Influence of Contrast on the Responses of Marmoset Lateral Geniculate Cells to Drifting Gratings

Jan Kremers,1 Luiz Carlos L. Silveira,2 and Bjørg E. Kilavik1

 1Department of Experimental Ophthalmology, University of Tübingen Eye Hospital, D-72076 Tubingen, Germany; and  2Departamento de Fisiologia, Universidade Federal do Pará, 66075-900 Belém, Pará, Brazil


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Kremers, Jan, Luiz Carlos L. Silveira, and Bjørg E. Kilavik. Influence of Contrast on the Responses of Marmoset Lateral Geniculate Cells to Drifting Gratings. J. Neurophysiol. 85: 235-246, 2001. The responses of lateral geniculate nucleus (LGN) cells in the common marmoset (Callithrix jacchus) to drifting luminance or cone isolating gratings of different spatial frequencies and contrasts were measured. The response noise, defined as the variability of the responses to single sweeps in the complex plane, was independent of stimulus contrast and spatial frequency but increased with increasing overall responsiveness of the cell. The signal-to-noise ratio of parvocellular (PC) cells was smaller than of magnocellular (MC) cells. At each contrast, the response amplitude as a function of spatial frequency could be described with a difference of Gaussians model. With this model, the sizes and the peak sensitivities of the receptive field centers and surrounds were estimated. It was found that receptive field center and surround sizes of LGN cells decrease slightly with increasing contrast. Further, the peak sensitivity decreases with increasing contrast. The two factors are involved in a decrease in responsivity (the response per unit contrast) with increasing contrast which is compatible to response saturation for low spatial frequency stimuli. PC cells did not saturate as much to luminance stimuli although some saturation was found with cone isolating gratings. We found that the response phase lag of both PC and MC cells decreased with increasing contrast, which cannot be explained on the basis of linear response behavior. Apparently the phase of LGN cell responses to drifting gratings is altered in comparison with the retinal inputs by additional nonlinearities.


    INTRODUCTION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The contrast of a visual stimulus is a quantification of stimulus strength and is an important factor to influence the magnitude of a visual response. Quite often the relationship between contrast and response amplitude is monotonic and sometimes even linear when the system under consideration is linear [such as the response of parvocellular (PC) retinal ganglion cells of macaques to luminance stimuli (Kaplan and Shapley 1986; Kremers et al. 1993; Lee et al. 1990, 1994)]. However, a response system is often not linear because the stimulus contrast has additional effects. Examples of such nonlinearities are saturation at high contrast and rectifying nonlinearities when cells are hyperpolarized. Another example is the contrast gain control that has been described in the responses of retinal ganglion cells and cells in the lateral geniculate nucleus (LGN) of cats (Shapley and Victor 1978, 1979, 1981) and monkeys (Kremers et al. 1997; Yeh et al. 1995a,b); this influences not only the response amplitude but also the response phase. At intermediate temporal frequencies (5-20 Hz), the contrast gain control involves an accelerating nonlinearity together with a decrease in phase lag when the contrast of the stimuli is increased (Shapley and Victor 1978; Yeh et al. 1995a). Although the nonlinearities are described extensively, only a few attempts have been made to look for their physiological origins.

It has been established that at low temporal frequencies the response amplitudes as a function of spatial frequency can be described with a difference of Gaussians (DOG) model (Croner and Kaplan 1995; Enroth-Cugell and Robson 1966). Model fits at the different contrasts of the gratings provide data on the sizes and sensitivities of receptive field centers and surrounds. In the present paper, the response properties of LGN cells are estimated using the DOG for a New World monkey: the common marmoset (Callithrix jacchus). The main topic of the present study is the relationship between the receptive field properties, as estimated with the DOG model, and stimulus contrast. In addition, some nonlinearities, that have not been described explicitly before, are apparent, and an attempt will be made to find some physiological origins for nonlinearities such as saturation.

Recent data show that contrast influences the receptive field sizes of neurons in the primary visual cortex (V1) of macaque monkeys (Sceniak et al. 1999). It has been suggested that contrast may have also an influence on the receptive field center sizes of retinal ganglion cells and of neurons in the LGN response owing to internal limitations at high firing rates (Lee et al. 1998). When the receptive field center size is estimated with bipartite field stimuli or gratings, either drifting or counterphase modulating, then the response amplitude depends on the position of the common edge of the bipartite field or on the spatial frequency of the grating. For the optimal edge position or the optimal spatial frequency, the responses of an LGN cell or a retinal ganglion cell might be constrained by intrinsic limitations. But only few direct data are available in the literature on the relationships between contrast and receptive field size in retinal ganglion cells and LGN cells. From comparisons of the center sizes of a limited amount of cells obtained with 75 and 10% contrast gratings, we previously concluded that contrast had only minor influence on the receptive field center size of marmoset LGN cells (Kremers and Weiss 1997). In the present paper, we reexamine the influence of contrast on receptive field sizes of a larger population of PC and magnocellular (MC) neurons in the marmoset LGN using measurements at more stimulus contrasts.

The signal-to-noise ratio of LGN cell responses in monkeys has not been studied intensively yet. In the macaque, PC and MC retinal ganglion cells have about the same internal noise (Croner et al. 1993). But there are large differences in response amplitude to luminance stimuli, resulting in differences in the signal-to-noise ratio (Kaplan and Shapley 1986; Lee et al. 1990). In the marmoset LGN, MC cells are more responsive than PC cells, but the difference is much smaller than in retinal ganglion cells (Kremers and Lee 1998) or LGN cells (Kaplan and Shapley 1982) of the macaque. If the noise in PC and MC cells is also similar in marmoset cells, then there is not much difference in the response quality between these cell groups. Alternatively there are differences in noise that are not present in the responses of retinal ganglion cells. In the present paper, we used an analysis of the cell responses that considers not only the response amplitudes and phases but also the variability of the responses as a measure for internal noise. With this analysis, the signal-to-noise ratio of PC and MC cells could be compared and the influence of contrast and spatial frequency could be studied.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Animal preparation

All animal experiments were conducted in accordance with the principles regarding the care and use of animals adopted by the American Physiological Society and the Society for Neuroscience.

The animals were initially sedated by an intramuscular injection of 15-30 mg/kg ketamine hydrochloride (Ketanest, Parke-Davies) and either 3.5 mg/kg xylazin hydrochloride with 1.5 mg/kg methyl-4-hydrobenzoate (0.15 ml/kg Rompun 2% solution, Bayer) or 1 mg/kg diazepam (Valium, MM Roche). The animals were respired with a mixture of 70% N2O and 30% O2 or carbogen. The animals were anesthetized with 0.2-0.8% enflurane (Ethrane; 0.4-0.8% during surgery and 0.2-0.4% during recordings) in the respired gas mixture. Two animals were anesthetized by a continuous intravenous application of 4-8 µg · kg-1 · h-1 sufentanil (Sufenta, Janssen) with an initial dose of 5 µg/kg sufentanil. Our observations confirmed previous reports that marmoset LGN cells are more responsive when the animals were anesthetized with sufentanil in comparison with isoflurane anesthesia, which is an isomere of enflurane (Solomon et al. 1999). To prevent eye movements, 5 mg · kg-1 · h-1 gallamine triethiodide (Flaxedil) was administered intravenously. A warming blanket connected to a rectal probe was used to maintain the rectal temperature at 37.2°C. Depth of anesthesia was controlled by continuous recording of electrocardiography (ECG) and electroencephalography (EEG).

The pupils were dilated with atropin sulfate (1%) and neosynephrine (5%). The eyes were refracted and focused on a tangent screen and the stimulus monitor at 114 cm distance with contact lenses. The contact lenses also protected the eyes against desiccation. Artificial pupils with 2 mm diam were placed in front of the eyes.

A craniotomy was performed, and a tungsten in glass electrode was lowered into the LGN. The layers from which we recorded were identified by the sequence of ocular input of the cells and from small lesions made at the end of the electrode track. After the experiments, the animals were killed by an overdose of pentobarbital sodium (Nembutal). Blood samples were obtained for genetic analysis. After perfusion, the brains were removed and prepared histologically to visualize the lesions.

The experiments were performed on 13 animals [10 dichromats (7 males, 3 females); 2 female trichromats; of 1 female the color vision phenotype could not be determined with certainty, but there was no indication of opponent responses in PC cells]. In 11 animals (6 males and 5 females), the present alleles on the gene locus coding for the cone photopigments were determined by a genetic analysis of blood samples of each animal (Weiss et al. 1998). In addition, the phenotype of the dichromats was determined electrophysiologically by searching for a silent substitution condition using the red and green phosphors of the computer controlled stimulus monitor (Weiss et al. 1998). Briefly, the red and green light sources were modulated in counterphase. The Michelson contrast of the modulation of the red phosphor was kept constant at 43%, whereas the Michelson contrast of the green modulation was varied between 5 and 80% in 5% steps. Dichromatic animals possess one of three possible cone photopigments in the middle and long wavelength range of the spectrum (with maximal absorption at 543, 556, or 563 nm). The excitation of each of these photopigments will not be modulated by the stimuli at a characteristic contrast of the green phosphor (the silent substitutions conditions: 32% for the 543-nm pigment, 45% for the 556-nm pigment and 54% for the 563-nm pigment). At high retinal illuminances, PC and MC cells receive their input exclusively from this cone type (they have no S-cone input, and the rod input will be negligible). The responses of the cells will therefore be minimal at the same stimulus conditions. Furthermore, reliable measurements on only a few cells are sufficient to determine the cone photopigment phenotype. The results from the genetical analysis and the electrophysiological measurements in the dichromats were always in agreement with each other.

Visual stimuli

The grating stimuli were presented on a BARCO monitor (CCID 7751 MKII) controlled by a VSG 2/2 graphics card (Cambridge Research System). The recordings in 11 animals involved stimuli in which the red and the green phosphors were activated with the same spatial phase, each with a mean luminance of 5 cd/m2. The gratings were therefore yellow and had a total mean luminance of 10 cd/m2. Because of the smaller marmoset eye, we calculated that the total retinal illuminance is about 4.9 times larger than in the human eye and is equivalent to about 150 td. Previous data have shown that at this retinal illuminance most cells will receive rod and cone input, although the cone input will generally dominate (Weiss et al. 1998). To exclude rod responses, we used in two animals (1 male, with a photopigment absorbing maximally at 563 nm; 1 dichromatic female, with a photopigment absorbing maximally at 543 nm) gratings that isolated the cone responses. The mean luminance in these measurements was 66 cd/m2. The red, green, and blue phosphors were modulated (with 20, 40, and 6 cd/m2 mean luminance, respectively) to provide a silent substitution condition for rods, thereby ensuring that the cell responses were determined solely by the activity in the cones. The stimulus contrast in these experiments was expressed in terms of cone contrast. The maximal cone contrast that was present in the stimulus was 37.3% for the animal with the 543-nm pigment and 50.5% for the animal with the 563-nm pigment. Thus, the dynamic range of the stimulus was smaller than with the luminance gratings.

Gratings of different spatial frequencies were drifted across the receptive field of the cells. The drift velocity was inversely related to the spatial frequency, so that the stimulus had a constant temporal frequency of 4 Hz, which is close to the optimal temporal frequency of most marmoset LGN cells (Kremers et al. 1997; Solomon et al. 1999). The responses were measured at each spatial frequency to gratings with Michelson contrasts between 18.5 and 100% for the luminance gratings and between 25 and 100% of the maximal cone contrast for the cone isolating stimuli. Each measurement lasted 6 s. The response amplitudes and phases were defined as the amplitudes and phases of the fundamental components (at 4 Hz) out of the Fourier analysis on the spike data. We estimated the internal noise amplitude by performing a Fourier analysis on each of the 24 cycles. The distances (Di) between the responses to the individual cycles and the geometric mean in a complex plane were calculated. The noise was defined as
<RAD><RCD><FR><NU>∑<IT>D</IT><SUB><IT>i</IT></SUB></NU><DE><IT>n</IT><IT>−1</IT></DE></FR></RCD></RAD>
in which n is the number of cycles (Croner et al. 1993).

The stimulus phase was defined as the phase of the red phosphor at the upper left corner of the monitor. The receptive fields were positioned at approximately the center of the monitor introducing large phase shifts in the cell responses. Although it is possible to correct for these phase shifts (Dawis et al. 1984), we did not do that because we were interested in the influence of contrast rather than spatial frequency on response phase. Therefore the response phase shifts relative to the response at 100% contrast are presented.


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Response amplitudes

We obtained measurements from 14 MC and 25 PC cells (of which 1 MC cell and 4 PC cells were measured in trichromatic animals) using the luminance gratings, whereas 15 MC and 6 PC cells (all from dichromats) were measured using the cone isolating gratings. In the former measurements, contrast is expressed as stimulus contrast (maximally being 100%), whereas in the latter stimulus strength is expressed in terms of cone contrast. The luminance gratings were used in two trichromatic animals. No obvious differences between the results obtained in dichromats and in trichromats were observed. Therefore we did not differentiate between the data obtained from dichromats and trichromats. Figure 1 shows the response and noise amplitudes of two MC and two PC cells to luminance gratings as a function of stimulus contrast. Similar to the responses of macaque retinal ganglion cells (Croner et al. 1993), the noise is fairly constant, indicating that the noise in the LGN cells is independent of stimulus contrast and response magnitude.



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Fig. 1. Response amplitude () and noise (open circle ) of 2 magnocellular (MC) cells (left) and 2 parvocellular (PC) cells (right) to luminance gratings as a function of the stimulus contrast. The curves are Naka-Rushton functions fitted to the amplitude data. The response amplitude increases with contrast, but the noise remains constant, indicating a increasing signal-to-noise ratio with increasing contrast.

In Fig. 2, the amplitudes of the responses [defined as the amplitude of the 1st harmonic component out of the Fourier analysis on the peristimulus time histograms (PSTHs)] of an off-center MC cell to luminance gratings at four contrasts are plotted as a function of spatial frequency. The noise calculated from the 75% contrast measurements is also plotted as a function of spatial frequency. Noise in the amplitude of the first harmonic was not influenced by the spatial frequency of the drifting grating.



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Fig. 2. Response amplitudes (, , black-down-triangle , black-lozenge ) of an off-center MC cell as a function of spatial frequency at 4 different contrast levels. The data are fitted with a difference of Gaussians' model (R = RC - RS = C{KCpi rC2 exp[-(pi rCnu )2- KSpi rS2 exp[-(pi rSnu )2]}). open circle , the calculated noise for the 75% contrast responses as a function of spatial frequency. The noise at the other contrasts is very similar because noise did not depend on contrast (see Fig. 1). Apparently, noise neither depends on spatial frequency. This was observed in all cells.

Although the internal noise can be large relative to the differences in response amplitude at different contrast levels, it is obvious that averaging the responses over the 24 cycles can nevertheless result in response data that are reliably different for different grating contrasts. From this we conclude that on the basis of the response to one cycle it would have been difficult to decide, for instance, whether a 100 or a 75% contrast grating was presented. On the basis of the averaged signal over 24 cycles (either by a temporal averaging of the responses of one cell or by the averaging of the responses of more cells), this decision can be performed reliably.

The response amplitudes are fitted with a DOG model (Rodieck 1965). Enroth-Cugell and Robson (1966) were the first to use this model to describe the response sensitivities of cat retinal ganglion cells to drifting gratings. For responses at different contrasts, this model was modified by Croner and Kaplan (1995) using the following mathematical formula
<IT>R</IT><IT>=</IT><IT>R</IT><SUB><IT>C</IT></SUB><IT>−</IT><IT>R</IT><SUB>S</SUB> = <IT>C</IT><IT>·</IT>(<IT>K</IT><SUB>C</SUB>&pgr;<IT>r</IT><SUP><IT>2</IT></SUP><SUB><IT>C</IT></SUB><IT> exp</IT>(−(<IT>&pgr;</IT><IT>r</IT><SUB><IT>C</IT></SUB><IT>&ngr;</IT>)<SUP><IT>2</IT></SUP>)<IT>−</IT><IT>K</IT><SUB><IT> 
S</IT></SUB><IT>&pgr;</IT><IT>r</IT><SUP><IT>2</IT></SUP><SUB><IT>S</IT></SUB><IT> exp</IT>(−(<IT>&pgr;</IT><IT>r</IT><SUB><IT>S</IT></SUB><IT>&ngr;</IT>)<SUP><IT>2</IT></SUP>)) (1)
in which R is the total response of the cell and RC and RS are the responses of the center and surround, respectively. They are assumed to be antagonistic, which is approximately true at the 4 Hz temporal frequency. At higher temporal frequencies, this assumption might not be valid, owing to a small latency difference between center and surround responses (Enroth-Cugell et al. 1983; Frishman et al. 1987; Gouras and Zrenner 1979; Smith et al. 1992; Yeh et al. 1995a). C in Eq. 1 is contrast, KC and KS [imp · s-1 · (% contrast)-1 · (deg)-2] are the peak sensitivities of the center and the surround, respectively, normalized to their area. The factors rC and rS are the center and surround radii, respectively. The fits to the response amplitude data are displayed in Fig. 2. The amplitude axis is linear rather than logarithmic (which is the more commonly used) because the definition of fit errors were defined as sum of the linear distances between the fits and the data points. Defining the errors as distances in a logarithmic amplitude plot would have resulted in a larger weighting of the low-amplitude data, despite of the lower signal to noise ratio at these conditions, and might result in less satisfactory fits.

It is of interest to estimate how the signal-to-noise ratio varies between individual cells. The overall responsiveness of a cell was quantified by averaging the three largest responses encountered. The mean noise level was calculated by averaging the noises at all stimulus conditions that resulted in a reliable response (defined as being larger than 2.5 imp/s). In Fig. 3, the mean noise and overall responsiveness of individual MC and PC cells are plotted against each other. There is a positive correlation between the two. Interestingly, PC cells display more internal noise than MC cells. The average signal to noise was 2.26 ± 0.90 for PC cells and 3.23 ± 1.18 for MC cells. This difference was significant (unpaired t-test on the logarithms of the ratios to make the data normally distributed: P < 0.005).



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Fig. 3. The mean of the noise [average of the response noises at all stimulus conditions to which the cell responded with a reliable response (more than 2.5 imp/s)] in individual cells as a function of the overall responsiveness of the cell (the mean of the 3 maximal responses encountered in all measurements). No distinctions were found between the measurements using the luminance and the cone isolating gratings.

The best fits of the DOG model were determined in an iterative manner. First, the whole space of model parameters was scanned for the parameter combination resulting in the least error (quantified by the sum of distances between the data points and the model predictions). The steps in the parameters were fairly coarse, so that the best fit gave only a first approximation. Subsequently, a more detailed search was performed around this first approximation. This procedure was repeated five times. With this procedure, a good fit was obtained while minimizing the chance of being captured in a "local minimum."

The center size (rC) and center sensitivity (KC) could be determined relatively precisely. These parameters were mainly determined by the data points in the high-frequency range (see also (Linsenmeier et al. 1982) for a discussion of how the fits are constrained by the data). To study how well the fits were constrained by the data, we repeated the fits while fixing the surround parameters at those values obtained from the grand fits (i.e., the fits in which all the parameters were free) and varied the center size. The center peak sensitivity was estimated at each center size from fits to the data using the solver routine of the Excel97 program. For each fit the error was calculated. A very similar method was used by Linsenmeier et al. (1982). The errors displayed a sharp minimum (Fig. 4A). The center size and peak sensitivity at this minimum were nearly identical to those estimated from the grand fits (Fig. 4A, ). From this, we conclude that the center parameters were well constrained by the data and that the center size could be determined with a precision of less than 1 min of arc.



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Fig. 4. Fitting error (left axes, ---) and peak sensitivities at best fits (right axes, · · ·) as a function of the chosen radius of the center (A) and the surround (B). The remaining parameters were fixed at the values obtained from the grand fits. For both center and surround, it can be seen that the fitting errors display a sharp minimum, defining the optimal combination of radius and peak sensitivity. The estimated parameters from the grand fits () are close to these optimal combinations, indicating that the grand fits indeed were well constrained by the data.

In some cases, the response amplitude roll-off at low spatial frequencies was very small or not distinguishable. We assumed that the surround sensitivity was very small in these cases. However, in most measurements a response amplitude roll-off at low spatial frequencies was observed (see Fig. 2 for an example). In those cases, the surround parameters were estimated from the fits. To establish the reliability of the surround parameter estimates, we repeated the above described procedure for the surround, i.e., we kept the center parameters constant and varied the surround size (rS). With the solver routine of the Excel97 program, we searched for the surround sensitivity (KS) that best fitted the data. We again found that the error displayed a sharp minimum and the surround parameters at this minimum were close to the estimates from the grand fits (see Fig. 4B), suggesting that the data did constrain the surround parameters well and that the grand fits were able to find the best describing surround parameters.

To compare the difference between MC and PC cells and the influence of retinal eccentricity, we only considered the responses at 25% contrast, at which the cells responded reliably without being to strongly distorted by saturation or other nonlinearities. For the cone isolating stimuli we used the responses to approximately 25% cone contrast. The results did not depend on the grating type (luminance or cone isolating) used as stimulus and were therefore lumped. In Fig. 5, the center radii (rC) are displayed as a function of retinal eccentricity. These are the distances between the center and the point where the sensitivity has decreased to 1/e times the peak sensitivity (Enroth-Cugell and Robson 1966). In measurements with bipartite field stimuli, the radius is defined as the standard deviation of the center or surround Gaussian, which is 1/radical 2 times the radii (rC and rS in Eq. 1) estimated from the responses to the drifting grating (Kremers and Weiss 1997). Three cells identified as PC cells (the encircled data points in Fig. 5) had relatively large receptive field centers. These cells were found at the borders of one of the PC layers of the LGN and therefore might actually be koniocellular (KC) cells, which are located in the interlaminar regions of the LGN. Alternatively, these might be recordings from "giant" PC cells as identified by Rodieck and Watanabe (1993). It can be seen that the differences between PC-cell and MC-cell center radii are too small, to be significant. However, in agreement with previous results, the linear regressions show that MC and PC cells have similar center sizes close to the fovea but that MC-cell center sizes increase more steeply with eccentricity than PC-cell center sizes (Kremers and Weiss 1997). The linear regressions are y = 8.81 + 0.57x (y is center radius in min of arc; x is retinal eccentricity in degrees) for PC cells and y = 9.13 + 0.65x for MC cells.



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Fig. 5. Receptive field center radii (rC) of PC cells () and MC cells (open circle ), measured with 25% contrast luminance gratings or cone isolating stimuli resulting in approximately 25% cone contrast, as a function of receptive field eccentricity. The PC cells with relatively large receptive fields (odot ) were found at the borders of the PC layers and therefore might actually be koniocellular (KC) cells.

We could also confirm previous findings (Croner and Kaplan 1995) that the sensitivity and radius of the center are closely related (Fig. 6). Only the estimated center parameters for the 25% contrast luminance gratings or approximately 25% cone contrast cone isolating gratings were used in Fig. 6. The linear regressions in this double logarithmic plot have a slope of -1.25 for PC cells and -2.13 for MC cells. A linear regression to all data points showed a slope of -1.58. The relationship between KC and rC can therefore be described as KC = a · rC-1.58 in which a is a constant. A similar relationship was found for the centers of macaque PC-retinal ganglion cells (Croner and Kaplan 1995). For stimuli containing exclusively low spatial frequency components (such as spatially homogeneous stimuli) Eq. 1 can be simplified to
<IT>R</IT><IT>=</IT><IT>R</IT><SUB><IT>C</IT></SUB><IT>−</IT><IT>R</IT><SUB><IT>S</IT></SUB><IT>=</IT><IT>C</IT><IT>·</IT>(<IT>K</IT><SUB><IT>C</IT></SUB><IT>&pgr;</IT><IT>r</IT><SUP><IT>2</IT></SUP><SUB><IT>C</IT></SUB><IT>−</IT><IT>K</IT><SUB><IT>S</IT></SUB><IT>&pgr;</IT><IT>r</IT><SUP><IT>2</IT></SUP><SUB><IT>S</IT></SUB>) (2)
Inserting the preceding relationship between KC and rC in Eq. 2 results in
<IT>R</IT><SUB><IT>C</IT></SUB><IT>=</IT><IT>Car</IT><SUP><IT>−1.58</IT></SUP><SUB><IT>C</IT></SUB><IT>&pgr;</IT><IT>r</IT><SUP><IT>2</IT></SUP><SUB><IT>C</IT></SUB><IT>=</IT><IT>Ca</IT><IT>&pgr;</IT><IT>r</IT><SUP><IT>0.42</IT></SUP><SUB><IT>C</IT></SUB> (3)
indicating that the center response amplitude to low spatial frequency stimuli does increase slightly with the size of the center. This might result in a response amplitude that is positively correlated with retinal eccentricity. A positive correlation between contrast gain to spatially homogeneous stimuli and retinal eccentricity is indeed described for marmoset LGN cells (Solomon et al. 1999).



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Fig. 6. Center sensitivity (KC) as a function of the center radius for PC cells () and MC cells (open circle ). The linear regressions in this double logarithmic plot have a slope of -1.25 for the PC cells and -2.13 for the MC cells. odot , from cells that were found on the borders of the PC layers.

In the measurements with the luminance gratings, the surrounds of five PC cells (20%) and seven MC cells (50%) were very weak so that a low spatial frequency roll-off was not observed. With the cone isolating stimuli, this was the case for one PC cell (16%) and five MC cells (33%). In these cases, only center parameters were estimated.

To study the influence of contrast of the luminance gratings on the receptive field size and receptive field sensitivity, we normalized the data at each contrast to the estimates obtained at 100% contrast for the same cell, thereby excluding the effects of retinal eccentricity and of variability between individual cells. These ratios are not normally distributed. To obtain an approximately normal distribution of the data, the logarithms of the normalized data were calculated on which an ANOVA was performed. We also calculated the means from these logarithms and converted them back to nonlogarithmic data to display the overall tendency.

The normalized center peak sensitivities and radii of the individual cells are displayed in Fig. 7 as a function of contrast. In these, and the next plots, only the data with the luminance gratings were considered because they spanned the whole contrast range between 0 and 100%. Unless explicitly stated, the results of the measurements with the cone isolating stimuli showed basically the same effects as those with the luminance gratings despite of the smaller contrast range in these measurements. Contrast has slight but consistent effects on the sizes and the sensitivities of MC cells (Fig. 7, A and B). Most ratios at lower contrasts were larger than unity, indicating that the receptive field center size and peak sensitivity increase with decreasing contrast. The ANOVA showed that the effects of contrast on the radius and the sensitivity were significant (F test; P < 0.025 for the radius and P < 0.025 for the sensitivity). The ratios for the centers of PC cells were more variable and were not biased to values larger or smaller than unity (Fig. 7, C and D). Accordingly, the ANOVA did not reveal a significant influence of contrast on the PC-cell center sizes and sensitivities. The measurements with the cone isolating stimuli revealed also an increase in center size and peak sensitivity with decreasing contrast. These effects were, however, observed for both PC and MC cells.



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Fig. 7. Center radii (top) and peak sensitivities (bottom) of individual MC (left) and PC cells (right). To exclude a confounding with other effects such as retinal eccentricity and differences between individual cells, the data have been normalized to the center characteristics at 100% contrast. In the MC cells, a small but significant increase in center sizes and center peak sensitivities with decreasing contrast of the gratings can be observed. This increase is not present in the responses of the PC cells.

In Fig. 8 the means of the center radii and sensitivities are plotted separately for MC and PC cells, once more showing the moderate but significant effect of contrast on the MC-cell center size and sensitivity and the less strong effect on the PC-cell properties. By definition, the cells' center responsivities [the responses divided by the stimulus contrast given in imp/(s. % contrast)] to low spatial frequency stimuli are proportional to the peak sensitivity and to the square of the radius (see Eq. 2). Because the center radii and sensitivities of MC cells depended significantly on contrast, it was not surprising that contrast also had a significant effect on the responsivity of MC-cell centers (F test; P < 0.005; Fig. 8A). Contrast had also a significant effect on the responsivity of PC-cell centers (F test; P < 0.01; Fig. 8C) albeit less strong. A decreasing responsivity with increasing contrast is equivalent with response saturation. By multiplying the mean responsivities with contrast, the mean normalized response amplitudes can be calculated. These are plotted in Fig. 8, B and D. The lines are fitted Naka-Rushton functions to the calculated normalized responses. These are often employed to describe the response amplitudes as a function of contrast (Croner and Kaplan 1995; Kaplan and Shapley 1986; Kremers et al. 1997; Lee et al. 1990). Indeed, they can also describe the mean normalized center response amplitudes in a satisfactory manner. We also measured the maintained firing activity of the cells in the absence of a stimulus. The first harmonic component of the maintained firing activity can be regarded as the response at 0% stimulus contrast and was about 5% of the first harmonic component at 100% contrast. Clearly, the MC-cell responses to low spatial frequencies saturate more strongly than the responses of PC cells. The measurements to cone isolating gratings showed that both center sizes and peak sensitivities increased with decreasing cone contrast in PC and MC cells. Thus the responses to low spatial frequency cone isolating stimuli seemed to saturate in both cell groups.



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Fig. 8. Mean normalized receptive field center peak sensitivities and radii as a function of contrast displayed separately for MC (A; 1 cell was measured in a trichromatic animal) and PC cells (C; 4 cells were measured in trichromatic animals). Especially in the MC cells the center sensitivity and radius decrease with increasing contrast. The product of the peak sensitivity and the square of the radius is proportional to the responsivity of the cells to low spatial frequency stimuli. The responsivities of PC and MC cells decrease significantly with increasing contrast, indicating response saturation. The product of responsivity and contrast is proportional to the response amplitude. Bottom: the resulting responses, normalized to the responses at 100% contrast. ---, fits of Naka-Rushton functions to the normalized response amplitude data. The response amplitude at 0% stimulus contrasts was assumed to be about 5% of the response amplitude at 100% contrast. There is a clear saturation in the center responses of MC cells. The saturation in the PC-cell centers is smaller. Similar effects were observed in measurements with the cone isolating gratings, despite of the more limited dynamic range.

The mean surround parameters estimated from the measurements with the luminance gratings are displayed in Fig. 9. The responsivity of MC-cell surrounds decreased significantly with increasing contrast (Fig. 9A; F test; P < 0.005), although neither the surround radius nor surround peak sensitivity depended significantly on contrast. As a result, the surround responses of MC cells to low spatial frequency stimuli saturate. The normalized response amplitudes of MC-cell surrounds are shown in Fig. 9B. Again, the data can be fitted with a Naka-Rushton function. The peak sensitivity, the surround radius, and the responsivity and of PC-cell surrounds did not show a significant dependence on contrast (Fig. 9C). As a result the surrounds of PC cells did not saturate (Fig. 9D). With the cone isolating gratings, no consistent changes in the surround parameters were observed.



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Fig. 9. Mean normalized receptive field surround sizes and peak sensitivities of MC (A) and PC cells (C). The data show that the responsivity of MC-cell surrounds to low spatial frequency stimuli decreases with increasing contrast. This decrease is mainly caused by an decreasing peak sensitivity. The surround size does not change. Thus the responses of MC-cell surrounds saturate at high contrasts (B). The size and the peak sensitivity of PC-cell surrounds do not change with changing stimulus contrast. As a result, the responsivity does not change either (C) and the responses (D) do not show any signs of saturation. --- in B and D, fits with Naka-Rushton functions to the response amplitude data. The measurements with the cone isolating stimuli did not show consistent effects, possibly owing to the smaller dynamic range.

Response phases

We measured the response phase shift at each contrast relative to the response phase at 100% contrast. In Fig. 10, the mean phase shifts of responses to luminance gratings measured in 21 PC and 8 MC cells are displayed as a function of stimulus contrast for four different spatial frequencies. The measurements of four PC cells and one MC cell were performed in trichromatic animals. We did not find any obvious differences in the response phases between cells from trichromats or dichromats. The data of four PC and six MC cells (all from dichromats) were not used for the plot, because other contrasts and spatial frequencies were used in the measurements on these cells. A separate analysis of the data from these cells gave very similar results. For both MC and PC cells, the response phases increase (and thus the phase lags decrease) with increasing contrast. A phase change with increasing contrast was previously described in MC cells but not in PC cells (Kremers and Lee 1998; Kremers et al. 1997; Lee et al. 1994; Yeh et al. 1995a,b).



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Fig. 10. The mean response phase shift at different contrasts relative to the response phase at 100% contrast measured in 21 PC and 8 MC cells. The phase shifts have been plotted for 4 different spatial frequencies. It can be observed that the responses of PC and MC cells shift with decreasing contrast. The phase shifts of the PC cells seem to increase with increasing spatial frequencies. Similar effects were observed in the measurements with the cone isolating stimuli. The data of 4 PC and 6 MC cells were not used for these plots because other contrasts and spatial frequencies were used in the measurements on these cells. However, similar effects were found.

The data displayed in Fig. 10 further indicate that the PC-cell response phases lagged the responses at 100% especially for higher spatial frequencies. To pursue this issue, we plotted the phase shifts at three different stimulus contrasts as a function of spatial frequency (Fig. 11). The linear regressions suggest that the extent of the PC-cell response phase shift increases with increasing spatial frequency. The phase shifts in MC-cell responses are apparently present at all spatial frequencies.



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Fig. 11. Phase shifts of PC and MC cells as a function of spatial frequency for 3 different contrast levels. Despite the noisiness of the data, the linear regressions confirm that PC-cell phase shifts increase with increasing spatial frequencies. At 0.05 cycles/°, the phase shifts are small. A dependency of the phase shift on spatial frequency is not present in the MC cells.

Despite of the smaller range of contrasts, the responses of PC and MC cells to cone isolating stimuli showed similar phase shifts as described in the preceding text for the luminance gratings.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The responses of retinal ganglion cells and neurons in the LGN of cats and monkeys to drifting or counterphase modulating gratings have been studied intensively before (Croner and Kaplan 1995; Enroth-Cugell and Robson 1966; Enroth-Cugell et al. 1983; Frishman et al. 1987; Linsenmeier et al. 1982). However, to our knowledge, this is the first study in which the effects of stimulus contrast on cell parameters have been investigated in detail. Furthermore we considered the noise in the cell responses.

Response saturation

Our data confirm previous data that MC-cell responses display a stronger response saturation to low spatial frequency stimuli than the responses of PC cells when using luminance gratings. With cone isolating stimuli, only minor differences were apparent. The response saturation is present in the centers and the surrounds. Our data further indicate that response saturation in the centers is related to two different processes: one caused by a decrease in peak sensitivity, the other involving a decrease in receptive field size. Although the decrease in receptive field radius is relatively moderate, it contributes substantially to the response saturation because the response amplitude is proportional to the square of the radius. It has been suggested before that stimulus contrast might influence the receptive center and surround size (Lee et al. 1998), but to our knowledge this was never substantiated by direct data. In the present paper the effects of contrast on cell response properties are explicitly investigated.

Receptive field sizes

Although the data seem to suggest that the decrease in receptive field center size contributes to response saturation, it is possible that the two are causally unrelated. Possibly, a third independent process, such as internal response limitations in the retinal or the LGN cells, is the cause for both saturation and the center size decrease. One possible internal limitation might reside in the spike generating mechanisms of the retinal ganglion cells and/or the LGN cells. By comparing generator potential with the spike behavior measured during intracellular recordings from cat retinal ganglion cells, Lankheet et al. (1989) proposed a threshold elevation in the spike-generating mechanism after the occurrence of a spike. This elevated threshold decayed exponentially with a time constant which was about 50 times larger than the time constant of the absolute refractory period of the cell. These slow recovery rates will substantially limit the largest response rate that a cell can achieve. If the spike rate of the cells, or the retinal ganglion cells providing the input, is high and approaches the maximally possible rate, then additional stimulus strengths will lead to a smaller than expected increase in the response amplitude, which is equivalent to response saturation. This type of saturation is independent of internal saturation processes that might occur in the generator potentials. Additional rate limitations may originate at the synaptic transmission in the LGN (Kaplan et al. 1987).

Figure 12 visualizes how response rate limitations can lead to an apparent decrease in receptive field center size. Original response data of an MC cell at 18.5% luminance contrast () with the model fit (---) are shown. In this cell, no obvious surround effects were measured. The model fit predicts a center radius (rC) of 25.2 min of arc. The open circle  are the responses to a higher contrast. It has been assumed that the responses at this contrast were about a factor 1.7 larger than the responses at 18.5%. In addition, the response amplitudes were not allowed to exceed the amplitude measured with the lowest spatial frequency of the 18.5% contrast gratings. This results in an increased spatial corner frequency and thus to a decreased apparent center size. The model fit to these data (· · ·) shows that the estimated center sizes has decreased by a factor of about 1.5 to 16.8 min of arc. Similar processes have been proposed to be involved in the responses to bipartite field stimuli in which the common edge of the halves of the stimulus is located on different positions relative to the receptive field (Lee et al. 1998) or to stimuli with varying sizes so that the spatial summation of a cell is measured (Sceniak et al. 1999).



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Fig. 12. Visualization of how response clipping can lead to a decrease in receptive field center size. , the responses of an MC cell as a function of spatial frequency using a 18.5% contrast drifting grating. The effect of the surround in the responses was negligible in this cell. The drawn curve is the model fit to these data. From this model fit, the estimated center radius is 25.2 min of arc. We then simulated the responses at a higher contrast by increasing these original response amplitudes by a factor of about 1.7. At the same time, the response amplitudes were not allowed to exceed the response amplitude measured with the lowest spatial frequency of the 18.5% contrast grating. · · ·, the model fit to these simulated data. The estimated center size using these data has decreased by a factor of about 1.5 to 16.8 min of arc.

To check whether response rate limitations can result in a decrease of the receptive field center size that is of the same order of magnitude as was actually measured, we reanalyzed the responses of five MC cells for which we obtained center response measurements at all contrasts. The responses to 18.5% contrast were used to simulate the responses at higher contrasts. It was assumed that the response is the result of two independent processes: an internal response (possibly the generator potential) and a spike-generating process. Saturation can occur in both processes.

We first assumed that the internal response increased linearly with increasing contrast. Further, the simulated response amplitude was not allowed to exceed the maximally measured response amplitude. We estimated mean sizes and peak sensitivities of the receptive field centers from these simulated responses and compared them with the actually measured receptive field center parameters (Fig. 13). The response rate limitations result in an increase of the peak sensitivity KC, whereas the sensitivities estimated from the real data decrease (Fig. 13A). From this we conclude that the decrease in KC has a physiological origin that is independent of the response rate limitations and might reflect saturation processes in the internal response. Because the response rate limitations would even lead to increases in the peak sensitivity, the presumed saturation in the internal response is probably larger than the saturation in the peak sensitivities.



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Fig. 13. Simulations of the effects of response clipping on the mean center peak sensitivity (A) and mean center radius (B) of 5 MC cells for which the responses at all contrasts could be measured.  --- , the center sizes and peak sensitivities estimated directly from the measurements. down-triangle  · ·  down-triangle, the mean center sizes and mean peak sensitivities estimated from simulated data in which the original responses at 18.5% contrast were used to predict the response amplitudes at the higher contrasts. It was assumed that the internal response amplitude (possibly in the generator potential) increases linearly with contrast and that the response amplitudes do not exceed the highest measured response rate. It can be seen that the center sizes estimated from these simulated data decrease with increasing contrast. But the decrease is larger than in the estimates based on the actual measurements. The peak sensitivities of the simulated responses increase with increasing contrast, whereas the peak sensitivities estimated from the original data decrease.  - - - , the results of a second simulation in which it was assumed that the internal responses saturate in a similar manner as the peak sensitivity (KC) and that the response amplitudes do not exceed the maximally measured response amplitude. Apparently, the change in center sizes and peak sensitivities using the simulated responses approximate the estimated changes using the real data more closely.

The simulated center sizes depend similarly on contrast as the sizes estimated from the measurements, suggesting that response rate limitations can indeed be the cause for a change in receptive field center size (Fig. 13B). Furthermore, the changes in receptive field center sizes mainly occur above 50% contrast which is also present in the simulations. But the calculated decrease in center size is larger than is estimated from the real data. This discrepancy is probably caused by our assumption that the internal response increases linearly with contrast, thereby neglecting the a priori saturation in the internal response. We therefore repeated the simulation but now incorporated an intrinsic sensitivity decrease. From the responses at 18.5% contrast, we calculated the responses at the other contrasts assuming an a priori internal response saturation that can be described by the saturation in the averaged estimated peak sensitivities (KC). As discussed before, the saturation of the averaged KC values is possibly an underestimation of the actual saturation of the internal response, but it is the best available estimate. The averaged KC values plotted against stimulus contrast could be described in a satisfactory manner by a Naka-Rushton function. The best-fitting Naka-Rushton function was used to describe the internal responses at the higher contrast. The response rate limitations clipped the responses when the calculated responses exceeded the maximally measured rate. The results of this simulation is also displayed in Fig. 13. It can be seen that indeed the calculated response size and peak sensitivities are now relatively close to the estimates obtained from the real measurements, although there are still some deviations. These deviations might be the result of the underestimation of the internal response saturation. Thus it seems that response rate limitations can indeed account for the change in receptive field center size and at least partially for the response saturation. The maximal response rate varies between cells, indicating that the response rate limitations are also variable. As a result, the change in receptive field center size will not depend on the absolute response rate of the cell.

We conclude that at least two independent processes are probably involved in response saturation: an internal response saturation and a limitation in the maximally feasible response rate. In addition to response saturation, the latter process will lead to a decrease in center size.

All the preceding processes might occur exclusively in the retinal ganglion cells. A saturation in the ganglion cell responses will also lead to a saturation in the LGN-cell responses. But the signal transmission ratio between the input and the output of LGN cells decrease with increasing contrast (Kaplan et al. 1987), indicating that at least some response compression occurs in the LGN cells.

There was no obvious relationship between surround size and stimulus contrast. At the spatial frequencies that are low enough to stimulate the surround, the responses are determined by the antagonistic activity in the center and the surround. The resulting response amplitudes are therefore generally too small to be affected by response rate limitations. This might account for the constant surround size.

Response phases

Earlier data on retinal ganglion cells and LGN neurons show that PC cells did not display phase shifts with spatially homogeneous luminance stimuli. The response phase shifts found in MC cells using the same stimuli are believed to be caused by a contrast gain control mechanism (Kremers and Lee 1998; Kremers et al. 1997; Lee et al. 1994; Yeh et al. 1995a,b). The phase shifts found for PC cells described in this paper indicate the presence of a nonlinearity that not has been described before for PC cells. However, the previous studies either involved recordings from retinal ganglion cells (Croner and Kaplan 1995; Lee et al. 1990) or from LGN recordings in combination with spatially uniform stimuli (Kremers et al. 1997). Possibly the nonlinearities causing a phase shift can only be found in LGN cells and not in retinal ganglion cells belonging to the PC pathway and are only apparent when high spatial frequencies are involved. Indeed, our data indicate that LGN cells belonging to the PC pathway show the phase shift only at higher spatial frequencies.

The data indicate that the magnitude of phase shifts versus contrast functions depends on spatial frequency. On the basis of the presented data, it is not possible to determine the influence of the spatial frequency on the response phase per se because we did not determine the response phase in relation to the relative positions between receptive field and the stimulus. The direct relationship between response phase and spatial frequency has been described for retinal ganglion cells and LGN cells of cats (Dawis et al. 1984) and macaques (Benardete and Kaplan 1997).

Signal to noise ratios in PC and MC cells

Our data are in agreement with a previous study (Croner et al. 1993) that the response noise of macaque retinal ganglion cells does not change with contrast and spatial frequency of the stimulus. Croner et al. found no correlation between noise and maintained activity of the cell and nor with cell type. Our data indicate that there is a correlation between noise and overall responsiveness (quantified by the mean of the three largest responses encountered in all measurements). Moreover, the signal-to-noise ratio of PC cells is significantly lower than of MC cells. The sensitivity difference to luminance modulation of PC and MC cells in the marmoset LGN is smaller than in the retina (Kremers and Lee 1998). Possibly there is a general downscaling of the MC-cell responses at the level of the LGN involving both signal and noise.


    ACKNOWLEDGMENTS

The authors thank E. Burkhardt for technical support and P. Martin and S. Solomon for comments on the manuscript.

J. Kremers was supported by Deutsche Forschungsgemeinschaft (DFG) (German Research Council) Grant SFB 430 C3 and a DFG Heisenberg fellowship (Kr 1317/5-1). L.C.L. Silveira is a Conselho Nacional de Desenvoluimento Científico e Tecnológico research fellow. L.C.L. Silveira and J. Kremers were supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Grant 079/99 and Deutscher Akademischer Austauschdienst Grant 415-br-probral/bu. J. Kremers and B. E. Kilavik were supported by DFG Grant Zr 1/9-3.


    FOOTNOTES

Address for reprint requests: J. Kremers, Dept. of Experimental Ophthalmology, University of Tübingen Eye Hospital, Röntgenweg 11, D-72076 Tubingen, Germany (E-mail: jan.kremers{at}uni-tuebingen.de).

Received 26 May 2000; accepted in final form 21 September 2000.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

0022-3077/01 $5.00 Copyright © 2001 The American Physiological Society