Higuchi’s fractal dimension, but not frontal or posterior alpha asymmetry, predicts PID-5 anxiousness more than depressivity

Depression is a major cause of health disability. EEG measures may provide one or more economical biomarkers for the diagnosis of depression. Here we compared frontal alpha asymmetry (FAA), posterior alpha asymmetry (PAA), and Higuchi’s fractal dimension (HFD) for their capacity to predict PID-5 depressivity and for the specificity of these predictions relative to PID-5 anxiousness. University students provided 8 or 10 minutes of resting EEG and PID-5 depressivity and PID-5 anxiousness questionnaire scores. FAA and PAA had no significant correlations with the measures at any electrode pair. There were distinct frontal and posterior factors underlying HFD that correlated significantly with anxiousness and with each other. Posterior HFD also correlated significantly with depressivity, though this was weaker than the correlation with anxiousness. The portion of depressivity variance accounted for by posterior HFD was not unique but shared with anxiousness. Inclusion of anxiety disorder patients into the sample rendered the frontal factor somewhat more predictive than the posterior one but generally strengthened the prior conclusions. Contrary to our predictions, none of our measures specifically predicted depressivity. Previous reports of links with depression may involve confounds with concurrent anxiety. Indeed, HFD may be a better measure of anxiety than depression; and its previous linkage to depression may be due to a confound between the two, given the high incidence of depression in cases of severe anxiety.


Supplementary material
Higuchi's Fractal Dimension -method details Higuchi's Fractal Dimension (Higuchi, 1988) is a method of calculating the Fractal Dimension (FD) of a time series. For EEG signals the HFD will return a value between 1 and 2 with a simple straight line delivering a value of 1 and higher values indicating increased complexity within the signal. A fractal is self-similar at all scales, large or small.
The HFD creates multiple time series by subsampling the signal repeatedly. This creates the original signal at a variety of different scales. The length of the curve for each new time series is then calculated and averaged across the sets. This is repeated for the different scales and plotted on a double logarithmic graph. The fractal dimension is the slope of this graph.
The HFD first generates new time series described as: Where X is the original time series, m indicates the initial time and k is the interval time. For each of the new time series the length of the curve is calculated by: While the length of the curve for , ( ) is the average value over sets of ( ). If ( ) is proportional to − then the curve has the fractal dimension . is the slope of a least mean squares straight line applied to ( ) and plotted on a double logarithmic graph for ranging from 1 to max.
log( ( ))~ log ( 1 ) In the current study we used a max value of 30, this was determined by plotting HFD over a range of max and selecting the value at which the slope plateauxed.

Condition analysis to reduce the number of measures analysed
Experiments with resting EEG in the previous literature have tested people with their eyes open, eyes closed, or alternating between the two states. Eyes open would be expected to maintain a higher level of vigilance than eyes closed; and switching regularly between the two conditions would be expected to maintain a more constant average level of relaxation and also to prevent participants going to sleep. Preventing sleep is important as this would generate quite distinct EEG from the normal relaxed state. The effect of eye conditions was analysed as described below.
One-way, repeated measures ANOVAs were used to separately test the effects on average depressivity variance accounted for by each of AA eye condition, HFD eye condition and frequency band (after choice of eye condition, see below). Correlations with depressivity were converted to signed percent of variance (r 2 * 100, with the sign of r retained), to avoid the skew of the raw correlation scores while keeping the results easy to interpret. The different calculation methods (varying in choice of electrode pair used) for AA provided the source of error variance for the ANOVA.

RM Eye Condition -Alpha Asymmetry
Signed percent variance accounted for by AA and HFD were submitted to a one-way, repeated measures ANOVA separately for depressivity and anxiousness to assess gender (male, female) and eye condition (close, combined, open) effects. Mean values are presented in Table S1 and plotted in Figure S1, while within-subjects contrasts are in Table S2.

RM Eye Condition -HFD
The highest overall HFD percent variances were obtained in the closed eye condition.  the highest values were seen in the high band, but differences between bands were not significant.

RM Bandwidth
Due to the Band x Gender effect seen for depressivity, bands were kept separate for further analysis.

HFD Factor Analysis
There was a high level of intercorrelation of HFD between channels. A principle components analysis initially identified 2 components with eigenvalues exceeding 1, a 3 rd component was included to account for residual noise. The three components (see Fig. 2