Three-directional acceleration phase mapping of myocardial function


  • Parts of this work were presented at the ISMRM 2008 and ISMRM 2009.


An optimized acceleration encoded phase contrast method termed “acceleration phase mapping” for the assessment of regional myocardial function is presented. Based on an efficient gradient waveform design using two-sided encoding for in vivo three-directional acceleration mapping, echo and repetition times TE = 12–14 ms and TR = 15–17 ms for low accelerations sensitivity aenc = 5–8 m/s2 were achieved. In addition to phantom validation, the technique was applied in a study with 10 healthy volunteers at 1.5T and 3T to evaluate its feasibility to assess regional myocardial acceleration at 1.5T and 3T. Results of the acceleration measurements were compared with the temporal derivative of myocardial velocities from three-directional velocity encoded standard phase contrast MRI in the same volunteers. The feasibility to assess myocardial acceleration along the radial, circumferential, and longitudinal direction of the left ventricle was demonstrated. Despite improved signal-to-noise-ratio at 3T (34% increase compared with 1.5T), image quality with respect to susceptibility artifacts was better 1.5T compared with 3T. Analysis of global and regional left ventricular acceleration showed characteristic patterns of systolic and diastolic acceleration and deceleration. Comparisons of directly measured and derived myocardial acceleration dynamics over the cardiac cycle revealed good correlation (r = 0.45–0.68, P < 0.01) between both methods. Magn Reson Med, 2011. © 2011 Wiley-Liss, Inc.


The analysis of regional left ventricular (LV) function is of high clinical interest to identify the effect of therapy or to monitor the progression of disease (1). Several MRI techniques evaluating regional wall thickening (CINE imaging) (2), regional myocardial displacement (MR tagging, HARP, DENSE) (3–5), LV velocities (phase contrast (PC) MRI) (6–9), or regional strain (SENC) (10) have been introduced and applied in numerous studies.

While these techniques can assess the dynamics of regional tissue displacement or myocardial velocities, little is known about myocardial acceleration. In contrast to displacement and velocities, regional LV acceleration is directly related to the force exerted by the myocardial fibers and may thus be a useful parameter for the characterization of normal and pathologically altered cardiac function.

Myocardial acceleration can be indirectly obtained by calculating the derivative of myocardial velocities obtained by PC-MRI or Tissue Doppler Imaging (TDI) (11–13). A previous TDI study has show that peak myocardial acceleration is an index of ventricular contractility and relaxation that is independent of preload and afterload conditions (14). Moreover, it has been suggested that peak acceleration during systole may constitute a sensitive marker of initial electrical stimulation (15).

However, to fully estimate local LV acceleration, its inertial (temporal derivative) and convective (spatial derivative) components need to be calculated, which requires time-resolved three-directional velocity information. The limited uni-directional velocities measured by TDI can therefore only provide incomplete information on regional LV acceleration and only provide inertial acceleration data. Alternatively, time-resolved PC-MRI with three-directional velocity encoding can be employed to derive regional LV acceleration maps (16–18). However, error propagation of the noise in PC-MR images can substantially limit the accuracy of the derived acceleration values (19). Furthermore, a three-dimensional (3D) measurement of velocities is required to compute the convective derivative in all spatial dimensions.

As has been shown previously, the PC principle can also be used to directly encode acceleration by tripolar gradients that refocus velocity induced phase shifts (20, 21). The advantage of direct acceleration encoding is that it measures the total pixel-wise tissue acceleration including both inertial and convective acceleration. However, tripolar gradient waveforms require longer echo times than bipolar velocity encoding gradients and acceleration maps can suffer from increased T2* sensitivity, reduced signal-to-noise-ratio (SNR), and artifacts.

Previous studies were limited to acquisitions with long echo times, single-directional acceleration encoding and nonoptimal gradient design. In addition, no systematic in vitro and in vivo evaluation of acceleration encoded MRI with respect to image quality, performance at different field strengths, and comparisons to acceleration derived from velocity data has been presented.

In this study, we present an optimized acceleration encoded PC method termed “acceleration phase mapping” (APM). The pulse sequence implementation is based on an efficient gradient waveform design based on two-sided encoding for three-directional acceleration mapping with minimal echo and repetition times. Blood saturation prepulses were used to suppress signal from ventricular blood and navigator gating was employed to permit imaging during free breathing.

In addition to phantom validation, the technique was applied in a study with five volunteers scanned at 1.5T, five at 3T to evaluate the feasibility of APM to assess regional myocardial acceleration at different field strengths. Three-directionally velocity encoded measurements using PC-MRI were obtained in the same volunteers. The temporal derivative of the velocity measurements was compared to the direct acceleration measurements.


Acceleration Encoding and Gradient Waveform Design

The design of the acceleration encoding waveforms was based on the PC principle (22, 23). In the presence of a magnetic field gradient equation image the MR signal originating from a moving object at equation image acquired at echo time TE (rf-excitation at t0) is given by

equation image(1)

where γ is the gyromagnetic ratio. The initial signal phase and the effects of field inhomogeneities are combined in the spatially dependent and typically unknown background phase equation image. To evaluate the effect of motion on the signal phase, the spatial location of a moving object can be approximated in second order as equation image with constant velocity equation image and acceleration equation image, i.e., it is implied that velocity and acceleration change slowly with respect to TE. Equation 1 then becomes

equation image(2)

In addition to the background phase equation image, the signal phase at TE is determined by the 0th, 1st, and 2nd order gradient moments equation image, respectively.

To measure myocardial acceleration, the signal phase originating from acceleration was isolated by designing a tripolar gradient waveform such that its symmetry resulted in vanishing 0th and 1st order gradient moments equation image.

As a result, stationary and constantly moving spins no longer contribute and the nonzero 2nd order gradient moment equation image determines the signal phase which is directly proportional to the acceleration of the moving spins:

equation image(3)

To eliminate the unknown background phase equation image two measurements with different equation image, i.e., two tripolar gradient waveforms with positive (up) and negative (down) second moments ( equation image), are necessary to encode acceleration along a single direction. As in standard PC-MRI processing, phase difference images equation image are then calculated to probe the acceleration equation image along the encoding direction i:

equation image(4)

To minimize gradient waveform duration, two-sided acceleration encoding similar to the approach by Bernstein et al. was used (24). The 2nd order encoding moment ΔM2 was thus equally distributed between the two measurements (up-case and down-case), resulting in the following set of equations defining the tripolar gradient waveform

equation image(5)

The second order gradient moment ΔM2 is determined by the user selected acceleration sensitivity (aenc), defined as the acceleration that produces a phase shift of π radians, i.e. equation image.

Acceleration encoding gradient waveforms were calculated as schematically illustrated in Fig. 1. It can be shown that whenever the 0th and 1st order moments M0 and M1 of a gradient waveforms vanish, i.e., as specified by the boundary conditions in Eq. 5, any temporal origin (t = 0) can be selected to calculate the second moment M2. For the slice direction, t = 0 was chosen at the end of the slice selection gradient (Fig. 1, top), for the read direction at the beginning of the readout gradient. The tripolar gradient waveform in read direction was thus a time-reversed version of the slice direction.

Figure 1.

Pulse sequence diagram illustrating acceleration encoding along the slice and phase encoding direction. Acceleration encoding along the readout direction (not shown) corresponds to a time-reversed version of the slice direction. Up and down denote the gradient waveforms for the up-case (encoding moment +ΔM2/2) and the down-case (encoding moment −ΔM2/2) along the slice direction. Acceleration encoding along the phase encoding direction was achieved by designing a symmetric tripolar gradient waveform adapted to the maximum phase encoding gradient strength (Ap). For details, see text.

For the read and slice direction, the slice selection rewinder and readout prephaser gradients were combined with the acceleration encoding tripolar gradient waveform to minimize echo time. For the down-cases in read and slice directions all three gradient lobes were assumed to be trapezoidal and have maximum gradient amplitude hmax and minimal rise time r from zero to hmax. The set of equations (5) and the desired encoding moment +ΔM2/2 were then used to calculate the timing of the down-case by solving for the gradient durations t1, t2, and t3. The up-case was calculated by assuming identical waveform timing (r, t1, t2, t3) and inverted encoding moment −ΔM2/2 by solving for gradient amplitudes h1, h2, and h3. Optimal gradient switching times were achieved by exploiting the relationship between the area A of a trapezoidal gradient and its minimum width equation image (24).

As illustrated in Fig. 1 (bottom), the acceleration encoding gradient waveform in the phase direction was designed by assuming a symmetric gradient waveform with identical ramp times r for all three gradient lobes and the additional condition that t2 = 2t1 + r. For all lobes, maximum gradient amplitudes hmax were assumed and gradient waveform timing was calculated according to Eq. 5. The phase encoding gradient needed for spatial encoding was added to the central gradient lobe by prolonging the duration t2 of the central gradient lobe by Ap/hmax, where Ap is the maximum gradient area required for phase encoding. The amplitude of the central encoding lobe was adjusted according to the respective phase encoding step. For the encoding of the up-case, the same tripolar gradient waveform with inverted gradient amplitudes was used.

The optimized acceleration encoding waveforms were integrated into a k-space segmented rf-spoiled gradient echo sequence. Analogous to balanced four-point velocity encoding in PC MRI, four differently acceleration encoded measurements were necessary for three-directional APM (23).

MR Imaging

All measurements were performed on a 1.5T Espree System and a 3T Trio System (Siemens, Erlangen, Germany). Depending on the performance of the gradient system for each scanner, the maximum gradient amplitude hmax and the ramp time r were chosen such that 2D slices with arbitrary angulations could be selected (hmax =21.9 mT/m at 3T, hmax = 19 mT/m at 1.5T), and stimulation limits were avoided (r = 300 μs at 3T, r = 330 μs at 1.5T).

Phantom Experiments

Three-directional APM with acceleration sensitivity aenc = ± 24 m/s2 was validated on the 3T system using a rotating phantom with known diameter and rotating frequency and thus known regional acceleration. Other imaging parameters were: TE = 8.7 ms, TR = 11.3 ms, image matrix 256 × 167, FOV = 360 × 360mm2, spatial resolution = 1.4 × 2.2 mm2, slice thickness = 8 mm, receiver bandwidth 450 Hz/Px, flip angle 15°. For validation of in-plane acceleration encoding along read and phase direction, 2D slices orthogonal to the rotation axis were acquired. Through plane acceleration encoding along the slice encoding direction was tested by acquiring transverse slices parallel to the axis of rotation. To correct for background phase errors, a stationary phantom measurement was performed and subtracted from the data of the rotating phantom.

Volunteer Study

APM was applied to assess regional three-directional LV acceleration in a study with 10 healthy young volunteers free of cardiovascular diseases as determined by case history. Five volunteers were examined at 1.5T (four males, one female, age = 24–28 years), and five at 3T (five males, age = 26–28 years). The study was approved by the local ethics board and informed consent was obtained from all participants.

MR Imaging was performed during free breathing using prospectively electrocardiogram gated and k-space segmented CINE APM in a midventricular short axis slice (aenc = 4.5–8 m/s2). For comparison, standard velocity encoded CINE PC-MRI (in-plane velocity sensitivity (venc) = 15 cm/s, through-plane venc = 25 cm/s) was performed in the same volunteers. The following imaging parameters were identical for both APM and PC-MRI: FOV = 360 × 360 mm2, slice thickness = 8 mm, image matrix 256 × 167, spatial resolution = 1.4 × 2.2 mm2, flip angle 13°, receiver bandwidth 450 Hz/Px, k-space segmentation with one k-space line per electrocardiogram cycle. The achieved echo and repetition times for all in vivo measurements are summarized in Table 1. Due to the long TRs of the acceleration encoded sequence (15–17 ms), sequential acquisition was used to guarantee that the up- and the down acquisitions for the same k-space line are performed within the same time frame relative to the electrocardiogram. Standard PC-MRI data were also measured with a sequential velocity encoding. The temporal resolution was thus equal to TR for both velocity and acceleration encoding.

Table 1. Pulse Sequence Parameters for Acceleration Encoding (APM) and Standard Velocity Mapping
 Acceleration encoding (APM)Velocity encoding
 aenc (m/s2)TE (ms)TR = temp. res (ms)venc (in/through plane) (m/s)TE (ms)TR = temp. res (ms)
  1. Note that the acceleration sensitivity (aenc) was increased during the course of the study to avoid phase wraps.


To minimize artifacts from ventricular blood flow and to permit imaging during free breathing, black blood saturation and prospective navigator gating was performed as described previously (25, 26). The execution of navigator pulses and on-line evaluation of the respiration pattern added 25 ms to the data acquisition at end-diastole.

The total scan time for both APM and TPM varied between 20 and 25 min depending on the volunteer's heart rate and navigator gating efficiency.

Data Analysis

Phase difference data from the stationary phantom were subtracted from the rotating phantom data which corrected for eddy currents and Maxwell terms. For in vivo measurements, Maxwell corrections were performed during the image reconstruction according to the strategy reported by Bernstein et al. (27). Eddy currents were corrected by determining linearly varying phase-difference offsets based on a planar fit to data in static regions (28). Both APM and standard PC-MRI data were analyzed using home built software programmed in Matlab (The Mathworks Inc., Natick, MA). Analysis included manual delineation of the epi- and endo-cardial contours of the left ventricle. To provide an adapted description of LV performance, the three-directional PC data were transformed into a cylindrical coordinate system oriented along the segmented myocardial contours. As a result myocardial acceleration or velocities can be represented by radial (ar, vr), circumferential (aϕ,vϕ), and longitudinal (az, vz) acceleration or velocity components (7, 29–31). To provide an anatomical landmark for segmental analysis and data consistency between subjects, the anteroseptal right ventricular connection of the LV was marked manually. To correct for remaining phase offsets, acceleration time-curves were normalized by dividing each value by the total acceleration during one heart cycle (i.e., sum of global acceleration over all time frames).

Phase wraps (i.e., acceleration aliasing) were corrected using home built software programmed in Matlab (The Mathworks, USA). Regions with aliasing were marked manually and unwrapped based on the know aenc.

To compare the APM data to results from PC-MRI, myocardial acceleration was derived from the velocity encoded data as illustrated in Fig. 2. For the calculation of myocardial acceleration of a specific cardiac phase t, the previous cardiac time frame t − Δt and the successive time frame t + Δt were used (Δt = temporal resolution). Each voxel within the segmentation contours at time frame t was tracked to its position at t − Δt and t + Δt (32, 33). The interpolated contributions of all tracks to each voxel were taken as its velocity value at t − Δt and t + Δt, respectively. The pixel-wise acceleration at time t was then calculated from the three cardiac time frames by a nonlinear curve fit to the three points and evaluating the derivative at t (18).

Figure 2.

Left: Schematic illustration of the analyzed myocardial velocity directions in a mid-ventricular short-axis 2D imaging slice. Right: The motion of a voxel was tracked within the segmented LV by estimating the voxel position at times t ± Δt based on the measured myocardial velocities. The tangent to the fitted curve at time t was taken as the acceleration acc(t) at time t.

For the analysis of global cardiac acceleration and to compare measured to derived acceleration data at 1.5T and 3T, acceleration components (ar, aϕ, az) were averaged over the entire segmentation mask. Peak systolic and diastolic acceleration and deceleration as well as times to peak were determined from the global acceleration time-curves for each volunteer. Systole was defined as the period in the cardiac cycle with positive radial velocities vr.

For the assessment of APM image quality, a SNR analysis was performed at 1.5T and 3T. SNR was estimated by the ratio of the average signal of the segmented myocardium divided by the standard deviation of the noise in regions outside the body.

Statistical Analysis

Continuous variables are reported as mean ± standard deviation. Comparisons between APM and standard PC-MRI were performed using linear regression. The overall quality of the regression was assessed using Pearson's correlation coefficient r; a correlation was considered significant for P < 0.05. To detect statistically significant differences between continuous variables, unpaired t-tests were applied for comparisons of SNR between 1.5 and 3T and paired t-tests for comparison of derived and measured acceleration values. Differences between measured and expected phantom acceleration as well as comparisons between derived and measured acceleration data were evaluated using Bland-Altman analysis by calculating the mean difference (d) and limits of agreement (d ± 1.96 SD, SD = standard deviation).


Phantom Validation

The results of the phantom validation are shown in Fig. 3a in a coronal cross-section through the rotating phantom. The distribution of measured local acceleration (black vectors) was in good agreement with theoretical values (reference, gray arrows, maximum acceleration = ± 9.2 m/s2). Bland-Altman comparison of measured and expected phantom acceleration (Fig. 3b) revealed only minimal bias (0.2 m/s2) and moderate limits of agreement (2SD = ± 2.2 m/s2 = 24% of maximum acceleration).

Figure 3.

Results of the phantom validation. a: Schematic illustration of the rotating phantom used for validation with directly measured (measurement, black arrows) and expected (reference, gray arrows) acceleration vectors. b: Bland-Altman comparison of the measured and expected phantom acceleration data. SD = standard deviation.

Volunteer Study - Image Quality

The achieved image quality is shown in Fig. 4 depicting the magnitude images of a mid-diastolic time-frame for all volunteers at 1.5T (top) and 3T (bottom) included in the study. For comparison, an example of a standard velocity encoded PC-MRI magnitude image at 1.5T (top) and 3 T (bottom) is shown. From a visual inspection of the APM images it is evident, that the image quality of the APM magnitude images at 1.5T was improved compared with images obtained at 3T which showed increased susceptibility artifacts. Note the signal voids in the inferolateral region of the myocardium which were more severe at 3T due to the increased variations of susceptibility in this area. Nevertheless, improved SNR was found at 3T (30 ± 13, range = 15–44) compared to 1.5 T (22 ± 5, range = 17–30). However, SNR values were not significantly different (P > 0.05). As shown for one exemplary volunteer in Fig. 4, images for standard velocity encoded PC-MRI were generally less affected by artifacts compared to APM at 3T and 1.5T.

Figure 4.

Mid-diastolic short axis APM magnitude images with blood pool saturation for all 10 volunteers included in this study at 1.5T (top) and 3T (bottom). The image quality of the magnitude images was clearly superior at 1.5T. For comparisons, two images acquired with standard velocity encoding are shown in the right column.

Volunteer Study—Myocardial Acceleration

Figs. 5 and 6 illustrate the regional functional information obtained with APM as color coded acceleration maps for a volunteer examination at 1.5T. Figure 5 displays the dynamics and distribution of radial LV acceleration for all measured time frames within the cardiac cycle. Note, that red color corresponds to positive acceleration and blue color to negative acceleration. During systole, blue areas thus indicate systolic radial deceleration. During diastole, however, blue areas reflect negative acceleration which corresponds to an increase, i.e. negative slope, of diastolic radial velocities and thus diastolic radial acceleration. In Fig. 6, the individual images depict the spatial distribution of radial, circumferential, and longitudinal acceleration for selected cardiac time-frames. Myocardial acceleration was generally higher in the radial and long-axis (longitudinal) direction compared with circumferential motion.

Figure 5.

Spatiotemporal distribution of left ventricular radial acceleration in a healthy volunteer. The individual plots illustrate the regional distribution of radial myocardial acceleration for all acquired time-frames during the cardiac cycle. Marked systolic radial deceleration in septal, lateral, and posterior is indicated by solid white arrows. Of note are pronounced diastolic radial acceleration in the lateral wall (open white arrows) and delayed peak diastolic septal acceleration (yellow arrowheads). The time within the cardiac cycle (time following R-wave) is indicated in the top right corner of each image.

Figure 6.

Color-coded acceleration maps of a midventricular slice of the left ventricular myocardium in a healthy volunteer. The individual plots illustrate the regional distribution of radial, circumferential and longitudinal myocardial acceleration for different time-frames within the cardiac cycle. For each acceleration direction, time frames were selected which represent the peak systolic and peak diastolic acceleration and deceleration, respectively. The time frame within the cardiac cycle (time following R-wave) is indicated in the top right corner of each image.

Comparison of measured and derived LV acceleration vector fields for maximum systolic circumferential acceleration (Fig. 7, left) and maximum systolic radial acceleration (Fig. 7, right) in a midventricular short axis plane demonstrated close agreement and showed the feasibility of the direct acceleration measurements using APM.

Figure 7.

Vector graphs of systolic regional left ventricular (LV) function based on directly measured (top) and derived (bottom) myocardial acceleration (acc). To aid the comparison between vector fields, yellow arrows have been added which represent the spatial average of acceleration vectors in eight angular segments.

Quantitative comparisons of results are shown in Fig. 8 depicting global and regional acceleration time courses for the three resolved directions (radial, circumferential, longitudinal) for 1.5T and 3T. Note that direct acceleration encoding (continuous blue line) revealed reduced peak values compared with data calculated form standard velocity encoded PC-MRI (dashed red line). Good agreement was observed between derived and directly measured myocardial acceleration (significant correlation, r = 0.45–0.68, P < 0.01) with better agreement between acceleration encoding and derived accelerations at 1.5T. Results of Bland Altman comparisons summarize the mean difference (d) and limits of agreement (± 2SD) between APM and velocity derived acceleration-time curves for radial acceleration (mean difference d = −4.4 cm/s2, limits of agreement ± 2SD = 119 cm/s2), longitudinal acceleration (d = 11.1 cm/s2, ±2SD = 162 cm/s2), and circumferential acceleration (d = −2.3 cm/s2, ± 2SD = 85 cm/s2).

Figure 8.

Comparison of directly measured (continuous blue line) and derived (red line) global myocardial acceleration. The time courses represent data averaged over 5 volunteers at 1.5T (top) and 3T (bottom). The errors bars reflect the inter-individual standard deviations among the volunteers. For each field strength, correlation analysis (scatter plots) was performed by comparing data from all volunteers and time points.

Table 2 summarizes the peak acceleration and deceleration and time to peak averaged over all 10 volunteers measured at both field strengths. Except for the radial systolic acceleration, all peak values were higher in the calculated compared to the measured accelerations but only significantly different (P < 0.05) for the peak longitudinal systolic deceleration and longitudinal diastolic acceleration. A significant difference for times to peak was only found for time to peak longitudinal systolic deceleration.

Table 2. Peak and Time to Peak (TTP) Acceleration (acc) and Deceleration (dec) During Systole and Diastole for Radial (ar) and Longitudinal (az) Components
 Radial acceleration arLongitudinal acceleration az
  • *

    indicates significant differences between directly measured and derived acceleration (P < 0.05).

TTPacc (ms)dec (ms)acc (ms)dec (ms)acc (ms)dec (ms)acc (ms)dec (ms)
Acceleration encoding48 ± 13304 ± 20415 ± 23488 ± 4040 ± 1285 ± 7*387 ± 18482 ± 23
Derived acceleration48 ± 9300 ± 16409 ± 22497 ± 2939 ± 1390 ± 8*394 ± 36482 ± 17
Peakacc (cm/s2)dec (cm/s2)acc (cm/s2)dec (cm/s2)acc (cm/s2)dec (cm/s2)acc (cm/s2)dec (cm/s2)
Acceleration encoding63 ± 15−95 ± 25−95 ± 37130 ± 45144 ± 42−94 ± 26*−124 ± 32*266 ± 88
Derived acceleration54 ± 9−102 ± 17−99 ± 18136 ± 47151 ± 36−148 ± 24*−158 ± 32*295 ± 81


The results of this study demonstrate the feasibility of APM for the direct measurement of three-directional myocardial acceleration with high spatial and temporal-resolution. To our knowledge, this study represents the first successful application of gradient optimized in vivo acceleration encoded PC MRI to study LV acceleration along all three major motion directions (radial, circumferential, longitudinal) of the heart. Global time courses of myocardial acceleration agreed well with numbers derived from PC velocity data at both field strengths. In addition, similar results for directly measured and calculated accelerations were achieved for regional acceleration maps during the cardiac cycle.

The acceleration encoding implementation presented in this study (TE = 12–14 ms, TR = 15–17 ms) resulted in considerably reduced acceleration sensitivities and/or echo times compared to a previous one-sided approach by Forster et al. (TE = 8–13 ms, TR = 14–18 ms) (20) and Fourier acceleration methods by Tasu et al (TE = 20–17 ms, TR = 29–46 ms) (21, 34). Note that optimized gradient waveform design in this study allowed for lower encoding sensitivities (aenc = 5–8 m/s2) compared to previously reported implementations (aenc = 12–250 m/s2).

Phantom validation at 3T revealed good agreement between measured and expected acceleration data. Additional phantom experiments at 1.5T were not performed which may have added information on image quality and its influence of acceleration quantification at 3T compared with 1.5T.

In the normal hearts of our volunteer cohort, distinct regional differences in LV acceleration were observed as illustrated in Figs. 5 and 6. Particularly for radial motion, peak acceleration and deceleration were not evenly distributed across the heart muscle but showed marked regional and temporal differences. For example, a marked systolic radial deceleration was found in septal, lateral, and posterior regions (Fig. 5). In contrast, deceleration in the lateral wall was less prominent. Similarly, pronounced acceleration was seen in the lateral wall during early diastolic expansion. In comparisons, peak diastolic septal acceleration was delayed. Also, a complex rotational behavior was observed with multiple changes of acceleration magnitude and direction (Figs. 6 and 8). The observed distribution of acceleration patterns are in line with previous studies which have demonstrated inhomogeneous spatio-temporal LV motion patterns such as temporal differences in the diastolic motion for septal and lateral regions (8, 30, 35).

Peak and time-to-peak myocardial acceleration are in good agreement with results from previous echocardiography studies using 2D TDI. In a study with 30 normal subjects, Zhang et al. (12) reported the TDI based analysis of segmental acceleration in the short axis plane with peak systolic acceleration of 35–46 cm/s2 and time-to-peak systolic acceleration of 65–87 ms. These findings correspond well to the radial and longitudinal peak and time-to-peak values found in out study (see Table 2). However, longitudinal acceleration in our study was higher compared to another TDI study investigated longitudinal LV motion and found: mid-ventricular peak systolic acceleration = 38–41 cm/s2, time-to-peak systolic acceleration = 69–86 ms, and diastolic peak acceleration of 52–70 cm/s2 (36). Note that, similar to our results, greater acceleration values for diastole compared to systole were reported.

One of the advantages of the direct encoding of acceleration is that it measures both temporal acceleration (time dependent changes of velocities dv/dt) and convective acceleration (spatially dependent changes of velocities dv/dr). It should be noted that sharp changes in the acceleration-time curves indicate that higher order motion terms may be needed to fully characterize cardiac motion. Such higher order motions may results in errors in the encoded acceleration data and should be investigated in future studies using higher order motion encoding and compensation techniques.

For LV acceleration derived from standard PC data only the time derivative of velocity and no convective acceleration was taken into account. However, in the myocardium, the convective acceleration is expected to be small. For instance, the maximum radial convective acceleration directed towards the center of the heart chamber can be estimated from known circumferential velocities. For a maximum circumferential velocity of the myocardium of ∼ 5 cm/s and a short axis diameter of 10 cm, the maximum radial convective acceleration can be estimated to be about 5 cm/s2. Since measured peak radial acceleration and deceleration in this study were on the order of 60–130 cm/s2, the convective contribution is expected to contribute only 4–8% of to the total acceleration in the radial direction.

Comparisons of directly measured and derived LV acceleration revealed a moderate to good correlation between both methods. Values for peak acceleration were higher in the calculated accelerations than in the directly measured accelerations. However, differences were only significant for motion along the longitudinal direction. We speculate that these differences might be related to the much lower temporal resolution of the velocity encoded sequence (7.4–8.5 ms) compared acceleration encoding (14.7–16.5 ms) which may result in increased temporal low pass filtering and thus underestimation of measured peak acceleration.

For derived acceleration data, two cardiac phases at the beginning and the end of the cardiac cycle were lost due to the necessary interpolation of three cardiac time frames. This could be prevented in future studies by applying retrospective cardiac gating (37) and a cyclical analysis. An additional drawback is related to the voxel tracking used for acceleration calculation in neighboring time frames. While the in-plane movement of the myocardium was fully taken into account, the through-plane motion of voxels was not included. An extension of the voxel tracking to the through-plane direction would require the acquisition of at least two additional adjacent slices or true 3D data which would increase measurement time (38).

Additional studies with matched TRs for velocity and acceleration encoded sequences should be performed to investigate the effect of repetition time on the measurement and calculation of peak acceleration. Further, an evaluation of the variability of in vivo APM was not performed. Future studies should thus include the systematic analysis of repeatability in volunteers and exemplary data from patients with compromised contractility, e.g., in dilated cardiomyopathy and/or hypertension.

Since regional LV acceleration is directly related to the force exerted by the myocardial muscle fibers, it may be a useful parameter for the characterization of the regional contractile force. Tracking of acceleration fields may thus provide information on the individual myocardial fiber direction and architecture. The spatial organization of myocardial fiber architecture affects many of the mechanical and electrical properties of the heart, influencing mechanical contraction and electrical propagation in the normal ventricle. A better understanding of the forces exerted by the fibers and their orientation may serve as a baseline for recognizing how alterations in the normal myocardial fiber structure impact cardiac function in diseases such as ischemic heart disease and ventricular hypertrophy or cardiomyopathy. For example, it could be hypothesized that LV dilation as in dilated cardiomyopathy results in increased angle between endo- and epicardial fibers resulting in altered regional acceleration patterns as measured by APM.

The APM technique could also be used to measure flow acceleration. A benefit of the application of acceleration encoded MRI to the measurement of flow acceleration may be related to the need for higher acceleration sensitivities on the order of 50–100 m/s2 which would potentially result in shorter TE and TR. Acceleration encoded flow MRI might be particularly interesting for the detection and quantification of pathologically altered hemodynamics with strong inertial or convective acceleration such as jet flow in stenotic regions or vortex flow in aneurysms, respectively. An advantage compared with derived acceleration may be related to the fact that the convective term of the acceleration is expected to play a bigger role in a fluid than in tissue.

A disadvantage of direct acceleration encoding compared with derived data is related to its longer echo and repetition times which results in stronger artifacts and increased scan time if the temporal resolution of the velocity encoded measurement is maintained. The comparison of APM at 1.5T and 3T additionally showed that the image quality was better at lower field strength and less degraded by susceptibility artifacts. The longer echo time of APM compared to velocity encoded techniques can cause artifacts and signal loss in the myocardium especially in the inferolateral region with increased variations of susceptibility as seen in Fig. 4. Although the SNR was improved at 3T, our initial results suggest that 1.5T is better suited for the application of acceleration encoding to the myocardium. Note that a systematic evaluation and grading of image quality and artifacts due to motion or susceptibility was not performed. In addition, the comparison of 1.5T and 3T data was based on different volunteers scanned at each field strength, which constitutes a further limitation of our study. Future investigations should systematically evaluate image quality parameters in a study with subjects examined at both 1.5T and 3T.

The measurement time for the in vivo measurements between 20 and 25 min was relatively long. A reduction in measurement time could be achieved by either parallel imaging (39) or k-space segmentation (2), i.e., by sacrificing temporal resolution to measurement time. This would also make the choice of the flip angle less dependent on the limitations related to the specific absorption rate (SAR) limit. In this study, the flip angle was set to 13° to avoid exceeding the SAR limit.

A further draw back of the presented APM implementation is related to the use of prospective gating and the application of end-diastolic navigator pulses for respiration control. As a result only limited coverage of 80–90% of the cardiac cycle could be achieved which limits the potential of the technique to assess late diastolic myocardial acceleration.

In conclusion, we presented the first in vivo application of APM providing three-direction inertial and convective myocardial acceleration maps with high spatial and temporal-resolution. In vitro validation and comparisons to velocity derived LV acceleration further support the consistency of the method. Future volunteer and patient studies are warranted to evaluate the potential of APM to provide useful information about the structure and function of the normal heart and the changes and diagnostic value associated with cardiac pathologies.