• Open Access

Orthogonalizing crusher and diffusion-encoding gradients to suppress undesired echo pathways in the twice-refocused spin echo diffusion sequence

Authors

  • Zoltán Nagy,

    Corresponding author
    1. Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK
    • Correspondence to: Zoltán Nagy, Ph.D., Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London WC1N 3BG, UK. E-mail: z.nagy@ucl.ac.uk

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  • David L. Thomas,

    1. Department of Brain Repair and Rehabilitation, UCL Institute of Neurology, University College London, London, UK
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  • Nikolaus Weiskopf

    1. Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK
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Abstract

Purpose

The twice-refocused spin echo sequence is widely used in diffusion imaging due to its excellent performance in reducing eddy currents. The three radio frequency pulses give rise to eight separate signal pathways. Because there is no general solution for the size and arrangement for crusher gradients, with constant size and orientation, that is effective for all arbitrary diffusion-sensitizing b-values and directions, this article introduces and validates a solution whereby the crusher and diffusion-encoding gradients are always kept orthogonal, thus ensuring their independence.

Methods

The cancellation of the crusher and diffusion gradients was demonstrated. Subsequently, crusher gradients were implemented in such a way that they were always orthogonal to the diffusion gradient. Phantom and in-vivo experiments were performed to ascertain that orthogonally implemented crusher gradients alleviate the problem without lowering image quality.

Results

In all experiments, when the crusher gradients' action was cancelled by the diffusion-encoding gradients artifactual signal modulation was observed. When orthogonal gradients were implemented the artifacts were eliminated without detrimental effects on image quality.

Conclusions

Orthogonal crushers are easy to implement and can be used for any variant of diffusion imaging sequences (e.g., diffusion tensor imaging, fiber diameter mapping) where the twice-refocused scheme is used. Magn Reson Med 71:506–515, 2014. © 2013 Wiley Periodicals, Inc.

The twice-refocused spin echo (TRSE) sequence [1] is widely used in diffusion imaging because it can be optimized to reduce eddy currents that otherwise arise due to the strong diffusion-encoding gradients [2]. The use of three radio frequency (RF) pulses results in eight signal pathways—three free induction decays (FIDs), a stimulated echo, three spin echoes and one TRSE [3-6]. Usually, only the main TRSE pathway is desired to contribute to the acquired k-space signal. Signal from the remaining seven pathways are diffusion-weighted to varying degrees and are ideally not allowed to interfere with signal from the TRSE pathway. The presence of signal from any of these eight signal pathways during the data-sampling period depends on the timing of the RF pulses and other imaging parameters, such as spatial resolution. Signals from the unwanted pathways that would appear during the data-sampling period are typically eliminated by crusher gradients straddling the two refocusing RF pulses (see Fig. 1).

Figure 1.

Schematic sequence diagram of the TRSE diffusion-encoded sequence. A single gradient axis is drawn depicting the crusher (purple), diffusion-encoding (orange), and image-encoding readout (blue) gradients. The vertical solid black lines indicate the centers of the three RF pulses while the vertical dashed lines locate the three spin echoes (black), the stimulated echo (green), and the TRSE echo of interest (red). The superscripts (e.g., SE1,2) indicate which two of the three RF pulses are involved in generating the echo. Note that three gradient echoes would also occur following the FIDs from each of the three RF pulses. The times T1 to T4 are calculated after the methods of Reese et al. [2] and the areas of the diffusion-encoding gradients are directly proportional to the phase dispersion (Ψj) provided by them. Note that Ψ1 ≠ Ψ4 and that Ψ2 ≠ Ψ3 in this example.

The eddy current optimization of the TRSE sequence [2] only includes the explicit boundary condition that the diffusion-encoding gradients must balance for the TRSE pathway (Fig. 1). The non-zero zeroth moment (henceforth referred to as 0th moment) of the diffusion gradients can alter the action of the crusher gradients for certain echo pathways, either by supplementing (i.e., reinforcing the crushers) or opposing (i.e., partly or fully cancelling) them. The sizes of crusher gradients are designed according to the spatial resolution of the image and set high enough to shift unwanted signals outside the acquisition k-space. If the angular density of the set of diffusion measurement directions is sufficiently sparse, for a specific choice of b-value (i.e., amplitude/area of diffusion gradient) it may be possible to define a fixed (or static) set of crushers on each axis for which the diffusion-encoding gradients do not cancel the crushers. However, with the current trend toward higher angular resolution measurements, multiple b-values and the ability to define customized diffusion directions in the user interface, the occurrence of such cancellations of crusher action becomes more likely. Because users are often unaware of the 0th moment of the diffusion gradients and directions of the crusher gradients, artifacts can appear suddenly and unexpectedly when the diffusion gradients cancel the crushers. The artifact may seem paradoxical to even experienced users. Because the diffusion-encoding gradients can be considered to be large crushers, one would expect that explicit crusher gradients would be necessary in the low b-value images with minimal diffusion weighting but less important in the more heavily diffusion-weighted images (DWIs). While this intuitive argument is valid for the traditional monopolar Stesjkal-Tanner [7] gradient scheme, which has a single refocusing RF pulse, it does not necessarily hold for some implementations of the TRSE sequence [2], which have diffusion-encoding gradients with non-zero 0th moments.

In this article, we demonstrate realistic circumstances in which these artifacts may appear in TRSE DWIs and provide a general solution for avoiding them, using crusher gradients that always remain orthogonal to the diffusion-encoding gradients. Images acquired using orthogonal crusher gradients were compared with those acquired with the static crusher gradients and were found to be free of interference artifacts without introducing any reductions in image quality.

THEORY

In every voxel, each crusher or diffusion gradient imparts a certain phase dispersion, φi or Ψj respectively with i, j ∈ [1, 2, 3, 4] in the TRSE sequence (see Fig. 1) where there are four crusher (i) and four diffusion (j) gradients. The total phase dispersion (Θ) imparted by the crusher and diffusion-encoding gradients are summed for any given pathway as

display math(1)

where ci and dj ∈ [–1, 0, +1] depending on whether the phase dispersion imparted by a gradient is inverted by a refocusing pulse (–1), not experienced by the pathway (0) or unmodified (+1), while the subscript, Pathway, identifies any of the eight signal pathways in a sequence with three RF pulses [3-6]. Apart from the TRSE pathway, where both the crusher and diffusion-encoding gradients must balance (i.e., both sums above must equal zero), the resultant phase dispersion should be designed to eliminate coherent signal completely from all pathways. The previous recommendation for the minimum phase dispersion needed for complete signal cancellation is at least 4π [3, 8] over a single voxel, but is best determined empirically by systematically varying the 0th moments of the crusher gradients while monitoring image artifacts.

The crusher and diffusion-encoding gradients combine differently for the different echo pathways. To illustrate this, we examine the FID1 pathway (the FID signal from the first RF pulse, i.e., the 90° excitation pulse). In this pathway, the two refocusing RF pulses can be considered to have a 0° flip angle, and hence each gradient phase dispersion is added without inversion (i.e., in Eq. (1), ci = dj = 1 for all i and j). Suppose all four crusher gradients have positive amplitudes and that the first and second crushers have identical 0th moments. Because the first refocusing RF pulse acts as a 0° pulse it does not invert the polarity of the phase dispersion imparted by the first crusher gradient so that math formula The same reasoning leads to math formula Thus, for the FID1 pathway, the summed effect of the four crushers can be simplified to math formula On the other hand, the total phase dispersion provided by the diffusion-encoding gradients for the FID1 echo pathway is math formula As shown in Figure 1, the four diffusion-encoding gradients have alternating polarity. When the first is negative the above expression becomes math formula By definition the four diffusion-encoding gradients must balance for the main TRSE pathway ( math formula) when the two RF pulses act as 180° pulses. Incorporating the alternating gradient polarity leads to math formula and this result can be used to simplify the expression for the FID1 pathway to math formula. Combining the phase dispersions provided by the crusher and diffusion-encoding gradients gives

display math(2)

In the Reese et al. [2] variant of the TRSE sequence, the phase dispersion imparted by the first and fourth diffusion gradients are not required to balance (similarly for the second and third diffusion gradients), and so their difference can potentially cancel the summed effect of the crusher gradients (i.e., it is possible that math formula. This cancellation can occur for an arbitrary b-value depending on the timing of the diffusion gradients required for a given eddy-current time constant [2], because (as shown by Eq. (2)) the total phase dispersion depends on the sum of 0th moments of the crushers but on the difference between the 0th moments of the diffusion-encoding gradients. Therefore, even if the diffusion gradient amplitudes are very large, the difference between their math formula values may be relatively small, and on the order of the summed math formula values of the crusher gradients.

Another example of an unwanted echo, noted previously [9], involves the stimulated echo pathway and can occur for small b-values depending on the diffusion gradient direction and the relative sizes of the first and second pair of crusher gradients:

display math(3)

Using Eq. (1), the total phase dispersion can be computed similarly for all other pathways.

From the above examples, it is clear that if the crushers are kept constant throughout the experiment, it is possible that the unwanted echo pathways may not be eliminated as desired.

As a general solution, we propose to vary the crusher gradients by always keeping them orthogonal to the diffusion-encoding gradient direction. To calculate the gradient directions that are always orthogonal to the diffusion-encoding vectors, let C and D represent two unit vectors defining the crusher and diffusion-encoding gradient directions respectively. Their dot product equals zero by definition (i.e. C·D = CxDx + CyDy + CzDz = 0). We set the 0th crusher moment in the anterior/posterior direction to zero (i.e., Cy = 0) since this reduces peripheral nerve stimulation across the largest body loop. This results in two orthogonal crusher gradients in the x–z plane for any diffusion vector direction (see Fig. 2). Because the different components of the crusher gradients act independently, we require math formula. For convenience, we also require that Cz ≥ 0.

display math(4)
Figure 2.

The arrangements of the orthogonal crusher gradients relative to the diffusion-encoding gradient vector set. The y-component of the crusher gradients was set to zero thus for each diffusion-encoding vector direction there are two possible crusher gradients in the x–z plane, one with positive (red) and one with negative (blue) z-component. While the diffusion gradient vectors (gray lines) have unit length and are distributed spherically, the phase dispersion imparted by the x- and z-components of the crusher gradients (colored lines) add independently, resulting in the unusual square-like distribution. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

The superscript, M, emphasizes that the length of the crusher vector is modulated depending upon its direction. Note that the sign functions are used to achieve a crusher gradient C with a positive z component (indicated in red in Fig. 2) that points either in the second quadrant of the x–z plane when D points in the first or third quadrants or into the first quadrant when D points in the second or fourth quadrants.

METHODS

All data were collected on a 3 T Tim Trio scanner (Siemens Healthcare, Erlangen, Germany) with a single channel body transmit RF coil and a 32-channel receive-only head coil. The TRSE diffusion sequence [2] was implemented locally [11] with single-shot echo planar imaging readout, and images were acquired on both a gel phantom [10] and a human subject. The local ethics committee approved the study and written informed consent was obtained from the subject before the examination. For the separate experiments, either orthogonal or static crushers were used as detailed below. The common imaging parameters were 2.3 mm isotropic resolution, field of view = 220 mm, acquisition matrix = 96 × 96 (echo-spacing and readout times were not varied). Matlab (Release 2010a, Mathworks, USA) was used for all statistical calculations, for numerical simulations, and to display the k-space and image data.

Experiment 1—Empirical Demonstration of the Artifact From the FID1 Pathway

For simplicity, in this experiment the crusher gradients have non-zero 0th moment only along the X-axis. The sizes of the crusher gradients were varied to provide between 9π and 17π total phase dispersion (i.e., math formula in Eq. (2)). Diffusion-encoding was implemented along the ±X, ±Y, and ±Z axes with a b-value of 1000 s/mm2 (resulting in a TE of 90 ms). Data were collected from both the gel phantom and a human subject.

Experiment 2—Numerical Simulations to Investigate Likelihood of Artifact Occurring

To assess the likelihood of a cancelation between diffusion-encoding and crusher gradients in a realistic DWI acquisition, numerical simulations were performed for a pulse sequence in which the phase dispersion imparted by the two crushers straddling the first and second 180° RF pulses was 8π and 4π respectively [3]. For example, in the FID1 pathway this results in a total of 24π phase dispersion due to the crushers (Fig. 1). The TE was varied between 60 ms and 100 ms in steps of 1 ms. For each TE, the maximum possible b-value was calculated for diffusion-encoding gradient amplitudes between 0 mT/m and 100 mT/m in steps of 1 mT/m. For each TE, the start/end times of the diffusion-encoding gradients (see T1–T4 in Fig. 1) were optimized for reduced eddy currents [2] and the time between the RF pulse and the start of the first diffusion-encoding gradient and the time between the end of the last diffusion-encoding gradient and TE were kept constant for all cases (i.e., imaging matrix, echo spacing, and total readout time were kept constant). For each combination of TE and diffusion-encoding gradient amplitude, the total phase dispersion due to both the crusher and diffusion-encoding gradients were calculated for each coherence pathway.

Experiment 3—Demonstration and Elimination of Artifact in Typical diffusion tensor imaging Acquisition

To demonstrate the occurrence of image artifacts caused by incomplete suppression of unwanted coherences using static crushers, and elimination of the artifacts using the orthogonal crusher scheme, in-vivo imaging was performed with acquisition parameters typically used for in-vivo diffusion tensor imaging. Twenty diffusion directions were used, distributed in 3D space according to the electrostatic repulsion method of Jones et al. [12] and the b-value was 1500 s/mm2. The maximum gradient strength used for diffusion-encoding was 32 mT/m. Six reference images with b = 0 s/mm2 were also collected and TE was 103.8 ms. Static crusher gradients were implemented on all three axes and set to provide 8π and 4π phase dispersion around the first and second refocusing RF pulses, respectively. The orthogonal crushers were implemented as described in the THEORY section and provided identical phase dispersions as the static scheme.

Data were fitted to a tensor using FSL (FMRIB, University of Oxford). The raw DW images were inspected for evidence of the artifact, and fractional anisotropy (FA) and maps were also assessed to evaluate the impact of image corruption on these parameter maps. In the region where the interference artifact was most apparent for the static crusher sequence, pixel-wise Bland-Altman plots [13] comparing FA and from the static and orthogonal crusher acquisitions were generated to quantitatively determine the bias introduced by the artifact.

Experiment 4—Image Quality Comparison Between Static and Orthogonal Crushers in the Absence of Artifacts

When using orthogonal crushers, the direction of the crusher gradients changes for each diffusion-encoding direction (by definition). To demonstrate that this does not degrade image quality, equivalent data sets were acquired using the static and orthogonal crusher gradient schemes. The static crusher gradient directions were implemented to avoid cancellation by the diffusion-encoding gradients. This was achieved by implementing the static crushers with positive amplitude on all three axes and using diffusion-encoding directions that were distributed evenly on the hemisphere [14] with only positive Z-components (i.e., the crusher and diffusion-encoding gradients were not allowed to point exactly opposite each other). The amplitudes of the orthogonal crusher gradients were chosen by empirically determining the minimum required amplitude to eliminate all unwanted coherence pathways when the diffusion gradients were set to zero amplitude (phase dispersions of 12.7π and 5.7π were found to be adequate.). For both sequences, seven reference images (b = 0 s/mm2) and 61 DWIs (b = 1000 s/mm2) were acquired and TE was 99 ms. Images were collected from both the human subject and the gel phantom. In-vivo data were fitted to a tensor and displayed as color-coded maps using FSL. For the phantom data, the mean apparent diffusion constant (ADC) was calculated in an ROI of 10-voxel radius in the center slice of each of the 61 DWIs collected. The range between the minimum and maximum ADC values was calculated. The mean and variance of the ADC values over all the diffusion-encoding directions were compared with a two-tailed t and F test, respectively, where statistical significance was set at p < 0.05. The ADC value for each DWI was displayed as a % signal where the mean of the first 10 images was taken as 100%.

RESULTS

Figure 3 indicates that even if the phase dispersion imparted by the crusher gradients is sufficient (here ∼12π) in the non-diffusion-weighted images, the unwanted signal can invade the acquisition k-space when the crusher and diffusion-weighting gradients cancel each other. For the image resolution (2.3 mm2) used in this experiment, artifacts occurred when the total phase dispersion imparted by both types of gradients in the FID1 pathway fell below approximately ±3π. An example in-vivo image of a human subject is shown on the right of Figure 3. Note that this cancellation only occurs when the diffusion-encoding gradients are opposite to that of the crusher gradients (i.e., positive crushers and −X diffusion gradients) but not when diffusion-encoding was along +X, ±Y, or ±Z (see bottom row of Fig. 3).

Figure 3.

Part a (Left) k-space (top row) and image data are displayed for a phantom. In all images of the phantom b = 1000 s/mm2. Middle row depicts coronal while the bottom row axial orientation. When the diffusion-encoding gradients cancel the action of the crusher gradients for the FID1 pathway a second signal can be observed within the acquisition window. For simplicity the amplitude of the second pair of crusher gradients is varied but the same result could be obtained by varying the diffusion-encoding gradient amplitudes. The legends above and below each k-space subplot indicate the total phase dispersion resulting from both the diffusion-encoding and the crusher gradients and the phase dispersion imparted only by the crusher gradients. (Right) Image data from the human subject is displayed (top: coronal, bottom: axial) collected with a total phase dispersion of approximately −0.8π in a DWI with b = 1000 s/mm2. Part b (Left) Corresponding images are shown in each column where the phase dispersion imparted by the crushers is identical to that in Part a but the diffusion-encoding gradient points in the same direction as the crusher. Thus, the phase dispersion of the crusher and diffusion-encoding gradients add rather than subtract (as in Part a). The total phase dispersion imparted is given above each figure. (Right) Corresponding axial image of the human volunteer from the same slice as in Part a above. The crusher gradient moment is identical to in Part a but the diffusion-encoding gradient points along the crusher gradient. The total phase dispersion is approximately 26.3π. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Results of the simulations are displayed in Figure 4, where the highlighted region indicates a total phase dispersion of less than ±2π (a conservative estimate of the minimum required dispersion to avoid the artifact). In Figure 4, the color of the surface is modulated according to the amount of total phase dispersion of the FID1 pathway provided by both the crusher and diffusion-encoding gradients. It can be seen that artifacts will occur for realistic parameter settings. For example, artifacts would be expected for a b-value of approximately 2000 s/mm2 for a gradient amplitude of 60 mT/m (resulting in TE = 80 ms). Similar b-values are used in the NODDI technique [15] and can be achieved on Philips (Best, The Netherlands) scanners with the dual gradient set (maximum strength of 80 mT/m). Also, for a b-value of approximately 1500 s/mm2, low phase dispersion occurs when gradient amplitude = 32 mT/m and TE = 100 ms. Such settings can be achieved with most current 3T scanners (see example below). Finally, problems will occur at a b-value of approximately 5000 s/mm2 (gradient amplitude = 95 mT/m, TE = 85ms). Similar gradient amplitudes and b-values can be achieved on scanners of the Human Connectome project [16]. Cancellation between the diffusion-encoding and crusher gradients in other pathways occurred for b-values of a few hundred s/mm2 or less (e.g. see [9]).

Figure 4.

Simulation results indicating the maximum b-value (vertical axis) at given TE and diffusion gradient amplitude in the TRSE diffusion-encoded sequence [2]. The color of the surface is modulated depending on the total phase dispersion imparted by both the crusher and diffusion-encoding gradients in the FID1 pathway. In the gray region, the total phase dispersion is within ±2π in that pathway and would allow both the TRSE and FID1 signals to enter the k-space acquisition window. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

The example DWIs shown in Figure 5 support the results of the simulations (here, b = 1500 s/mm2; maximum gradient strength = 32 mT/m; and TE = 103.8 ms). With the static crusher implementation, artifacts can occur if the diffusion-encoding gradient counteracts the intended phase dispersion provided by the crusher gradients (diffusion direction 1 in Fig. 5). Note that the diffusion-encoding gradient need not point exactly opposite the crusher gradient direction. The orthogonal gradient implementation eliminates the artifacts.

Figure 5.

In-vivo example showing a situation where artifacts appear in a DWI acquired with the TRSE using static crusher gradients. The first and second pair of crushers (see Fig. 1) were set to impart 8π and 4π phase dispersion respectively and implemented both statically or orthogonally. Static crushers pointed along the vector (1,1,1). The b-value was 1500 s/mm2 and the diffusion-encoding gradients had a maximum strength of 32 mT/m. (Left) When the static crusher and diffusion gradients subtended an angle of ∼170° artifacts occurred. For the same diffusion-encoding direction orthogonal crushers provided artifact free data. (Right) Other diffusion-encoding directions did not show any artifacts with either crusher implementation. One example is shown where the subtended angle between the static and diffusion-encoding gradients is ∼147°. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

The detrimental effect of the image artifact seen in Figure 5 on a diffusion parameter (FA) map is shown in Figure 6. In the data set with static crushers, only one of the twenty directions was corrupted (left hand panel of Fig. 5); nevertheless, the artifact propagates through to the FA map. While this is not immediately apparent on visual inspection (Fig. 6a shows the FA map generated from the 20 direction data set with static crushers and Fig. 6d shows the FA map generated from the 20 direction orthogonal crusher data set), it can be clearly seen from the differences between these FA maps and those generated using a 19 direction subset, in which the direction associated with the artifacted image is removed (difference images shown in Fig. 6b,e for the static and orthogonal crushers respectively). Bland-Altman plots (showing the FA difference as a function of mean FA in Fig. 6c,f for the pixels from the strongly affected region indicated in red in Fig. 6b,e) highlight the detrimental effect of the artifact. When static crushers are used, the variance of FA increases. FA tends to be overestimated at low values and the maximum FA within the ROI is increased when the artifacted image is included in the calculation. When the orthogonal crushers are used the difference remains close to zero for all FA values, i.e., no systematic FA bias is introduced.

Figure 6.

The effect of inadequate crushing on FA maps of the brain. a: FA map produced using static crusher data (same data set as shown in Fig. 5). While the FA map appears on first inspection to be of good quality, the difference between this map and one generated using only the 19 DWIs without visible artifacts show clear differences (b). c: Plots of the difference pixel values [from the ROI highlighted in red in (B)] versus mean FA show a clear bias towards overestimation of FA at low values. Equivalent evaluation of data acquired using the orthogonal crusher scheme [(d) FA map; (e) difference between FA maps generated using 20 and 19 directions; and (f) pixel-wise FA difference versus mean FA] show no evidence of such bias. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 7 shows the results of the comparison between static and orthogonal crusher TRSE images acquired with 61 directions and static crusher directions chosen to avoid cancellation with any of the diffusion gradient directions. Figure 7 (top) displays color-coded diffusion direction maps from a human subject indicating equally high quality images for both crusher gradient schemes. The bottom of Figure 7 depicts the variation in the ADC value measured from the gel phantom in % units relative to the mean of the first 10 measurements. The mean ADC values measured in the gel phantom with the static and orthogonal crusher gradients were 1.867 × 10−3 and 1.863 × 10−3 mm2/s, respectively (three decimal places are shown only to demonstrate the small magnitude of the difference not to indicate the accuracy of the method). The range of ADC values in the two experiments with static and orthogonal crushers were 5.8 × 10−5 and 5.1 × 10−5 mm2/s, respectively. The two-sided t and F tests indicated no statistically significant differences in the mean (p = 0.06) or variance (p = 0.45) of the ADC values, indicating that the data provided by the static and orthogonal crusher gradients were highly comparable.

Figure 7.

Comparing high angular resolution diffusion imaging data quality using static or orthogonal crusher gradients in the absence of artifacts. In each case, the phase dispersion imparted by the crusher gradients were 12.7π and 5.7π for the first and second refocusing RF pulse, respectively. Top shows color-coded maps of the main diffusion tensor direction from a human volunteer. (Blue = superior-inferior, Green = anterior-posterior, Red = left-right). The plots on the bottom are the mean of data extracted from the gel phantom from a ROI with a radius of 10 voxels. a: Orthogonal crushers were implemented on the x–z plane. b: Static crushers on all three axes were implemented so that the diffusion and crusher gradients did not cancel. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

DISCUSSION

We have demonstrated that unless care is taken, the crusher and diffusion-encoding gradients in the TRSE diffusion-weighted sequence can cancel each other and result in unexpected artifacts at typically used b-values. These artifacts can appear in any implementation of the TRSE diffusion sequence in which the diffusion-encoding gradients are allowed to have non-zero 0th moments for different signal pathways. Our proposed modification, in which crusher gradients are dynamically rotated to always remain orthogonal to the diffusion-encoding gradients, remedies the problem in general.

Cancellation between the crusher and diffusion gradients only becomes an issue for those implementations of the TRSE diffusion sequence with non-zero 0th moments of the diffusion-encoding gradients. The widely used eddy-current-optimized variant [2] is one such sequence. The orthogonal crusher gradient implementation reported here is only necessary for those types of sequences. In other implementations where the 0th moments of the diffusion gradients balance for some or all of the pathways [17, 18] or where the crusher gradients are merged with the diffusion-encoding gradients [19], there will be no residual 0th moment that can cancel the phase dispersion imparted by the crushers.

Orthogonally oriented crusher gradients are not the only possible solution to avoiding their interaction with the diffusion-encoding gradients. With the knowledge of the diffusion-encoding vector set it may be possible to find a certain direction and amplitude for the crusher gradients that avoids cancellation for all diffusion gradient directions in that set. However, with the trend toward high angular resolution diffusion imaging [12, 20] and the collection of several datasets with different b-values or q-values [15, 21-23] it becomes increasingly difficult to achieve this. Clearly in the limit of continuous angular and b-value distributions there can be no set of static crusher gradients that could be used. Orthogonal crushers are simple to implement and allow complete freedom for user defined diffusion directions while inherently avoiding these artifacts.

In experiment 1, the crusher gradients were implemented only along the X gradient axis and showed that artifacts occur when the diffusion-encoding gradient direction is exactly opposite (i.e. −X). A sole axis was chosen for convenience of the demonstration only. This experiment can be rotated arbitrarily in 3D, resulting in similar artifacts if the crusher and diffusion-encoding gradients cancel each other. Also in that experiment, the amplitude (i.e., phase dispersion) of the crusher gradients was varied for convenience. Similar artifacts could have been generated just as easily by varying the diffusion-encoding gradient amplitude. However, since only the difference between the 0th moments of the first and fourth diffusion-encoding gradients cancel the crushers, the 0th moments of the diffusion-encoding gradients would need to be varied more, inherently leading to changes in b-value. We chose to vary the crushers in order to avoid the confounding effect of signal amplitude variation dependent upon b-value.

In this work, the anterior/posterior (i.e., y) component of the crusher gradient was set to zero for two reasons. First, we wanted to ensure that crusher gradients would not hinder the acquisition due to peripheral nerve stimulation limits. Second, it simplifies the definition and implementation of a unique analytical solution, since otherwise an infinite number of vectors are available in a plane orthogonal to each diffusion-encoding vector direction. Practically it may be more advantageous to allow the crusher vector to have a small y-component (say Cy ≤ L ≤ 1), to help reduce demand on the other two gradient axes but small enough to avoid peripheral nerve stimulation.

In the numerical simulations, it was shown that cancellation of the diffusion-encoding and crusher gradients can occur for the FID1 pathway at practically relevant b-values. In other pathways, the cancellation between crusher and diffusion-encoding gradients occurred for b-values of a few hundred s/mm2, which are not often used for in-vivo human imaging. It is important to note however that varying the imaging parameters and sequence details will affect these results. For example, at higher spatial resolution, the 0th moments of the crusher gradients must be increased as well. In that case, cancellation of the crusher gradients in other pathways may also occur for typical b-values.

An important implication of the results shown in Figure 6 is that the inclusion of an artifactual image in the diffusion tensor fit can result in bias errors that may not be obvious from visual inspection of the parameter maps (e.g., the FA map shown in Fig. 6a) but considerably affect the quantitative parameter values. For example, in the region highlighted in Figure 6b, many of the voxels displaying low FA values (∼0.1) are overestimated by up to 50% when the artifacted image is included, with a clear asymmetric bias. If this type of situation occurs in practice, there is a strong possibility that such an artifact may pass through unnoticed (since it is rare for multi-slice, multi-direction diffusion to be thoroughly examined on a slice-by-slice basis), impacting on any quantitative analysis subsequently performed. In addition, techniques, which make use of the directional diffusion profile to characterize features of tissue microstructure [e.g., for cortical parcellation [24]] will be compromised. Also, recent methods on physiological noise [25] and vibration artifact [26] correction may be biased.

In addition to the crusher and diffusion-encoding gradients the signal in each pathway is additionally affected by the local susceptibility-induced gradients. Note for example the curved lines of the artifact in the coronal orientation and the spatially varying frequency of the artifact in the axial orientation in the in-vivo data shown in Figure 3a. Similarly, in Figure 5, the artifact has a large extent (see coronal orientation) but in the axial image shown the artifact is most prominent on the right of the image (anatomical left) anteriorly and on the left of the image (anatomical right) posteriorly. When the crusher and diffusion-encoding gradients almost cancel each other, the spatially varying susceptibility-induced gradients provide an additional contribution, which will cause the artifact to appear in some regions but not the others. For a detailed explanation of the fundamental mechanism of susceptibility-induced k-space shifts and signal dropout/modulation refer to the study by Weiskopf et al. [27], which also contains figures of maps of typical susceptibility gradients in the brain. The artificial asymmetry introduced into the data by this effect could lead to clinical misinterpretation of diffusion parameter maps and/or fiber tracking results, highlighting the need to eliminate this source of artifact.

Eddy currents always accompany the changing magnetic fields in MRI pulse sequences. One possible limitation of the method presented here could be that if orthogonal crusher gradients produce eddy currents that affect the data (e.g., interacting with the slice select gradient between them), these eddy currents will be different for the different diffusion-encoding gradient directions. We investigated this and did not observe such issues. Another limitation of the method may be that, depending on how orthogonal crushers are implemented, the minimum echo time will increase. Here, for example, the orthogonal crushers were placed in the x–z plane. While for the static gradients it was possible to use all three axes to impart a certain phase dispersion, in the orthogonal crusher implementation it was necessary to allow for the case where the same phase dispersion had to be imparted solely along the x or z gradient axis. For this reason, the echo time was increased by 9 ms when orthogonal crushers were used. However, in these experiments the maximum available slew rate or gradient amplitude were not used, since the objective was merely proof of principle. Had this been done, the increase in TE would have been a more modest 4 ms. This cost in minimum TE could be further reduced if the plane in which the orthogonal crushers are implemented is rotated away from the x–z plane (i.e., for any vector in 3D space it is possible to find an orthogonal vector in any 2D plane in that 3D space). If this plane is rotated away from all three gradient axes (i.e., that plane could include the original static crushers as well) there are always at least two gradient axes available to impart the required phase dispersion and the increase in minimum TE will be even less.

In conclusion, crusher gradients must be implemented in the TRSE diffusion-sequence to avoid unwanted echoes from entering the k-space acquisition window. The use of crusher gradients that are orthogonally oriented to each given diffusion-encoding direction is beneficial as it avoids the possible cancellation of the effect of the crusher gradients without negatively affecting data quality.

ACKNOWLEDGMENTS

David L. Thomas and Nikolaus Weiskopf contributed equally to this article as senior authors. This work and open access to the publication were supported by the Wellcome Trust (079866/Z/06/Z).

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