Neural Basis Of Number Representation

What area of the brain is involved in representing number and making arithmetic calculations? The neural basis of numerical cognition has been studied in adult humans using ERPs, functional magnetic resonance imaging (fMRI), positron emission tomography (PET), and patient populations (for a review, see Dehaene, 2000). Generally, this literature implicates the parietal cortex in number processing (inferior or superior parietal lobule). However, the majority of these studies have employed tasks that require the recognition and manipulation of arabic numerals and therefore engage symbolic numerical processing and not enumeration per se (but see Fink et al., 2001; Sathian et al., 1999).

Comparably little is known about the neural basis of number representation in animals. For many years, the only report of number-related neural activity was that in the association cortex of the anesthetized cat (Thompson et al., 1970). In that study, neural activity was recorded in response to a series of ten auditory or visual stimuli. A small number of neurons recorded (5 of 500) discharged more to a particular position in the sequence of lights or tones (see Figure 6.12a). These five number cells responded to the values 2, 5, 6, 6, and 7 in the series, regardless of stimulus modality (auditory or visual) and frequency (interstimulus intervals varied from 1 to 5 sec). A similar, but more broadly tuned, cell was found in an 8-day-old kitten. These results are intriguing in that they suggest that single cells may be selective for particular numerical values and that tuning for number may increase over development. However, replication and extension of these results are sorely needed.

More recently, number-related activity was found in the parietal cortex of monkeys as they performed a series of repetitive arm movements (Sawamura et al., 2002). Monkeys were trained to repeat a movement (pushing or turning a handle) for five trials and then switch to the other movement for five trials, and so on. There were no external cues as to how many movements the monkey had made; thus the monkey needed to keep track of the number of repetitions he had performed. The duration of each trial was varied to prevent monkeys from switching to the other movement on the basis of elapsed time, and electromyograms were recorded to insure that the five movements within a series did not differ in any systematic fashion.

The investigators selected neurons from the superior lobule of the parietal cortex with somatosensory receptive fields in the proximal forelimb and trunk of the arm performing the movement. However, they found that the neurons' responses also depended on the number of movements the monkey made. This number-modulated activity was observed during a period in which the monkeys waited for a "go" signal to execute the movement. As shown in Figure 6.12b, many of the cells were selective for only one of the positions in the sequence (e.g., third). In the remaining neurons, firing rate increased during more than one period, such as the first and second. Across the population of neurons studied, there were neurons that were selective for each of the ordinal positions in the sequence.

Although the cumulative amount of motor effort and the cumulative amount of juice within a sequence were both confounded with number behaviorally, the fact that there were neurons selective for each of the ordinal positions within the sequence suggests that these neurons may function as cardinal rather than ordinal number detectors. It was not reported, but it would be interesting to determine whether variability in activity increased with number.

An exciting new study has isolated neural activity in the prefrontal cortex of awake, behaving macaque monkeys that is associated with the number of

FIGURE 6.12 Neural basis of number representation. (a) Number 6 neuron from cat association cortex. Action potentials were recorded as a sequence of ten tones or lights with different interstimulus intervals presented to an anesthetized cat. Each sequence was repeated ten times. The probability that the neuron discharged to a stimulus is plotted as a function of the stimulus's position in the sequence. This neuron was most active to the sixth stimulus in the sequence, regardless of modality or ISI. (b) Number 5 neuron from monkey parietal cortex. Data are presented from ten blocks of trials in which a monkey repeated an arm movement (push) five times. Each of the panels depicts the trials from a particular movement in the sequence. On the top half of each panel, each row represents one trial. The vertical tick marks indicate the time of each action potential relative to the time of the "go" signal to start the movement (arrows). On the bottom of each panel, the average activity from all trials was calculated in 50-msec time bins. Activity of this neuron was elevated before the fifth movement of the sequence, despite the fact that the movement itself did not differ from any others in the sequence. (Reprinted by permission from Nature 415, 918, © 2002 Macmillan Publishers Ltd.)

FIGURE 6.12 Neural basis of number representation. (a) Number 6 neuron from cat association cortex. Action potentials were recorded as a sequence of ten tones or lights with different interstimulus intervals presented to an anesthetized cat. Each sequence was repeated ten times. The probability that the neuron discharged to a stimulus is plotted as a function of the stimulus's position in the sequence. This neuron was most active to the sixth stimulus in the sequence, regardless of modality or ISI. (b) Number 5 neuron from monkey parietal cortex. Data are presented from ten blocks of trials in which a monkey repeated an arm movement (push) five times. Each of the panels depicts the trials from a particular movement in the sequence. On the top half of each panel, each row represents one trial. The vertical tick marks indicate the time of each action potential relative to the time of the "go" signal to start the movement (arrows). On the bottom of each panel, the average activity from all trials was calculated in 50-msec time bins. Activity of this neuron was elevated before the fifth movement of the sequence, despite the fact that the movement itself did not differ from any others in the sequence. (Reprinted by permission from Nature 415, 918, © 2002 Macmillan Publishers Ltd.)

simultaneously presented elements in a visual display (Nieder et al., 2002). In this study, monkeys were trained to perform a delayed same-different task in which a "same" answer was rewarded if the second stimulus was an exemplar of the equivalent numerosity as the first stimulus. Monkeys initiated each trial by grasping a lever, and subsequently a sample stimulus was presented, which contained between one and five items. Following a delay period, a test stimulus containing either the same number of elements or a set that differed by one element was presented. Monkeys reported that the sample and test stimuli were the same by releasing the lever. The area, circumference, arrangement, density, and shapes of the items in the stimuli were systematically varied to ensure that number alone was the basis for judgment.

Consistent with previous behavioral observations, accuracy in responding declined as the number of items in the sample increased. In an additional set of behavioral experiments where the sample and test stimuli differed by more than one element, performance improved as the difference between the sample and test stimuli increased. The performance of monkeys in this task thus demonstrated distance and magnitude effects typically associated with numerical discrimination in humans and other animals in a wide variety of tasks.

While monkeys performed the delayed same-different task, the activity of randomly selected neurons in the prefrontal cortex was measured. For approximately one third of neurons studied, activity measured during stimulus presentation or the delay period was maximal for one quantity and declined as distance from that quantity increased. Many neurons in the prefrontal cortex were selective for a single numerosity, but the largest proportion of these number-selective neurons preferred the numerosity 1. The authors showed that numerical selectivity was broader for larger numbers, suggesting a possible mechanism for numerical distance and magnitude effects. They also reported that the onset of prefrontal activity was approximately 120 msec following sample presentation, possibly implicating a parallel model of numerical processing (Dehaene, 2002). This conclusion must be viewed with caution, however, since this measure actually indicates the point in time at which neuronal activity increased above baseline and does not indicate the time at which neurons differentially responded to a given quantity.

In contrast with previous studies, the authors found that neurons in the prefrontal cortex were much more likely to be selective for number than neurons in the parietal cortex (about one third compared with 7% of those sampled). This discrepancy may be due to a difference in the spatial response properties of neurons in the two areas. Parietal neurons are much more spatially selective than prefrontal neurons, but stimuli in this study were presented in random spatial locations. Future studies should probe number-related activity in the parietal cortex using stimuli tailored to the spatially selective response properties of each neuron.

Activity in the parietal lobe has also been shown to correlate with monkeys' performance on an interval time discrimination task (Leon and Shadlen, 2000). Monkeys were trained to compare the duration of two sequentially presented colored lights. On each trial, a short or long standard stimulus (316 or 800 msec) was presented, followed by a test stimulus of varying duration (126 to 800 msec for short and 400 to 1600 msec for long). The monkey indicated whether the test stimulus was longer or shorter than the standard with a saccadic eye movement directed to one of two corresponding choice targets. The monkeys' accuracy increased with the ratio of the standard to the target value, as predicted by Weber's law.

Leon and Shadlen (2000) recorded the activity of neurons in the lateral intra-parietal area. These neurons discharge before saccades to a particular location; however, their activity also appeared to represent the duration of the test stimulus compared to the standard. The investigators placed one of the targets within the neuron's receptive field and the other outside it. When the test stimulus was first presented, the neurons behaved as if the monkey intended to choose the shorter target; however, if the test stimulus was in fact longer than the standard, the neuron's firing rate began to indicate that the longer target would be chosen. Future studies should investigate the relationship between the representation of time and number in the parietal cortex.

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