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.