Multifocal visual evoked potentials (mfVEP) were recorded simultaneously for both the target and the neighbor stimuli, each varying over 6 levels of contrast: 0%, 4%, 8%, 16%, 32%, and 64%. For most conditions, the relationship between the amplitude of target response and the contrast of the neighbor stimulus, as well as the amplitude of the response to the target stimulus, were described with a simple, normalization model. However, when the neighbor stimulus had a much higher contrast than the target stimulus, the amplitude of the target response was larger than the prediction from the normalization model. These results suggest that spatial interaction observed in the mfVEP requires (1) multiplicative mechanisms, (2) mutual inhibition between neighboring regions, and (3) a mechanism that saturates when the ratio between the contrasts of the target and that of the neighbor is large. A modified multiplicative model that incorporates these elements describes the results.

*R*is the amplitude of the response to stimulus

*t,*the target stimulus,

*R*

_{max}is the asymptotic amplitude of the response,

*C*

_{t}is the contrast of the stimulus,

*α*is the exponential term that alters the steepness of the CRF, and

*σ*is the semi-saturation contrast. Although this equation is only descriptive, it is thought that the nonlinearity may be due to the interactions among the neurons responding to the stimulus(Albrecht et al., 2002). In this study, we used the following formula for describing the CRF:

*α*and

*β*have been used for fitting the CRF of single cell data (Chen, Kasamatsu, Polat, & Norcia, 2001; Li & Creutzfeldt, 1984), VEP (Ross & Speed, 1991; Ross, Speed, & Morgan, 1993), and behavioral data (Xing & Heeger, 2000). For example, the amplitude of a response to a high contrast stimulus can be smaller than that of the response to a lower contrast stimulus, a phenomenon referred to as “oversaturation” (Li & Creutzfeldt, 1984; Regan, 1989; Sclar et al., 1990). Such data cannot be fitted by Equation 1, which is monotonic. Studies involving spatial interaction in the visual system of the monkey (Chen et al., 2001; Somers et al., 1998) have suggested that

*α*and

*β*are related to the excitatory and inhibitory modulations, respectively.

*C*

_{n}is the contrast of a neighbor stimulus, and

*k*is factor that determines the strength of the inhibitory effect.

*C*

_{t}is much larger than

*C*

_{n}, the effect of

*C*

_{n}can be neglected. When

*C*

_{t}is similar to

*C*

_{n},

*kC*

_{n}

^{β}effectively is added to the

*σ*

^{β}term, and thus the effective semi-saturation contrast is increased. This effect has been called a “contrast gain” change. In other words, spatial interaction changes the effective contrast of the target stimulus in the CRF, a result often found in electrophysiological and psychophysical studies (for a review, see Boynton, 2005; Kanwisher & Wojciulik, 2000; Reynolds & Chelazzi, 2004; Treue, 2001). In addition, the normalization model has been shown, with information theory, to allow the visual system to code nature images more efficiently (Schwartz & Simoncelli, 2001; Valerio & Navarro, 2003).

*.*

*n*is number of observations, RSS is residual sum of squares, and

*k*is the number of parameters in the model.

*R*) of this model is given by

*B*is the factor describing the strength of the spatial interaction,

*γ*is a power term that describes nonlinearity of the spatial interaction, and

*k*is a factor that describes the effective contrast of the neighbor stimulus. Note that when

*C*

_{ n}is zero,

*A*(

*1*+

*B*) is the

*R*

_{max}term in Equations 1, 2, and 3. Although it appears more complex, the spatial interaction term is a mathematic description of a sigmoid curve.

Subject | A | B | σ | α | β | γ | k | ΔAIC |
---|---|---|---|---|---|---|---|---|

1 | 0.77 | 2.54 | 9% | 2.16 | 2.19 | 1.87 | 1.27 | −17 |

2 | 0.70 | 2.02 | 18% | 1.33 | 1.85 | 2.72 | 1.30 | −31 |

3 | 0.67 | 2.17 | 17% | 1.63 | 2.08 | 4.07 | 1.37 | −26 |

*γ*term in Equation 5 is larger than 1. Therefore, when

*C*

_{ n}/

*C*

_{ t}deviates slightly from 1.0 (

*C*

_{ n}/

*C*

_{ t})

^{ γ}, and the spatial interaction term will change dramatically. This reflects the mutual inhibition between target and neighbor, where the stimulus with the slightly larger contrast exerts a much stronger influence than predicted by the difference in contrasts of the two stimuli. Consequently, the difference between target contrast and the neighbor stimuli is amplified. Third, the multiplicative model emphasizes the saturation of the spatial interaction when two stimuli have very difference contrasts. Therefore, a weak target stimulus among strong neighbor stimuli can remain visible because the spatial inhibition from the neighbor response is limited. In contrast, the normalization model describes the divisive inhibition as

*C*

_{ n}

^{ β}, where

*β*is larger than 1. Therefore, the normalization model predicts that the target response will approach zero when

*C*

_{ n}is large.