Topographic maps representing haptic numerosity reveals distinct sensory representations in supramodal networks

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

Neurocognitive Assessment of Mathematics-Related Capacities in Neurosurgical Patients

A precise neuropsychological assessment is of the utmost importance for neurosurgical patients undergoing the surgical excision of cerebral lesions. The assessment of mathematical abilities is usually limited to arithmetical operations while other fundamental visuo-spatial aspects closely linked to mathematics proficiency, such as the perception of numerical quantities and geometrical reasoning, are completely neglected. We evaluated these abilities with two objective and reproducible psychophysical tests, measuring numerosity perception and non-symbolic geometry, respectively. We tested sixteen neuro-oncological patients before the operation and six after the operation with classical neuropsychological tests and with two psychophysical tests. The scores of the classical neuropsychological tests were very heterogeneous, possibly due to the distinct location and histology of the tumors that might have spared (or not) brain areas subserving these abilities or allowed for plastic reorganization. Performance in the two non-symbolic tests reflected, on average, the presumed functional role of the lesioned areas, with participants with parietal and frontal lesions performing worse on these tests than patients with occipital and temporal lesions. Single-case analyses not only revealed some interesting exceptions to the group-level results (e.g., patients with parietal lesions performing well in the numerosity test), but also indicated that performance in the two tests was independent of non-verbal reasoning and visuo-spatial working memory. Our results highlight the importance of assessing non-symbolic numerical and geometrical abilities to complement typical neuropsychological batteries. However, they also suggest an avoidance of reliance on an excessively rigid localizationist approach when evaluating the neuropsychological profile of oncological patients.

The more numerous the longer: how the integration between numerosity and time leads to a common neural response

If you are stuck in a traffic jam, the more numerous the queuing cars are, the longer you expect to wait. Time and numerosity are stimulus dimensions often associated in the same percept and whose interaction can lead to misjudgements. At brain level it is unclear to which extent time and numerosity recruit same/different neural populations and how their perceptual integration leads to changes in these populations' responses. Here we used high-spatial-resolution functional magnetic resonance imaging with neural model-based analyses to investigate how the topographic representations of numerosity and time change when these dimensions are varied together on the same visual stimulus in a congruent (the more numerous the items, the longer the display time) or incongruent manner. Compared to baseline conditions, where only one dimension was changed at a time, the variation of both stimulus dimensions led to changes in neural population responses that became more sensitive either to the two features or to one of them. Magnitude integration led also to degradation of topographies and shifts in response preferences. These changes were more pronounced in the comparison between parietal and frontal maps. Our results while pointing to partially distinct representations of time and numerosity show a common neural response to magnitude integration.

Overlapping but separate number representations in the intraparietal sulcus – probing format- and modality-independence in sighted Braille readers

The Triple-Code Model stipulates that numerical information from different formats and modalities converges on a common magnitude representation in the Intraparietal Sulcus (IPS). To what extent the representations of all numerosity forms overlap remains unsolved. It has been postulated that the representation of symbolic numerosities (for example, Arabic digits) is sparser and grounded in an existing representation that codes for non-symbolic numerosity information (i.e., sets of objects). Other theories argue that numerical symbols represent a separate number category that emerges only during education. Here, we tested a unique group of sighted tactile Braille readers with numerosities 2, 4, 6 and 8 in three number notations: Arabic digits, sets of dots, tactile Braille numbers. Using univariate methods, we showed a consistent overlap in activations evoked by these three number notations. This result shows that all three used notations are represented in the IPS, which may suggest at least a partial overlap between the representations of the three notations used in this experiment. Using MVPA, we found that only non-automatized number information (Braille and sets of dots) allowed successful number classification. However, the numerosity of one notation could not be predicted above chance from the brain activation patterns evoked by another notation (no cross-classification). These results show that the IPS may host independent number codes in overlapping cortical circuits. In addition, they suggest that the level of training in encoding a given type of number information is an important factor that determines the amount of exploitable information and needs to be controlled for in order to identify the neural code underlying numerical information per se.

Assessing the ecological validity of numerosity-selective neuronal populations with real-world natural scenes

Animals and humans are able to quickly and effortlessly estimate the number of items in a set: their numerosity. Numerosity perception is thought to be critical to behavior, from feeding to escaping predators to human mathematical cognition. Virtually, all scientific studies on numerosity mechanisms use well controlled but artificial stimuli to isolate the numerosity dimension from other physical quantities. Here, we probed the ecological validity of these artificial stimuli and evaluate whether an important component in numerosity processing, the numerosity-selective neural populations, also respond to numerosity of items in real-world natural scenes. Using 7T MRI and natural images from a wide range of categories, we provide evidence that the numerosity-tuned neuronal populations show numerosity-selective responses when viewing images from a real-world natural scene. Our findings strengthen the role of numerosity-selective neurons in numerosity perception and provide an important link to their function in numerosity perception in real-world settings.

Intracranial recordings show evidence of numerosity tuning in human parietal cortex

Numerosity is the set size of a group of items. Numerosity perception is a trait shared across numerous species. Numerosity-selective neural populations are thought to underlie numerosity perception. These neurons have been identified primarily using electrical recordings in animal models and blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) in humans. Here we use electrical intracranial recordings to investigate numerosity tuning in humans, focusing on high-frequency transient activations. These recordings combine a high spatial and temporal resolution and can bridge the gap between animal models and human recordings. In line with previous studies, we find numerosity-tuned responses at parietal sites in two out of three participants. Neuronal populations at these locations did not respond to other visual stimuli, i.e. faces, houses, and letters, in contrast to several occipital sites. Our findings further corroborate the specificity of numerosity tuning of in parietal cortex, and further link fMRI results and electrophysiological recordings.

Visual timing-tuned responses in human association cortices and response dynamics in early visual cortex

Quantifying the timing (duration and frequency) of brief visual events is vital to human perception, multisensory integration and action planning. Tuned neural responses to visual event timing have been found in association cortices, in areas implicated in these processes. Here we ask how these timing-tuned responses are related to the responses of early visual cortex, which monotonically increase with event duration and frequency. Using 7-Tesla functional magnetic resonance imaging and neural model-based analyses, we find a gradual transition from monotonically increasing to timing-tuned neural responses beginning in the medial temporal area (MT/V5). Therefore, across successive stages of visual processing, timing-tuned response components gradually become dominant over inherent sensory response modulation by event timing. This additional timing-tuned response component is independent of retinotopic location. We propose that this hierarchical emergence of timing-tuned responses from sensory processing areas quantifies sensory event timing while abstracting temporal representations from spatial properties of their inputs.

Early visual cortical responses increase with event duration and frequency, while later timing-tuned responses quantify event timing. Here, the authors show timing tuning gradually emerges up the visual hierarchy, and separates temporal and spatial event features.

Attention drives human numerosity-selective responses

Numerosity, the set size of a group of items, helps guide behavior and decisions. Previous studies have shown that neural populations respond selectively to numerosities. How numerosity is extracted from the visual scene is a longstanding debate, often contrasting low-level visual with high-level cognitive processes. Here, we investigate how attention influences numerosity-selective responses. The stimuli consisted of black and white dots within the same display. Participants' attention was focused on either black or white dots, while we systematically changed the numerosity of black, white, and total dots. Using 7 T fMRI, we show that the numerosity-tuned neural populations respond only when attention is focused on their preferred numerosity, irrespective of the unattended or total numerosities. Without attention, responses to preferred numerosity are suppressed. Unlike traditional effects of attention in the visual cortex, where attention enhances already existing responses, these results suggest that attention is required to drive numerosity-selective responses.

Auditory timing-tuned neural responses in the human auditory cortices

Perception of sub-second auditory event timing supports multisensory integration, and speech and music perception and production. Neural populations tuned for the timing (duration and rate) of visual events were recently described in several human extrastriate visual areas. Here we ask whether the brain also contains neural populations tuned for auditory event timing, and whether these are shared with visual timing. Using 7T fMRI, we measured responses to white noise bursts of changing duration and rate. We analyzed these responses using neural response models describing different parametric relationships between event timing and neural response amplitude. This revealed auditory timing-tuned responses in the primary auditory cortex, and auditory association areas of the belt, parabelt and premotor cortex. While these areas also showed tonotopic tuning for auditory pitch, pitch and timing preferences were not consistently correlated. Auditory timing-tuned response functions differed between these areas, though without clear hierarchical integration of responses. The similarity of auditory and visual timing tuned responses, together with the lack of overlap between the areas showing these responses for each modality, suggests modality-specific responses to event timing are computed similarly but from different sensory inputs, and then transformed differently to suit the needs of each modality.

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.

The authors show that spatial frequency domain Fourier power closely but nonlinearly follows numerosity, simplifying computing numerosity from early visual responses. Monotonic early visual cortex and neural network responses follow Fourier power, while later tuned responses follow numerosity.

Comparing BOLD and VASO-CBV population receptive field estimates in human visual cortex

Vascular Space Occupancy (VASO) is an alternative fMRI approach based on changes in Cerebral Blood Volume (CBV). VASO-CBV fMRI can provide higher spatial specificity than the blood oxygenation level-dependent (BOLD) method because the CBV response is thought to be limited to smaller vessels. To investigate how this technique compares to BOLD fMRI for cognitive neuroscience applications, we compared population receptive field (pRF) mapping estimates between BOLD and VASO-CBV. We hypothesized that VASO-CBV would elicit distinct pRF properties compared to BOLD. Specifically, since pRF size estimates also depend on vascular sources, we hypothesized that reduced vascular blurring might yield narrower pRFs for VASO-CBV measurements. We used a VASO sequence with a double readout 3D EPI sequence at 7T to simultaneously measure VASO-CBV and BOLD responses in the visual cortex while participants viewed conventional pRF mapping stimuli. Both VASO-CBV and BOLD images show similar eccentricity and polar angle maps across all participants. Compared to BOLD-based measurements, VASO-CBV yielded lower tSNR and variance explained. The pRF size changed with eccentricity similarly for VASO-CBV and BOLD, and the pRF size estimates were similar for VASO-CBV and BOLD, even when we equate variance explained between VASO-CBV and BOLD. This result suggests that the vascular component of the pRF size is not dominating in either VASO-CBV or BOLD.

Spontaneous representation of numerosity zero in a deep neural network for visual object recognition

Conceiving "nothing" as a numerical value zero is considered a sophisticated numerical capability that humans share with cognitively advanced animals. We demonstrate that representation of zero spontaneously emerges in a deep learning neural network without any number training. As a signature of numerical quantity representation, and similar to real neurons from animals, numerosity zero network units show maximum activity to empty sets and a gradual decrease in activity with increasing countable numerosities. This indicates that the network spontaneously ordered numerosity zero as the smallest numerical value along the number line. Removal of empty-set network units caused specific deficits in the network's judgment of numerosity zero, thus reflecting these units' functional relevance. These findings suggest that processing visual information is sufficient for a visual number sense that includes zero to emerge and explains why cognitively advanced animals with whom we share a nonverbal number system exhibit rudiments of numerosity zero.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Laminar processing of numerosity supports a canonical cortical microcircuit in human parietal cortex

As neural signals travel through the visual hierarchy, spatial precision decreases and specificity for stimulus features increases.^1-4 A similar hierarchy has been found for laminar processing in V1, where information from the thalamus predominantly targets the central layers, while spatial precision decreases and feature specificity increases toward superficial and deeper layers.^5-17 This laminar processing scheme is proposed to represent a canonical cortical microcircuit that is similar across the cortex.^11,18-21 Here, we go beyond early visual cortex and investigate whether processing of numerosity (the set size of a group of items) across cortical depth in the parietal association cortex follows this hypothesis. Numerosity processing is implicated in many tasks such as multiple object tracking,²² mathematics,^23-25 decision making,²⁶ and dividing attention.²⁷ Neurons in the parietal association cortex are tuned to numerosity, with both a preferred numerosity tuning and tuning width (i.e., specificity).^28-30 We quantified preferred numerosity responses across cortical depth in the parietal association cortex with ultra-high field fMRI and population receptive field-based numerosity modeling.^1,28,31 We find that numerosity responses sharpen, i.e., become increasingly specific, moving away from the central layers. This suggests that the laminar processing scheme for numerosity processing in the parietal cortex is similar to primary visual cortex, providing support for the canonical cortical microcircuit hypothesis beyond primary visual cortex.

Individualized cognitive neuroscience needs 7T: Comparing numerosity maps at 3T and 7T MRI

The field of cognitive neuroscience is weighing evidence about whether to move from the current standard field strength of 3 Tesla (3T) to ultra-high field (UHF) of 7T and above. The present study contributes to the evidence by comparing a computational cognitive neuroscience paradigm at 3T and 7T. The goal was to evaluate the practical effects, i.e. model predictive power, of field strength on a numerosity task using accessible pre-processing and analysis tools. Previously, using 7T functional magnetic resonance imaging and biologically-inspired analyses, i.e. population receptive field modelling, we discovered topographical organization of numerosity-selective neural populations in human parietal cortex. Here we show that these topographic maps are also detectable at 3T. However, averaging of many more functional runs was required at 3T to reliably reconstruct numerosity maps. On average, one 7T run had about four times the model predictive power of one 3T run. We believe that this amount of scanning would have made the initial discovery of the numerosity maps on 3T highly infeasible in practice. Therefore, we suggest that the higher signal-to-noise ratio and signal sensitivity of UHF MRI is necessary to build mechanistic models of the organization and function of our cognitive abilities in individual participants.

Tuned neural responses to haptic numerosity in the putamen

The ability to perceive the numerosity of items in the environment is critical for behavior of species across the evolutionary tree. Though the focus of studies of numerosity perception lays on the parietal and frontal cortices, the ability to perceive numerosity by a range of species suggests that subcortical nuclei may be implicated in the process. Recently, we have uncovered tuned neural responses to haptic numerosity in the human cortex. Here, we questioned whether subcortical nuclei are also engaged in perception of haptic numerosity. To that end, we utilized a task of haptic numerosity exploration, together with population receptive field model of numerosity selective responses measured at ultra-high field MRI (7T). We found tuned neural responses to haptic numerosity in the bilateral putamen. Similar to the cortex, the population receptive fields tuning width increased with numerosity. The tuned responses to numerosity in the putamen extend its role in cognition and propose that the motor-sensory loops of the putamen and basal ganglia might take an active part in numerosity perception and preparation for future action.