The relationship of stimulus intensity to ERG response has been widely studied in healthy and diseased retinas.^{9–11,13–15,23,24,34,61,66,67} The ERG stimulus-response functions summarize the graded responses of the distal retinal cells to a range of flash intensities. Stimulus-response (S-R) functions for the amplitudes and implicit times of the several components of the intact ERG waveform in human and animal subjects have been described and provide a foundation on which the interpretation of cellular processes is built. This chapter will focus on scotopic b-wave functions. Other chapters are devoted to derivation of the photoreceptor response from the a-wave (chapter 35) and postreceptoral components such as the oscillatory potentials (chapter 43).

The hyperbolic function

reasonably well describes^2,3,23,44,61 the relationship of the scotopic b-wave potential, V, to stimulus intensity, I. The value of I that produces a half-maximum (semisaturated) response is σ. Thus, 1/σ is an index of sensitivity. The exponent in equation (1) indicates the slope of the function at σ.

As is shown in figure 33.1, the two parameters logσ and V_max provide a compact representation of a large number of b-wave responses (figure 33.1A). On a log-log plot of the S-R function, response voltage increases linearly as low-intensity lights are incremented and then, as I is increased further, approaches a maximum (figure 33.1B). The implicit time of the response decreases with increasing intensity (figure 33.1C). If n is 1, as usually is the case,^{3,5,6,18,19,25,26,38,44,46,69} the linear range covers about 1.8 decadic log units of stimulus intensity.⁵⁹ With progression to higher flash intensities at which the a-wave is present, a second limb of the S-R function becomes apparent.⁵¹ The complete b-wave function (figure 33.1B) is not monotonic. The fit of equation (1) does not include the second limb.^16,23,51,61 For normal adults, the reported values^{3,4,6,16,23,44,52,58} of logσ range from 0 to −0.5log scotopic troland seconds with standard deviations less than 0.2log unit. Normal adult values of V_max range from 281µV to 521µV with a standard deviations of less than 100µV.^{3,4,6,16,23,44,52,58}

Figure 33.1.  

The scotopic stimulus-response (S-R) functions. A, Sample ERG records from a normal subject. The amplitude of the b-wave response increases with increasing stimulus intensity. At the higher intensities, a-waves are also seen. The troland values of the stimuli are indicated to the left of every other trace. B, The amplitudes of the a- and b-wave responses in panel A are shown as a function of stimulus intensity on a log-log plot. The arrow indicates logσ, the flash intensity that elicits a half-maximum b-wave amplitude. The smooth curve represents equation (1) (see the text) with n = 1 fit to the monotonic portion of the S-R function. The upper limb is ignored in the curve fit. The dashed lines are an oblique with a slope of 1.0 and a horizontal at V_max. The dashed lines intersect at logs. C, The implicit times of the a- and b-waves are plotted as a function of log stimulus intensity.

In the first reports that equation (1) summarizes the voltage of the response of distal retinal cells to a range of stimulus light intensities, Naka and Rushton^47,48 noted that the mathematical function also represents a logistic growth curve⁶⁴ such as describes the growth of the U.S. population between 1790 and 1940. Perhaps more relevant to changes in potential across the membranes of retinal cells are models of enzyme⁴⁵ or adsorption⁴² kinetics that may be cast as a hyperbolic function and summarized by equation (1). Examples of physical events fulfilling the prediction of this mathematical model are enzyme and adsorption kinetics.^42,45 As substrate is added, enzyme velocities increase linearly until enzyme sites approach saturation and velocities approach a maximum.⁴² Adsorption of particles on a surface proceeds linearly until sites become occupied, and then, no matter how many more particles are made available, the rate of adsorption reaches a never-to-be-exceeded rate.⁴²

Since the first mathematical summary of ERG S-R functions,²⁶ a good deal more has been learned about the S-R functions of the photoreceptors and the postreceptoral cells and the origins of the components of the ERG (chapter 12). No single class of cells accounts entirely for the behavior of b-wave S-R functions.^53,57 The current understanding is that the scotopic b-wave S-R function represents the observed relationship of the mass activity of ON-bipolar cells with lesser contributions from other second- and third-order neurons.^{1,29,30,49,50,65,68,70}

To obtain S-R curves such as those shown in figure 33.1, stimulus intensities sufficiently low to establish the linear portion of the curve and sufficiently high to establish saturation are needed. In practice, a several log unit range of stimuli, incremented in 0.2–0.5log unit steps, are used to obtain data sets from which the parameters of equation (1) can be determined. Curve-fitting programs minimize the root mean square deviation of the observed responses from equation (1). Larger step sizes and fewer experimental points may reduce the precision with which the parameters of equation (1) can be determined.

Procedural and technical explanations are usually offered for the scotopic b-wave S-R functions that are not well described by equation (1). The most straightforward and common explanations are that the stimuli are not well placed. For instance, definition of the lower end of the function depends on sufficient stimulation with low intensities. In the normal adult eye, stimuli producing approximately −1 to −2log scotopic troland seconds retinal illuminance evoke small b-waves. At very low intensities, producing approximately −3log scotopic troland seconds retinal illuminance, the small (≤20µV) scotopic threshold response (STR) is evoked from the thoroughly dark-adapted eye.^17,57,63 Besides being evoked by lower-intensity stimuli, the STR is a corneal-negative potential and has longer implicit times, typically in the range of 100–180ms. Insufficient intensity and large step size would leave the upper portion of the curve, including the second limb (figure 33.1B), incompletely defined. The lack of demonstrable saturation at higher intensities may be due to several factors that are not necessarily mutually exclusive. These include the failure to limit responses to those mediated by one class of photoreceptors and, especially at higher stimulus intensities, repetition rates that suppress amplitudes of subsequent responses. The scotopic b-wave S-R functions in normal subjects are similar, whether the cone contribution is subtracted or not. However, the cone contribution may have a significant effect on the b-wave S-R functions recorded from dark-adapted patients with retinal disease.^52,60

Responses to test lights that uniformly stimulate as much of the retina as possible^39,40 are more readily interpreted than those elicited by smaller, nonuniform fields. International Society for Clinical Electrophysiology of Vision (ISCEV) standards recommend full-field stimulation.⁴³ An integrating sphere or a flash lamp and diffuser at close range are used. It is recognized that the integrating sphere does not provide perfectly uniform intensity of stimulation over the entire retinal surface.^39,40 Full-field and less than full-field stimuli yield nearly identical S-R functions in normal subjects.²¹ However, valid comparisons of responses from normal and diseased retina are best based on responses to full-field stimulation. Disease may reduce the area of functional retina and alter the parameters of the S-R function.^12,37,62

In retinal degenerative disorders or in early infancy, the range of response amplitudes between the noise level and saturation is attenuated. To improve signal-to-noise ratio, signal averaging becomes necessary if interpretable S-R data are to be obtained. Maintenance of a constant state of retinal adaptation is critical. Care must be taken that repeated stimulations do not themselves attenuate the response. The on-line observation of the trough-to-peak amplitudes of successive b-waves is often used to make this determination. At high stimulus intensities, 60-s or longer intervals may be necessary.

In an analysis reminiscent of that of Granit,^27,28 the ERG waveform is considered to be the sum of the photoreceptor and postreceptoral retinal responses.^33,35 Contemporary analyses digitally subtract the rod photoreceptor response, which is derived mathematically from the a-wave and called P₃,^34,41,54 from the intact ERG waveform to obtain P₂ (figure 33.2A). P₂ is thought to represent mainly the ON-bipolar cell response but also activity in other second- and third-order retinal neurons.^{1,29,30,33,35,50,55,56,65,68} The isolated P₂ component (figure 33.2B) may be a clearer representation of the postreceptoral activity than is the b-wave.¹⁵ In a mathematical analysis similar to that using equation (1) for the b-wave, the P₂ S-R function (figure 33.2C) is fit with

Figure 33.2.  

Derivation of the postreceptoral response, P₂. A, P₂ is derived by subtraction of the rod photoresponse (labeled P₃) from the intact ERG waveform. B, The family of P₂ waves in a normal subject is shown. A horizontal line marks the 50-mV level. C, The points show the amplitude of P₂ (waves displayed in B) as a function of stimulus intensity on a log-log plot. The smooth curve is the equation P₂/P_2max = I/(I + K_P2) fit to the points. The dashed curve shows the S-R function for the b-wave from which the P₂ records were derived. The arrow indicates the semisaturating stimulus (logs or logK_p2), which, for the normal retina, is the same for the b-wave and P₂. The saturated amplitude of P₂ (P_2max) exceeds that of the b-wave (V_max). D, For the records shown in B, the latency of P₂ at 50mV is shown as a function of stimulus intensity of a log-log plot.

where P_2max is the saturated amplitude and K_P2 is the semisaturation constant. The ON-bipolar cells have their own G-protein cascade. To evaluate the kinetics of the G-protein cascade,⁵⁵ the latency at which P₂ reaches 50µV is noted (figure 33.2D). In the normal retina, this latency, plotted as a function of stimulus intensity on log-log coordinates, is a linear function with slope approximately −0.2. Departures from this relationship are taken as evidence of dysfunction of the ON-bipolar cells' G-protein cascade.⁵⁵

Theoretical and experimental studies of P₂ have led to more complete specification of factors that control the parameters of the S-R function.^14,15,33,35 For instance, low photoreceptor sensitivity^33,35 alone shifts logσ and logK_P2. Also, low saturated amplitude^33,35 of the rod photoresponse alone shifts logσ and logK_P2. Furthermore, there is evidence that if rod outer segment function is intact (that is, rod photoreceptor sensitivity and amplitude the saturated response are normal), rod inner segment dysfunction is transmitted to the bipolar cell so as to shift logσ and logK_P2.¹⁵

Analyses of S-R functions have found applications in studies of development,^19–23,31 aging,^4,7,67 photoreceptor degenerations,^{3,6,18,19,25,44,46} and retinal vascular diseases.^8,38,66 The two parameters of the b-wave S-R function, logσ and V_max, can be examined separately as shown for studies of normal development (figure 33.3). In normal human development, logσ and V_max follow indistinguishable courses of maturation.²³ The age at which logσ and V_max are half the adult value is approximately 10 weeks (figure 33.3). In some retinal diseases, logσ and V_max follow disparate courses (figure 33.4). Study of the behavior of the parameters of the S-R functions, logσ and V_max, offers an opportunity to consider cellular mechanisms such as variation in number of retinal cells and photopigment or simple response compression.^32,36

Figure 33.3.  

Normal development of the parameters of the b-wave S-R function, logs (upper panel) and V_max (lower panel) are shown. The solid line is a logistic growth curve fit to these data,²³ and the upper and lower 95% and 99% prediction limits of normal are shown. The data are logσ and V_max values of 166 subjects with normal eyes (circles) recruited for studies of visual development²³ and 54 patients (triangles) referred for ERG testing who were found to have normal eyes.^22,23

Figure 33.4.  

The course of the scotopic b-wave parameters, logs (upper panel) and V_max (lower panel), in a patient with cone-rod degeneration. The b-wave sensitivity (logσ) decreased approximately 1.5log units, and V_max declined by about 0.25log unit. Responses to the ISCEV cone stimulus averaged less than 15% of normal during this interval.