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Resting state electroretinography: An innovative approach to intrinsic retinal function monitoring

The electroretinogram (ERG) represents the biopotential evoked by the retina in response to a light stimulus. The flash evoked ERG (fERG) is the ERG modality most frequently used clinically to diagnose and monitor retinal disorders. We hereby present a new method to record spontaneous retinal activity, without the use of a flash stimulus, that we named the resting-state ERG (rsERG). The recordings were done in normal subjects under light- and dark-adaptation and with different background light conditions (i.e., variations of wavelength and intensity). Additionally, rsERG recordings were obtained in five patients with retinopathies. The signals were subsequently analyzed in the frequency domain, extracting both periodic (i.e., frequency peaks) and aperiodic (i.e., background trend) components of the signal. The later was further assessed through a multifractal analysis using Wavelet Leaders. Results show that, irrespective of the recording conditions used, the rsERG always includes the same 90 Hz component; a frequency component also present in the fERG response, suggesting a retinally-intrinsic origin. However, in addition, the fERGs also includes a low-frequency component which is absent in the rsERGs, a finding supporting a retinally-induced origin. Comparing rsERGs with fERGs in selected patients with various retinal disorders indicates that the two retinal signals are not always similarly affected (either as a result of underlying retinal pathology or otherwise), suggesting an added value in the assessment of retinal function. Thus, the rsERG could have a similar role in clinical visual electrophysiology as that of the resting-state EEG in neurology namely, to quantify changes in spontaneous activity that result from a given disease processes.

For large time delays , the autocovariance of these increments behave as: From here, the process will have one of 2 possible fluctuation types in the time series, according to the value of (Flandrin, 1992). If is between 0.5 and 1, then the process shows persistence or long-range dependency. If on the other hand is between 0 and 0.5, then the process shows antipersistence or more complexity. Furthermore, the PSD of the increment process will follow approximately a 1/ behavior, while the power spectrum of its original signal ( ) will follow approximately a 1/ +2 , thus about 1/ with = 2 + 1.

Wavelet analysis for scale-invariance
As shown in Annex I, we can define the SI with increments, which are fluctuations at a specific time scale . We can analyze this in terms of discrete wavelet coefficients, defined as: where each time-frequency coefficient ( , ) is obtained by transforming the signal ( ) by a wavelet , which is itself scaled by 2 − and translated by 2 (Daubechies, 1992b, Daubechies, 1992a. By doing so, the increments ( ) are obtained at the scale = 2 , with the wavelet ( ) = ( − 1) − ( ). Thus, with the wavelet coefficients ( , ) of signal ( ) and with the scale = 2 , we can rewrite eq. (1) and (2) as: This generalized the process, giving it a unique and exact exponent, but a range of many such exponents ℎ( ) could be needed to describe the process. Instead of a single value , a function ( ) can be needed to describe the self-similar behavior in the signal. The multifractal formalism uses this function (Muzy et al., 1994), and rewrites the structure functions as ( ) ∼ 2 ( ) . A monofractal process would have single value, thus ( ) = , and we retrieve eq. (5).
This work will consider a multifractal framework, with the quadratic expansion ( ) = + 1/2 2 to generalize the signal's SI. Thus, the goal is to find the most prevalent exponent termed and the dispersion of these exponents around . If = 0, then the signal is monofractal: there is no dispersion, i.e., a single exponent exists. If on the other hand < 0 [ cannot be positive since ( ) needs to be convex (Wendt and Abry, 2007)], then the signal is multifractal and thus increases in complexity.

Wavelet Leaders calculation
The WLBMF Matlab toolbox (Wendt et al., 2007) estimates the set of Hölder exponents by estimating a local power law from a modified discrete wavelet transform (DWT) termed the Wavelet Leaders (Jaffard, 2004, Jaffard et al., 2006, Wendt and Abry, 2007, Wendt et al., 2007. First, the DWT was calculated on the signal at hand as in eq. (3). Second, the DWT was modified to obtain the Wavelet Leader coefficients ( , ). Each coefficient was compared to its neighbors in a specific set: where the set is called a dyadic interval, defined as: Thus, each ( , ) coefficient becomes the maximum value of a set of neighboring coefficients belonging to its dyadic interval and the 2 others adjacent to it, such that: This modification of the DWT regularizes the time-frequency scalogram, with coefficients increasing with the analyzed scale (frequency), thus making it possible to calculate the Hölder exponent ℎ at each time point 0 as a local power law behavior over a set of scales , such that: ( , 0 ) ∼ 2 ℎ( 0 ) (A.10)

Log-Cumulants
To describe the signal using the WLBMF toolbox, as proposed by Wendt et al. (2007), we used what is called log-cumulants (specifically the first 2: 1 and 2 ). In this study, these were referred as the main Hölder exponent (i.e., 1 ), and the dispersion index (i.e., 2 ), that accounts for the multifractality of the process, i.e., the dispersion in Holder exponents. The necessary concavity of the scaling exponents with respect to the statistical orders was used to validate the multifractal model (Wendt and Abry, 2007). Examples of the multifractal spectrums obtained can be found in suppl. Fig. S4. The scales between 2 and 9 (corresponding to a range of frequencies going from 3.5 Hz to 901.5 Hz) were used, as well as moments of order going between -5 and 5, using 49 bootstrap resamples of wavelet leaders. The mother wavelet chosen was Daubechies 4 (with 4 vanishing moments).

Supplementary Figures
Supplementary Figure 1. Representation of an individual's electrode setup. Electrodes were placed in four different locations on a subject's head for this study. For the fERG and rsERG, the active electrodes (DTL in blue) were placed deep in the inferior conjunctival bags of each eye, the reference electrodes (B in purple) were placed on the externa canthi and the ground (A in red) was placed on the forehead. For the EEG setup, the active electrode was on the forehead (A in red), the reference was on the right external canthus (B in purple) and the ground was on the right earlobe (C in green). Fig. 4 and Table 1. Row a shows an example of a normal subject, while each subsequent row (b-f) shows a different patient, as in Fig. 4. Columns show data as follows: (I) mfERG traces; (II) mfERG group tracings for each ring; (III) mfERG 3D plots.

Supplementary Figure 4. Multifractal spectrums of all three types of signals used in the study.
Multifractal spectrums D(h) are shown for individual epochs recorded (i.e., multiple spectrums shown per signal type). EEG and rsERG examples are of all epochs for one subject, given as an example.