Chemistry Reference
In-Depth Information
Figure 20.
The
∗
represent the diffusion decay in the diffusion experiment where once again
rectangular gradients were employed, but their strength was increased instead of their duration. The
solid line represents the fit using the gradient-echo fractional diffusion expression Eq. (181).
large molecules. Figures 19 and 20 shows the fit using the bipolar Eq. (181), which
in the case of free diffusion (
α
1) reduces to Eq. (64).
Table I and Fig. 21 show the values of
α
obtained for each region of interest
(ROI), for each experimental design. A fit of the stretched exponential expres-
sion [40] against the increasing gradient duration experiment with the rectangular
gradient shape was also calculated for comparison.
=
exp
−
(
bD
DC
)
α
S
(
t
)
S
(0)
=
(184)
1, as expected for free diffusion.
Table II shows the values of the diffusion coefficient from the fitting of
the water phantom data. The diffusion coefficient of pure water at 25
◦
Cis
The value for
α
is
∼
TABLE I
Fitted Values of the Parameter
α
for the Five Regions in the Water Phantom
ROI
1
2
3
4
5
Average
Rectangular
1.000
0.984
1.000
0.982
1.000
0.992
Triangular
0.998
0.997
0.999
0.999
1.0
0.999
Ramped
0.999
0.999
0.999
0.999
0.999
0.999
Stretched Exp.
1.002
0.995
1.004
0.995
1.000
0.999
