Alpha and slow gamma FC shrinks with healthy aging
We first studied the dependency of alpha, slow gamma, and fast gamma FC
on age by contrasting between the middle-aged (N=91) and elderly (N=127)
groups. Figure 2a shows the median change in power (in the stimulus
period from baseline) in alpha (top row), slow-gamma (middle) and
fast-gamma (bottom row) for the two age groups. As shown previously
(Murty et al. , 2020), power in the alpha range remained unchanged
whereas the power in slow gamma and fast gamma reduced across the age
groups, primarily in the occipital electrodes. Figure 2b depicts the
average FC maps for the middle-aged and elderly age groups over both the
left and right occipital group of electrodes as seed for FC computation
(FC map with right group is flipped horizontally since the individual
maps for left and right electrode groups showed similar results; refer
‘visualizing average connectivity’ section in Methods for more details).
This plot shows a subtle (but highly significant; as shown below)
reduction in the FC of the elderly group compared to the middle-aged in
the alpha range, which can be observed by comparing the red coloured
contours that represent FC of 0.25. The shrinkage of this contour for
the elderly group can also be observed in the gamma bands, although the
effect is weaker.
To quantify these differences, FC values for all electrode pairs falling
within a specific inter-electrode distance range were averaged to yield
a single FC versus distance plot for each electrode groups in each
subject. Figure 2c shows the median FC versus distance plot for subjects
within each age group, averaged over the left and right seed electrodes
for each subject. FC for elderly subjects was significantly lower than
middle-aged subjects in most of the bins in the alpha band, as indicated
by the asterisks (p-value<0.01; not corrected for multiple
comparisons) in Figure 2c, top row. The FC values for elderly were lower
than middle-aged for some bins in the slow-gamma band as well (middle
panel), although the difference did not reach significance. For
fast-gamma band (bottom plot), the differences were negligible.
We further averaged all FC values of electrode pairs within
inter-electrode distance range of [-0.5 to 0.5] to yield a single FC
value per electrode group per subject (Figure 2d; see Methods for
details). This range was chosen to limit the dominance of high FC values
close to seed electrode in the average which could be more affected by
volume conduction. Figure 2d shows median FC values within the two age
groups, separately for each seed electrode group. Both electrode groups
showed significantly reduced alpha FC (top row) in the elderly over the
middle-aged subjects (left group:\(\chi^{2}\left(1\right)=7.21,\ n=91/127,\ p\ =0.007\); Kruskal
Wallis (KW) test; right group:\(\chi^{2}\left(1\right)=11.98,\ n=91/127,\ p\ =0.0005\); KW
test). Similar findings were observed for the back electrode group as
well (\(\chi^{2}\left(1\right)=4.78,\ n=91/127,\ p\ =0.028,\);
KW test; Supplementary Fig. 4). FC was not significantly different
across the age groups in both the slow (middle row) and fast gamma
(bottom row) bands (statistics are shown in the plots), although slow
gamma FC almost reached significance (Figure 2d, second row).
The reduction in alpha FC was small in absolute terms (0.185 for
middle-aged and 0.167 for elderly when all sides were pooled, or a
reduction of 9.6%), potentially due to the method of averaging that was
done over a wide range of inter-electrode distance with varying FC
values. Nevertheless, the reduction was consistent across individual
inter-electrode bins and electrode groups and therefore highly
significant. We quantified the robustness of these results by estimating
the Bayes factor (BF), which is the ratio of the marginal likelihood of
the alternate hypothesis (higher FC in middle-aged than the elderly) and
the null hypotheses (comparable FC in middle-aged and elderly), given
the observed data (see Methods for details). BF values above 10 provide
“strong” evidence in favor of the alternative, while BF above 3
provide “substantial” evidence (Jeffreys, 1998). For alpha FC, BF
values were 20.42, 37.83 and 6.78 for the Left, Right and Back electrode
groups, and 21.32 when electrode groups were pooled. For slow-gamma, BF
values were 2.73, 2.31, 0.93 and 1.89 for left, right, back and combined
groups, suggesting “anecdotal” evidence (see Methods for details). For
fast gamma, these values were 0.90, 0.77, 0.33 and 0.67, suggesting
insufficient evidence in favor of the alternate hypothesis.
To test whether FC results could be due to differences in power in the
two groups, we performed a power-matching analysis. We first uniformly
binned subjects from both middle-aged and elderly groups into several
sub-groups based on their power, and subsequently randomly selected an
equal number of subjects from each sub-group (see Methods for more
details). This procedure ensured that the power distribution across the
two age groups matched (thereby matching the average, median, and other
statistics). Figure 3a shows the mean change in PSD for the left group
of electrodes after performing the power matching procedure in alpha
(top row, N=88 subjects in both age groups), slow-gamma (middle row,
N=84) and fast-gamma bands (bottom row, N=84). The frequency bands based
on which power matching was done is highlighted by dashed lines. Figure
3b and 3c shows the corresponding PPC maps and PPC versus distance plots
for the left electrode group (note that unlike Figure 2b-c, left and
right electrode groups cannot be averaged since different subjects are
chosen for each side). Corresponding results for the back electrode
group is shown in Supplementary Fig. 5.
Overall, the results remained similar after power matching. Alpha FC
reduced with age (Left:\(\chi^{2}\left(1\right)=6.6,\ n=88,\ p\ =0.01,\ \ \ BF\ =17.33\);
Right:\(\chi^{2}\left(1\right)=7.60,\ n=81,\ p\ =0.005,\ \ \ BF\ =11.16\);
Back:\(\chi^{2}\left(1\right)=3.09,\ n=87,\ p\ =0.07,\ \ \ BF\ =2.44\)).
Reduction in slow gamma FC also approached significance (Left:\(\chi^{2}\left(1\right)=3.65,\ n=84,\ p\ =0.05\ ,\ \text{\ \ }BF\ =3.91\),
KW test, Right:\(\chi^{2}\left(1\right)=4.49,\ n=81,\ p\ =0.03,\ \ BF\ =4.45\);
Back:\(\chi^{2}\left(1\right)=2.17,\ n=78,\ p\ =0.141,\ \ \ BF\ =1.05\)),
while fast gamma FC remained indifferent across age groups (Left:\(\chi^{2}\left(1\right)=2.27,\ n=84,\ p\ =0.13,\ \ \ BF\ =1.72\),
Right:\(\chi^{2}\left(1\right)=3.18,\ n=81,\ p\ =0.07,\ \ \ BF\ =1.94\);
Back:\(\chi^{2}\left(1\right)=0.54,\ n=79,\ p\ =0.45,\ \ \ BF\ =0.36\)).
Similar results were obtained when we used coherence or PLV instead of
PPC (data not shown).
Results after power matching varied slightly across different iterations
since different subset of subjects could be selected within each age
group, under the power distribution matching criteria. Figure 3 shows
results of an iteration for which the p-values in Figure 3d were close
to the median of the p-values computed over 50 iterations. The p-values
for alpha, slow-gamma and fast-gamma FC were less than 0.05 for
~96%, ~56% and ~18%
of the iterations, implying consistent, borderline (weak) and
insignificant reductions in FC in these three bands, respectively.
Slow
gamma but not alpha connectivity spread shrinks with cognitive
impairment
The MCI subjects (referred hereafter as cases) were compared with age
(±1 year) and gender matched healthy subjects (referred to as controls)
to study the effect of cognitive disorder on FC. As in our previous
study (Murty et al. , 2021), since the number of controls far
exceeded the cases (see Methods for details), we averaged the relevant
metrics (power, FC) across all age and gender matched controls for each
case subject, culminating in the same number of cases and controls.
Figure 4 and Supplementary Fig. 6 show the results in the same format as
Figure 2 and Supplementary Fig. 4. Figure 4a illustrates notable
reduction in occipital slow gamma and fast gamma power but not alpha
power in cases over the respective control group, as reported previously
(Murty et al. , 2021). Although these power trends were similar to
the effect of aging (Figure 2a), the corresponding FC results were
different. Now, the highest reduction in FC was observed in the
slow-gamma band, with negligible effect on alpha or fast-gamma bands.
Reduction in slow gamma FC for the cases over controls was observed in
all electrode groups, with BF values in the ‘anecdotal’ to ‘substantial’
range in spite of the small sample size (Left:\(w\ =56,\ n=11,\ \ P\left(W\geq w\right)=0.02,\ BF\ =3.6\),
Wilcoxon signed rank (WSR) test); Right:\(w\ =50,\ n=11,\ P\left(W\geq w\right)=0.07,\ BF\ =2.21\),
WSR test; Back:\(w\ =58,\ n=11,\ P\left(W\geq w\right)=0.01,\ BF\ =10.67\),
WSR test). When all electrodes were averaged, the reduction was highly
significant:
(\(w\ =59,\ n=11,\ \ P\left(W\geq w\right)=0.009,\ BF\ =6.87\),
WSR test). In contrast, alpha and fast-gamma FC values were not
significantly different (statistics shown in the Figure), with BF rarely
exceeding 1 (not shown). Note that the small sample size does not
necessarily increase false alarm rate.
Figure 5 shows the same results after choosing a single control subject
for each case subject with minimal difference in band power (note that
different control subject may get chosen for the same case subject in
different frequency bands and seed electrode group). Interestingly, the
reduction in slow-gamma FC was more prominent now, with BF values in the
“strong” range (Left:\(w\ =59,\ n=11,\ P\left(W\geq w\right)=0.009,\ BF\ =10.73\),
WSR test; Right:\(w\ =56,\ n=11,\ P\left(W\geq w\right)=0.02,\ BF\ =3.71\),
WSR test; Back:\(w\ =66,\ n=11,\ P\left(W\geq w\right)=0.0005,\ BF\ =\)17.65,
WSR test; Overall:\(w\ =60,\ n=11,\ P\left(W\geq w\right)=0.007,\ \ BF\ =10.47\),
WSR test), while no differences were observed in alpha and fast-gamma
FC. Corresponding results for the back electrode group is shown in
Supplementary Fig. 7.