Extracting the ON and OFF Contributions to the Full-Field Photopic Flash Electroretinogram Using Summed Growth Curves

Abstract

Under cone-mediated (photopic) conditions, an “instantaneous” flash of light, including both stimulus onset and offset, will simultaneously activate both “ON” and “OFF” bipolar cells, which either depolarize (ON) or hyperpolarize (OFF) in response and, respectively, produce positive-going and negative-going deflections in the electroretinogram (ERG). The stimulus-response (SR) relationship of the photopic ON response demonstrates logistic growth, like that manifested in the rod-mediated (scotopic) b-wave, which is driven by a single class of depolarizing bipolar cell. However, the photopic b-wave SR function is importantly shaped by OFF responses, leading to a “photopic hill.” Furthermore, both on and off stimuli elicit activity in both ON and OFF bipolar cells. This has made it difficult to produce meaningful parameters for ready interpretation of the photopic b-wave SR relationship. Therefore, we evaluated whether the sum of sigmoidal SR functions, as descriptors of the depolarizing and hyperpolarizing components of the photopic flash ERG, could be used to elucidate and quantitate the mechanisms that produce the photopic hill. We used a novel fitting routine to optimize a sum of simple sigmoidal curves to SR data in five groups of subjects: Healthy adult, 10-week-old infant, congenital stationary night blindness (CSNB), X-linked juvenile retinoschisis (XJR), and preterm-born, both without and with a history of retinopathy of prematurity (ROP). Differences in ON and OFF amplitude, sensitivity, and implicit time among the groups were then compared using parameters extracted from these fits. We found that our modeling procedure enabled plausible derivations of ON and OFF pathway contributions to the ERG, and that the parameters produced appeared to have physiological relevance. In adult subjects, the ON and OFF amplitudes were similar in magnitude with respectively longer and shorter implicit times. Infant, CSNB, and XJR subjects showed significant ON pathway deficits. History of preterm-birth, without or with a diagnosis of ROP, did not much affect cone responses.

1. Introduction

At intermediate stimulus intensities, the relationship of log stimulus intensity to electrical potential in the postreceptor retina is linear. Since, on the one hand, the log of darkness is undefined, and, on the other hand, ion pumps can only operate over a limited range before their exchange capacity is saturated, this relationship asymptotically flattens at both the bottom and top and is thus well-described by a logistic (i.e., sigmoidal) function. This empirical relationship, documented in the “S-potentials” of the “colour units” of the isolated tench retina by Naka and Rushton (1966), has been extended with remarkable efficacy to the stimulus-response (SR) function of the full-field, rod-mediated, dark-adapted (scotopic), electroretinographic (ERG) b-wave in human (Peachey et al., 1989), compelling evidence that, under certain conditions, the b-wave mainly reflects the activity of a single class of bipolar cell that receives input almost exclusively from rods (Aleman et al., 2001; Pugh et al., 1998; Robson and Frishman, 1995; Stockton and Slaughter, 1989; Wurziger et al., 2001).

However, the rod-driven bipolar cell is only one of a family of bipolar cells, the rest of which receive input from cones. In the light, some depolarize (ON) and others hyperpolarize (OFF), mediated by the release of glutamate by photoreceptors (Massey, 1990). That is, light abates the release of glutamate, which respectively disinhibits ON and inhibits OFF bipolar cells due to differences in the type of synaptic contact each makes (Nelson and Kolb, 1983; Raviola and Gilula, 1975). Therefore, at high intensities, an “instantaneous” (i.e., sufficiently brief) flash of light, which includes both stimulus onset and offset, will simultaneously elicit both ON and OFF retinal responses that respectively “push” and “pull” the amplitude of the ERG (Sieving et al., 1994). Presumably, the SR relationship of the cone-mediated (photopic) ON responses demonstrates logistic growth like that manifested in the scotopic b-wave. But, unlike the scotopic b-wave, OFF responses importantly shape the b-wave SR function, leading to the “photopic hill” in the trough-to-peak amplitude of the photopic SR relationship, as described by Wali and Leguire (1992). We presume that the OFF responses also follow logistic growth. For clarity, we hereinafter adopt the convention of lower-case “on” and “off” when referencing the massed SR relationship elicited by each stimulus condition and capital “ON” and “OFF” when referencing responses in the respective, canonical depolarizing and hyperpolarizing bipolar cells.

Attempts to produce meaningful parameters for ready interpretation of the photopic b-wave SR relationship have proved problematic (Rufiange et al., 2002). This is due, in part, to the fact that both on and off stimuli elicit activity in both ON and OFF bipolar cells (presumably mediated by activity in horizontal and other cells; Sieving et al., 1994). One approach adopted an analysis of “function descriptors” and produced important observations (Rufiange et al., 2003). For one, the amplitude of the photopic b-wave likely results from the interaction of ON and OFF bipolar cells that respectively increment and decrement the “trough-to-peak” ERG amplitude. For another, the ON response is probably more sensitive than the OFF response, under these conditions (i.e., increments in stimulus energy increase b-wave amplitude at lower intensities but decrease b-wave amplitude at higher intensities). However, the model could not accommodate pathological changes observed in conditions such as congenital stationary night blindness (CSNB). Another approach, by Hamilton et al. (2007), designed to account for both the sigmoidal shape of the scotopic b-wave SR function and the waxing-and-waning pattern of the SR function of the photopic ERG response to a light offset (the d-wave), resulted in the construction of a model of the photopic SR function as the sum of a sigmoidal curve and a Gaussian curve; this model was better able to account for the effects of CSNB.

The International Society for Clinical Electrophysiology of Vision (ISCEV) recently released step-by-step instructions for the recording and fitting of the “Hamilton model” (McCulloch et al., 2019). However, any formulation, such as this one, that depends on the trough-to-peak amplitude of the photopic flash response has limited physiological relevance, since neither the trough nor the peak of the response should be considered a measure of any particular cellular activity. For example, if the OFF response is larger than the ON response, the measured amplitude should be negative, but this is impossible in a trough-to-peak measurement. Furthermore, ISCEV recommends an extended protocol (see their Appendix 1) for reliable curve fitting (see their Appendix 2) that includes a large number of flash stimuli (≥9) up to a minimum of 2.5 log cd·s·m⁻² (see their Table 1) and, in patients with abnormal retinal function, very strong flashes of 3 log cd·s·m⁻² or more (Hamilton et al., 2007); these stimuli can be uncomfortable and may require long interstimulus durations to normalize. The model also does not provide comparable measures of ON and OFF function, since the sigmoid and the Gaussian do not share parameters.

Table 1.

Median and 5th to 95th prediction limits for key parameters of each group.

Group	Amplitude (μV)	ON Sensitivity (cd−1·s−1·m2)	Implicit Time (ms)	Amplitude (μV)	OFF Sensitivity (cd−1·s−1·m2)	Implicit Time (ms)
Adult	73.3 (25.6–121)	1.48 (0.299–4.37)	31.3 (28.7–35.3)	63.4 (28.2–106)	0.165 (0.0539–1.13)	18.9 (14.8–26.4)
Infant	51.7 (22.9–88.5)	0.467 (0.138–1.79)	37.4 (35.2–44.7)	61.9 (38.7–97.7)	0.116 (0.0316–0.635)	17.0 (14.6–24.8)
CSNB2	6.72 (4.56–6.91)	0.552 (0.407–0.961)	34.8 (30.7–41.8)	26.0 (21.3–40.3)	0.0849 (0.0770–0.130)	21.5 (19.8–26.0)
CSNB1	34.4 (25.5–44.0)	1.14 (0.880–1.69)	35.2 (32.4–41.8)	81.3 (56.2–101)	0.121 (0.0846–0.320)	24.2 (21.8–28.4)
XJR	26.1 (8.65–55.3)	0.560 (0.292–5.22)	39.8 (33.5–45.9)	45.4 (19.6–62.2)	0.108 (0.0386–0.570)	19.5 (15.5–32.6)
NROP	96.4 (46.5–218)	0.724 (0.272–3.11)	32.6 (30.3–37.8)	67.1 (39.7–334)	0.101 (0.0375–1.37)	24.0 (14.0–45.6)
UROP	74.7 (21.5–132)	0.965 (0.351–27.3)	32.3 (29.7–40.0)	60.1 (41.5–132)	0.167 (0.0731–0.813)	18.1 (13.9–32.8)
TROP	69.9 (24.8–103)	0.833 (0.660–23.4)	34.9 (31.2–37.2)	49.4 (23.8–71.5)	0.122 (0.0474–0.159)	17.8 (13.8–21.0)

Therefore, we evaluated the principle that the sum of respective, sigmoidal SR functions could describe the photopic ERG at arbitrary times after a flash and consequently be used to extract putative ON and OFF contributions to the ERG. Concluding that this process can, indeed, produce approximations of the ON and OFF contributions to the ERG, we developed a model of the photopic full-field flash ERG that produces parameters aligned with physiological principles.

2. Material and methods

2.1. Subjects

We studied extant photopic ERG responses obtained in healthy Adult (n=32), Infant (~10±1 weeks; n=29), CSNB, X-linked juvenile retinoschisis (XJR; n=9) and preterm-born subjects. We stratified the CSNB subjects’ data into “incomplete” (CSNB2; n=3) and “complete” (CSNB1; n=4) diagnoses, of which all were genetically secured: CACNA1F for all CSNB2s; NYX×2, GPR179×1, and TRPM1×1 for the CSNB1s. The preterm subjects were born between 21- and 32-weeks postmenstrual age, and their weights at birth were 450–2,275 g. We stratified these subjects by the maximum severity of acute ROP recorded in their medical charts in the course of serial indirect ophthalmoscopic examinations in the neonatal intensive care unit, including whether or not they received treatment: subjects in whom ROP was never detected (NROP; n=10), those in whom ROP was detected but was untreated because it was so mild that it did not meet criteria for intervention (UROP; n=21), and those in whom ROP was treated (TROP; n=4). In the UROP group, the maximum severity was stage 1 or 2 in zone II or III and, by clinical criteria, their ROP spontaneously resolved. For all members of the TROP group, the maximally acute ROP observed was Stage 3 and, accordingly, all received laser ablation of the peripheral retina (Hardy et al., 2004). Further details about our preterm population can be found elsewhere (Fulton et al., 2008; Fulton et al., 2009; Hansen et al., 2017). All subjects, other than those in the Infant group, were adolescent or adult at the time of testing.

The procedures by which the ERGs were recorded are thoroughly documented elsewhere (Fulton and Hansen, 2006; Fulton et al., 2008; Fulton et al., 2001; Hansen and Fulton, 2005). To summarize, we induced cycloplegia and mydriases using 1% cyclopentolate hydrochloride and recorded responses using a Burian-Allen bipolar electrode grounded on the skin over the ipsilateral mastoid. Long wavelength or white flashes and white adapting backgrounds were delivered into a Ganzfeld and responses were differentially amplified and digitized. We expressed the intensity of the stimuli, I, as the logarithm of flash power (cd·m⁻²), measured using an ILT1700 Photometer (International Light Technologies, Peabody, MA), integrated over the brief (<0.003 s) flash duration. To avoid implying that the resulting stimulus energies (log cd·s·m⁻²) were emitted by a point source (McCulloch et al., 2015), we hereinafter identify I as “flash strength.”

Adult subjects and parents of infants and children consented to have their ERG records obtained and analyzed; assent was obtained from older children. All studies conformed to the tenets of the Declaration of Helsinki and were approved by the Boston Children's Hospital Committee on Clinical Investigation.

2.2. Modeling the ON and OFF Components of the Photopic ERG

We made the assumptions that, 1) in the respective ON and OFF pathways, the relationship of flash strength to bipolar cell response can be characterized by a simple saturating function with parameters that estimate the saturating amplitude and sensitivity of the SR relationship, and 2) that our first assumption holds true at any proximal time after a flash. Thus, we began with the common sigmoidal function

$$f(I)=a(1-{\mathrm{e}}^{-b\cdot {10}^I})$$ eq. 1

where f(I) is the amplitude (μV) of the response to a flash strength of I and a and b are the saturating amplitude (μV) and sensitivity (m²·cd⁻¹·s⁻¹) of the response, respectively. Then we assumed that ON and OFF components algebraically sum in the ERG, and that ON responses are reflected in cornea-positive and OFF responses in cornea-negative potentials (Sieving et al., 1994), such that we might anticipate their interaction would be well-described by the relationship

$$f_{\text{ON}}(I)=a_{\text{ON}}(1-{\mathrm{e}}^{-b_{\text{ON}}\cdot {10}^I})$$ eq. 2a

$$f_{\text{OFF}}(I)=-a_{\text{OFF}}(1-{\mathrm{e}}^{-b_{\text{OFF}}\cdot {10}^I})$$ eq. 2b

$$f_{\text{sum}}(I)=f_{\text{ON}}(I)+f_{\text{OFF}}(I)=a_{\text{ON}}(1-{\mathrm{e}}^{-b_{\text{ON}}\cdot {10}^I})-a_{\text{OFF}}(1-{\mathrm{e}}^{-b_{\text{OFF}}\cdot {10}^I})$$ eq. 2c

where a_ON and a_OFF denote the distinct saturating amplitudes and b_ON and b_OFF denote the distinct sensitivities of the respective ON and OFF responses.

As illustrated in the left panel of Figure 1, prior to applying our model, we passed each response through a forward-reverse (i.e., zero-phase) 5th-order 60–235 Hz Butterworth band-stop filter (filtfilt; MATLAB, The MathWorks, Natick, MA) to remove cone activation and the oscillatory potentials from every response (Akula et al., 2007; Liu et al., 2006) and, putatively, restrict the analysis to those contributions from cone bipolar cells. We then “extracted” the ON and OFF components of the photopic flash ERG to produce a model response at selected times and arbitrary intensities, as follows: First, we sampled the amplitude, relative to baseline, of the (filtered) ERG response to every flash at 2-ms intervals from 0–50 ms following stimulus presentation to produce 26 points per wave. Then, at each of the 26 timepoints, we optimized the parameters of eq. 2c to the SR relationship using a least-squares minimization routine (lsqcurvefit; MATLAB). The resulting fits could then be plotted as a function of I and time-after-the-flash, t, in eqs. 2a, 2b, and 2c, to produce models of the ON component, the OFF component, and the intact ERG, respectively.

Fig. 1.

Illustration of how ERGs were filtered and sampled. At the left, a representative intact, Adult ERG (green trace) and the result of passing it through a forward-reverse, 5th-order, 60–235 Hz Butterworth band-stop filter (black trace) are shown. Before fitting eqs. 2a-3c, we sampled each filtered response at 2-ms intervals for a total of 26 points (red marks) per wave. At the right, the amplitude of the filtered waves (black circles) at one sampled timepoint (X on filtered wave) is plotted for each flash strength; values of eq. 3a (dashed blue line) and eq. 3b (dashed brown line) are plotted using the parameter values of eq. 3c (green line), optimized using eq. 4 as the error term. Note that, although the measured amplitude at this timepoint is never negative, the model nonetheless predicts a prominent OFF potential (eq. 3b) at higher flash strengths.

As shown in the results, the fits closely described the data, but it became immediately clear that, under certain not-too-rare circumstances, the values of a could be implausibly large (compensated by quite-small values of b). In these cases, although the fits looked appropriate over the range of flash strengths studied, it was clear by extending I past the studied range that these values were not physiological. Therefore, we adopted a solution that penalized values of a as they became too large and that consequently conducted the fits to solutions wherein the amplitude values were reasonable, as follows: First, we reformulated eqs. 2a-c to include a parameter capturing the total magnitude of the response (ON – OFF) with a single value, c (μV),

$$f_{\text{ON}}(I)=a(1-{\mathrm{e}}^{-b_{\text{ON}}\cdot {10}^I})c$$ eq. 3a

$$f_{\text{OFF}}(I)=-(1-a)(1-{\mathrm{e}}^{-b_{\text{OFF}}\cdot {10}^I})c$$ eq. 3b

$$f_{\text{sum}}(I)=f_{\text{ON}}(I)+f_{\text{OFF}}(I)=\left(a(1-{\mathrm{e}}^{-b_{\text{ON}}\cdot {10}^I})-(1-a)(1-{\mathrm{e}}^{-b_{\text{OFF}}\cdot {10}^I})\right)c$$ eq. 3c

where a is a value between zero and one such that a and (1 − a) represent the respective proportions of the total amplitude, c, in the ON and the OFF pathways. Next, we modified the error term for the fit so that c, itself, was included in whatever proportion (γ) was desired. That is, the error to be minimized was calculated as a weighted average of the root mean square (RMS) error (i.e., standard deviation of the fit to the data) and c itself,

$$error=\text{RMS}(1-\gamma )+c\cdot \gamma$$ eq. 4

Finally, as shown in the right panel of Figure 1, we refit the data using eq. 3c as the model and eq. 4 as the error term (fminsearch; MATLAB), taking a · c and (1 − a)c as the respective saturating amplitudes in the ON and OFF responses. We found that even very small values of γ worked well, settling on 0.01 (that is, the final fit was based 99% on the RMS and 1% on the value of c). Therefore, for each family of responses, as a function of time up to 50 ms after the flash, we obtained subjectively reasonable amplitude and sensitivity parameters for the ON and OFF pathways. However, to be most convenient, having single values for amplitude and sensitivity for these pathways is desirable.

2.3. Parameterizing the ON and OFF Components of the Photopic ERG

To achieve single values for amplitude and sensitivity in the ON and OFF responses, we inspected the product of this first round of modeling, which we detail in the Results, below. The modeling, particularly of the Adult group, revealed that the first 50 ms of responses in the putative ON and OFF pathways were reasonable likenesses of skewed distributions with similar (though opposite polarity) amplitudes and respectively longer and shorter implicit times. The Infant, CSNB2, CSNB1, and XJR, and subjects (all of whom lacked prominent photopic hills) showed clear ON pathway deficits. Therefore, we developed a second model of the photopic ERG to provide convenient amplitude and sensitivity values for the respective ON and OFF pathways; this model is diagrammed in Figure 2.

Fig. 2.

Illustration of how peak (eq. 5) and growth (eqs. 3a-c) functions are combined to produce eq. 7. At the left, peak functions with shape and scale consistent with the typical time-course of ON (dashed blue line) and OFF (dashed brown line) activity following a flash, are shown; their amplitudes are normalized but the OFF response has a markedly shorter implicit time than the ON response. In the middle panel, typical growth, as a function of flash strength, in ON and OFF ERG components are plotted; though opposite in polarity, with ON responses reaching a positive plateau and OFF responses reaching a negative plateau, the saturating amplitudes are similar, but the ON response approaches its asymptotic value at lower flash strengths than the OFF. At the right, the ON and OFF peak functions are scaled by the amplitudes obtained from the growth functions (Xs on sigmoids) at a flash strength near the peak of the photopic hill; the sum of these two products (green line) approximates a filtered ERG.

To fit the responses without any predetermined ideas about the distribution of the data, we adopted the Weibull (1951) function (because it includes a shape descriptor),

$$W_2(t)=\frac{k{\left(\frac{t}{\lambda }\right)}^{k-1}{\mathrm{e}}^{-{\left(\frac{t}{\lambda }\right)}^k}}{\lambda }\text{for}t>0,$$ eq. 5

where t is the time (ms) after the flash, k is the shape descriptor, and λ is a scale parameter. The mode (ms) of eq. 5 is given by λ[(k − 1)/k]^1/k and, by dividing W₂(t) by W₂(mode), a normalized distribution is obtained (such distributions, representative of ON and OFF activity, are presented in the left panel of Figure 2); this, in turn, can be multiplied by a scalar, α (μV), to produce a three-parameter function of specified amplitude, W₃(t):

$$W_3(t)=\left(\frac{W_2(t)}{W_2\left(\lambda {\left(\frac{k-1}{k}\right)}^{\frac{1}{k}}\right)}\right)\alpha =\frac{{\left(\frac{t}{\lambda }\right)}^{k-1}\cdot {\mathrm{e}}^{-{\left(\frac{t}{\lambda }\right)}^k}\cdot \alpha }{{\left({\left(\frac{k-1}{k}\right)}^{\frac{1}{k}}\right)}^{k-1}\cdot {\mathrm{e}}^{-{\left({\left(\frac{k-1}{k}\right)}^{\frac{1}{k}}\right)}^k}}$$ eq. 6

Finally (as illustrated in the middle and right panels of Figure 2), to combine eq. 6 with eqs. 3a-c, we took the sum of two three-parameter Weibull functions, W₃(t) (eq. 6), substituting f_ON(I) (eq. 3a) and f_OFF(I) (eq. 3b) for the respective values of α, to arrive at our final model,

$$m(I,t)=\left(\frac{{\left(\frac{t}{{\lambda }_{\text{ON}}}\right)}^{k_{\text{ON}}-1}{e}^{-{\left(\frac{t}{{\lambda }_{\text{ON}}}\right)}^{k_{\text{ON}}}}a\left(1-e^{-b_{\text{ON}}{10}^{\mathrm{I}}}\right)}{{\left({\left(\frac{k_{\text{ON}}-1}{k_{\text{ON}}}\right)}^{\frac{1}{k_{\text{ON}}}}\right)}^{k_{\text{ON}}-1}{e}^{-{\left({\left(\frac{k_{\text{ON}}-1}{k_{\text{ON}}}\right)}^{\frac{1}{k_{\text{ON}}}}\right)}^{k_{\text{ON}}}}}-\frac{{\left(\frac{t}{{\lambda }_{\text{OFF}}}\right)}^{k_{\text{OFF}}-1}{e}^{-{\left(\frac{t}{{\lambda }_{\text{OFF}}}\right)}^{k_{\text{OFF}}}}(1-a)\left(1-e^{-b_{\text{OFF}}{10}^{\mathrm{I}}}\right)}{{\left({\left(\frac{k_{\text{OFF}}-1}{k_{\text{OFF}}}\right)}^{\frac{1}{k_{\text{OFF}}}}\right)}^{k_{\text{OFF}}-1}{e}^{-{\left({\left(\frac{k_{\text{OFF}}-1}{k_{\text{OFF}}}\right)}^{\frac{1}{k_{\text{OFF}}}}\right)}^{k_{\text{OFF}}}}}\right)c$$ eq. 7

We fit eq. 7, with k_ON > 1 and k_OFF > 1, to the (I, t, μV) data cubes for each subject’s ERG using eq. 4, again with γ = 0.01, as the error term, and obtained amplitude (ON: a · c; OFF: (1 − a)c), sensitivity (ON: b_ON; OFF: b_OFF), and implicit time (ON: λ_ON[(k_ON − 1)/k_ON]^1/k_ON; OFF: λ_OFF[(k_OFF − 1)/k_OFF]^1/k_OFF) parameters for each subject.

2.4. Comparison with an Existing Model

In addition to fitting eq. 7 to the ERG data, we also fit the trough-to-peak amplitude of the b-wave in each subject to the Hamilton et al. (2007) model, as recently adopted by ISCEV (McCulloch et al., 2019). This model, the sum of a sigmoidal curve and a Gaussian, was expressed as

$$H(I)=V_{\max }\left(\frac{{10}^I}{{10}^I+{10}^{\sigma }}\right)+G\left({\left(\frac{{10}^I}{\mu }\right)}^{\frac{\text{ln}\left(\frac{\mu }{{10}^I}\right)}{B^2}}\right)$$ eq. 8

where V_max is the saturating amplitude (μV] of the sigmoid, σ is the semi-saturating flash strength (log cd·s·m⁻²] of the sigmoid, G is the amplitude (μV] of the Gaussian, μ is the mode (ms] of the Gaussian, and B defines the breadth (∝ ms] of the Gaussian. In this formulation, V_max is related to the saturating amplitude of the ON component and G is related to the saturating amplitude of the OFF component of the photopic b-wave (although note, being a positive value, G is undoubtedly interacting problematically with ON responses]. However, this model, too, occasionally produced amplitude parameter values (V_max, G) that exceeded plausibility, and thus we adapted eq. 8 so that it, too, could be fit using eq. 4 as the error term, as

$$H_{c_{weight}}(I)=\left(a\left(\frac{{10}^I}{{10}^I+{10}^{\sigma }}\right)+(1-a)\left({\left(\frac{{10}^I}{\mu }\right)}^{\frac{\text{ln}\left(\frac{\mu }{{10}^I}\right)}{B^2}}\right)\right)c$$ eq. 9

where a is a proportion and the respective saturating amplitudes of the ON and OFF components are a · c and (1 − a)c; again, we set γ to 0.01.

2.5. Statistical Analyses

We calculated the Pearson product moment (r) correlations of the fits of eq. 7 to the data and evaluated them for significant differences between Adult and other groups. We then expressed the amplitude and sensitivity parameters obtained from the fits as the log change from Adult (ΔLogAdult; Akula et al., 2008). We evaluated differences in ΔLogAdult amplitude and sensitivity by a single, three-factor, repeated measures (RM) analysis of variance (ANOVA) with factors group, pathway (ON, OFF) and parameter (amplitude, sensitivity); we evaluated the corresponding implicit times (in ms) by a separate, two-factor RM-ANOVA with factors group and pathway. We performed pairwise post hoc testing using Tukey’s (1949) honestly significant difference (q) statistical test. We set the significance level (α) for all tests at p<0.05.

We did not evaluate data from the Hamilton models (eqs. 8, 9) statistically, since our stimuli usually did not cover the full range of recommended strengths (McCulloch et al., 2019), but representative fits are presented for discussion.

3. Results

Figure 3 shows respective series of representative photopic ERG responses obtained in Infant, CSNB2 and CSNB1, XJR, and preterm-born subjects (NROP, UROP, TROP), each superimposed over the same series of representative Adult responses. Inspection of these responses revealed qualitative differences, relative to Adult responses, that changed with flash strength. For example, Infant b-waves were smaller at low strengths but became slightly supernormal at higher strengths. CSNB2 subjects’ responses were markedly attenuated at every strength but, interestingly, CSNB1 subjects, whose nyctalopia is greater (Allen et al., 2003; Pearce et al., 1990; Zeitz et al., 2015), nonetheless had preserved a-wave amplitudes and, at least at the lower intensities, prominent b-waves; this is consistent with ERG results reported elsewhere (Audo et al., 2008; Bijveld et al., 2013). XJR subjects appeared to have pathology somewhere between CSNB2 and CSNB1 subjects. However, NROP, UROP, and TROP subjects did not differ much from normal.

Fig. 3.

Families of intact (i.e., unfiltered) ERG responses representative of Adult (green traces) control and each experimental group (black traces), indicated at top, to flash strengths (log cd·s·m⁻²) indicated at left.

We used the fits of eq. 3c, performed every 2 ms, to extract the ON (eq. 3a) and OFF (eq. 3b) components from each subject’s responses. Figure 4 shows representative extracted responses to a range of intensities (−0.5–1.6 log cd·s·m⁻²) from each group. Inspection of the responses revealed that, although the ON and OFF responses wax and wane with time after the flash, there is nonetheless a strong suggestion of multimodality (that is, multiple peaks or troughs)—particularly in the OFF responses—that is not apparent in the summed records.

Fig. 4.

Representative ON (blue traces) and OFF (brown traces) components of the ERG “extracted” by fit of eqs. 3a-c to the data of subjects in each of the groups indicated above at 2-ms intervals from 0–50 ms following the flash. Traces plot putative responses to flashes of doubling strengths from −0.5–1.6 log cd·s·m⁻². Their sums (green traces) approximate the filtered ERG.

Figure 5 shows fits of eq. 7 to the representative records shown in Figure 3. With eight free parameters, the model (eq. 7) does an impressive job conforming to the photopic ERG of retinae with a range of pathologies that include conspicuous alterations in on and off responses; overall, the correlation of the model and the data was r = 0.915 with the 95% confidence interval for r spanning 0.904–0.926 and no group’s r differing significantly from that in Adult. The results of the fits of eq. 7 are summarized for each group in Table 1 and, following conversion to ΔLogAdult units, Figure 6. The group×pathway×parameter ANOVA in the amplitude and sensitivity data detected significant main effects of group (F = 9.69; df = 7,104; p = 3.09·10⁻⁹) and pathway (F = 6.33; df = 1,104; p = 0.0134) and significant group×parameter (F = 2.75; df = 7,104; p = 0.0108), group×pathway (F = 3.61; df = 7,104; p = 0.00161), and parameter×pathway (F = 6.84; df = 7,104; p = 0.0102) interactions. Pairwise post hoc evaluation of overall group differences detected that Infant, CSNB2, and XJR subjects had significantly lower parameter values than did Adult subjects. Specifically, Adult subjects had significantly larger ON amplitude than did CSNB2 (p = 1.00·10⁻¹⁰) and XJR (p = 6.00·10⁻⁶) subjects, significantly higher ON sensitivity than Infant (p = 0.00256) subjects, and significantly larger OFF amplitude than CSNB2 (p = 0.0363) subjects; there were no significant intergroup differences in OFF sensitivity. No amplitude or sensitivity parameter in any group significantly exceeded the value in Adult subjects. Notably, CSNB2 subjects’ ON amplitudes were significantly lower than all other groups.

Fig. 5.

Representative processed (i.e., band-stop filtered) responses (black traces) from each group, as indicated, plotted as a function of flash strength, and respective fits of eq. 7.

Fig. 6.

Mean±SD amplitude and sensitivity deficit (top) and implicit time (bottom) in ON (left) and OFF (right) responses, obtained by fit of eq. 7.

The group×pathway ANOVA in the implicit time data detected significant main effects of group (F = 5.16; df = 7,104; p = 4.60·10⁻⁵) and pathway (F = 301; df = 1,104; p = 1.89·10⁻³²) and a significant group×pathway (F = 7.47; df = 7,104; p = 2.88·10⁻⁷) interaction. Pairwise post hoc evaluation of overall group differences detected that Infant (p = 0.00541), CSNB1 (p = 0.0194), XJR (p = 0.00148), and NROP (p = 0.0174) subjects had significantly elongated implicit times, relative to Adult. Specifically, Adult subjects had significantly shorter ON implicit times than did Infant (p = 5.54·10⁻¹⁴) and XJR (p = 2.58·10⁻⁹) subjects; there were no significant intergroup differences in OFF implicit times. Notably, implicit times in NROP subjects did not differ from those in Adult subjects when ON and OFF were considered discretely. Neither implicit time parameter in any group was significantly shorter than the value in Adult subjects.

The Hamilton model for each photopic b-wave SR function of the sample records shown in Figure 3 is plotted in Figure 7. The photopic hill, which is quite pronounced in the Adult records in the stimulus range plotted, was markedly less pronounced or even absent in several other groups. For those groups that did have a pronounced photopic hill (Adult, NROP, UROP), the best-fitting model included prominent sigmoidal and Gaussian contributions. However, for one of the groups that didn’t display the photopic hill (CSNB1), the best-fitting model depended almost entirely on the sigmoidal component. For two other groups without a photopic hill (Infant, XJR), the best-fitting model depended almost entirely on the Gaussian component, and for yet two more (CSNB2, TROP) both sigmoidal and Gaussian components contributed. Thus, over this range of intensities, the lack of a photopic hill did not seem to associate with any particular sigmoidal or Gaussian contribution.

Fig. 7.

Fits of the Hamilton model (eq. 9) to b-wave amplitude (black dots) SR functions. The constitutive sigmoidal (blue dashed lines) and Gaussian (brown dashed lines) components of the complete model (solid green line) are shown.

4. Discussion

4.1. Extracted ON and OFF Signals

A sum of sigmoidal functions representing the depolarizing and hyperpolarizing components of the full-field photopic flash ERG provides an accurate description of the SR relationship at arbitrary times after stimulus presentation. When the components are plotted separately, as functions of time and flash strength, they may reveal the underlying ON and OFF responses. We thusly derived these responses, and their sum, for the first 50 ms of the human photopic ERG. In healthy adults and in subjects with a range of retinal conditions, our model produced reasonable-looking response families for each group. Differences among these families suggested changes in the properties of the underlying responses, in particular, the ON response.

The postreceptor ON and OFF components of the photopic ERG have been studied using techniques that isolate each respective pathway. For example, first inner retinal responses can be blocked pharmacologically (N-methyl-D-aspartate and tetrodotoxin, NMDA+TTX; Massey, 1990; Narahashi, 1974). Then, selective block of either the ON (L-2-amino-4-phosphonobutyric acid, APB; Slaughter and Miller, 1981) or OFF (cis-2,3-piperidine dicarboxylic acid, PDA; Slaughter and Miller, 1983) pathways at the level of the bipolar cell can be performed. Finally, to isolate the on and off ERG to the depolarizing and hyperpolarizing bipolar cell, the residual, pure photoreceptor potential that remains following APB+PDA+NMDA+TTX administration can be digitally subtracted from the records. Such a study of the photopic hill has been performed in simian eyes (Ueno et al., 2004). In our noninvasive studies in human eyes, we instead adopted a band-stop filter to eliminate the rapid, oscillatory potentials known to originate in the inner retina (Wachtmeister, 1998) as well as to eliminate the activation of phototransduction (which is likewise fast; Pugh and Lamb, 1993).

We acknowledge that digital filtering is not equivalent to pharmacological isolation of bipolar cell signals; undoubtedly, our extracted ON and OFF responses are contaminated by noncanonical signals (i.e., signals not originating in bipolar cells). Nevertheless, comparison of the pharmacologically isolated simian ON and OFF components with our mathematically extracted counterparts revealed commonalities. Notably, both methods show that the ON and OFF components are dominated by a “peak function” but also contain oscillations that are rapidly waning by ~50 ms. Furthermore, the simian ON responses and those produced by our model look strikingly similar. However, the OFF responses in the simian retina were dominated by cornea-positive potentials (relative to baseline), which is something that our model, by definition, cannot recapitulate. Indeed, our model defines ON responses as cornea-positive and OFF responses as cornea-negative, on the presumption that this reflects the predominating physiological reality in the bipolar cell population. That on and off stimuli elicit respective OFF and ON responses suggests lateral connections between these pathways and consequently some mismatch with our nomenclature. In other words, our so-called “ON” and “OFF” responses might better be dubbed “depolarizing” and “hyperpolarizing” responses. That said, in the simian studies (Ueno et al., 2004), due to the long timeframes (days to weeks) needed for full recovery from the drugs, it was not possible to separate the activity of depolarizing and hyperpolarizing bipolar cells completely, and thus we reserve judgement as to the actual strength of the association between ON and OFF and polarization. We note, however, that depending on what one wishes to measure, a model that accounts all depolarizing responses as “ON” and all hyperpolarizing responses as “OFF” (irrespective of what element of the stimulus elicits them) may be an asset rather than a liability.

If our model is, indeed, approximating the ON and OFF components, then there is little support for the position that either the ON or the OFF response initially rises in response to increasing flash strength and then falls as flash strength further increases, as has been previously suggested (Rufiange et al., 2002; Ueno et al., 2004). Rather, the diminishment of the trough-to-peak amplitude of the photopic b-wave at higher intensities can be fully explained by lower sensitivity in the OFF pathway relative to ON. That is, the ON pathway dominates responses to weaker stimuli but is countered by OFF signals, which pull amplitudes lower, at higher flash strengths. This seems, to us, to be a physiologically plausible explanation. It is also in agreement with Gauvin et al. (2017) who found that, while the response to the offset of a long-duration stimulus (e.g., the d-wave) waxes and wanes, the OFF component of the response to a brief (5 ms) flash, measured using discrete wavelet transform (Gauvin et al., 2015), increases monotonically with stimulus strength.

4.2. ON, OFF, and Retinal Dysfunction

Our three-dimensional (I, t, μV) model (eq. 7) ignored the multimodality of the ON and OFF responses but nevertheless fit the filtered records well (Figure 5). Critically, the model provided convenient, objective parameterization of the constitutive ON and OFF elements of the ERG, including typical amplitude (i.e., force) and sensitivity (i.e., per intensity and time) units as well as implicit times (a convenient feature of the Weibull function is that it includes an easily determined mode). These parameters differed significantly between groups in manners that were consistent with current understanding. Thus, trusting in our model, we noted a few interesting features of retinal development and disease manifest in our dataset.

First, in infancy, the OFF pathway is relatively mature, displaying activity not differing significantly from adult responses, while the ON pathway, although normal in saturating amplitude, is less sensitive and slower. We had earlier hypothesized that the absence of the photopic hill in infants results from an immaturity in the relative contributions of ON and OFF bipolar cell responses (Hansen and Fulton, 2005); we can now specify that the immaturity is predominantly in the former.

Defects at the first retinal synapse—between photoreceptors and bipolar cells—are the recognized cause of pathology in CSNB (Zeitz et al., 2015). They have also been implicated in a mouse model of XJR (Ou et al., 2015). Interestingly, CSNB1 typically produces more severe deficits in dark-adapted visual sensitivity than CSNB2 (although the severity of phenotypes is overlapping). This is most likely due to the locations of the defects caused by the mutations (Zeitz et al., 2015). In CSNB1, affected proteins are thought to be expressed in the ON (but not the OFF) bipolar cells, whereat they severely disrupt cellular function (Gregg et al., 2007), thus completely interrupting rod signaling (since the rod bipolar cell is depolarizing). In CSNB2, affected proteins are, instead, found in the terminal of the presynaptic (i.e., photoreceptor) cell, where they prolong calcium-dependent neurotransmitter release (Chang et al., 2006), putatively affecting both ON and OFF signal transmission (Littink et al., 2009; Zeitz et al., 2006) with a wide range of severity (Allen et al., 2003; Pearce et al., 1990). Thus, CSNB1 patients’ pathology is typically considered more severe—and in the dark, it usually is—but otherwise, CSNB2 patients’ visual impairment may, in fact, be greater (Bijveld et al., 2013; Raghuram et al., 2013). Indeed, in our CSNB2 data, we found an extraordinary reduction in ON pathway response amplitudes as well as significant OFF pathway impairment. In contrast, CSNB1 subjects displayed only ON pathway deficits. That the ON deficits were less severe than in CSNB1 may be because the depolarizing bipolar cells were laterally excited by off activity. Both ON and OFF activity would be diminished in CSNB2 because the defect occurs prior to the initiation of both pathways; indeed, CSNB2 was the only group in which we detected any significant OFF pathway defect. In this respect, the model agrees well with traditional interpretations of the molecular mechanisms of CSNB and the ERG (Miyake et al., 1987; Quigley et al., 1996; Sustar et al., 2008).

The severity of the overall pathology in our XJR subjects (mean ΔLogAdult value, Figure 6) was somewhere between that in our CSNB2 and our CSNB1 subjects. In XJR, there are alterations in the glutamatergic signaling cascade in the depolarizing bipolar cell dendrites that disrupt ON bipolar cell calcium signaling (as occurs in CSNB1). But furthermore, there are separate, “mottled” anatomic disruptions in the photoreceptor and bipolar cell layers that often do not fall in the same “vertical column.” Consequently, the measured loss of bipolar-cell signals probably results both from dysfunction in the bipolar cells themselves and also from diminished photoreceptor inputs (Tanimoto et al., 2016; Weber et al., 2002). These disruptions may also result in there being plentiful “current sinks” through which the dipolar retinal potentials that manifest as the ERG at the cornea (Pugh et al., 1998) are diminished.

Our previous investigations into the effects of preterm birth and ROP on cone and cone-mediated ERG responses found that the impact was small (Fulton et al., 2008), relative to the effect on the rod system (Fulton and Hansen, 1996; Harris et al., 2011). Our present results confirm this, finding no significant effect of preterm-birth (with any associated ROP severity) on ON or OFF amplitude or sensitivity; we did, however, note significant lengthening of implicit times, but only in the NROP subjects—a surprising result. Indeed, the fact that post hoc testing detected no significant differences in ON or OFF NROP implicit times compared with those in Adult leads us to suspect that this result may be erroneous.

4.3. A Comment on the Novel Curve-fitting Protocol

Finally, we recognize that a common complaint in curve fitting is that the resulting parameters, while mathematically optimal, are unlikely to be meaningful because they fall outside of plausible ranges. Another common difficulty is that small changes in initial parameters can have profound effects on the optimized values, meaning there are discrete, local minima in the fitting space, and consequently even the mathematical optimality is equivocal. When we extracted the ON and OFF components of the responses (i.e., when we fit eq. 3c) and when we parameterized these components (i.e., when we fit eq. 7), we did not identify any cases of the latter problem, but we were stymied on several occasions by the former; we encountered both difficulties in fitting eq. 9, where a broader range of data would undoubtedly have helped (there has been exploration into the impact of abbreviated SR data; McCulloch et al., 2019). Thus, we developed an approach that enhanced the fitting, resulting in plausible numerical descriptions of the physiological processes underpinning ON and OFF responses. This approach, encapsulated in eq. 4, is, to our knowledge, novel.

The impact of this novel fitting routine is unclear and, in most cases, small (we estimate the median change in parameter values between using the standard RMS fit or eq. 4. is less than 7%), but, as shown in Figure 8, it can sometimes be profound. The commonly adopted alternative of which we are aware—setting parameter boundaries—was another option, but neither could we find a way to do that objectively nor would it have had any less profound an impact on the final parameter fits. At a minimum, our approach allows the data itself to guide the solution. But beyond that, in every case where we did observe a large difference between the two fitting methods, the fit that adopted eq. 4 was, subjectively, superior, at least with respect to interpretability. It even seemed to aid in fitting the Hamilton model to more limited ranges of flash strengths. Thus, we think that our approach may warrant further investigation and, if borne out, adoption.

Fig. 8.

The effect of using standard RMS fitting, as opposed to eq. 4 (with γ = 0.01) as the error term is shown for the sample CSNB2 response family. The left panel shows the fit of eq. 7, and the middle panel shows the constitutive ON (blue) and OFF (green) components; note the implausibly different units. The right panel shows the Hamilton model fits (symbology as above); note the implausibility of the Gaussian component.

• The depolarizing (ON) and hyperpolarizing (OFF) bipolar cell responses to the photopic full-field flash electroretinogram can be extracted from an intensity series using a sum of sigmoidal growth curves.

• The “photopic hill” can be explained by the summation of ON and OFF contributions to the ERG of approximately equal (although opposite) amplitudes but respectively greater and lower sensitivity.

• The ON response is relatively late-maturing.

• Congenital stationary night blindness (CSNB) and retinoschisis, two inherited retinal disorders characterized by a “negative ERG” and an absence of the photopic hill, can be explained by deficits in the ON response.

• CSNB2 is distinguished from CSNB1 by the additional presence of an OFF deficit.