Neuropsychologia 50 (2012) 2365–2370

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Dissociation between numerosity and duration processing in aging and earlyParkinson’s disease

Valerie Dormal a, Stephane Grade a, Eric Mormont b,c, Mauro Pesenti a,c,n

a Centre de Neuroscience Syst�eme et Cognition, Institut de Recherche en Sciences Psychologiques, Universite catholique de Louvain, Louvain-la-Neuve, Belgiumb Service de Neurologie, CHU Mont-Godinne, Yvoir, Belgiumc Institute of Neuroscience, Universite catholique de Louvain, Bruxelles, Belgium

a r t i c l e i n f o

Article history:

Received 25 January 2012

Received in revised form

6 June 2012

Accepted 11 June 2012Available online 21 June 2012

Keywords:

Numerosity

Duration

Aging

Parkinson’s disease

32/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.neuropsychologia.2012.06

espondence to: Centre de Neuroscience Syst

he en Sciences Psychologiques, Universite C

l Mercier, 10, B-1348 Louvain-la-Neuve, Bel

2 10 47 37 74.

ail addresses: valerie.dormal@uclouvain.be (V

esenti@uclouvain.be (M. Pesenti).

a b s t r a c t

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

Parkinson’s 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 signifi-

cantly 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.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

It has been suggested that numerical and temporal estimationsrely on a similar representational mechanism, taking the form ofan accumulator (Meck & Church, 1983). This hypothesis hasrecently been integrated within a neuro-functional theory ofgeneralized magnitude processing (ATOM) in which number, timeand space are processed and represented within a commonmagnitude processing system possibly located in the parietalcortex (Bueti & Walsh, 2009; Walsh, 2003). Over the past decade,several behavioral and neuroanatomical studies have shown aclose link between numbers and time. Both numerosity and timeestimation obey Weber’s law (i.e., the precision of magnitudeestimation decreases logarithmically as the size of the magnitudeto be estimated increases) as reflected by distance and size effects(Buckley & Gillman, 1974; Cohen Kadosh, Lammertyn, & Izard,

ll rights reserved.

.006

�eme et Cognition, Institut de

atholique de Louvain, Place

gium. Tel.: þ32 10 47 88 22;

. Dormal),

2008; Dormal, Seron, & Pesenti, 2006; Meck & Church, 1983;Moyer & Landauer, 1967), and by strong interactions betweennumerical and temporal factors observed in behavioral interfer-ence paradigms (for a review, see Dormal & Pesenti, 2012b).Moreover, the investigation of the cerebral substrates of theseprocesses has revealed a common right fronto-parietal network(Dormal, Dormal, Joassin, & Pesenti, 2011).

However, recent lesional data from neuropsychological andtranscranial magnetic stimulation (TMS) studies revealed somedissimilarities. A double dissociation between numerosity andduration processing was observed in two neuropsychologicalstudies (Cappelletti, Freeman, & Cipolotti, 2009, 2011): a patientwith a left parietal lesion was selectively impaired in processingnumerical magnitudes as indicated by poor performance inarithmetical and numerosity estimation tasks, whereas a patientwith a right temporo-parietal lesion had difficulty in estimatingand comparing duration intervals, but no problems with numer-osity processing. Similarly, in a TMS experiment on healthyadults, stimulating the left intraparietal sulcus (IPS) impairedperformance in a numerosity comparison task, but durationcomparison was not affected (Dormal, Andres, & Pesenti, 2008).

This double dissociation suggests the existence of a specificand partially independent mechanism dedicated to duration

V. Dormal et al. / Neuropsychologia 50 (2012) 2365–23702366

processing, but needs further empirical support. In order to testthis hypothesis, numerosity and duration discrimination taskswere compared in patients suffering from Parkinson’s disease(PD) and in healthy elderly participants, two populations forwhich temporal difficulties have been found in previous studies.

PD is a degenerative disorder of the central nervous systemwhose major symptoms are impairments of motor, autonomicand neuropsychiatric (including mood, cognition, behavior, sen-sory or sleep) functions appearing as a result of the death ofdopamine-generating cells in the substantia nigra and the dis-turbance of the fronto-striatal circuits (Ibarretxe-Bilbao, Junque,Marti, & Tolosa, 2011). Among the cognitive deficits, severalneuropsychological group studies have reported impairments oftemporal estimation (Malapani, Deweer, & Gibbon, 2002), butmany contradictory results have been observed. The presence ofsuch a deficit in PD patients seems to be dependent on the rangeof durations used in the studies: some PD patients were able toestimate intervals in the millisecond range (Ivry & Keele, 1989;Koch et al., 2008; Spencer & Ivry, 2005; but for alternative resultssee Rammsayer & Classen, 1997; Riesen & Schnider, 2001; Smith,Harper, Gittings, & Abernethy, 2007). Severe impairments weresometimes observed when patients processed temporal informa-tion in the range of 1 to several seconds (e.g., Koch et al., 2008;Malapani et al., 1998; Pastor, Artieda, Jahanshahi, & Obeso, 1992;Smith et al., 2007). Various patterns of performance werereported, with an overestimation of short durations (78 s;Harrington & Haaland, 1999; Malapani et al., 1998) and anunderestimation of long durations (715 s; Koch et al., 2008;Malapani et al., 1998; Pastor et al., 1992). This can be interpretedas a dysfunctional representation of memory for time (Malapaniet al., 1998).

The nature of the task may also affect the severity of temporaldeficits in these patients. For example, a greater impairment wasobserved when temporal estimation was closely linked to motorprocesses (e.g., finger tapping or time production task; Elsingeret al., 2003; Jones, Malone, Dirnberger, Edwards, & Jahanshahi,2008; Torta et al., 2010), whereas tasks based more on memory(e.g., reproduction task) than on the speed of the internal clock(e.g., perception task) were better preserved (Perbal et al., 2005).The substantial PD heterogeneity present in the samples ofprevious studies (e.g., rates of clinical progression, age of onset,medication dosage or cognitive performance on neuropsycholo-gical tests) could be the main source of all these discrepancies(Merchant, Luciana, Hooper, Majestic, & Tuite, 2008). To date, onlya few studies have explored numerical abilities in PD patients,focusing mainly on arithmetical performance to reveal difficultiesin complex mental calculation (Goebel, Mehdorn, & Leplow, 2010;Tamura, Kikuchi, Otsuki, Kitagawa, & Tashiro, 2003; Zamarian et al.,2006). To the best of our knowledge, non-symbolic numericalestimation has never been explored with this population.

As PD corresponds to a neurodegenerative disease with a meanonset age of over 60 (Hindle, 2010), the mean age of all thepatients and of control samples in these studies is relatively high.Importantly, aging seems to be a factor influencing performancein both numerical and temporal estimation. Numerous studieshave reported declining timing performance with age, especiallywhen durations had to be produced (e.g., Baudouin, Vanneste,Isingrini, & Pouthas, 2006; Craik & Hay, 1999; Espinosa-Fernandez, Miro, Cano, & Buela-Casal, 2003; Gooch, Stern &Rakitin, 2009; Lustig & Meck, 2011; Wild-Wall, Willemssen,Falkenstein, & Beste, 2008). As underlined by a meta-analyticreview (Block, Zakay, & Hancock, 1998), different dysfunctionsemerged in elderly participants as a function of the experimentalprotocols or the range of the duration intervals to be timed(e.g., global under- or over-estimations, increasing variability,slower response latencies). Consequently, several explanatory

hypotheses have been proposed. Age-related differences in theaccuracy and variability of temporal estimates have been attrib-uted either to changes in processing speed (Craik & Hay, 1999),attention (Block et al., 1998; Lustig & Meck, 2011; Vanneste &Pouthas, 1999) or memory (Baudouin et al., 2006; Perbal, Droit-Volet, Isingrini, & Pouthas, 2002; Rakitin, Stern, & Malapani,2005). Investigation of numerical processing in an aging popula-tion highlighted different patterns of performance, suggestingthat numerical cognition is one of the cognitive domains whereaging has mixed effects (Duverne & Lemaire, 2005). Even whenelderly adults have no difficulty with visual enumeration (e.g., Liet al., 2010; Trick, Enns, & Brodeur, 1996; Watson, Maylor, &Bruce, 2005) or approximate quantification tasks (Gandini,Lemaire, & Michel, 2009; Lemaire & Lecacheur, 2007), theirsubitizing and counting speed decreases slightly with aging(Geary & Lin, 1998; Li et al., 2010; Sliwinski, 1997; Trick et al.,1996; Watson, Maylor, & Manson, 2002). Moreover, elderly adultsuse multiple strategies when solving arithmetical problems andare influenced by problem difficulty (Arnaud, Lemaire, Allen, &Michel, 2008; Gandini, Lemaire, & Dufau, 2008; see Duverne &Lemaire, 2005 for a review). However, to our knowledge, theeffect of aging on non-symbolic sequential numerical comparisoncapacities has never been investigated.

The aim of the present study was to test the idea of commonand distinct mechanisms for numerosity and duration processingby assessing whether these deficits associate or dissociate in tworelevant groups of participants. Firstly, using carefully controlled(i.e., with no potential confound) sequential material and simplevisual tasks, we tested for the first time whether the durationprocessing impairment previously reported in PD patients (e.g.,Malapani et al., 1998) is also associated with numerosity proces-sing in this population. Secondly, the performance of healthyelderly adults during duration and numerosity comparison taskswas compared for the first time to that of healthy young controlsin order to assess whether aging exerts a similar effect onnumerosity and duration processing. We thus tested three groupsof participants (PD patients, healthy elderly adults and healthyyoung adults). They were asked to compare either the numerosityof flashed dot sequences or the duration of single dot displays.Based on the results of previous studies in PD patients (e.g.,Malapani et al., 1998) and in elderly participants (e.g., Goochet al., 2009), we predicted that these two groups would have moredifficulty in processing durations than young adults and, more-over, that the performance of PD patients would be worse thanthat of healthy elderly adults. A similar impairment in thenumerosity task in both elderly adults and PD groups wouldsupport the assumption that numerosity and duration sharecritical mechanisms and/or representations, possibly sustainedby common frontal region; a dissociation between numerosityand duration either in elderly adults or in PD patients wouldsupport the idea that a particular and independent durationmechanism and/or representation, serviced by specific cerebralareas, would be responsible for temporal difficulties in thesepopulations.

2. Materials and methods

2.1. Participants

A total of 54 volunteers, including 18 individuals with idiopathic PD (11 males,

mean age: 64.279.3 years), 18 healthy elderly controls (HE) closely matched for

sex and age (11 males, mean age: 63.879.8 years; t(34)¼�0.140, ns), and 18

healthy young adults (HY; 6 males, mean age: 21.172.4 years) participated in the

study. All participants had normal or corrected-to-normal vision and were right-

handed except for two in the HE group. The clinical diagnosis of idiopathic PD was

established by a neurologist. All PD participants were prescribed dopaminergic

Table 1Socio-demographic and clinical background variables.

PD patients HE participants HY participants

Socio-demographic variables Mean age7SD 64.279.3 63.879.8 21.172.4

Gender 11M/7F 11M/7F 6M/12F

Laterality 18R 16R/2L 18R

Mean years of education7SD 12.273.12 11.472.9 a

Clinical background variables Duration since diagnostic7SD 3.672.3 years

Hoehn & Yahr stage7SD 1.870.4

MMSE7SD 28.670.5

Note: SD: standard deviation; MMSE: Mini Mental State Examination; PD: Parkinson disease; HE: Healthy Elderly; HY: Healthy Young; M: Male; F: Female; R: Right-

handed; L: Left-handed.a All the HY participants were students at the Universite catholique de Louvain.

1 To avoid mere pattern identification in the numerosity task, the 10

presentations corresponded to non-periodical items with same numerical proper-

ties but with different temporal characteristics.2 A separate analysis with the order of tasks (duration/numerosity vs.

numerosity/duration) as a supplementary between-subject variable revealed no

main effect and no interaction involving order. Therefore, this variable was not

included in the main analysis.

V. Dormal et al. / Neuropsychologia 50 (2012) 2365–2370 2367

replacement medication for Parkinsonian symptoms and were tested in their ‘‘on’’

state. Mean time after diagnosis was 3.6 years (range 1–9 years).

Exclusion criteria for PD participants were (i) a Hoehn and Yahr (1967)

score42.5; (ii) dementia based on a MMSE score below 26 (Folstein, Folstein, &

McHugh, 1975) and defined as significant impairment on at least two cognitive

domains (executive functions and attention, verbal learning and memory, or

visuo-spatial abilities) in association with functional impairment due to cognitive

impairment (defined as an inability to self-administer medication independently

or to undertake any basic or instrumental activity of daily living, due to cognitive

loss; Dubois et al., 2007); and (iii) severe functional impairment of the autonomic

nervous system. PD patients and control participants had no history of substance

abuse and no concomitant major neurological, psychiatric or medical disease. The

experimental protocol was approved by the Biomedical Ethical Committee of the

Universite catholique de Louvain and written informed consent was given by each

participant prior to the experiment. The clinical and socio-demographic charac-

teristics of the PD and healthy participants are reported in Table 1.

2.2. Tasks and stimuli

The participants had to perform two tasks: (1) a numerosity comparison of

two successive series of flashing dots and (2) a duration comparison of two

successive single dots. Stimuli in the numerosity task were composed of a black

dot (diameter: 3.5 cm) flashed rapidly at the centre of the screen. The series were

constructed using non-periodic signals so that temporal ratios did not constitute a

potential confounding variable, and rhythm biases and pattern recognition were

avoided (Breukelaar & Dalrymple-Alford, 1998; Dormal et al., 2006). The total

duration of the series (i.e., the duration of the dots plus the inter-dot intervals)

was constant (1500 ms), whereas the duration of each dot presentation and the

duration of the inter-dot intervals varied randomly from 50 to 270 ms. In the

duration task, the stimuli were composed of pairs of single black dots (diameter:

3.5 cm) presented sequentially at the center of the screen. To avoid as far as

possible potential explicit or implicit counting strategies, non-subitizable numer-

osities (from 5 to 9 dots, excluding 7) and short durations (from 500 to 900 ms)

that have been shown to make a counting strategy little efficient (Grondin,

Meilleur-Wells, & Lachance, 1999) were used. Pairs of series or dots were chosen

to constitute two distances: a large distance (3 dots for numerosity: pairs 5–8, and

6–9; 300 ms for duration: pairs 500–800, and 600–900) and a small distance (1

dot for numerosity: pairs 5–6, and 8–9; 100 ms for duration: pairs 500–600, and

800–900). The order of presentation of the two series/dots within the pairs was

also manipulated: half of the pairs began with the smaller/shorter series or dot (S–

L), and the other half with the larger/longer one (L–S).

2.3. Experimental procedure

Stimulus presentation and data collection were controlled by a Dell laptop

using a customized E-prime program (Schneider, Eschman, & Zuccolotto, 2002).

The viewing distance was approximately 50 cm. At the beginning of each trial, a

white fixation cross was presented in the centre of the screen on a black

background. After 1000 ms, the first series of flashing dots or a single dot was

displayed in the centre of a white rectangle (9.5 cm�16 cm) for a given duration,

after which the rectangle disappeared and was replaced by a black screen for

750 ms. Then the second series or dot was presented, and was followed by a

yellow centered question mark on a black screen, during which presentation the

participants were supposed to answer (Fig. 1). As soon as the answer was given,

the next trial started.

In the numerosity comparison task, the participants had to decide which series

contained more dots by pressing one of two 13 cm-distant keys on a keyboard

with the left index finger for the first array, and the right index finger for the

second series. In the duration comparison, they had to decide which dot was

displayed for longer, using the same key presses. Each task was composed of

2 blocks of 40 randomized items, corresponding to 10 presentations of each item1;

a practice block of 10 items was administered first but not included in the

analyses. The order of the tasks was counterbalanced across participants. The

whole experiment lasted about 40 min.

3. Results

An analysis of variance (ANOVA) was performed on error rateswith Group (HY, HE vs. PD) as the between-subject variable andTask (Numerosity vs. Duration) and Distance (Small vs. Large) aswithin-subject variables.2 Significant main effects were observedfor Task (F(1,51)¼26.714, po0.001, Z2

¼0.344) and Distance(F(1,51)¼15393.548, po0.001, Z2

¼0.838). Overall, there weremore errors in the duration than in the numerosity task (meanpercentage of errors for duration: 27.8712.8; for numerosity:20.078.9), and more errors for items with a small than with alarge distance (mean percentage of errors for small: 32.377.9;for large: 15.5711.6).

By exploring the individual profiles of the distance effect (i.e.,the mean error rates for small distances minus the mean errorrates for large distances), it is worth noting that 29 participantsshowed a larger distance effect for the duration task (10/18 of theHY group, 10/18 of the HO and 9/18 of the PD group), 21 had alarger effect for the numerosity task (6/18 of the HY group, 8/18 ofthe HO and 7/18 of the PD group), while 4 showed similar effect inboth tasks (2/18 of the HY group, and 2/18 of the PD group). A w2

analysis revealed that this distribution of participants in eachgroup could easily have arisen by chance (all p-values40.6).

A significant effect of Group was also present (F(2,51)¼3.875,po0.03, Z2

¼0.132). Overall, HY participants made fewer errorsthan HE and PD participants (mean percentage of errors for HY:19.676.7; for HE: 24.677.6; for PD: 27.5711.1; HY–HE:t(34)¼–2.092, po0.05; HY–PD: t(34)¼�2.608, po0.02). Nosignificant difference was observed between HE and PD groups(HE–PD: t(34)¼�0.935, ns). Importantly, these main effects werequalified by a Task by Group interaction (F(2,51)¼6.886,po0.003, Z2

¼0.213; see Fig. 2). The three groups did not differsignificantly on the numerosity task (mean % of errors fornumerosity in HY: 18.677.7; in HE: 21.578.4; in PD:19.8710.5; all p-values40.2), whereas in the duration task, theHY group differed significantly from the HE and PD groups which

Fig. 1. Schematic representation of the temporal structure of the (A) numerosity and (B) duration comparison tasks. Note: Each trial was composed of a fixation cross,

followed by a first stimulus (i.e., (A) a series of flashing dots or (B) a single dot), after which a black screen appeared for 750 ms. Then a second series or single dot was

flashed. Finally, a black response screen with a central question mark was presented, remaining on the screen until the participant responded.

Fig. 2. Mean percentage of errors (7SE) as functions of task (numerosity or

duration) and group. Note: HY: Healthy Young adults; HE: Healthy Elderly adults;

PD: Parkinson Disease patients.

V. Dormal et al. / Neuropsychologia 50 (2012) 2365–23702368

in turn differed marginally from each other (mean % of errors forduration in HY: 20.676.5; in HE: 27.679.6; in PD: 35.2716.1;HY–HE: t(34)¼�2.598, po0.02, HY–PD: t(34)¼�3.574,po0.002; HE–PD: t(34)¼�1.714, po0.09). Moreover, therewas no difference between the numerosity and duration tasksin the HY group (t(17)¼1.673, ns), while there were differencesbetween the two tasks in the HE (t(17)¼2.703, po0.015) and inthe PD group (t(17)¼4.096, po0.002). There were no othersignificant interactions (all p-values40.3).

A close inspection of individual performances revealed that 42out of 54 participants made more errors in the duration task thanin the numerosity task (HY: 11/18, HE: 14/18, PD: 17/18). Whileno significant difference was observed in the HY group(w2¼0.889, p¼), participants in the HE and PD groups made

significantly more errors in the duration task than in the numer-osity task (HE: w2

¼5.556, po0.02; PD: w2¼14.22, po0.001).

In order to test a potential effect of task difficulty, an additionalanalysis was carried out on error rates contrasting the easiestcondition of the duration task (i.e., the large distance) and thehardest condition in the numerosity task (i.e., the small distance).A similar interaction between Task and Group was revealed(F(2,51)¼6.061, po0.005, Z2

¼0.192), reflecting an absence ofsignificant differences between the three groups only in the numer-osity comparison task (all p-values40.5). In the duration task, theHY group differed significantly from the HE and PD groups that didnot differ from each other (mean % of errors HY: 9.476.2; in HE:20.0714.5; in PD: 27.1722.8; HY–HE: t(34)¼�2.838, po0.009;HY–PD: t(34)¼�3.168, po0.004; HE–PD: t(34)¼�1.116, ns).

A similar ANOVA was performed for response latencies (RLs). Thisrevealed only a significant main effect of distance (F(1,51)¼39.174,po0.001, Z2

¼0.434): the participants were faster for the large thanfor the small distance (mean RLs for small distance: 6257184 ms;for large distance: 5577158 ms). There were no other significantmain effects or interactions (all p-values40.1).

4. Discussion

In this study, we have investigated numerosity and durationcomparison in healthy young (HY) and healthy elderly (HE) adultsand in Parkinson’s disease (PD) patients to establish whether

distinct processes or representation are involved in the processingof these two magnitudes. To this end, we assessed the impact ofPD, on the one hand, and the possible effect of aging, on the otherhand, on both numerosity and duration processing.

Our results showed that HE adults have difficulty performing aduration comparison task correctly. Indeed, they made signifi-cantly more errors on this task than did HY participants. Thisfinding fits with the results of previous studies (e.g., Gooch et al.,2009; Wild-Wall et al., 2008), supporting the idea of an onset ofduration impairment between the ages of 51 and 60 (Espinosa-Fernandez et al., 2003). Moreover, the performance of PD parti-cipants was slightly worse than that of HE participants, suggest-ing a greater duration deficit in this pathological population.Previous studies exploring duration processing abilities in a PDpopulation reported contradictory results, sometimes revealingdifficulties (Riesen & Schnider, 2001), and sometimes no impair-ment for short durations (Koch et al., 2008; Spencer & Ivry, 2005).Additionally, a recent study reported differences between thecontrol group and HE and PD participants, whereas the latter twogroups did not differ during interval-reproduction tasks of similar

V. Dormal et al. / Neuropsychologia 50 (2012) 2365–2370 2369

duration to ours (i.e., over 1 s; Wild-Wall et al., 2008). Here, byusing a simple comparison task (i.e., requiring two durations to beencoded and compared, but involving no production or reproduc-tion) with a duration range of just under one second, wedemonstrated a strong deficit in non-demented PD patients. It isworth noting that this impairment was present although thepatients were tested during a period of on-medication.

Our results have demonstrated for the first time the absence ofdifference between the three groups of participants on thenumerosity comparison task. Thus, aging and PD do not seem toaffect numerosity processing. Importantly, as no difference wasfound between the two tasks in the HY group (i.e., the responselatencies and error rates were similar), the differences betweenthe tasks observed in the HE and PD groups are not related todifferences in attentional or difficulty demands across the tasks.The unaffected performance in numerosity comparison, coupledwith impairment in temporal processing in both HE and PDparticipants, suggested the involvement of distinct mechanismsand/or representations for numerosity and duration processing.Interestingly, the reverse dissociation was induced by TMS overthe left IPS, leading to a temporary disruption of numerosityprocessing, whereas there was no effect on temporal judgment(Dormal et al., 2008).

Our results are also in line with two recent lesional studies(Cappelletti et al., 2009, 2011) that reported a double dissociationbetween numerosity and duration processing: one patient with aright parietal lesion showed impaired duration judgment andpreserved numerical abilities, whereas the reverse pattern ofdeficits was present in another patient with a left hemisphericlesion. All these data converge on the idea that numerosity andduration do not share a single totally common system of magni-tude processing, but that, in addition to the functional andanatomical similarities already established (e.g., Dormal et al.,2012; Droit-Volet, 2010), there also exist distinct mechanismsand, hence, anatomical substrates. The fronto-striatal circuits, thedopaminergic system and the basal ganglia, known to play acrucial role in timing processes (Buhusi & Meck, 2005; Mattell &Meck, 2004), may correspond to the impaired regions and lead todifficulties in the duration comparison task. Indeed, the function-ing of these neural systems is known to be worse in HE (e.g.,Backman, Nyberg, Lindenberger, Li, & Farde, 2006; Ota et al.,2006) and in PD patients (e.g., Bondi, Kaszniak, Bayles, & Vance,1993; Nieoullon, 2002) than in HY individuals.

More precisely, for HE adults, the temporal deficit may be theconsequence of dysfunctional fronto-striatal circuits (Buckner,2004), while the degeneration of the nigrostriatal pathway andthe dysfunction of the dopaminergic system in PD may beresponsible for the duration impairment observed in this popula-tion (Lustig & Meck, 2005). As a difference was observed betweenthe performance of HE adults and PD patients in our study(corresponding to an amplification of the deficit in durationprocessing), these cerebral systems may be affected to differentdegrees by aging and PD. It is worth noting that although thebasal ganglia sustain arithmetical fact retrieval (Delazer et al.,2004) and complex calculation (Zamarian et al., 2006), they donot seem to be crucially involved in non-symbolic numerositycomparison. Given that little is known concerning the exactlesional aspects of the disease in the PD group, this proposalremains partly speculative, and further studies are required toclarify it.

Finally, although we controlled the stimuli parameters (e.g.,non-periodic signals, non-subitizable numerosities, short dura-tions, etc.) carefully and gave explicit instructions to discouragethe use of counting strategies, we did not explicitly assess therepertoire of strategies used by our participants. Therefore, wecannot exclude the possibility that the different groups used

different strategies that could be equally efficient on one taskbut perform differently on another task. As demonstrated inapproximate quantification (Gandini et al., 2008, 2009) or in asimple subtraction solving task (Arnaud et al., 2008), some age-related differences might be observed in strategy use and/or instrategy execution in our categorization tasks leading to differ-ences in performance across groups. Future studies controllingthis aspect would help to clarify this issue.

5. Conclusions

Impairments in duration processing were observed both in HEadults and in PD patients, although both groups performed wellon numerosity comparisons. Such a dissociation supports theexistence of common and partially independent, rather than fullyshared, magnitude systems (Cappelletti et al., 2011; Dormal &Pesenti, 2012a). At a clinical level, the present results suggest thata duration comparison task might be a useful and rapid screeningtool to confirm the suspected presence of dysfunction of thefronto-striatal circuit and dopaminergic system in HE adults andin patients with suspected PD.

Acknowledgements

VD is a post-doctoral researcher, SG is a research fellow andMP is a research associate at the National Fund for ScientificResearch (Belgium). We thank Marie D. Lecl�ere for her help indata collection.

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