of rotation about the centroid of the endocardial contour at end-diastole. Twist was positive for counterclockwise rotation when viewing the short-axis slice from the apex towards the base. Peak global twist was quantified in the same manner as the peak global strains.

As many recent studies have used a k_e of 0.10 cycles/mm, the peak strains and twists quantified with the other k_e were compared to the same measures quantified with a k_e of 0.10 cycles/mm. Paired t-tests (with significance defined as p < 0.05), Bland-Altman analyses [15], and modified coefficients of variation (CoV) were used for statistical comparison. The equation for CoV is below for a given measurement, X, quantified in N subjects with two encoding frequencies (ke1 and ke2) [6, 16].

The amount of phase wrapping that occurred for a given subject and k_e was measured by first considering the phase images for the X and Y directions separately. For each of the two directions, the cardiac frame with the largest percentage of wrapped pixels within the cardiac segmentation was found. The cardiac frame with this largest percentage may have been at slightly different time points for the two directions, though always near end-systole because that is when the most displacement and wrapping occurred. The average of those two percentages was taken as the amount of phase wrapping for that subject and k_e.

Dephasing of the blood signal through the cardiac cycle for each k_e was quantified by calculating the average pixel intensity of the DENSE magnitude images within a set of manually defined contours that denoted the blood pool. Care was taken to ensure that the papillary muscles and trabeculations were not included within the blood pool for this analysis. The magnitude of the blood pool signal was quantified and expressed through the cardiac cycle as a percentage of its signal in the first cardiac phase. To demonstrate the amount of dephasing that has occurred by early systole, the blood pool signal remaining at the fifth cardiac frame (85 ms into the cardiac cycle) was compared between the acquisitions with different k_e

To compare the effects of intra-voxel dephasing between the different k_e, the signal to noise ratio (SNR) was calculated for each cardiac phase. The end-systolic SNR for each lower k_e was compared to the SNR for k_e of 0.10 cycles/mm with a paired t-test. SNR was calculated from the magnitude images by finding the average signal within the myocardium and the standard deviation (noise) of signal within a region of zero signal outside of the body. Care was taken to avoid image artifacts in the region of zero signal. Corrections were applied for the Rician distribution of the MR signal [17]. The true standard deviation of the signal, σ, was calculated from the measured standard deviation, σ_M, by

The true myocardial signal, S, was calculated from the measured myocardial signal, M, by

To assess the relationship between phase noise and SNR, the same DENSE acquisitions above were performed on a stationary water phantom. SNR was quantified in the same manner as for the human studies. For each k_e, the phase noise in the X and Y phase images was quantified via the root mean squared error (RMSE) in radians. To compute the RMSE of the 2D displacements, the previous RMSEs were converted from radians to millimeters via the k_e. The X and Y RMSEs in millimeters were then added together via vector addition to yield the 2D RMSE. The phase noise in radians is theoretically inversely proportional to the SNR [17].

Negligible differences were seen in strains and twist for all k_e between 0.04 and 0.10 cycles/mm (Fig. 3, Table 1). These differences were of the same magnitude as inter-test differences. The comparison between k_e of 0.02 and 0.10 cycles/mm, however, demonstrated larger biases, larger 95 % limits of agreement (LoA), and larger CoVs for both strains and twist. The differences in circumferential strain and twist between k_e of 0.02 and 0.10 cycles/mm were significant (p = <0.01 and p = 0.04, respectively).

For k_e of 0.02, 0.04, 0.06, 0.08, and 0.10 cycles/mm, the largest percentage of wrapped pixels in the phase images was 0 ± 0, 0 ± 0, 5 ± 6, 17 ± 10, and 32 ± 9 %, respectively. Thus, phase images acquired with a k_e of 0.04 cycles/mm had zero wrapped pixels. In contrast, the same phase images acquired with a k_e of 0.10 cycles/mm had about 32 % of the pixels wrapped in the cardiac frame with the most displacement.

As k_e increased, the rate of blood pool dephasing increased, however, the standard deviations demonstrated considerable overlap among the different k_e (Fig. 4). Across the 20 subjects and using the fifth cardiac phase as an example, the amount of blood pool signal remaining as a percentage of its initial value was 28 ± 11, 26 ± 10, 24 ± 9, 23 ± 8, and 21 ± 7 % for k_e of 0.02, 0.04, 0.06, 0.08, and 0.10 cycles/mm, respectively. Frame 20 was the average end-systolic frame and there was no effective difference in blood pool dephasing by that time.

SNR throughout the cardiac cycle was similar for the different k_e (Fig. 5), with a trend towards higher SNR at lower k_e. Across the 20 subjects, the mean SNR at end-systole, which occurred at different cardiac frames for the different subjects, was 23 ± 9, 24 ± 9, 23 ± 9, 23 ± 10, and 22 ± 9 for k_e of 0.02, 0.04, 0.06, 0.08, and 0.10 cycles/mm, respectively. The end-systolic SNR for k_e = 0.02, 0.04, 0.06, and 0.08 were each significantly different than the end-systolic SNR for k_e = 0.10 cycles/mm (p = 0.010, 0.003, 0.005, 0.03, respectively). This represents a 9 % increase in SNR for k_e of 0.04 cycles/mm compared to a k_e of 0.10 cycles/mm.

In the stationary water phantom, the inverse relationship between the phase noise (as measured by RMSE in radians) and the SNR was similar for all k_e (Fig. 6a). However, the RMSE in millimeters, which required division by the appropriate k_e, was substantially higher for lower k_e (Fig. 6b). For example, for SNR near 20, the RMSEs in millimeters were 1.17, 0.60, 0.38, 0.30, and 0.23 mm, for k_e = 0.02, 0.04, 0.06, 0.08, and 0.10 cycles/mm, respectively.

Spiral cine DENSE is primarily used to measure cardiac displacements and deformation in the forms of twist and strain [3, 10, 12]. The k_e is the proportionality constant between the tissue displacement in millimeters and the measured signal phase. It also determines the strength of the encoding gradient that is applied. A high value of k_e provides high sensitivity to small displacements, but at the cost of intra-voxel dephasing and increased phase wrapping. The results from this study suggest that the k_e can be lowered to 0.04 cycles/mm, which significantly reduces the presence of phase wrapping, without compromising measures of circumferential strain, radial strain, or twist. In addition, studies that use different k_e between 0.04 and 0.10 cycles/mm can be directly compared as no systematic differences in strain or twist due to differences in k_e were found. This is valuable as not all DENSE studies have used the typical value of 0.10 cycles/mm. In particular, some previous studies have used 0.06 cycles/mm [12, 13], which is within the range of this study.

The measures of strain and twist were compromised as the k_e was lowered to 0.02 cycles/mm (Fig. 3). This was likely caused by the increased effect of phase errors at low k_e (Fig. 6b). For a given phase error in radians, the corresponding error in displacement (mm) was larger for lower k_e. This same phenomenon is present in phase contrast velocity imaging as the velocity encoding (VENC) is increased [18].

The amount of phase wrapping decreased as the k_e was decreased. Lowering the k_e to the point that there is no wrapping puts DENSE on a similar level as phase contrast velocity imaging, where the VENC is commonly adjusted to prevent wrapping in the blood velocities [19]. The use of this low value was possible due to the artifact suppression techniques of CSPAMM [3] and through-plane dephasing [7]. As seen in the representative subject (Fig. 2), no stripe artifacts were present in the images for the low k_e.

The rate of blood pool dephasing decreased as the k_e was decreased (Fig. 4). However, the difference between the acquisitions with 0.10 and 0.02 cycles/mm was not large. By the fifth cardiac frame, the acquisition with 0.02 cycles/mm had approximately 7 % more of its blood pool signal remaining. This difference was not practically significant as the delineation between the myocardium and the blood pool was still possible at the lowest k_e. The drop in blood pool signal through the cardiac cycle is due to dephasing [10]. This dephasing can be due to both in-plane and through-plane gradients. While the in-plane gradients necessarily changed with the k_e, the through-plane gradient remained constant for all acquisitions and likely contributed to the blood pool dephasing at similar rates for all k_e. Thus, the advent of through-plane dephasing removed dependence on high k_e to accomplish blood pool dephasing.

The SNR was 9 % higher for k_e of 0.04 cycles/mm compared to 0.10 cycles/mm. This is a reflection of the decreased intra-voxel dephasing that occurs due to the decreased gradient strengths that accompany lower k_e. This modest increase in SNR is generally beneficial and results in a reduction in phase noise [17].

It is important to note that both the in-plane encoding gradient and the through-plane dephasing gradient are capable of producing intra-voxel dephasing of the stimulated echo in deforming tissue [7]. The voxel size in the through-plane direction was larger than the in-plane direction (8 mm vs. 2.8 mm). Thus, the amount of intra-voxel dephasing may have been largely controlled by the through-plane dephasing gradient, which was constant (0.08 cycles/mm) for all acquisitions in this study. Further increases in SNR could be possible by reducing the through-plane dephasing gradient, however, this value was chosen to cause more than one half cycle of dephasing across the 8 mm slice [7]. Reducing the amount of through-plane dephasing could lead to the presence of stripe artifacts in the images.

This study assessed a single mid-ventricular short-axis slice without consideration of long-axis images. The longitudinal motion of the left ventricle (particularly near the base) is often larger than the circumferential and radial components [20]. Long-axis images would likely have demonstrated phase wrapping with a k_e of 0.04 cycles/mm. While this implies that unwrapping algorithms cannot be removed from the post-processing, the amount of wrapping can be substantially reduced with a lower value. As the circumferential and radial strains were not compromised in the short-axis images with this low value, the longitudinal strains from the long-axis images should also not be compromised.

The acquisitions in this study were performed at 3 T, which yields higher SNR compared to 1.5 T [21]. Acquisitions at 1.5 T may have larger phase errors (due to decreased SNR) than those present in this study. However, those errors could be offset by better field homogeneity at the lower field strength. It has recently been reported that the displacement errors from spiral cine DENSE are the same at 3 T and 1.5 T [16]. Thus, the results from this study are likely applicable to 1.5 T.

We performed the acquisitions in this study with the simple encoding strategy because of the reported ability to handle phase wrapping due to k_e as high as 0.10 cycles/mm [10]. A motivation for this study, however, was to investigate the ability to lower the k_e during acquisitions that use the balanced encoding strategy. This strategy has been used for DENSE acquisitions that encode displacements in all three directions [11‐13]. However, in those studies, the k_e was reduced to 0.06 cycles/mm due to the increased wrapping that is present in the online reconstructed images [11]. We could not guarantee successful unwrapping from images acquired with the balanced strategy and a k_e of 0.10 cycles/mm, so the simple strategy was used to be able to accurately test up to 0.10 cycles/mm. The results from this study suggest that the k_e could likely be lowered to 0.04 cycles/mm with the balanced strategy, which has better noise performance than the simple encoding strategy [11]. This lower value would reduce the load on the unwrapping algorithm for 3D DENSE studies and any DENSE studies that use the balanced encoding strategy. The strain and twist results from this study suggest that these measures of cardiac mechanics would not be compromised with the lower value.