Assessment of contrast gain signature in inferred magnocellular and parvocellular pathways in patients with glaucoma

Abstract

PURPOSE

Contrast gain signatures of inferred magnocellular and parvocellular postreceptoral pathways were assessed for patients with glaucoma using a contrast discrimination paradigm developed by Pokorny and Smith. The potential causes for changes in contrast gain signature were investigated using model simulations of ganglion cell contrast responses.

METHODS

Foveal contrast discrimination thresholds were measured with a pedestal-Δ-pedestal paradigm developed by Pokorny and Smith (1997). Stimuli were 27 msec luminance increments superimposed on 227 msec pulsed Δ-pedestals. Contrast thresholds and contrast gain signatures mediated by the inferred magnocellular (MC) and parvocellular (PC) pathways were assessed using linear fits to contrast discrimination thresholds at either lower or higher Δ-pedestal contrasts, respectively. Twenty-seven patients with glaucoma were tested, as well as 16 age-similar control subjects free of eye disease.

RESULTS

Contrast sensitivity and contrast gain signature mediated by the inferred MC pathway were lower for the glaucoma group, and reduced contrast gain signature was correlated with reduced contrast sensitivity (r²=45%, p<0.0005). These two parameters mediated by the inferred PC pathway were little affected for the glaucoma group. Model simulations suggest that the reduced contrast sensitivity and contrast gain signature were consistent with the hypothesis that reduced MC ganglion cell dendritic complexity can lead to reduced effective retinal illuminance, and hence increased semi-saturation contrast of the ganglion cell contrast response functions.

CONCLUSIONS

The contrast sensitivity and contrast gain signature of the inferred MC pathway were reduced in patients with glaucoma. The results were consistent with a model of ganglion cell dysfunction due to reduced synaptic density.

INTRODUCTION

Glaucoma is one of the leading causes of blindness worldwide. The diagnosis of glaucoma is primarily based on the clinical assessment of the optic nerve head and surrounding structures, and examination of the visual field (perimetry). Compared to the optic disc evaluation, perimetry actually measures visual function, and therefore is particularly important in following and assessing the effect of glaucoma treatment.

Functional defects observed in perimetric tests manifest as decreased contrast sensitivity, e.g.: decreased sensitivity to luminance increments as in conventional perimetry, or decreased sensitivity to contrast modulation as in frequency-doubling perimetry. Decreased contrast sensitivity has been associated with retinal ganglion cell death (Harwerth, Crawford, Frishman, Viswanathan, Smith & Carter-Dawson, 2002; Kerrigan-Baumrind, Quigley, Pease, Kerrigan & Mitchell, 2000), but many authors have also argued that retinal ganglion cell dysfunction can also cause reduced contrast sensitivity (Greve, Dake & Verduin, 1977; Katz, Spaeth, Cantor, Poryzees & Steinmann, 1989; Spaeth, 1985; Tsai, Shin, Wan & Zeiter, 1991; Tytla, Trope & Buncic, 1990; Ventura & Porciatti, 2005). Anatomical and functional studies show that, in primates with induced glaucoma, magnocellular (MC) ganglion cells can have reduced synaptic density and responsiveness before cell death (Weber & Harman, 2005; Weber, Kaufman & Hubbard, 1998). Reduction in the thickness and complexity of the MC cell dendritic arbor may cause changes similar to reduced effective retinal illuminance, resulting in decreased contrast gain (Graham & Hood, 1992). If dysfunction of retinal ganglion cells occurs in people with glaucoma, it may be detected by psychophysical tests designed to evaluate contrast gain properties of retinal ganglion cells.

Recently Pokorny and Smith developed a psychophysical technique to assess the “contrast gain signatures” of both inferred MC and inferred parvocellular (PC) pathways (Pokorny & Smith, 1997; Smith, Sun & Pokorny, 2001). They analyzed data from three paradigms: (1) steady-pedestal paradigm: four squares were continuously presented against a uniform field, and during a trial the luminance of one square changed; (2) pulsed-pedestal paradigm: four squares were briefly pulsed on during a trial with the test square differing in luminance from the other three; (3) pedestal-Δ-pedestal paradigm: four squares were continuously presented against a uniform background, and during a trial, all four squares changed in luminance with the test square differing in luminance from the other three. The steady-pedestal and pulsed-pedestal paradigms measure discrimination threshold mediated by the inferred MC and PC pathways respectively; the pedestal-Δ-pedestal and pulsed-pedestal paradigms can be used to assess the contrast gain signature of the inferred MC and PC pathways.

McKendrick et al. (McKendrick, Badcock & Morgan, 2004) have used the steady-pedestal and pulsed-pedestal paradigms to assess defects in the inferred MC and PC pathways in glaucoma observers, and Alexander and colleagues (Alexander, Barnes, Fishman, Pokorny & Smith, 2004a; Alexander, Barnes, Fishman, Pokorny & Smith, 2004b; Alexander, Pokorny, Smith, Fishman & Barnes, 2001) used these two paradigms in other ocular diseases to evaluate performance mediated by the inferred PC and MC pathways. These studies emphasized comparison of relative sensitivities of the inferred MC and PC pathways rather than estimating their contrast gain signatures.

In this study the pedestal-Δ-pedestal paradigm was employed to assess contrast gain signatures of the inferred MC and PC pathways and to test the prediction that ganglion cell dysfunction (such as reduced synaptic density) may cause reduced contrast gain signatures in people with glaucoma. The results showed that contrast sensitivity and contrast gain signature mediated by the inferred MC pathway were indeed reduced in the glaucoma group.

METHODS

Subjects

Twenty-seven patients with early to advanced glaucoma (age: 44 to 70 years (yrs); mean ± 1SD = 59 ± 8 yrs), 16 control subjects of similar ages (45 to 70 yrs; mean ± 1SD = 56 ± 8 yrs), and 13 young control subjects (22 to 33 yrs; mean ± 1SD = 25 ± 3 yrs) were recruited. All patients were previously diagnosed with glaucoma by an experienced clinician (MWD, one of the authors. See Table 1 for age and clinical measures). All observers in the glaucoma group showed consecutive, repeatable abnormal defects on Conventional Automated Perimetry (CAP) that were consistent with glaucoma, and were considered stable with quarterly or more frequent monitoring for several years. Both glaucoma and control observers were required to have visual acuity of 20/30 or better, refractive errors of less than ±6D of sphere and 3D of cylinder, clear ocular media, no systemic disorder or medication known to affect visual function, and no eye disease (other than glaucoma). One eye was tested per observer. The chosen eye was usually the one with better visual acuity, or in the case of a glaucoma observer, the one with less severe visual field loss. This study followed the tenets of the Declaration of Helsinki. Written informed consent was obtained from all observers after the nature and possible consequences of the study were explained. This research was approved by the Institutional Review Board of the SUNY State College of Optometry. Financial compensation was given to subjects for their travel expenses and time.

Table 1.

Glaucoma observer information: ID number, age (59±8), diagnosis, distance refractive error, visual acuity, Pelli-Robson contrast sensitivity (1.55±0.14), MD (−5.56±6.01) and PSD (5.65±4.44) of the SITA 24-2 test from Peridata, MD (−5.56±6.01) and PSD (5.65±4.44) of the four central points near the macula from the SITA 24-2 test. POAG: primary open angle glaucoma; MXMG: mixed mechanism glaucoma; NTG: normal tension glaucoma.

ID	Age	Diagnosis	Refractive error	Visual Acuity	Pelli-Robson	MD	PSD	MD Central	PSD Central
1	44	POAG	+0.75	20/20	1.50	−14.78	11.91	−24.1	15.0
2	68	POAG	−2.75	20/20	1.50	−12.96	12.89	−15.8	16.5
3	59	POAG	+2.25−1.0x180	20/36	1.05	−9.32	6.76	−11.8	13.5
4	62	POAG	+0.25	20/22	1.50	−12.77	11.98	−9.3	14.9
5	70	POAG	PL	20/20	1.60	−12.70	11.68	−8.3	15.5
6	57	POAG	+1.0−1.0x90	20/20	1.50	−3.15	5.16	−6.3	9.2
7	70	POAG	+4.75	20/25	1.50	−10.73	6.98	−6.1	1.3
8	70	NTG	+2.5−0.75x90	20/25	1.45	−5.41	4.59	−6.1	7.7
9	59	POAG	+0.75−0.75x90	20/22	1.65	−4.01	2.48	−5.1	1.3
10	49	POAG	−1.5	20/20	1.50	−26.45	8.92	−4.8	7.9
11	64	POAG	0.0−1.0x135	20/20	1.65	−7.09	5.02	−3.8	1.3
12	55	NTG	+1.75 −1.00x90	20/20	1.50	−6.43	6.24	−3.6	0.8
13	67	POAG	+1.25−1.25x85	20/16	1.55	−11.54	8.37	−3.6	1.4
14	53	POAG	−5.5−0.5x175	20/30	1.45	−5.35	3.05	−2.8	4.0
15	68	MXMG	+1.00−1.00x90	20/32	1.45	−9.94	8.63	−2.1	1.7
16	44	POAG	−1.50	20/16	1.65	−5.76	6.28	−1.8	2.5
17	65	MXMG	+3.0−1.0x15	20/36	1.50	−1.14	1.67	−1.6	0.0
18	52	POAG	−1.50 −1.50 x70	20/20	1.65	−3.20	2.47	−1.3	2.1
19	59	POAG	PL	20/16	1.65	−6.08	3.53	−1.1	1.3
20	52	POAG	−3.75	20/20	1.65	−7.29	5.09	0.4	1.4
21	62	POAG	−3.0	20/20	1.65	−0.22	1.47	0.7	0.5
22	67	POAG	0.0−1.0x60	20/25	1.25	−2.11	1.30	0.7	1.3
23	58	POAG	+1.25−1.0x90	20/20	1.65	−1.38	2.17	1.4	0.8
24	56	POAG	+3.0	20/14	1.65	−0.71	1.23	1.4	0.8
25	48	POAG	PL	20/20	1.75	−0.16	1.18	1.7	1.3
26	56	POAG	+2.5−0.75x95	20/16	1.65	−1.13	2.11	2.2	1.7
27	57	POAG	+0.75−0.5x70	20/20	1.65	−0.25	1.76	2.4	1.8

Apparatus and stimulus

The stimuli were generated on a VSG 2/5 stimulus generator (Cambridge Research Systems Ltd., Rochester, United Kingdom) that was controlled by a Dell computer, and were presented on a Sony Trinitron monitor (GDM-F500) with a framerate of 150 Hz. The mean luminance of the Sony display was measured using a Minolta LS-100 luminance meter (Konica Minolta Sensing Inc., Osaka, Japan), and the luminance versus voltage functions for the three phosphors were calibrated using the OptiCal Photometer (Cambridge Research Systems Ltd., Rochester, United Kingdom). The stimulus duration was verified using a photodetector head connected to a Hitachi VC-6025 digital storage oscilloscope.

The stimulus was a modified version of the Pokorny-Smith pedestal-Δ-pedestal stimulus (Figure 1). Similar to the Pokorny-Smith pedestal-Δ-pedestal stimulus, it consisted of four 1 deg × 1 deg squares, separated by a 9-arcmin (0.15 deg) gap, presented foveally with the aid of a fixation cross against a uniform background. Each 1 deg × 1 deg square had an area between that of Goldmann sizes IV (0.6 deg²) and V (2.3 deg²). The luminance of the background was 30 cd/m², and the initial luminance of each square was 0.2 log unit higher than the background (47.5 cd/m²). In the Pokorny-Smith pedestal-Δ-pedestal paradigm, during a trial the fixation cross disappeared and all four squares changed in luminance, either as an increment or a decrement, for a fixed pulse duration with the test square differing in luminance from the other three. The observer’s task was to indicate which of the four squares looked different from the other three. Many of our subjects found this task too difficult to perform, stating that they could tell that one square was brighter than the rest but the flash was too brief to decide which one.

Figure 1.

Stimulus configuration. The stimulus was a modified version of the Pokorny-Smith pedestal-Δ-pedestal stimulus. It consisted of four 1 deg x 1 deg squares. During each trial, the luminance of three squares were increased by a fixed amount for 227 msec, and for the test square the luminance was increased to a higher level for the first 27 msec before it was set at the same luminance level as the other three. The observer’s task was to indicate which one of the four squares was brighter than the other three.

In our experiment, the stimulus was modified so that during each trial, the luminance of three squares was increased by a fixed Δ-pedestal level ΔL_Ped (47.5×10^ΔL_Ped cd/m²) for longer period, 227 msec (34 frames). The test square, which was randomly chosen, contained an additional luminance increment, L_Stim (47.5×10^ΔL_Ped+L_Stim cd/m²), for the first 27 msec (4 frames), and then returned to the same luminance level as the other squares (47.5×10^ΔL_Ped cd/m²) for the remaining 200 ms (30 frames). Subjects found this much easier to perform. As shown in the results section, this modification does not reduce the effectiveness of the paradigm in probing different postreceptoral pathways.

Procedures

Observers pressed buttons on a four-button response box to initiate an experimental session and give responses. During each trial, the observer was asked to identify the position of the square that had an extra luminance increment by pressing the corresponding button on the response box. By giving an answer, the observer also initiated the next trial. The tasks were performed monocularly with the other eye patched, and only one eye was tested per participant. The pupil size was not controlled besides the fact that no glaucoma observer in our sample took medications that could affect the pupil size. The pupil size measured on a Humphrey Field Analyzer averaged 5.3 ± 1.1 mm for the glaucoma group and 5.4 ± 1.1 mm for the age-similar controls.

Contrast discrimination thresholds were measured by varying the luminance increment of the test square L_Stim with a 2-down-1-up, 4-alternative forced-choice staircase procedure. L_Stim began above threshold (if below threshold, the trial was terminated and a new staircase was started at a higher contrast). The initial step size was 0.3 log unit, and step size was reduced to 0.15 log unit after the first reversal and to 0.075 log unit after the second reversal. The staircase was terminated after 13 reversals, and threshold was calculated as the mean of the last 10 reversals at the smallest step size. The participant was asked to perform 1 or 2 staircases for each Δ-pedestal level ΔL_Ped (2 staircases each for ΔL_Ped = 0.00, 0.03, 0.06, 0.09 log unit, and 1 staircase each for ΔL_Ped = 0.12, 0.20, 0.30 log unit). The Δ-pedestal level ΔL_Ped was fixed for each experimental session, and was varied in a pseudo-random order across 0.00 to 0.30 log unit from one session to the next.

As a control, a full set of contrast discrimination thresholds was collected from one young normal observer using all three Pokorny-Smith paradigms: steady-pedestal, pulsed-pedestal, and pedestal-Δ-pedestal paradigms. This was to ensure that the contrast discrimination thresholds for the modified stimuli showed similar characteristics as those in Pokorny and Smith (1997).

Data analysis and Model predictions

Ganglion cell contrast response functions for the MC pathway and PC pathway (Figure 2a) can be described by the conventional Michaelis-Menten function

Figure 2.

The contrast response functions (a) and contrast discrimination functions (b) for MC and PC cells replotted from Pokorny and Smith (1997).

$$R=R_0+R_{max}\frac{C}{C_{\mathit{sat}}+C}$$ (1)

where R represents a cell’s response amplitude in impulses per second; R_o represents a cell’s spontaneous firing rate; R_max represents a cell’s maximal response amplitude; C represents the stimulus contrast; and C_sat is a semi-saturation constant, i.e., the stimulus contrast at which a cell’s response reaches half of R_max. Contrast gain is defined as R_max/C_sat, which is the rate of increase in response with contrast, at low contrast levels.

The contrast discrimination function (Figure 2b) can be derived from Equation (1), as shown by Pokorny and Smith (1997):

$$\mathrm{\Delta }C=k\frac{\delta }{R_{max}}\frac{{(C_{\mathit{sat}}+C)}^2}{C_{\mathit{sat}}-\frac{\delta }{R_{max}}(C_{\mathit{sat}}+C)}$$ (2)

where ΔC represents the contrast discrimination threshold, δ represents the threshold criterion, and C, R_max and C_sat have the same meaning as in equation (1). The constant k is a scaling factor used to account for cortical processing.

The parameters used here were the same as in Pokorny and Smith (1997): R_max=65 and C_sat=0.13 for MC cells, and R_max=45 and C_sat=1.74 for PC cells. These parameters were based on published data from primate LGN cells (Kaplan & Shapley, 1986). Threshold criterion δ is set at 10 impulses/sec as in Pokorny and Smith. For a 27 msec test flash, this δ value gives an average increase of 0.27 spikes per ganglion cell for any given trial, and is consistent with pooling of a number of ganglion cell responses by central cortical detectors.

Contrast discrimination functions derived from the contrast response functions for the MC and PC pathways are shown in Figure 2b. For the MC pathway contrast discrimination threshold increases rapidly with pedestal contrast, while for the PC pathway it increases much more slowly. If the most sensitive pathway mediates the contrast discrimination task, the contrast discrimination thresholds should be mediated by the MC pathway at lower pedestal contrast (ΔL_Ped) levels and by the PC pathway at higher pedestal contrast levels (Pokorny & Smith, 1997; Smith et al., 2001).

Pokorny and Smith applied this analysis to the steady-pedestal, pulsed-pedestal, and pedestal-Δ-pedestal paradigms (Figure 3). They argued that the steady-pedestal thresholds are mediated by the MC pathway, and the pulsed-pedestal thresholds are mediated by the PC pathway. The pedestal-Δ-pedestal thresholds that are sandwiched between the steady-pedestal and pulsed-pedestal curves (at small Δ-pedestal levels) are considered to be mediated by the MC pathway; at higher Δ-pedestal levels, the pedestal-Δ-pedestal thresholds follow the pulsed-pedestal curves and thresholds are considered to be mediated by the PC pathway. In this analysis, the slope of the pedestal-Δ-pedestal curve at small Δ-pedestal levels reveals the contrast gain signature of the MC pathway, while at higher Δ-pedestal levels it reveals the contrast gain signature of the PC pathway (the contrast gain signature of the PC pathway can also be assessed from the pulsed-pedestal curve). The pedestal-Δ-pedestal data in Figure 3 were fit with a MC contrast discrimination template, while the steady- and pulsed-pedestal data were fit simply with a straight line.

Figure 3.

A complete contrast threshold data set for a young normal observer using steady-pedestal (circles), pulsed-pedestal (squares) and pedestal-Δ-pedestal (triangles) paradigms. The data are plotted in a similar format as in Pokorny et al. (1997). The x-axis represents the log luminance level of the three identical squares (=log(30)+0.2+ΔL_Ped), and is called “pedestal luminance” as in the other studies. The y-axis represents the log of L_Stim at discrimination threshold. Luminances of the background and the steady-pedestal squares are indicated by the arrows. Note that the figure only shows data for increment stimuli. For decrement stimuli, the pulsed-pedestal data give a V shape almost symmetric around the background adaptation level, while the steady-pedestal data give a straight line (Pokorny et al., 1997). This figure confirms that with the slightly modified stimuli, our results show a similar pattern as that of Pokorny and Smith.

Based on analysis of Pokorny and Smith (Pokorny & Smith, 1997; Smith et al., 2001), the contrast discrimination thresholds for the pedestal-Δ-pedestal paradigm should be mediated by the inferred MC pathway at lower Δ-pedestal (ΔL_Ped) levels and by the inferred PC pathway at higher Δ-pedestal levels. Hence to analyze the data, a MC contrast discrimination template (Equation 2) was fit to data gathered with ΔL_Ped from 0.00 to 0.06 log unit and a PC template was fit to data with ΔL_Ped from 0.09 to 0.30 log unit. Both templates were only allowed to shift vertically by varying the scaling factor k. The final fit to each individual observer’s data was determined by probability summation between the MC and PC templates with exponent n=4 (Quick, 1974). For a few glaucoma observers whose data did not show clear separation of MC and PC pathways, their data were also fit with the PC template alone and the results were compared with MC-PC template fits.

The contrast gain signatures of the inferred MC and PC pathways were estimated using the slopes of linear fits to the pedestal-Δ-pedestal curves at lower and high Δ-pedestal levels respectively (MC pathway: data points between 1.68 and 1.74 log pedestal luminance levels in Figure 3, equivalent to ΔL_Ped from 0.0 to 0.06; PC pathway: data points above 1.74 log pedestal luminance levels in Figure 3, equivalent to ΔL_Ped levels from 0.09 to 0.30 log unit). The slopes are referred to as the “contrast gain signature” to differentiate it from the contrast gain for the contrast response function. The y-intercept of this line was used as an estimate of contrast sensitivity threshold, when ΔL_Ped = 0.

RESULTS

Contrast discrimination threshold

Figure 4 shows the average contrast discrimination thresholds for the glaucoma group (circles) and age-similar control group (squares). The glaucoma group and the age-similar control group showed similar mean contrast discrimination thresholds at larger Δ-pedestal (ΔL_Ped) levels, but for 0.0 and 0.03 ΔL_Ped levels (1.68 and 1.71 log cd/m² for the pedestal luminance) the mean contrast discrimination thresholds were higher for the glaucoma group by 0.2 log unit and 0.1 log unit respectively. The mean discrimination thresholds for the young control group were ~0.1 log unit lower than those for the older control group at all pedestal luminance levels (data not shown).

Figure 4.

The contrast discrimination thresholds as a function of log pedestal increment (1.68+ΔL_Ped) averaged for the glaucoma group (circles) and the age-similar control group (squares). The error bars represent one standard error of the mean for each group. The dotted and dashed lines represent the Pokorny-Smith MC and PC contrast discrimination template fit to the data by vertical scaling.

Data fits with MC and PC templates

Figure 5 shows contrast discrimination thresholds from eight individual observers, four from the age-similar control group (top row) and four from the glaucoma group (bottom row), along with the fits of MC and PC contrast discrimination templates. Solid circles represent contrast discrimination thresholds, the dotted and dashed curves represent MC and PC template fits respectively, and the continuous gray curve represents probability summation between the MC and PC templates. The four left panels (a, b, e, f) show results for two control observers and two glaucoma observers with the best template fits, and the four right panels (c, d, g, h) show results for two control observers and two glaucoma observers with the worst template fits (evaluation based on root-mean-square error).

Figure 5.

Contrast discrimination thresholds and template fits for four age-similar control observers (top row) and four glaucoma observers (bottom row) with either the best fits (a, b, e, f) or the worst fits (c, d, g, h). Solid circles represent contrast discrimination thresholds. Error bars represent standard deviations. The dotted and dashed curves represent the MC and PC contrast discrimination templates respectively; the solid gray curves represent probability summation of the MC and PC templates; the solid dark lines represent the linear fits for data at ΔL_Ped levels between 0 and 0.06.

Contrast gain signatures for the inferred MC pathways

For data from each observer, a straight line was fit to the data points between 0.00 and 0.06 ΔL_Ped levels, and the contrast gain signature and contrast threshold mediated by the inferred MC pathway were estimated based on the slope and the y-axis intercept of the linear fit. The results for age-similar control group (squares) and young control group (triangles) are shown in Figure 6a, and results for glaucoma group (circles) are shown in Figure 6b. The glaucoma group was further divided into three subgroups based on the mean defect (MD) of the 24-2 visual field, with the small dark circles representing the subgroup with modest sensitivity loss (MD > −5dB), medium gray circles representing the subgroup with intermediate sensitivity loss (−5dB > MD > −10dB), and large gray circles represent the subgroup with more severe sensitivity loss (−10dB > MD). The ellipse shows the 95% confidence limits for the age-similar control group. The horizontal and vertical straight lines represent the one-tailed lower 95% confidence limit for contrast gain signature and one-tailed upper 95% confidence limit for contrast threshold for the age-similar control observers.

Figure 6.

Contrast gain signatures vs. contrast thresholds mediated by the inferred MC pathway for age-similar (squares) and young control (triangles) observers (a) and glaucoma observers (circles, b). Glaucoma observers were grouped based on the severity of visual field loss (small dark circles: MD < −5db; medium gray circles: −5db > MD > −10db; large gray circles: −10db > MD). Ellipses represent the 95% confidence limits for age-similar control observers, the vertical and horizontal lines represent the one-tailed lower 95% confidence limit for contrast gain signature and one-tailed upper 95% confidence limit for contrast threshold.

For both glaucoma and control groups, the PC template gave good fits at higher pedestal levels for all observers, while the MC template gave good fits at lower pedestal levels for some observers (Figs. 5a, b, e, f), but not others (Figs. 5c, d, g, h). In the latter situation, the poor fits are primarily due to the relative elevation of contrast thresholds at ΔL_Ped = 0.0, 0.03.

For glaucoma group, the contrast gain signature mediated by the inferred MC pathway was inversely related to the contrast threshold, with higher contrast gain signature tending to be associated with lower contrast threshold (r=−0.67, p<0.0005). This was also true for the control group (combined young and old, r=−0.5, p<0.012). Compared to the age-similar control group, the glaucoma group tended to show lower contrast gain signature (t=1.65, p<0.05) and higher contrast thresholds (t=1.71, p<0.05). There were 11 out of 27 glaucoma observers (41%) whose data points fell outside the 95% confidence-limit ellipse for normal. Ten of them had abnormally low contrast gain signature and 6 of them had abnormally high contrast thresholds. However, there was no clear relation between severity of visual field loss (SITA 24-2) and abnormalities in foveal contrast gain signature or contrast threshold: in all three groups, some glaucoma observers had reduced contrast gain signature while others were well within the normal range. A similar pattern was also obtained when the glaucoma observers were grouped based on the visual field loss at only the 4 visual field points that were closest to the fovea.

Contrast gain signatures for the inferred PC pathways

A straight line was fit to the data points between 0.09 and 0.30 ΔL_Ped levels in the contrast discrimination function, and the contrast gain signature and the contrast threshold mediated by the inferred PC pathway can be estimated based on the slope and the y-axis intercept of the linear fit. Results are shown in Figure 7a for glaucoma (circles) and age-similar control observers (squares). Ellipses represent the 95% confidence limits for age-similar control observers, the vertical and horizontal lines represent the one-tailed lower 95% confidence limit for contrast gain signature and one-tailed upper 95% confidence limit for contrast threshold.

Figure 7.

(a) Contrast gain signatures vs. contrast thresholds mediated by the inferred PC pathway for glaucoma and control groups. Ellipses represent the 95% confidence limits for age-similar control observers, the vertical and horizontal lines represent the one-tailed lower 95% confidence limit for contrast gain signature and one-tailed upper 95% confidence limit for contrast threshold. (b) Contrast gain signatures vs. contrast thresholds mediated by the inferred MC pathway for the glaucoma group replotted from Figure 6b. The small dark circles represent glaucoma observers whose data are better fit with the combination of MC-PC template; the large gray circles represent glaucoma observers whose data are better fit with the PC template alone (lower RMS error), and medium gray circles represent glaucoma observers whose data seemed to be fit better with PC template only (lower RMS error), but fewer data points actually fell on or close to the PC template compared to the combination of MC-PC template fit.

The contrast gain signatures for the inferred PC pathway were very similar for the glaucoma and the age-similar control groups (t=0.05, p>0.4): only 2 observers in the glaucoma group (no. 3 and 13 in Table 1) had contrast gain signatures below the 95% confidence limit for normal. The similarity of contrast gain signatures for the glaucoma and control groups is not surprising since the same PC contrast discrimination template, without variation in gain, gave good fits (ΔL_Ped between 0.09 and 0.3) for both glaucoma and control groups.

Contrast thresholds mediated by the inferred PC pathway were also similar for the glaucoma and control groups (t=0.85, p>0.15). This was different from the thresholds mediated by the inferred MC pathway, where the glaucoma group had an elevated mean contrast threshold both from direct measures of contrast detection threshold (Figure 4, pedestal ΔL_Ped=0.0) and from estimation based on the intercepts of the linear fits (Figure 6).

The 2 glaucoma observers with the worst template fits in Figure 5 have elevated contrast thresholds at ΔL_Ped=0.0, and the data between 0.0 and 0.06 ΔL_Ped levels were better fit with PC contrast discrimination template rather than MC contrast discrimination template. We speculated that this could be explained by a shift of mechanism mediating detection, from MC to PC pathways. Hence, the data were re-analyzed and each data set was fit with PC template alone and the error of fit was compared with that of combined MC-PC template fits (Figure 7b). For all observers of the age-similar control group, the data were fit better using the MC-PC template rather than the PC template alone (not shown). This was true for only 15 out of 27 observers from the glaucoma group (small circles in Figure 7b); and almost all of them (14 of 15) had estimated contrast gain signature and contrast thresholds for the inferred MC pathway inside the 95% confidence-limit ellipse for normal. For the remaining 12 whose data were better fit with PC template alone, ten fell on or outside the 95% confidence-limit ellipse for normal in Figure 7b. Seven out of these 12 (large circles) had discrimination functions that were better fit with PC template only (lower RMS error) and the remaining 5 (medium circles) had data that seemed to be fit better with PC template only (lower RMS error), but fewer data points actually fell on or close to the PC template compared to the combination of MC-PC template fit.

Model simulations

The contrast discrimination thresholds and the contrast gain signatures mediated by the inferred MC pathway showed clear differences between glaucoma and control groups; in contrast, there was little difference for the contrast thresholds and contrast gain signatures mediated by the inferred PC pathway between the two groups (Figure 7). What could this tell us about changes in retinal ganglion cells?

Anatomical and functional studies in primate retina with induced glaucoma have shown that magnocellular (MC) ganglion cells show reduction in the thickness and complexity of the dendritic arbor before cell death (Weber & Harman, 2005; Weber et al., 1998). Assuming that reduced synaptic density leads to decrease in effective retinal illuminance level, this would predict an increase in the semi-saturation constant C_sat and a decrease in contrast gain in Equation 1 (Graham & Hood, 1992). To test this prediction, we simulated the effects of variation of (1) maximal response amplitude R_max, (2) threshold criterion δ, and (3) semi-saturation constant C_sat on the contrast thresholds and contrast gain signature of the MC pathway (see Equation 2). Increase in C_sat and decrease in R_max can be used to simulate two different types of ganglion cell dysfunction that affect contrast gain of a cell: decrease in maximum spike rate (reduced R_max) and decrease in synaptic input (increased C_sat). Increase in threshold criterion δ can be used to simulate effects of ganglion cell death, assuming the remaining cells would need to have greater increases in firing rate in order for cortical mechanisms to detect the increment.

Figure 8 shows three sets of simulated contrast discrimination functions with reduced maximal response amplitude R_max, increased threshold criterion δ, and increased semi-saturation constant C_sat. Increase in semi-saturation constant C_sat will increase contrast threshold (i.e., the y-intercept of the linear fit) and decrease contrast gain signature (the slope of the linear fit), while decrease in maximal response amplitude R_max will increase both the contrast threshold and the contrast gain signature. Increase in threshold criterion δ will increase the contrast threshold, and only slightly increase the contrast gain signature.

Figure 8.

A set of contrast discrimination functions with variation in R_max, C_sat, and δ. Decrease in maximal response amplitude R_max or increase in threshold criterion δ will increase both the detection threshold and contrast discrimination gain, while increase in semi-saturation constant C_sat will increase detection threshold and decrease contrast discrimination gain. The number near each curve indicates the value of the parameter that is varied (R_max, C_sat, or δ).

A quantitative analysis of the contrast discrimination thresholds and contrast gain signatures for the model simulation was performed using a similar method as in psychophysical experiments, i.e., linear fit to the initial slope of each curve to find the y-axis intercept and slope of the linear fit. The result is shown in Figure 9 (dotted lines). Increase in semi-saturation constant C_sat will increase contrast threshold and decrease contrast gain signature, giving a line with a slope near −1.0. This is consistent with the overall differences between glaucoma and age-similar control observers. Increase in threshold criterion δ increases mainly the contrast threshold, and only slightly increases the contrast gain signature; this is consistent with only one data point. Decrease in maximal response amplitude R_max increases both the contrast threshold and the contrast gain signature, and is not consistent with any data points. Combinations of increases in C_sat and δ can account for all of the glaucoma data that fall outside the normal range, but increase in C_sat alone is sufficient to account for most of the data points.

Figure 9.

Contrast gain signature vs. contrast threshold replotted from Figure 6b along with model predictions for three types of variations in MC cell contrast response functions (dotted lines).

To further evaluate the extent to which increase in semi-saturation constant C_sat is consistent with data from individual glaucoma observer, we refit the data from those observers whose parameters fell outside of the 95% confidence-limit ellipse for normal in Figure 6b, allowing both the vertical scaling factor k and semi-saturation constant C_sat to vary for the MC template. All of the observers in the glaucoma group required higher C_sat than that of the standard MC template (C_sat > 0.13), and the new fits gave lower RMS errors. The glaucoma observer whose C_sat was the lowest (C_sat=0.22) was the one whose data point fell near the model prediction for increased δ. Another glaucoma observer required an extremely high value for C_sat (7.40) but the new fit only lowered the RMS error slightly. When we excluded these two observers, the average C_sat for the other 9 glaucoma observers was 0.72, nearly 6-fold higher than the value used for the standard MC template (0.13), yet it was still less than half the value of C_sat used for the standard PC template (1.74). Increase in C_sat for these glaucoma observers is consistent with the finding that many of the data points falling outside of the 95% confidence-limit ellipse of normal range are from datasets that can be better fit with PC template alone than with a combination of MC and PC templates. Increase in C_sat for the MC template would cause increase in thresholds at Δ-pedestal ΔL_Ped from 0.0 to 0.06 log unit; since the standard PC template has a higher C_sat and higher contrast discrimination thresholds than the standard MC template at these Δ-pedestal levels, thresholds would move closer to the standard PC template.

For contrast threshold and contrast gain signature mediated by the inferred MC pathways, there is clear difference between the glaucoma and control groups: the glaucoma group showed an increase in contrast thresholds and a decrease in contrast gain signatures. The change between the glaucoma and control groups is mostly consistent with increased semi-saturation constant C_sat as shown by the results of model simulations. However, for contrast thresholds and contrast gain signatures mediated by the PC pathway, the glaucoma and control groups showed similar results. An increase in contrast threshold combined with a decrease in contrast gain signature of the inferred MC pathway are consistent with the prediction that reduced dendritic complexity of the MC ganglion cells (Weber & Harman, 2005; Weber et al., 1998) can lead to reduced effective retinal illuminance, and hence reduced contrast gain signature. We propose that this method can be used as a tool to assess MC ganglion cell dysfunction in people with glaucoma.

DISCUSSION

Contrast discrimination thresholds were measured for patients with glaucoma and age-similar control subjects with large and brief foveal luminance increments (more than 6 times the area and less than one-seventh the duration of the Goldmann size III stimulus commonly used in conventional automated static perimetry), and contrast gain signatures mediated by the inferred MC and PC pathways were assessed using a method developed by Pokorny and Smith (1997). The contrast sensitivity mediated by the inferred MC pathway was reduced for the glaucoma group both in terms of group means and in the terms of the number of observers with abnormally low sensitivity. Reduced contrast gain signature of the inferred MC pathway accounted for much of the loss in contrast sensitivity (r²> 45%). In contrast, both contrast gain signature and contrast sensitivity for the inferred PC pathway were little affected for the glaucoma group. Further analysis with modeling suggests that the reduced contrast gain signature is mostly consistent with increased semi-saturation contrast C_sat, rather than reduced maximal response R_max or increased threshold criterion δ of the ganglion cell contrast response function. The result supports the prediction of increased semi-saturation contrast C_sat and decreased contrast gain signature due to MC ganglion cells in glaucomatous retina having reduced dendritic complexity.

However, we do not suggest that cells in the MC pathway are selectively damaged in the glaucomatous retina. Indeed, suggestions of possible selective damage to MC (Quigley, Sanchez, Dunkelburger, Henaut & Baginski, 1987) or S-cone pathway (Sample, Weinreb & Boynton, 1986) have been challenged (Morgan, 1994; Pearson, Swanson & Fellman, 2001; Sample, Medeiros, Racette, Pascual, Boden, Zangwill, Bowd & Weinreb, 2006). The reason that we did not find any difference in contrast discrimination thresholds and contrast gain signatures of the inferred PC pathway between glaucoma and control groups may be because, even though glaucoma may not selectively damage cells of a particular retinocortical pathway, the depth of defect for visual functions mediated by each pathway can still differ due to the different anatomical and physiological characteristics of each pathway. For instance, Smith, Sun and Pokorny (2001) found very different spatial summation properties for the MC-pathway and PC-pathway mediated thresholds, and proposed that this reflected differences in higher cortical processes mediating these thresholds.

McKendrick et al.(2004) tested glaucoma and age-similar control subjects with the Pokorny-Smith steady-pedestal and pulsed-pedestal paradigms at both foveal and peripheral locations, and found that glaucoma group thresholds were significantly elevated compared with control group thresholds foveally and peripherally on both the pulsed-pedestal (inferred PC pathway) and steady-pedestal (inferred MC pathway) tasks. In contrast, we found that contrast gain signatures and contrast thresholds mediated by the inferred PC pathway were all within the 95% normal confidence ellipse for our glaucoma group. This may be due to the difference in the paradigms between the two studies: we used only increment stimuli while they used interleaved increment and decrement stimuli; we used staircases with 4-alternative forced choice while they used staircases with 2-alternative forced choice; we extended the Δ-pedestal duration to 200 msec longer than the test while they used same duration for the Δ-pedestal and the test.

We modified the Smith and Pokorny protocol to produce a more rapid test, measuring thresholds only for luminance increments rather than for both luminance increments and decrements. The Δ-pedestal luminance (ΔL_Ped) added on top of the steady-pedestal luminance (47.5 cd/m²) was varied from 0.0 to 0.3 log unit and the luminance of the test square was 170 cd/m² at maximal available contrast (some observers reached the maximum pedestal luminance limit at pedestal level ΔL_Ped =0.2, 0.3). There are several other variants of the original Pokorny and Smith protocol (Kachinsky, Smith & Pokorny, 2003; Leonova, Pokorny & Smith, 2003) which could also be developed for studies of different postreceptoral pathways.

A pulsed probe presented against an adapting background has long been used to study the dynamics of light adaptation (see review by Graham and Hood (1992)). In the conventional pulsed-probe paradigm, the detection thresholds were measured as a function of various stimulus-onset asynchrony (SOA). The Pokorny-Smith stimuli were, in a way, modified versions of the pulsed-probe stimuli. Both the steady and pulsed pedestal can be considered as a background which has the same spatial size as the pulsed test (i.e., the probe): the steady-pedestal stimulus had an infinitely-long SOA between the test and the pedestal, the pulsed-pedestal stimulus had a zero SOA, and the pedestal-Δ-pedestal stimulus had an infinitely-long SOA between the test and the initial steady pedestal, but zero SOA between the test and the Δ-pedestal. Conventional pulsed-probe paradigms measured detection thresholds, and were designed to study the dynamics of light adaptation, while the Pokorny-Smith paradigms measured contrast discrimination thresholds and were designed to assess contrast thresholds and contrast gain signatures mediated by different postreceptoral pathways. The modification of the stimulus in this study, longer pulse durations for the Δ-pedestal than for the stimulus, makes the stimulus more similar to the conventional pulsed-probe stimuli. However, as mentioned earlier in the results section, the modification does not affect of the ability of the paradigm to assess the different postreceptoral pathways.

We gathered data from young control observers and found that, at all seven Δ-pedestal levels, mean thresholds were ~0.1 log unit lower than for the older control group that was age-similar to the glaucoma subjects. Data points for all of the younger subjects fell within the 95% confidence-limit ellipse for the older group, so the effect of age was assumed to be low relative to within-subject variability in the control group. The finding that the age effect was similar at all pedestal contrasts would be consistent with loss of ganglion cells during aging (Pearson et al., 2006), but not with elevation of C_sat with aging. A complete analysis of age effects is beyond the scope of this paper.

For contrast detection tasks, spatial summation data can be used to estimate the widths of cortical receptive fields mediating contrast detection (Pan & Swanson, 2006). Based on spatial summation data from Smith, Sun and Pokorny (2001), if the detection threshold was determined by probability summation across multiple cortical mechanisms, each of which was centered at different locations (Swanson, Felius & Pan, 2004), the width of the receptive field for the cortical process would be estimated to be on the order of 0.2 deg for contrast detection at ΔL_Ped = 0.00 to 0.06 log unit. As long as the ganglion cell number and contrast gain remained normal for a 0.2 deg-wide patch of the retina covered by the stimulus, the contrast sensitivity would be expected to remain near normal. Our stimuli were four 1 deg² squares, so cell death would be expected to have relatively minor effects on contrast threshold until a large percentage of ganglion cells had died (Pan, Swanson & Dul, 2006). The analysis shown in Figure 9 is also consistent with this analysis – only one glaucoma observer’s data point was consistent with the predictions for cell death (increased threshold criterion δ) as the primary cause of threshold elevation. If the study had been conducted with 0.2 deg² squares rather than 1 deg² squares, more glaucoma observers might have had data points consistent with the model simulation of cell death.

Weber et al. (2005; 1998) carried out physiological studies on MC cells in glaucomatous retinas. They compared the MC cells’ dendritic trees and their response properties in glaucomatous retina and normal retina, and found that in glaucomatous retinas there is reduction in the thickness and complexity of the dendritic arbor. Such changes may cause reduction of effective retinal illuminance level, which can result in an increase in semi-saturation constant C_sat. Alterations in glial cells (Neufeld & Liu, 2003) could also affect contrast gain of ganglion cells. This result provides support for the hypothesis that ganglion cell dysfunction can affect visual thresholds in patients with glaucoma, but further work is needed. To better evaluate the theoretical framework used in this study, it would be useful to know more about ganglion cell responses to the stimuli used in the Pokorny and Smith paradigms, particularly in primates with experimental glaucoma. To assess potential clinical utility, it would be helpful to evaluate the long-term variability of contrast gain measures in normal eyes and in patients with glaucoma.