The precision of attention controls attraction of population receptive fields

Abstract

We alter our sampling of visual space not only by where we direct our gaze, but also by where and how we direct our attention. Attention attracts receptive fields toward the attended position, but our understanding of this process is limited. Here we show that the degree of this attraction toward the attended locus is dictated not just by the attended position, but also by the precision of attention. We manipulated attentional precision while using 7T functional magnetic resonance imaging to measure population receptive field (pRF) properties. Participants performed the same color-proportion detection task either focused at fixation (0.1° radius) or distributed across the entire display (>5° radius). We observed blood oxygenation level-dependent response amplitude increases as a function of the task, with selective increases in foveal pRFs for the focused attention task and vice versa for the distributed attention task. Furthermore, cortical spatial tuning changed as a function of attentional precision. Specifically, focused attention more strongly attracted pRFs toward the attended locus compared with distributed attention. This attraction also depended on the degree of overlap between a pRF and the attention field. A Gaussian attention field model with an offset on the attention field explained our results. Together, our observations indicate the spatial distribution of attention dictates the degree of its resampling of visual space.

Introduction

Attention is often described as a zoom lens because it enhances visual perception at the attended location (Carrasco, 2011; Eriksen & St James, 1986). Voluntary spatial attention alters neuronal activity and representations of visual space (Carrasco, 2011; Datta & DeYoe, 2009; Fischer & Whitney, 2009; Kastner, Pinsk, Weerd, Desimone, & Ungerleider, 1999; Kay, Weiner, & Grill-Spector, 2015; Liu et al., 2022; McAdams & Maunsell, 1999; Moran & Desimone, 1985; Tootell et al., 1998; Tünçok, Carrasco, & Winawer, 2024; Vo, Sprague, & Serences, 2017). Attention attracts receptive fields (RFs) toward the attended location, resulting in better sampling at the attended location (Klein, Harvey, & Dumoulin, 2014; Klein et al., 2018; van Es, Theeuwes, & Knapen, 2018; Womelsdorf, Anton-Erxleben, Pieper, & Treue, 2006; Womelsdorf, Anton-Erxleben, K., & Treue, 2008). This RF attraction is thought to underlie improved spatial resolution and enhanced perception at the attended location—akin to a neural implementation of a zoom lens (Anton-Erxleben & Carrasco, 2013; Baruch & Yeshurun, 2014; Klein, Paffen, te Pas, & Dumoulin, 2016). However, the factors that determine the degree of attraction toward the attended locus (i.e., the magnification of the zoom lens) has yet to be elucidated.

Attention field (AF) models are widely used to describe and predict the influence of attention on cortical visual responses (Klein, Harvey, & Dumoulin, 2014; Puckett & DeYoe, 2015; Reynolds & Heeger, 2009; Womelsdorf et al., 2008). The Gaussian AF model summarizes both attention and RFs as Gaussians and their interaction as a multiplication of Gaussians (Klein et al., 2014; Reynolds & Heeger, 2009; Womelsdorf et al., 2008) (Equation 1; Figure 1A). This model predicts that the precision of the AF determines the attraction of RFs (Klein et al., 2014; van Es et al., 2018; Womelsdorf et al., 2006). In line with these predictions, attentional precision alters response gain and contrast gain (Herrmann, Montaser-Kouhsari, Carrasco, & Heeger, 2010; Itthipuripat, Garcia, Rungratsameetaweemana, Sprague, & Serences, 2014). Specifically, the AF model predicts that more precise, focused attention (i.e., a smaller Gaussian standard deviation) will result in stronger reweighting toward the attended locus (Figure 1A), under conditions of equal task difficulty and performance.

Figure 1.

(A) The AF model describes the influence of attention as a multiplication of a Gaussian AF with a Gaussian pRF (Klein et al., 2014; Reynolds & Heeger, 2009; van Es et al., 2018; Womelsdorf et al., 2008). Focused attention (a narrower Gaussian) attracts resulting attention-driven RFs more compared with distributed attention (a wider Gaussian). (B) (Top) One stimulus example. A color-proportion discrimination task is performed either across the entirety of the screen (distributed attention) or within the fixation circle (focused attention). (Middle) Illustration of the stimulus sequence during 1 fMRI volume acquisition. (Bottom) Time course of one experimental run. Each run begins and ends with a mean luminance fixation block, after which the attention task and bar passes begin. (C) Sensitivity (D′) for the focused and distributed attention conditions are indistinguishable.

Our aim was to investigate whether precision of attention indeed dictates the degree of attraction of population RFs (pRFs) toward the attended locus. We developed a paradigm to reconstruct pRF properties (Dumoulin & Wandell, 2008) while we manipulated the precision of attention (Figure 1B, Supplementary Movie S1). To maximize the difference in attentional precision, we used two conditions: attention directed at fixation (0.1° radius) and attention distributed across the entire screen (∼5° × 11°).

We observed blood oxygenation level-dependent (BOLD) response amplitude differences as a function of the task. pRFs falling within the stimulus extent of the focused task showed increased BOLD amplitude for the focused task. Similarly, pRFs falling within the stimulus extent of the distributed task showed increased BOLD amplitude for the distributed task. We also observed that the precision of attention alters pRF properties within visual field maps and along the visual hierarchy. The influence of attentional precision varies with increasing distance from the attentional locus. Additionally, these observations were well-captured by a Gaussian AF model with an offset on the AF.

Materials and methods

Participants

In the final analysis, 10 participants were included (5 female, aged 24–42 years); 3 participants were excluded (one for not completing all scanning sessions, one owing to poor signal-to-noise ratio because of distance from the coil, and one because behavioral performance in the two conditions were not matched). All participants had normal or corrected-to-normal visual acuity. This study was approved by the Human Ethics Committee of Vrije Universiteit Amsterdam and was conducted with informed written consent of all participants.

Experimental design

Visual stimuli were presented on an MR compatible Cambridge Research Systems LCD screen (69.84 × 39.29 cm; 1,920 × 1,080 pixels, 120-Hz refresh rate). The screen was located outside of the bore and participants viewed it through a mirror mounted on the coil, the screen was 210 cm from the mirror. For training on the task outside of the scanner, we used a comparable setup with an identical screen, screen distance, and visual stimuli.

The visual stimuli were created using the PsychoPy python package (Peirce, 2007) and the exptools2 wrapper for PsychoPy (https://github.com/VU-Cog-Sci/exptools2). A visual field mapping experimental design was used in combination with a demanding attentional task. A black diagonal fixation cross filled the screen and a fixation circle (0.1° visual angle radius) was placed in the center of the screen. An overview of the stimulus and task can be found in Figure 1B and Supplementary Movie S1.

Participants were instructed to fixate, to conduct a task, and ignore the checkerboard bar traversing the screen. The task was either focused within the fixation circle (0.1° visual angle radius) or distributed across the entire screen (5.6° × 11.1° visual angle). In both the focused and distributed conditions, the visual stimulus presented and the task participants carried out were identical. The only difference between these two conditions was the spatial extent to which participants would need to focus or distribute their attention to perform the task.

Across the screen (0.5°–5.0° height, 0.5°–11.0° width) a number of pink (RGBA:1,0.35,0.87,0.25) and blue (RGBA: 0.1,0.6,1,0.25) dots were presented on a mean luminance background. Simultaneously, within the 0.1° radius fixation circle, a number of identically colored dots were presented on a mean luminance background. Each trial consisted of 375-ms color-dot stimulus presentation and 375-ms interstimulus interval. The dot positions jittered trial by trial and each dot color was updated trial by trial.

The task was a color-proportion detection task. Participants were instructed to detect target trials where the proportion of dots filling the screen deviated from 50–50, becoming overall more pink or more blue. On non-target trials (i.e., no-response trials), the proportion of pink:blue dots was 50–50. Roughly 1 in 12 stimulus presentations was a target, and a jitter was used to avoid predictability. This proportion detection task becomes more difficult the closer the target trials are to the 50–50 proportion. To titrate the difficulty of the task and to match performance across conditions and participants, the target proportion was adjusted. Target proportions were set independently for each condition. A reaction time window of 1 second was used to log correct responses.

At the beginning of each run, participants were assigned a task condition (focused at fixation or distributed across the whole screen) that spanned the duration of the run. There were two mean-luminance fixation blocks at the start (20 seconds) and end (30 seconds) of every run, where no color-dot stimulus was presented. After the first 20-second fixation block, the color-dot stimulus was presented and the attentional task began.

The visual field mapper started 15 seconds after the start of the color-dot stimulus. A checkerboard bar (1.25° width, 50% Michelson contrast) was used as a visual field mapper. It traversed the screen within a circular aperture with a diameter of ∼10° of visual angle. The bar swept the screen with four orientations (0°, 45°, 90°, and 135°) and four motion directions (perpendicular to bar orientation), resulting in a total of eight bar passes per run. The checkerboard pattern within the bar also moved parallel to bar orientation. The bar motion was time-locked to the magnetic resonance imaging (MRI) acquisition and moved 0.625° each TR (1.5 seconds). There was a 15-second gap after every two bar sweeps, during which the attentional task continued. The bar sweeps were only presented within the duration of an attentional task. After the last bar sweep there is an additional 30 seconds of the task followed by 30 seconds of mean luminance fixation.

All participants were trained on the task prior to scanning to avoid learning effects during scanning. During training we also used a two-alternative forced-choice version of the task to set an initial task difficulty. In this task, on each trial participants would respond whether the stimulus presented was more pink or more blue. Again, participants either focused attention within the fixation circle or distributed attention across the entire screen. This task was used to obtain a psychometric curve for each participant for the two attention conditions. These psychometric curves were used to choose values of task difficulty that were matched for the two conditions and matched across participants. Following this two-alternative forced-choice task, participants trained on the color-proportion detection task (described elsewhere in this article) to be used in the scanner.

For each participant, six to eight runs of this experiment were collected in the scanner, as well as an independent pRF mapping session.

Independent visual field mapper

In addition to this experimental paradigm, a standard visual field mapping session was collected for all participants. The visual stimulus and task follow those outlined in the methods of Aqil, Knapen, and Dumoulin (2021) and Dumoulin and Wandell (2008). This visual field mapper used a contrast-defined checkboard bar traversing the screen on a mean luminance background. It moved in eight motion directions (4 cardinal, 4 oblique). Participants were instructed to fix their gaze on a dot at the center of the screen and press a button whenever the dot changed color. Attention toward the fixation may, therefore, influence pRF properties in the mapper; however, the independent mapper can never be an estimate of attention-free pRF properties because attention is always used, even without task demands. The primary use of the visual field mapper was to provide independent estimates and prevent circular analyses and regression to the mean (Stoll et al., 2022). The pRF parameters acquired from this independent mapper session were used for all the binning along eccentricity (Figures 2B and 2C, Figures 3D and 3E).

Figure 2.

Increased BOLD task responses are dependent on eccentricity and attentional precision. (A) Example participant V1 peripheral pRF time course (top) and V1 foveal pRF time course (bottom) showing response differences for the distributed and focused attention task. For the peripheral pRF, task response is increased for the distributed task relative to the focused task. Conversely, for the foveal pRF task response is increased for the focused task relative to the distributed task. (B) Task response difference (distributed task response minus focused task response) for pRFs in V1, binned for both tasks based on an independent pRF condition. The orange line at the top of the plot denotes the stimulus extent of the focused attention task, teal line denotes the stimulus extent of the distributed attention task. The results show that the response difference varies across eccentricity in line with the task extent. Each individual point is an average of all participants within each eccentricity bin. The solid purple line is an exponential function fit to the data. The shaded area denotes a bootstrapped 95% confidence interval of the exponential curve fit. (C) Task response difference across the visual hierarchy for pRFs within the distributed task stimulus extent (0.3–5.0 dva). Each point is an individual participant average. Error bars are the standard error of the mean. These results suggest that the response amplitude elicited by the color-dot stimulus is modulated by eccentricity and task.

Figure 3.

Focused attention more strongly attracts pRF position toward the fovea. (A) One example participant eccentricity map for distributed attention and (B) focused attention for one example participant. (C) Difference in eccentricity maps (distributed minus focused). Vertices were masked based on variance explained (R² ≥ 0.1) and eccentricity (<5°). (D) Eccentricity difference (distributed minus focused) across the visual hierarchy for pRFs falling within the distributed color task stimulus (0.3–5.0° radius). Values per participant are shown in the scatter plot nested within each bar, group averages in bar plots, and error bars are the standard error of the mean. (E) Eccentricity difference (distributed minus focused) for pRFs in each visual area binned for both tasks based on an independent pRF condition. The orange line at the top of the plot denotes the stimulus extent of the focused attention task (0–0.3° radius), the teal line denotes the stimulus extent of the distributed attention task (0.3–5.0° radius), and the dashed vertical line the boundary between the two tasks. The results show that pRF attraction is not uniform across eccentricity, with pRFs in V1 and V2 closest to the locus of attention showing more attraction (positive eccentricity difference) that is not visible in pRFs further away. Each individual point is an average of all participants within each eccentricity bin. The thick solid lines are exponential functions fit to the data. The shaded area denotes a bootstrapped 95% confidence interval of the exponential curve fit. All error bars are the standard error of the mean.

Statistics

We used both Bayesian and frequentist statistics to determine whether the two attentional conditions were matched in behavioral performance. The discriminability index (D′) for each condition was compared across participants (Figure 1C). JASP Bayesian analysis of variance was performed to test for evidence in favor of the null hypothesis. D′ was the dependent variable, the attention conditions were the fixed factors, and participant and run were modeled as random effects variables (van Doorn et al., 2021). We also used a frequentist linear mixed model, with the same dependent variable, fixed effect variables, and random effect variables.

For the functional MRI (fMRI) data, first a Shapiro–Wilk test was used to test for normality. The data were not normally distributed, so we used non-parametric statistical tests for subsequent analyses. We performed a Wilcoxon signed-rank test to determine whether task response (Figure 2C) and eccentricity (Figure 3D) differed significantly between conditions. To correct for multiple comparisons the false discovery rate (FDR) correction was used.

Eye tracking

Before carrying out the experiment in the MRI, participants were trained on an equivalent set-up (same screen properties and distance). During this training gaze position was recorded using an Eyelink 1000 (SR Research, Osgoode, Ontario, Canada). The eye tracker was calibrated using a five-point procedure. Owing to technical constraints, eye tracking data could not be recorded for all participants during the scanning session. For these participants without eye tracking data during scanning, gaze position recorded during the training session was used.

MRI data acquisition

All scans were acquired on a Philips Achieva 7T scanner with a 32-channel Nova Medical head coil.

T1-weighted MP2RAGE and T2-weighted turbo-spin echo structural MRI scans were acquired at a resolution of 0.7 mm isotropic (T1-weighted field of view = 220 × 220 × 200 mm³; matrix = 352 × 352 × 263; TR/TE = 6.2 ms/3 ms; flip angle_1/flip angle₂ = 5°/7°; TR_MP2RAGE/TI₁/TI = 5,500 ms/ 800 ms/2,700 ms; duration = 9 minutes 45 seconds; and T2-weighted field of view = 245 × 245 × 184 mm³; matrix = 352 × 349 × 263; TR/TE = 3,000/390 ms; TSE-factor = 182; duration = 7 minutes).

For functional scans, a two-dimensional EPI sequence was used with 60 coronal slices, 216 × 216 field of view, 1,500 ms TR, 23 ms TE, 65° flip angle, PA phase encoding direction, and 1.7-mm isotropic resolution. To avoid start-up magnetization transients, the first 10s of recorded data were discarded. Four top-up scans with opposing phase-encoding directions were collected throughout each scan session, which was later used for susceptibility distortion correction. Each run had a scan duration of 330 seconds (independent pRF mapper) or 390 seconds (attentional task experiment).

Preprocessing

The anatomical preprocessing pipeline by Heij et al. (2023) was used (https://github.com/gjheij/linescanning). MP2RAGE images were combined from the first and second inversions. Anatomical surfaces were reconstructed using Freesurfer 7.2 combining T1 and T2 images. Functional data was sampled to the reconstructed surface using the default fMRIprep pipeline (version 21; Esteban et al., 2019). BOLD volumes were averaged, linear de-trended, and converted to percent signal change before fitting procedures. This process was carried out separately for each experimental condition and separately for each participant.

AF models

The AF model is given by Equation 1:

$$\begin{array}{c}\hfill R\left({\mu }_3,{\sigma }_3\right)=A\left({\mu }_1,{\sigma }_1\right)*S\left({\mu }_2,{\sigma }_2\right),\end{array}$$ (1)

where μ and σ are the position and size of a Gaussian RF, A represents the Gaussian AF, and S represents the Gaussian stimulus-driven RF. R is the resulting attention driven RF, resulting from the multiplication of the stimulus-driven RF and Gaussian the AF. This model (Klein et al., 2014) has an analytical solution for the attention-induced position changes (Equation 2):

$$\begin{array}{c}\hfill {\mu }_3^{}=\frac{{\mu }_1{\sigma }_2^2+{\mu }_2{\sigma }_1^2}{{\sigma }_2^2+{\sigma }_1^2}\end{array}$$ (2)

$$\begin{array}{c}\hfill {\sigma }_3^2=\frac{{\sigma }_2^2{\sigma }_1^2}{{\sigma }_2^2+{\sigma }_1^2}.\end{array}$$ (3)

The position of the attention-driven RF is estimated by μ₃. μ₁ and σ₁ are the position and size of the Gaussian AF, respectively, and μ₂ and σ₂ are the position and size of the Gaussian stimulus-driven RF.

The AF+ model (Reynolds & Heeger, 2009; Womelsdorf et al., 2008), adds an offset to the AF (Figure 4) and is given by Equation 3:

$$\begin{array}{c}\hfill R\left({\mu }_3,{\sigma }_3\right)=a*\left[A\left({\mu }_1,{\sigma }_1\right)+b\right]*S\left({\mu }_2,{\sigma }_2\right).\end{array}$$ (4)

Figure 4.

Adding an offset to the AF improves predictions. (A) Predictions of the Gaussian AF model without an offset (AF model; Equation 1) when the SD-pRF and AF are far apart the resulting Gaussian has a very small amplitude. (B) Simulated predictions of this AF model, showing increasing or plateauing eccentricity difference with increasing eccentricity. (C) The AF model with an offset on the AF (AF+ model; Equation 3) does not result in infinitely small amplitudes when SD-pRF and AF are far apart, instead the relative influence of the AF becomes negligible and the resulting Gaussian is the SD-pRF. Instead when the SD-pRF and AF are closer, the influence of the AF is larger and there is a greater position change. (D) Simulated predictions of the AF+ model. For V1–V3, there are only position differences foveally and peripherally there are no differences. In higher visual areas, there is a plateau of differences along the eccentricity range. This model better captures the patterns in the data.

This AF+ model has two additional parameters, b, which is a constant added to the AF, and a, a scaling factor.

pRF and general linear model fitting

In every run, a block design was nested into the event-related experiment design. The blocks were 14 TRs (21 seconds) passive fixation, 224 TRs (5.6 minutes) attention task with pRF mapping, and 21 TRs (31.5 seconds) passive fixation (Figure 1B, bottom). We first truncated the time course to exclude the passive fixation blocks and any transient responses at the onset and offset of the task. pRF fitting was then performed on these truncated time courses using the Python package Prfpy (Aqil & Knapen, 2023) (https://github.com/VU-Cog-Sci/prfpy), following the procedure outlined by Dumoulin and Wandell (2008). Only pRFs with a variance explained of 0.1 or greater and with an eccentricity of less than 5° were used for subsequent analyses.

Next, on the uncut time courses, a general linear model was used to account for the blocks in the experimental design. The two passive fixation blocks served to estimate a BOLD baseline outside of the attentional task. The predictors in the design matrix were the predicted time course resulting from the pRF fitting, the attentional task, and two nuisance regressors at the TR for the task onset and offset. All regressors were convolved with a canonical hemodynamic response function. Least squares minimization was used. The beta value for the attentional task obtained from the general linear model is subsequently referred to as the task response (Figure 2).

AF model simulations

Using the size–eccentricity curves from the independent pRF mapper, pRFs were simulated to predict how their positions would be altered by simulated AFs. To do this, we used the AF model equations. Because stimulus-driven pRFs (SD-pRFs) are only hypothetical and cannot be measured, we simulated pRF positions and sizes to use as the stimulus-driven input. Two simulated AFs were used to mimic our experimental design: one with a small standard deviation and one with a larger standard deviation. Both simulated AFs were centered at 0. These simulated AFs when multiplied by the simulated SD-pRFs resulted in position differences. These position differences were used to fit the simulated AFs to the observed data, the eccentricity differences shown in Figure 3E. We used the exponential functions which captured the observed position changes across the eccentricity range (Figure 3E). These simulated position differences are shown in Figure 4B and 4D. Klein et al. (2014) demonstrated that a single AF could be used to explain effects along the entire visual hierarchy. Correspondingly, we used one shared AF across the entire visual hierarchy within each of our conditions. We further investigated two formulations of the AF model: the AF model with an offset on the AF (AF+) and without an offset on the AF (Figure 4). For the AF+, there is no formulaic solution. As a result, for each simulated attention-driven pRF arising from a multiplication with the AF+, we fit a new Gaussian function to provide an estimate for the center of mass of the resulting distribution.

Regions of interest

Visual field maps of eccentricity, polar angle, and pRF size were obtained from the independent pRF mapper for each participant. These maps were used to draw regions of interest (V1, V2, V3, hV4, V3ab, LO, TO, VO, lower IPS, and upper IPS) (Amano, Wandell, & Dumoulin, 2009; Swisher, Halko, Merabet, McMains, & Somers, 2007; Wandell, Brewer, & Dougherty, 2005; Wandell, Dumoulin, & Brewer, 2007).

Results

Behavioral performance for distributed and focused spatial attention is matched

As intended, participants performed the task comparably in the two conditions (Figure 1C) with an average D′ and standard error of 2.709 ± 0.089 and 2.745 ± 0.103 for the focused and distributed attention conditions, respectively. A permutation test was performed to obtain a null distribution for D′ (Figure 1C). All participants’ performance surpassed that of the null distribution, with no differences between the two attention conditions (linear mixed model, p = 0.941, i.e., no significant difference; Bayesian analysis of variance BF₀₁ 3.959, i.e., strong evidence that performance was similar). We also observed no significant differences in reaction time or criterion. Furthermore, all participants were trained to fixate comparably for the two conditions. Owing to technical constraints we could not record eye tracking for all participants in the scanner; however, we collected these data outside of the scanner for all participants. Fixation was comparable for our two experimental conditions. Thus, the focused and distributed attention conditions were matched in terms of behavior.

Responses elicited by color-dot stimuli are modulated by eccentricity and attentional precision

Attention increases responses in the attended parts of the visual field in line with both fMRI studies (Datta & DeYoe, 2009; Kastner et al., 1999; Müller, Bartelt, Donner, Villringer, & Brandt, 2003; Puckett & DeYoe, 2015; Tootell et al., 1998) and neurophysiology studies (Connor, Gallant, Preddie, & Van Essen, 1996; Luck, Chelazzi, Hillyard, & Desimone, 1997; Moran & Desimone, 1985; Reynolds, Pasternak, & Desimone, 2000). For V1 pRFs falling within the extent of the focused attention task (0°–0.3° radius), there was a higher BOLD task response for the focused attention task compared with the distributed attention task (Figure 2A and 2B). Conversely, for V1 pRFs falling within the extent of the distributed attention task (0.3°–5.0° radius), BOLD task response was higher for the distributed attention task compared with the focused attention task (Figure 2A and 2B). This result demonstrates a selective enhancement of the BOLD response for V1 pRFs encoding parts of the visual field where the task is being performed.

A limited number of pRFs fell within the 0.3° extent of the focused attention task, yet this pattern in the BOLD task response can still be observed across the visual hierarchy in peripheral pRFs. Across V1-3, hV4 and V3A/B, peripheral pRFs (0.3°–5.0° radius) showed positive task response differences (i.e., higher BOLD task response for the distributed task compared with the focused task) reflecting those seen in V1 (Figure 2C; Wilcoxon signed-rank test, FDR-corrected p_V1 = 0.009, p_V2 = 0.009, p_V3 = 0.009, p_hV4 = 0.009, p_V3A/B = 0.025). In some visual areas (LO, TO, VO, and IPS) this distinction was not significant. This could be due to the increased pRF sizes and smaller visual field maps in higher visual areas resulting in less clear distinction of foveal and peripheral signals.

Focused attention more strongly attracts pRF position preference

Across the visual hierarchy, precision of attention alters changes in visual spatial tuning. Eccentricity maps for the focused and distributed attention conditions are shown for one example participant in Figure 3A and 3B, respectively. Visibly, there are position differences in these maps with more foveal pRF positions for the focused attention task compared with the distributed attention task. Vertex-wise subtracting the pRF positions from each condition reveals smaller eccentricity values in the focused condition compared with the distributed condition. This means more foveal pRFs for the focused attention condition, indicating stronger attraction toward the attended locus (Figure 3C). Notably, this pattern of position changes can not be explained by foveal–peripheral differences resulting from the task. Were this the case, we would expect the opposite pattern of results, increased attentional effects for the distributed, more peripheral, task (Anton-Erxleben & Carrasco, 2013; Carrasco, 2011; Rosenholtz, 2016). Instead, we see the opposite—a stronger attraction toward the attended locus in the focused condition.

These results are in line with predictions from the AF model (Figure 1A). Moreover, these differences in attraction between focused and distributed attention are more pronounced higher up the visual hierarchy, plotted for peripheral pRFs in Figure 3D. The AF model also predicts this, as pRF sizes increase up the visual hierarchy so does the expected attraction toward the attended locus. The difference in position between the two tasks significantly differed for V3, hV4, V3A/B, LO, TO, VO, and IPS (Wilcoxon signed-rank test, FDR-corrected p_V3 = 0.009, p_hV4 = 0.009, p_LO = 0.035, p_TO = 0.035, p_VO = 0.035, p_IPS = 0.012). Although there were no significant differences in position change in V1 and V2 (Figure 3D), examining pRFs across eccentricity reveals non-linearities in the response depending on distance from the attended locus (Figure 3E).

Attraction depends on distance from the attentional locus

In early visual cortex (Figure 3E, V1–V3), greater attraction for focused attention compared with distributed attention was only seen in foveal pRFs (0°–0.3° eccentricity) falling within the stimulus range of the focused attention task. However, for peripheral pRFs (0.3°–5.0° eccentricity), falling within the eccentricity range of the distributed task, no significant differences in positions were observed. This result is better captured by an AF model with an offset on the AF (Figure 4). Without an offset, the AF model predicts the attraction of a RF toward the attended locus should linearly increase with distance from the attended locus (Klein et al., 2014). Further up the visual hierarchy where pRFs are larger, a constant difference between focused and distributed attention conditions was observed, with narrow attention resulting in a stronger attraction along the entire eccentricity range (Figure 3E). These results indicate that attraction of pRFs toward the attended locus is determined not only by the precision of attention, but also by the distance between a given RF and the attentional locus, with greater attentional influence resulting from greater overlap.

Importantly, this observed pattern of results cannot be explained by foveal peripheral differences. Both tasks are centered at fixation, making the focused attention task more foveal and the distributed task more peripheral. Many examples in the literature point to larger attention effects in the periphery because spatial resolution is poorer there (Anton-Erxleben & Carrasco, 2013; Carrasco, 2011; Rosenholtz, 2016). If our observations were purely a result of foveal–peripheral differences, we would expect stronger attention effects in the distributed condition since it is more peripheral. What we observed was the opposite, a stronger attraction toward the attended locus during the focused (i.e., foveal) task. Furthermore, when looking along the eccentricity range, this effect increased as pRFs became more peripheral (Figure 3E), in keeping with the literature (Anton-Erxleben & Carrasco, 2013; Carrasco, 2011; Klein et al., 2014; van Es et al., 2018). Thus, we can deduce the results are not due to foveal–peripheral differences.

We observed that the influence of attention is also a function of the amount of overlap between the SD-pRF and the AF. An attentional field model without an offset on the AF predicts the position change increase or plateau with distance from the attended locus and with increasing pRF size (Figure 4B). This AF model does capture the pattern of position we see in higher visual areas (LO, TO, VO, and IPS); however, it fails to capture the increase in position changes foveally in early visual areas (V1–V3) (Figure 3E). Moreover, this model further predicts that as the SD-pRF and the AF become increasingly far apart, the resulting attention-driven pRF amplitude approaches zero (Figure 4A). For this reason, this model discards the amplitude parameters and only takes into account the Gaussians’ positions and sizes.

Adding an offset of parameter to the AF (Figure 4C; Equation 2) (Reynolds & Heeger, 2009; Womelsdorf et al., 2008) better captures and contextualizes the results observed. With an offset on the AF, the relative contribution of the AF depends on the distance between the SD-pRF and the attentional locus. The influence of attention decreases with distance from the attended locus (Figure 4D). As the SD-pRF becomes farther from the attended locus, this model predicts that the resulting attention-driven pRF approaches the SD-pRF, that is, less attraction toward the attended locus for pRFs that are farther away. This phenomenon is present in our data within the early visual cortex (Figure 3E, V1–V3), characterized by smaller pRFs, resulting in less potential overlap with the AF. Indeed, as this model predicts, we observe that the influence of attention is present in pRFs close to the attentional locus declines with pRFs that are more distant from the attended locus.

Discussion

We used an fMRI attentional experiment to selectively manipulate the precision of attention while clamping attended location, visual stimulus, and task difficulty. This design narrowly constrained the spatial extent of attention in one condition and maximally distributed it in another. In comparing these conditions, we saw that attentional precision influenced two separate components of cortical responses. First, we observed modulation of the BOLD baseline in response to the task. Specifically, increased BOLD task response in cortical regions which spatially encode color-dot stimulus. This result is in keeping with the attentional gain modulation literature (Brefczynski & DeYoe, 1999; Kastner et al., 1999; Maunsell, 2015; McAdams & Maunsell, 1999; Moran & Desimone, 1985; Treue & Trujillo, 1999). Second, we observed changes in cortical spatial tuning. Within a region of interest, there was a greater overall re-weighting of the Gaussian population responses toward the attended locus for focused compared with distributed attention. This result follows predictions of the AF model (Klein et al., 2014; Reynolds & Heeger, 2009; Womelsdorf et al., 2008) and demonstrates that precision of attention acts as a magnification dial for the zoom lens of attention.

The attraction of pRFs toward the attended locus was not uniform across the eccentricity range. Our experimental design intentionally constrained the AF in the focused attention condition, allowing us to probe how distance from the AF influences attraction of pRFs. In early visual areas, where pRFs are small, position differences were largest closest to the attended locus and declined with distance from the attended locus (V1–V3; Figure 3E). In higher visual areas, with larger pRFs, attraction toward the attended locus increased and plateaued with distance from the attended locus (hV4–IPS; Figure 3E). Notably, these results could only be explained by an AF model with an offset on the AF (AF+, Figure 4C and 4D, Equation 3).

Although the AF model can capture the position changes in higher visual areas, it fails to capture the patterns observed in early visual cortex. The AF+ model (Figure 4C and 4D), which adds an offset to the AF encompasses all the predictions of the AF model (by having an offset of zero) and further extends it (when the offset is non-zero). Notably, in our simulations we fit a single shared AF for all visual areas field per condition. Because there are parameter trade-offs in the AF+ model, in Figure 4D, the pattern of differences in early visual areas is visible and the plateauing in higher visual areas is less well-captured. This perhaps suggests that, although all visual areas may share a uniform AF size, the offset on the AF may vary across visual areas. The AF+ model does not suffer from the limitations of the AF model and is able to capture the variety of effects observed along the eccentricity range and visual hierarchy.

Our task encouraged participants to distribute their attention in one condition by attending to a stimulus that spanned the entire screen. An inherent limitation of distributed attention paradigms is that it is possible that participants differed in how much and where they allocate attention. The same limitation is present in other paradigms of distributed attention (e.g., spatial uncertainty, using a neutral cue). Even if attention was not distributed evenly across the entirety of the screen, participants are forced to distribute their attention more than in the focused condition. Furthermore, if attention moves to different locations in the distributed attention condition, this would result in an averaged distributed AF as we averaged all runs within each condition. So, we can deduce that, even if there is variation in the degree to which participants distribute their attention, this design is sufficient for our purposes: investigating the influence of precision of attention on visual responses.

Even if participants only attended to a sub-area of the distributed task stimulus, by necessity of doing the task, they would still be distributing their attention more than in the spatial extent of the focused attention condition (0.1° radius). Consequently, even if attention was not spread across the entirety of the screen, the distributed condition would still be more distributed than the focused condition. Furthermore, if this sub-area was consistently in one location not centered on fixation, the pattern of position changes would be toward the sub-area they were attending (Klein et al., 2014; van Es et al., 2018; Womelsdorf et al., 2006). Depending on the attended sub-area location, this would result in a well-documented but different pattern of position changes than what we observe (Klein et al., 2014; van Es et al., 2018; Womelsdorf et al., 2006), namely, some pRFs becoming more foveal and others becoming more peripheral. Instead, we observed more foveal pRFs across the entire visual field for the focused attention condition compared with the distributed attention condition (Figure 3). If the sub-area they were attending to moved throughout the session, this would average to a distributed AF because we averaged all runs of the same condition. In fact, this would be akin to using spatial uncertainty as a means of distributing attention (Herrmann et al., 2010; Huang, Xue, Wang, & Chen, 2016; Itthipuripat et al., 2014). Despite being unable to resolve how much participants are distributing attention solely from behavior, the distributed attention task fulfills the intended purpose of the experiment: to focus attention in one condition and distribute it in another.

Could the observed data be explained by eye movement differences between the conditions? We do not believe differences in eye movements can explain our data. Unstable fixation would result in changes in pRF size but not position (Levin, Dumoulin, Winawer, Dougherty, & Wandell, 2010). However, in our data we observe changes in pRF position but no significant differences in pRF size (Supplementary Figure S1). Moreover, all participants were trained to fixate comparably in the two tasks outside of the scanner. Owing to technical constraints, we were not able to acquire eye tracking for all participants during scanning. For the participants for whom we also measured eye position and movements in the scanner during the tasks. We observed no differences between conditions. Thus, differences in eye movements cannot explain our data.

Where could the attentional modulation be coming from? In the present study, we were unable to investigate directly where attentional modulation may be coming from. Based on chemical inactivation studies in primates and transcranial magnetic stimulation studies in humans, frontal eye fields, superior colliculi, and posterior parietal areas are all candidates for the source of attentional modulation (Bollimunta, Bogadhi, & Krauzlis, 2018; Fernández, Hanning, & Carrasco, 2023; Krauzlis, Lovejoy, & Zénon,2013; Maunsell, 2015).

In this study, we are measuring pRFs. These pRFs differ from RFs, which are defined as stimulus locations that evoke or modulate neuronal responses (Hartline, 1938; Hubel & Wiesel, 1959; Sherrington, 1906). pRFs are a statistical summary of response properties of a population, in our case a population within a voxel measured using BOLD fMRI (Dumoulin & Wandell, 2008). Previous investigations have found concordance between the properties of pRFs measured with BOLD fMRI and those measured with invasive electrophysiology (Harvey et al., 2013; Klink, Chen, Vanduffel, & Roelfsema, 2021). In our data, we observed a change in the position preference driven by the precision of attention. This could be due to relative amplitude changes within the population that we measure, due to a change in position preference of the underlying neuronal population, or some combination of the two. Indeed, both changes in neuronal firing rates as a result of attention (Moran & Desimone, 1985) and changes in the spatial profile of single neurons (Womelsdorf et al., 2006) have been observed using invasive electrophysiology. With the techniques used in this study, we cannot disentangle which of these phenomena is the driver of our observations.

What is the relationship between pRF position changes and attentional gain? pRF position changes and attentional gain are closely related. Gain changes at lower levels will give rise to position changes at higher levels of the hierarchy (Compte & Wang, 2006; McAdams & Maunsell, 1999; Womelsdorf et al., 2008). This relationship is captured by the AF model: multiplying a SD-pRF by an AF (i.e., increased gain at the attended location) produces a spatial change in the resulting attention-driven pRF (Figure 1A). In this study, we observe both gain changes as a result of the attentional task (Figure 2) and spatial position changes arising from a difference in the precision of attention (Figure 3). However, Fox, Birman, and Gardner (2023), using a convolutional neural network, propose that gain changes, rather than position changes, are the main driver of the behavioral enhancement of attention. By independently manipulating gain, RF shifts, and RF sizes in their convolutional neural network, they concluded that gain modulation alone accounts for most of the behavioral enhancement. In the brain, these responses do not appear in isolation; they are entangled. So, further studies are required to continue to tease apart the underlying mechanisms responsible for attentional enhancement of perception in humans.

Would our observed attentional effects alter perception? Our behavioral paradigm cannot determine whether the cortical differences owing to attentional precision would also result in perceptual differences. However, previous behavioral studies indicate that attention can bias perception consistent with attraction toward the attended locus (Carrasco, 2018; Carrasco & Barbot, 2019; Klein et al., 2016).

Our results are in keeping with the zoom lens analogy for attention (Eriksen & St James, 1986; Müller et al., 2003). In this study, we demonstrated that precision of attention altered the attraction of RFs toward the attended locus. Specifically, more precise, focused attention resulted in a greater attraction toward the attended locus. These position changes were observed across the entire visual hierarchy. Interestingly, we observed that this attraction also depends on the degree of overlap between a pRF and the AF. These results were best captured by a Gaussian AF model with an offset on the AF.

Supplementary material

Supplementary Movie S1. Example video of part of the experimental stimulus and task. Pink and blue dots fill the screen, typically at a proportion of 50–50. Independently for the two conditions, there are target trials where the dot proportion deviates from 50–50 and becomes more pink or more blue. During the task, a black and white checkerboard bar traverses the screen. The video is contrast enhanced for the purposes of visualization.