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1Department of Physical Medicine and Rehabilitation, Feinberg School of Medicine, Northwestern University, Chicago; and 2Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, Illinois 60611
Submitted 4 June 2003; accepted in final form 29 August 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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However, this freedom adds a layer of complexity to the control scheme, as a particular trajectory must be selectively planned and executed. Some researchers suggest that the nervous system typically reduces the potential solution space for multi-joint movements by using specific patterns of activation, or synergies (Latash et al. 2002b; Li et al. 1998).
Certainly, patterns of movement often emerge in a variety of upper extremity tasks. During planar reaching, for example, subjects have exhibited a tendency to produce a straight-line hand movement between two points (Flash and Hogan 1985; Wolpert et al. 1995), with a single peak in the tangential velocity curve (Morasso 1981). A number of planning strategies have been proposed to account for these consistent patterns. These include efforts to minimize jerk in the movement (Flash and Hogan 1985), change in joint torque (Uno et al. 1989), or discomfort (Cruse et al. 1990; for a review, see Engelbrecht 2001).
Researchers have observed characteristic hand postures during grasping as well. In reach-to-grasp tasks, the aperture between the thumb and index finger has often been used to describe the grasp. When the task is initiated with the index finger and thumb in contact, the aperture between them typically shows a trajectory with a single peak with characteristic timing (Gentilucci et al. 1992; Haggard and Wing 1995; Jeannerod 1984).
A limited set of joint configurations has been shown to provide a basis for a variety of grasping tasks (Santello et al. 1998, 2002) and typing (Soechting and Flanders 1997). Similarly, a few eigenpostures with temporal weightings were sufficient to describe hand configurations during reach-to-grasp movements for a variety of objects (Mason et al. 2001).
However, the fingertip trajectories with respect to the hand during the reach-to-grasp tasks have not been well described. We were interested in whether stereotypical movement patterns might be present, and if so, whether these patterns would be similar to those observed for hand movement with respect to the shoulder.
This study attempted to characterize motion of the digits during grasping. Subjects performed multiple trials for objects of varying size and shape in as natural a manner as possible, with no constraints on forearm or wrist orientation or on grasping strategy. Fingertip motion followed a stereotypical trajectory, which could be described with a basic mathematical function. The trajectory was largely unaffected by initial finger posture.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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Every subject performed 20 grasping trials. The participant was instructed to either grasp a single object (10 trials) or all five objects in succession (10 trials). Object order between and within trials was randomly selected. Subjects rested for 1 min between each trial.
For each trial, the participant was told to begin with his/her hand placed in a relaxed posture on the thigh. Once instructed to move, the subject reached for the appropriate object, which he or she lightly grasped as though to lift. No instructions regarding use of specific fingers or specific arm orientations were given. Thus the subjects were free to approach and contact the object in any manner they deemed appropriate. Participants were told not to actually lift or squeeze the object on grasping, in an effort to focus on planned fingertip trajectories, distinct from the finger motion that might result from forceful contact with the object. On receiving a verbal cue, the subject released the object and moved his/her arm either to the next object or back to the starting position.
Each subject performed all trials with her/his dominant hand. Thus nine subjects used their right hands, and one subject used his left hand. Finger joint angles were recorded at 50 Hz throughout the trials with a CyberGlove (Immersion Corp., San Jose, CA). Specifically, the flexion/extension of the distal interphalangeal (DIP), proximal interphalangeal, (PIP), and metacarpophalangeal (MCP) joints were recorded for the fingers, along with MCP abduction/adduction. Thumb carpometacarpal (CMC) abduction/adduction and flexion/extension were also measured, along with thumb MCP and interphalangeal (IP) flexion/extension.
After completion of the trials, the length of each digit segment (distal, middle, proximal, and thumb metacarpal) was measured with digital calipers. For the more proximal segments, the distance was taken from joint-center to joint-center. For the distal segments, the measurement was made from the joint-center to the fingertip. These data were saved and used to compute fingertip path and workspace values.
Five of these subjects participated in a further experiment during a separate testing session. This experiment was designed to test for the possible influence of initial finger posture on finger trajectory. The subjects completed the same protocol as described but with initial and final posture consisting of a closed fist.
Calibration
Calibration was performed at each joint of interest. Prior to performance of the trials, data were recorded at multiple known joint angles (measured with a finger goniometer (Pluri-Dig, Sammons Preston, Chicago, IL). Calibration curves were formulated from this data for each joint by creating a polynomial function relating known joint angle to voltage measured by the CyberGlove sensors.
All data subsequently acquired during the testing session were digitally filtered forward and backward with a 20th-order finite impulse response having a cut-off frequency of 5 Hz, a value similar to that used in other studies (Mason et al. 2001). Examination of the power spectral density of the raw data confirmed that the power of the signal resided predominantly below 5 Hz. The data were calibrated according to the aforementioned functions.
Data analysis
The potential for linear relationships between joints for a given finger was assessed using linear regression. For each finger, the best fit for a line relating PIP joint angle to MCP joint angle was found using the least-squares error for each trial. In like manner, a line was fit to the DIP versus PIP joint angle data for each subject for each trial. To reduce spurious weighting, the portions of the trial at the beginning and end when neither joint angle was changing were first removed from the record. The beginning of the active portion of the trial was defined by the point at which the absolute difference between joint angle, averaged across a 60-ms moving window, and initial angle first exceeded 0.5°. The end of the active portion of the trial was defined as the last point at which the absolute difference between the actual and final joint angles exceeded 0.5°.
The slope and coefficient of the linear relationship between the two joint angles were computed using linear regression. R2 values were computed for each regression to provide an estimate of the fit. The R2 and slope values were averaged across all trials for each subject. These values for the PIP-MCP relationship were compared with those of the DIP-PIP relationship across subjects using a repeated measures ANOVA, with finger and joint pair serving as the independent variables.
Relationships between angular movements for the same joint in different fingers were also examined. Correlation matrices were computed for the MCP, PIP, and DIP joints. A mean value for each element in the matrices was computed across all subjects.
Locations of the tips of the digits were computed from the joint angle data and segment lengths using forward kinematics. For the four fingers, fingertip location was computed with respect to a base coordinate system located on the MCP joint for each finger. Thus fingertips were always located within a plane coincident with the sagittal plane of the phalanges. Coordinate systems were assigned to the finger segments at each of the finger joints, with the z axis aligned with the joint of rotation, characterizing MCP extension/flexion (
1), PIP extension/flexion (2), and DIP extension/flexion (3). The y axis pointed from the proximal to distal coordinate system, while the x axis was directed dorsally (Buchholz and Armstrong 1992). All of the y axes were aligned when the joints were in the neutral position. Thus fingertip location could be described by
 | (1) |
. When the fingertip is aligned with the metacarpal bone, = 90°.
A variety of curves were fit to the fingertip trajectory data to be used in quantifying how stereotypical the trajectories were. Data from all of the trials were pooled for each subject. From inspection, it was decided to try to fit the data with either a second-order polynomial in the x-y plane (Eq. 2) or a logarithmic spiral in the -r plane (Eq. 3). The polynomial coefficients were determined from multiple regression by least-squares estimation. The spiral coefficients were obtained using a nonlinear least-squares estimation with a Levenberg-Marquardt search algorithm
 | (2) |
 | (3) |
Goodness of fit was quantified by computing the absolute error between the dependent value estimated from the function (
or 
) and the actual value from the data (y or r). The average and SD of the absolute error were computed for each subject. Absolute errors of the logarithmic spiral and polynomial fits were compared using a paired t-test. The errors for the different fingers were compared using a repeated measures ANOVA. Variance accounted for (VAF) was also computed to determine the fit of the estimated 
and values, calculated from the , to the actual x-y fingertip locations (Perreault et al. 1999).
For the subjects completing the second experiment, data from the 10 grasping trials for multiple objects were pooled to quantify voluntary fingertip trajectory. We excluded all data in which fingertip trajectory was constrained due to requirements to begin or end in a fisted posture. Thus the data from the single object trials were not used for estimating the trajectory. Only the data occurring between the grasp of the first object and the release of the fifth object in the multi-object trials were used.
Temporal movement properties were also assessed, both in terms of position and velocity. These data were examined in Cartesian space, where it was most readily visualized. Since the x and y positions were related, as described above, we focused our analysis on only the x position data. We computed the number of peaks in the x position curve plotted versus time during an entire trial. The x position data were searched for local minima and maxima. An absolute difference in position between adjacent extrema greater than a threshold value signified a peak. A relatively conservative threshold value of 20% of the range of x during a given trial was arbitrarily chosen (Kamper et al. 2002b). A repeated measures ANOVA was performed on these data to determine if object shape/size affected the temporal pattern of hand opening and closing.
Movement velocity was quantified by examining the tangential velocity. We determined the number of peaks that appeared during the entire trial in the speed curve, given by the norm of the tangential velocity. An absolute difference in speed between consecutive extrema greater than a threshold value signified a peak. A threshold value equal to 20% of the peak tangential speed for a given trial was employed.
Location of the tip of the thumb was computed in three-dimensional Cartesian space for a coordinate system attached to the carpal side of the CMC joint. The z axis for this coordinate system is parallel to those of the finger base coordinate systems. Seven coordinate transformations were used to convert location of the tip of the thumb (EpE) to the base coordinate system (0pE; Eq. 4). The homogeneous transformations (T) correspond to CMC axial rotation (1), followed by CMC abduction (2), followed by CMC flexion (3), followed by MCP axial rotation (4), followed by MCP flexion (5), followed by IP flexion (6), followed by translation from the IP joint to the tip of the thumb (Giurintano et al. 1995; Imaeda et al. 1996). CMC axial rotation (1) was fixed to be a constant value of 45°. This was estimated by measuring the angle of the plane containing the thumb, with the MP and IP joints at zero flexion, to the plane containing the fingers with the MCP, PIP, and DIP joints at zero flexion. Similarly, measurements on subjects led us to compute MCP axial rotation (4) as a linear function of CMC flexion (see APPENDIX A). Namely, we set 4 = 0.4 x 3
 | (4) |
). Because the planar projection of the space was crescent-shaped, convex hulls were fit to both the inner and outer surfaces comprising the thumb workspace (Fig. 1). Subtraction of the volume encompassed by the inner hull from the volume encompassed by the outer hull yielded the workspace volume. Volume of the thumb workspace actually spanned during the trials was computed in a similar fashion. This volume was expressed as a percentage of the theoretical workspace volume.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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For a given subject, finger trajectories were quite consistent across trials. These trajectories were curved rather than straight in the plane of the finger. Subjects tended to move along different portions of a specific trajectory for differently sized objects rather than to create new trajectories (Fig. 2).
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The logarithmic spiral (Fig. 3) provided a better fit to the data than the polynomial, as determined by the size of the absolute error (0.22 ± 0.25 vs. 0.51 ± 0.61 cm, P < 0.01). For the spiral, mean error for each finger from the spiral trajectory was always <0.5 cm, except for one finger for one subject. This subject displayed a fairly consistent pattern for the little finger, but one that was unique and involved curling of the finger. Across all subjects, the mean error for different fingers was only marginally significant (P = 0.1), with mean error from the spiral tending to be smaller for the index and ring fingers (0.20 cm) than for the middle finger (0.27 cm). Mean VAF across all trials and subjects was >98% for both the x and y directions. The estimated x and y positions matched the experimental data quite well (Fig. 6).
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A variety of grasping strategies was used among subjects and among objects. For example, some subjects used the thumb and two digits to grasp the softball while others used all five digits. Some subjects supinated the forearm to grasp the playing card with a palmar pinch, some pronated the forearm, and others kept the forearm somewhere between the two extremes and grasped the opposing edges of the card. However, the spiral shape of the trajectories was quite consistent, as quantified by the 
coefficient (Eq. 3), which had a value across all fingers of 1.66 ± 0.05 radians. This term controls the rate of decay of the spiral. Because it is significantly greater than 
/2, the finger is not merely sweeping along a circular arc. This assertion is further supported by the fact that the mean error of the spiral fit was always less than that for an arc of constant radius.
Five subjects completed the second experiment with finger posture starting and ending in a fist. Mean starting finger posture was 50° of MCP flexion, 100° of PIP flexion, and 45° of DIP flexion. For these subjects, a similar spiral pattern was also observed for the portions of the trials not constrained by the fisted posture, i.e., the portion between the grasp of the first object and release of the fifth object in the multi-object trials. For a spiral fit to this pooled data, mean VAF in both the x and y directions was again >98%. The pattern closely matched that observed during the previous session. In fact, using the coefficient estimates from the first experiment to predict x and y positions for the second experiment led to mean VAF = 95% for both directions.
Relationships between joint angles for a given finger were considerably more variable than the fingertip trajectories. While highly linear relationships between consecutive joint angles could sometimes be found (R2 > 0.9), for many other trials, this was not the case (see Fig. 4B). Significant variation could be observed even between consecutive trials with the same object. Overall, the linear relationship better defined the PIP-DIP correspondence (R2 = 0.61 across all fingers) than the MCP-PIP correspondence (R2 = 0.40 across all fingers; P = 0.001). The repeated measures ANOVA for the slope indicated a significant interaction between finger and joint pair (P = 0.001), with the slope of the PIP-MCP relationship being significantly larger than the slope of the DIP-PIP relationship for the ring and little fingers (Table 2). All of the slopes are less than one, thereby indicating that MCP flexion was greater than PIP flexion, which was, in turn, greater than DIP flexion.
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Between fingers, the correlations between corresponding joints were significant. These correlations were greatest for adjacent fingers, and for the MCP joints (Table 3). Comparison of the relationships between pairs of joints within and across fingers can be made by squaring the coefficients of correlation in Table 3 to obtain the coefficients of determination, similar to the R2 values in Table 2. Especially for the MCP and PIP joints, correlations between fingers are much greater than those within a finger.
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Thumb motion tended to vary more according to object size/shape. The volume traversed, however, was still quite selective. Across all 20 trials, subjects used 3.6 ± 1.3% of their potential workspace. The majority of the movement occurred near the surface of the potential workspace (Fig. 5).
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The temporal finger pattern generally did not exhibit a monotonic change between initial and final posture, especially for the x direction. For the single-object trials in which subjects had an extended initial hand posture, multiple peaks in the temporal curves were typically present, indicating hand closure during the transport phase (Fig. 6). The pattern was similar for grasp and release. The x position data had 4.4 ± 1.6 peaks for each trial.
The temporal pattern was dependent on object size/shape. For the smaller diameter objects such as the marker, the hand closure could sometimes be incorporated into the object grasp so that little or no change in direction occurred (Fig. 7). The numbers of peaks in the x position curves for the card (3.3) and marker (3.2) were statistically different from the number of peaks for the ball (5.0), CD (5.3), and cup (5.4; P < 0.001).
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For the trials begun with a closed fist, the temporal x position curve looked similar to that obtained with an initially extended finger posture (Fig. 8). The initial decrease in the x position was due in this case, however, to the fingers following a curved rather than straight trajectory during hand opening. The corresponding velocity curve, obtained by numerical differentiation of the position curve, displayed multiple peaks and three zero-crossings after the start of movement.
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The tangential velocity profiles also displayed multiple peaks (Fig. 9). Across single-object trials for the 10 subjects, the mean number of speed peaks (NSP) was 5.0 ± 1.5. In accordance with the described temporal movement patterns, NSP was greater for the larger diameter objects, such as the cup, than for smaller diameter objects, such as the marker (P < 0.001).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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).
In accordance with another study, thumb movement was more variable than finger motion, with a greater dependency on object shape and size (Smeets and Brenner 2001). The percentage of the available workspace used, however, was still quite small. Flexion of the MP and IP joints was limited, as seen elsewhere (Santello et al. 2002), thereby leaving most of the thumb trajectories to reside on the surface of the workspace.
The consistency of the movements corresponds well to other studies having displayed highly repeatable movement paths for the hand during reaching (Wolpert et al. 1995). However, unlike the hand trajectories in planar movements (Shadmehr and Mussa-Ivaldi 1994), fingertip trajectories are curved. These trajectories thus do not follow the straight-line trajectory predicted by the minimum jerk hypothesis (Flash and Hogan 1985) and postulated as the preferred finger pathway (Secco and Magenes 2002).
Smeets and Brenner (1999) did show how minimum jerk theory could still predict a curved path without via points. A nonzero boundary condition on the acceleration at the time of contact with the target could produce curved finger trajectories that were still minimum jerk. For our results, however, such as those seen in Figs. 6 and 8, a minimum jerk solution is not possible. Three roots for the x velocity are seen after initiation of movement (Fig. 8), and only two are possible for the minimum jerk solution (APPENDIX B).
Certainly, curved motion pathways have been observed in a number of other experimental paradigms. Unconstrained planar reaching resulted in significantly greater hand path curvature than planar reaching in which interaction with an external object was required (Desmurget et al. 1997). The curvature also increased with increasing angle of the target from the midline, a phenomenon also seen in unconstrained three-dimensional reaching (Kamper et al. 2002b).
The observed spatial pattern of movement does require a coordinated effort of a number of different muscles. For example, excitation of the intrinsic muscles alone, resulting in MCP flexion with PIP and DIP extension, is insufficient to generate the observed patterns. PIP and DIP flexion were significant during the grasping, as evidenced by the spiral fit (Fig. 4A). Alternatively, stimulation of only the extrinsic finger flexors, flexor digitorum superficialis and profundus, produces a very different pattern of movement than the one seen, with the greatest rotation occurring at the PIP joint (Kamper et al. 2002a). Electromyographic studies of finger movement have verified the large percentage of finger muscles active for even a relatively simple movement (Brandell 1970; Rose et al. 1999).
Governing principles for the spatial patterns of finger movement remain elusive. As correlations for movements between pairs of joints varied widely, synergistic planning of movement in joint space (Desmurget et al. 1995; Gandolfo et al. 1996; Soechting and Lacquaniti 1981) does not seem to provide a plausible alternative. Incidentally, the slope value of 0.3 that we obtained for the PIP-DIP relationship was actually less than one-half of that described by others (Hahn et al. 1995), but the tasks were different. Where our tasks entailed grasping and releasing objects, the task in that study was to open and close the fist, an exercise requiring much greater PIP and DIP flexion. It is also possible that the CyberGlove itself altered DIP movement by providing resistance to DIP flexion.
For a given type of joint (MCP, PIP, DIP), movement in one finger was closely correlated with that in adjacent fingers. The correlation between joints of the same type on different fingers was greater than the correlation between joints of different type on the same finger (Tables 2 and 3). This phenomenon was also observed in studies with a greater variety of objects (Santello et al. 2002), although objects with nonuniform diameters may preclude its occurrence (Santello and Soechting 1998). The high correlations between pairs of fingers seem to result from neural rather than mechanical constraints, in accordance with studies describing neural enslaving of fingers during isometric force generation (Latash et al. 2002a; Zatsiorsky et al. 1998). Indeed, anatomical studies in primates have detected motor units that exert tension on multiple finger tendons (Schieber et al. 1997).
Possibly, the observed fingertip trajectories represent the paths of minimal resistance against passive torques, which appear to fundamentally affect finger motion (Kamper et al. 2002a). It is intriguing that even from an initial fisted posture, the finger trajectories largely returned to the pathways obtained with an initially relaxed hand.
Temporal fingertip motion was affected by object size/shape. Whether or not appropriate for object grasp, the hand began to close during transport to the object, as described elsewhere (Hoff and Arbib 1993). For objects of a particular shape, especially those with a smaller diameter, this motion would sometimes segue into hand closure for grasp, without an interceding overshoot in hand opening. For the larger diameter objects, however, hand closure during transport was typically followed by hand opening and then hand closing for grasp, with a reversal of this sequence for release and hand transport to a new position. This is very similar to what was observed in other studies when subjects were instructed to begin reach-to-grasp tasks with the fingers extended rather than in contact with the thumb (Saling et al. 1996; Timmann et al. 1996). These temporal patterns may result from interdependence between reaching and grasping (Haggard and Wing 1995). Alternatively, the initial hand closing could be produced by passive joint mechanics.
Certainly, the human hand is capable of exploring and working throughout its physically available workspace. When required, vastly different digit trajectories than the ones observed in this study can be produced. However, for a variety of grasping tasks, specific trajectories covering a small portion of the workspace are routinely employed by healthy individuals. This suggests that, following impairment of the hand, return of control over even this small percentage of the workspace through rehabilitation or external assistance could lead to considerable improvement in function. Restoration of the active range of motion of the MCP and CMC joints appears most critical for production of the grasping motions used in this study.
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APPENDIX A |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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APPENDIX B |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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)
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(0) = 0, 
(0) = 0]. Arbitrarily setting x0 = 0, yields
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 | (7) |
thus has only two roots for t 
0, irrespective of the final boundary conditions. To match Fig. 6, three roots are needed after the starting time t = 0. Figure 1 was generated with software written at the Geometry Center, University of Minnesota.
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DISCLOSURES |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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FOOTNOTES |
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Address for reprint requests and other correspondence: D. Kamper, Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Suite 1406, 345 E. Superior St., Chicago, IL 60611 (E-mail: d-kamper{at}northwestern.edu).
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REFERENCES |
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