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also incorporated in the customized sequence design. For the same subjects, the
measured diffusion coefficients should be the same for experiments with varying
diffusion gradient strength, duration, and shape, if the fractional diffusion model
is to be a good fit of the experimental data.
Four customized pulse sequences were prepared to fully explore the suitability
of the anomalous diffusion model to describe the diffusion behavior in human brain
tissue. Each employed a gradient-echo multishot echo-planar imaging sequence
with a repetition time of 2 s and an echo time of 64.2 ms. While a spin-echo
sequence would be preferred for diffusion imaging due to improved image qual-
ity, time was a limiting factor in these experiments. To minimize the echo time
while applying diffusion gradients with a large enough duration to produce a high
diffusion weighting required the minimum achievable time for the other sequence
components. The gap required between the diffusion gradient lobes in the spin-
echo sequence would have resulted in an unacceptably long echo time and severe
degradation of image quality. A sensitivity encoding factor of two was also em-
ployed to minimize the echo time. Ten 4-mm axial slices with a field of view of
23
23 cm were acquired to encompass the whole brain. Ten diffusion weightings
were repeated sequentially for a total of 30 times for each slice for averaging pur-
poses. Inversion recovery images of each subject were also acquired as a map of
gray and white matter, from which regions of interest could be chosen for analysis.
The diffusion weighting gradients were applied in the axial direction only, thus
the directional sensitivity of white matter was not explored.
The first sequence applied a bipolar diffusion weighting gradient, with trape-
zoidal gradient shape. After acquiring a
b
0
image, each gradient lobe increased
in duration from 12 to 24 ms in steps of 1.5 ms. With a gradient strength of
50 mT m
−
1
used for each gradient. This produced an effective range of
b
-values
of 200-1600 s mm
−
2
. The gradients were applied in the axial direction only.
The second sequence also used a customized gradient-echo EPI sequence,
however, the bipolar diffusion weighting gradients now had a fixed duration of
24 ms and the gradient strength was varied over eights steps from 8 mT/ m
−
1
×
to
48 mT m
−
1
, producing a maximum
b
-value of 1440 s mm
−
2
.
The third customized sequence used ramped shape gradients, as described in
earlier section. The duration of these gradients was varied over the same range as
the trapezoidal gradients, from 12 to 24 ms after the acquisition with no diffusion
weighting (
b
0
). A maximum gradient strength of 50 mT m
−
1
was also chosen.
However, in this case, due to the gradient shape, a much lower range of
b
-values
was achieved, 90-670 s mm
−
2
.
The fourth experiment was designed to include the triangular gradients de-
scribed in Section IV. The maximum gradient strength of these gradients was
also 50 mT m
−
1
and the duration of the gradients varied over the range used for
the previous experiments. Due to the requirement that human subjects should
spend no more than1hinthescanner, it was not possible to include this
