Number neurons

How might numerosity be encoded by populations of neurons in the IPS? Although animal models of numerical tasks have been known for many decades, it is only very recently that the neural bases of animal numerical abilities have begun to be investigated. Andreas Nieder and Earl Miller (Nieder et al. 2002; Nieder and Miller 2003, 2004) recorded from single neurons in awake monkeys trained to perform a visual number match-to-sample task. Many neurons were tuned to a preferred numerosity: some neurons responded preferentially to sets of one object, others to two objects, and so on up to five objects (Fig. 1). The tuning was coarse and became increasingly imprecise as numerosity increased. The characteristics of this neural code were exactly as expected from a neural network model that had been proposed to account for the distance effect and other characteristics of numerical processing in adults and infants (Dehaene and Changeux 1993). Most important is the location where the number neurons were recorded. Initially, a large proportion was observed in dorsolateral prefrontal cortex, but more recently another population of neurons with a shorter latency was observed in the parietal lobe (Nieder and Miller 2004; see also Sawamura et al. 2002).

The latter number neurons are located in monkey area VIP, in the depth of the intraparietal sulcus, a location that is a plausible homolog of the human HIPS area, which is active during many number tasks. With Olivier Simon, I performed a detailed fMRI investigation of the relative location of the human activation during calculation, relative to other landmarks of the parietal lobe (Simon et al.

Predicted tuning (Dehaene & Changeux, 1993) Observed Neurons {Nieder etal, 2002)

Predicted tuning (Dehaene & Changeux, 1993) Observed Neurons {Nieder etal, 2002)

Fig. 1. Number neurons (a) as predicted by a neural network model of arithmetic (Dehaene and Changeux 1993) and (b) as observed in the macaque monkey prefrontal and parietal cortices (Nieder et al. 2002; Nieder and Miller 2003,2004). Each neuron responds to a preferred number of visual objects, with a tuning curve that respects Weber's law (the tuning becomes increasingly imprecise for larger numbers), (c) Possible homology between number representations in humans and macaque monkeys. The left panel shows an inflated human brain and the location of voxels activated in common to many arithmetic tasks (Dehaene et al. 2003). The right panel shows an inflated monkey brain with the approximate location of prefrontal and parietal areas where a large proportion of number neurons was found.

Fig. 1. Number neurons (a) as predicted by a neural network model of arithmetic (Dehaene and Changeux 1993) and (b) as observed in the macaque monkey prefrontal and parietal cortices (Nieder et al. 2002; Nieder and Miller 2003,2004). Each neuron responds to a preferred number of visual objects, with a tuning curve that respects Weber's law (the tuning becomes increasingly imprecise for larger numbers), (c) Possible homology between number representations in humans and macaque monkeys. The left panel shows an inflated human brain and the location of voxels activated in common to many arithmetic tasks (Dehaene et al. 2003). The right panel shows an inflated monkey brain with the approximate location of prefrontal and parietal areas where a large proportion of number neurons was found.

2002, 2004 ). This study revealed that number-related activations are anterior to saccade-, attention-, and space-related activations in the posterior IPS (plausibly corresponding to areas LIP and V6a), and posterior to the anterior IPS activations associated with grasping movements (area AIP). Thus, the relative placement of eye movement, calculation and grasping-related brain areas seems to be similar in macaques and humans (Dehaene et al. 2004).

The observation of a common, geometrical brain organization strengthens the possibility that the monkey number neurons in VIP bear a direct evolutionary relation to human arithmetic abilities. However, establishing a genuine interspecies homology would require demonstrating that the human intraparietal cortex also contains distinct populations of neurons, each tuned to a specific number. Yet single neurons cannot be investigated non-invasively in the human brain (although see, e.g., Kreiman et al. 2000). With Manuela Piazza, we recently designed an indirect adaptation method that allowed us to investigate numerosity tuning in humans (Piazza et al. 2004). During fMRI, we repeatedly presented sets of dots with a fixed number (say, 16 dots). The purpose was to "adapt" the neural population coding for this value, thus leading putative human number neurons to progressively reduce their firing rate, as observed in macaque electrophysiological experiments (Miller et al. 1991). We then presented occasional deviant numbers that could range from half to twice the adapted number. fMRI revealed that only two regions, left and right IPS, responded to the change in numerosity by increasing their activation in relation to the distance between the adapted number and the deviant one. Detailed analyses of the activation profile revealed that these regions behave as predicted based on the hypothesis that they contain number neurons. Both human fMRI and monkey electrophysiological data yield tuning profiles that 1) depend only on number independently of other parameters such as shape, density, or spatial arrangement; 2) are smooth and monotonic in response to increasing degrees of deviation in number; 3) are increasingly broader when plotted on a linear scale (Weber's law); and 4) can be expressed as a simple Gaussian function of number ratio. This functional homology, together with the compatible anatomical localization in the depth of the IPS, suggests that humans and macaque monkeys possess similar populations of intraparietal number-sensitive neurons. It provides important support for the notion that all humans start life with a non-verbal representation of approximate number inherited from our evolutionary history

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