Comparison of metrics reveal that they fall into two groups 104

Of the ten features we have examined, it is likely that there is some redundancy in the electrophysiological characteristics they capture. For example, RMSA and LL both reflect information about voltage amplitude, though the two measures are not precisely the same; consider, if the voltage trace for a particular epoch consisted of a shape like a sigmoid with a sharp change in the center, RMSA would be large at almost every point

due to the large absolute distance from zero, while line length would be small due to the small variation between subsequent points. However, in most cases, we expect the two measures to be correlated. To examine this, we consider comparisons between different pairs of measures, and determine how well these different measure correlate (Fig 4).

Figure IV.4. Metric cross-correlation and scatter plot comparisons of metrics in wake and sleep show several features are highly correlated.

A Cross correlation analysis of metrics shows they fall into two distinct groups, within which there is high correlation. RMSA, Line Length, and all frequency band spectral powers are highly positively correlated. Zero crossings are highly positively correlated to local maxima and minima, and highly negatively correlated to weighted network density. Weighted network density and local maxima and minima do not show a strong

correlation. Binary density is not correlated with other features. Zero crossings are

positively correlated with higher frequency bands and less with lower frequency bands, in order. Local maxima and minima show this trend as well, though less strongly. B RMSA and delta frequency power show a strong positive correlation (IS wake in blue, IS sleep in green, control wake in red, control sleep in black). C RMSA and line length show a strong positive correlation, but less so. D Zero crossings have a negative correlation with weighted network density.

Computing the cross correlation between all pairs of metrics reveals that there are broadly two categories into which the measures fall (Fig 4A, and Supplementary

Materials). One category includes root mean squared amplitude, line length, and the frequency domain metrics, in particular delta power, all of which are highly positively

correlated. The second category includes zero crossings, local maxima and minima, and weighted network density. Zero crossings are positively correlated with local maxima and minima and negatively correlated with weighted network density, while local maxima and minima and weighted network density do not appear to be as strongly correlated with each other. Zero crossings also exhibit an inverse correlation with the frequency of the power spectra; the number of zero crossings is positively correlated with higher frequencies, such as in the beta range, and negatively correlated with lower

frequencies, such as in the delta range. This is consistent with the intuition that a higher frequency rhythm will tend to cross zero more than a lower frequency rhythm, and thus result in more zero crossings. We see a similar but less pronounced relationship between local maxima and minima and the frequency of the power spectra. In Figure 5 we further illustrate some of these relationships by plotting the values of one measure against

another for each patient for three example cases. RMSA and delta power possess a strong positive linear relationship in wake and sleep (Fig 4B). RMSA and line length also possess a positive linear relationship, though less so than RMSA and delta power (Fig 4C). Weighted network density and zero crossing have a clear negative linear relationship in wake and sleep (Fig 4D).

We interpret these relationships between the different measures as follows. The category including RMSA, line length, and the frequency domain features all capture aspects of the high amplitude, low frequency voltage traces that occur in hypsarrhythmia, and therefore are linearly correlated with one another. The second category, which includes zero crossings, local maxima and minima, and weighted network density. Both

zero crossing and local maxima and minima may be more strongly associated with aspects of high frequency rhythms, than low frequency rhythms. Therefore, these measures may capture different features of the data that are unrelated to the low

frequency rhythms characteristic of hypsarrhythmia. The interpretation of the weighted network density is more complex. Typically, lower frequency rhythms are associated with increased functional connectivity, while higher frequency rhythms are associated with reduced functional connectivity [167,168]. The observed negative correlation between weighted network density and zero crossing – which increase with frequency - is consistent with this phenomena. We note that the binary density does not strongly correlate with any other metric, and moreover does not strongly distinguish between IS or control groups, is made up of very sparse networks, and also changes its relationship between the two groups between wake and sleep. Since every other metric retains a consistent relationship between IS and control over both wake and sleep, either the binary density is not a useful metric in this instance, or it is measuring a subtle feature that is not obvious in any of the other features.