Ricco’s law of spatial summation1 states that, for sufficiently small stimuli, stimulus area and intensity are inversely proportional at threshold (Intensity × Area = k, where k = constant). During a response to such a stimulus, the visual system is said to be operating under conditions of complete spatial summation. For larger stimuli, the threshold signal response is governed by incomplete levels of spatial summation. The limit to complete spatial summation is known as Ricco’s area or the area of complete spatial summation. The schematic diagram in Fig. 1 illustrates these concepts.
Although the exact physiological basis for Ricco’s area is a subject of ongoing debate, it has been found to differ with different experimental conditions, including retinal illuminance2–5 and locus,6–8 chromatic pathway,7,9,10 the temporal profile of the stimulus,2 and optical correction.11 Ricco’s area has also been shown to increase with age under scotopic conditions12 but not under photopic conditions for achromatic stimuli or under S-cone–selective conditions.13 Using achromatic stimuli, Barlow2 and Glezer4 demonstrated an increase in the achromatic Ricco’s area with a decrease in background adaptation level down to scotopic levels. Glezer4 hypothesised that Ricco’s area represented the size of ganglion cell receptive field center mechanisms, a proposition discussed further by subsequent investigators.5,8,14,15 Glezer4 reported that decreased involvement of the receptive field OFF-surround at low adaptation levels caused an enlargement of the effective size of Ricco’s area. Davila and Geisler3 also found that the area of complete spatial summation enlarged under low background adaptation levels and suggested that this was caused by a change in the neuron population that detects the stimulus under dark adaptation conditions, namely, an increased contribution from the magnocellular cells with large receptive fields. Although it is clear from the studies of Davila and Geisler3 and Dalimier and Dainty11 that optical factors also influence the size of Ricco’s area, the presence of a region of complete summation after correction with adaptive optics11 indicates that it is first and foremost a neural phenomenon.
No study to date has purposefully examined the effect of background luminance on Ricco’s area in the S-cone pathway. The S-cone–driven ganglion cells, namely, small bistratified cells,16–18 which likely constitute the main route of S-ON signals to the brain, have no identified S-cone antagonistic (S+/S-) center-surround organization18 and no such antagonism is known to exist at the pre-lateral geniculate nucleus (LGN) level.
In this study, we investigate changes in Ricco’s area for different levels of blue background under S-cone–isolating conditions. If any previously observed decrease in Ricco’s area as a function of background luminance results solely from increased center-surround antagonism in the retinal receptive field, one could expect Ricco’s area to remain constant with increasing blue background luminance in the human S-cone pathway. Any change in the area of complete spatial summation with blue background illumination must be attributable to some other cause.
Knowledge of the way in which Ricco’s area changes with background luminance is important clinically, particularly, in the design of psychophysical tests of the visual field for conditions such as glaucoma. Short-wavelength automated perimetry (SWAP), using blue stimuli superimposed on a yellow adapting field, is used clinically to uncover damage to the S-cone pathway in early glaucoma. However, high response variability with SWAP in glaucoma patients19 likely limits the performance of the technique in measuring visual field damage. There is no blue component to the adapting field in SWAP, thus, for the isolated S-cone pathway, the task is detection of blue stimuli on a dark background. Felius and Swanson20 point out that response variability in SWAP may be reduced by increasing S-cone adaptation. If Ricco’s area changes with blue background luminance in the S-cone pathway, it may be appropriate to scale the perimetric stimulus size to Ricco’s area under the altered conditions to improve the sensitivity of the test to glaucomatous damage.21,22
Four young healthy subjects ranging in age from 20 to 27 years took part in the experiment, including one of the authors (T.R.). The right eye was used as the test eye in all cases. Subjects were refracted both centrally and peripherally (at 10 degrees) using retinoscopy before the experiment. There was no measurable difference in refraction between the central and peripheral location for these subjects. All subjects achieved a best-corrected visual acuity of 6/4 and did not demonstrate any visual field defects (Humphrey HFA II, SITA-Standard, 24-2 strategy; Carl Zeiss Meditec, Dublin, Calif). None was found to have any ocular abnormality, as determined by an eye examination including binocular indirect fundoscopy. Each subject had clear media. No color vision defects were found using an Ishihara plate test and a Farnsworth D-15 test. To permit a high retinal illuminance and to control it throughout the tests, a drop of tropicamide hydrochloride (1%) was instilled in the test eye. Each pupil measured 8 mm in diameter after mydriasis. The pupil diameter remained unchanged throughout the experiment. The refractive error found during the initial refraction was refined subjectively (postmydriasis) for a working distance of 60 cm using full-aperture trial lenses and a peripheral blue sinusoidal grating stimulus, projected to the same retinal location as the test stimulus. The lens that gave the optimum subjective peripheral acuity was used in all tests for each individual. Only one of the subjects (subject D.G.) was inexperienced at psychophysical observing; however, two extra clinical visual field tests (Humphrey HFA II, SITA-Standard, 24-2 strategy; Carl Zeiss Meditec, Dublin, Calif) were performed as a practice session in peripheral spot stimulus detection before the commencement of experiments. Informed consent was obtained from each observer, and the study conformed to the tenets of the Declaration of Helsinki. Ethical approval was granted by the University of Ulster Research Ethics Committee.
Apparatus and Stimuli
To study the effect of blue background adaptation level on Ricco’s area under S-cone isolation conditions, we used Stiles’ “two-color threshold” method,23,24 whereby a blue background was added to an intense yellow adapting field. The experimental setup was similar to that previously described by Anderson et al.25 and is demonstrated in Fig. 2. Stimuli and the blue background component were generated on the blue gun of a gamma-corrected 21-inch SONY GDM-F500 monitor (SONY Corp., Tokyo, Japan; pixel resolution 1280 × 965, frame rate 73 Hz) using a Visual Stimulus Generator VSG 2/3 card (Cambridge Research Systems, Rochester, UK). The CIE coordinates of the blue phosphor were x = 0.147, y = 0.07. The monitor was placed at 60 cm from the test eye and the screen subtended 37.2 degrees. A chinrest and forehead bar were used to keep the viewing distance constant and to assist better alignment. The yellow adapting field was produced by passing white light from a projection system through a glass long-wavelength pass filter (Schott OG530, 530 nm half-height) and a diffuser screen. The spectrum of the yellow component of the background is shown in Fig. 2. The CIE coordinates were x = 0.521, y = 0.474. A luminance level of 600 cd/m2 was used. This level was chosen after determining threshold-versus-luminance (TvL) functions (see the paragraph below and Fig. 3). A beam splitter (Edmund Optics Ltd., York, UK) angled at 45 degrees was used to superimpose the yellow light and the blue light from the monitor. Luminance and chromaticity coordinates were measured before and after each experiment using a calibrated SpectraScan PR-650 Spectra Colorimeter (Photo Research Inc., Chatsworth, Calif), and no variation was found. Stimuli were presented at an eccentricity of 10 degrees in the nasal field at a meridian of 175 degrees (as shown in Fig. 2). This meridian was specifically chosen so that thresholds for the largest stimulus would not be influenced by the anatomical midline separating the superior and inferior retina. Two increment squares separated vertically by 0.2 degrees and of the same chromaticity as the blue background field served as a fixation target. The size of each stimulus was regularly measured at the monitor surface using a compound magnifier containing a 0.1-mm increment graticule scale to more accurately describe the on-screen stimulus size. Blue background components used in this study ranged from 0 cd/m2 to 2.2 cd/m2. Background luminance levels were subsequently considered in terms of retinal illuminance. In particular, we wished to assess the S-cone quantal catch from the composite background; therefore, S-cone retinal illuminance was calculated and expressed in S-cone Trolands (S-Td), where 1 S-Td equates to 1 Troland of an equal-energy white.26 The blue and yellow light spectra were measured in 4-nm steps using the SpectraScan PR650 at the eye position. The calculations are based on the Judd luminosity function27 and Smith and Pokorny fundamentals.28 Because we tested retinal locations virtually free from macular pigment, we used modified Smith and Pokorny fundamentals with the macular pigment spectrum removed. The resulting values were corrected for the Stiles-Crawford directional effect using the Le Grand formula.29 The calculated retinal illuminance in photopic Td and S-Td (for a standard observer) is shown in Table 1. The increment threshold data were also expressed in S-Td units.
To ensure that S-cone pathway isolation had been achieved, it was necessary to carry out an initial experiment investigating the relationship between detection thresholds for our stimuli and the luminance of the yellow adapting field. The TvL functions (increment threshold ΔL versus luminance L) were determined for subject TR. Using the same experimental setup as previously described, thresholds were measured for our smallest (-1.22 log square degrees; 0.28 degrees diameter) and largest (0.92 log square degrees; 3.25 degrees diameter) stimuli using a black (0 cm/m2) background adaptation field and a high (4.5 cd/m2) blue background adaptation field and yellow light of various luminance levels (13 to 1203 cd/m2). Varying intensities of yellow light were achieved by placing a series of neutral density filters in front of the projector emitting the yellow light. The subject was allowed to dark-adapt initially for 20 minutes and then for 3 minutes to each yellow background level, starting with the lowest level. Increment threshold values were determined using a two-alternative forced choice paradigm for each level of yellow background luminance and are shown in Fig. 3. Background adaptation level was expressed in photopic Trolands (Td) and corrected for the Stiles-Crawford effect for an 8-mm pupil. Two distinct branches were initially evident under all conditions. The data points were fitted using the equation:
Equation (Uncited)Image Tools
as used by Kalloniatis and Harwerth,30 where ΔL represents increment threshold, A represents the intercept on the ordinate, Le characterizes the horizontal position of the TvL function, and n is the slope of the function. The second branch was demonstrated for both small and large stimuli, indicating that S-cone isolation was achieved under these conditions.31 The value of the yellow background at the intersection of the two branches is typical for the point at which the signal response becomes predominantly mediated by the S-cone pathway. We have previously shown6 that under similar background conditions, the threshold for detection of small blue stimuli changes in accordance with the known distribution of S-cones (foveal tritanopia and maximal sensitivity at 1.5 degrees eccentricity) and its variation with wavelength resembles the spectral curve of Stiles π1 mechanism, with a maximum at 440 nm.10 It was also noticed by the observer that the color appearance of the test stimuli shifted at that point to a violet/white color with nondistinct edges, typical of S-cone vision. The yellow luminance value of 600 cd/m2, chosen to isolate the S-cone pathway in the current study, is represented by the vertical dotted line in Fig. 3. This background gave rise to a retinal illuminance of 4.3 log Td (for an 8-mm pupil), which exceeds the background level below which rod involvement is known to contribute to threshold measurements.31
Threshold was measured for eight stimuli of varying size (and in random order) under different blue background levels between 1.78 and 2.82 log S-Td. The non–test eye was occluded. A temporal two-alternative forced choice procedure was used for all subjects. The stimulus was presented in one of two intervals marked by tones. The subject was required to decide whether the stimulus presentation was made during the first or second interval and respond accordingly by pressing one of two buttons on a response box. No feedback was given, and the subject was encouraged to guess if unable to see the stimulus. Stimulus duration was 200 milliseconds with a square temporal profile. A 3-up/1-down staircase method was used, with contrast reducing by 0.8 dB after three correct responses and rising by 0.8 dB after each incorrect answer. Under these conditions, the staircase would converge toward a threshold corresponding to 79% correct responses.32 Threshold was recorded after six reversals. Three sessions were undertaken under each blue background level (each chosen at random), and detection thresholds were averaged accordingly. To avoid subject fatigue, only one session (i.e., generation of one spatial summation curve) was performed each day.
Before the commencement of the psychophysical experiments, a short practice session was given using a circular incremental stimulus, the diameter of which was chosen at random. This practice session lasted until two reversals were reached.
Fig. 4 shows log increment threshold as a function of log stimulus area for each participant and at each blue background level expressed in S-Td. Increment thresholds for all stimuli increased with a higher blue background luminance, and the difference in increment threshold between low and high levels of blue background luminance was larger for large stimuli. It is also noticeable on inspection of the data points alone that complete spatial summation is limited to smaller stimuli under high blue background conditions (i.e., Ricco’s area is smaller). To quantify this, a two-phase regression analysis (Levenberg-Marquardt estimation) was performed on each data set using the method of Seber and Wild,33 and regression lines were plotted accordingly. The slope of the first line segment was constrained to -1 (obeying Ricco’s law), whereas its intercept, the slope of the second line segment, and the point of intersection of the two segments were allowed to vary. The intersection of the two line segments was taken to represent the area of complete spatial summation (Ricco’s area). This method has been well accepted in published literature as a means of estimating spatial summation characteristics.7,10–13,22,34 The coefficient of determination (r2) exceeded 0.95 in all cases. Values for the slope of the second line (as determined by the software) are given in Table 2. Fig. 4 shows that, for each subject, the spatial summation curve undergoes an upward shift along the threshold axis and a leftward shift along the area axis as the blue background luminance is increased. Fig. 5 summarizes the changes in Ricco’s area with blue background luminance. The area of complete spatial summation becomes notably smaller with increased background luminance in each subject. On average, Ricco’s area decreased in size by 0.39 log units per log unit increase in blue background luminance. Subject D.G. displayed the largest change; a 0.53-log decrease in Ricco’s area after a 1.04-log increase in background retinal illuminance. Subject L.M.I. demonstrated the least change over the same change in background: a 0.31-log unit decrease in Ricco’s area. Values for Ricco’s area under low background conditions in the current study are typical of those found for subjects of similar age for similar background conditions.13
Although changes in Ricco’s area with background adaptation level have previously been shown for achromatic stimuli, the current study is the first to report a reduction in Ricco’s area with background luminance in the S-cone pathway. The difference in vertical separation of TvL curves for large and small stimuli with background luminance supports these findings.
What mechanism subserves the changes in S-cone spatial summation with the level of adaptation? A long-held belief is that the change in the achromatic Ricco’s area with background adaptation level is a result of center-surround antagonism at the level of the retinal ganglion cells. The main difficulty with this hypothesis for the current study is the absence of physiological data supporting the existence of retinal receptive fields with antagonistic S-cone inputs to their center and surround. The receptive fields of ganglion cells with S-cone ON input in the primate retina have spatially coextensive excitatory blue-on and inhibitory yellow-off fields.17,35 Although more recent studies on the primate retina and LGN have shown that S-ON cell receptive fields can demonstrate center-surround antagonism,36–38 this is S/(L + M) antagonism39 rather than S+/S- antagonism. Such receptive fields should not be capable of producing the changes in Ricco’s area observed in the present study. An alternative hypothesis is that changes in Ricco’s area occur at a post-LGN site, where both spatial and S-cone antagonistic receptive fields exist. So-called double-opponent cells have been found in the primate visual cortex,40–42 including those with spatial S+/S- antagonism.40,43 It is therefore possible that these cells are involved in the changes in Ricco’s area that we have seen here. Other studies also point to double-opponent cortical cells as a possible neural substrate for a range of S-cone–mediated phenomena. Monnier and Shevell44 demonstrated that the color shifts created by a background of concentric circles, distinguished by S-cones only, are predicted by receptive field organization observed in cortical neurons—an S-cone antagonistic center-surround (S+/S-) receptive field. The ability to demonstrate Westheimer functions under S-cone isolation under both monoptic and dichoptic conditions45,46 is suggestive of spatial and S-cone antagonism that occurs after the merging of signals from both eyes.
Nonetheless, the notion that the observed effect occurs at a retinal level is not inconceivable. Dacey et al.47 (their Fig. 4c) indicate variation in local dendritic tree size of small bistratified cells, and it is likely that similar variation exists in their receptive field size. It may be that under low levels of background luminance, ganglion cells with large receptive fields are more sensitive and become the dominant responders in an S-cone–driven task while summing light over a larger area. Chichilnisky and Baylor48 reported considerable variation in the strength of input from individual S-cones to the receptive fields of blue-ON ganglion cells in the macaque and attributed this to differences in gain arising from synaptic connections. During a 75-millisecond impulse response from the ganglion cell, they estimated that approximately 700 additional S-cone photo-isomerizations added 1 extra cell spike to a 1-spike maintained discharge rate and there was some evidence of a quantized S-cone input. In our experiment, if at some point the isomerization level of those S-cones affording a weaker input dropped below the required level to elicit a response, and those cones input to the periphery of the receptive field, the field would appear to shrink. Thus, a sophisticated feedback mechanism may not be necessary to alter the area of complete spatial summation for the more primitive S-cone pathway.
Regardless of the mechanism underlying the changes that we report here, the size of Ricco’s area depends on the state of adaptation of the S-cone system, and this has implications for visual function. A smaller Ricco’s area under higher levels of blue background adaptation level can be seen as an effective means of increasing S-cone–mediated spatial resolution while decreasing the extent of S-cone signal pooling, similar to the effect observed for achromatic vision between scotopic and photopic levels. Indeed, Stiles23 and other investigators49–52 have shown that acuity for blue stimuli increases with blue background luminance.
Our findings have implications for clinical testing of the visual field. Under achromatic conditions in the normal eye (as used in conventional perimetry), the relationship between sensitivity to the stimulus and local ganglion cell number depends on the size of the stimulus relative to the achromatic Ricco’s area53; specifically, the stimulus size should be closely scaled to the normal Ricco’s area to maximize spatial summation and the sensitivity of the test to conditions such as glaucoma.21,22 Here we have shown that when the background contains no blue component, as is the case in SWAP, Ricco’s area at our test locations (mean, -0.01 log square degrees; 1.11 degrees diameter) is already smaller than the Goldmann V stimulus (0.36 log square degrees; 1.7 degrees diameter) used in SWAP. Although addition of a blue component to the adapting background should reduce threshold variability,20 Ricco’s area would only shrink further, relative to the stimulus size. Thus, to boost the sensitivity of the test, it may also be appropriate to scale the SWAP stimulus size to equate to Ricco’s area under increased background adaptation conditions at each test location in the normal visual field.21,22
In conclusion, spatial reorganization by the suppressive surround of the receptive fields (most probably at a cortical level), a change in the population of the most sensitive neurons with different receptive field sizes, reduction in the contribution from S-cones with the lowest weights (in the retinal receptive field periphery) might all be among the possible mechanisms of spatial summation changes observed under selective S-cone stimulation.
School of Optometry and Vision Sciences
Cardiff, CF24 4LU
Supported by a PhD studentship from the Department for Employment and Learning, Northern Ireland, and the NIHR Biomedical Research Centre for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, and UCL Institute of Ophthalmology (T. Redmond).
Received January 30, 2012; accepted September 21, 2012.
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