Numerosity tuning in human association cortices and local image contrast representations in early visual cortex

Human early visual cortex response amplitudes monotonically increase with numerosity (object number), regardless of object size and spacing. However, numerosity is typically considered a high-level visual or cognitive feature, while early visual responses follow image contrast in the spatial frequency domain. We find that, at fixed contrast, aggregate Fourier power (at all orientations and spatial frequencies) follows numerosity closely but nonlinearly with little effect of object size, spacing or shape. This would allow straightforward numerosity estimation from spatial frequency domain image representations. Using 7T fMRI, we show monotonic responses originate in primary visual cortex (V1) at the stimulus’s retinotopic location. Responses here and in neural network models follow aggregate Fourier power more closely than numerosity. Truly numerosity tuned responses emerge after lateral occipital cortex and are independent of retinotopic location. We propose numerosity’s straightforward perception and neural responses may result from the pervasive spatial frequency analyses of early visual processing.


Reporting for specific materials, systems and methods
We require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response. Quantitative -functional magnetic resonance imaging (fMRI) We acquired fMRI data from eleven participants (aged 25-39 years, one female, one left-handed). All had normal or corrected-tonormal visual acuity, good mathematical abilities and were well educated. The rationale for selecting a research sample of healthy neurotypical participants is that we were interested in studying normal brain function.
We acquired fMRI data from a convenience sample of 11 researchers (aged 25-39 years, one female, one left-handed). Six of these were members of our lab and associated labs, five were graduate students from elsewhere in Utrecht University and University Medical Center Utrecht recruited through advertising. No sample size calculation was performed, as all data were originally collected for other studies (Harvey & Dumoulin, 2017, Nature Human Behaviour;Harvey, Dumoulin, Fracasso & Paul, 2020, Current Biology). The data analysis is primarily on an individual participant level, and provides high statistical significance in each individual participant. Multiple participants used to demonstrate that results are reproducible across participants. In the studies for which the data were originally collected, sample sizes were chosen based on the sample sizes that had previously been used to convincingly demonstrate reproducibility in experiments with similar designs throughout the field.
We acquired MRI data on a 7T Philips Achieva scanner. No one else was present besides the participant(s) and the researchers during data collection, and the researchers were not blinded because there were no experimental conditions. Data for participants 1 -5 were collected from 03/04/2013 to 23/04/2014. Data for participants 6 -11 were collected from 21/11/2017 to 18/07/2019. Data from all scanned participants was included. However, we acquired data from the whole brain, although only a small set of regions was analyzed, as in all fMRI experiments. Most locations in the brain do not respond to the changes in numerosity. We first excluded from analysis any recording sites (voxels) that lay outside the gray matter, which was pre-established and a standard procedure in the field. After the fit of population receptive field models and monotonic response models, we excluded from further analyses voxels where the numerosity preference was beyond the range of the presented stimuli or when the variance explained of either model was lower than 20% in cross-validated data. This was in total several million excluded voxels.
No participants dropped out/declined participation. Participants were recruited from Utrecht University and Utrecht Medical Center either in response to recruitment posters for the study or from the lab. Although there are potential self-selection biases in using a convenient sample, such a recruitment strategy in this case is likely to self-select for an interest in neuroimaging or brain function more generally, which is unlikely to have any impact on an individuals' brain activity and therefore no impact on our results.
All experimental procedures were approved by the ethics committee of University Medical Center Utrecht.

Task fMRI
The numerosities one through seven were first presented in ascending order, with numerosity changing every 4200 ms (two TRs). Within this period, a numerosity pattern was shown for 300 ms, alternating with 400 ms of gray background, repeated six times. Each numerosity pattern had items drawn in new, random positions. These short presentations prevented participants from counting. Following this, twenty items were presented in the same way for eight TRs (16.8s, 24 presentations of a pattern). These periods of twenty items served to distinguish between very small and very large tuning widths. Then numerosities one through seven were presented as before, but in descending order, followed by another long period of twenty items. This cycle was repeated 4 times in each scanning run. Each functional run acquired 182 images (382.2s) of which the first six (12.6s) were discarded to ensure a steady signal state. In each scan session, we acquired six to eight repeated runs in one stimulus configuration, plus a top-up scan with the opposite phase-encoding direction to correct for image distortion in the gradient encoding direction, and a T1-weighted anatomical image with the same resolution, position and orientation as the functional data. Different stimulus configurations were tested in different sessions. For visual field mapping, a bar filled with a moving checkerboard pattern stepped across a 6.35°( radius) circle in the display center in eight (cardinal and diagonal) directions.
During visual field mapping the central fixation cross changed color (red/green) and on 10% of trials during presentation of visual numerosity stimuli the dots changed color (black/white). Participants were instructed to press a button when a color change occurred to confirm they were paying attention to the stimuli and remained awake throughout scanning.

Functional 7 Tesla
We acquired T1-weighted anatomical scans and T2*-weighted functional images using a 32-channel head coil at a resolution of 1.77×1.77×1.75 mm, with 41 interleaved slices of 128×128 voxels. The resulting field of view was 227×227×72 mm. TR was 2100 ms, TE was 25 ms, and flip angle was 70 degrees. We used a single shot gradient echo sequence with SENSE acceleration factor 3.0 and anterior-posterior encoding.
Whole brain scan (excluding anterior frontal and temporal lobes, where 7T fMRI has low response amplitudes and large spatial distortions).
Freesurfer 6.0, ITK-SNAP 1.6.0.1, AFNI 19.1.21 (afni.nimh.nih.gov) Analyses were performed in each participants' native space. Data were not normalized because there we no group comparisons or experimental conditions, and we were interested in fine-scale structures of individual healthy brains which would have been obscured with group normalization to a single template.
Analyses were performed in each participants' native space. Data were not normalized because there we no group comparisons or experimental conditions, and we were interested in fine-scale structures of individual healthy brains which would have been obscured with group normalization to a single template.
Functional scans were corrected for head movement and motion with two series of images that were acquired using opposing phase-encoding directions, with transformations calculated using AFNI (3dvolreg, 3dQwarp, 3dNwarpApply). No other spatial or temporal smoothing procedures were applied.