Population receptive field estimates in human visual cortex

Abstract

We introduce functional MRI methods for estimating the neuronal population receptive field (pRF). These methods build on conventional visual field mapping that measures responses to ring and wedge patterns shown at a series of visual field locations and estimates the single position in the visual field that produces the largest response. The new method computes a model of the population receptive field from responses to a wide range of stimuli and estimates the visual field map as well as other neuronal population properties, such as receptive field size and laterality. The visual field maps obtained with the pRF method are more accurate than those obtained using conventional visual field mapping, and we trace with high precision the visual field maps to the center of the foveal representation. We report quantitative estimates of pRF size in medial, lateral and ventral occipital regions of human visual cortex. Also, we quantify the amount of input from ipsi- and contralateral visual fields. The human pRF size estimates in V1-V3 agree well with electrophysiological receptive field measurements at a range of eccentricities in corresponding locations within monkey and human visual field maps. The pRF method is non-invasive and can be applied to a wide range of conditions when it is useful to link fMRI signals in the visual pathways to neuronal receptive fields.

Fig. 1

Illustration of the stimuli. (A–D) Static images of the wedge, ring, mean-luminance and bar stimulus, respectively. Panels E–G illustrate how the stimuli change within a single fMRI scan. (E) The wedge rotates through 6 full cycles per scan. (F) The rotating wedge with the mean-luminance blocks (gray regions); mean-luminance replaces the wedges at four intervals in time. (G) The bar moves through each of four orientations in two opposing directions during one scan.

Fig. 2

A flow chart describing the pRF linear model estimation procedure. The pRF linear model is calculated for every voxel independently. See text for details.

Fig. 3

BOLD fMRI time-series from two voxels located in V1 (left panels) and lateral occipital cortex (LO, right panels). The circles in the top two panels (A and B) indicate the position of each voxel. The middle two panels (C and D) illustrate the responses to a conventional rotating wedge mapping stimulus. The arrows indicate the wedge orientations that elicit the strongest fMRI response; the peak response is slightly delayed with respect to the presentation of the best orientation due to the hemodynamic lag. The two cortical locations responded best to similar wedge positions, but the percent BOLD modulation in V1 is about three to four times stronger than the modulation in LO. The bottom two panels (E and F) show the responses to the new stimulus with mean-luminance blocks inserted (gray regions). In V1, the insertion of mean-luminance blocks replaces some presentations of the preferred wedge position (first and third block) and hence no fMRI modulation is observed. In LO, the insertion of mean-luminance blocks causes a drop in the BOLD modulation, demonstrating that this LO voxel is responsive to all wedge orientations.

Fig. 4

Example of a model fit to BOLD time-series at cortical samples in V1 (left panels) and LO (right panels, see Fig. 3). The model is simultaneously fit to the rotating wedge (A and B) and expanding ring (C and D) data. The best fitting Gaussian isotropic model is shown in the bottom row (E and F). The thick lines pass through the horizontal (y=0) and vertical (x=0) meridians, whereas the thin lines identify the pRF center. These models explain 72% and 68% of the variance in the time series, respectively. In panels A–D, the BOLD time-series are shown with dotted lines and black dots; the model fits are shown with solid lines (E and F). The response amplitude of the pRF models for a given stimulus is given by the integral within the stimulus aperture (see Fig. 2).

Fig. 5

pRF position estimates on an inflated cortical surface. The corpus collosum (CC) and the calcarine sulcus (CS) are labeled to clarify the orientation of the inflated cortical surface. The position maps are displayed on the enlarged part of the occipital lobe, as indicated by the large black square in (A). The maps for polar-angle (B) and eccentricity (C) are shown. The insets indicate the color map that defines the visual field representation. The boundaries between V1 and V3 are identified by the solid black lines.

Fig. 6

pRF size estimates on an inflated cortical surface. The pRF size maps are displayed on the enlarged part of the occipital lobe, as indicated by the black squares in the top two cortical surfaces. The colors indicate the different pRF sizes as shown in the color bar. The pRF size map for one subject is shown from the medial (A) and lateral view (B). The borders between visual field maps V1 and V3 are delineated by the solid lines. Lateral views from two additional subjects are shown in panels (C and D). The pRF sizes are much smaller in the maps near V1 than those on the lateral occipital surface. Supplementary Fig. 1 shows right, left, medial and lateral views for all three subjects.

Fig. 7

The percent of the pRF within the ipsilateral visual field is shown on an inflated cortical surface of one subject. The pRF in lateral (LO) and ventral (VO) occipital cortex overlaps substantially into the ipsilateral visual field.

Fig. 8

The relationship between eccentricity and pRF size in visual field maps V1–V3. Within each field, the pRF size increases with eccentricity. Furthermore, pRF size increases systematically from V1 to V3. Separate panels are data from separate subjects. The solid lines are fit to the data (circles) within each visual field map.

Fig. 9

A comparison between fMRI–pRF (A) and electrophysiological receptive field sizes (B) in visual field maps V1–V3. The average fMRI–pRF estimates are indicated by the solid lines from Fig. 8; the average of single- and multi-unit receptive field size measurements from the literature are indicated by the solid lines (Burkhalter and Van Essen, 1986; Felleman and Van Essen, 1987; Gattass et al., 1981; Gattass et al., 1987; Newsome et al., 1986; Rosa et al., 1988, 2000; Van Essen et al., 1984). We also plot LFP–pRF size and range estimates with a black square, white cross and dashed lines, respectively (Victor et al., 1994).

Fig. 10

The average relationship of the HRF width and estimated pRF size. The horizontal axis represents the full-width at half-maximum of the HRF. The vertical axis represents the pRF size. The data are averaged from three subjects. There is a weak inverse relationship (r=−0.1), suggesting that HRF variations cannot explain the large estimated pRF variations.

Fig. 11

The average BOLD fMRI time series in V1 (5°–9°) following a 3-s stimulus presentation. Each panel shows measurements from a different subject. The circles connected by the dotted lines show the measured data. The solid lines indicate the fit of the data with an HRF model using a difference of two gamma functions (Friston et al., 1998; Glover, 1999a; Worsley et al., 2002). The dashed line shows the HRF model prediction to a 1.5-s stimulus presentation. The HRF model explains 97.1%, 98.7% and 98.7% of the variance in the data (A–C, respectively).

Fig. 12

Illustration of the bias in pRF center estimates using phase-encoded methods. (A) The background image shows a theoretical pRF. The solid white line indicates the predicted BOLD response amplitude as a function of ring eccentricity. The maximal response is at a position slightly beyond the center of the pRF unit (large ring), not for the ring that overlaps with the center of the pRF (small ring). The phase-encoded method incorrectly takes the phase of the larger ring as an estimate of the pRF’s center. (B) The graph illustrates the eccentricity estimates of the phase-encoded method (y-axis) for different simulated pRF sizes (σ). These phase-encoded estimates deviate increasingly from the true pRF eccentricity (x-axis) as a function of eccentricity and pRF size. (C–D) The three graphs show the eccentricity estimates of the pRF model-based method (x-axis) versus phase-encoded method (y-axis) of one subject. The three graphs are divided according to the pRF size estimates similar to the pRF sizes used in the simulation (panel B). These plots indicate that (i) the phase-encoded estimates are close to the smooth curves predicted by the theoretical calculations, (ii) the eccentricity distortions do not appear in the estimates derived from the pRF model-based method, and that (iii) the pRF model-based method estimates the positions of near foveal pRFs with large sizes, while the phase-encoded method fails.

Fig. 13

The relationship between the HRF model parameters and the pRF size estimates for the same dataset. (A) The different HRFs used to estimate the pRF parameters are shown. The HRFs are generated by a 30% perturbation of the optimal HRF (thick lines, see Fig. 11) of both the one- and two-gamma HRF model (Boynton et al., 1996; Friston et al., 1998). (B) We computed the average pRF size in V1 to V3 between 1° and 13° eccentricity for each HRF. The resulting pRF sizes are plotted as a function of the HRF width (full-width at half-maximum, FWHM). Increasing HRF width yields decreasing pRF size estimates for the same data set. (C) The relative pRF size as a function of HRF width. The relative pRF size was computed by dividing the V1–V3 estimates by their mean for each HRF. The relative estimates are constant over a range of HRF width values.