Valérie Dormal

Dissociation of numerosity and duration processing in the left intraparietal sulcus: a transcranial magnetic stimulation study.

A possible dissociation of duration and numerosity processing was tested in an off-line repetitive transcranial magnetic stimulation (rTMS) design. Participants had to compare the numerosity of flashed dot sequences or the duration of single dot displays before and after 15 min of 1 Hz rTMS over one of three sites (the left or right intraparietal sulcus (IPS), or the vertex chosen as a control site). Compared to the control site, performance was only slowed down for the numerosity comparison task after the left IPS stimulation, whereas it was not affected for the duration comparison task for any of the parietal sites. These results show that the parietal area critically involved in numerosity processing is not involved in duration processing, revealing at least one cerebral site where duration and numerosity comparison processes dissociate.

A common right fronto-parietal network for numerosity and duration processing: An fMRI study

Numerosity and duration processing have been modeled by a functional mechanism taking the form of an accumulator working under two different operative modes. Separate investigations of their cerebral substrates have revealed partly similar patterns of activation, mainly in parietal and frontal areas. However, the precise cerebral implementation of the accumulator model within these areas has not yet been directly assessed. In this study, we asked participants to categorize the numerosity of flashed dot sequences or the duration of single dot displays, and we used functional magnetic resonance imaging (fMRI) to examine the common neural correlates of these processes. The results reveal a large right‐lateralized fronto‐parietal network, including the intraparietal sulcus (IPS) and areas in the precentral, middle and superior frontal gyri, which is activated by both numerosity and duration processing. Complementary psychophysiological interaction (PPI) analyses show a functional connectivity between the right IPS and the frontal areas in both tasks, whereas the right IPS was functionally connected to the left IPS and the right precentral area in the numerosity categorization task only. We propose that the right IPS underlies a common magnitude processing system for both numerosity and duration, possibly corresponding to the encoding and accumulation stages of the accumulator model, whereas the frontal areas are involved in subsequent working‐memory storage and decision‐making processes. Hum Brain Mapp, 2011.

Common and specific contributions of the intraparietal sulci to numerosity and length processing

Numerical and spatial magnitude processing have long been intimately associated, leading to the suggestion that they share a common system of magnitude representation. Although separate investigations on the cerebral areas involved in numerosity and spatial estimation point toward the parietal cortex, the precise anatomical overlap, if any, has not yet been directly established. Here, functional magnetic resonance imaging was used to localize the cerebral network involved in processing both numerosity and length. Blood oxygenation level‐dependent signal changes were measured while healthy volunteers were making numerosity comparisons on linear arrays of dots, and length comparisons on discrete linear arrays of dots and continuous rectangles. The results show the bilateral involvement of parietal regions around the intraparietal sulci in explicit and implicit processing of numerosity, and a right lateralized occipitoparietal network activation in length processing; numerosity and length processing both activate the right IPS and the precentral gyrus. By excluding the mandatory intrinsic spatial processing of arrays, we demonstrate that the left IPS is involved in numerosity processing only, whereas the right IPS underlies a common processing mechanism or representation of spatial and numerical magnitude. Hum Brain Mapp 2009.

Numerosity-length interference: a Stroop experiment.

The existence of a common mechanism for length and numerosity processing was tested with a Stroop task. Participants compared the length or the numerosity of arrays of dots, for which the two variables were manipulated independently to create congruent, incongruent, or neutral pairs. Results showed that the spatial cues strongly interfered with the processing of numerosity, whereas the numerical cues only moderately interfered with the processing of length. These findings reflect a different mandatory processing of numerosity and length.

Mode-dependent and mode-independent representations of numerosity in the right intraparietal sulcus

In humans, areas around the intraparietal sulcus (IPS) have been found to play a crucial role in coding nonsymbolic numerosities (i.e., number of elements in a collection). In the parietal cortex of monkeys, some populations of neurons were found to respond selectively to sequentially- or simultaneously-presented numerosities, whereas other populations showed similar activation in both modes of presentation. However, whether such mode-dependent and -independent representations of numerosity also exist in humans is still unknown. Here, we used fMRI to identify the areas involved in numerosity processing while participants classified linear arrays of dots (simultaneous stimuli) or flashed dot sequences (sequential stimuli). The processing of simultaneous numerosities induced activations bilaterally in several areas of the IPS, whereas activations during the processing of sequential numerosities were restricted to the right hemisphere. A conjunction analysis showed that only the right IPS and precentral gyrus showed overlapping activations during the judgement of sequential and simultaneous stimuli. Voxelwise correlations confirmed the highly similar pattern of activation found in these regions during both tasks. This pattern was weaker or absent in mode-dependent regions, like the right inferior frontal cortex and the lateral occipital complex. Finally, a close look at the right IPS revealed an anterior-to-posterior gradient of activation with selective activation for sequential and simultaneous stimuli in the anterior and posterior areas, respectively, and overlapping activations in-between. This study provides the first direct evidence that, in humans, the right IPS contains both mode-dependent and mode-independent representations of numerosity.

Causal role of spatial attention in arithmetic problem solving: evidence from left unilateral neglect.

Recent behavioural and brain imaging studies have provided evidence for rightward and leftward attention shifts while solving addition and subtraction problems respectively, suggesting that mental arithmetic makes use of mechanisms akin to those underlying spatial attention. However, this hypothesis mainly relies on correlative data and the causal relevance of spatial attention for mental arithmetic remains unclear. In order to test whether the mechanisms underlying spatial attention are necessary to perform arithmetic operations, we compared the performance of right brain-lesioned patients, with and without left unilateral neglect, and healthy controls in addition and subtraction of two-digit numbers. We predicted that patients with left unilateral neglect would be selectively impaired in the subtraction task while being unimpaired in the addition task. The results showed that neglect patients made more errors than the two other groups to subtract large numbers, whereas they were still able to solve large addition problems matched for difficulty and magnitude of the answer. This finding demonstrates a causal relationship between the ability to attend the left side of space and the solving of large subtraction problems. A plausible account is that attention shifts help localizing the position of the answer on a spatial continuum while subtracting large numbers.

Spatial bias in symbolic and non-symbolic numerical comparison in neglect

When asked to bisect mentally numerical intervals, neglect patients show a displacement of the numerical midpoint similar to the one observed in physical line bisection. This spatial-numerical bias has been taken as evidence of the spatial nature of numerical magnitude representations. However, to date, neuropsychological studies in neglect patients have only used symbolic numerical material. Here, we compare the results of patients with right-hemisphere damage with and without unilateral left neglect and age-matched healthy control participants in two numerical comparison tasks using symbolic and non-symbolic materials, in order to determine whether the representation of non-symbolic numerosities was altered or not by the presence of neglect. When asked to judge if an Arabic digit or a sequence of flashed dots was smaller or larger than a reference value (i.e., 5), the responses of neglect patients to smaller magnitudes (i.e., 4) were impaired. Moreover, only neglect patients presented an asymmetrical distance effect (i.e., an enhanced effect only for stimuli of smaller numerical magnitude than the reference). These results provide the first direct evidence of a spatial bias in non-symbolic numerosity in neglect patients, and support the existence of common processing mechanisms and/or a representational system for symbolic and non-symbolic inputs.

Dissociation between numerosity and duration processing in aging and early Parkinson's disease

Numerosity and duration processing have been shown to be underlain by a single representational mechanism, namely an accumulator, and to rely on a common cerebral network located principally in areas around the right intraparietal sulcus. However, recent neuropsychological findings reveal a dissociation between numerosity and duration processing, which suggests the existence of partially distinct mechanisms. In this study, we tested the idea of partially common and distinct mechanisms by investigating, for the first time, both numerical and temporal processing abilities in non-demented Parkinsons disease (PD) patients known to suffer from duration impairment and in healthy elderly adults known to have impaired performance in duration tasks. The aim was to assess whether this impaired duration processing would extend to numerosity processing. The participants had to compare either the numerosity of flashed dot sequences or the duration of single dot displays. The results demonstrate an effect of aging on duration comparison, healthy elderly participants making significantly more errors than healthy young participants. Importantly, the performance of PD patients on the duration task was worse than that of the healthy young and elderly groups, whereas no difference was found for numerosity comparison. This dissociation supports the idea that partly independent systems underlie the processing of numerosity and duration.

Impact of optokinetic stimulation on mental arithmetic.

Solving arithmetic problems has been shown to induce shifts of spatial attention, subtraction problems orienting attention to the left side, and addition problems to the right side of space. At the neurofunctional level, the activations elicited by the solving of arithmetical problems resemble those elicited by horizontal eye movements. Whether overt orientation of attention (i.e., eye movements) can be linked to the solving procedure is, however, still under debate. In the present study, we used optokinetic stimulation (OKS) to trigger automatic eye movements to orient participants’ overt attention to the right or to the left of their visual field while they were solving addition or subtraction problems. The results show that, in comparison to leftward OKS and a control condition, rightward OKS facilitates the solving of addition problems that necessitate a carrying procedure. Subtraction solving was unaffected by leftward or rightward OKS. These results converge with previous findings to show that attentional shifts are functionally related to mental arithmetic processing.

A common metric magnitude system for the perception and production of numerosity, length, and duration.

Numerosity, length, and duration processing may share a common functional mechanism situated within the parietal cortex. A strong parallelism between the processing of these three magnitudes has been revealed by similar behavioral signatures (e.g., Weber–Fechners law, the distance effect) and reciprocal interference effects. Here, we extend the behavioral evidence for a common magnitude processing mechanism by exploring whether the under- and overestimation patterns observed during numerical perception and production tasks are also present in length and duration perception and production. In a first experiment, participants had to perform two estimation tasks (i.e., perception and production) on three magnitudes (i.e., numerosities, lengths, and durations). The results demonstrate similar patterns for the three magnitudes: underestimation was observed in all perception tasks, whereas overestimation was found in all production tasks. A second experiment ensured that this pattern of under- and over-estimation was not solely generated by the mere process of perceiving or producing something. Participants were required to estimate the alphabetical position of a letter (i.e., perception task) or to produce the letter corresponding to a given position (i.e., production task). No under- or overestimation were observed in this experiment, which suggests that the process of perceiving or producing something alone cannot explain the systematic pattern of estimation observed on magnitudes. Together, these findings strengthen the idea that magnitude estimations share a common metric system, requiring similar mechanisms and/or representations.