Effects of motor imagery on finger force responses to transcranial magnetic stimulation

Effects of motor imagery on finger force responses to transcranial magnetic stimulation

Cognitive Brain Research 20 (2004) 273 – 280 www.elsevier.com/locate/cogbrainres Research report Effects of motor imagery on finger force responses ...

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Cognitive Brain Research 20 (2004) 273 – 280 www.elsevier.com/locate/cogbrainres

Research report

Effects of motor imagery on finger force responses to transcranial magnetic stimulation Sheng Li *, Mark L. Latash, Vladimir M. Zatsiorsky Department of Kinesiology, Pennsylvania State University, University Park, PA 16802, USA Accepted 11 March 2004 Available online 27 April 2004

Abstract The purpose of this study was to investigate whether characteristics of finger interaction seen in voluntary finger force production tasks could also be observed during motor imagery. Transcranial magnetic stimulation (TMS) was applied over the contralateral M1 hand area. Three conditions were tested in eight young healthy volunteers: At rest, during motor imagery of maximal force production by the index finger (ImIn), and during motor imagery of maximal force production by all four fingers simultaneously (ImAll). We obtained measures of motor threshold (MT), motor-evoked potentials (MEP) from the contralateral flexor digitorium superficialis, and TMS-induced forces from individual fingers. Increased MEP and decreased MT during motor imagery tasks suggested enhanced excitability of structures involved in the generation of TMS-induced responses. TMS-induced forces were larger during motor imagery tasks than at rest. This effect was present, albeit significantly smaller, in the middle, ring, and little fingers during ImIn as compared to ImAll. This finding has been interpreted as a correlate of the phenomenon of unintended finger force production (enslaving). The motor imagery effect on finger forces evoked by TMS was significantly larger during ImIn (4% MVC) than during ImAll (2.8% MVC) tasks, corresponding to the phenomenon of force deficit. These results provide direct evidence of the neural origin of the main phenomena of finger interaction. Furthermore, the similarities between characteristics of finger interaction during motor imagery and during voluntary movement suggest the involvement of similar neural structures (including M1). D 2004 Elsevier B.V. All rights reserved. Theme: Motor systems and sensorimotor integration Topic: Control of posture and movement Keywords: Motor imagery; Transcranial magnetic stimulation; Finger; Enslaving; Deficit

1. Introduction Motor imagery, i.e., imagining doing a certain movement without executing them, has been an object of several research papers [8,12 –14,18,19,34,45,46,48– 50]. Repeated evidence in the literature shows that motor imagery shares features involved in the actual movement, such as involvements of common neural structures [1,3,8], kinematic constraints [43], temporal properties [9,43], effects on motor performances [52], the role in skill acquisition [33] and in motor recovery after stroke [31,51]. * Corresponding author. Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Northwestern University, 345 E. Superior St. Room 1406, Chicago, IL 60611, USA. Tel.: +1-312-238-2227; fax: +1-312238-2208. E-mail address: [email protected] (S. Li). 0926-6410/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cogbrainres.2004.03.003

However, there has been some controversy in the literature regarding the involvement of the primary motor cortex (M1) during motor imagery. On one hand, evidence of the M1 involvement in motor imagery includes reports on focal enhancement of corticospinal excitability during the application of transcranial magnetic stimulation (TMS) over M1 [12,13,15,19] and increased M1 activity revealed in fMRI experiments [30,36,38]. We use the term ‘‘corticospinal excitability’’ to refer to the excitability of all the structures involved in the generation of finger responses to TMS; these responses may be mediated by the corticospinal tract as well as by other descending pathways [35]. On the other hand, the conclusion on an M1 involvement in motor imagery has not been supported by other neuroimaging studies [10,16,32,47]. Due to its unique and complex peripheral anatomy and representations in M1, the human hand is an appealing object to study the physiology of motor imagery. In particular,

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cortical control of the distal hand muscles in monkeys is the most direct of any of the muscles of the extremities [37]. Finger representations in M1 are highly interconnected [42]. Convergence and divergence of des-cending pathways as well as widespread finger representations lead to an extensive activity in the cortical network, even during a singlefinger movement [41]. A few characteristics of finger interaction during multi-finger voluntary force production have been attributed to this complex organization—unfortunately, without a direct proof of the hypothesis [4,23,26,29]. When a finger produces force, other uninstructed fingers also produce forces. The phenomenon, named enslaving, has been repeatedly observed during voluntary contraction tasks at maximal [20,21,25,54], moderate [44], and low levels [20,21]. Another characteristic is force deficit: a finger produces less peak force during a multi-finger task than during its single-finger maximal voluntary contraction (MVC) task [24]. Enslaving and force deficit have been interpreted as reflecting both the peripheral design of the hand muscles and their neural control [53]. Within this study, we accept a hypothesis that motor imagery and actual movements involve common neural structures, including M1. In particular, if phenomena of force deficit and enslaving are predominantly defined by neural factors the phenomena are expected to be revealed in responses of fingers to TMS applied over the contralateral M1 area during motor imagery. Specifically, motor imagery of an action by a finger should be reflected in TMS-induced responses of other fingers (cf. enslaving) and larger effects on TMS-induced finger responses during motor imagery of a one-finger MVC than during imagery of a four-finger MVC (cf. force deficit). Alternatively, if these phenomena are crucially dependent on the peripheral factors, such as the presence of multi-digit muscles and connective tissue interdigit connections, they are not expected to be reflected in modulation of TMS-induced finger force responses during motor imagery.

respect to the body midline with the upper arms at approximately 45j of abduction in the frontal plane and 45j of flexion in the sagittal plane, elbow joints at approximately 135j of flexion. The right hand and fingers were positioned and stabilized into a suspension device for force measurement using four unidirectional piezoelectric force sensors (208A03, PCB Piezotronics, Depew, NY) (cf. Ref. [23]). The resolution of sensors was 2.714 mN/byte. In the suspension device, the sensors were each connected in series with wire cables that were suspended by swivel attachments from slots in the top plate of the inverted U-shaped frame. The rubbercoated loops, located at the bottom of each wire, were placed in the middle of the distal phalanxes. Due to the employed experimental procedure, all four-finger forces were parallel. A hand-fixation device was located at the bottom of the frame and used to stabilise the palm of the hand and to ensure a constant hand configuration throughout the experiment (the wrist was fixed at approximately 20j of extension and the fingers were positioned so that there was also approximately 20j of flexion at the metacarpophalangeal joints). The left forearm and hand rested on the testing table at the same height as the right forearm. 2.3. EMG recordings Bipolar electromyographic (EMG) recordings from the flexor digitorum superficialis (FDS) of the right forearm were obtained from pairs of disposable surface electrodes placed over the muscle belly. The diameter of each electrode was 1 cm, the distance between the centres of two electrodes within a pair was 3 cm. The EMG signals were amplified, high pass filtered at 10 Hz and low pass filtered at 500 Hz. The signal from the right forearm was displayed on-line on the monitor. EMG signals were set at a high gain (25 AV per division) to ensure complete EMG silence during the experiment. 2.4. Magnetic stimulation of the brain

2. Materials and methods 2.1. Subjects Eight healthy volunteers, all males, participated in the experiments. All of them were right-handed according to their preferential use of the right hand during writing and eating. The age of the subjects was 27 F 4 (mean F S.D.) years. Their weight was 80.3 F 15.5 kg, and their height was 1.79 F 0.11 m. All the subjects gave informed consent according to the procedures approved by the Office for Regulatory Compliance of the Pennsylvania State University. 2.2. Apparatus During testing, the subject was seated in a chair in front of a testing table. Two upper limbs were symmetrical with

The method and procedures of application of TMS was the same as previously described (cf. Ref. [7]). Briefly, focal TMS was performed with a figure-of-8-shaped stimulation coil (mean diameter of each wing 45 mm) connected to a Magstim 200 magnetic stimulator with the maximal magnetic field strength of 2.2 Tesla (Magstim, UK). A tight elastic cap was placed on the subject’s head. A grid of 1  1 cm was marked on the left side of the scalp, with its centre positioned 2 cm to the left of Cz. The intersection of the coils was placed tangentially to the center of the grid with the handle pointing backward and laterally at a 45j angle away from the midline. In this way, the current induced in the neural tissue was directed approximately perpendicular to the line of the central sulcus in a direction parallel to the mid-line between the two coils and therefore optimal for activating the corticospinal pathways transsynaptically [2]. First, the stimulus intensity was set at 60% of the stimulator

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output, and an optimal position for eliciting the largest increment in the total force of all fingers that was stable in three consecutive trials was found by moving the coil over the scalp in steps of 1 cm. The optimal position was then marked with a pen to ensure constant positioning of the coil throughout the experiment. Keeping the coil at the optimal location, the intensity of the stimulation was slowly decreased until the motor threshold (MT) was found. The MT was defined as the lowest stimulus capable of evoking at least three of six motor-evoked potentials (MEPs) with the amplitude of at least 50 AV for both the rest condition and the conditions of motor imagery (see below). The coil position and orientation was ensured with double-sided adhesive tape; besides, at all times, the coil position was stabilized by an experimenter. A Gateway 450 MHz computer was used for data acquisition and processing. All signals were sampled at 1000 Hz by a 16-bit A/D board using LabView software (National Instrument). 2.5. Procedures During the experiment, the instruction for motor imagery was to mentally press down with the intended finger(s) as hard as possible (MVCI). Subjects were asked to practice this mental task for a few minutes prior to testing to ensure that they are able to keep the EMG silent during motor imagery. EMG silence was defined as the absence of any background activity at the sensitivity of 25 AV per division. Three experimental conditions were investigated: (1) Rest: the absence of motor imagery; (2) ImIn: motor imagery of MVCI by the right index finger only; (3) ImAll: motor imagery of MVCI by all four fingers of the right hand simultaneously. At the end of the experiment, subjects were asked to produce MVCs at the fingertips using the index finger only and using all four fingers simultaneously. The highest peak value from three trials was considered as MVC forces for the index finger and four-finger tasks, respectively. The subject was asked to start to imagine pressing finger down as hard as possible after a verbal command and sustain this condition until a TMS stimulus was delivered (unexpectedly, within 3 s). Then the subject was instructed to relax. Due to the employed high resolution of EMG/force sensing systems, deviation of EMG and force signals from the background levels due to the slightest movement of individual fingers was able to be detected by the sensing systems during the experiment. Such trials, if happened, were discarded by the experimenter to ensure motor imagery tasks purely imagined. The stimulation intensity was the same for the rest and motor imagery conditions at 150% of the resting MT (rMT), on average 60.9% of the stimulator output. The order of conditions was randomized. Five trials were conducted for each condition. The interval between two consecutive trials was approximately 15 s.

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2.6. Data processing Changes in individual and combined finger forces were used as the main indices to evaluate the effects of TMS and motor imagery, while EMG signals were used to monitor the background activity during motor imagery tasks and to quantify changes in the corticospinal excitability. Two parameters were calculated from the measured finger forces—TMS-induced force increments (DF) and changes in DF due to the motor imagery (DFIMAG). The former index (DF) for a finger was defined as the difference between its force at the time of peak force response to TMS of all fingers and its background force, defined as the mean force from 100 ms to the moment of TMS application (t0 = 0 ms). This index was also calculated for all four fingers, DFTOTAL = SDFi (i = I, M, R, and L—the index, middle, ring, and little fingers, respectively), for the index finger (DFINDEX), and for the three other fingers DFMRL = SDFi (i = M, R, and L). To quantify effects of motor imagery on DF indices during different motor imagery tasks, DF at rest was subtracted from DF during a motor imagery test resulting in a DFIMAG index. DF was expressed in absolute units (N). DFIMAG was expressed in percent with respect to the peak force value (MVC) observed in its corresponding voluntary task. The normalized DFIMAG was used to compare the motor imagery effect for different imagery tasks. The latency of TMS-induced force responses was defined as the time interval between the application of the stimulation and the time when the total force exceeded two standard deviations (S.D.) of its background value, i.e., the weight of fingers (offset to zeros). The EMG signal was rectified and low-pass filtered at 100 Hz using a second-order, zero-lag Butterworth filter. The background EMG (EMGBG) was defined as the mean rectified, filtered EMG calculated from 100 ms to the moment of TMS application. The MEP latency was computed as the time it took the baseline EMG to increase by 2 S.D. The size of the MEP was defined as the difference between the peak EMG in the rectified signal and EMGBG. The MEP size was expressed in arbitrary units (AU). Both the force and EMG indices were averaged across five trials for each condition. Other data processing techniques were similar to those described earlier [7]. 2.7. Statistics The data in the text are presented as means while figures show means and standard error bars. Repeated-measures ANOVAs were used with a factor CONDITION (three levels, Rest, ImIn, and ImAll). Whenever necessary, post hoc Tukey’s honest significant difference tests were used to compare the various levels of the factors. Paired Student’s ttest was also used.

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3. Results A single TMS stimulus produced a sequence of mechanical and EMG effects. It was followed, after a short delay, by a burst of activity (MEPs) in the FDS muscle, frequently followed by a silent period. The silent period was not analyzed in the current study. The latency of the MEP ranged in different subjects from 11.8 to 17 ms with the average value of 14.7 ms. Following a suggestion by an anonymous reviewer, we re-analyzed the data without the 100-Hz filter. The results showed the FDS MEP latency in the range between 11 and 19.3 ms (mean = 15.7 ms) for the rest condition across the eight subjects, i.e., about 1 ms longer than the values obtained from analysis with the filter. This latency is comparable to the MEP latency in extensor digitorum communis (12.2 to 18.4 ms, mean = 15.2 ms) at rest reported in an earlier study [11]. Changes in finger force were seen about 14 ms after the beginning of the MEP. They were typically seen in all four fingers of the hand. 3.1. Motor imagery effects on EMG responses During motor imagery trials, a decrease in the motor threshold (MT) was observed accompanied by an increase in the MEP amplitude. At rest, the motor threshold (MT) was, on average, 40.8% of the stimulator output. It was significantly lower during both ImIn (36.6%) and ImAll (37.4%) conditions as supported by the one-way ANOVA ( F[2,14] = 24.49, p < 0.001). MT did not differ between the ImIn and ImAll tasks. These data are presented in Table 1. At the same stimulus intensity of 150% of resting MT, the MEP magnitude was significantly lower at Rest (7.7, in arbitrary units, AU) than in the ImIn tasks (13.8 AU) and in the ImAll tasks (16.4 AU) ( F[2,14] = 11.78, p < 0.001). No difference was found between the two imagery conditions, i.e., the described effects did not depend on whether the subject imagined pressing with the index finger only (ImIn) or with all four fingers of the hand (ImAll). 3.2. Motor imagery effect on finger force responses As mentioned earlier, the application of TMS induced an increase in the forces of all four fingers. Fig. 1 illustrates typical traces of TMS-induced force increments (DF) during different conditions from a representative subject. Note that, (1) in the ImIn test, there is a larger DF of the intended Table 1 Motor threshold (MT) and motor-evoked potentials (MEPs)

MT (%) MEP (AU)

Rest

ImIn

ImAll

40.8 F 2.0 7.7 F 0.9

36.6 F 2.5 13.8 F 2.6

37.4 F 2.0 16.4 F 2.6

MT was recorded as the percentage of the stimulator output; MEP was recorded from the flexor digitorum superficialis (FDS) during different conditions and was expressed in arbitrary unit (AU). Standard errors are presented.

Fig. 1. Typical traces of individual and combined forces induced by focal TMS application on the contralateral motor cortex from one subject. Note that (1) in the ImIn test, there is a larger DF of the intended finger as compared to the rest condition. (2) In the ImAll test, there is a larger DF of the total force than for the ImIn tests. (3) DF of the unintended M, R, L fingers (ImIn task) increases when these fingers become the intended fingers (ImAll task). Rest: absence of motor imagery; ImIn: motor imagery of maximal force production of index finger only; ImAll: motor imagery of maximal force production of four finger simultaneously.

finger (DFINDEX) as compared to the rest condition. (2) In the ImAll test, there is a larger DF of the total force (DFTOTAL) than for the ImIn tests. (3) DF of the unintended M, R, L fingers (ImIn task) increases when these fingers become the intended fingers (ImAll task). Fig. 2A shows the DF of the total force and of the index finger averaged across subjects during different conditions. The mean DFTOTAL was the lowest at rest (2.4 N), higher during ImIn (4.4 N), and the highest during ImAll (5.8 N). DFTOTAL was significantly larger during motor imagery tasks than at rest ( F[2,14] = 4.16, p < 0.001). The difference between DFTOTAL in ImAll and in ImIn was just at the boundary of statistical significance ( p = 0.059). DFINDEX was larger for imagery tasks than at rest; the mean DFINDEX was 0.7, 1.9, 1.5 N for Rest, ImIn, ImAll tasks, respectively. According to a one-way ANOVA ( F[2,14] = 7.92, p < 0.005) and post hoc tests, DFINDEX for the ImIn and ImAll tasks were larger than that at rest, while no difference was found between the motor imagery tasks. The amount of force increment reflecting the motor imagery effect (DFIMAG) showed a different pattern from

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DF (Fig. 2B). In absolute units, DFIMAG was smaller for ImAll tasks (2.1 N) than for ImIn tasks (3.4 N), according to paired t-tests (t[7] = 2.37, p < 0.05). To compare the motor imagery effect on finger force responses during different tasks, DFIMAG was normalized to corresponding MVC values. DFIMAG of the total force was larger for ImIn tasks than for ImAll tasks. DFIMAG for ImIn tasks ranged from 1.2% to 10.3% MVC with the average of 4% MVC, while for ImAll tasks it ranged from 0.2% to 6% MVC with the average of 2.8% MVC. Paired t-tests confirmed that this difference (on average 30%) was statistically significant (t[7] = 3.67, p < 0.01). To investigate whether enslaving effects exist during motor imagery, comparisons between TMS-induced force increments in the unintended fingers at rest and during motor imagery tasks were performed. The combined force produced by unintended fingers (DFMRL) was significantly larger during ImIn tasks (2.6 N) than that at rest (1.6 N) (see Fig. 3). However, when these fingers became the intended fingers in ImAll tasks, DFMRL increased signifi-

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Fig. 3. The individual and combined (DFMRL) TMS-induced force increments in middle, ring and little fingers, averaged across trials and subjects, are shown. DFMRL is the difference between two lines shown in Fig. 2A. DFMRL in ImIn tasks was larger than at rest, but smaller than in ImAll tasks. Motor imagery showed strong effects in the middle and ring fingers, but not in the little finger. Standard error bars are shown.

cantly (4.3 N). These differences were confirmed by a oneway ANOVA ( F[2,14] = 9.82, p < 0.005) and post hoc tests. Further paired t-tests were used to compare DF for each unintended finger at rest and in ImIn tasks separately and showed significant effects on DFMIDDLE and DFRING (0.4 vs. 0.8 N and 0.4 vs. 1.0 N, for the Rest and ImIn, respectively; p < 0.05), but not on DFLITTLE (0.8 vs. 0.9 N for the Rest and ImIn, respectively).

4. Discussion

Fig. 2. (A) TMS-induced force increment (DF) in the index finger and total forces, averaged across trials and subjects, are shown. DF was larger for motor imagery tasks than at rest. (B) The motor imagery component (DFIMAG) of DF of the total force was larger for the ImAll task than for the ImIn task. Note that DFIMAG was computed by subtracting DF at rest and normalizing to corresponding MVCs. I: index finger; TOT: all fingers. Standard error bars are shown.

Motor imagery in our experiments was associated with a decrease in the threshold for TMS-induced responses and an increase in the MEP amplitude. These observations agree well with previous reports on an enhanced corticospinal excitability during motor imagery [12,13]. Our experiment used two sets of measures to quantify effects of motor imagery on TMS-induced responses in EMG and force. The more traditional EMG measures, as used in the previous TMS studies of motor imagery [12 –14,19,34,45,46,48– 50], showed effects of motor imagery but failed to reveal differences between the imagery conditions. This may partly be due to the fact that the surface EMG signal effectively averaged signals over several compartments of the FDS muscle with possible effects from the deep flexor, FDP [6]. Recording the EMG signals from only one muscle is a limitation of our study. However, as mentioned, placing the electrodes over the FDS typically allows to record signals from both FDS and FDP. The tendons of these muscles attach at the middle and distal phalanges and make them prime movers during force production at the fingertips.

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Hence, we view monitoring the lack of the EMG activity at a high gain (25 AV per division) during motor imagery in addition to controlling the lack of background forces of the fingers during the experiment as practically adequate. 4.1. Comparisons with data from actual finger force production Finger interactions during one- (index) and four-finger MVC tasks have been extensively studied earlier and phenomena of enslaving and force deficit have been described and quantified [4,5,22 – 29,53,54]. Patterns of TMSinduced finger force responses during motor imagery showed effects of finger interaction similar to those early described during voluntary force production. In particular, during motor imagery of MVC by the index finger, TMSinduced responses were higher in the other three fingers (middle, ring, and little) than at rest (Fig. 3) (enslaving). When these fingers become explicitly involved, in the ImAll condition, their response increased even more suggesting a graded involvement of neural structures responsible for finger force production [37,39,40] depending whether a finger is instructed or not instructed to produce imagined force. Another feature of enslaving described in voluntary force production tasks [53] is that it is larger for neighboring fingers. Our results of significant effects of motor imagery in the ImIn condition on the TMS-induced responses in the middle and ring fingers, but not in the little finger, illustrate this feature of enslaving for motor imagery. Furthermore, these results are consistent with those during actual finger production reported in a recent paper [7]. This paper, in particular, showed an inverted U-shaped dependence of the TMS-induced force responses on the background finger forces over the whole range of finger forces up to the MVC. Peak finger force responses to the TMS were seen at about 50% of the MVC. Graded increments in the TMSinduced force responses in the middle, ring and little fingers across the Rest, ImIn and ImAll tasks could be viewed as reflecting the rising part of the inverted U-shaped relation. Force deficit (FD), was quantified in earlier studies as the difference between the sum of peak forces of individual fingers during a multi-finger task and the sum of their MVCs in one-finger tasks [25]. FD measures an inability to produce maximal force by a finger during a multi-finger MVC task; it was interpreted as a consequence of a limit to the total central neural drive (ceiling hypothesis) [25]. However, direct evidence of a neural origin of the force deficit phenomenon has been lacking. In the present study, the motor imagery effect on finger responses was quantified using DFIMAG. After subtracting TMS-induced force increment at rest, the remaining component reflects the motor imagery effect on finger force res ponse s in duce d by TMS. Norma liz ed to its corresponding MVC to make the data comparable despite the different numbers of intended fingers during the ImIn and ImAll tasks, DFIMAG could then be used to compare the

relative effects of motor imagery on one-finger and fourfinger tasks. The DFIMAG index was significantly higher during the one-finger (ImIn, 4%) tasks than during fourfinger (ImAll, 2.8%) tasks. This result implies that the effect of motor imagery, per unit of force in MVC tasks, is lower during the ImAll task than during the ImIn task. This result could be interpreted as a correlate of the phenomenon of force deficit during voluntary force production tasks. Note that the relative amount of ‘‘imagery deficit’’ was about 30%, which is close to typical force deficit values described earlier [25,29]. 4.2. Movement-specific effect Observation of enslaving effects during motor imagery supports an earlier hypothesis that enslaving is of a central origin [4,23,26]. On the other hand, this result seems to be in contrast to movement-specific effects of motor imagery [12,13], which imply that humans are able to specifically facilitate an intended movement. For example, Facchini et al. [12] showed no facilitatory effect on the MEP in the first dorsal interosseus during motor imagery of thumb abduction on the same side. It is possible, however, that the observation of enslaving effects of motor imagery in our study is associated with the unique and complex organization of finger representations in the primary motor cortex. Previous studies have shown that finger representations are highly interconnected, and that activation is distributed throughout the M1 hand area whenever any finger movement is made [17,37,39,40]. Furthermore, due to the diverging effect of output projections from finger representations, activation of one finger representation could project onto adjacent fingers [40,42]. Indeed, the observation of enslaving effects supports movement-specific effects of motor imagery. Combined effects on middle, ring and little fingers (DFMRL) were larger in ImAll tasks when these fingers were explicitly involved (Fig. 3). This result means that motor imagery of a movement specifically affects effectors that would be involved in actual execution of the movement (cf. Refs. [12,13]). To conclude, the results illustrate similarities in characteristics of finger interactions, such as enslaving and force deficit, during motor imagery and voluntary action. They provide direct evidence of the neural origin of the main phenomena of finger interactions and suggest the involvement of similar neural structures (including M1) in voluntary action and motor imagery.

Acknowledgements The authors thank Desmond Oathes and Jared Bruce for assistance in data acquisition. The study was in part supported by NIH grants NS-35032, AG-018751 and AR-048563. S. Li was supported by a NIDRR training grant H133P990006. We thank the anonymous reviewers for useful comments.

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