OSCILLATORY POTENTIALS OF THE SLOW-SEQUENCE MULTIFOCAL ERG IN PRIMATES EXTRACTED USING THE MATCHING PURSUIT METHOD

Abstract

This study used the Matching Pursuit (MP) method, a time-frequency analysis, to identify and characterize oscillatory potentials (OPs) in the primate electroretinogram (ERG). When the slow-sequence mfERG from the macular region of the retina was matched with Gabor functions, OPs were identified in two distinct bands: a high-frequency band peaking around 150 Hz that contributes to early OPs, and a low-frequency band peaking around 80 Hz that contributes to both early and late OPs. Pharmacological blockade and experimental glaucoma studies showed that the high-frequency OPs depend upon sodium-dependent spiking activity of retinal ganglion cells, whereas the low-frequency OPs depend primarily upon non-spiking activity of amacrine cells, and more distal retinal activity.

Introduction

The electroretinogram (ERG) is a mass potential recorded at the surface of the eye that can be used for functional assessment of the various stages of retinal processing in the laboratory and the clinic. The major components of photopic (i.e., cone-driven) ERG response to a flash stimulus presented on a rod-saturating background originate from different stages of retinal processing in the cone-pathway. In macaque monkeys, primates whose retinas and ERGs are very similar to those of humans, it has been shown that the initial negative a-wave represents the activity of the cone photoreceptors and postsynaptic neurons (hyperpolarizing bipolar cells and third-order neurons) (Bush and Sieving, 1994; Robson, Saszik, Ahmed and Frishman, 2003). The positive b-wave that follows the a-wave originates from responses of depolarizing bipolar cells, and it is shaped by hyperpolarizing bipolar cells and horizontal cells, and, depending upon the stimulus conditions, more proximally located neurons (Sieving, Murayama and Naarendorp, 1994; Viswanathan, Frishman, Robson, Harwerth and Smith, 1999). When a flash of high intensity is presented, a group (3 – 5 or more) of small high-frequency waves, called oscillatory potentials (OPs), are superimposed on the b-wave. Although these potentials are generally thought to arise from amacrine and ganglion cells (e.g., Wachtmeister, 1998), the exact origin and mechanism of generation of the OPs are not completely understood. Because attenuation of the OPs can be an indication of inner retinal diseases, such as diabetic retinopathy and glaucoma, a better understanding of the characteristics and origins of OPs is needed (Algvere and Gjotterberg, 1974; Speros and Price, 1981; Coupland, 1987; Gur, Zeevi, Bielik and Neumann, 1987; Lan, Jian and Liu, 1996; Rangaswamy, Zhou, Harwerth and Frishman, 2006).

The full-field flash ERG provides a response that is summed over the entire retina. However, the cellular composition and function of the primate retina varies with retinal eccentricity. With respect to OPs, previous work using focal stimuli in humans has shown that they are larger in the temporal macula than in the nasal macula (Miyake, Shiroyama, Horiguchi and Ota, 1989; Miyake, 1990). Variations of the photopic ERG across the retina can be assessed more efficiently by recording a multifocal ERG (mfERG) (Sutter, 1991; Sutter and Tran, 1992). Multiple small regions of the retina are stimulated with a pseudorandom stimulus sequence, called an “m-sequence”, and regional responses are obtained. Multifocal stimuli are typically presented on a CRT which has the frame rate of 75 Hz, with a separation of 13.3 ms (1 frame) between each element of the m-sequence (fast-sequence mfERG). However, the waveform of fast-sequence mfERG is different from that of the conventional full-field flash ERG. To obtain a waveform similar to that of the full-field ERG, the m-sequence presentation must be slowed. This can be done by interleaving blank frames between each element of the m-sequence (slow-sequence mfERG; Hood, Seiple, Holopigian and Greenstein, 1997). The slow-sequence mfERG contains OPs resembling those in the full-field flash ERG (Hood et al., 1997), and it has been used to study the regional variations and origins of OPs in the primate retina, as well as in human subjects (Wu and Sutter, 1995; Bearse, Shimada and Sutter, 2000; Rangaswamy, Hood and Frishman, 2003; Rangaswamy et al., 2006).

Extraction of OPs has hitherto been performed mainly by band-pass filtering of the ERG. The International Society for the Clinical Electrophysiology of Vision (ISCEV) standard recommends filtering between 75-100 Hz (low-frequency filter cut-off) and 300 Hz (high-frequency filter cut-off) to extract OPs from the human ERG (Marmor, Holder, Seeliger and Yamamoto, 2004). After extraction, individual OPs in a train of 3 – 5 or more are then analyzed by measuring their implicit times and amplitudes. However, OPs may possess a range of time-frequency characteristics. For example, trains of OPs may not always occur for the same duration, or at the same latency in an ERG waveform, and certain OP frequencies may be more or less dominant. These differences were apparent in previous studies of OPs in the primate slow-sequence mfERG (Rangaswamy et al., 2003, 2006), but in those studies, only specific frequency bands and time intervals in the records were analyzed.

In the present study, a time-frequency analysis method called Matching Pursuit (MP; Mallat and Zhang, 1993) was used to extract the OPs in the slow-sequence mfERG from the macular region of the macaque monkey retina The MP method successively extracts and identifies the components in a waveform by matching them with time-frequency localized waveforms (in this study, the Gabor functions). Using the MP method, OP components in two distinct frequency bands were identified in the slow-sequence mfERG, which, in addition to frequency differences, showed differences in energy, latency and duration of the train of OPs. Using experimental glaucoma to minimize ganglion cell responses, and pharmacological blockade of inner retinal activity, we found evidence that the higher-band OPs (100-200 Hz), peaking around 150 Hz, derive from the sodium-dependent spiking activity of retinal ganglion cells, whereas the lower-band OPs (50-100 Hz), peaking around 80 Hz, have a predominantly non-spiking origin, mainly from amacrine cells, with contributions from more distal retinal neurons.

Methods

Subjects

MfERGs were recorded in 18 macaque monkeys, 3-10 years of age. Recordings were made from 18 normal eyes (one eye from each of 18 monkeys), 5 severely glaucomatous eyes, 4 eyes with intravitreal injections of tetrodotoxin citrate (TTX), 2 eyes with N-methyl-d-aspartic acid (NMDA)+TTX injection, 2 eyes with injection of γ-aminobutyric acid (GABA), and 2 eyes with cis-2, 3 piperidine dicarboxylic acid (PDA) injection. All animals were also subjects in other studies. Some datasets for the normal eyes analyzed in the present study were also used in one or two previous studies, Rangaswamy et al., 2003 and 2006, whereas other normal data sets were from the same animals used in the two previous studies, but were not the same records. The datasets obtained following intravitreal injections of pharmacological agents were used in Rangaswamy et al., 2003, and the datasets from severely glaucomatous eyes were included in Rangaswamy et al., 2006. In the present work, the mfERGs were completely reanalyzed with the Matching Pursuit method to gain new insights about the OPs. When recording the mfERG, animals were anesthetized intramuscularly with ketamine (20-25 mg/kg per hour) and xylazine (0.8-0.9 mg/kg per hour), and were treated with atropine sulfate (0.04 mg/kg, injected subcutaneously). The anesthesia was maintained at a level sufficient to keep the animals from blinking or moving. Pediatric eyelid specula were used to keep the eyes open, and pupils were dilated fully to 8.5 mm in diameter with topical tropicamide (1%) and phenylephrine hydrochloride (2.5%). Heart rate and blood oxygen were monitored with a pulse oximeter (model 44021; Heska Corp., USA) and body temperature maintained between 36.5 and 38°C with a thermostatically controlled blanket (TC1000-Temperature Controller, CWE, USA). All experimental and animal care procedures followed the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research and were approved by the Institutional Animal Care Committee of the University of Houston.

Slow-Sequence MfERG Recording and Grouping

Slow-sequence mfERGs were recorded noninvasively between Dawson-Trick-Litzkow (DTL) (Dawson, Trick and Litzkow, 1979) electrodes placed across the center of the cornea of each eye. Both eyes were covered with corneal contact lenses of appropriate power for the viewing distance, that were filled with methycellulose sodium to keep the corneas and electrodes moist. The reference eye was further covered with a black patch. A needle electrode inserted in the scalp was used as the ground. A modified monocular direct ophthalmoscope (American Optical Company, U.S.A) was used to center the projection of the fovea on the midpoint of the stimulus pattern (Figure 1-A).

Figure 1.

The slow sequence multifocal ERG (mfERG)

1. One frame of the m-sequence presentation of the unscaled stimulus array (103 equal-size hexagons) used in the mfERG recordings of this study. White hexagons represent brief flashes in the respective areas, while black hexagons represent un-stimulated areas.
2. The slow-sequence mfERG trace array from the left eye of a control monkey. The circle outlines the regions that have larger oscillations. The “×” on the left corresponds to the position of the optic nerve head or the blind spot in the visual field. This trace array was published previously in Figure 1 of Rangaswamy et al., 2003.
3. The foveal (F) and chevron (N2, N1, T1 and T2) groups at different eccentricities, analyzed in this study. The “×” corresponds to the blind spot.
   D. Grouped (averaged) mfERG waveforms at different retinal locations (N2, N1, F, T1 and T2) from the left eye of a control monkey.

As shown in Figure 1-A, the stimulus consisted of 103 equal-size hexagons within 17° of the fovea. During the m-sequence presentation, the fovea was centered on the central hexagon (the “×” in Figure 1-A), using a modified ophthalmoscope. Every 200 ms (15 frames; 13.3 ms a frame) each hexagon had a 0.5 probability of staying at an average luminance of 20 cd/m² or flashing with energy of 4.7 cd-s/m². An anti-aliasing filter cutoff at 300 Hz was used, and the mfERG was digitized with a sampling frequency of 1200 Hz. An example of an mfERG trace array is shown in Figure 1-B.

MfERG responses from several hexagons can be grouped (averaged) to analyze the retinal activity in specific regions of the retina. Regions were selected where OPs were most prominent (see encircled region in Figure 1-B). As indicated in Figure 1-C, the “foveal” group consisted of the central 7 hexagons (marked by F), and each of nasal (N1 and N2) and temporal (T1 and T2) “chevron” groups consisted of three hexagons equidistant from the fovea on the horizontal meridian. An example of the grouped responses from those retinal locations is shown in Figure 1-D. In this work, we used the grouped responses at retinal location F (fovea), N1 (nasal) and T1 (temporal). The OPs in the more peripheral chevrons N2 and T2 were not analyzed, because they were much smaller than in the other groups. In Figure 1-D, it can be seen that OPs in F lasted for a longer duration than in the other selected locations, and that the response in T1 contained larger OPs than that in N1. These differences were quantified in the present study.

In order to maximize the length of the mfERG data trace, while avoiding OPs from the next stimulus cycle, a trace length of 212.5 ms post-stimulus (255 samples with sampling frequency of 1200 Hz) was analyzed. This was one sample point (0.83 ms) less than the slowed m-sequence interval due to interleaved blanks (200 ms) plus the length of the interval that contained the stimulus (13.3 ms).

Intravitreal Injections

Intravitreal injections of 40 to 50 μL were made both nasally and temporally in the globe behind the limbus with a sterile 30-gauge needle inserted through the pars plana into the vitreous cavity. Intravitreal concentrations of the pharmacologic agents were estimated by assuming the vitreous volume to be 2.1 ml. TTX (1.2-2.1 μM vitreal concentration) was injected into 4 eyes of 4 monkeys, NMDA (1.4-6.4 mM) was injected into 2 eyes of 2 monkeys, GABA (3.3-3.8 mM) was injected into 2 eyes of 2 monkeys followed by L-2 amino-4-phosphonobutylic acid (L-APB; 2 mM) in one case, and PDA (3.3-3.8 mM) was injected into 2 eyes of 2 monkeys.

Experimental Glaucoma

The methods of inducing experimental glaucoma have been described elsewhere (Smith, Chino, Harwerth, Ridder, Crawford and DeSantis, 1993). Briefly, a monkey was anesthetized, and the intraocular pressure (IOP) in the right eye (left eye remained normal) was elevated by applying blue-green argon laser treatment spots (size 50 μm, power 1.0 W and duration 0.5 sec) to the trabecular meshwork with a slit-lamp delivery system. The spots were placed to produce contiguous tissue blanching.

As part of other studies, static perimetry was performed frequently on monkeys with experimental glaucoma using a Humphrey Visual Field Analyzer (model 630, Humphrey Allergan, USA) running the central 24-2 full-threshold program (Goldmann Size III target, 0.43 degrees in diameter) modified for measuring animal behavior. The perimetric testing methods for monkeys have been described previously (e.g., Harwerth, Smith and DeSantis, 1993). For the present study, mfERGs from 5 animals with severe visual field defects at the time of recording, i.e., Mean Deviations (MD) worse than -10 dB, were included.

Statistical Analysis

For comparison of mfERG responses in different retinal locations, a repeated measures ANOVA test with a post-ANOVA mean comparison was used. To test for significant changes after drug treatment, and differences between normal and glaucomatous eyes, a paired Student t-test was used. The paired t-test also was used to test differences between the signal energy and noise energy.

Time-frequency Structure of the OPs in the MfERG: The Matching Pursuit (MP) Method

The components of a signal in the frequency domain can be identified using Fourier analysis. For example, Figure 2 shows the slow-sequence mfERG waveform for a typical temporal chevron (T1) and its power spectrum, produced by Fourier analysis. The spectrum contains two distinct peaks beyond 50 Hz, one between 50 and 100 Hz, the other between 100 and 200 Hz. Related work has shown that, in some of the same animals used in the present study, the mfERGs in foveal, nasal and temporal regions always have these two main high-frequency components in their power spectra (Rangaswamy et al., 2006). However, the Fourier power spectrum analysis conceals information about the signal that is in the time domain. In the present study, we used the Matching Pursuit method to localize the slow-sequence mfERG in both time and frequency domains, within the same analysis.

Figure 2.

The temporal chevron (T1) mfERG and its power spectrum, from the normal left eye of a monkey. The inset shows the entire power spectrum to illustrate the relative power at low versus high frequencies.

The Matching Pursuit method, first introduced by Mallat and Zhang in 1993, decomposes a signal into a set of weighted elemental waveforms. These waveforms (e.g., sinusoids and Gabor functions), designated as the time-frequency “atoms”, are assumed to occur within a time interval and a frequency band. Since the atoms usually are not orthogonal to each other, they can provide a flexible representation of the signal structure. However, a collection of such atoms forms a redundant function dictionary, which introduced computational inefficiency in the method.

In the present study, we used Gabor atoms to match and quantify the OPs in the slow-sequence mfERG. As illustrated by the example in Figure 3-A, a real Gabor atom is a Gaussian-modulated sinusoidal function. With a Gaussian envelope in the time domain and a Gaussian-shaped magnitude spectrum in the frequency domain, the oscillatory activity of a Gabor atom can be assumed to be duration-limited and band-limited. Theoretically, Gabor atoms provide the optimal time-frequency resolution combination in that they minimize the product of the effective duration and the effective bandwidth of a function (Gabor, 1946). Previous studies have shown that the OPs can be modeled using a Gabor function (Bui, Armitage and Vingrys, 2002).

Figure 3.

Gabor atoms

1. A real Gabor atom (top) and its magnitude spectrum (bottom).
2. The waveforms of real Gabor atoms with variations of the parameters. Each column represents the waveform changes by varying a single parameter. These parameters, from left to right, are frequency f (50 Hz, 100 Hz and 200 Hz, from the top to bottom row), scale s (10 ms, 20 ms and 40 ms) position in time u (30 ms, 50 ms and 70 ms) and phase ϕ (0, 0.5π and π). For convenience of illustration, the atoms are scaled to the same peak amplitude.

A normalized real Gabor atom, g_γ(t), can be described by

$$\begin{array}{l}{g}_{\gamma }\left(t\right)=K\left(\gamma \right)e^{-\pi {\left(\frac{t-u}{s}\right)}^2}\cos \left(2\pi f\left(t-u\right)+\varphi \right),\\ \gamma =\left(f,s,u,\varphi \right)\end{array}$$ (1)

where K(γ) is the coefficient chosen such that $\underset{-\infty }{\overset{+\infty }{\int }}{g}_{\gamma }\left(t\right)g_{\gamma }^{\ast }\left(t\right)=1$ (unity energy).

Four parameters determine a Gabor atom: as illustrated in Figure 3-A, the frequency f (frequency of the sinusoid (Hz), used to quantify the frequency of the OPs in this work), the position in time u (ms, the peak of the Gaussian envelope, which is the center of the atom, used to quantify the central timing of an OP train), the scale s (ms, approximate width of the Gaussian, a representation of duration of the atom, used to quantify the duration of an OP train) and, not illustrated, the phase ϕ (rad, the phase term of the sinusoid). Figure 3-B shows, within a 100 ms window, how the waveform of an atom varies with changes in these parameters.

An estimate of the onset of a Gabor atom (used to quantify the onset of an OP train) can be derived from the position and scale parameters as

$$o=u-\frac{s}{2}.$$ (2)

Because onset is an indirectly derived parameter, it is subject to the variability of both parameters from which it is derived, and it therefore is more variable than either other parameter. Nevertheless, it has been included in the analysis presented in this paper because it most closely resembles commonly used onset latency measures.

The frequency band of a Gabor atom, B_G, can be further quantified by the frequency of the atom, f, ± 2 standard deviations of its Gaussian-shaped magnitude spectrum, as shown below

$$B_G=(f-2\sigma ,f+2\sigma ),$$ (3)

where the standard deviation σ can be derived from the scale parameter, s, through

$$\sigma =\frac{1}{s\sqrt{2\pi }}.$$ (4)

To decompose a signal, the MP method chooses the atom from the function dictionary that is most correlated with the signal. This atom is regarded as a best match in the sense that a weighted version of the atom represents the largest portion of the signal’s energy for any of the atoms in the function dictionary. A residual is obtained by subtracting the weighted atom from the signal, and it is further decomposed by identifying the next “best-match” atom from the dictionary, which maximizes the correlation with the residual. This successive procedure continues until a specific stopping criterion is met (e.g., 99% of the signal’s energy has been represented by the summation of the weighted atoms). Hence, the resultant best-match atoms will represent the time-frequency characteristics of the original signal.

Given a signal S(t), the MP procedure can be described in detail by the following steps:

• (1)Construction of Function Dictionary, D

The function dictionary contains the atoms, g(t). Generally speaking, any arbitrary waveform can be an atom. However, to construct D reasonably and effectively, the g(t)’s should be chosen to relate to the time-frequency characteristics of the signal. In addition, all atoms are normalized to have unity energy. That is $\underset{-\infty }{\overset{+\infty }{\int }}g\left(t\right)g^{\ast }\left(t\right)\mathit{dt}=1$, where “*” stands for complex conjugate.

In the present study, as described above, the function dictionary was constructed using Gabor atoms. Due to the sampling frequency (1200 Hz) and length of the mfERG traces (212.5 ms, 255 samples) to be analyzed, the frequency of the Gabor atoms was restricted to the range between 0 and 600 Hz. A total of 127 atoms, in 4.7 (1200/255) Hz steps, were included in the dictionary. The parameters for the time domain were expressed with an accuracy of 0.83 (1/1200) ms. The same function dictionary was used for all analysis

• (2)Searching for the Best-Match Atom, g_i(t)

The search for the best-match atom is performed iteratively within D. At the i th (i = 1,2,…) iteration, a best-match atom g_i(t) is selected from D, which maximizes the correlation with the signal/residual (i.e., max $\left(\mid \underset{-\infty }{\overset{+\infty }{\int }}{R}^i(t)g^{\ast }(t)\mathit{dt}\mid \right)$). The procedure can be described by

$$g_i(t)=\left\{g(t)\in D\mid \max \left(\mid \underset{-\infty }{\overset{+\infty }{\int }}{R}^i(t)g^{\ast }(t)\mathit{dt}\mid \right)\right\},$$ (5)

where Rⁱ (t) is the residual to be matched at the i th iteration, and R¹ (t) is the signal S(t).

• (3)Residual after Matching

At the i th iteration, the weighted best-match atom, $g_i^W\left(t\right)$, is derived from g_i(t), through

$$g_i^W(t)=\left(\underset{-\infty }{\overset{+\infty }{\int }}{R}^i(t)g_i^{\ast }(t)\mathit{dt}\right)g_i(t),$$ (6)

where $\left(\underset{-\infty }{\overset{+\infty }{\int }}{R}^i(t)g_i^{\ast }(t)\mathit{dt}\right)$ is the weight.

An important parameter, the energy of $g_i^W\left(t\right)$, can be further derived by the square of the weight ${\mid \underset{-\infty }{\overset{+\infty }{\int }}{R}^i(t)g_i^{\ast }(t)\mathit{dt}\mid }^2$, which resembles a portion of the signal energy. In this study, when OPs are matched by $g_i^W\left(t\right)$, the energy of $g_i^W\left(t\right)$ can be used to quantify the OP energy.

The next residual, R^i+l(t), can be obtained by subtracting $g_i^W\left(t\right)$ from the previous residual Rⁱ (t), as shown below

$$R^{i+1}(t)=R^i(t)-g_i^W(t).$$ (7)

• (4)Stopping Criterion

At the i th iteration, the stopping criterion can be defined as no less than a certain amount of the signal energy has been represented by the weighted best-match atoms, i.e.,

$$\text{stop the procedure if}:\hspace{0.17em}\underset{-\infty }{\overset{+\infty }{\int }}{\mid \mathrm{\sum }_{j=1}^i{g}_j^W(t)\mid }^2\mathit{dt}\ge P•\underset{-\infty }{\overset{+\infty }{\int }}{\mid S(t)\mid }^2\mathit{dt},$$

where P is a percentage figure. In the present study of slow-sequence mfERG, P was specified at 99%. This criterion was chosen so that the mfERG components, especially the OPs, could be well extracted.

If the stopping criterion is not met at the i th iteration, the (i + 1) th iteration will start from step (2) with residual Rⁱ⁺¹ (t); otherwise, the procedure stops. At this time, the decomposition of signal S(t) can be described by

$$S(t)=\mathrm{\sum }_{j=1}^i{g}_j^W(t)+R^{i+1}(t),$$ (8)

where the summation of all the weighted best-match atoms, $\mathrm{\sum }_{j=1}^i{g}_j^W(t)$, provides an approximation to S(t) with residual R^i+l (t).

Noise Energy Estimation

Once the MP method extracted and represented OPs with the corresponding Gabor atoms, it was important to identify the noise level for an mfERG response, in the same frequency bands as the atoms. Examination of the data showed that the extracted OPs (atoms) lasted up to 139 ms after the stimulus. Therefore we defined the noise epoch as the post-stimulus generated activity in the time interval of 140 – 212.5 ms. In this way, the noise record was as close as in time to the signal record as possible, instead, for example, of recording noise in a separate trial run with the eye covered. The noise energy could then be estimated by taking the area under the power spectrum curve of the noise epoch that was within the frequency bands of the selected atoms. For this analysis the noise epoch was padded so it contained the same number of points fir analysis as the signal record contained.

Results

High-frequency and Low-frequency OPs Extracted by the MP Method

The mfERG from a temporal chevron group (T1) shown in Figure 2 provides a typical example for illustrating the decomposition using the MP method. The decomposition of the mfERG trace in Figure 2 completed 12 iterations before representation of ≥ 99% of the energy (the stopping criterion) was achieved. To reach the same stopping criterion, 11 to 21 iterations (median of 16 iterations) were completed for the 18 normal eyes (3 retinal locations) in this study. Figure 4 demonstrates the residuals and the best-match Gabor atoms from the first 4 iterations, for the decomposition of the mfERG in Figure 2.

Figure 4.

First four MP decompositions of the temporal chevron (T1) mfERG shown in Figure 2. The black curves represent the mfERG and residuals for each decomposition, while the gray curves represent the best-match atoms.

Table 1 shows the parameters for the 12 atoms; the second to last column gives the percent energy of the signal represented by each atom; the last column gives the cumulative total percent energy of the signal represented by all the previous atoms. The table shows that the first 4 atoms represented most of the energy of the signal (92.7%).

Table 1.

Parameters of the best-match Gabor atoms given by the MP decomposition of the signal in Figure 2.

Atom No.	Frequency - f (Hz)	Scale - s (ms)	Position - u (ms)	Phase - ϕ (rad)	Signal Energy (percent)	Cumulative Energy (percent)
1	23.5	53.3	31.7	6.2	49.6	49.6
2	4.7	212.2	115.0	4.3	29.7	79.3
3	70.6	26.7	34.2	2.0	8.6	87.9
4	150.6	25.8	31.7	1.5	4.8	92.7
5	18.8	52.1	69.2	3.2	3.1	95.8
6	4.7	25.0	0.8	4.4	1.1	96.9
7	42.4	103.2	159.2	0.1	0.4	97.3
8	188.2	27.2	40.8	5.4	0.4	97.7
9	103.5	24.6	30.0	2.3	0.4	98.1
10	42.4	53.2	25.0	5.8	0.4	98.5
11	211.8	13.3	18.3	1.2	0.3	98.8
12	131.7	14.1	57.5	4.3	0.2	99.0

In this example, the first Gabor atom with a frequency parameter of f = 23.5 Hz accounted for most of the energy of the a-wave and b-wave (Figure 4, top panel). Although a mismatch occurred after 60 ms, it only affected the very low frequency band, and not the extraction of OPs in subsequent decompositions. The second atom was a drift at 4.7 Hz. Due to the sampling frequency (1200 Hz) and the length of the mfERG trace analyzed, frequencies below 4.7 Hz were not resolvable, so the drift could have represented atoms at any frequency below 4.7 Hz. At least one “drift” atom was present in all records, regardless of experimental manipulation. In the following two decompositions, atom 3 and 4 were found in the frequency range of the traditional OPs. One occurred in a lower frequency band (with frequency parameter of f = 70.6 Hz), while the other was in a higher frequency band (with frequency parameter of f = 150.6 Hz). Overlapping with the b-wave in the time domain, they were the main components corresponding to the two major spectrum peaks beyond 50 Hz seen in Figure 2. Although atoms 8, 9, 11 and 12 also represented high-frequency oscillations, they carry minimal energy (<0.5 percent, individually, and 1.3 percent, totally, of the signal energy).

Figure 5-A (upper plot) illustrates the first four atoms whose parameters are listed in Table 1, superimposed on the original temporal chevron mfERG. The plot directly below shows the power spectra of the four atoms. Figure 5-B, upper plot, illustrates the reconstructed waveform of the mfERG, achieved by summing all 12 atoms in Table 1, and the power spectrum of the reconstructed waveform is shown in the lower plot. In both the time and the frequency domain, the reconstructed mfERG was quite similar to the original one. This supports the appropriateness of Gabor atoms for producing an adequate approximation to the mfERG, and their utility in modeling and analyzing the OPs.

Figure 5.

Power spectrum of responses in the temporal chevron (T1) mfERG shown in Figure 2.

1. The waveforms (upper plot) and power spectra (lower plot) of the temporal chevron mfERG and the first four best-match Gabor atoms (shown individually in Figure 4).
2. The waveform (upper plot) and power spectrum (lower plot) of the temporal chevron mfERG (solid lines). Reconstruction (dashed lines) by summing of the 12 atoms listed in Table 1 (99% energy representation).

In the mfERG traces (N1, F and T1) of all normal eyes studied, two main atoms similar to atoms 3 & 4 in this example were consistently found, representing most of the signal energy within 50-300 Hz band, and overlapping in time, to some extent, with the b-wave. Other low-energy atoms in the 50-300 Hz band were inconsistent in either the frequency or the time domain, across retinal locations and monkeys. Therefore, our analysis of the OPs was focused on the two main atoms. According to the frequency band in which they resided, they were designated as the high-frequency OPs and the low-frequency OPs. For the individual chevron locations, the high-frequency and low-frequency OPs always occurred in separable frequency bands. However, across chevron locations and monkeys these frequency bands showed a small amount of overlap, as will be quantified in Figure 9.

Figure 9.

Frequency bands of the high-frequency and low-frequency OPs

1. Frequency band estimates from the high-frequency and low-frequency OPs’ power spectra. The frequency band is defined as the peak frequency plus or minus 2 standard deviations of the Gaussian spectrum.
2. The frequency bands of the high-frequency (black bar) and low-frequency (gray bar) OPs in the retinal location N1 (squares), F (diamonds) and T1 (triangles), averaged from 18 normal eyes of 18 monkeys. Solid and open symbols represent the average frequencies of the high-frequency and low-frequency OPs, respectively.

Although in the example of Figure 4 the MP method extracted the high-frequency and low-frequency OPs at the 4th and 3rd decomposition (4th and 3rd atom), respectively, they were not always represented by these atoms. The lower frequency components (e.g., a-wave, b-wave and those below 50 Hz) could be represented by several Gabor atoms, before the high-frequency and low-frequency OPs were extracted. For the mfERGs of the control subjects (18 monkey eyes, 3 retinal locations), the high-frequency OPs were extracted as the 2nd to the 7th atom (the median was the 4th atom), while the low-frequency OPs were extracted as the 2nd to the 9th atom (the median was the 5th atom). These two OPs together represented, on average, 81% of the energy of the mfERGs beyond 50 Hz (individual cases varied from 70% to 98%). Results from 3 foveal (F) mfERG recordings were excluded because the combined energy of the high-frequency and low-frequency OPs fell below 70%, which was thought to be a reasonable energy criterion for the main OPs.

Using the Wigner-Ville transform, we calculated the time-frequency energy distribution of the sum of atom 1 (accounts for a-wave and b-wave), atom 3 (low-frequency OPs) and atom 4 (high-frequency OPs) (as in Table 1 for the typical example in Figure 4). This distribution is illustrated in Figure 6. The Wigner-Ville transform of a signal, S(t), can be represented by a function of time, t, and frequency, f, as

Figure 6.

The time-frequency energy distribution map for the sum of the 1st, 3rd and 4th best-match atoms extracted from the temporal chevron mfERG illustrated in Figure 2, 4 & 5. The X-Y coordinates represent the time-frequency plane. The Z axis represents energy. Each hump in the map represents the energy distribution of the corresponding best-match atom in the time-frequency domain.

$$W(t,f)=\underset{-\infty }{\overset{+\infty }{\int }}S(t+\frac{\tau }{2})S^{\ast }(t-\frac{\tau }{2})e^{-j2\pi f\tau }d\tau ,$$ (9)

where * stands for complex conjugate (Mallat and Zhang, 1993). Figure 6 nicely illustrates the time-frequency characteristics of the high-frequency and low-frequency OPs. Specifically as noted above, they were cleanly separated in the frequency domain, and they overlapped in the time domain with the b-wave.

Reproducibility of the High-frequency and Low-frequency OPs Extracted by the MP Method

To assess the reproducibility of the OP extraction with the MP method, mfERGs were recorded from one normal monkey eye four times in the same session. The high-frequency and low-frequency OPs were then extracted using the MP method. The mean and standard deviation of the frequency f, energy, position u, duration (represented by the scale parameter s, see Equation (1)) and phase of the two OPs are shown in Figure 7. Except for the phase, the standard deviation of each of these parameter was within 10% of the mean value (as high as 7.2%; as low as 0%), confirming the reproducibility of the method. Because the phase parameter had a much higher standard deviation, it was deemed to be unstable and was excluded from the following results. The instability of the phase parameter precluded analysis of potentially important additive (and subtractive) interactions between the high- and low-frequency OPs at different retinal locations.

Figure 7.

Reproducibility of the parameters (frequency, energy, position in time, duration and phase) of the high-frequency and low-frequency OPs obtained with the MP decomposition in the retinal locations N1, F and T1 from the normal left eye of one monkey. Gray and striped bars represent the values of the high-frequency and low-frequency OPs’ parameters, respectively. The error bars are standard deviations. In plot B, the horizontal line inside the bar represents the estimated noise level at each location.

Naso-temporal Asymmetries and Comparison of High-frequency and Low-frequency OPs in Normal Eyes

Average frequency, energy, position, duration and onset of the high-frequency and low-frequency OPs in retinal locations N1, F and T1 obtained for 18 normal eyes are illustrated in Figure 8. These parameters were compared across the 3 retinal locations using a repeated measures ANOVA. If a significant difference was found (P<0.05), a post-ANOVA mean comparison was then used to further identify the locations that were different. The resulting P values are listed in Table 2. In addition, the parameters of the high-frequency and low-frequency OPs in each location were compared, using a Student t-test (results are shown in Figure 8, but not in the table).

Figure 8.

Parameters of the high-frequency and low-frequency OPs in the retinal locations N1, F and T1 from 18 normal eyes of 18 monkeys. Gray and striped bars represent the values of the high-frequency and low-frequency OP parameters, respectively. The error bars represent standard errors. “*” represents significant statistical difference for a given location between the parameters of the high-frequency and low-frequency OPs with P<0.05, while “**” represents the same, but with P<0.01. In plot B, the horizontal line inside the bar represents the estimated noise level at each location.

Table 2.

The frequency (A), energy (B), position (C) duration (D) and onset (E) of the high-frequency (High) and low-frequency (Low) OPs compared between retinal locations (post-ANOVA mean comparison). The column and row represent the corresponding locations compared. “*” represents significant statistical difference with P<0.05, while “**” represents the same, but with P<0.01. If the difference between two locations was significant, the location with larger values is shown in parenthesis.

A. Frequency
	F		T1
N1	High	0.04 * (N1)	High	0.001 ** (N1)
	Low	0.44	Low	0.23
F	\		High	0.08
			Low	0.12
B. Energy
	F		T1
N1	High	0.10	High	0.03 * (T1)
	Low	0.004 ** (F)	Low	0.70
F	\		High	0.35
			Low	0.002** (F)
C. Position
	F		T1
N1	High	0.001 ** (F)	High	0.004 ** (T1)
	Low	0.046 * (F)	Low	0.41
F	\		High	0.50
			Low	0.01 ** (F)
D. Duration
	F		T1
N1	High	0.54	High	0.10
	Low	0.19	Low	0.22
F	\		High	0.34
			Low	0.08
E. Onset
	F		T1
N1	High	0.006 ** (F)	High	0.14
	Low	0.001 ** (F)	Low	0.11
F	\		High	0.11
			Low	0.0002 ** (F)

The high-frequency OPs evidenced significant naso-temporal assymetries in energy, frequency and position. The energy of the high-frequency OPs was higher in the temporal location T1 than in the nasal location N1 (P<0.05). This agrees with previous reports that OPs are larger in the temporal than nasal macula (Miyake, 1990; Wu and Sutter, 1995; Bearse et al., 2000; Rangaswamy et al., 2003, 2006). The high-frequency OPs had a higher frequency peak in N1 than in T1 (P<0.01) and F (P<0.05), and the position of these OPs was more delayed in locations T1 and F than in N1 (P<0.01). Duration did not differ among locations. The onset showed no significant difference between N1 and T1, but it was more delayed in F than in N1 (P<0.01). In contrast to the high-frequency OPs, the low-frequency OPs showed no significant differences in energy between location N1 and T1; but had higher energy in location F than in the other two locations (P<0.01). There were no frequency differences among locations. The low-frequency OPs’ position (P<0.05) and onset (P<0.01) were more delayed in F than in the other two locations; as found for the high-frequency OPs, duration did not differ among locations, although the difference was nearly significant between T1 and F (P<0.06).

A comparison between the two OPs (see Figure 8) revealed that in location T1, the high-frequency OPs had significantly higher energy than the low frequency OPs (P<0.01). The high-frequency OPs’ position was earlier in the record than the low-frequency OPs position in all three retinal locations (for N1 and F, P<0.01; for T1, p<0.05), and so was the onset in F (P<0.01). The high-frequency OPs also had a shorter duration than the low-frequency OPs in location N1 (P<0.05) and T1 (P<0.01).

Separation of Fast and Slow OPs in the Frequency Domain

An important question was whether the frequency bands that were used to define the high-frequency and low-frequency OPs for analysis and comparison were entirely separable in all subjects and in all locations. To answer this question, the frequency bands were compared. In Figure 9-A, σ_High and σ_Low (obtained from Equation (4)) designate one standard deviation of the Gaussian spectra for the high-frequency and the low-frequency OPs, respectively, f_High and f_Low represent their frequency parameters. Thus, the frequency bands of the high-frequency and low-frequency OPs, B_High and B_Low, were quantified as

$$\begin{array}{ccc}{B}_{\mathit{High}}& =& (f_{\mathit{High}}-2{\sigma }_{\mathit{High}},f_{\mathit{HIgh}}+2{\sigma }_{\mathit{HIgh}})\\ B_{\mathit{Low}}& =& (f_{\mathit{Low}}-2{\sigma }_{\mathit{Low}},f_{\mathit{Low}}+2{\sigma }_{\mathit{Low}})\end{array}.$$ (10)

The B_HIgh and B_Low were obtained for the all 18 normal eyes, in location N1, F and T1. The average frequencies of the high-frequency ( $\overline{f_{\mathit{High}}}$, solid symbols) and low-frequency OPs ( $\overline{f_{\mathit{Low}}}$, open symbols) and the corresponding average frequency bands ( $\overline{B_{\mathit{High}}}$ and $\overline{B_{\mathit{Low}}}$) in the three locations are shown in Figure 9-B. Neither $\overline{B_{\mathit{High}}}$ nor $\overline{B_{\mathit{Low}}}$ showed significant differences among the three regions (P>0.05). The $\overline{B_{\mathit{High}}}$ and $\overline{B_{\mathit{Low}}}$ were separable at locations N1 and T1, while they overlapped slightly at location F (106.2-123.8 Hz).

To further investigate the separation of the high-frequency and low-frequency OPs in the frequency domain, we defined the frequency separation ratio, r_f, by

$$r_f=\frac{\mid f_{\mathit{High}}-f_{\mathit{Low}}\mid }{{\sigma }_{\mathit{High}}+{\sigma }_{\mathit{Low}}}.$$ (11)

The larger the value of r_f, the more separated the two OPs were in the frequency domain.

r_f was calculated at location F, N1 and T1 for the same 18 normal eyes. The mean ratio, $\overline{r_f}$, ± standard deviation, ${\sigma }_{r_f}$, at each retinal location are listed in Table 3. Although no significant difference in r_f was found among the 3 locations, as illustrated in Figure 9 and noted above, the frequency bands of the high-frequency and low-frequency OPs tended to be more separated in the nasal (N1) and temporal (T1) retina than in the fovea (F).

Table 3.

The mean, $\overline{r_f}$, ± standard deviation, ${\sigma }_{r_f}$, of the frequency separation ratio, r_f, calculated for the three retinal locations (N1, F and T1) of 18 normal eyes of 18 monkeys

	N1	F	T1
$\overline{r_f}\pm {\sigma }_{r_f}$	2.4 ± 1.1	1.9 ± 1.0	2.7 ± 1.1

Effect of Experimental Glaucoma on Fast and Slow OPs

In order to assess the retinal ganglion cell contribution to the OPs, the mfERG was recorded from 5 monkeys with monocular experimental glaucoma that had progressed sufficiently to cause severe visual sensitivity losses (mean deviation (MD) worse than -10 dB), and hence severe ganglion cell loss (Frishman, Shen, Du, Robson, Harwerth, Smith, Carter-Dawson and Crawford, 1996; Hare, Ton, Ruiz, Feldmann, Wijono and Woldemussie, 2001; Harwerth, Carter-Dawson, Smith, Barnes, Holt and Crawford, 2004). The frequency, energy, position, duration and onset of the high-frequency and low-frequency OPs were derived for the normal eye (left eye) and glaucomatous eye (right eye) in each animal. The noise energy in the frequency bands of the OPs was also estimated. The results for the eyes with experimental glaucoma are shown in Figure 10.

Figure 10.

Parameters of the high-frequency (left column) and low-frequency (right column) OPs in retinal locations N1, F and T1 from the normal fellow eyes (left eyes) and glaucomatous eyes (right eyes) of five monkeys. The high-frequency and low-frequency OPs’ parameters in normal eyes (gray and striped bars) and glaucomatous eyes (open bars) are illustrated. The error bars represent standard errors. “*” represents significant statistical difference of OP parameters between normal and glaucomatous eyes with P<0.05, while “**” represents the same, but with P<0.01. In plot C and D, the horizontal line inside the bar represents the estimated noise level at each location.

Glaucoma significantly reduced the energy of the high-frequency OPs (P<0.05; see Figure 10 and Table 4), but not the low-frequency OPs in all three retinal locations. However, the high-frequency OPs’ energy in all locations remained above noise levels (P<0.05). The frequency of the high-frequency OPs was significantly decreased in N1 and F (P<0.05), while the position changed slightly, but not significantly, in all retinal locations. As a result, the naso-temporal asymmetries present in control eyes and in the normal sample described above in frequency and position were removed in glaucomatous eyes. The glaucomatous eyes also lacked the naso-temporal difference in high-frequency OPs’ energy found in the 18 normal subjects. However, the energy asymmetry was not significant in the five glaucoma control eyes, perhaps due to variability in the small sample. Parameters of the low-frequency OPs were not affected by glaucoma, except that the frequency was reduced in location F (P<0.05).

Table 4.

Energy reduction (%) of the high-frequency (High) and low-frequency (Low) OPs due to experimental glaucoma or pharmacological agents (TTX, NMDA+TTX, GABA, or PDA). The percent reduction was calculated after subtracting the corresponding noise energy from that of the high-frequency and low-frequency OPs. For TTX injections (N=4) and severe experimental glaucoma (N=5), the mean percent energy reduction is listed. For NMDA+TTX, GABA and PDA injections, the energy reductions in the right eyes of two monkeys are shown. Negative numbers represent energy increases. A reduction of 100% indicates that the energy fell below the noise level. “*” represents statistically significant energy reduction with P<0.05, while “**” represents the same, but for P<0.01.

	N1 (%)		F (%)		T1 (%)
Glaucoma	High	65 **	High	68 *	High	70 *
	Low	-15	Low	35	Low	28
TTX	High	56 *	High	56 *	High	74 **
	Low	-140	Low	11	Low	10
NMDA+TTX	High	92 89	High	84 88	High	93 60
	Low	31 77	Low	52 65	Low	67 46
GABA	High	73 80	High	95 95	High	92 85
	Low	40 42	Low	59 63	Low	72 62
PDA	High	95 97	High	97 96	High	95 99
	Low	100 94	Low	96 98	Low	100 100

Effect of Pharmacological Inner Retina Blockade by TTX on the High-frequency and Low-frequency OPs

TTX was injected to block sodium-dependent action potentials, known to be generated by inner retinal cells, ganglion cells, some amacrine cells and interplexiform cells (Bloomfield, 1996; Stafford and Dacey, 1997). The MP analysis was performed on recordings before and after TTX injection in one eye each of four monkeys. The results are shown in Figure 11.

Figure 11.

Parameters of the high-frequency (left column) and low-frequency (right column) OPs in retinal location N1, F and T1 from one eye each of four monkeys before and after TTX injection. The high-frequency and low-frequency OPs’ parameters in normal eyes (gray and striped bars) and after TTX injection (open bars) are shown. The error bars represent standard errors. “*” represents significant statistical difference of OPs’ parameters before and after TTX injection with P<0.05, while “**” represents the same, but with P<0.01. In plot C and D, the horizontal line inside the bar represents the estimated noise level at each location.

The effects of TTX injection were similar to those of experimental glaucoma, suggesting that effects seen in both experiments were mainly on spiking ganglion cells. TTX significantly reduced the high-frequency OPs’ energy in all three retinal locations (P<0.05; see Figure 11 and Table 4), but again the energy remained above the noise level (P<0.05). The frequency as well as the position of the high-frequency OPs changed slightly, but not significantly, in all locations. As a result, though, the naso-temporal asymmetries present in recordings before TTX (as in the 18 normal eyes) in energy, frequency and position were removed by TTX injection. The duration and onset of the high-frequency OPs was unaffected. Although the low-frequency OPs were not significantly affected in any location, TTX eliminated some differences between high-frequency and low-frequency OPs, which were significant in TTX control recordings and in the 18 normal eyes. These were the position difference in location F, and, the onset difference in location F and T1.

Effect of Pharmacological Inner Retina Blockade by NMDA+TTX on High-frequency and Low-frequency OPs

Injection of NMDA (together with TTX) was used to remove both spiking and non-spiking inner retinal activity in the normal right eyes of 2 monkeys (e.g., see Robson and Frishman, 1995 for effects of NMDA). The energies of the high-frequency and low-frequency OPs were compared before and after NMDA+TTX injection. The results are shown for individual animals in Figure 12 and in Table 4. After NMDA+TTX injection, the high-frequency OPs’ energy fell close to the noise level. In contrast, the low-frequency OPs’ energy, while reduced by as much as 77%, stayed well above the noise level. These results suggest that the all of the high-frequency OPs and part of the low-frequency OPs originate from inner retina. No consistent changes were found in other parameters, therefore, they are not plotted here.

Figure 12.

The high-frequency and low-frequency OPs’ energy in location N1, F and T1 from one eye each of two monkeys before and after NMDA+TTX injection. Energy of OPs in the eye of a monkey before (gray and striped bars) and after NMDA+TTX injection (open bars) is illustrated. At each retinal location, the first two bars from the left (indicated by “1”) represent the results of monkey 1, while the other two bars (indicated by “2”) represent the same, but for monkey 2. The horizontal line inside the bar represents the noise level in each case.

Effect of Pharmacological Inner Retina Blockade by GABA on High-frequency and Low-frequency OPs

Intravitreal injection of GABA also eliminates inner retinal activity (Naarendorp and Sieving, 1991). The energies of the high-frequency and low-frequency OPs were compared before and after GABA injection in two monkeys. The results shown for individual animals in Figure 13 and in Table 4 are similar to those after NMDA+TTX. After GABA injection, the high-frequency OPs’ energy fell close to the noise level. In contrast, the low-frequency OPs’ energy was still well above the noise level. The results also indicate that the high-frequency OPs and part of the low-frequency OPs originate from inner retina.

Figure 13.

The high-frequency and low-frequency OPs’ energy in location N1, F and T1 from one eye each of two monkeys before and after GABA injection. Energy of OPs in the eye of a monkey before (gray and striped bars) and after GABA injection (open bars) is illustrated. At each retinal location, the first two bars from the left (indicated by “1”) represent the results of monkey 1, while the other two bars (indicated by “2”) represent the same, but for monkey 2. The horizontal line inside the bar represents the noise level in each case.

Effect of Pharmacological Inner Retina Blockade by PDA on High-frequency and Low-frequency OPs

PDA is known to block the light responses of hyperpolarizing second-order neurons as well as from inner retinal cells (e.g., Bush and Sieving, 1994). The energies of the high-frequency and low-frequency OPs, before and after PDA injection, are shown for one eye each of two monkeys in Figure 14 and in Table 4. After PDA injection, energies of both OPs fell close to the noise level. PDA was the only drug used in this study that blocks light-evoked activity of second-order neurons in addition to inner retinal activity, raising the possibility that the low-frequency OPs may have contributions from more distal retinal elements than amacrine or ganglion cells.

Figure 14.

The high-frequency and low-frequency OPs’ energy in locations N1, F and T1 from one eye each of of two monkeys before and after PDA injection. Energy of OPs in the eye of a monkey before (gray and striped bars) and after PDA injection (open bars) is illustrated. At each retinal location, the first two bars from the left (indicated by “1”) represent the results of monkey 1, while the other two bars (indicated by “2”) represent the same, but for monkey 2. The horizontal line placed inside the bar represents the noise level, except for the low-frequency OPs after PDA injection at location T1 in monkey 1, and locations N1 and T1 in monkey 2 (marked by “#” in the plot). In those three cases, the energy was below the noise level and horizontal lines were above the bars.

Discussion

In this study of the slow-sequence mfERG of primate retina, the time-frequency characteristics of the OPs were analyzed in detail using the MP method. OPs in two main frequency bands, which we called, the high-frequency OPs and the low-frequency OPs, were identified in all normal eyes. In agreement with previous work in human subjects (Miyake, 1990), and previous work in the macaque using the same animals, and datasets in some cases (Rangaswamy et al., 2003, 2006) documenting larger OPs in temporal macula than in nasal macula, the energy of the high-frequency OPs was significantly higher in the temporal macula. Using the MP method, we also found that both OPs’ positions were delayed in foveal regions relative to more peripheral regions, in agreement with fovea vs periphery latency differences noted for the b-wave in a previous study (Rangaswamy et al., 2003). In addition, the high-frequency OPs’ position was delayed in temporal retina, relative to nasal retina, consistent with these OPs representing the optic nerve head component initially described in human retinas (Sutter and Bearse, 1999), which will be discussed more thoroughly in a later section.

Through the use of an experimental glaucoma model and intravitreally injected pharmacological agents in a primate model for the human ERG, evidence was found to support the idea that the high-frequency OPs originate primarily from spiking ganglion cells of inner retina (Rangaswamy et al., 2006), and that the low-frequency OPs depend on both inner retinal activity, and retinal activity in elements distal to amacrine and ganglion cells.

OP Extraction Techniques

Several optimized band-pass filtering techniques have been developed to extract OPs more accurately than simple band-pass filtering. For example, Bui et al. (2002) used signal conditioning to extract the OPs. Specifically, contamination of OPs from the sharp trough of the a-wave was eliminated with a temporal window, and contamination by the b-wave was removed by fitting its rising edge with a straight line, and subtracting the fitted line from the ERG. Band-pass filtering in a fixed frequency range was applied to extract the OPs, which were then modeled by a single Gabor atom. This conditioning approach would be difficult to apply to the small signals of the mfERG (see Figure 2). Furthermore, a predefined filter band would have missed the two types of OPs found in this study.

Another approach, in which the OPs were modeled as sinusoids modulated by a skewed exponential function, was employed by Derr, Meyer, Haupt and Brigell (2002). The ERG was first windowed to pick out the portion of the waveform containing the OPs. To remove the discontinuity caused by windowing, the waveform was extended by padding both sides with a low-pass filtered, inverted version of the original waveform, and the OPs were extracted using a band-pass filter in a fixed frequency range. Again, the fixed band would not separate the high-frequency and low frequency OPs, and extracting OPs using a priori defined window, as in the study of Derr et al. (2002), would have led to inaccuracies in the present study.

Compared to previous methods, the MP method brought a more flexible OP extraction, by decomposing the ERG waveforms into time-frequency localized components in the form of Gabor atoms. Although the real OPs might not have fitted exactly the shape of Gabor atoms used in this study (and that of Bui et al., 2002), considering the accuracy of the matching (see Figure 4), the Gabor atoms, nevertheless, provided representations of the major OP components adequate to allow comparisons between normal eyes and eyes with glaucoma, and before and after injection of pharmacologic agents. Furthermore, the lower frequency components of the mfERG (e.g., a-wave and b-wave) were also effectively represented by Gabor atoms. This can be seen in the reconstruction in Figure 5-B, where the summation of the 12 atoms provide a close approximation to the original mfERG waveform. In addition, in the two eyes with PDA injections, where the high-frequency OPs and low-frequency OPs (and many other contributions) were no longer present, the first three atoms obtained from the MP method, which represented the a-wave, b-wave (~ 23 Hz) and the drift (4.7 Hz or lower frequencies), accounted for more than 92% of the energy of the mfERG, and the 99% stopping criterion was met in 5 to 6 iterations. It is interesting to note that the drift nominally at 4.7 Hz was present in all control eyes, and was not removed by any pharmacological agent used in this study, or by severe glaucoma. In addition, in experiments, where the eyes were both covered so that light-stimulated responses were eliminated, the recorded “responses” to slow-sequence multifocal stimulation, after decomposition, also contained this drift. This indicates that the “drift” could have been unrelated to the light-stimulated activity, and simply a DC component to be expected in such decompositions. However, if any retinal signal also contributed to the drift in light-stimulated responses, the contribution would likely have been photoreceptor-dependent, given its persistence when either On or Off pathways were blocked.

Retinal Origins of OPs

Severe glaucoma, known to selectively kill retinal ganglion cells in the primate model, partially eliminated the high-frequency OPs and affected the responses in location T1 more than those in N1 (Frishman et al., 1996; Harwerth et al., 2004; Rangaswamy et al., 2006). TTX had similar effects, suggesting that the sodium-dependent spiking activity of inner retinal neurons contribute strongly to these OPs. Previous studies have attributed naso-temporal asymmetries in oscillatory behavior in the mfERG to an optic nerve head potential created by spikes in ganglion cell axons in the optic nerve head (Sutter and Bearse, 1999; Bearse et al., 2000; Hood, Bearse, Sutter, Viswanathan and Frishman, 2001; Fortune, Bearse, Cioffi and Johnson, 2002; Fortune, Wang, Bui, Cull, Dong and Cioffi, 2004; Rangaswamy et al., 2003, 2006). To explain briefly, ganglion cell responses occur not only locally at the cell body, but also in the axon as the spikes propagate to the optic nerve head. Due to the introduction of high-resistance myelination (insulation) of the axons as the optic nerve fibers leave the orbit of the eye, a potential at the nerve head is thought to be generated that can be recorded at the cornea due to the radial orientation of the nerve head fibers (Sutter and Bearse, 1999). The different latencies of the spiking response to a local stimulus, due to distance of the local ganglion cell from the optic nerve head, e.g., farther in temporal than in nasal retina, and the resulting addition or cancellation of the local and the remotely generated signals, lead to naso-temporal asymmetries in responses, as were observed in the present and previous studies. While the present results are consistent with spiking activity of ganglion cells contributing to the high-frequency OPs, they also must have originated partially from amacrine cells, as they were completely eliminated by either NMDA or GABA injections to block inner retina activity.

In contrast to the high-frequency OPs, the low-frequency OPs were hardly affected by experimental glaucoma or TTX, suggesting that these OPs possess non-sodium-spiking origins in cells distal to ganglion cells. The low-frequency OPs were only partially removed by NMDA+TTX or GABA, and were fully eliminated only by PDA. The additional effect of PDA was probably on second order hyperpolarizing neurons (OFF bipolar or horizontal cells). We say this because in preliminary experiments, injection with APB (~2 mM) (following GABA) to remove ON bipolar cell contributions, did not reduce the low-frequency OPs more than GABA alone.

Rangaswamy et al., in 2003, analyzed the same datasets after pharmacological blockade that were used for the present analysis. They also reported a loss of naso-temporal asymmetries in OPs after injection of TTX, but smaller reductions of OPs by NMDA+TTX and GABA than observed for the high-frequency OPs of the present study. In that study, done before the two frequency bands were appreciated, OPs had been extracted by band-pass filtering from 90-300 Hz, and the root-mean-square (RMS) of the filtered OPs was calculated only between 10 and 60 ms post-stimulus. Based on the present results, that frequency band and time interval should have captured most of the high-frequency OPs, and part of the low-frequency OPs. In that study, it also was observed that blockade of the ON pathway with APB injected alone eliminated almost all of the OPs measured in the band starting at 90 Hz. Thus the PDA-sensitive contribution in the present study must have made contributions to low-frequency OPs in a band lower than 90 Hz.,

Rangaswamy et al., (2006) studied the same severely glaucomatous eyes for which mfERGs were analyzed in the present study, but instead of MP analysis, they simply separated high and low frequency bands in a fixed time window overlapping the b-wave between 10 and 60 ms post-stimulus. Most findings were consistent between the two studies, however, Rangaswamy et al. found significant reduction of the low-frequency OPs’ RMS at retinal location F (P<0.05), that was not observed in the present study. In the present analysis, the low-frequency OPs’ energy did not show significant changes in any location. This difference in the results may have been due to the more flexible time window for low-frequency OPs in the present study, which sometimes extended to 139 msec. Because of the MP analysis, for eyes with severe glaucoma we also observed significant reductions in the frequency of the high-frequency OPs in location N1 and F, and in the frequency of the low-frequency OPs in location F, that could not have been observed when only band-pass filtering was applied. The changes in frequency were unique to the glaucomatous eyes, and did not occur after injection of TTX, or any of the other pharmacological agents used in the study.

Comparison of Traditionally Extracted OP Peaks to the Fast and Slow OPs

In numerous studies in humans and animals, OPs have been identified as individual waves or peaks, numbered as such, e.g., OP1 - OP5, and amplitudes and implicit times of each peak analyzed. In the present study, instead of measuring the implicit time of each peak, we used the time position parameter (u in Equation (1)) to represent the overall latency of the OPs. This parameter was the center time, corresponding to the peak of the Gaussian envelope defining the duration of the high-frequency or low-frequency OPs (see Figure 3-A). To investigate how the duration of the OPs relates to the timing of the individual peaks, we extracted the high-frequency and low-frequency OPs from the summed slow-sequence mfERGs, and compared them in the time domain to the individual OP peaks in the mfERG waveform. Figure 15 shows this comparison for the normal (left) and severely glaucomatous (right) eye of one of the monkeys used in the study. The train of OPs was extracted using standard band-pass filtering between 50 and 300 Hz.

Figure 15.

The high-frequency and low-frequency OPs extracted from the summed slow-sequence mfERG of the normal (left) and severely glaucomatous (right) eye of a monkey, as well as the OPs extracted by band-pass filtering between 50 – 300 Hz. OP1 – OP7 are OP peaks identified in the band-pass filtered OPs of the normal eye. Their amplitudes and timings are indicated by the asterisks in the severe glaucoma plot. Gray dashed line indicates the timing of each OP peak in the filtered OP.

In control eyes (n=9 analyzed), as typified in Figure 15 (left column), we could identify up to 7 individual peaks (OP1 – OP7) in the band-pass filtered waveform. The high-frequency OPs corresponded mainly to the early OPs, OP 1-3, with a small contribution to OP4. The low-frequency OPs corresponded to the odd OPs: OPs 1, 3, 5, as well as later OPs (i.e., OP6 and OP7). The correspondence of the high-frequency OPs with early OPs, and the low-frequency OPs with both early and late OPs is consistent with the later position and longer duration of the low-frequency OPs reported in the Results.

Severe glaucoma illustrated in Figure 15 (right column; and TTX, not illustrated here) reduced the high-frequency OPs, while leaving the low-frequency OPs more intact. In the time domain, the amplitudes of all OPs past OP1 were reduced. The high-frequency OPs corresponding to OP1 – OP3 or 4 became very small. In contrast, the low-frequency OPs corresponding to OP1 and 3 were still present, or slightly enhanced (in the case of TTX injections). Hence, as reported in the Results, the energy of the low-frequency OPs did not change significantly, and the position difference between the high-frequency and low-frequency OPs, present in the control eye, was diminished. The timing of each OP peak appeared to be unaffected by glaucoma or TTX.

The finding in the present study that the high-frequency, TTX-sensitive, OPs were predominately the early OPs differs from findings for the full-field ERG of the Dutch-belted rabbit. Following intravitreal injection of TTX in the rabbit, Dong, Agey and Hare (2004) found that the late OPs (OP5 and OP6) rather than the early ones were most reduced. However, the two studies differed in a number of ways. In addition to species differences, and the use of multifocal vs full field stimulation, adaptation conditions also were different in the two studies. Whereas the present study was done under photopic conditions, the rabbit study was done under conditions where both rod and cone signals were contributing to the response. Although the specific effects of TTX on the OPs differed in the two studies, the studies agree on the important point that there are multiple neuronal mechanisms involved in generating the OPs.

It should be noted that although the studies of eyes with experimental glaucoma and with pharmacological agents injected showed that the high-frequency and low-frequency OPs have different cellular origins, neither OP component appeared to derive from a single generator. Resolution of the issue of OP generation remains for future studies.

Existence of the Fast and Slow OPs in the Full-field Flash ERG

An important question is whether the high-frequency and low-frequency OPs only existed in responses to the slow-sequence mfERG stimulus, where the responses were generated by a stimulus that had only a 50% probability of flashing for each presentation, and only in the macula which was the region that we analyzed. To answer this question, we analyzed the full-field flash ERG from monkey eyes, using the MP method. Figure 16 shows an example of a flash ERG recorded from a normal eye. With a flash energy of 3.2 cd-s/m², the stimulus condition was similar to that used to record mfERGs (brief flash with energy of 4.7 cd-s/m²). The MP decomposition provided two main OP frequency bands, comparable to the high-frequency and low-frequency OPs found in the mfERG. Similar bands were found in all analyzed monkey flash ERGs (n=7), recorded under the same stimulus condition. Thus, for the stimulus conditions used in the present study, the high-frequency and low-frequency OPs were the main OPs in both mfERGs and flash ERGs. The presence of OPs at similar frequencies in the flash ERG also eliminates any possibility that the low-frequency OPs were being driven by the frame rate of the mfERG presentation (75 Hz). Because we did not alter stimulus energy in this study, we cannot comment on stability of the kinetics of the OPs over a range of stimulus conditions (e.g., Hancock and Kraft, 2004).

Figure 16.

The full-field flash ERG from the normal eye of a monkey, and the high-frequency and low-frequency OPs extracted by the MP method.

Another important question is whether the high-frequency and low-frequency OPs exist in the human mfERG. Although not analyzed here, Rangaswamy et al. (2006), showed comparable high and low frequency bands in summed human mfERGs. Therefore, the results of this analysis on a primate model, whose retina is similar to humans, should be relevant to studies in humans.

Optimization of the MP Method – the Supervised MP (SMP) Method

In the present study, the utility of the MP method in extracting and quantifying OPs in the slow-sequence mfERG of monkeys was demonstrated. However, at each iteration, the MP method that we used required a complete search in the redundant function dictionary for the best-match atom (see Equation (5)), which is very demanding computationally. The time to search for a best-match atom, at each iteration, was about three minutes on average (using a personal computer with an Intel Pentium III CPU at 800 MHz), which would be inefficient for the analysis of a large amount of data even with a faster microprocessor.

To address this issue, we have begun to develop a better-optimized MP method, called the Supervised Matching Pursuit (SMP) method. The method reduces the search time dramatically to about one second by using a reduced function dictionary. A “training” dataset of mfERGs, decomposed using the traditional MP method, guides the selection of atoms for the reduced function dictionary. The SMP method will be presented in detail elsewhere, and even greater improvements in efficiency may be found in the future.