Second‐order motion‐compensated spin echo diffusion tensor imaging of the human heart

Myocardial microstructure has been challenging to probe in vivo. Spin echo–based diffusion‐weighted sequences allow for single‐shot acquisitions but are highly sensitive to cardiac motion. In this study, the use of second‐order motion‐compensated diffusion encoding was compared with first‐order motion‐compensated diffusion‐weighted imaging during systolic contraction of the heart.


INTRODUCTION
Ex vivo diffusion tensor imaging (DTI) and diffusion spectrum imaging have provided invaluable insight into myocardial fiber architecture of the human heart (1-3).
While a static view of cardiac myofiber arrangement is of interest, it cannot address some of the crucial questions related to dynamic rearrangement of myofiber aggregates during the cardiac cycle. Moreover, the study of longitudinal microscopic changes of myocardium in a range of relevant cardiovascular diseases necessitates in vivo imaging of the human heart. Furthermore, personalized myofiber architecture remains one of the main bottlenecks in the design of patient-specific cardiac models for the systematic and quantitative diagnosis and prognosis of cardiovascular patients (4,5).
To date, only a limited number of studies have demonstrated the feasibility of diffusion-weighted imaging of the in vivo human heart (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16). The lack of data is due to the fact that in vivo cardiac DTI faces considerable challenges in relation to bulk motion and myocardial strain during diffusion encoding.
Two sequence types have been investigated for in vivo DTI. The stimulated echo acquisition mode (STEAM) was initially proposed for cardiac diffusion-weighted imaging (DWI) (17) and subsequently used to perform DTI during breath holds (6)(7)(8)(9) and during free-breathing in combination with a dedicated visual patient feedback system (18). The advantage of STEAM-based sequences is their feasibility on standard clinical MR systems without the need for high-performance gradient hardware. The nature of STEAM imaging, however, requires echo encoding across two consecutive heartbeats while the position of the heart in two consecutive heartbeat is only allowed to vary within narrow limits (18). As a consequence of this fact and the required motion control, examination times are very long and considerable patient cooperation is required. In addition, there is an intrinsic weighting of the diffusion signal due to myocardial strain (6,19). This issue may be addressed by imaging in the so-called "sweet spots" (7) although these limit imaging to two predefined cardiac phases that do not coincide with end systole and end diastole. Alternatively, strain correction may be applied in postprocessing based on the knowledge of the time course of myocardial strain (19).
Diffusion-weighted single-shot spin echo imaging has been proposed as an alternative to STEAM and has been demonstrated to provide diffusion tensor information of the in vivo human heart (10,11,(13)(14)(15)20,21). The acquisition scheme permits free-breathing imaging without the need for dedicated patient feedback systems. However, the nonrigid component of bulk motion leads to a direct strain encoding during the application of the diffusion gradients, which needs to be addressed. To minimize the effects of strain and bulk motion, spin echo DWI and DTI have primarily been applied in diastole (12,14,22).
An approach to overcome signal attenuation caused by changes in cardiac motion is to design higher-order motion compensated diffusion gradient waveforms, which have been proposed as part of spin echo schemes for diastolic DWI (22) or as part of T 2 prepulses in conjunction with balanced steady-state free precession sequences (23). The latter variant allowed separating diffusion contrast generation from imaging. However, such a scheme may be very sensitive to residual phase due to radiofrequency pulse imperfections and uncompensated cardiac motion components.
Finally, image postprocessing methods may be employed to correct for strain and bulk motion-induced signal attenuation of conventional twice-refocused diffusion-weighted spin echo images. To this end, diffusion-weighted images are acquired at different trigger delays during the diastolic rest period (12,14) and temporal filtering and projection is used to combine image information from the set of temporally resolved images (24). Potential drawbacks of this approach, however, include the fact that the myocardium is thinnest in diastole, hence partial voluming is increased. In addition, diffusion weighting is limited to rather low bvalues, which reduces the diffusion-related contrast, and signal attenuation due to perfusion may confound results.
Systolic cardiac DTI in humans has been proposed based on first-order motion-compensated diffusion gradients incorporated into a spin echo sequence (10,11,13). With this approach, careful sequence timing is required when applied on clinical MRI equipment (21). Stronger gradient systems on animal imaging systems delivering up to 1.5T/m maximum gradient amplitudes allow for significantly reduced diffusion gradient durations (16), and third-order gradient moment nulling has been investigated in the in vivo rat heart (25).
The objective of the present study was to propose and implement second-order motion-compensated spin echo diffusion tensor imaging of the human heart on a clinical scanner. It is hypothesized that second-order motioncompensated diffusion encoding reduces the effect of strain and bulk motion on imaging in vivo myocardial fiber architecture as well as scalar diffusion parameters when being compared with current spin echo-based cardiac DTI approaches.

METHODS
The signal phase accumulated during diffusion encoding is described by wr t ð Þ ð Þ¼g R t encoding 0G t ð Þr t ð Þdt, with t encoding representing the duration of the diffusion gradient,G t ð Þ representing the gradient waveform, andr t ð Þ representing the spatial trajectory of magnetization. Upon Taylor expansion ofr t ð Þ, the phase can be written as: GðtÞ € r t¼0 t 2 dt þ :::: with the associated n th order gradient momentsm n : From Equation [1], it is evident that nulling of higherorder moments results in phase insensitivity to higherorder motion (the derivatives ofr t ð Þ). To achieve higherorder gradient moment nulling while minimizing the overall gradient durations and echo time for a given bvalue, the maximum gradient amplitude is used. Figure  1a illustrates a first-order motion-compensated gradient waveform (10,16) Figure 1b, both first-and second-order motion compensation is achieved and

Study Protocol
First-and second-order motion-compensated diffusion tensor imaging were implemented on a clinical 1.5T Philips Achieva System (Philips Healthcare, Best, the Netherlands) equipped with a gradient system delivering 80 mT/m per physical axis at a slew rate of 100 mT/m/ms.
Five subjects (female, n ¼ 4; male, n ¼ 1; age: 21 6 2 years; heart rate, 66 6 13 bpm; minimum/maximum heart rate, 47/85 bpm) with no known cardiac disease were imaged. Written informed consent was obtained from all subjects prior to scanning and the protocol was approved by the institutional review and ethics boards.
Diffusion imaging was performed in the short-axis view orientation. A reduced field of view technique was applied (26) employing a spectral spatial pulse for fat suppression (27). The duration of the 180 refocusing pulse was minimized using variable rate selective excitation (28) (Fig. 1). Imaging parameters were as follows: in-plane resolution ¼ 2.7 Â 2.7 mm 2 ; slice thickness ¼ 6 mm; field of view ¼ 230 Â 98 mm 2 ; repetition time (TR)/echo time (TE) ¼ 1R-R/73 ms; flip angle ¼ heart rate dependent Ernst angle assuming a T 1 of 1030 ms (29). The echo time was kept equal for both diffusion encoding approaches. The only parameter that changed was the waveform of the diffusion encoding gradients.
Images were acquired during free-breathing and were gated using a respiratory navigator with an acceptance window of 5 mm. During contraction and during the first half of the echo time, blood below the imaging slice may move into the imaging plane and experience the 180 refocussing pulse. Within the second half of the echo time, blood within the imaging slices will move toward the aorta and exit the heart. To avoid signal projection of the emptying blood pool onto the image, magnetization below the imaging plane was saturated in a slab parallel to the imaging plane.
Diffusion-weighted imaging was performed at trigger delay intervals of 10 ms from the shortest trigger delay possible (45 ms) to peak systole (time point of maximal circumferential contraction). At each trigger delay, eight signal averages of a b¼ 0 s/mm 2 image and three diffusionencoded images with the encoding direction in the readout, phase encoding, and through-slice direction with a bvalue of 450 s/mm 2 were acquired. Slices were positioned at basal and apical locations (Fig. 2), where rotational motion and through-plane contraction are largest.
DTI data with 10 diffusion encoding directions (30) were acquired in an additional session in five healthy volunteers (female, n ¼ 4; male, n ¼ 1; age, 25 6 2 years; heart rate, 71 6 13 bpm; minimum/maximum heart rate, 50/87 bpm) including one volunteer on whom DWI was performed. The sequence parameters were as follows: in plane resolution ¼ 2.7 Â 2.7 mm 2 , reconstructed to 1.35 Â 1.35 mm 2 ; slice thickness ¼ 6 mm; field of view ¼ 230 Â 98 mm 2 ; TR/TE ¼ 3R-R/73 ms (R-R corresponds to the R-wave of the ECG); flip angle ¼ 90 ; and number of signal averages ¼ 12. To reduce total scan time while allowing for a TR of 3R-R intervals, a slice cycling scheme with non-coplanar excitation according to Wilm and colleagues (31) and (32) was used. Data were acquired at 38%, 47%, 56%, 66%, and 75% of peak systole employing both first-and second-order motion-compensated gradient schemes. Imaging slices were positioned at the apical level (20% of long-axis length from the tip of the apex), midventricular level, and basal level (20% of long-axis length below the mitral valve).

Data Analysis
The apparent diffusion coefficient (ADC) for each diffusion encoding direction as well as the mean diffusivity (MD) were calculated for each dataset as function of different trigger delays acquired. The average of ADC/MD and the corresponding standard deviation across the myocardium were analyzed for each slice. The trigger delay is reported as percentage values relative to peak systole (100% corresponds to peak systole). To avoid partial voluming effects, epicardial and endocardial voxels were not taken into account. The duration of the plateau of the mean diffusivity as a function of trigger delay was defined using a range between the minimum MD and 2.14 Â 10 À4 mm 2 /s above the minimum MD. The range was derived based on the standard deviation of MD values across volunteers within 40% and 60% peak systole for second-order motion compensation at basal and apical level. Upon calculation of the diffusion tensors, the local helix and transverse angles were estimated (33,34). To do so, the mask of the LV was warped onto an ideal ring by means of coherent point drift registration (35). Within the ring, the canonical cylindrical basis was defined and associated to every tensor coordinate inside the LV. For the helix angle analysis, the transmural depth was normalized along the radial coordinate. Upon identification of the cylindrical basis, the helix angle was defined as the angle between the diffusion tensor's first eigenvector projected onto the local cylindrical surface and the imaging plane. The transverse angle was defined as angle between the component of the first eigenvector within the imaging plane and the circumferential direction. To avoid partial volume effects of bright blood signal in the b ¼ 0 s/mm 2 images, the averaged image of all diffusion encoding directions was calculated and scaled (corresponding to signal attenuation caused by an ADC of 10 Â 10 À4 mm 2 /s). This image was used as an unweighted reference signal for myofiber angle analysis. Helix angles were calculated for each heart phase, and transmural variation is reported in boxplots representing the helix angle distribution along the circumferential dimension at different transmural depths. The transverse angle histograms are reported including mean 6 standard deviation across the myocardium averaged across volunteers.

RESULTS
An example of first-and second-order motion-compensated DWI acquired throughout systole is shown in FIG. 1. First-order (a) and second-order (b) motion-compensated diffusion encoding using spin echoes. Following a respiratory navigator (Nav), regional saturation (REST) is applied parallel to the imaging slice to saturate blood signal apically of the imaging slice. A spatial spectral pulse for fat suppression is used for reduced field of view imaging (LL). A variable rate selective excitation (VERSE) pulse is used for radiofrequency refocusing. The timing of gradients is given in milliseconds. For each gradient waveform, the 0th to 2nd moments (m 0 , m 1 , m 2 ) are plotted as a function of time.
Supporting Figure S1. Partial motion-induced signal voids are visible prior to complete signal cancelation. While signal voids are readily apparent with first-order motion compensation, second-order motion compensation yields a wider range of applicable trigger delays. Signal originating from the blood pool within the lumen of the LV was visible in three out of the five subjects. At the basal level, blood signal was only visible if secondorder motion compensation was applied.
In Figure 2, ADC values based on encoding along the readout (M), phase encode (P), and slice select (S) directions as well as MD values as a function of the trigger delay are shown. Second-order motion-compensated diffusion encoding yielded a trigger delay range of 15%-77% of peak systole for the apical and 15%-79% for the basal slices on average. In comparison, for first-order motion compensation, the corresponding trigger delay windows were 30%-56% (apical) and 25%-50% (basal).
The standard deviation of ADCs and MDs across the myocardium were found to be lower on a wider range for second-order motion compensation, relative to firstorder motion-compensated diffusion encoding. Figure 3 shows helix as well as transverse angle maps at the midventricular level for 38%, 47%, 56%, 66%, and 75% peak systole. For first-order motion-compensated diffusion encoding, the characteristic transmural variation of helix angles was absent and patches of high angulation (dark blue/red) were found in the myocardium for trigger delays of 66% and 75% peak systole. Patches of large deviation from the circumferential direction for the first eigenvector (transverse angulation of 690 ) are visible at trigger delays >66% peak systole. Second-order motion compensation results in better circumferential alignment of the principal diffusion direction. Figure 4 shows the transmural helix angle box-plots for basal, midventricular, and apical slices pooled across all volunteers. Second-FIG. 2. ADCs for in-plane (ADC M, ADC P) and through-plane (ADC S) encoding and mean diffusivity (MD) for first-and second-order motion-compensated (MC) diffusion encoding as a function of trigger delay (in % peak systole) for an apical and basal slice location. The accepted range is indicated in green and is spanned by the horizontal dotted lines (range between minimal ADC and 2.14 Â 10 À4 mm 2 /s above). Average ADC/MD values across the myocardium within each slice are shown (black lines) along with the corresponding standard deviation (gray lines). Solid lines correspond to the mean across the volunteers and dashed lines to the standard deviation across volunteers.
order motion-compensated diffusion encoding shows a linear dependency of the helix angles as a function of transmural depth for all trigger delays and reduced variation along the ventricular circumference. First-order motion-compensated diffusion encoding matched results from second-order motion compensated acquisition best at mid-ventricular level for trigger delays of early to midsystole. The root mean squared difference of helix angles  Figure 5 shows the transverse angle histograms for both motion compensation schemes averaged across volunteers. Using second-order motion-compensated gradients, the standard deviation of the transverse angle is on average 51% smaller when compared with data obtained with first-order motion compensation. A transition from negative to positive transverse angles is found when going from apex to base.

DISCUSSION
In the present study, second-order motion-compensated cardiac diffusion imaging was implemented on a clinical MR system and compared with first-order motion compensation.
Whereas MD values across the myocardium were found to be relatively constant over a wide range of trigger delays for second-order motion-compensated diffusion encoding, first-order motion-compensated diffusion encoding resulted in a strong dependency on the trigger delay in accordance to previous findings (21). Secondorder motion-compensated diffusion encoding not only yielded reduced variation of MD values within the myo-cardium, it also reduced the standard deviation of MD values across volunteers.
For first-order motion-compensated diffusion encoding, the optimal trigger delay for DTI was found in a narrow range between 30% and 50% of peak systole, similar to previous reports (10,21). Tensor reconstruction suggests that the window of feasible trigger delays is narrow. At 630 ms offset from the optimal trigger delay time, tensor alignment deviated locally from the expected circumferential arrangement and the characteristic transmural course of helix angles is lost in parts of the myocardium.
In this study, the helix angle was calculated upon projection of the first eigenvector onto a cylindrical surface (33). Hence large deviations from a circumferential course result in an overestimation of the helix angle. At the basal and midventricular level, considerable cardiac contraction in through-plane direction occurs leading to a loss of the characteristic transmural variation of helix angles for early and late systole for first-order motion compensation. The loss of transmural variation of the helix angle is also reflected in a wider angle distribution along the circumference.
For second-order motion-compensated diffusion encoding, a 2.5-fold wider window of trigger delays was found. A coherent circumferential course of myofibers with a linear transmural course of helix angles was detected with a smaller spread in angle distribution along the circumference. The results agree with previously reported fiber angulations in the ex vivo human heart (36). The variation of transverse angles between apex and base agrees with previously reported STEAM based in vivo imaging (34) and ex vivo studies (37,38). In this study, the echo time was kept the same for both diffusion encoding gradient waveforms to ensure similar T 2 weighting. For first-order motion-compensated encoding, however, the echo time may be reduced by 4 ms.
In the second-order compensation scheme used in this study, the duration of the gap between the pairs of gradient lobes was dependent on the b-value. There is a minimum value for this gap, as it must be wide enough to accommodate the refocussing pulse. Note that in the second-order compensation scheme, because the gradient's zeroth moment is non-zero at this time, the free induction decay crushers around the refocussing pulse are not required.
In this study, a clinically available high-performance gradient system was employed enabling gradient durations of 43/50 ms for first-/second-order motioncompensated gradient schemes. For clinical systems with lower maximum gradient strengths such as 60 mT/ m or 40 mT/m the total gradient durations increase to 51/60 ms and 64/78 ms. Prolonged gradient duration increases the sensitivity to motion, since bulk motion is more likely to deviate from its first-and second-order Taylor approximation.
Diffusion-weighted imaging generally suffers from low signal-to-noise ratio (SNR). In this study, a 1.5T clinical system was used. Increasing the main magnetic field strength leads to an increase in SNR at the cost of larger susceptibility effects, particularly in the proximity of the posterior vein (39). To reduce susceptibility-induced image distortions, the readout duration may be shortened using parallel imaging at the cost of SNR.
In this study, a rather coarse spatial resolution was used to maintain SNR while keeping the duration of the scan session within applicable limits. Other studies have reported a spatial resolution of 2 Â 2 Â 5 mm 3 (11,13) which further reduces sensitivity to bulk motion for first-order (10) and second-order motion compensation.

CONCLUSION
In this study, second-order motion-compensated spin echo diffusion encoding was implemented and compared with first-order motion-compensated diffusion gradient waveforms for systolic cardiac diffusion tensor imaging. A significantly decreased sensitivity to bulk motion compared with first-order motion-compensated diffusion gradients was found, enabling cardiac DTI from base to apex at various time points during systolic contraction.