Chemistry Reference
In-Depth Information
3. A Kurtosis Model
A method to quantify diffusion kurtosis in tissue using DWI was first proposed
by Jensen et al. [51]. The aim was to measure the degree to which water diffusion
was non-Gaussian. Their fitting function, which is very similar to that presented
later by Kiselev et al. [52], and like the statistical model of Yablonskiy [50], has
only two fitting parameters compared to the biexponential model's four. They
begin by writing
S
bD
), as a
b
2
cumulant expansion, and truncated the
expansion at the second term, leaving the quadratic function,
=
S
0
exp(
−
K
apparent
ADC
2
6
b
2
ln
S
=
ln
S
0
−
b
ADC
+
+···
(80)
where
K
is the apparent“kurtosis excess” factor and is a measure of the peakedness
of a distribution (Fig 12). Kiselev explored the goodness-of-fit of this kurtosis
model and the biexponential model in human brain diffusion data. The decay
curves examined were gray matter (GM), white matter (WM), cerebrospinal fluid
(CSF) and partial volume voxels, presumed to contain both GM and CSF. In GM,
the kurtosis model fits as accurately as the biexponential model, but the added
parameters of the latter were required in order to best fit the voxels containing WM
and partial volume. The authors did not include a study of directional dependence.
In the earlier study of Jensen et al., when three diffusion directions were applied,
the diffusional kurtosis excess was found to be significantly higher in WM than in
GM. The authors conjectured that this difference reflects the structural differences
between the tissue types [51]. More recently, diffusion kurtosis imaging has been
used to achieve increased sensitivity and directional specificity to microstructural
changes associated with brain maturation in the rat [53], and to increased sensitivity
to fiber directions in DTI.
Ln
S S
0
1.0
k
1
k
0.8
0.9
k
0.6
k
0.4
0.8
Figure 12.
These plots
of the kurtosis model show
how the shape of the decay
curves change with incremen-
tal steps of
k
. (See insert
for color representation of the
figure).
k
0.2
0.7
2.0
b
0.0
0.5
1.0
1.5
