Assessment of Time Perception the Effect of Aging

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    Assessment of time perception: The effect of aging

    MIGUEL COELHO,1 JOAQUIM JOS FERREIRA,1,2 BEATRIZ DIAS,1 CRISTINA SAMPAIO,2

    ISABEL PAVO MARTINS,1 and ALEXANDRE CASTRO-CALDAS11Laboratrio de Estudos da Linguagem, Centro de Estudos Egas Moniz, Faculdade de Medicina de Lisboa, Hospital Santa Maria,Av. Egas Muniz, 1649-028 Lisboa, Portugal

    2Instituto de Farmacologia e Teraputica Geral, Faculdade de Medicina de Lisboa, Hospital Santa Maria, Av. Egas Muniz,1649-028 Lisboa, Portugal

    (Received June 3, 2002; Revised July 28, 2003; Accepted August 26, 2003)

    Abstract

    Studies concerning time perception lack a validated assessment tool and a consensual gold-standard measure.Moreover, the present evidence suggests modification of timing with aging. This study aimed to develop andvalidate a neuropsychological tool to measure time perception and to study temporal perception with aging.Eighty-six healthy participants, aged 1590 years old, were asked to verbally estimate and produce emptyintervals signaled by auditory beeps, of 7-, 32-, and 58-s duration. Two tests were used as gold-standards:estimation of the duration of time necessary to draw a clock (clock time) and estimation of the duration ofneuropsychological evaluation (global time). Results showed a correlation between estimation and production(p , .01) and a correlation between estimation or production and global time (p , .01). The correlationbetween either estimation or production and age (p , .01), suggested a faster internal-clock in the olderparticipants. However, this finding lost significance when controlled for literacy. The results suggest that thesetests are potentially a useful tool to measure subjective perception of time. They also corroborate the hypothesisof a change in subjective time perception with aging. It was not possible to conclude if this effect was a specificresult of aging or biased by the interference of literacy. (JINS, 2004, 10, 332341.)

    Keywords: Time perception, Aging, Working memory, Attention

    INTRODUCTION

    Time perception and measure are essential components ofcognition, behavior, and motor performance, representingone of the basic mechanisms of cerebral function (Artieda& Pastor, 1996). Accordingly, temporal processing is anintegral part of many everyday goal-oriented behaviors

    (Mangels & Ivry, 2001), making it a crucial tool for plan-ning future actions.Temporal perception comprises several subjective phe-

    nomena including the judgement of subjective duration (Pop-pel, 1997). The different aspects of psychological time areinterlinked with various attentional, memory, and other cog-nitive processes (Binkofski & Block, 1996). However, the

    explanation for subjective timing also assumes the exis-tence of an internal-clock mechanism (Binkofski & Block,1996).

    Classically, time perception has been explained by twodifferent theoretical models: scalar expectancy theory (SET)(Gibbon et al., 1984) and attentional-gate theory (AG)(Block, 1990). Both models postulate the existence of a

    pacemaker (the clock) that generates neuronal pulses andthe existence of a counter accumulating them. This countersignals when the number of pulses generated reaches a tar-get value corresponding to a given interval duration (Fortin& Breton, 1995). The accumulator serves as a working mem-ory buffer and attention as the gate to working memory.Concomitant nontemporal tasks interfering with workingmemory and0or competing for attention will reduce the ac-curacy in temporal perception (Fortin et al., 1993). To ourbest knowledge there is no data regarding the effect of lit-eracy on time perception.

    Reprint requests to: Miguel Coelho, Laboratrio de Estudos daLinguagem, Centro de Estudos Egas Moniz, Faculdade de Medicina deLisboa, Hospital Santa Maria, Av. Egas Muniz, 1649-028 Lisboa, Portu-gal. E-mail: [email protected]

    Journal of the International Neuropsychological Society (2004), 10, 332341.Copyright 2004 INS. Published by Cambridge University Press. Printed in the USA.DOI: 10.10170S1355617704103019

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    Quantifying timing is difficult because there is no vali-dated method, despite many tools being available (Bindra& Waksberg, 1956), and it is still lacking a consensualgold-standard test to measure temporal perception. Thereis also some evidence that timing changes with age(Carrasco et al., 2001; Craik & Hay, 1999; Fraisse, 1963),but to what extent and in what direction is still a matter of

    debate. Since timing is dependent on working memoryand attention, it is hypothesized that it should deterioratealong neuropathological processes that interfere with thosecognitive functions.

    The aims of our study were twofold: to develop and testa neuropsychological tool to measure time perception andto study time perception along normal aging.

    MATERIAL AND METHODS

    Research Participants

    The study was performed in healthy volunteers, defined asparticipants with no known diseases and not taking drugsknown to interfere directly with the central nervous system.Itwas intendedto include tenpatients perdecade of life, withan age spectrum ranging from 1590 years old. This samplewas not controlled for literacy due to the pragmatic need todefinenormativevaluesforthePortuguesepopulation,whichis characterized by a natural higher literacy in younger indi-viduals;moreover,wewerenotawareofapreviouscleardoc-umentation of a specific effect of literacy on time perception.Exclusioncriteriawereadiagnosisofmajordepression(MINIInternational Neuropsychiatry Interview version 4.4Portuguese version) (Sheehan et al., 1998), a diagnosis ofdementia [Mini Mental State Examination (MMSE) vali-

    dated for the Portuguese population] (Folstein et al., 1975;Guerreiro et al., 1994), the presence of any relevant neuro-logical or psychiatric disease, and the consumption of drugswith central nervous system effect (benzodiazepines withanequivalent dose of diazepam less than 10mg daily were how-everaccepted).Participantswerealsoexcludediftheyabusedalcohol, consumed more than four espresso coffee cups aday, and if they were illiterate or unable to understand thetests. Participants could only be evaluated if they had had agood night sleep according to their usual sleep pattern. Allparticipants gave informed consent.

    Experimental Tasks

    Temporal estimation and production tests were carried outwith a standard Toshiba laptop personal computer and par-ticipants wore headphones to listen to the auditory stimuli.The digits on the Digit Span Forward (DSF) and Digit SpanReverse (DSR) (Garcia, 1984; Wechsler, 1969) tests wereread by the examiner. Participants sat in a comfortable chair,in a quiet and empty room without any rhythmic sound(e.g., wall clock) and they were asked to remove their watchduring the test. All participants were evaluated in the after-noon due to logistical constraints.

    The experimental tasks were performed as follows:

    Verbal estimation and production of a time

    interval

    This experiment tested the ability to verbally estimate andproduce the duration of empty time intervals signaled byauditory beeps. The auditory beeps were of 20-ms duration.A specific software was developed to meet this aim. Thedurations of time intervals were of 7, 32, and 58 s for bothestimation and production tests; every duration was re-peated three times in a pseudorandom order (not allowingthe repetition of the same number in sequence), so that forboth estimation and production tests nine tasks were per-formed. Participants were not aware they would make ninetrials and they did not know the test involved only threepossible interval durations.

    Estimation test. Participants were told that they wouldhave to verbally estimate the duration of different intervals;one auditory beep indicated the onset of the interval whileanother indicated its end; the beeps were separated by asilent interval. Participants were instructed to start internal(mental) counting of seconds after listening to the firstauditory beep and to stop counting when they heard thesecond beep. They were specifically instructed not to countaloud nor to perform any digital counting, or use any bodyrhythm to help in the estimation. Then they were askedhow many seconds elapsed between the two beeps?. Thetest proper was preceded by a test run with an interval du-ration of 4 s. The outcome measure was the ratio betweenthe estimated duration and the target (7, 32, or 58 s) one.For each participant, we calculated the mean of the nineratios and this value was entered for the group statisticalanalysis.

    Production test. Participants were told that they wouldhave to verbally produce different interval durations. In thistask, an auditory beep indicated the onset of the intervaland its end was indicated by the participants, by telling theexaminer when they thought they had reached the targetduration. Participants were asked to start internal countingof seconds after they heard the first beep and to tell theexaminer when they thought they had reached the targetduration. The examiner wore a chronometer to know howmany seconds had the participant really produced. The testproper was preceded by a test run with an interval durationof 4 s. The outcome measure was the ratio between the

    produced duration (the value on the examiners chronom-eter) and the target (7, 32, or 58 s) one. For each partici-pant, we calculated the mean of the nine ratios and thisvalue was entered for the group statistical analysis.

    Gold-standards

    We assumed as gold-standards two tests we accepted asecological, which replicate real-life time measurements. Inboth cases, the participants were not aware they would beasked to retrospectively estimate the time elapsed during acertain task.

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    Clock time. Participants were asked to draw a clock ona blank sheet of paper. After finishing the drawing, the ex-aminer asked the participant how much time had elapsedbetween the moment he held the pen and finished the draw-ing. The examiner used a chronometer to measure the du-ration of the task. The chronometer was started when theparticipant picked up the pen and stopped when the partici-

    pant placed it on the paper. The outcome measure was theratio between the estimated time and the real durationmeasured by the examiner.

    Global time. At the very end of the neuropsychologicalevaluation,theexamineraskedtheparticipanthowmuchtimehadelapsedsincetheystartedthecurrentevaluation.Theon-set of the evaluation had been indicated out loud by the ex-aminerwiththesentence:wearegoingtostartthetestsnowand the examiner specifically referred to that moment whenasking the participant about the elapsed time. The examinerwore a chronometer to know how much time the evaluationhad lasted. The chronometer was started when the examiner

    said the mentioned sentence and stopped just before the ex-amineraskedtheparticipantabouttheelapsedtime.Theout-come measure was the ratio between the estimated time andthe duration measured by the examiner.

    Digit Span Forward and Digit Span Reverse

    These tests were used to measure the attention0short-termand working-memory capacity of the participants. In theDigit Span Forward, the examiner told the participant amaximum of seven sequences of digits, each with an in-creasing number of digits (up to a maximum of nine digits)and at the end of each sequence the participants were asked

    to repeat it in the same order. The Digit Span Reverse wasidentical but the participant had to repeat each sequence ofdigits in the reverse order. The outcome was the highestnumber of digits the participants could repeat correctly. Thedigit span was the last test to be performed at the end of theevaluation.

    Statistical Analysis

    Estimation test

    The outcome measure was the ratio between the estimatedduration and the target (7, 32, or 58 s) duration. For each

    participant, we calculated the mean of the nine ratios.If the ratio was superior to 1, the participant was said tooverestimate, indicating that the hypothetical internal-clock was going faster. If the ratio was inferior to 1, theparticipant was said to underestimate, indicating that theinternal-clock was going slower.

    Production test

    The outcome measure was the ratio between the producedduration (the value on the examiners chronometer) and thetarget (7, 32, or 58 s) duration. For each participant, we

    calculated the mean of the nine ratios. If the ratio was su-perior to 1, the participant was said to overproduce, indi-cating that the hypothetical internal-clock was goingslower. If the ratio was inferior to 1, the participant wassaid to underproduce, indicating that the internal-clockwas going faster.

    Clock timeThe outcome measure was the ratio between the estimatedtime and the duration measured by the examiner.

    Global time

    The outcome measure was the ratio between the estimatedtime and the duration measured by the examiner.

    Digit Span

    For each participant, we recorded the highest number ofdigits the participant could repeat, both in DSF and DSR.

    We studied the relation between estimation and produc-tion tests results and the two gold-standards. A sub-analysis was also performed, studying the relation betweenthe different time intervals (7, 32, and 58 s) and both clockand global time.

    The age effect on estimation, production, clock time, glo-bal time, and digit span were studied. The relation betweenthe digit span and estimation, production, clock time, andglobal time was also investigated.

    A comparison of estimation, production, clock time, andglobal time was made between three predefined age groups(group A: 1540 years old; group B: 4164 years old;group C: 6590 years old). These age intervals were chosen

    according to what we assumed represents different stagesof aging: young, middle-age, and elderly people, respec-tively. We studied the effect of education and gender inestimation, production, clock time, and global time. Educa-tion (number of years in school) was compared between thethree aforementioned age groups. The effect of literacy ontime perception was analyzed as a covariate. The analysisof metric properties of estimation and production variablesshowed they had a near-normal distribution. Although thesize of the sample allowed for parametric tests, we chose tomake use of nonparametric tests in statistical analysis. Re-lations between variables were studied using nonparamet-ric tests for correlations (Spearman test), and comparisons

    of variables between the three age groups were made usingnonparametric tests of variance (Kruskal-Wallis test).

    RESULTS

    Ninety-seven participants were screened to participate inthis study. Seven participants were excluded due to diagno-sis of dementia according to MMSE (4 participants) anddiagnosis of major depression according to the MINI Inter-national Neuropsychiatry Interview (3 participants). Oneparticipant was excluded because she was not able to un-

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    derstand the test instructions. Three individuals did not com-plete the evaluation due to tiredness, and their results werenot included in the analysis. The final sample was of 86participants and the data of these participants were the ba-sis for the analysis. Their age ranged from 1590 years old.There were 58 female and 28 male participants. There wereroughly ten participants per decade of life (Table 1).

    Overall, the verbal estimation and production tests wereeasy to explain and perform.

    Concerning the metric properties of estimation and pro-

    duction, the median value for estimation was 1.081 (Min.2128 and Max 6.3988) and the median value for produc-tion was .8224 ( Min .3382 and Max 1.788), with a statisti-cal significant negative correlation between estimation andproduction (p , .01; r52.5509).

    A positive correlation was found between estimation andglobal time (p, .01; r5 .0712), and a negative correlationbetween production and global time (p, .01; r52.1591).A correlation of estimation or production and clock timewas not demonstrated, as well as a correlation between clockand global time. The different time intervals (7, 32, and58 s), in both estimation and production tests, were all cor-related with global time but not with clock time, and the

    power of correlation was similar between them.

    A positive correlation was found between estimation andage, suggesting that older participants had faster internal-clocks (p , .01; r5 .2978) (Figure 1a). Conversely, anegative correlation was found between production and age,also indicating an association between older participantsand faster internal-clocks (p , .01; r5 2.2731) (Fig-ure 1b). We could not find a correlation between age andeither clock time or global time. All previous analysis loststatistical significance when controlled for literacy. Age wasnegatively correlated with education (p , .01; r5 2.6).

    The results showed a negative correlation between educa-tion and estimation (p , .01; r52.3951) and global time(p , .05; r52.2521), and a positive correlation betweeneducation and production (p , .01; r5 .3612), suggestingthat participants with lower level of education had fasterinternal-clocks.

    We compared the difference in performance between threepredefined age groups (group A: 1540 years old, mean26.84, SD (standard deviation) 7.21; group B: 41 64 yearsold, mean 50.72, SD 4.93; group C: 6590 years old, mean75.84, SD 7.18; 95% confidence interval). When estimationwas compared between the age groups there was a trendtoward overestimation with older age, suggesting accelera-

    tion of internal-clocks with age (Figure 2a). The same

    Table 1. Demographics

    Age groups (years) 1520 2130 31 40 4150 51 60 6170 7180 8190N (total5 58) 10 12 10 10 11 10 14 9F0M 109 1101 802 703 1001 505 905 702Education (years) mean 11.8 17.3 14 12.2 8.8 7.1 7.0 7.5

    Note. N5 number of participants; F5 female; M5male.

    Fig. 1a. Correlation of age with time es-timation. Age was positively correlated[p , .01 (Spearman test r5 .29)] withthe estimation of time, suggesting an ac-celeration of the internal-clock withaging.

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    analysis about production showed a trend toward underpro-duction with age, also suggesting acceleration of internal-clock with age (Figure 2b).

    The performance on estimation, production, clock time,and global time tasks was not significantly different be-tween female and male participants.

    As expected from the literature, we found a negative cor-relation between DSF0DSR and age (p , .01; r52.4715,for DSF; p , .01; r52.4658, for DSR) (Figure 3).

    The results showed a negative correlation between DSF0

    DSR and estimation (p , .01; r52.3398, for DSF; p ,

    .05; r52.2434 for DSR) (Figure 4a). There was a positivecorrelation between production and DSF0 DSR (p , .01;r5 .3286, for DSF;p, .01; r5 .3902, for DSR) (Figure 4b).

    DISCUSSION

    The results of this study showed an internal consistencybetween the performance on estimation and production tests,and found a correlation between those tasks and one of thechosen gold-standards tests, suggesting that our assess-

    ment tool is a potentially good measure of time duration.

    Fig. 1b. Correlation of age with time pro-duction. Age was negatively correlated[p , .01 (Spearman test r52.27)] withthe production of time, suggesting an ac-celeration of the internal-clock with

    aging.

    Fig. 2a. Comparison of mean values oftime estimation between three age groups.There was a trend towards overestima-tion of time with aging.

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    The results also showed a change of estimation and produc-tion of time intervals with aging, suggesting an associationof aging with a faster internal-clock.

    The extensive literature on time perception often differon the methods used to measure temporal perception. How-ever, none of these methods has yet been properly validatedin a normal population, casting doubt on the theoreticalmodels based on their results. Also, as recognized by Allan(1979) and McConchie and Rutschmann (1971), no single

    method can claim a consistent superiority over the othersand the correlation between them is either poor or absent.

    The aim of this study was to develop a neuropsycholog-ical tool to measure subjective duration and, secondly, tostudy temporal perception along normal aging. Firstly, wetried to overcome the lack of a gold-standard test, that is,a test that reliably measures what we want it to measuresubjective time perception. Thus, the first step was to iden-tify a real-life measure against which our tests could be

    Fig. 2b. Comparison of mean values oftimeproduction between three age groups.There was a trend towards underproduc-tion of time with aging.

    Fig. 3. Correlation of Digit Span Forward with age [p , .01 (Spearman test r5 2.47), left figure] and Digit SpanReverse with age [p , .01 (Spearman test r52.46), right figure] showing a decrease performance with aging.

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    compared. The gold-standard, which is in any case rela-tive, should be as feasible and as close as possible a mea-sure of temporal perception of everyday life, that is to say,a pragmatic measure of the processing of temporal infor-mation by the brain in real-life conditions. We assumed as agold-standard for subjective duration the clock timetest and the global time test. In both tests, the participants

    performed tasks without knowing they would be asked toestimate the time elapsed during their performance. Theymade retrospective evaluations, not paying attention to thepassage of time, instead allocating attention towards thetasks themselves. We believe they inferred duration fromcontents of memory, memory for events, number of transi-tions between events, and expectation for duration of events(Block & Zakay, 1997; Ornstein, 1969). Thus, retrospec-tive timing seems to depend mostly on long-term memoryand contextual events (Mangels & Ivry, 2001; Zakay, 1990).On the other hand, during the tests of verbal estimation andproduction, participants knew they should actively monitorthe passage of time. Their prospective measurement was

    mostly dependent on attention, mostly attention to the vari-able time, and working memory (Mangels & Ivry, 2001;Zakay, 1990).

    The evidence that retrospective and prospective timingdepend upon different cognitive processes may explain theweak association we found of estimation and productionwith global time and the lacking association of estima-tion and production with clock time. Besides, an ecolog-ical measure of time perception should have some utilityfor the participant, acting as a motivational drive. While theglobal time measure was surely being subjectively as-sessed for its duration, the clock time measure had littleusefulness or meaning for the participants of the experi-

    ment. This may explain its lack of correlation with moreconscious measures of time perception. Possibly, this dif-ference in usefulness between the global time and theclock time measures also explains the lack of associationbetween each other. An alternative explanation could betheir difference in magnitude duration (the global time inthe range of 2025 min while the clock time in the rangeof a few seconds). In future experiments, we plan to com-pare the estimation and production measures with ecologi-cal gold-standards that require prospective timing andmore meaningful time intervals, eventually increasing thestrength of their statistical association; moreover, if morethan one gold-standard is used, they should be of samemagnitude and duration. Interestingly, when comparing es-

    timation, production, global time, and clock time be-tween the three age groups, we found the same trend towardsacceleration of the internal-clock in older participants,suggesting that prospective and retrospective timing mayshare common cognitive mechanisms.

    We found an association of estimation with production,which gives internal consistency to our results, and allows

    speculating about a common internal-clock subservingestimation and production (Ivry & Hazeltine, 1995; Keeleet al., 1985).

    This study showed an age effect on Digit Span, and achange of estimation and production with aging when com-pared between the three predefined age groups. This trendwas towards an acceleration of internal-clock in olderparticipants. A smaller study performed by Carrasco andcoworkers (2001) found similar results when comparingtime estimation between young and elderly healthy partici-pants. The study consisted of 25 adults, and the mean age ofthe young (26.15 years) and the elderly groups (79.1 years)were similar to that of groups A and C in our study. The

    methodology and the time-interval duration (10 s) were verysimilar to ours. Surprisingly, both results are in contrastwith a previous study that found an association of older agewith slower internal-clock (Craik & Hay, 1999). In thatstudy, the interval durations were of the same range (30, 60,and 120 s) as ours, but the paradigms of estimation andproduction differed slightly, namely, participants per-formed the estimation and production tests while perform-ing other tasks at different levels of complexity, and thisdiscrepancy in methodology can make comparison diffi-cult. Data concerning age and short time intervals is stillscanty and inconclusive though (Nichelli, 1993). A studyfrom Fraisse (1963) showed an association of aging with

    acceleration of internal-clock regarding large units of timesuch as days or years; however, people estimates of inter-vals in range of hours may be related to sleepwake cycles(Artieda & Pastor, 1996).

    The effect of education on cognition is well established,although we are not aware of any clear documentation of aspecific effect of literacy on time perception. We found acorrelation of education with estimation, production andglobal time, suggesting faster internal-clocks in partici-pants with lower education. However, as it was anticipatedfrom the characteristics of the Portuguese population andas our sample was not purposefully controlled for literacy,older participants were less literate. The correlation be-tween either estimation or production and aging lost signif-

    Fig. 4a. Correlation of time estimation with Digit Span Forward [p , .01 (Spearman test r52.34), left figure] andtime estimation with Digit Span Reverse [p, .05 (Spearman test r52.24), right figure] showing that overestimationof time is associated with a decrease performance in tests of attention and short-term memory0working memory.

    Fig. 4b. Correlation of time production with digit span forward [p, .01 (Spearman test r5 .39), left figure] and timeproduction with Digit Span Reverse [p , .01 (Spearman test r5 .33), right figure] showing that underproduction oftime is associated with a decrease performance in tests of attention and short-term memory0working memory.

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    icance when education was analyzed as a co-variate. Theabsence of a statistical difference of years of education be-tween the three predefined age groups argues against a pri-mary effect of education on our results, suggesting that theassociation of older participants with faster internal-clocks derives mainly from aging. Nevertheless, it is notpossible to firmly conclude if the association of older par-

    ticipants with faster internal-clocks is a specific result ofaging or biased by the interference of literacy. As the de-sign of the present study was not intended to look for aneffect of education on timing, future studies must be con-ducted specifically to address this interesting question.

    Our results demonstrated an association between estima-tion and production and both DSF and DSR, while there wasnoassociationbetweenDSFandDSR,andeitherbothclocktime or global time. This adds further evidenceregardingtheroleofattention0short-termandworkingmemoryinpro-spective timing but not in retrospective timing(Block, 1992;Block& Zakay, 1997; Brown, 1997; Mangels & Ivry, 2001).Nevertheless, the association of estimation and production

    withDigitSpanmayresultfromaneffectofageonbothtasks.The performance was similar between female and male

    participants in all tasks, though a disproportionate numberof females were present in our sample.

    Participants were explicitly asked to perform the estima-tion and production tests by internal counting of secondsand the intention was to have them producing their idea of1 s. The strategy of internal counting has been consideredto increase the accuracy of estimation (Davis, 1962; Fraisse,1984; Wearden, 1991). Counting was also aimed at giving ahomogeneous activity for all participants during estimationand production tasks (Rubia et al., 1997).

    Physiopathologic speculations may be too premature, be-

    cause replication of our results is still needed. Nevertheless,and according to present theoretical models (Block, 1990;Gibbon et al., 1984), the observed deficit in time estimationcould derive from a change in the speed of the internal-clock, which has been associated with several conditions(Binkoski, 1996; Carrasco et al., 2000; Meck, 1996; Pastoret al., 1992). Alternatively, a deficit in attention and workingmemoryassociated withaging could disrupt the counter sys-tem that accumulates the pulses generated by the internal-clock. Studies demonstrating deficits in time perception inAlzheimer andParkinson disease(Carrascoet al.,2000; Pas-tor et al., 1992; Riesen & Schnider, 2001) suggest the possi-ble involvement of neurotransmitters such as acetylcholineand dopamine in time perception.

    Our results showed an acceleration of internal-clockwith aging, and also suggested a role for attention and short-term0working memory on prospective timing. The assess-ment tool presented was easy to perform and was related toone ecological measure of time perception. Nevertheless,and due to its moderate association with the gold-standardsand possible bias of results due to literacy, future well-designed studies are needed to replicate the present find-ings, to analyze its interobserver and intrasubject validity,and to confirm its potential usefulness. If the present find-

    ings are confirmed, they must be explained in the light ofcurrent theoretical models for time perception.

    ACKNOWLEDGMENTS

    This study was supported by Grant 59098 from Fundao Bial,Portugal.

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