The neural basis of number processing

J’ai voulu vous transmettre ceci dans les annonces de pontt. Mais c’est un peu long et ça passe mal. J’en ai donc fait un billet car je crois que tout ce qui suit mérite d’être partagé ici.

calculmental

Annual seminar series of the IUAP/PAI P6/29

The neural basis of number processing

April 8 & April 15, 2010

Organizer:     Wim Fias, Ghent University

Support:         Interuniversity Attraction Poles Programme – Belgian Science Policy
Center for Cognitive Neuroscience – Ghent University
Department of Experimental Psychology – Ghent
University

Location:        Room 2B (2nd floor)
Faculty of Psychology and Educational Sciences
Henri Dunantlaan 2
9000 Ghent

http://expsy.ugent.be/contact/cdirections.htm

Contact: wim.fias@ugent.be

APRIL 8

2 p.m. – 3 p.m.

Elena Rusconi (University College London, UK)

Revisiting Gerstmann’s syndrome

3 p.m. – 4 p.m.

André Knops

Mental arithmetic – psychophysics and neural correlates

4 p.m. – 5 p.m.

Roland H. Grabner (Institute for Behavioral Sciences, ETH, Zurich)

Successful mathematics learning: Insights from brain imaging studies on mental arithmetic

APRIL 15

2 p.m. – 3 p.m.

Simon Jacob (University of Tuebingen, Germany)

INVESTIGATING THE NEURAL CODE FOR PROPORTIONAL MAGNITUDE IN THE HUMAN BRAIN

3 p.m. – 4 p.m.

Valérie Dormal (Université Catholique de Louvain, Belgium)

A magnitude system in the parietal cortex? Behavioural, TMS and fMRI studies

4 p.m. – 5 p.m.

Fabrizio Doricchi (La Sapienza & Fondazione Santa Lucia, Rome, Italy)

Dissociations between space processing and number processing: evidence from the study of right brain damaged patients and healthy participants

ABSTRACTS

Elena Rusconi (University College London, UK)

Revisiting Gerstmann’s syndrome

Eighty years ago, the Austrian neurologist Josef Gerstmann observed in a few patients a concomitant impairment in discriminating their own fingers, writing by hand, distinguishing left from right
and performing calculations. He claimed that this tetrad of symptoms constituted a syndromal entity, assigned it to a lesion of the dominant parietal lobe and suggested that it was due to damage to
a common functional denominator. Ever since, these claims have been debated and an astute synopsis and sceptical discussion was presented 40 years ago by MacDonald Critchley. Nonetheless,
Gerstmann’s syndrome has continued to intrigue both clinical neurologists and researchers in neuropsychology, and more frequently than not is described in textbooks as an example of parietal lobe
damage. I will briefly revisit the chequered history of this syndrome which can be seen as a case study of the dialectic evolution of concepts in neuropsychology. In light of several modern era
findings of pure cases I will conclude that it is legitimate to label the conjunction of symptoms first described by Gerstmann a “syndrome” but that it is very unlikely that damage to the same
population of cortical neurons should account for all of the four symptoms. I’ll thus propose that a pure form of Gerstmann’s syndrome might arise from disconnection in the subcortical parietal
white matter. This hypothesis has been tested by using structural and functional neuroimaging at high spatial resolution in healthy subjects to seek a shared cortical substrate of the
/Grundstörung/ posited by Gerstmann, i.e., a common functional denominator accounting for this clinical tetrad. A functional activation paradigm was construed that mirrors each of the four clinical
deficits in Gerstmann’s syndrome and determined cortical activation patterns. Fiber tracking was then applied to diffusion tensor images and cortical activation foci were used in the four
functional domains as seed regions. None of the subjects showed parietal overlap of cortical activation patterns from the four cognitive domains. In every subject, however, the parietal activation
patterns across all four domains consistently connected to a small region of subcortical parietal white matter at a location that is congruent with the lesion in a well documented case of pure
Gerstmann syndrome. Such functional neuroimaging findings are not in agreement with Gerstmann’s postulate of damage to a common cognitive function underpinning clinical semiology. Such evidence
suggests that pure forms of Gerstmann’s tetrad do not arise from lesion to a shared cortical substrate but from intraparietal disconnection after damage to a focal region of subcortical white
matter.

Rusconi, E., Pinel, P., Dehaene, S., & Kleinschmidt, A. (2010). The enigma of Gerstmann’s syndrome revisited: A telling tale of the vicissitudes of neuropsychology. Brain, 133, 320-332.

Rusconi, E., Pinel, P., Eger, E., LeBihan, D., Thirion, B., Dehaene, S., Kleinschmidt, A. (2009). A disconnection account of Gerstmann syndrome: Functional neuroanatomy evidence. Annals of
Neurology, 66, 654-662.

André Knops

Mental arithmetic – psychophysics and neural correlates

Our understanding of the numerical magnitude representation has improved fundamentally over the last years. In contrast, the exact mechanisms how magnitudes are manipulated during simple mental
calculations are not yet well defined.

In a series of experiments I investigated the psychophysical characteristics of simple addition and subtraction problems both in symbolic and non-symbolic notation. A number of characteristics were
observed for both notations, implying largely overlapping mechanisms. In detail, I observed a tendency of participants to overestimate the results for additions while underestimating the results
for subtractions, the operational momentum (OM) effect. This effect was intertwined with a spatial bias for upper right space with addition and upper left space with subtraction. This implies the
contribution of spatial shifts of attention to mental calculation.

In an fMRI study this idea was tested by training a multivariate classifier to infer the direction of an eye movement, left or right, from the brain activation measured in posterior parietal
cortex. Without further training, the classifier then generalized to an arithmetic task. Its left versus right classification could be used to sort out subtraction versus addition trials, whether
performed with symbols or with sets of dots. These results are in line with the idea that both symbolic and non-symbolic mental calculation co-opts brain circuitry that evolved for spatial
coding.

Together, these findings suggest that approximate mental arithmetic involves dynamic shifts on a spatially organized mental representation of numbers.

Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence of the operational momentum effect. Attention Perception &
Psychophysics, 71, 803-821.

Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). The recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583-1585.

Roland H. Grabner (Institute for Behavioral Sciences, ETH, Zurich)

Successful mathematics learning: Insights from brain imaging studies on mental arithmetic

Successful learning of arithmetic skills is an essential step in the development of mathematical competence. This long-term learning process is typically accompanied by changes in problem solving
strategies in terms of a shift from procedural (calculation) strategies to arithmetic fact retrieval from memory. Brain imaging studies have recently begun to uncover the neural underpinnings of
arithmetic learning by demonstrating developmental and training-related changes in the functional specialization of parietal brain areas during mental arithmetic. Starting from these findings, I
will present functional magnetic resonance imaging (fMRI) studies on the brain correlates of arithmetic strategies and mathematical competence. These studies show that a specific region of the
temporo-parietal cortex, the angular gyrus (AG), mediates arithmetic fact retrieval. Moreover, AG activation differs between individuals of higher and lower mathematical competence not only in
arithmetic problems but also in tasks requiring the mapping of numerical information between different representation formats (symbolic vs. non-symbolic). I will conclude by proposing that the AG
plays a key role in symbol-referent mapping during arithmetic skill acquisition.

Grabner, R. H., Ansari, D., Reishofer, G., Stern, E., Ebner, F., & Neuper, C. (2007). Individual differences in mathematical competence predict parietal brain activation during mental
calculation. NeuroImage, 38, 346-356.

Grabner, R. H., Ischebeck, A., Reishofer, G., Koschutnig, K., Delazer, M., Ebner, F., & Neuper, C. (2009). Fact learning in complex arithmetic and figural-spatial tasks: The role of the angular
gyrus and its relation to mathematical competence. Human Brain Mapping, 30, 2936-2952.

Simon Jacob (University of Tuebingen, Germany)

INVESTIGATING THE NEURAL CODE FOR PROPORTIONAL MAGNITUDE IN THE HUMAN BRAIN

Grasping the concept of absolute magnitude comes naturally to most species. Simple enumeration or quantification, however, is often insufficient to make decisions and guide behavior. In many
instances, we need to relate two quantities, generating a new composite construct: a proportion or magnitude ratio.

I will present recent experiments to investigate the neural representation of proportional magnitude in the human brain using fMRI adaptation techniques with non-symbolic (ratios of line lengths
and numerosities) as well as symbolic stimuli (fractions and proportion words).

Following adaptation to visually presented constant proportions, novel deviant ratios were introduced to examine the tuning characteristics of the population of stimulated neurons. With both
stimulus categories, distance effects for BOLD signal recovery were found in the intraparietal sulcus (IPS) and bilateral frontal cortex. Tuning was automatic, independent of the exact
configuration of the visual display, independent of notation (even within the same experimental run) and strongest in cortical structures previously reported to be dedicated to the processing of
whole numbers.

These findings demonstrate that populations of neurons in the human parietal and frontal cortex are tuned to preferred magnitude ratios using the same non-verbal analog code to create abstract
concepts of both absolute and relative number. I will argue that these results add to the magnitude system a remarkable level of sophistication by suggesting automatic access to a composite,
derived quantitative measure.

Jacob, S. N., & Nieder, A. (2009). Notation-independent representation of fractions in the human parietal cortex. Journal of Neuroscience, 29, 4652-4657.

Jacob, S. N., & Nieder, A. (2009). Tuning to non-symbolic proportions in the human frontoparietal cortex. European Journal of Neuroscience, 30, 1432-1442.

Valérie Dormal (Université Catholique de Louvain, Belgium)

A magnitude system in the parietal cortex? Behavioural, TMS and fMRI studies

Adults, infants and animals process and represent numerosity, time and length and they use these quantitative dimensions to guide learning and behaviour. From a broad range of behavioural,
physiological, developmental, lesional and neuroanatomical data on magnitude processing, Walsh (2003) recently proposed the existence of a generalised magnitude system located in the parietal
cortex.

In a series of behavioural, neurophysiological and neuroimaging studies with healthy adult participants, we assessed the functional interactions between these magnitudes, we isolated the common and
specific brain areas underlying their processing, and we tested the causal role played by these areas. Our results demonstrate for the first time in within-participant designs the implication of an
area along the right intraparietal sulcus (IPS) commonly activated in numerosity, duration and length processing. However, this common area appears causally involved only in numerosity and length
judgements, as demonstrated by transcranial magnetic stimulation studies.

Together, our findings support the idea that the IPS holds both a common and partially distinct and specific representations and/or mechanisms for numerosity, time and length processing.

Dormal, V., & Pesenti, M. (2009). Common and specific contributions of the intraparietal sulci to numerosity and length processing. Human Brain Mapping, 30, 2466-2476.

Dormal, V., Andres, M., & Pesenti, M. (2008). Dissociation of numerosity and duration processing in the left intraparietal sulcus: A transcranial magnetic stimulation study. Cortex,
44,      462-469.

Fabrizio Doricchi (La Sapienza & Fondazione Santa Lucia, Rome, Italy)

Dissociations between space processing and number processing: evidence from the study of right brain damaged patients and healthy participants

Spatial coding has a pervasive influence on both human intuition of numbers and human intuition of numerical cognition in the brain. As an example, the “mental number line” is usually taken as
synonymous of a line in which small numbers are located to the left of larger ones. However, it is poorly understood, and it is a matter of debate, at which stage of cognitive processing spatial
mapping (i.e. left/right, up/down) becomes associated with the neural representation of numerosities, in which coding of increasing numerosities shows progressively larger representation overlaps
with adjacent ones. Through a series of investigations in right brain damaged patients and healthy participants we addressed this issue. The results of these investigations allowed us to draw the
following main conclusions:

1)     Lateralised deficits of spatial attention (i.e. left spatial neglect) are systematically dissociated from lateralised biases in the bisection of the mental number
line.

2)     Right brain damage disrupts the representation of numerosity at a level of cognitive processing that precedes the use of a mental spatial layout for number mapping and
manipulation.

3)     The association between space coding and number coding is not an automatic one

It is proposed that the term “mental number line” should be used only if devoid of any spatial feature, just to indicate overlapping in the representation of adjacent magnitudes.

Doricchi, F., Merola, S., Aiello, M., et al. (2009). Spatial orienting biases in the decimal numeral system. Current Biology, 19, 682-687.

Doricchi, F., Guariglia, P., Gasparini, M., et al. (2005). Dissociation between physical and mental number line bisection in right hemisphere brain damaga. Nature Neuroscience, 8, 1663-1665.


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