What is the difference between synchrony and alpha block

Some subjects do not show any reduction in alpha power between EC and EO states e. Subject 34 ; others exhibit partial blocking where the alpha activity in EO state is weaker than that of EC but is still pronounced e. Subject 25 ; while some show total blocking where the alpha activity in the EO spectra completely disappears e. Subject To quantify the degree to which the EEG spectrum changes upon opening of the eyes, we compute the Jensen-Shannon divergence, D JS , between the eyes-closed EC and eyes-open EO normalized experimental spectrum for each subject.

Our approach is to use this individual variability to quantify how much each parameter shifts between EC to EO states and how these shifts scale with the degree of alpha blocking.

To do this quantitatively, we needed to define a measure of alpha blocking strength. Although we explored alternative measures such as the change in relative strength of the alpha band component, we use D JS since it is a more global measure of function change that does not rely on defining a particular frequency band. As we will show, by comparing how parameter differences scale with increasing D JS we are able to establish how much each microscopic parameter changes with the degree of alpha-blocking.

The model used in this paper is the local variant of the mean-field model originally described in Refs [ 22 , 26 ]. As described in our previous study [ 33 ], this model consists of a coupled set of first and second order non-linear ordinary differential equations parameterized by 22 physiologically-motivated parameters see Table 1 as presented below: 1 2 3 4 5 6 where 7 Local equations are linearized around a fixed point and the power spectral density PSD is derived assuming a stochastic driving signal of the excitatory population that represents thalamo-cortical and long range cortico-cortical inputs, assumed to be Gaussian white noise.

The modelled PSD can then be written as a rational function of frequency derived from the transfer function for the linearized system. As was explained in earlier studies [ 33 , 42 ], tonic excitatory signals to the inhibitory p ei and excitatory p ee populations are included as unknown parameters to account for potential constant offsets in extracortical inputs. In this study, we use the identical model but with two changes. The first is to introduce an additional parameter to allow for a non-white background spectrum giving a total of 23 parameters—see Table 1.

Though this adds an extra degree of freedom it is necessary in order to achieve fits to some of the eyes-open spectra. While various approaches have been suggested to account for such a dependence, we have chosen the simplest way to incorporate it into our model by relaxing the white noise assumption and using coloured noise for the driving signal.

This was reproduced here in the eyes-open data when the EEG had a detectable peak in the alpha band; if no peak was observed, the posterior distribution resembled the assumed prior distribution.

In this 2-state fitting problem, the EC spectrum and the EO counterpart from a given subject are treated as a single dataset to be jointly fit by the model. Given that a single spectrum fit has 23 unknown parameters, a naive fit to two spectra would have 46 potentially unknown parameters. To reduce the number of unknowns we implement two types of constraint.

This set is referred to as state-common parameters. The remaining 9 parameters are allowed to vary between conditions and are thus referred to as state-distinct parameters , giving a total of 32 unknown parameters. The list of parameters belonging to both types is presented in Table 1. This joint-fitting approach for the two spectra allows us to couple together the dependency between the EC and EO parameters while at the same time allowing their actual values to be determined by the data.

This helps to identify the important parameter differences driving the change in spectral shape from EC to EO. Our regularization procedure is a variant on the standard procedure employed in high-dimensional inference problems searching for sparse, or parsimonious, solutions [ 44 ].

We use the same fitting scheme to that described in [ 33 ]: Fitted parameters are obtained using particle swarm optimization PSO [ 45 , 46 ] starting from a random set of initial states. Each of the 82 subjects was fit separately as a parallel job on the OzStar supercomputer at Swinburne University of Technology, generating independent fit samples per subject. Computations were performed using a parallel for-loop with 30 workers and 30 CPUs each with 1 GB of memory.

From the resulting sample of optimized parameter sets, the 10 percent with the lowest cost function values are accepted as final estimates a detailed discussion justifying this threshold was given previously [ 33 ]. Fig 2 shows the best model fits to EC and EO spectra from 5 different subjects, ordered vertically by degree of alpha blocking.

Both regularized and unregularized cases exhibit good fits to the data. The similarity between regularized and unregularized cases confirms that the bias caused by regularization is within acceptable limits. 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. 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. Plots for the 5 subjects are ordered vertically by degree of alpha blocking, as in Fig 2.

Distributions are estimated from the best fit parameter sets for each subject. Differences between distributions for EC and EO states are weakly visible for p ee and mostly negligible for other parameters. 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. The distributions are calculated using kernel density estimates from the best of randomly seeded particle swarm optimizations for each subject.

The parameter p ei is the only parameter where the difference between EC and EO distributions increases consistently with the degree of alpha blocking.

Weaker shifts in p ee are also apparent. To better quantify the difference between EC and EO states for each parameter and how it scales with the degree of alpha blocking, we calculate the difference between each EC to EO parameter estimate. In Fig 4 , to examine the association between each parameter response and the degree of alpha blocking, we plot versus for each of the 82 subjects i. Results are shown for all 9 state-distinct parameters. The EC-to-EO parameter response Eq 8 is calculated from the 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, D JS , 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.

This result suggests that alpha blocking by visual stimulus can largely be attributed to an increase in a tonic afferent signal p ei to the inhibitory cortical population, with weak or negligible contributions from the other parameters. We use linearity simply to characterize the trend, not because of any expectation of linearity. Most parameter responses are either zero or show an insignificant trend with the degree of alpha blocking. In the context of our model this implies that excitatory input to the inhibitory population is the dominant factor determining the response of alpha oscillations to a visual stimulus.

By fitting a neural population model to EEG data from 82 individuals, we have demonstrated a clear association between the degree of alpha blocking and a single model parameter, p ei : the strength of a tonic excitatory input to the inhibitory population.

Most of the change between eyes-closed and eyes-open spectra is explained by variation in this external input level. This single-parameter explanation for the difference between eyes-closed and eyes-open spectra contrasts with previous explanations for alpha blocking which invoked changes in multiple parameters [ 31 , 32 ].

As a consistency check, we perform a forward calculation to test how the EEG spectrum is affected by changes in each state-distinct parameter.

In Fig 5 we compare the spectra calculated from the best fit parameter set for a particular subject , to the spectra calculated when the best-fit values for the 9 state-distinct parameters are individually perturbed.

Results show that the magnitude of the alpha rhythm is most sensitive to perturbations of p ei , with increasing p ei resulting in less alpha-band power. This is consistent with the tendency for p ei to increase with alpha blocking Fig 4. Interestingly, decreases in p ee also cause a weaker alpha peak, although the effect is less sensitive than that for p ei.

We note that the relative effects of different parameter perturbations can vary among the different individuals, making it important to compare data across multiple individuals when performing the inverse problem. 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 We observe that perturbing p ei changes the alpha rhythm amplitude most significantly, with a comparatively small change to the peak frequency. The same perturbations applied to p ee had a similar type of effect, though reversed and to a smaller extent. We note in general that perturbations applied to the other parameters have significantly smaller effects than perturbations to p ei.

The sensitivity of the alpha peak amplitude to changes in p ei helps explain why the inverse problem identified p ei as the dominant driver of alpha blocking: regularization is, after all, designed to identify sensitive input parameters.

While this consistency is comforting, it does not rule out the role of other factors. One could, for example, contrive large changes in multiple weakly-sensitive parameters to give the same effect as a small change in a single, sensitive parameter.

These are, in fact, the types of solution that a fit commonly finds without any regularization. Thus, in our effort to tame the unidentifiability problem, we are pushed towards simplicity as a guiding principle for identifying the microscopic drivers of macroscopic observations.

Importantly, we have now shown how both alpha generation and blocking can arise within a single model in a way that is justified by fits to real EEG spectra.

This confirmed the importance of intracortical inhibition in generating alpha activity. Our present work shows how extra-cortical input , particularly to inhibitory neurons, is the modulator of classical alpha blocking, making inhibition central to both the generation and modulation of alpha waves.

We have thus identified the respective loci of physiological control for both the generation and attenuation of alpha oscillations. As mentioned earlier, our model does not specify the origin of extra-cortical inputs, only that these inputs are tonic.

Nevertheless, because alpha-blocking occurs throughout cortex it is reasonable to presume that these inputs are thalamo-cortical rather than long-range cortico-cortical. This is in line with previous models of thalamo-cortical dynamics [ 31 , 32 ]. However, while those models invoked complex feedback between thalamus and cortex to explain alpha generation and blocking, here we claim that opening of the eyes simply alters the tonic level of thalamo-cortical afference.

Thus, rather than being a driver of cortical alpha activity, the thalamus is a modulator of it. An important feature of our results is that we find excitation of inhibitory cortical neurons to be a more sensitive modulator of the alpha rhythm than excitation of excitatory cortical neurons. This increased sensitivity to p ei over p ee arises from the state of the cortex, a cortex whose intracortical inhibition is tuned to generate spontaneous alpha oscillations.

There is also anatomical evidence which indicates that thalamocortical afferents make stronger and more probable contact with inhibitory, rather than excitatory, cortical neurons [ 47 , 48 ]. This means that, not only are inhibitory cortical neurons more sensitive to external inputs, they also have greater connectivity to the thalamus than do their excitatory counterparts. Both these factors indicate that thalamo-cortical excitation of inhibitory neurons is likely the dominant pathway for modulating the alpha rhythm.

They also explain why opening of the eyes, which would reasonably be expected to increase thalamo-cortical input to the occipital cortex and thereby increase both p ei and p ee , still causes a net attenuation of alpha activity. In the future, the approach we have described could be used to determine the parameter response associated with anesthetic induction.

Changes in EEG spectra under general anesthesia, from the loss of consciousness to the period of anaesthetic maintenance, are well characterized [ 49 , 50 ]. Implementing the procedure we have outlined here, may allow us to identify a subset of the parameters driving the changes of brain state, connecting them to specific disruptions in interneuronal communication associated with a particular anesthetic.

This may provide quantitative insight into the mechanisms underlying the loss of consciousness. It is symmetric, non-negative, finite, and bounded [ 53 ]. D JS , is traditionally used to measure the difference between two probability distributions.

D JS thus measures the difference in shape between EC and EO spectra, since power differences among original experimental spectra are irrelevant due to the normalization. We have chosen the Jensen-Shannon divergence based on the postulate that the greater the degree of alpha blocking, the larger the D JS.

This is qualitatively confirmed by examination of the spectra from different subjects Fig 1 and Fig A in S1 Appendix. We are interested in how the parameter response scales with D JS and thus alpha blocking , since this relates changes in the spectra to changes in the model. Distances in spectral space, captured by D JS , thus scale smoothly with distances in parameter space, providing a link between microscopic parameters and macroscopic observables over 82 different subjects. Physiological interpretability depends, of course, on whether individual parameters scale with D JS see Fig 4.

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