Fig 1.
Different subjects exhibit different degrees of alpha blocking upon opening of the eyes.
Here five subjects have been selected to illustrate the range of alpha blocking behaviour observed in the dataset. The vertical axis on each plot represents an arbitrary scale for the normalized power spectral density (PSD). Some subjects do not show any reduction in alpha power between EC and EO states (e.g. Subject 34); others exhibit partial blocking where the alpha activity in EO state is weaker than that of EC but is still pronounced (e.g. Subject 25); while some show total blocking where the alpha activity in the EO spectra completely disappears (e.g. Subject 80). To quantify the degree to which the EEG spectrum changes upon opening of the eyes, we compute the Jensen-Shannon divergence, DJS, between the eyes-closed (EC) and eyes-open (EO) normalized experimental spectrum for each subject. A larger value of DJS implies more pronounced EEG spectrum changes, or alpha-wave suppression. The complete set of spectra for all subjects is presented in Fig A in S1 Appendix, ordered by DJS.
Table 1.
State-distinct parameters and state-common parameters.
Fig 2.
Regularized and unregularized best fits to EC and EO spectra.
Best fit results for the 5 subjects shown in Fig 1. Subjects are ordered vertically by the degree of alpha blocking, with alpha blocking increasing downwards. Regularized fits (red) deviate only slightly from the unregularized fits (green). The 16% and 84% uncertainty quantiles (based on the gamma distribution for the unregularized best fits) are shown in black. These boundaries define the acceptable error of a fit. Regularized best fits deviate only slightly from the unregularized ones and generally stay within these uncertainty quantiles. In order to visualize the different fits, EC and EO spectra for a given subject are not necessarily shown on the same vertical scale.
Fig 3.
Posterior distributions for each parameter.
Posterior distributions for state-distinct parameters (with EC in orange and EO in green) and state-common parameters (grey), again for the 5 subjects in Figs 1 and 2. Subjects are ordered vertically by the degree of alpha blocking, with alpha blocking increasing downwards. The distributions are calculated using kernel density estimates from the best 100 of 1000 randomly seeded particle swarm optimizations for each subject. Each parameter is plotted in normalized coordinates, where -1 corresponds to the lower limit of the plausible parameter interval and +1 corresponds to the upper limit. The parameter pei is the only parameter where the difference between EC and EO distributions increases consistently with the degree of alpha blocking. Weaker shifts in pee are also apparent.
Fig 4.
EC to EO parameter responses and how they scale with the degree of alpha blocking.
The EC-to-EO parameter response (Eq 8) is calculated from the 100 best samples fits for each of the 82 subjects. The mean (black dot), calculated from Eq 9, and interquartile ranges (error bar) for each subject are plotted against the Jensen-Shannon divergence, DJS, for that subject. In order to quantify how much each parameter response scales with the degree of alpha blocking we performed a linear regression through the sample fits; errors in the fit were estimated by randomly sampling from the distributions estimated from the sample fits. The resulting trend line is shown in blue, with its slope and error reported on each subplot. Several of the parameters (τe, τi, Γe, η) show essentially zero response to alpha blocking. Of the others, only Δpei (lower right subplot) shows a clear trend, increasing monotonically with DJS. pee shows a non-zero parameter response but its trend with DJS is weak and not monotonic. This result suggests that alpha blocking by visual stimulus can largely be attributed to an increase in a tonic afferent signal pei to the inhibitory cortical population, with weak or negligible contributions from the other parameters.
Fig 5.
Forward calculation of the sensitivity of the alpha-rhythm to individual parameters.
Shown are calculations depicting the sensitivity of the alpha-rhythm to each of the nine state-distinct parameters. The initial state (green) is that of the best fit for EO Subject 25. Each parameter is then perturbed by +3% (red) or -3% (blue) of the plausible interval, keeping other parameters constant. We observe that perturbing pei changes the alpha rhythm amplitude most significantly, with a comparatively small change to the peak frequency. The same perturbations applied to pee had a similar type of effect, though reversed and to a smaller extent. Alpha band power is only weakly affected by γe or γi though they both control the frequency. We note in general that perturbations applied to the other parameters have significantly smaller effects than perturbations to pei.