Chemistry Reference
In-Depth Information
sequence design in the data acquisition, and it was applied to the water experiments
phantom only.
To assess the performance of the fractional expressions in measuring mono-
exponential behavior, each customized sequence was used to acquire diffusion
image data with a spherical phantom filled with water before use on human sub-
jects. These images were analyzed to ensure that expected values for the fitting
parameters (
D
and
α
) were obtained. It was predicted that the value of
α
≈
1 and
10
−
3
mm
2
s
−
1
would be measured. These measurements were used to
validate each step of the process from the sequence programming, to the curve
fitting, and the derivation of the fitting expressions.
D
≈
2
.
4
×
4. Analysis
Postprocessing and fitting were performed using IDL 7.0 (ITT Visual Informa-
tion Solutions, Boulder, CO). Before fitting was performed, the average of the
30 repetitions of each diffusion weighting value was calculated. The signal decay
curves created by the increasing gradient duration in each pixel, were fitted to the
appropriate fractional diffusion expression, as well as the Bennett stretched ex-
ponential equation for comparison. Bounds were placed on the parameter
α
such
that 0
<α<
1. The fitting was performed using the Levenberg-Marquardt algo-
rithm [126] as implemented in IDL to provide values for
D
and
α
. This algorithm
minimizes the cost function
n
a
))
2
C
=
(
y
i
−
f
(
x
i
,
(180)
i
=
1
where
y
i
is the experimental diffusion data of length
n
,
f
(
x
i
,
a
) is the fitting function
to evaluate the variables
[
D, α
]. The parameters returned for each diffusion
weighted image pixel were then displayed as an image. A fit was rejected that did
not achieve a chi-squared goodness of fit of
<
0
.
001.
a
=
B.
7T Spin-Echo experiments
All animal imaging was performed on a Bruker Biospin animal MR system with a
7T static magnetic field and a 30-cm bore (Bruker Biospin, Ettlingen, Germany).
Male Wistar rats (
n
= 3) one aged 4 months (young) and two aged 20-24 (aged)
months were used for these experiments in accordance with the protocols approved
by the Trinity College Dublin ethics committee and the Irish Department of Health.
The animals were anesthetized using isoflurane gas (1.5-2% at 1 L min
1
of
oxygen) administered via a facemask during each experiment. The rat was placed
on a fibreglass cradle and the animal's temperature was monitored with a rectal
thermometer. The temperature was maintained by application of a warming surface
controlled by a water pump driven temperature regulator (SA Instruments Inc.,
Stony Brook, NY). A mechanical ventilator (Ugo Basile, Comerio, VA, Italy) was
−
