Numerical encoding in early visual cortex

Abstract

The ability to estimate numerosity in a visual array arose early in evolution, develops early in human development, and is correlated with mathematical ability. Previous work with visually presented arrays indicates that the intraparietal sulcus (IPS) represents number. However, it is not clear if the number signal originates in IPS or is propagated from earlier visual areas. Previous work from our group has demonstrated a rapidly instantiated representation of number in low-level regions of visual cortex using the high temporal resolution of event-related electro-encephalography (EEG). Here, we use a rapid event-related functional magnetic resonance imaging (fMRI) paradigm and find convergent evidence for a number signal in low-level visual cortex (areas V1, V2, and V3). Employing a stringent set of stimulus controls, we demonstrate that this signal cannot be explained by the total extent of the array, the density of the items in the array, the aggregate visual area of the items, the size of individual items, the proportion of the array covered by items, nor the overall scale of the array and items. Our findings thus provide strong support for the hypothesis that number is rapidly and directly encoded early in the visual processing stream.

Introduction

The number sense describes our ability to estimate the number of objects or events without counting them (Dehaene, 1997). Symbolic mathematics is unique to educated adult humans, but we share the number sense with infants (Izard et al., 2009, Xu and Spelke, 2000), adults from cultures that lack a verbal counting system (Pica, Lemer, Izard, & Dehaene, 2004), and diverse vertebrate taxa including monkeys (Brannon & Terrace, 1998), rodents (Meck & Church, 1983), and birds (Honig & Stewart, 1989). Although the number sense is distinct from symbolic calculation, the acuity of numerical estimation is correlated with math achievement (e.g., Chen and Li, 2014, Halberda et al., 2008, Halberda et al., 2012), and the number sense is theorized to provide a cognitive scaffold for more complex mathematical concepts (Feigenson et al., 2004, Spelke, 2003).

Research into the neural basis of the number sense has implicated a parieto-frontal network in approximate enumeration (Nieder, 2016). The number of items is thought to be encoded in the intraparietal sulcus (IPS) and utilized for decision-making processes in the dorsolateral prefrontal cortex (DLPFC) (Nieder & Dehaene, 2009). Single-cell recordings in monkeys have revealed neurons tuned to particular numerosities (Nieder & Miller, 2004) and other neurons that vary monotonically with number (Roitman, Brannon, & Platt, 2007). Functional imaging studies have shown that the horizontal segment of the IPS in humans includes topographic representations that are tuned to the number of items in a visual array (Harvey et al., 2013, Piazza et al., 2004). Furthermore, multi-voxel pattern analysis (MVPA) approaches have been able to decode stimulus number from the blood-oxygen-level dependent (BOLD) signal in IPS (Eger et al., 2009).

Recently, however, new evidence for number encoding in early visual cortex (EVC) arose in several human scalp electroencephalography (EEG) studies. In particular, Park, DeWind, Woldorff, & Brannon (2016) demonstrated event-related potentials specifically sensitive to number very early in visual processing (75 msec) over medial occipital regions. This signal varied monotonically with number: larger numbers were associated with greater scalp voltage. A subsequent experiment counter-balanced the visual hemifield (upper vs lower) within which the stimuli were displayed and demonstrated a polarity reversal in the number-related scalp potential; the polarity reversal provides strong evidence that the early number signal originated in V2 or V3 with a potential contribution of V1 (Fornaciai, Brannon, Woldorff, & Park, 2017).

There are several open questions regarding the EVC signal and how it relates to IPS signals reported previously. Although EEG has very high temporal resolution, it is intrinsically limited in spatial resolution, and the exact source of the number signal within EVC is still unclear. It is also unclear whether the EVC signal is tuned to individual numbers as previously reported in IPS (Harvey et al., 2013, Nieder and Miller, 2004, Piazza et al., 2004) or varies monotonically with number as the EEG findings suggest. Finally, the IPS signal is robust enough to allow stimulus numerosity to be decoded from recorded BOLD signal using MVPA (Eger et al., 2009), but it is unclear if the same could be done using the EVC signal.

Here we used a fast-event-related functional MRI design to test for a numerical signal in EVC with greater spatial resolution. Using a whole-brain approach allowed us to compare the EVC number signal to any potential number signals in IPS. Our stimuli sampled a three-dimensional stimulus space that allowed number to be disentangled from multiple key non-numerical visual stimulus dimensions, including the visual area of the array, the density of the items in the array, the combined visual area of the items, the size of individual items, the proportion of the array covered by items, and the overall scale of the array and items. Participants viewed these stimuli while performing an orthogonal detection task unrelated to magnitude.

We utilized a continuous carry-over (CCO) sequence of stimulus presentation (Aguirre, 2007, Aguirre et al., 2011), which has been used to probe the representational structure of object shape and color in the ventral visual stream (Drucker and Aguirre, 2009, Drucker et al., 2009) and of locations in hippocampus and scene selective cortex (Morgan, MacEvoy, Aguirre, & Epstein, 2011). CCO sequences have the unique advantage of allowing the simultaneous estimation of the effect of viewing the stimulus on BOLD signal and the modulation in BOLD signal caused by any neural adaptation to the previous stimulus. This approach allowed us to conduct three analyses previously utilized in different paradigms to discover number signals in the brain and apply all three to the hypothesized EVC and IPS number signals. First we examined the monotonic effect of changes in number on signal intensity to test and extend the EEG finding of a number signal in EVC (Fornaciai et al., 2017, Park et al., 2015). Second, we examined the modulatory effect the previous stimulus had on the signal. We note that this allowed us to look for adaptation effects as a result of habituation to the immediately previous stimulus rather than by a long stream of stimuli as in previous work (Jacob and Nieder, 2009, Piazza et al., 2004, Piazza et al., 2007). Finally, we attempted to decode numerosity from signal intensity using MVPA. This approach could provide evidence for encoding of numerosities in a given region even if no univariate effects were found in that area (e.g., Bulthé et al., 2015, Eger et al., 2009, Lyons and Beilock, 2011).

The results demonstrate a robust number signal in EVC, which cannot be explained by any of the other non-numerical visual features we tested. In contrast, no number signal was found in the IPS or in any other areas of the brain, contrary to many prior reports. We conclude that our data provide strong evidence for a number signal in EVC and discuss the possible reasons we did not find numerical coding in IPS despite the rich literature that implicates IPS in numerical coding.