Chemistry Reference
In-Depth Information
15
20
10
15
10
5
5
0
0
0.8
0.6
0.4
0
.2
0.0
0.2
0.4
0.6
0.8
0.6
0.4
0
.2
0.0
0.2
0.4
0.6
SE
F
SE
B
SE
F
SE
B
SE
F
SE
B
SE
F
SE
B
(a)
Fractional versus biexponential fit in GM
(b)
Fractional versus biexponential fit in WM
30
20
25
15
20
15
10
10
5
5
0
0
0.8
0.6
0.4
0
.2
0.0
0.2
0.4
0.6
0.8
0.6
0.4
0
.2
0.0
0.2
0.4
0.6
SE
F
SE
S
SE
F
SE
S
SE
F
SE
S
SE
F
SE
S
(c)
Fractional versus stretched exp. fit in GM
(d)
Fractional versus stretched exp. fit in WM
20
20
15
15
10
10
5
5
0
0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
0.6
0.4
0
.2
0.0
0.2
0.4
0.6
SE
B
SE
S
SE
B
SE
S
SE
B
SE
S
SE
B
SE
S
(e)
Biexp. versus stretched exp. fit in GM
(f)
Biexp. versus stretched exp. fit in WM
Figure 34.
Frequency distributions for a comparison of goodness of fit of the fractional,
stretched, and biexponential equations to the image data from nine human subjects, where SE
F
is
the sum of the squared residuals for the fractional equation, SE
B
is the standard error for the biexpo-
nential equation and SE
S
is that for the stretched exponential model. Negative values indicate lower
sum-of-squared residuals for the first quoted equation.
of the diffusion weighting gradients. Despite the much lower diffusion weighting
achieved with the ramped gradient shape, consistent values of the diffusion coeffi-
cient were calculated for the same signal decay for each experiment. The fractional
diffusion equation was found to fit the experimental data very accurately and when
