Comparison of human population receptive field estimates between scanners and the effect of temporal filtering

Participants

We recruited three healthy adult volunteers (2 female, 1 left-handed, aged 30, 39 and 47) from our pool of repeat participants in functional brain imaging studies in London, United Kingdom. An important criterion for their participation was that they would also visit Auckland, New Zealand, within a few months after the first scan in London. Generally, we could only include participants with normal or corrected-to-normal visual acuity (contact lenses only), and no history of eye disease or neurological, neurodevelopmental or neuropsychiatric disorders. Moreover, they could have no other contraindications to magnetic resonance imaging (e.g. claustrophobia, metal implants). All participants gave written informed consent to take part and henceforth referred to as P1, P2, and P3. All procedures were approved by local ethics review boards at University College London (fMRI/2012/007) and the University of Auckland (017477).

Procedure

Participants were scanned twice with a pRF mapping protocol. The first scan took place inside a MAGNETOM Avanto 1.5T MRI scanner (Siemens Healthcare, Erlangen, Germany) at the Birkbeck/UCL Centre for NeuroImaging (BUCNI) in the Experimental Psychology department of University College London, United Kingdom (henceforth referred to as London site). The second scan took place several months later in a MAGNETOM Skyra 3T MRI scanner (Siemens Healthcare, Erlangen, Germany) at the Centre for Advanced Magnetic Resonance Imaging (CAMRI) in the Faculty of Medical & Health Sciences of the University of Auckland, New Zealand (henceforth referred to as Auckland site). In both scans, participants were scanned with six runs for pRF mapping lasting 4 min 20 s each during which functional echo-planar images were acquired. Moreover, at both centres a structural T1 weighted brain image was acquired although the structural image from the second scan (at 3T) was not used in any further analysis. During the scans, participants were instructed to remain as still as possible and fixate continuously on a small dot in the centre of the screen. They were instructed to press a button whenever the fixation dot changed colour.

Stimuli

Stimuli were generated and presented using MATLAB (Mathworks; Version R2017a, 9.2.0.538062) and Psychtoolbox (Version 3.0.14)³³ at a resolution of 1920 * 1080. At both sites, the screen subtended 34° by 19° of visual angle. Stimuli were presented on a screen at the back of the bore via a mirror mounted on the head coil. At the London site, stimuli were projected onto a screen in the back of the bore while in the Auckland site stimuli were presented on an MRI compatible 32’’ widescreen LCD (Cambridge Research Systems Ltd).

At both sites, the stimuli generated were matched, and comprised bars containing a dynamic high-contrast ripple pattern as used in previous studies^6,13,15,22 on a uniform grey background. Bars traversed the visual field in a regular sequence (e.g. from the bottom to the top), jumping by 0.38° every second. Each sweep of the bar lasted 25 s and so there were 25 jumps of the bar. Each run started with a sweep from the bottom to the top and then the sweep direction was rotated by 45° clockwise on the next sweep. There were thus eight sweeps covering a complete rotation. After the fourth and eighth sweep, a 25 s baseline period (no bars) was presented.

Bars were always 0.53° wide and at the longest (when crossing the centre of the visual field) subtended the full screen height, but because they were presented only within a circular region (diameter: 19°, i.e. the height of the screen) they were accordingly shorter at the start and end of each sweep. The outer edge of the ripple stimulus was smoothed by ramping it down to zero over 0.1°. Similarly, the stimulus contrast ramped down to zero from 0.53° to 0.43° eccentricity, thus creating a blank hole around fixation.

A blue dot (diameter: 0.09°) was present in the centre of the screen throughout each scanning run. The whole run was divided into 200 ms epochs. At each epoch, there was a 0.01 probability that the dot could change colour to purple with the constraint that no such colour changes could occur in a row. Participants were instructed to fixate the dot and press a button on a magnetic resonance-compatible button box whenever it changed colour. In addition, a radar screen pattern comprising low-contrast radial and concentric lines around fixation was presented at all times to aid fixation compliance (see 25). The fixation dot and radar screen pattern were also presented during the baseline period.

Prior to each run, we collected 10 dummy volumes to allow ample time for steady-state magnetisation to be reached. During this time, only the fixation dot was presented on a blank grey screen.

Scanning parameters

At both sites, we used a 32-channel head coil where we removed the front elements because it impeded the view of the stimulus. This resulted in 20 effective channels covering the back and the sides of the head. Six pRF mapping runs of 260 T2*-weighted image volumes were acquired (including the 10 dummy volumes). We used 36 transverse slices angled to be approximately parallel to the calcarine sulcus (planned using the T1-weighted anatomical image). At both sites, we used an accelerated multiband sequence^34,35 at 2.3 mm isotropic voxel resolution, field of view 96x96, and a TR of 1 s. At the London site, the scan had an echo time (TE) of 55 ms, flip angle of 75°, and a multiband/slice acceleration factor of 4 and rBW 1628 Hz/pixel. At the Auckland site, the scan had a TE of 30 ms, flip angle of 62°, a multiband/slice acceleration factor of 3, an in-plane/parallel imaging acceleration factor of 2 and rBW was 1680 Hz/Px. After acquiring the functional data at the London site, the front portion of the coil was put back on to ensure maximal signal-to-noise levels for collecting a structural scan (a T1-weighted anatomical magnetization-prepared rapid acquisition with gradient echo scan with a 1 mm isotropic voxel size and full brain coverage).

Data preprocessing

Functional data were preprocessed in SPM12 (Wellcome Centre for Human NeuroImaging; Version 6906). The first 10 dummy volumes were removed. Then we performed mean bias intensity correction, realignment and unwarping of motion-induced distortions, and coregistration to the structural scan acquired at the London site using default parameters in SPM12. Using FreeSurfer (Version 6.0.0) we further used the structural scan for automatic segmentation and reconstruction as a three-dimensional surface mesh of the pial and grey-white matter boundaries^36,37. The grey-white matter surface was then further inflated into a smooth model and a spherical model.

All further analysis was conducted using our custom SamSrf 6 toolbox³⁸. Functional data were projected from volume space to the surface mesh by finding the nearest voxel located halfway between each vertex in the pial and grey-white matter surface mesh. The time series at each vertex was then linearly detrended and z-standardized before being averaged across the six runs at each scanning site.

For the temporal filtering analysis, we then further convolved the time series of each vertex with a Gaussian filter with standard deviation of 1 or 2 s, respectively.

pRF modelling

We modelled pRFs as a symmetric, two-dimensional Gaussian defined by x₀ and y₀, the Cartesian coordinates of the pRF centre in visual space, and the standard deviation of the Gaussian, σ, as a measure of the pRF size. The pRF model predicted the neural response at each TR of the scan by calculating the overlap of the mapping stimulus with this Gaussian pRF profile. A binary mask of 100-by-100 pixels indicated where the stimulus appeared on the screen for each time point. The neural responses were then determined by multiplying each frame of the stimulus mask with the pRF profile and summing over the 10,000 pixels. Subsequently, the time series was convolved with a canonical hemodynamic response function (HRF) determined from previous empirical data⁶ and z-standardized. The same HRF function was used for all participants given that the effect of individualized HRF on pRF parameters is expected to be small²⁵.

The pRF parameters at each vertex were fit using a two-stage procedure. First, we applied a coarse fit which involved an extensive grid search by correlating the actually observed time series against a set of 7650 predicted time series derived from a combination of x₀, y₀, and σ covering the plausible range for each parameter (see 25,29). The parameters giving rise to the maximal correlation were then retained for the second stage, the fine fit, provided the squared correlation, R², exceeded 0.01. The fine fit entailed an optimization procedure^39,40 to refine the three pRF parameters to further maximize the correlation between observed and predicted time series. Subsequently, we used linear regression between the observed and predicted time series to fit the amplitude, β₁, and the baseline intercept, β₀. Up until this point, all analyses used raw data without any smoothing or interpolation. However, we then applied a Gaussian smoothing kernel (full width at half maximum = 3 mm) to the final pRF parameter maps on the spherical surface mesh. These smooth maps were used for visualization purposes and delineation of the visual areas. Moreover, they are necessary for calculating the local cortical magnification factor (CMF; Harvey and Dumoulin⁴¹) because it requires a smooth visual field map without gaps and scatter. For this we determined the cortical neighbours of each vertex and calculated the area subtended by the polygon formed by their pRF centres. The same procedure was used to determine the cortical surface area (calculation performed by FreeSurfer). To calculate the CMF, we then divided the square root of cortical area by the square root of visual area.

In addition, for the data comparing the London and Auckland sites we also calculated the noise ceiling as an estimate of the maximum goodness-of-fit that could theoretically be achieved from the data of each voxel. For this, we split the six pRF mapping runs from each site into even and odd numbered runs and averaged them separately. We then calculated the Pearson correlation between these split time series, r_obs’, and used the Spearman-Brown prophecy formula^42,43 to determine, r_obs, the expected reliability for the average of all six runs:

The theoretical maximum observable correlation between the predicted and observed time series, ρ_o, for each voxel is given by the square root of this correlation⁴⁴ because

where r_pred is the reliability of the predictors, which is 1, and we assume the hypothetical correlation between the observed and predicted time series, ρ_h, also to be 1. The noise ceiling, the maximum observable goodness-of-fit ρ_o² is therefore equal to r_obs.

Further analysis

We manually delineated visual areas V1-V4 and V3A using smoothed maps from the London site by determining the borders between regions from the polar angle reversals⁴⁵ and then also applied these delineations to the maps generated in Auckland. For each region of interest (ROIs) we then extracted pRF data and binned them into eccentricity bands 1° in width, starting from 0.5° and increasing up to 9.5°. For each bin, we then calculated the mean pRF size, and the median CMF, R², noise ceiling ρ_o², or the normalized goodness-of-fit, that is R² divided by ρ_o². To bootstrap the dispersion of these summary statistics, we resampled the data in each bin 1000 times with replacement and determined the central 95% of this bootstrap distribution as a confidence interval. To avoid the inclusion of artifactual data, for pRF size and CMF we only included data from voxels where R² exceeded 0.15.

Comparison between scanning sites

We first compared visual field maps from the two sites, London 1.5T and Auckland 3T, by visual inspection. Figure 2 shows polar angle and eccentricity maps of the left hemisphere of one participant from both sites. It is immediately apparent that more voxels survive statistical thresholding (R²>0.1) for the 3T data. The cortical territory occupied by visual field maps is somewhat more extensive and more complete. Nevertheless, the orderly organization of V1-V4, V3A, as well as regions in the LO complex is clearly visible in both scans, and their borders are very similar. We further quantified the map similarity by calculating correlations across all voxels above threshold in both scans (circular correlation for polar angle, Spearman’s ρ correlation for eccentricity). This showed that the polar angle maps were well correlated for two participants (P1: 0.71; P2: 0.71) although the correlation was not as strong in the final participant (P3: 0.44). Eccentricity maps were strongly correlated in all three participants (P1: 0.70; P2: 0.75; P3: 0.67).

Figure 2.

Polar angle (A) and eccentricity (B) maps of one participant from the London 1.5T site (left) and the Auckland 3T site (right) displayed on a spherical model of the left hemisphere. Colour wheels denote the pseudo-colour code for visual field maps. No smoothing or interpolation was applied to the mapping data. Voxels were thresholded at R²>0.1. In A, the position of the visual regions have been labelled for reference. The greyscale indicates the cortical folding pattern.

Next, we compared pRF size using 1° wide eccentricity bands to bin the data from each site and then calculating the mean for each bin. We observed that pRF size consistently increased across eccentricities and also along the visual pathway as expected. But crucially, while pRF size varied somewhat between sites, this difference was not systematic across the five regions of interest (Figure 3A). In V4 and V3A there was somewhat greater variance at some eccentricities, likely due to the smaller size of these regions compared to V1-V3. Overall, pRF sizes were, however, very similar between sites. Similarly, the median cortical magnification factor (CMF) showed the expected exponential decrease from the central to the peripheral visual field. CMF curves were very comparable for the two sites (Figure 3B), except for somewhat greater CMF at 3T in V1 and V2 in the very central visual field of participants P2 and P3⁴⁶ (see supplementary figure 1A and B⁴⁶)) for individual participants’ pRF size and CMF respectively).

Figure 3.

Mean population receptive field (pRF) size (A) and median cortical magnification factor CMF (B), median goodness-of-fit (C), normalized goodness-of-fit (D), and noise ceiling (E) binned into eccentricity bands for the London 1.5T site (red) and the Auckland 3T site (black) and averaged across the three participants. Columns show different visual regions. Error bars denote ±1 standard error of the mean across participants.

We then repeated this analysis for the goodness-of-fit of the pRF model across eccentricities (Figure 3C). This showed that in V1 and V2 goodness-of-fit was notably greater for the Auckland 3T site than the London 1.5T site. In higher extrastriate regions, the pattern of results was less clear, although at least for P3 see supplementary figure 2 for individual participants data fitting results⁴⁶) goodness-of-fit was greater also in V3 and V4 (although note that in V4 for P1 very little data with very low model fits was present beyond 6° eccentricity in the Auckland data). In V3A, the model fits (see Figure 3C last column) at both sites were similar, but generally lower than in the other regions and with greater variability. However, this was presumably largely driven by the overall signal-to-noise ratio. When we normalized model fits relative to the noise ceiling, ρ o 2, the maximum goodness-of-fit that could theoretically be achieved given the data from each site, we found no systematic difference in goodness-of-fit between sites (Figure 3D). The curves mostly overlapped for P1 and P2 except in V1 where the London data outperformed the Auckland data (see Figure 2B). In contrast, for P3 normalized model fits for the Auckland site outperformed the London site in all regions except V3A. The noise ceiling itself was consistently higher for the Auckland data than the London data (Figure 4E).

Effect of temporal filtering

Goodness-of-fit of the modelled time course derived from pRF estimates and the measured fMRI time course are typically quantified by R². However, the pRF model does not account for the high frequency noise observed in fast temporal resolution acquisitions like the 1 s TR we used here, which therefore likely results in lower R² values. Theoretically, high frequency signals could be removed from the data and thus the model fits artifactually improved (Figure 1). We therefore reanalysed the data from the 3T site after temporal low-pass filtering the time series of each voxel by convolving it with a Gaussian kernel of either 1 s or 2 s standard deviation (e.g. Figures 1B and 1C, respectively).

Figure 4 shows visual field maps from the left hemisphere of one participant using the raw data and those after low-pass filtering. A very similar map structure is apparent in all three images. There are, however, also a lot of noise voxels surviving thresholding (R²>0.1) outside the general visual field maps. Conversely, while filtering filled in a few missing voxels within the maps, filtering did not affect the overall structure and did not increase the cortical territory of the responsive region.

Figure 4. Polar angle maps of one participant from the Auckland 3T site displayed on a spherical model of the left hemisphere.

Colour wheels denote the pseudo-colour code for visual field maps. No smoothing or interpolation was applied to the mapping data. Voxels were thresholded at R²>0.1. The position of the visual regions have been labelled for reference. The greyscale indicates the cortical folding pattern. A. Unfiltered data. B. Low-pass filtered with kernel 1 s. C. Low-pass filtered with kernel 2 s.

Next, we quantified mean pRF size and compared this for the three data sets (Figure 5A). In the early areas V1-V3, pRF size is consistently greater for the filtered time series, especially at the longer kernel of 2 s. In V4 and V3A, pRF size remained relatively similar between conditions. We also quantified the median goodness-of-fit of the pRF model (Figure 5B) and observed consistently greater model fits for both the low-pass filtered time series in V1 to V4. A similar pattern could be seen in V3A but results were generally more variable, especially in P1 (see supplementary figure 3 for individual participant results⁴⁶.

Figure 5.

Mean population receptive field (pRF) size (A) and median goodness-of-fit (B) binned into eccentricity bands for the Auckland data without filtering (black), and low-pass filtering with kernel 1 s (blue) and 2 s (green), averaged across participants. Columns show different visual regions. Error bars denote ±1 standard error of the mean across participants.

Raw results are available from Open Science Framework as Underlying data⁴⁷.

Underlying data

Open Science Framework: pRF data comparison between London 1.5T & Auckland 3T. https://doi.org/10.17605/OSF.IO/WX4HP⁴⁷.

This project contains Lon-Akl.zip, which itself contains underlying data for each participant in folders 30fl, 39mr and 47fr. These files each contain the following underlying data:

Extended data

Supplementary Figure 1.

https://osf.io/chtra

Mean population receptive field (pRF) size (A), median cortical magnification factor CMF (B) and response amplitude (beta) (C) binned into eccentricity bands for the London 1.5T site (red) and the Auckland 3T site (black). Panels in columns show different visual regions. Panels in rows show the three participants. Error bars denote 95% confidence intervals based on bootstrapping.

Supplementary Figure 2.

https://osf.io/chtra

Median goodness-of-fit (A), normalized goodness-of-fit (B), and noise ceiling (C) binned into eccentricity bands for the London 1.5T site (red) and the Auckland 3T site (black). Panels in columns show different visual regions. Panels in rows show the three participants. Error bars denote 95% confidence intervals based on bootstrapping.

Supplementary Figure 3.

https://osf.io/chtra

Mean population receptive field (pRF) size (A) and median goodness-of-fit (B) binned into eccentricity bands for the Auckland data without filtering (black), and low-pass filtering with kernel 1 s (blue) and 2 s (green). Panels in columns show different visual regions. Panels in rows show the three participants. Error bars denote 95% confidence intervals based on bootstrapping.

Data are available under the terms of the Creative Commons Zero “No rights reserved” data waiver (CC0 1.0 Public domain dedication).