Richard Buschbeck^{1}, Seong Dae Yun^{1}, Markus Zimmermann^{1}, Ezequiel Farrher^{1}, and N. Jon Shah^{1,2}

A new method is proposed that allows for the omission of crusher gradients in the Twice-Refocused Spin Echo (TRSE) sequence. The proper spoiling of the unwanted signal pathways is achieved by modifying the amplitudes and durations of the diffusion gradients. Both the crusher moment as well as the desired diffusion weighting is eventually provided only by the diffusion gradients. This results in several advantages like shorter minimum TEs and higher SNRs, all of which can be beneficial in diffusion MRI.

The
Twice-Refocused Spin Echo (TRSE) diffusion sequence by Reese et al.^{1} is normally executed with four separate crusher gradients
alongside the two refocusing RF pulses (see Fig. 1 top). The crusher
gradients are necessary to spoil unwanted signal pathways while
maintaining the desired TRSE pathway. There are several possibilities
regarding the orientation of the crusher gradients, e.g. orthogonal
to the diffusion gradients^{2}. It is impractical to apply separate
crushers (anti-)parallel to the diffusion gradients since this could
lead to cancellation effects compromising the crusher efficiency^{2}.
However, having four separate crusher gradients not aligned with the
diffusion gradients is time-consuming and leads to a TE that is
longer than inherently necessary in diffusion MRI as well as a
correspondingly lower SNR. Besides, the common design introduces a
bias in the b-value due to the crusher contributions off the
principal diffusion direction.

Here, we propose a new crusher concept which circumvents both drawbacks. Our approach is to omit separate crusher gradients completely and, instead, modify the diffusion gradient amplitudes and durations (see Fig. 1 bottom) such that both correct diffusion weighting and proper crushing is provided only by the diffusion gradients. Using the combined crusher scheme it is possible to either reduce the minimum TE, decreasing the total scan time and increasing the SNR, or to increase the maximum possible b-value or combinations thereof.

The
combined crusher method was implemented in an in-house TRSE diffusion
EPI sequence. A calculation method was developed to determine the
crusher moments, C_{i}, which have to be added to the
diffusion gradients (see Fig. 1 bottom) to reliably spoil all seven
unwanted signal pathways while preserving the desired TRSE signal.
Note that depending on the timing and the b-value, the diffusion
gradients might already provide enough crusher moment themselves in
which case the C_{i} can be zero. In either case, care was
taken such that the modified diffusion gradients (with moment D_{i}+C_{i},
see Fig. 1 bottom) provide the desired b-value without bias, i.e. any
diffusion gradient modifications are taken into account for the
b-value calculation.

To prove the effectiveness of our method, phantom and in vivo experiments were performed with conventional and combined crushers on a commercial 3T Trio MRI scanner (Siemens Healthineers, Erlangen, Germany). The body coil was used for excitation, a 12-element phased array head coil was used for signal reception. Prior to the in vivo measurements written informed consent was obtained from a single healthy male volunteer.

The
following sequence parameters were used in all experiments:
TR=2000ms, resolution 1.8×1.8×3.0 mm^{3}, matrix size
128×128, no. of slices 10, distance factor 100%. Six diffusion
directions, comprising the positive and negative directions along the
three gradient axes, were measured. The
experiments were performed with the standard TE, which is possible
with conventional and combined crushers, and a reduced TE which is
only possible with combined crushers.

From the in vivo images, apparent diffusion coefficient (ADC) maps were computed after reconstruction and visually inspected for artefacts. A spherical water phantom was used to assess the expected SNR gains. The mean SNR was computed in a ROI by repeating the measurement in one diffusion direction 100 times and dividing the mean signal magnitude in every voxel by the corresponding standard deviation. Raw data reconstruction was performed with the online reconstruction system of the scanner. Post-processing for SNR and ADC calculations was performed using MATLAB (The Mathworks Inc., Natick, USA).

Our
experiments demonstrate that the combined crusher concept is feasible
and visual inspection of the ADC maps shows that it can provide
artefact-free DWI results comparable to conventional crusher schemes.
However, the proposed method allows one to improve several aspects of
the TRSE diffusion sequence whereby the most prominent are a
reduction of the minimum possible TE and an SNR increase. Although
the original TRSE design^{1}, aiming at optimal eddy-current
suppression, is slightly changed, no eddy current effects have arisen
during our investigations. In fact, numerical simulations suggest
that omitting the separate crusher gradients (which were not
considered for eddy current suppression in the original design) can
even be beneficial in terms of reducing the overall eddy currents.

All in all, the combined crusher approach could become helpful for improving the performance and feasibility of diffusion MRI.

^{1}Reese T, Heid O, Weisskoff R, Wedeen V. Reduction of
Eddy-Current-Induced Distortion in Diffusion MRI Using a
Twice-Refocused Spin Echo. Magnetic Resonance in Medicine
2003;49:177–182

^{2}Nagy Z, Thomas DL, Weiskopf N. Orthogonalizing crusher and
diffusion-encoding gradients to suppress undesired echo pathways in
the twice-refocused spin echo diffusion sequence. Magnetic Resonance
in Medicine 2014;71:506–515

_{}
Figure 1: Schematic comparison
of the conventional TRSE sequence with separate crusher gradients
(top) and the combined crusher version without (bottom).

The original diffusion
gradient amplitude, G_{D}, and the gradient durations δ_{i}
are
modified in the combined crusher scheme. The
diffusion
and crusher gradient moments D_{i}
and C_{i}
are calculated to assure
proper spoiling of all unwanted pathways while
simultaneously
providing
the
desired diffusion weighting
in
the correct direction. Note that at maximum amplitude,
the D_{i} provide enough crusher moment themselves such that
all C_{i} can be zero and the maximum allowed gradient
amplitude is not exceeded.

Figure 2:
ADC maps calculated from images acquired with (a) the combined
crusher method at reduced TE, (b) the combined crusher method at
standard
TE and (c) the standard crusher method at standard
TE; Row
(d) shows the difference
between the maps
in row (b)
and (c).
The combined crusher scheme provides very similar results compared to
the standard crusher scheme while enabling significant TE reductions
between 10ms and 11ms. This equals a relative TE reduction by 8.8% to 12.7% depending on the b-value and the GRAPPA factor.

Figure 3:
Results of the SNR measurements in a
ROI of
an
isotropic water
phantom (top left).
The bar colours
indicate the measurements with the standard crusher scheme, the
combined crusher scheme at the
standard
TE and the combined crusher
scheme at reduced TE (the TE
times at b=500s/mm^{2}
and 1000s/mm^{2}
are the same as in Fig. 2, at b=50s/mm^{2}
the TEs are the same as at b=500s/mm^{2}).
The percentages
state the relative SNR difference between the standard and
the combined crusher scheme at reduced TE. The
combined crusher scheme enabled
an SNR increase
of 5.2%
to 7.7%
in the images.