Chemistry Reference
In-Depth Information
components exist [41] so that the decay may be described by the simple equation
S
(
t
)
S
(0)
=
V
1
e
−
bD
1
V
2
e
−
bD
2
+
(76)
Here
V
1
and
V
2
are considered as the volume fractions of protons in fast and
slow diffusing pools within neuronal structures, with the distinct diffusion coef-
ficients
D
1
and
D
2
(Fig 10). Once again,
b
contains the experimental parameters
γ
2
G
2
δ
2
(
δ/
3) . This equation, which is useful in practice [41-44], has a simple
theoretical explanation, namely, that the signal from two separate compartments
is the sum of the signals from each compartment (although this statement should
be regarded as approximate because of the presence of a boundary). The diffusion
coefficients are thought to correspond to two compartments, in slow exchange,
one with a fast and one with a slow diffusion coefficient. The relative volume of
each pool and their corresponding diffusion coefficients, have been consistently
reported by many groups [42, 44, 45] to be 0.7:0.3 for the fast-slow diffusing
pools, with corresponding diffusion coefficients of 1.3:0.3 mm
2
s
−
1
.
Neindorf et al. [41] performed diffusion weighted experiments in the rat brain
with
b
-values up to 10,000 smm
−
2
. The possibility of other causes for the observed
nonmonoexponential behavior, such as internal gradients due to cross-terms, par-
tial volume effects, vascular contributions, echo time (TE) dependence and diffu-
sion time dependence, were eliminated experimentally in this study. It was thought
that the fast and slow diffusing pools might correspond to the intracellular and
extracellular compartments, where diffusion is expected to be faster in the extra-
cellular compartment due to lower viscosity. However, the volume fractions as
noted above, do not correspond to the known volume fractions for intra- and ex-
tracellular water, as intracellular water is known to account for
>
80% of the total
water volume. The magnitude of the volume fractions changes in ischaemic tis-
sue, as the space occupied by intracellular and extracellular water changes during
cell swelling. It remains impossible, however, to assign the slow and fast diffus-
ing pools to intracellular and extracellular compartments [39]. It is now widely
accepted that biexponential behavior can be observed in the intracellular environ-
ment independently [46-49].
−
2. A Statistical Model of Yablonskiy
The simplest and most logical extension of the Stejskal and Tanner expression,
Eq.(75), to account for the nonmonoexponential behavior observed in human neu-
ronal tissue, resulted in the biexponential model above. While this expression con-
tains
two
discrete diffusion coefficients, the majority of alternative fitting functions
that have been proposed in the literature to date, instead suppose a distribution of
diffusion coefficients. This hypothesis was clearly described by Yablonskiy et al.
[50] when they proposed their “statistical model”. These models, that is, empirical
