Antagonistic center–surround configurations are a central organizational principle of our visual system. In visual cortex, stimulation outside the classical receptive field can decrease neural activity and also decrease functional Magnetic Resonance Imaging (fMRI) signal amplitudes. Decreased fMRI amplitudes below baseline—0% contrast—are often referred to as “negative” responses. Using neural model-based fMRI data analyses, we can estimate the region of visual space to which each cortical location responds, i.e., the population receptive field (pRF). Current models of the pRF do not account for a center–surround organization or negative fMRI responses. Here, we extend the pRF model by adding surround suppression. Where the conventional model uses a circular symmetric Gaussian function to describe the pRF, the new model uses a circular symmetric difference-of-Gaussians (DoG) function. The DoG model allows the pRF analysis to capture fMRI signals below baseline and surround suppression. Comparing the fits of the models, an increased variance explained is found for the DoG model. This improvement was predominantly present in V1/2/3 and decreased in later visual areas. The improvement of the fits was particularly striking in the parts of the fMRI signal below baseline. Estimates for the surround size of the pRF show an increase with eccentricity and over visual areas V1/2/3. For the suppression index, which is based on the ratio between the volumes of both Gaussians, we show a decrease over visual areas V1 and V2. Using non-invasive fMRI techniques, this method gives the possibility to examine assumptions about center–surround receptive fields in human subjects.

*negative Blood Oxygenation Level-Dependent (BOLD) responses*(NBRs) have been reported in the visual cortex (Shmuel, Augath, Oeltermann, & Logothetis, 2006; Shmuel et al., 2002; Smith, Williams, & Singh, 2004). These NBRs are defined as BOLD responses below those elicited by viewing mean luminance gray (0% contrast). In addition, when identifying or reconstructing visual stimuli from the fMRI signals, local cortical sites may contribute either positively or negatively (Kay, Naselaris, Prenger, & Gallant, 2008; Miyawaki et al., 2008). The coupling between measured fMRI responses and the underlying neural activity is complex (for review, see Logothetis & Wandell, 2004) and neural inhibition per se may not necessarily result in a decrease of the BOLD response. Studies combining electrophysiology and fMRI report that these NBRs are caused by decreases in overall neural activation (Shmuel et al., 2006, 2002). They state that the NBR can be either caused by a suppression of the local neuronal activity and/or a decrease in afferent input, both caused by the activation of the positively responding regions. These results suggest that the neural center–surround organization influences the fMRI signal and also suggest that the spatial center–surround profile of the recorded neural population may be resolvable at the resolution of fMRI.

*population receptive field*(pRF; Dumoulin & Wandell, 2008; Victor, Purpura, Katz, & Mao, 1994). This method fits a model of the pRF to the fMRI data. We compare two models of the pRF. The original pRF method describes the pRF with one single circular symmetric Gaussian (OG) in the visual field. This model can only represent positive responses to stimulation in any region of the visual field and cannot, therefore, explain negative fMRI responses. We extended the current pRF model by incorporating a suppressive surround using a

*Difference-of-Gaussians*(DoG) function to represent the pRF. This model can account for suppression effects.

*repetition time*(TR) = 1500 ms,

*echo time*(TE) = 30 ms, and flip angle = 70°. The functional resolution was 2.5 × 2.5 × 2.5 mm, given a

*field of view*(FOV) of 224 × 224 mm.

^{3}isotropic. The functional MRI scans were aligned with the anatomical MRI using an automatic alignment technique (Nestares & Heeger, 2000). From the anatomical MRI, white matter was automatically segmented using the

*FMRIB's Software Library*(FSL; Smith, Jenkinson et al., 2004). After the automatic segmentation, it was hand-edited to minimize segmentation errors (Yushkevich et al., 2006). The gray matter was grown from the white matter and to form a 4-mm layer surrounding the white matter. A smoothed 3D cortical surface can be rendered by reconstruction of the cortical surface at the border of the white and gray matter (Wandell, Chial, & Backus, 2000).

*x*

_{0},

*y*

_{0}), size (

*σ*

_{1}), and amplitude (

*β*

_{1}). Here, we extend the pRF model to add an inhibitory surround. This model represents the pRF using a difference-of-Gaussians (DoG) function. The DoG model is made up of a subtraction of 2 Gaussian functions, in which the Gaussian with the largest standard deviation is subtracted from the smaller one. The center of the two Gaussians is at the same position, and therefore, the DoG adds two extra parameters to the model, the size of the negative surround (

*σ*

_{2}) and the amplitude of the surround (

*β*

_{2}). All parameters are in degrees of visual angle (°), except for the amplitudes (% BOLD/deg

^{2}/s). Restrictions of the DoG model are that

*σ*

_{2}is larger than or equal to

*σ*

_{1}, and

*β*

_{2}is negative with an absolute value that is smaller than

*β*

_{1}. These restrictions ensure a center–surround configuration.

*g*(

*x*,

*y*)) is defined as a combination of two Gaussians (

*g*

_{+}(

*x*,

*y*) and (

*g*

_{−}(

*x*,

*y*)):

*s*(

*x*,

*y*,

*t*). Combining the position of the pRF in the visual field with the stimulus positions over time, the response of the pRF,

*r*(

*t*), is obtained by calculating the overlap for each Gaussian. We obtain two values of

*r*(

*t*),

*r*

_{+}(

*t*) for the positive Gaussian and

*r*

_{−}(

*t*) for the negative Gaussian:

*p*(

*t*), is then calculated by convolution of the response of the pRF,

*r*(

*t*), with the HRF,

*h*(

*t*). Two different predictions of the time series are made: one for the positive Gaussian and one for the negative Gaussian of the pRF. Since the negative BOLD responses exhibit a similar HRF as the positive BOLD response (Shmuel et al., 2006), the same HRF (

*h*(

*t*)) is used for both parts of the pRF:

*β*(no 1) is used on

*p*(

*t*). This scaling factor accounts for the unknown units of the fMRI signal, which in turn represents the amplitude of the pRF.

*β*

_{1}is calculated by using a

*general linear model*(GLM) in which measurement noise,

*e*, is taken into account as well. The two values for the amplitudes of the Gaussians are calculated using a GLM with two unknown values for

*β*,

*β*

_{1}for the positive amplitude and

*β*

_{2}for the negative amplitude:

*x*

_{0}and

*y*

_{0}of the pRF model, values for the polar angle (atan(

*y*

_{0}/

*x*

_{0})) and eccentricity (√(

*x*

_{0}

^{2}+

*y*

_{0}

^{2})) can be calculated. By rendering these polar angle and eccentricity maps onto the inflated cortical surface (Wandell et al., 2000), the borders of the visual areas can be drawn on the basis of their location in the visual field (DeYoe et al., 1996; Engel et al., 1997; Sereno et al., 1995; Wandell, Dumoulin, & Brewer, 2007). Visual areas V1, V2, V3, V3a, hV4, and LO-1 are defined as

*regions of interest*(ROIs).

*σ*

_{1}) of a Gaussian to represent the positive part of the pRF. The DoG model subtracts a second Gaussian from the positive one to obtain the total pRF. This subtraction leads to a change in the effective positive pRF size. For this reason, the

*full width at half-maximum*(FWHM) was used to compare the effective positive pRF size. Figure 6 shows the relationship between eccentricity and FWHM in V1–V3. The averaged data are from the voxels of all subjects that have a variance explained >30% and with eccentricity values between 1.5 and 6 deg. The lines are fit by a linear regression analysis. Both the linear regression and the averaging procedure are weighted by the variance explained of the individual voxels. The error bars represent one standard error of the mean. For both models of the pRF, an increase of FWHM with eccentricity is shown as well as an increase of FWHM from V1–V3.

*σ*

_{2}and

*β*

_{2}. The addition of these extra parameters leads to a model with more degrees of freedom, which may result in an increase of the variance explained. Because the increase of variance explained is mostly seen in V1–V3 but not in higher visual areas, we do not expect that the gain in variance explained is solely caused by the extra parameters. If it would be just the addition of the extra parameters causing the gain in variance explained, one would expect to see this gain throughout the visual cortex.

*negative BOLD responses*(NBRs; Harel, Lee, Nagaoka, Kim, & Kim, 2002; Shmuel et al., 2006, 2002; Smith, Williams et al., 2004; Tootell, Mendola, Hadjikhani, Liu, & Dale, 1998; Wade & Rowland, 2010). Visual stimuli can elicit NBRs, typically adjacent to positively responding regions. Studies combining electrophysiology with fMRI in early visual cortex couple this NBR to a decrease in neural activation (Shmuel et al., 2006, 2002). Furthermore, the NBR shows a similar onset time and time course as compared to the positive BOLD response. Consequently, we believe that the negative signals are neuronal in origin. We extend these observations by showing that the negative parts of the measured time series can be explained by a center–surround configuration of the pRF.

*σ*

_{position_variance}

^{2}, as well as with the average receptive field size of the neuronal population,

*σ*

_{neuronal_RF}

^{2}(Dumoulin & Wandell, 2008):

*k*is a constant factor for capturing non-neural contributions to the pRF.

*k*= 0). Figure A1C shows a representation of the pRFs that are calculated for neuronal populations with different position variances. Increasing position variance leads to a decrease in center–surround configuration of the pRF. Specifically, the amplitude of the negative surround becomes less pronounced (Figure A1D).