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<p>Resolving multiple fiber orientations within one imaging voxel is critical for
accurate quantification of tissue microstructure and faithful reconstruction of the
complex neural fiber pathways. It is recognized that the diffusion process in brain
tissues is generally non-Gaussian and recently there have been multiple methods developed
specifically to account for this non-Gaussian property. Many of these efforts, however,
have been largely focused on improving fiber tracking algorithms rather than providing
a quantitative assessment of the deviation from Gaussian diffusion. Consequently,
fast and quantitative assessment of this non-Gaussian property is critically needed.
Developing a quantitative measurement of the non-Gaussian diffusion processes may
provide powerful tools to assess changes in white matter that are due to axonal damage
or degeneration. Generalized diffusion tensor imaging (GDTI) with the use of higher
order tensors (HOT) provides one such method to identify, characterize and visualize
underlying fiber structures. An optimal scan protocol, which estimates the fourth-order
diffusion tensor, is needed in order to maximize the efficiency and speed of the data
acquisition. This optimization was investigated for a phantom that models crossing
white matter fibers and compared to in vivo scans. The minimum number of b-values,
b-value magnitudes, and the minimum number of gradient directions sufficient to estimate
fourth order diffusion tensors was identified.</p><p>Gold standards were established
by acquiring images using five b-values and a large number of gradient directions
for both the phantom and in vivo data sets. The fourth order diffusion tensors were
then calculated for one, two, and three b-value subsets of the original five b-value
data for both phantom and in vivo cases. For each subset, the tensors were converted
to a two-dimensional 9×9 matrix and decomposed using eigenvalue decomposition. Three
scalar metrics were developed to characterize the non-Gaussian diffusion. The mean
of the eigenvalues represents the fourth-order deviation from a Gaussian diffusion,
the fourth order FA provides a measure of the variance within the fourth order diffusion
distribution, and the variance-to-mean ratio (VMR) characterizes the signal distribution
across the eigenvalues. </p><p>The scalar metrics for each b-value subset was compared
to the gold standard by way of a Root Mean Square Error (RMSE). The normalized RMSE
was then plotted for each metric across all subsets and the b-value magnitude combination
corresponding to the lowest error was identified. It was found that a single b-value
is not sufficient for the scalar representation of the fourth order diffusion tensor.
While a three b-value subset had the lowest error, it was shown that two b-values
provided acceptable image quality and fourth order diffusion information.</p>
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