May 2011
Volume 52, Issue 6
Free
Letters to the Editor  |   May 2011
Author Response: Frequency-Doubling Technology and Parasol Cells
Author Affiliations & Notes
  • William H. Swanson
    School of Optometry, Indiana University, Bloomington, Indiana;
  • Hao Sun
    the Department of Optometry and Visual Sciences, Buskerud University College, Kongsberg, Norway;
  • Barry B. Lee
    the Department of Biological Sciences, SUNY State College of Optometry, New York, New York;
    Max Planck Institute for Biophysical Chemistry, Göttingen, Germany; and
  • Dingcai Cao
    the Department of Surgery, Sections of Surgical Research and Ophthalmology and Visual Science, University of Chicago, Chicago, Illinois.
Investigative Ophthalmology & Visual Science May 2011, Vol.52, 3759-3760. doi:10.1167/iovs.11-7468
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      William H. Swanson, Hao Sun, Barry B. Lee, Dingcai Cao; Author Response: Frequency-Doubling Technology and Parasol Cells. Invest. Ophthalmol. Vis. Sci. 2011;52(6):3759-3760. doi: 10.1167/iovs.11-7468.

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      © ARVO (1962-2015); The Authors (2016-present)

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The authors thank Dr. Maddess for his letter. As previously, 1 he suggests that nonlinear Y-like retinal ganglion cells are responsible for the frequency-doubling (FD) illusion, an argument that we challenged in White et al., 2 on three grounds: (1) No evidence was obvious at that time of a separate nonlinear Y-like MC cell class in primate retina ganglion cells; (2) even if there were such nonlinear ganglion cells, the responses of linear MC cells to FD stimuli are robust, and there is no reason they should be ignored; (3) no spatially modulated signals (which might underlie the FD illusion) could be expected from the nonlinear responses of such ganglion cells; their response is nonlinear in time but not in space. We suggested that the FD illusion is due to a psychophysical loss of phase sensitivity at a central site. Dr. Maddess only addresses item (1), the existence of nonlinear cells, referring to new anatomic and physiological studies that demonstrate the presence of a rare Y-like class of primate retinal ganglion cells. However, items (2) and (3) still refute his suggestion: The linear MC cells respond robustly to the FD stimuli, and the FD illusion cannot be explained by nonlinear responses of Y-like ganglion cells. 2  
The purpose of our recent study 3 was to compare MC and PC cell responses to stimuli used in conventional perimetry and FD perimetry. We did not make assumptions as to whether FD perimetry is related to the FD illusion, or whether My cells mediate the FD illusion. FD perimetry is a flicker-detection task, and there is very good evidence that the “regular” MC pathway mediates sensitivity to luminance flicker. 4 We chose our FD stimulus parameters on the basis of stimuli used in clinical FD perimetry, which measures flicker sensitivity and not the FD illusion. In a prior clinical study 5 we used the 12-Hz, 0.5-cyc/deg stimulus for FD perimetry and generated predictions that we tested with the present study, using a 13-Hz, 0.5-cyc/deg stimulus; 13 Hz was the closest approximation we could make to 12 Hz with this monitor, and any effect caused by such a small change in temporal frequency should be insignificant. 
At the end of his letter, Dr. Maddess suggested that conventional size III stimuli may “promote” test–retest variability. We addressed this before 5 and in the present study 3 : For both FD and size III stimuli, as contrast increases above normal contrast threshold, the ganglion cell responses begin to saturate, and this effect will increase test–retest variability. Much of the reported high test–retest variability for size III can be accounted for by the large range of high stimulus contrasts. Perimetry with the size III stimulus uses a much greater range of contrasts than does perimetry with FD stimuli, because FD stimuli cannot exceed 100% contrast. Ganglion cell saturation means that contrasts greater than 100% produce little additional visual response, so that the use of these high contrasts increases variability. Figure 1 illustrates this with unpublished size III and FD variability data from five patients with advanced field loss, with variability for the size III stimulus computed using both the entire 3.5-log-unit range, as well as with a range comparable to that of FD (created by assigning all size III contrast thresholds greater than 100% contrast to be equal to 100% contrast). When the difference in range is accounted for, variability for size III and FD are comparable (solid and dashed horizontal lines show averaged SDs for FD and size III perimetry with comparable ranges). 
Figure 1.
 
Test–retest variability versus contrast sensitivity for FD perimetry (open triangles) with a 1.2-log-unit range of contrast sensitivities, and conventional (size III) perimetry with both 1.2-log-unit (open circles) and 3.5-log-unit (solid triangles) ranges. For size III with the 3.5-log-unit range, SD increased as mean decreased (P < 0.001), but this was not the case for FD or size III with a 1.2-log-unit range (P > 0.12).
Figure 1.
 
Test–retest variability versus contrast sensitivity for FD perimetry (open triangles) with a 1.2-log-unit range of contrast sensitivities, and conventional (size III) perimetry with both 1.2-log-unit (open circles) and 3.5-log-unit (solid triangles) ranges. For size III with the 3.5-log-unit range, SD increased as mean decreased (P < 0.001), but this was not the case for FD or size III with a 1.2-log-unit range (P > 0.12).
There is very good evidence that the “regular” MC pathway can account for sensitivity to luminance flicker; it appears that MC cells can mediate contrast sensitivity for stimuli such as those used in FD perimetry: low spatial frequencies modulated at high temporal frequencies. These stimuli are in what Kelly 4 called the “high-velocity corner” of the spatiotemporal contrast-sensitivity surface. Behavioral studies in macaques with lesions showed that damage to the M-pathway reduces contrast sensitivity for this high-velocity corner. 6 Single-unit electrophysiology showed that M-cells have a signature characteristic of such psychophysical mechanisms. 4  
The origin of the FD percept is more difficult to pin down. We originally proposed it to be due to a loss of phase discrimination at a central site 2 and provided some other arguments against an origin in an My-based cell type. It is interesting to note that Y-like cells, although delivering a frequency-doubled response to counterphase-modulated gratings, also deliver a very strong first-harmonic response to such a stimulus at low spatial frequencies. Since the FD illusion is independent of spatial frequencies in the lower spatial frequency range (as shown in the recent paper by Maddess et al., 7 ), this would be in favor of the phase explanation rather than one involving Y-like cells. Another interesting point is that with the FD illusion, the transition areas between the flickering bars appear rather static (“null points”), yet this is the point at which the second harmonic (2F) response should be most obvious. In general, we have found it difficult to provide a strong link between the frequency-doubled response and the FD illusion. 
Footnotes
 Supported by National Institutes of Health Grants EY007716 (WHS), EY013112 (BBL), and EY019651 (DC).
Footnotes
 Disclosure: W.H. Swanson, Carl Zeiss Meditec (C); H. Sun, None; B.B. Lee, None; D. Cao, None
References
Maddess T Hemmi JM James AC . Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway. Vision Res. 1998;38(12):1843–1859. [CrossRef] [PubMed]
White AJ Sun H Swanson WH Lee BB An examination of physiological mechanisms underlying the frequency- doubling illusion. Invest Ophthalmol Vis Sci. 2002;43:3590–3599. [PubMed]
Swanson WH Sun H Lee BB Cao D . Responses of primate retinal ganglion cells to perimetric stimuli. Invest Ophthalmol Vis Sci. 2011;52(2):764–771. [CrossRef] [PubMed]
Swanson WH Time, color and phase. In: Kelly DH ed. Visual Science and Engineering: Models and Applications. New York: Marcel Dekker, Inc., 1994:191–225.
Sun H Dul MW Swanson WH . Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula. Optom Vis Sci. 2006;83(7):455–465. [CrossRef] [PubMed]
Merigan WH Maunsell JH . How parallel are the primate visual pathways? Annu Rev Neurosci. 1993;16:369–402. [CrossRef] [PubMed]
Rosli Y Maddess T Bedford SM . Low spatial frequency channels and the spatial frequency doubling illusion. Invest Ophthalmol Vis Sci. 2009;50:1956–1963. [CrossRef] [PubMed]
Figure 1.
 
Test–retest variability versus contrast sensitivity for FD perimetry (open triangles) with a 1.2-log-unit range of contrast sensitivities, and conventional (size III) perimetry with both 1.2-log-unit (open circles) and 3.5-log-unit (solid triangles) ranges. For size III with the 3.5-log-unit range, SD increased as mean decreased (P < 0.001), but this was not the case for FD or size III with a 1.2-log-unit range (P > 0.12).
Figure 1.
 
Test–retest variability versus contrast sensitivity for FD perimetry (open triangles) with a 1.2-log-unit range of contrast sensitivities, and conventional (size III) perimetry with both 1.2-log-unit (open circles) and 3.5-log-unit (solid triangles) ranges. For size III with the 3.5-log-unit range, SD increased as mean decreased (P < 0.001), but this was not the case for FD or size III with a 1.2-log-unit range (P > 0.12).
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