Chemistry Reference
In-Depth Information
fitting functions, assume that the image signal from any voxel will originate from a
variety of cells, and intracellular and extracellular spaces. The detected MR signal
is the sum of contributions from groups of protons in different locations within the
voxel, and each group will have a characteristic apparent diffusion coefficient. In
the statistical model, the signal decay is written as (in their notation),
S
0
∞
0
S
=
P
(
D
) exp(
−
bD
)
dD
(77)
where
P
(
D
) is the distribution function of the apparent diffusion coefficient that
is defined using a Gaussian-like function,
B
exp
−
ADC
)
2
2
σ
2
(
D
−
P
(
D
)
=
for
D>
0
,
(78)
P
(
D
)
=
0
for
D<
0
where
B
is a normalization constant, the apparent diffusion coefficient (ADC)
corresponds to the position of the distribution peak, and
σ
is its width (Fig 11).
Equation (77) and (78) then yield,
S
0
exp
2
σ
2
b
2
1
S
=
−
b
ADC
+
(79)
Yablonskiy et al. [50] found that this expression fitted experimental data from
the human brain well, although the second parameter, the distribution width
σ
,was
not sensitive to different tissue types within the brain. Thus the potential benefit
in using this model must simply arise from the possibility of measuring the ADC
more accurately for each voxel.
Ln
S S
0
1.0
1
0.8
0.9
0.6
0.8
0.4
0.2
0.7
0.6
Figure 11.
The statisti-
cal model. (See insert for color
representation of the figure).
3.5
b
0.0
0.5
1.0
1.5
2.0
2.5
3.0
