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The ability to assess muscular force in asymmetrical
Gilles Lafarguea,b, Andrea D’Amicoa, Ste ´phane Thoboisc, Emmanuel Broussollec
and Angela Sirigua,*
aCentre de Neuroscience Cognitive, CNRS, Bron, France
bLaboratoire URECA, Universite ´ Charles de Gaulle-Lille3, Villeneuve d’Ascq cedex, France
cService de Neurologie C, Neurological Hospital Pierre Wertheimer, Lyon, France
a r t i c l e i n f o
Received 2 May 2005
Reviewed 30 August 2005
Accepted 16 November 2005
Action editor Jordan Grafman
Published online 17 November 2007
a b s t r a c t
We tested the ability of eight Parkinson’s disease (PD) patients with clearly asymmetrical
right-sided motor signs and eight control subjects to assess different levels of muscular
forces. In Experiment 1, subjects had first to produce a target-force with one hand (the
reference hand) with the assistance of visual feedback, and then match that force with
the other hand (the matching hand) without any visual feedback. In Experiment 2, they
had to produce a target-force with one hand and then estimate it by attributing a numerical
value. In Experiment 1, the results showed that PD patients could normally reach the
target-forces with the more affected left hand but they were impaired in inter-manual
force transfer. They were also impaired, in Experiment 2, in estimating forces produced
by their more affected hand. Our findings suggest that PD patients present a deficit in
sensing motor effort. Effort awareness might be mediated by the basal ganglia.
ª 2007 Elsevier Masson Srl. All rights reserved.
function of the basal ganglia (BG) circuit. Individuals with this
pathology exhibit a variety of motor symptoms including
tremor, rigidity, akinesia and bradykinesia (Marsden and
disorder. However, there is also growingevidence for the pres-
enceofabnormalsensorimotor integration in PD(Moore,1987;
PD patients are particularly impaired in motor control when
they are deprived of visual cues, that is when they have to ex-
clusively rely on central motor representation or in sensory
kinaesthetic feedback. For instance, they are less accurate
than normal controls in assessing the position of the limbs
(Schneider et al., 1987), in estimating the amplitude of arm
movements (Moore, 1987) or in matching somatosensory and
strated that the cortico-basal ganglia loop was necessary for
conscious perception of limb position and orientation (Zia
stant force output when they are deprived of visual feedback
about the force level they exerted (Vaillancourt et al., 2001).
Finally, when lifting an object at a fixed height, it take them
longer to develop peak grip force and squeeze it compared to
normal controls (Fellows et al., 1998). These abnormalities are
* Corresponding author. Centre de Neuroscience Cognitive, CNRS, 67 Boulevard Pinel, 69675 Bron, France.
E-mail address: email@example.com (A. Sirigu).
0010-9452/$ – see front matter ª 2007 Elsevier Masson Srl. All rights reserved.
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/cortex
cortex 44 (2008) 82–89
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not the result of dopamine medication because they are also
present in de novo PD patients with no exposure to levodopa
(Fellows and Noth, 2004).
In the present study, we assessed one aspect of kinaesthe-
sia not yet addressed in PD, the perception of voluntary mus-
cular force. The ability to perceive the heaviness of a lifted
object or the level of isometric tension exerted by muscles,
in the context of a voluntary action, has been shown to de-
pend on both efferent and afferent neural signals (Gandevia
and McCloskey, 1978). Recent data have shown, however,
that deafferented patients are able to make inter-manual
transfer of voluntary produced forces (Lafargue et al., 2003),
thus suggesting that efferent signals play a dominant role in
the perception of muscular force. Sensory input would cali-
brate and modulate the central signal of effort. A likely candi-
date structure involved in the process of effort perception is
the BG. First, the BG receive sensory and motor input (Flaherty
and Graybiel, 1995) and are activated by passive sensory stim-
ulation (Boecker et al., 1999). Second, major BG output is di-
rected towards frontal lobe areas including motor and
premotor cortex (Alexander et al., 1986). A possible hypothesis
is that aninteraction betweensensoryinput andmotor output
signals, crucial for sensing effort, is made in the BG.
To directly test this hypothesis, we tested the ability of PD
sess different levels of isometric forces in two experimental
tasks. In asymmetrical Parkinson pathology, the exam of the
tutesa usefulmodel toinvestigatethe statusofthemoreversus
Eight patients (four males, four females), mean age 53.4
years (SD: 14; range: 36–81), with mild or moderate idiopathic
PD (Hoehn and Yahr staging 1.5–2.5) were tested. All had
markedly asymmetric disease with no sensory loss detect-
able by conventional clinical examination. All patients
were clearly right side-impaired and right-handed before
the illness, according to the Edinburgh handedness question-
naire (Oldfield, 1971). Their motor disability was assessed
while they were on their normal medication schedule by us-
ing the Unified Parkinson’s Disease Rating Scale (UPDRS)
score (Fahn and Elton, 1987). Comparison of UPDRS lateral-
ised motor score (items 20–26) demonstrated a marked
asymmetry in motor disability between the right side (desig-
nated as the more affected hemibody or more affected
hand), and the left side (referred as the less affected hemi-
body or less affected hand). According to the UPDRS items
20 and 21, our patients did not exhibit minor resting or pos-
tural tremor. In all patients, no tremor was noted during vol-
untary movements. All patients were chronically treated
with dopaminergic drugs at the time of the study. The exper-
imental testing was performed once, and started on average
5 h after the last dose of dopaminergic drug. All subjects ex-
cept patient 1 were under levodopa therapy. Their levodopa
dose ranged from 200 to 1400 mg per day. All patients were
receiving a dopaminergic agonist, ropinirol in three cases,
pergolide in three others, bromocriptine in one case and pir-
ibedil in another case. In addition, two patients were taking
entacapone, two other amantadine, and one trihexypheni-
dyle. Patients did not display any signs of dementia. They
were matched for age, sex and handedness with eight neuro-
logically unimpaired right-handed control subjects. The
mean age of the control subjects was 55.4 years?12.7 (range:
44–78). A summary of PD patients clinical data is provided in
For statistical comparisons, control subjects in Experi-
ment 1 were studied using the same experimental task
employed with patients. In Experiment 2, each patient
served as his/her own control. We made within subject com-
parisons between the more akinetic and the less akinetic
Table 1 – Clinical description and maximal grip force of the eight PD patients
Duration of disease (years)
Max left grip (Newton)
Max right grip (Newton)
Hoehn and Yahr (0–5)
UPDRS motor score (maximum 108)
UPDRS lateralized motor score
(maximum per side ¼ 36) (R/L)
Dopaminergic agonist (R; B; Pi; Pe)
Other treatments (E, AC, Am)
53.4 ? 14
5.6 ? 3.1
18.9 ? 4.1
R: 11.3 ? 2;
L: 2.3 ?.9
_ Am, AC
Total motor score refers to items 18–31 of UPDRS and lateralised motor score to items 20–26 of UPDRS. R: right; L: left; R: ropinirol; B: bromocrip-
tine; Pi: piribedil; Pe: pergolide; E: entacapone; AC: anticholinergic drug; Am: amantadine.
cortex 44 (2008) 82–89
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In the two experiments, muscular force was recorded with
a clinical analysis system. The sensors used consisted of two
grip-dynamometers. Each of them was U shaped with two
arms parallel and distant to each other of 30 mm. Pressure ap-
plied to them was converted by a transducer into an electrical
signal which was amplified and fed into a personal computer.
Sampling frequency was 20 Hz. Accuracy of force measure-
ment was .1 N.
3. Experiment 1: contralateral matching
Prior to the experimental trials, subjects were asked to de-
velop two maximal grip forces with each hand lasting 4 sec.
The larger force for each hand was taken as the subject’s max-
imum voluntary contraction (MVC) (see Table 1).
We then used a contralateral matching procedure (see
Fig. 1A). Subjects seated in front of a table facing a PC monitor,
their forearms laying on the table. They had to produce a tar-
get-force with one hand (the reference hand) and then to
match it with the other hand (the matching hand). The actual
grip force produced by the reference hand was indicated on
the monitor by the length of a vertical bar, which constituted
the subject’s visual feedback. Subjects were instructed first to
adjust the grip force of their reference hand so that the upper
end of the vertical bar reached a target line at the centre of
the monitor. Then, after 3 sec delay, while maintaining the
reference force, they had to match it with the other hand.
subjective magnitude the effort put into the reference contra-
lateral contraction. Instructions stressed to squeeze equally
hard with both hands. During one trial, the contractions of
Fig. 1 – (A) Contralateral matching task. The subject has to produce a target-force with one hand (the reference hand), under
the assistance of visual feedback, and then to match it with the other hand (the matching hand). As measures of matching
force, for each trial, we took the highest point at the initial peak (I1), and the MF produced during the last second of the trial
(I2). For each individual, the measure of matching performance was the strength of the relationship (r2) between reference
and matching force calculated on the basis of 16 trials (4 trials x4 levels of force). Each subject performed the task in two
conditions: with the right and left hand (respectively, the more affected and the less affected hand for patients) and each
hand acting as reference or matching hand. (B) Force estimation task. The subject has first to reach and maintain the
target-force and then to estimate its intensity by attributing a number between ‘‘0’’ (no effort) and ‘‘10’’ (maximal effort).
In the example of the figure the estimation given by the subject for the target-force (red line) is ‘‘3’’.
cortex 44 (2008) 82–89
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the reference and the matching hands lasted, respectively, 7
and 4 sec.
For each subject, matching performance was tested under
two conditions: (1) target-forces generated by the left hand
had to be matched with the right hand and (2) target-forces
generated by the right hand had to be matched with the left
hand. There were four target-forces, corresponding to 10, 20,
30 and 40% of the MVC. Each subject made a total of 32
get-forces) in condition 2. The intervals were 1 min between
trials. Reference forces were presented in randomised order.
3.2. Data analysis
To avoid initial force change, the first 60 samples (data for
3 sec) corresponding to the adjustment period to the target
were omitted in the data analysis. Two measures were calcu-
lated from the remaining 4 sec interval: (i) the mean force (MF)
and (ii) the coefficient of variation (CV¼ standard deviation/MF)
in order to measure the variability in maintaining the force.
The results for MF and CV were submitted to a three way
ANOVA with hand (left, right) and target-force (10, 20, 30 and
40% MVC) as within subject factors and group (patients, con-
trols) as a between subject factor.
As a measure of matching force, for each trial, we took the
highest point at the initial peak (I1), and the MF produced dur-
ing the last second of the trial (I2).
We did not analyse matching force per se, i.e., the ability to
reproduce the target-forces. Numerous studies since Holling-
worth (1910) showed that when a subject varies one stimulus
to match a variable criterion of some sort, he/she tends to
shorten or constrict the range of his/her adjustments, a phe-
nomenon called ‘‘compression bias’’. For this reason, we
analysed matching performance in terms of relationship be-
dividual, linear equations were calculated onthe basisofthe 16
trials (4 trials?4 levels of force), in two conditions: when the
right and the left hand (respectively, the more affected and the
less affected hand for patients) acted as reference hand.
For each group, mean values for r2, slope and intercept
were submitted to a three way ANOVA with hand (left, right)
and target-force (10, 20, 30 and 40% MVC) as within subject fac-
tors and group (patients, controls) as a between subject factor.
It must be underlined that the critical result for this experi-
ment was represented by the strength of the relationship be-
tween reference and matching forces, as measured by the
squared correlation coefficient (r2). This measure represents
the percentage of the matching forces variance that can be
explained by the target-forces.
4. Experiment 2: force estimation
The patients were required to produce a pre-selected force
with one hand. This force was fixed at 10, 20, 30 or 40% of
the MVC. The actual grip force produced was indicated on
the monitor by the length of a vertical bar, which consti-
tuted the subject’s visual feedback. Patients could not attri-
bute a number to each trial just according to the length of
the vertical bar because, as in Experiment 1, this length
was the same for all target-forces. At the end of each trial,
lasting 4 sec, the subject had to estimate the force by attrib-
uting a number between ‘‘0’’ (no effort) and ‘‘10’’ (maximal
effort). Trials were distributed across two blocks of 6 trials
each, and for both the more affected and the less affected
hand. Thus a total of 12 trials were performed for each
hand. In each block forces were randomly selected. Blocks
were alternated between hands: half of patients started
with the left hand, the other half with the right hand. The
intervals were 30 sec between trials and 1 min between
blocks. The different effort levels in a subset were rando-
mised (see Fig. 1B).
4.2. Data analysis
As in the previousexperiment, the force data wereanalysed in
percentage of MVC. We first analysed patients’ ability to reach
and maintain the pre-selected forces, in terms of MF and force
variability. Second, we characterised the strength of the rela-
tionship between produced forces (MF for the last second of
each contraction) and numerical estimations. Linear equa-
tions between produced forces and numerical estimations
were calculated for each individual and for each hand. Mean
values for r2, slope and intercept were submitted to the Stu-
5.1. Contralateral matching
5.1.1. Reference force
188.8.131.52. MF. With the reference control hand, PD patients
produced similar levels of MF compared to control subjects
[F(1,14)¼.28; p >.05]. As expected, the MF increased with the
target-force level [F(1,14)¼5762.61; p <.001]: 10.41, 20.22,
29.93, and 39.67% MVC, respectively, for target of 10, 20, 30
and 40% MVC. Neither effect of hand (less affected vs. more af-
fected for patients; left versus right for controls) nor any first or
second order interaction effects was observed for MF.
The ANOVAdidnotrevealanystatistically mainor interaction
effects for CV. Thus, for the side receiving visual feedback, no
fundamental abnormality in PD patients’ force traces was
found. For each condition, that is for each target-force exerted
either with the left (less affected) or with the right (more af-
fected) hand, patients’ MF and CV were not different from
those found for controls.
PD patients’ best measure of matching performance – as mea-
sured by r2values – was obtained with I1. The control subjects’
matching performances were not statistically different with I1
cortex 44 (2008) 82–89
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and I2. Therefore, we only show here the linear regression pa-
rameters when I1was the indicator of matching force. Data for
a representative normal subject and one PD patient (patient 5)
are presented in Fig. 2.
On average, r2was smaller for the PD group (.48) than for
the control group (.88) [F(1,14)¼32.83; p<.001]. There was
also an effect of hand with r2higher when the right hand
(the more affected hand in the PD group) was the matching
hand [F(1,14)¼13.89; p <.01]. This effect was due to the inter-
action effect group by hand [F(1,14)¼12.87; p <.01], explained
by the fact that PD patients had lower r2when the more af-
fected hand was the reference hand (r2¼.35) than in the re-
verse condition (r2¼.61). On the other hand, the control
group had similar r2in these two conditions. For this later
group, r2were equal to .88 and .89 when the reference hands
were the right and the left hand, respectively (see Fig. 3 for
Comparison between slope and intercept for the linear re-
gression between reference and matching force revealed sig-
nificant differences. Mean slope was lower for patients (.59)
than for controls (.89) [F(1,14)¼19.02; p <.01] and lower
when the right(.66) rather than the lefthand was acting as ref-
erence hand (.82) [F(1,14)¼19.02; p <.01]. This latter effect is
due to the fact that mean slope was lower for patients when
the more affected (.45) rather than the less affected hand
(.72) was acting as reference hand. Mean intercept was higher
for patients (18.36) than for controls (11.77) [F(1,14)¼7.96;
p <.01] and higher when the right (15.95) rather than the left
hand was actingas referencehand (11.87).However,thislatter
effect did not reach significance [F(1,14)¼ 4.23; p¼ .06].
Fig. 2 – Relationship (linear regression) between reference and matching force (both in percent of maximum) for
a representative control subject (A) and a PD patient (B). The right hand (the more affected hand for the patient) is the
Fig. 3 – Squared correlation coefficient (r2) between reference and matching force for each control subject (C1–C8) and each
Parkinsonian patient (P1–P8). Black bars represent r2when the left hand (the less affected hand for patients) was acting as
reference hand and the right hand (the more affected hand for patients) was acting as the matching hand. White bars
represent r2in the reverse condition.
cortex 44 (2008) 82–89
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As expected, we observed an effect of target-force: the MF pro-
duced was 10.47, 21.03, 31.58 and 40.14%, respectively for tar-
getof 10,20, 30and40%MVC.We didnotobservea handeffect.
With both hands, the more affected and the less affected, pa-
tients were able to maintain equally well (with a visual feed-
back) the four pre-selected force levels. The mean CV was
not statistically different for the four force levels and for
Ability to maintain the pre-selected forces
The relationshipbetweentarget-forces andnumerical estima-
tions, for each patient and for both hands, was always well
described by a linear regression (in all the cases p <.05).
However, all patients had more difficulty to estimate a force
produced by the more affected hand than with the less af-
fected hand (see Fig. 4 for individual and mean r2values). In-
deed, the mean squared linear correlation (r2) was lower
when the forces were produced with the more affected hand
(mean: .49; range: .37–.70) compared to the less affected one
(mean: .80; range: .73–.88) [t(7)¼7.96; p <.0001]. In the previ-
ous section, we describe the characteristics of target-force
production as similar for both hands. Consequently, the dif-
ference we found in the present experiment cannot be as-
cribed to noisy signals related to impaired force production
of the more affected hand.
The mean slope was lower when the more affected hand
(mean: .64; range: .43–.93) rather than the less affected hand
[t(7) ¼5.92; p< .001]. The mean intercept was not statistically
different ( p¼ .42) when the more affected (mean: 12.7; range:
8.3–16.7) and the less affected hand (mean: 11.7; range: 6.7–
15.0) exerted the target-force. Mean slope and intercept values
reflect patients tendency (i) to compress the differences
between the target-forces and (ii) to give, in average, lower
numerical values in the condition where the more affected
Relationship between target-forces and numerical
hand exerted the target-force compared to the condition
where the less affected hand was acting.
The present study was designed to test the ability of individ-
uals with PD to assess different level of muscular force. In
Experiment 1, control subjects and PD patients were required
to produce,in the presence of visual feedback, a specified level
of force with one hand (the reference hand). After 3 sec delay,
while they maintained the reference force, they had to match
its subjective magnitude by producing a force with the contra-
lateral hand. The matching hand was acting without any
visual feedback. The control subjects were able to maintain
a constant relationshipbetweenthe force exertedby therefer-
ence hand and the force exerted by the matching hand. The
strength of this relationship was significantly lower in the
PD group when both the less affected and the more affected
hand acted as reference hand. Seven patients out of nine
were much more impaired in the condition where their
more affected hand acted as the reference hand. Since the
matches were made by the less affected hand, this argues
against the hypothesis of a deficit in force production to ac-
count for poor matching performance. Interestingly, in the
present study, PD patients performed better in the contralat-
eral matching task when the more affected hand was acting
as a matching hand. This means that when the target-force
and therefore the signal of effort was generated by the less af-
fected hand, this could be correctly perceived and matched on
the more impaired side. It seems however paradoxical that
patients cannot perceive and then transfer sensation of effort
when generated by the more affected hand and yet be able to
scale different force levels when the same hand acts as
a matching effector. A possible explanation is that the ability
to increment distinct force levels is different from the ability
to accurately assess or compare two produced forces. This
view is supported by data suggesting that PD patients are
able to form accurate internal models of desired forces and
to transform them into motor output (Stelmach and Worring-
ham,1988). Note that we considered as a measureof matching
force, for each trial, the highest point at the initial peak. In the
case of patients, this point was the measure giving the highest
r2. One could argue that PD patients’ ability to make contralat-
eral matching was poor in Experiment 1, not because of an al-
tered perception of force but because of the well known deficit
in bimanual co-ordination often described in PD (Schwab
et al., 1954). However, the absence of difference in force vari-
ability between patients and controls, for the reference
hand, does not support this hypothesis.
The results obtained in the second experiment support the
hypothesis that perception of muscular force is affected in PD.
In this experiment, first patients had to produce different pre-
selected forces with visual feedback, with one hand, and sec-
ond to estimate these forces by attributing them numerical
values. We found that the strength of the relationship
between numerical values and the target-forces was low,
specifically when the more affected hand produced the
target-forces. Since in this experiment we did not observe dif-
ferences in force variability for the forces exerted either by the
Fig. 4 – Squared correlation coefficient (r2) between
target-force and force estimation (numerical value ranged
between ‘‘0’’ and ‘‘10’’ given by the patients) for each PD
patient (P1–P8). Black bars represent r2when the
target-force was produced by the less affected hand.
White bars represent r2when the target-force was
produced by the more affected hand.
cortex 44 (2008) 82–89
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more affected or the less affected hand, we must reject the hy-
pothesis of poor force perception due to an impaired mecha-
nism involved in the generation of motor output.
An alternative interpretation could be that impaired volun-
tary force perception in PD may result from impaired proprio-
ceptive (Klockgether et al., 1995; Khudados et al., 1999) and
cutaneous reflexes mechanisms (Fuhr and Priebe, 1992). How-
ever, such interpretation seems unlikely because voluntary
force perception is not directly derived from afferent signals.
Extensive phenomenological and experimental data since
the end of the 19th century suggest that efferent signals re-
lated to the size of the motor command play a dominant
role in the perception of voluntary muscular force. Voluntary
muscular force appears to be experienced indirectly through
the central effort send to motoneurons. In other words, we
do not perceive voluntary force through a sense of muscular
tension. We perceive the central effort necessary to contract
our muscles. A classical argument emphasising the predomi-
nance of centrally generated signals in the perception of vol-
untary muscular force comes from the performance of
patients with hemiparesis who report a strong feeling of ap-
plied force at the beginning of motor recovery, when they at-
tempt to move their paretic limb (Mach, 1906; Brodal, 1973). If
force perception was derived from signals arising from pe-
ripheral receptors, these subjects should not experience a dis-
sociation between achieved and perceived muscular tension.
Indeed, weak muscular tension should have been associated
with a weak sensation. Such a dissociation between sensation
of effort and achieved muscular tension has been experimen-
tally confirmedin healthy subjects weakened by fatigue (Jones
and Hunter, 1983) or local curarization (Gandevia and McClos-
key, 1977a), and in patients suffering from weakness caused
by cerebellar (Holmes, 1922; Gandevia and McCloskey, 1977b;
Angel, 1980) or internal capsule (Gandevia, 1982; Rode et al.,
1996) lesions. In all these cases, subjects overestimated,
when performing a contralateral matching task, weights lifted
(or forces exerted) with their weakened hand.
The predominance of centrally generated signals in the
perception of voluntary muscular force is confirmed by the
fact that, in normal subjects with anaesthetised digits, there
is no significant difference in the reproducibility of the esti-
mates of perceived heaviness between non-anaesthetised
and anaesthetised conditions (Kilbreath et al., 1995). Further-
more, data obtained in a deafferented patient (Lafargue
et al., 2003) show that this patient is able to accurately dis-
criminate isometric forces solely on the basis of internal sig-
nals. The contribution of afferent input in sensing effort
must however not be minimised. Peripheral feedback would
allow to modulate and calibrate the central signal of effort
via, 1982). Moreover, it is likely that to reach consciousness,
centrally generated signals related to the size of motor com-
mand need to interact with sensory feedback arising from
muscles, tendons or skin receptors. For instance, in one of
our previous study, a deafferented patient, GL, was able to
make inter-manual force transfers but she was not able to
feel how hard she tried when carried out this motor task
(Lafargue et al., 2003).
Altogether, these arguments let us favour the hypothesis
that the deficit in voluntary force perception in PD patients,
found in the present study, is due to altered sensorimotor in-
tegration. It seems unlikely that this deficit is due to impaired
proprioceptive and reflex mechanisms per se. Moreover, as re-
duced sensory-evoked brain activation in parietal and frontal
areas has been observed in PD patients (Boecker et al., 1999),
our opinion is that this faulty integration is located at a high
cortical level in PD.
It has been proposedthat two functionally and possibly an-
atomically distinct processes are at work during the construc-
tion of a motor representation: (i) storing and (ii) updating the
representation (Wolpert, 1997). In our study, PD patients could
not correctly match or estimate a prolonged muscular con-
traction. Dettmers et al. (1996) observed an important activity
in the BG during such contraction. Since neural signals from
motor and sensory origin converge in the striatum (see Flah-
erty and Graybiel, 1995), we propose that the BG take part in
the process of updating the cortical representation of volun-
tary force during sustained contractions. Consequently, in
our motor tasks, PD patients could lack the ability to correctly
update the internal estimate of their current motor output. A
dysfunction at the level of the interaction between motor and
sensory originated signals, in the BG, might progressively ‘dis-
rupt’ higher order motor representation processed at the cor-
tical level. This process is compatible with functional models
(see Plenz and Aertsen, 1994), according to which the BG de-
tect and reinforce distant but coherent cortical activities. In
healthy subjects, neuro-imagery studies showed that many
sensory and motor areas are activated during voluntary force
production (Dettmers et al., 1996; Dai et al., 2001; Liu et al.,
2003). The assumption that BG could ensure the consistency
of these multiple cortical activities seems to provide a coher-
ent interpretation of our results.
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