Functional decomposition of the human ERG based on the discrete wavelet transform

Abstract

The morphology of the electroretinogram (ERG) can be altered as a result of normal and pathological processes of the retina. However, given that the ERG is almost solely assessed in terms of its amplitude and timing, defining the shape of the ERG waveform so that subtle, physiologically driven, morphological changes can be systematically and reproducibly detected remains a challenging problem. We examined if the discrete wavelet transform (DWT) could meet this challenge. Normal human photopic ERGs evoked to a broad range of luminance intensities (to yield waveforms of various shapes, amplitudes, and timings) were analyzed using DWT descriptors of the ERG. Luminance-response curves that were generated using the various DWT descriptors revealed distinct (p < 0.05) luminance-dependence patterns, indicating that the stimulus luminance differently modulates the various time-frequency components of the ERG and thus its morphology. The latter represents the first attempt to study the luminance-dependence of ERG descriptors obtained with the DWT. Analyses of ERGs obtained from patients affected with ON or OFF retinal pathway anomalies were also presented. We show here for the first time that distinct time-frequency descriptors can be specifically associated to the function of the ON and OFF cone pathway. Therefore, in this study, the DWT revealed reproducible, physiologically meaningful and diagnostically relevant descriptors of the ERG over a wide range of signal amplitudes and morphologies. The DWT analysis thus represents a valuable addition to the electrophysiologist's armamentarium that will improve the quantification and interpretation of normal and pathological ERG responses.

Comparison of photopic negative response measurements in the time and time–frequency domains

“…As an additional detail to consider, the DWT is not a shift-invariant transform, in that shifting (translating) the complete ERG waveform in time can affect the energy of the presumed PhNR time-frequency bin. However, in contrast to the results reported for analysis of the a- and b-waves [16], preliminary evidence indicated that the effect of shifting the waveform on the PhNR energy (11 Hz, 60 – 120 ms time-frequency bin) was minimal. As such, only non-shifted data (i.e.…”

“…1. The DWT was computed in MATLAB according to standard techniques that are described in detail elsewhere [16]. In brief, DWTs were obtained using the fast wavelet transform algorithm of Mallat [17].…”

“…In brief, DWTs were obtained using the fast wavelet transform algorithm of Mallat [17]. The db2 wavelet, which was also used in previous work [16], was selected as the mother wavelet; although numerous mother wavelet possibilities are available, preliminary evidence indicated that the db2 resulted in less variation in DWT energy among the subjects, as compared to the Haar and db3 wavelets. Eight levels of decomposition were obtained (i.e.…”

“…In this figure, the energy (μV•s) contained in the response is shown for each time-frequency bin. Previous work has shown that the dominant energy of the a- and b-waves in the DWT occurs at relatively short durations (less than approximately 60 ms) and moderate temporal frequencies (greater than 20 Hz) [16]. Although no previous attempt has been made to define the PhNR component of the DWT, our data indicate that the dominant energy is localized to relatively late durations (60 to 120 ms) and low temporal frequencies (near approximately 11 Hz), as expected.…”

“…For example, the discrete wavelet transform (DWT) is a wavelet-based approach to analyze non-stationary signals that has recently been used to extract the a- and b-wave components of the single flash ERG [15,16]. The DWT permits localizing the energy content of the ERG in both time and frequency, and it has been suggested that this approach may be able to identify subtle diagnostic features of the ERG that are less apparent in time domain measures [16]. The DWT may be particularly useful for analysis of the PhNR because it is objective, not based on a single time-point, and is capable of defining slow, small amplitude responses.…”