Yi-Xi Peng^{1}, Chang-Le Chen^{2}, Yung-Chin Hsu^{3}, and Wen-Yih Isaac Tseng^{2,4,5}

**In this study, we calculated tract covariance to describe the
phenomenon of white matter differentiation and
de-differentiation across lifespan,
using diffusion spectrum imaging (DSI) and whole brain tract-based automatic
analysis (TBAA) techniques. Differentiation was found to be highest in
the 2 ^{nd} decade and
de-differentiation started to emerge
at 3^{rd} decade and peaked at 6^{th} decade.**

Subjects: We divided
the participants into six groups per decade^{2} (See
Table 1).

Imaging: We acquired data of T1-weighted imaging and DSI on a 3T
MRI system (TIM Trio, Siemen) with a 32-channel
phased array coil. T1-weighted imaging utilized a MPRAGE pulse sequence: TR/TE =
2000/3 ms, flip angle = 9^{o}, FOV = 256 X 192 X 208mm^{3},
resolution = 1 X 1 X 1 mm^{3}. DSI used a pulsed gradient twice-refocused
spin-echo diffusion echo-planar imaging sequence: 102 diffusion-encoding gradients with
bmax of 4000 s/mm^{2}, TR/TE =
9600/130 ms, FOV = 200 X 200 mm^{2}, matrix size = 80 X 80, 56 slices, and slice thickness = 2.5 mm.

Analysis: We used TBAA to obtain GFA profiles of
76 white matter tract bundles for each participant^{3}, and mean
generalized fractional anisotropy (GFA), fractional anisotropy (FA), and
relative anisotropy (RA) values were calculated for each tract. Among the 6
groups, we compared tract
covariance which we defined as the partial correlation between each pair of
tracts in variations of GFA, FA, RA values across subjects, with age, gender and dropout number of diffusion-weighted images
being regressors. For
statistics analysis, we used a permutation test to determine whether there
were significant differences and describe the differences between group 1 and any
other groups as well as the adjacent groups. We disturbed the data of
the selected groups and regrouped them randomly. We
calculated the new tract covariance and evaluated the
difference of the original
covariance maps across 2850 pixels. We permutated it for 342000 times and got 342000 tract covariance
matrices to obtain 2850 empirical distributions of the differences. We put the
difference of the original covariance and found
the p value which was defined to be significant if it was located beyond 2 standard deviations. We
took the -log of all p values for visualize the difference distribution, the greater the -log│p│, the more dramatic the difference. We overlapped the -log│p│ of
the two comparisons groups to show the major trend of the dynamics.

1. Cox, Simon R., et al. "Ageing and brain white matter structure in 3,513 UK Biobank participants." Nature communications 7 (2016): 13629.

2. Westlye, Lars T., et al. "Life-span changes of the human brain white matter: diffusion tensor imaging (DTI) and volumetry." Cerebral cortex 20.9 (2009): 2055-2068.

3. Chen, Yu‐Jen, et al. "Automatic whole brain tract‐based analysis using predefined tracts in a diffusion spectrum imaging template and an accurate registration strategy." Human brain mapping 36.9 (2015): 3441-3458.

4. Chechik, Gal, Isaac Meilijson, and Eytan Ruppin. "Neuronal regulation: A mechanism for synaptic pruning during brain maturation." Neural computation 11.8 (1999): 2061-2080.

Table 1: Subjects information

Figure 1: Matrices of tract covariance of 76 tracts s across 6 age groups.
Correlations are color-coded as indicated by the color bars on right.

Figure 2: The variation of the tract covariance of diffusion indices (GFA/FA/RA) across 6 age groups.

Figure 3: (1) The ∣p∣ values
after permutation were selected by the threshold of ∣p∣≤0.025
and were illustrated by∣p∣maps
with positive
p (yellow) and negative p (white). Positive p denotes that the correlation of the former group is higher than that of the latter group and vice
versa. (2) Illustrative -log ∣p∣ histogram, comparing the counts and values of -log∣p∣between
group1 and other groups.

Figure 4: Comparison of the 2850 ∣p∣ values between adjacent age
groups.