(PDF) Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence

Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence D. J. S. Mattos, M. L. Latash, E. Park, J. Kuhl and J. P. Scholz J Neurophysiol 106:1424-1436, 2011. First published 15 June 2011; doi:10.1152/jn.00163.2011 You might find this additional info useful... This article cites 51 articles, 10 of which can be accessed free at: /content/106/3/1424.full.html#ref-list-1 This article has been cited by 4 other HighWire hosted articles Stability of multifinger action in different state spaces Sasha Reschechtko, Vladimir M. Zatsiorsky and Mark L. Latash J Neurophysiol, December 15, 2014; 112 (12): 3209-3218. [Abstract] [Full Text] [PDF] Equifinality and its violations in a redundant system: multifinger accurate force production Luke Wilhelm, Vladimir M. Zatsiorsky and Mark L. Latash J Neurophysiol, October 15, 2013; 110 (8): 1965-1973. [Abstract] [Full Text] [PDF] Changes in multifinger interaction and coordination in Parkinson's disease Downloaded from on February 28, 2015 Jaebum Park, Yen-Hsun Wu, Mechelle M. Lewis, Xuemei Huang and Mark L. Latash J Neurophysiol, August 1, 2012; 108 (3): 915-924. [Abstract] [Full Text] [PDF] Updated information and services including high resolution figures, can be found at: /content/106/3/1424.full.html Additional material and information about Journal of Neurophysiology can be found at: http://www.the-aps.org/publications/jn This information is current as of February 28, 2015. Journal of Neurophysiology publishes original articles on the function of the nervous system. It is published 12 times a year (monthly) by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991. Copyright © 2011 by the American Physiological Society. ISSN: 0022-3077, ESSN: 1522-1598. Visit our website at http://www.the-aps.org/. J Neurophysiol 106: 1424 –1436, 2011. First published June 15, 2011; doi:10.1152/jn.00163.2011. Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence D. J. S. Mattos,1 M. L. Latash,2 E. Park,1 J. Kuhl,3 and J. P. Scholz1,4 1 Biomechanics and Movement Science Program, University of Delaware, Newark, Delaware; 2Department of Kinesiology, Pennsylvania State University, University Park, Pennsylvania; and 3Department of Biology and 4Department of Physical Therapy, University of Delaware, Newark, Delaware Submitted 24 February 2011; accepted in final form 14 June 2011 Mattos DJ, Latash ML, Park E, Kuhl J, Scholz JP. Unpredict- straight reaches (Torres and Andersen 2006) leads, however, to able elbow joint perturbation during reaching results in multijoint different terminal configurations. In addition, results of studies motor equivalence. J Neurophysiol 106: 1424 –1436, 2011. First of unperturbed reaching from a fixed initial position by Cruse published June 15, 2011; doi:10.1152/jn.00163.2011.—Motor equiv- alence expresses the idea that movement components reorganize in et al. (1993) have provided equivocal evidence for planning in the face of perturbations to preserve the value of important perfor- terms of terminal joint postures. mance variables, such as the hand’s position in reaching. A formal Evidence exists for the preservation of the spatial orientation method is introduced to evaluate this concept quantitatively: changes of the plane of the arm (which has a complex relationship to in joint configuration due to unpredictable elbow perturbation lead to joint angle changes) and the three-dimensional (3D) curvature a smaller change in performance variables than expected given the of the hand path when performing 3D reaches over a wide Downloaded from on February 28, 2015 magnitude of joint configuration change. This study investigated range of movement speeds (Nishikawa et al. 1999). Similarly, whether motor equivalence was present during the entire movement trajectory and how magnitude of motor equivalence was affected by monkeys learning an obstacle avoidance task were shown to constraints imposed by two different target types. Subjects pointed to keep the spatial trajectories of individual joints relatively spherical and cylindrical targets both with and without an elbow joint constant despite variations of movement speed (Torres and perturbation produced by a low- or high-stiffness elastic band. Sub- Andersen 2006). These results suggest that the entire temporal jects’ view of their arm was blocked in the initial position, and the sequence of joint configurations for a given hand trajectory perturbation condition was randomized to avoid prediction of the may be planned by the CNS (Rosenbaum et al. 1999). Such a perturbation or its magnitude. A modification of the uncontrolled strategy could presumably simplify trajectory control because manifold method variance analysis was used to investigate how differences in movement velocity could be achieved by simply changes in joint configuration on perturbed vs. nonperturbed trials (joint deviation vector) affected the hand’s position or orientation. scaling the transition time between a planned sequence of joint Evidence for motor equivalence induced by the perturbation was postures without significantly affecting the postures themselves present from the reach onset and increased with the strength of the (Hollerbach and Flash 1982; Rosenbaum et al. 1999; Torres perturbation after 40% of the reach, becoming more prominent as the and Zipser 2002). In contrast, a study of targeted reaching at reach progressed. Hand orientation was stabilized more strongly by different speeds by Thomas et al. (2003) showed that reaching motor equivalent changes in joint configuration than was three- at different speeds did not lead to a simple scaling of segmental dimensional position regardless of the target condition. Results are kinematics. consistent with a recent model of neural control that allows for The challenge of answering the question of whether a flexible patterns of joint coordination while resisting joint configura- movement’s terminal joint configuration is planned in advance tion deviations in directions that affect salient performance variables. is that the motor system is inherently noisy. Thus even reach- The observations also fit a general scheme of synergic control with referent configurations defined across different levels of the motor ing from a relatively fixed initial hand position and arm posture hierarchy. will result in some trial-to-trial variation in the hand’s path and its terminal position, as well as in the joint configuration. A motor control; synergies method is needed, then, to distinguish between differences in joint configurations due to noisy control versus different move- IT HAS BEEN SUGGESTED that the central nervous system’s (CNS) ment plans. The uncontrolled manifold (UCM) approach pro- plan for targeted reaching involves specifying a terminal joint vides tools that allow such differences to be tested quantita- configuration (Desmurget et al. 1998; Grea et al. 2000; Tillery tively by comparing task-relevant to task-irrelevant variance in et al. 1995). If this is true, relatively invariant terminal joint the space of the motor elements (i.e., joints or muscles). For configurations could be expected if reaching is performed example, recent investigations of a variety of upper extremity repetitively from a fixed initial hand location and arm config- tasks used such tools to map joint variance across repetitive uration to a fixed target location. Pointing to a given target reaches onto end-effector variance. The results of those studies location from different starting positions (Soechting et al. suggested that the CNS uses a family of joint postures that are 1995) or when reaching around obstacles compared with equivalent with respect to producing a consistent hand path when performance occurs under identical task conditions (Scholz et al. 2000; Tseng et al. 2002, 2003; Tseng and Scholz Address for reprint requests and other correspondence: J. P. Scholz, 307 McKinly Laboratory, Dept. of Physical Therapy and Biomechanics and 2005; Yang et al. 2007). Such results make it difficult to argue Movement Sciences, Univ. of Delaware, Newark, DE 19711 (e-mail: that the CNS typically plans for specific joint configurations or

). muscle activation patterns (see, e.g., Krishnamoorthy et al. 1424 0022-3077/11 Copyright © 2011 the American Physiological Society www.jn.org MULTIJOINT MOTOR EQUIVALENCE 1425 2003, 2004, 2007), although the CNS can certainly plan for produce internal perturbations of the entire arm. The results of such detail when the task requires it (e.g., artistic endeavors). that study indicated that performance-relevant changes of the Further evidence that planning likely involves the specifica- joint configuration across speed conditions, i.e., those that tion of relatively global, performance-related variables comes affected the terminal pointer-tip position, were significantly from studies of motor equivalence. Motor equivalence often is smaller than configuration changes that did not affect the defined as the preservation of a parameter most related to task terminal pointer position. The UCM method was also used to performance despite changes in the values of the underlying study postural perturbations induced by support surface move- motor elements. It has been investigated by measuring the ment and revealed that changes in joint configuration due to a ability of individuals to complete a goal or produce accurate perturbation were largely motor equivalent compared with end-effector movements when the motor elements are per- preperturbation postural states (Scholz et al. 2007). turbed (Schöner et al. 2008). For example, spinal frogs were The present study had three goals. The first goal was to shown to be able to remove noxious stimuli from their skin determine whether perturbation of a 10 degrees of freedom with their foot even immediately after restriction of a joint’s (DOFs) reaching task exhibited motor equivalence both at the motion (Berkinblit et al. 1986). Kelso et al. (1984) found that target of reaching and during the reach path and, if so, where despite the application of unexpected forces to perturb jaw along that path it became manifest. For example, it is in movements during the production of different speech utter- principle unnecessary to preserve the pointer-tip path during ances, those utterances could still be perceived by independent the reach itself as long as the pointer ultimately reaches the listeners, indicating preservation of the acoustic goal. More- target. A second goal was to determine how the use of motor over, they showed that the primary articulatory compensations equivalence was affected by different constraints imposed by occurred in effectors most appropriate for the production of a two different target types, one with only position constraints, given utterance. Similar effects were reported by Cole and the other with both position and orientation constraints. A final Abbs (1987) from studies of a perturbed precision grasp. Levin goal was to confirm that the results from the motor equivalence Downloaded from on February 28, 2015 et al. (2003) used a spring load to perturb the forearm during a analysis, comparing perturbed to nonperturbed trials, provided two-joint, star drawing task and found that the kinematics of different information than the typical UCM variance analysis nonperturbed drawing was preserved with the perturbation by (Scholz and Schoner 1999), which evaluates the structure of significant changes in muscle electromyographic patterns. joint variance across repetitions of the same condition. We Each of these studies evaluated the relative level of terminal hypothesized that motor equivalence, related to the pointer goal achievement as the criterion for motor equivalence and tip’s path and the hand’s orientation, would be present from provided evidence for changes in the activation of certain relatively early in the reach until movement termination be- motor elements associated with this preservation. Despite these cause typical reaching movements occur in quasi-straight line clear patterns of behavior, the idea of motor equivalence is less paths (Abend et al. 1982; Morasso 1981) and motor synergies well defined conceptually than it appears. For example, the are organized to stabilize important performance-related vari- variable that describes the goal of a task, e.g., bilabial closure ables like the hand path (Latash et al. 2007). A second (Kelso et al. 1984), thumb-fingertip contact (Cole and Abbs hypothesis was that the magnitude of the motor equivalence 1987), or foot contact (Berkinblit et al. 1986), will not be effect would depend on the strength of the perturbation, i.e., unchanged perfectly when a perturbation is applied. Small that the greater the tendency to perturb the arm, the stronger changes of these variables induced by the perturbation or by would be the restoring forces to preserve the hand path. Two any other variations of task conditions that may occur naturally different target types were used in this study: a cylindrical are generally observed. Thus a more relevant definition of target, where subjects had to insert the pointer halfway into the motor equivalence would be that changes in the configuration cylinder, and a spherical target that had to be touched by the of motor elements that lead to changes in variables relevant to pointer. We hypothesized that the motor equivalence effect the task goals are small compared with other changes of the relative to the hand’s orientation would be strongest when configuration not directly relevant to those goals. Those other reaching to insert the pointer into a cylindrical target because changes of the articulatory configuration thus represent the only that target had an explicit orientation constraint. Finally, “motor equivalent” solution to the task (Schöner et al. 2008). it was predicted that motor equivalence analysis would provide This definition presupposes, first, that there is a shared metric different information about reaching coordination than the with which to compare the changes that occur at the level of the typical UCM variance analysis. task goal to changes that occur at the level of the configuration of motor elements and, second, that there is a way to compare METHODS the many variables that describe the motor elements to the few Subjects variables that describe the task goal. Similar to the problem of assessing the role of natural variability of the motor elements Eight healthy men participated in the study, averaging 20.1 (⫾1.5) during repetitive tasks mentioned above, the UCM approach yr old and 184.2 (⫾2.4) cm in height and weighing 79.0 (⫾7.8) kg. provides a potential solution to these problems. All participants were right-handed as determined by the Edinburgh A recent study applied a version of the UCM approach to handedness questionnaire (Oldfield 1971). They gave written in- resolve whether differences in the terminal joint configuration formed consent as approved by the University of Delaware Human induced by reaching and pointing to targets at different veloc- Subjects Committee. ities were due primarily to differences in the terminal pointer- Experimental Procedures tip position across speed conditions or reflected motor equiv- alence (Scholz et al. 2011). Different dynamics due to changes Experimental setup. Participants sat on a chair in front of a table in joint interaction torques with movement speed were used to that had a rectangle cut out of one side into which the chair was J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org 1426 MULTIJOINT MOTOR EQUIVALENCE placed. The participants sat with their trunk upright, feet flat on the the spherical target, subjects were instructed to lightly touch the target floor, and arms supported laterally by the table (Fig. 1). The heights with the pointer-tip. For the cylindrical target they were told to insert of both chair and table were adjusted to keep the shoulder of the arm the pointer-tip halfway into the opening of the cylinder. Subjects were that performed the task immediately next to the trunk in a slightly asked to try to perform all trials at the same speed and to touch/insert adducted position, the elbow in ⬃90° of flexion, and the forearm the pointer-tip as accurately as possible. resting on the table in a neutral position. The subjects were instructed Experimental conditions. Each target condition involved 75 trials to hold a cylindrical shaped handle (5 cm in diameter and 11 cm high) of reaching, 25 in each of three perturbation conditions that were with their most comfortable grasp. Solidly embedded in the center of completely randomized: 1) no perturbation (0-K); 2) a single elastic one end of the handle was a 12-cm-long knitting needle that served as band (Thera-Band) placed across the elbow joint (stiffness ⫽ 4.8 N/m; a pointer. To maintain the handle’s orientation in the hand during Low-K); and 3) two elastic bands (stiffness ⫽ 12.5 N/m; High-K). the trials, the handle and the subject’s palm were covered with the Participants wore goggles with the brim of a hat attached, permitting loop-and-hook type of Velcro strips. Once the subjects held the them to see the targets clearly while eliminating the view of their arm. handle, they were not allowed to change their grasp until the end of Cuffs with D-rings were placed around the upper arm and proximal to the data collection. After the subject was positioned, the chair was the wrist, to which hooks attached on each end of the Thera-Band locked in place and the subject’s trunk was secured to the chair with could be attached. Prior to each trial, one experimenter attached the a harness to limit compensatory trunk movements, but still allowing appropriate band (perturbed conditions) or pretended to attach the normal scapular motion. To guarantee the reliability of the initial band (no perturbation condition) with a tug on the D-rings so that position throughout the experiment, a vacuum air bag was fitted subjects could not tell whether or not there would be a perturbation. underneath and around the lateral, medial, and back sides of the The bands were at their resting lengths in the initial position so that participants’ arm, leaving their elbow, forearm, wrist, and hand the subjects felt no pull in this position. This was confirmed verbally secured in a depression with rigid sides. with subjects. Individuals performed practice trials or reaching with- The experiment included reaching to two target types, providing out a band before the beginning of the experimental task. A break was different constraints on reaching: a spherical target (2.54-cm diameter; permitted when requested by the subjects. Participants never reported 3 positional constraints) and a cylindrical target (2.54-cm diameter, fatigue. 5.08 cm wide; 3 positional and 2 orientation constraints). Each Downloaded from on February 28, 2015 target’s center was positioned at a distance corresponding to 95% of Data Collection the subject’s extended arm length (defined as the distance from the lateral aspect of the acromion process of the shoulder to the proximal Three-dimensional kinematic data were collected with an eight- interphalangeal joint of the index finger) and at 70% of the height of camera Vicon MX-13 motion-measurement system (Vicon, Oxford the subject’s eye from the table while in the sitting position. The Metrics) at a sampling frequency of 120 Hz. The cameras were spread targets were suspended from a rigid pole by a string to require greater out in a circle around the subject and were spatially calibrated before final position control than if subjects were able to forcefully hit the each data collection. Rigid bodies with four reflective markers each target. The cylindrical target was oriented at 45° relative to the global were placed on the right arm at 1) two-thirds of the distance between coordinate system, for which the y-axis pointed forward from the the neck and the acromion process, to acquire clavicle/scapula motion, subject’s body, rotated in the counterclockwise direction so that the and midway and along the lateral part of the 2) upper arm, 3) the opening in the cylinder into which the pointer was inserted faced dorsum of the forearm, and 4) the posterior surface of the hand. toward the subject. The targets were suspended so that the centers of Individual markers used to estimate the joint locations were placed on the spherical and cylindrical targets were in the same spatial location. the sternum notch, which served as the base frame of the local Instructions. The subjects were instructed as follows: “Following coordinate system, 2 cm below the acromion process, on the medial my ‘go’ command, begin reaching when you are ready and then move and lateral humeral epicondyles to estimate the elbow joint axis and the pointer as quickly as possible to the target while still maintaining on the radial and ulnar styloid processes of the forearm to estimate the accuracy. You should stop at the target location without disturbing its wrist joint axes. An additional reflective marker was placed near the position.” It was emphasized that this was not a reaction time task. For base of the pointer. The spherical and cylindrical targets were cali- brated after each session by using the known fixed position of the pointer-tip relative to the hand rigid body and recording the hand while the subject held the pointer-tip statically at the target locations. One static calibration trial was recorded with the arm extended forward prior to the experiment. In this trial, the arm was facing forward from the shoulder, with the upper arm, forearm, and hand aligned and held parallel to the floor with the thumb pointing upward. In this position, the arm was parallel to the global y-axes and all joint angles were defined as zero. The positive axes of each joint coordinate system in this position pointed laterally (x-axis), forward (y-axis), and vertically upward (z-axis). Joint angle computation involved comput- ing the rotation matrices required to take the arm rigid bodies from the dynamic trial into the calibration position. Data Processing Vicon Nexus 1.6.1 software was used to label the reflective mark- ers and create the geometric model of their kinematic motion. The Fig. 1. Cartoon depicting the experimental setup. Subjects wore safety goggles signals were then processed with a customized Matlab program with a cardboard brim attached to the bottom to block vision of their arm and hand during approximately the first half of the reach. Either a spherical target (version 7.1, Mathworks). Marker coordinates were low-pass filtered or a cylinder (illustrated here) was hung from strings from a post to increase at 5 Hz with a bidirectional 4th-order Butterworth filter. The resultant the need to control the terminal reach precisely. The Thera-Band was attached velocity of the pointer-tip marker was obtained after differentiation of with hooks to padded cuffs placed around the upper arm and distal forearm so its x, y, and z coordinates. Kinematic variables of each trial were that they spanned the elbow joint. time-normalized to 100% for most analyses after differentiation. J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org MULTIJOINT MOTOR EQUIVALENCE 1427 Joint angle computation. The joint angles were calculated from the configuration across trials at each 1% of the three conditions markers’ coordinates as follows: The rigid bodies at each sample of an (i.e., ␪៮ 0-K, ␪៮ Low-K, ␪៮ High-K) was calculated. Then, the geometric experimental trial were rotated into their static position in the cali- model describing how changes in the joint configuration from the bration trial and used to compute the rotation matrices required to take mean of the nonperturbed condition (␪៮ 0-K) affect either the 3D one into the other (Soderkvist and Wedin 1993). The product of these pointer-tip path or the 3D hand orientation was computed. From rotation matrices for adjacent segments was then used to extract Euler this, the Jacobian matrix (J) was computed, reflecting how small angles in Z-X-Y order. The result provided 10 rotational DOFs: 3 at the changes in a given joint angle while keeping other angles constant clavicle/scapula (abduction-adduction about the z-axis; elevation-de- affects the 3D pointer-tip path or the 3D hand orientation. Details of the pression about the x-axis, and upward-downward rotation about the method can be obtained from recent publications (Scholz et al. 2007, y-axis) and shoulder (horizontal abduction-adduction about the z-axis; 2011; Scholz and Schoner 1999). The nullspace of this Jacobian provides flexion-extension about the x-axis, and internal-external rotation about a linear estimate of the subspace of joint space within which changes in the y-axis) and 2 at the elbow (flexion-extension about an axis oblique the joint configuration have no effect on the performance variable of to the local coordinate system; forearm pronation-supination about the interest (i.e., the mean pointer-tip path or hand orientation of nonper- y-axis) and wrist (flexion-extension about the z-axis; abduction-ad- turbed trials). duction about the x-axis). Rodrigues’ rotation formula was used to Then, a joint deviation vector (JDVi0 ⫽ ␪៮ i-K ⫺ ␪៮ 0-K) between each rotate the elbow flexion-extension axes from the x-axis of the global stiffness (Low-K and High-K) condition and the nonperturbed (0-K) coordinate frame to the axes formed by markers placed at the medial condition was obtained at each percentage of the reach. The JDV was and lateral epicondyles (Murray et al. 1994). then projected onto the nullspace of the Jacobian for the nonperturbed Movement time. Both movement onset and termination were deter- condition and into the complementary subspace, or range space. The mined for each trial as follows. The pointer-tip position was rotated length of the projection into the nullspace represents an estimate of the into a local coordinate frame with the x-axis pointing from its average change in the joint configuration due to the perturbation that did not starting position before trial onsets to the calibrated target position. affect the performance variables, 3D pointer-tip path or 3D hand The local coordinate along this axis, i.e., movement extent, was then orientation, compared with the nonperturbed trials, while the length of differentiated. Onset and termination were determined as the times projection into the range space estimates the effect of that change on when the velocity profile along movement extent first exceeded or the performance variable. Because the dimensions of the nullspace Downloaded from on February 28, 2015 returned to, respectively, 5% of its peak velocity. The time between (dUCM ⫽ 7), a linear estimate of the UCM (i.e., the motor equivalent movement onset and movement termination was computed as move- subspace), are larger than the dimensions of the complementary or ment time (MT). range space (dORT ⫽ 3), we divide the respective projections by the Target error. Deviations of the pointer-tip at movement termina- square root of the dimension to make comparisons fairer. If the length tion with respect to the calibrated target position (x-, y-, and z-coor- of projection within the nullspace (ME or motor equivalent compo- dinates) were obtained, and the constant errors (CE) and variable nent) was significantly larger for a given stiffness/band condition than errors (VE) were computed (Schmidt and Lee 2005). the projection into the range space (Non-ME, or non-motor equivalent Pointer-tip path and hand orientation. The path of the pointer-tip component), then we concluded that most of the change in the joint was obtained as the sequence of its global x-, y-, and z-coordinates. configuration due to perturbation of the elbow joint primarily acted to The resultant hand path was then calculated from these individual preserve the 3D pointer-tip path and/or the 3D hand orientation, i.e., coordinates. Hand orientation for both target conditions was obtained that the deviation was not primarily a reflection of induced differences by forming a target coordinate system for the cylindrical target, where in the performance variable. the ytarget-axis was the major axis of the cylinder, the xtarget-axis was Components of joint configuration variance. In addition, the typical the minor axis, parallel to the floor, and the ztarget-axis pointed UCM variance analysis was performed addressing how trial-to-trial upwards. Euler angles (roll, pitch, and yaw) were then extracted from variations of the joint configuration within a condition are structured, the rotation matrix, computed at each sample in time, required to take i.e., whether they led primarily to changes in the performance variable a local coordinate system formed by the hand rigid body into the across repetitions (i.e., contributed to “bad” variance) or were more target coordinate system. The angles corresponded to rotation about consistent with a stable pointer-tip path or 3D hand orientation across the xtarget-, ytarget-, and ztarget-axes of the target coordinate system, repetitions (“good” variance). The method used to estimate the two respectively. components of joint configuration variance is outlined in detail else- Peak movement velocity. The x-, y-, and z-coordinates of the where (de Freitas et al. 2007; Reisman and Scholz 2003; Scholz et al. pointer-tip position were differentiated to obtain the end-effector 2000) and is similar to that outlined above for estimating motor velocity. The resultant pointer-tip velocity was calculated as the norm equivalence. In this case, however, the Jacobian and nullspace are of the differentiated coordinates at each point in the trial. The portion computed based on the mean joint configuration of each condition. of the resultant velocity between the onset and termination of each Then, for each percentage i of the reach trajectory of each trial j of a reach was then extracted. A custom Matlab program was then used to given condition k, the mean-free joint configuration is obtained (i.e., automatically pick the peak of the resultant velocity and determine its ␾ijk ⫽ ␪ijk ⫺ ␪៮ ijk) and projected into the estimated UCM, or nullspace, time of occurrence within the reach (onset to termination). Averages and range space for that condition. The variance across trials of the across trials were obtained for each combination of target and pertur- projections into each subspace is then computed. Each variance bation strength. component is then normalized by dividing by the number of dimen- Motor equivalence estimate. The perturbation caused by extension sions of each subspace (dUCM ⫽ 7 for “good” variance within the of the elastic bands placed across the elbow joint will naturally lead to estimated UCM, or VUCM, and dORT ⫽ 3 for “bad” variance in the some deviation of the pointer-tip path compared with the nonper- range space, or VORT). turbed condition. In fact, some variability of the pointer-tip path is expected across trials of reaching even without a perturbation. The Statistical Analysis goal of this analysis, then, was to provide a quantitative test to determine whether differences in the pointer-tip position between All statistical analyses were performed in SPSS version 18. A P perturbed and nonperturbed reaches fully accounted for measured value ⬍ 0.05 was considered statistically significant for all analysis. differences in the joint configuration, or whether more of this differ- A two-way, repeated-measures ANOVA with independent factors ence in the joint configuration was motor equivalent. 1) target type (sphere vs. cylinder) and 2) stiffness (0-K, Low-K, To investigate this question, all trials were time-normalized to High-K) was performed to identify their effects on each of the mean 100% (movement onset to termination) and the average joint and standard deviation of movement time, peak movement velocity, J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org 1428 MULTIJOINT MOTOR EQUIVALENCE and time of occurrence of the peak. Post hoc comparisons of means effect was slightly stronger for the High-K than for the Low-K were performed with the least significant mean (LSD) test. condition regardless of target type. A multivariate analysis of variance (MANOVA) was used to test Figure 3, top, presents for a representative subject the mean for differences in constant and variable target errors (dependent resultant path (⫾SD) of the pointer-tip when reaching to both variables ⫽ x-, y-, and z-coordinates) with factors 1) target type (sphere vs. cylinder) and 2) stiffness (0-K, Low-K, or High-K). Post the spherical (left) and cylindrical (right) targets. Figure 3, hoc comparisons of means using the LSD test were performed for the bottom, presents the mean resultant velocity ⫾ SD for the same dependent variables that exhibited significant univariate results. reaches. All subjects showed similar pointer-tip/hand trajecto- For purposes of statistical analysis of both motor equivalence and ries. joint configuration variance, the results for each subject were averaged Subjects showed more individual variation of the hand across 10 equal phases of the reach trajectory (each accounting for orientation path throughout the reaches, although the presence or 10% of the trajectory) in order to evaluate the evolution of these absence of a perturbation did not appear to affect the hand variables, since the perturbation strength increases along the reach trajectory because of the elastic nature of the elbow joint perturbation. orientation substantially. Figure 4 illustrates the mean hand To evaluate motor equivalence effects, a four-way repeated-measures orientation (⫾SD) relative to coordinates (pitch, roll, and yaw) ANOVA with independent factors 1) target type (sphere vs. cylinder), for the spherical and cylindrical targets for two participants 2) performance variable (3D path vs. 3D orientation), 3) stiffness (Low-K showing somewhat different changes in orientation across the or High-K), and 4) component of projection (ME vs. Non-ME) was reach. Subjects 06 (Fig. 4A) and 08 (Fig. 4B) exhibited, performed separately for each of the 10 phases of the reach. The respectively, the smallest and largest proportion of ME projec- M-matrix function in SPSS was used to further analyze significant tion compared with Non-ME projection across the reach tra- interactions. If there was a significant interaction, e.g., projection com- jectory. Rotation about the z-axis (yaw) was most important, ponent by stiffness, and M-matrix tests revealed that both ME and given the fact that the cylinder was rotated 45° about this axis Non-ME components increased with the High-K perturbation, then the in the x-y plane, and this coordinate changed the most. This slope of change of each component from the Low-K to the High-K condition [e.g., (MEHigh-K ⫺ MELow-K)/(12.5 ⫺ 4.8)] was computed and was, of course, only critical for pointing to the cylindrical Downloaded from on February 28, 2015 a repeated-measures ANOVA was used to confirm which component target, and it can be noted that the yaw rotation was greatest for was more affected by the stronger perturbation. this target condition for both subjects. Finally, a four-way repeated-measures ANOVA was used to iden- tify differences between the variance components VUCM and VORT Movement Time and Peak Velocity across conditions, with factors 1) target type (sphere vs. cylinder), 2) performance variable (3D path vs. 3D orientation), 3) stiffness (0-K, Table 1 presents the mean and standard deviation of move- Low-K, or High-K), and 4) variance component (VUCM vs. VORT). This ment time, peak velocity of the pointer-tip, and time of occur- was again performed for each 10% of the reach trajectory. rence of the peak as a percentage of the reach for the three stiffness conditions and both spherical and cylindrical targets across the subjects. RESULTS Both target type (F1,7 ⫽ 16.342, P ⬍ 0.01) and perturbation Movement Kinematics strength (F1,7 ⫽ 14.881, P ⬍ 0.01) affected the mean MT. No interaction between target type and perturbation strength was Figure 2 shows the average (⫾SD) elbow joint angle (flex- found (P ⬎ 0.3). MT was, on average, 59 ms longer for the ion-extension) for a representative subject during the reach for cylindrical than the spherical target (MTCY ⫽ 0.811 ⫾ 0.037 s each stiffness condition (0-K, Low-K, and High-K) and both vs. MTSP ⫽ 0.752 ⫾ 0.033 s). In addition, MT was ⬃39 ms targets (spherical and cylindrical). Although the Thera-Band and 14 ms longer for the High-K condition compared with the length was adjusted so that it became engaged nearly imme- 0-K (P ⬍ 0.01) and Low-K (P ⬍ 0.05) conditions, respec- diately after the subject began to reach, elbow movement was tively. MT for the Low-K condition was also 25 ms longer than similar to the 0-K condition in the Low-K and High-K condi- for the 0-K condition (P ⬍ 0.01). MT variability was not tions up until ⬃25% of the reach path, after which time the affected by target type (P ⬎ 0.9), perturbation strength (P ⬎ torque produced by the band restricted elbow extension. The 0.7), or their interaction (P ⬎ 0.6). Fig. 2. Mean (⫾SD) of elbow joint excur- sion for a representative subject during the reach for the 3 conditions of stiffness (0-K, Low-K, and High-K) and for the spherical and cylindrical targets. ␪elbow, elbow joint angle. Flex, flexion; Ext, extension. J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org MULTIJOINT MOTOR EQUIVALENCE 1429 Fig. 3. Time series (⫾SD) is shown of the resultant hand path (top) for the same subject as in Fig. 2 for the 3 stiffness conditions when reaching to the spherical (left) or cylin- drical (right) targets. Bottom: mean (⫾SD) resul- tant velocity profiles associated with the reaches shown at top. Downloaded from on February 28, 2015 The peak value of the resultant velocity was not affected by subjected to a stronger perturbation. However, CE was not the target type (P ⬎ 0.9), the perturbation strength (P ⬎ 0.7), different between target types (P ⬎ 0.05), and there was no or their interaction (P ⬎ 0.07; Fig. 3). The peak occurred interaction between target type and stiffness (P ⬎ 0.2). relatively earlier in the reach when pointing to the cylindrical Analysis of VE revealed no effect of target type (spherical compared with the spherical target (F1,7 ⫽ 10.3, P ⬍ 0.05), vs. cylindrical, P ⬎ 0.7) or stiffness condition (0-K, Low-K, indicating a longer deceleration phase when the pointer had to and High-K, P ⬎ 0.5). There was also not a significant be inserted into the target (Table 1). The time of peak velocity interaction between these factors (P ⬎ 0.7). was also affected by the perturbation strength (F2,14 ⫽ 8.9, P ⬍ 0.01). Specifically, peak velocity occurred earlier when sub- Projection Components of Joint Difference Vector jects reached in the High-K condition than in either the 0-K (F1,7 ⫽ 13.88, P ⬍ 0.01) or Low-K (F1,7 ⫽ 7.1, P ⬍ 0.05) To illustrate continuous changes in the ME and Non-ME condition. The time of occurrence of the velocity peak did not components of the JDV projection, the averages ⫾ SD across differ between the 0-K and Low-K conditions (P ⬎ 0.15). subjects are plotted in Fig. 5 for each target condition and There was no interaction between target type and perturbation performance variable (i.e., 3D pointer-tip position and 3D hand strength, although it approached significance (P ⬍ 0.06), orientation). Of note, the component of the JDV lying in the probably because of a greater difference between the 0-K and nullspace (ME) was always somewhat larger than the compo- Low-K conditions when reaching to the cylindrical target nent lying in the range space (Non-ME), particularly for the compared with the sphere. spherical target, and this difference became larger as the reach Target Error progressed beyond 30 – 40%. This was true independent of target type (sphere or cylinder) or performance variable (3D The MANOVA revealed that the CE of targeting (Table 2) position vs. orientation). The continuous plots suggest that depended on the stiffness condition (Wilks’ ␭ ⫽ 0.152, F6,24 ⫽ although the Non-ME component also increased with exten- 6.26, P ⬍ 0.05) for both the x-coordinate (F1,7 ⫽ 13.740, P ⬍ sion of the elastic band, the ME component increased by a 0.01) and the y-coordinate (F1,7 ⫽ 11.933, P ⬍ 0.005). Post greater amount. hoc tests revealed that CE in the x-dimension was significantly The main effect of the projection component (ME ⬎ Non- greater for the 0-K compared with either the Low-K (P ⬍ 0.05) ME) was significant no matter what phase of the reach was or High-K (P ⬍ 0.005) condition, and for the 0-K compared examined (all phases had P ⬍ 0.05). None of the three-way or with the High-K (P ⬍ 0.005) condition. Analysis of the the four-way interactions was found to be consistently signif- y-dimension revealed that CE for the High-K condition was icant across phases of the reach. The most consistent effects significantly larger and more negative compared with both the across phases were observed for the performance variable by 0-K (P ⬍ 0.005) and Low-K (P ⬍ 0.01) conditions, indicating projection component (Fig. 6) and stiffness by projection that there was more undershoot of the target when the arm was component (Fig. 7) interactions. J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org 1430 MULTIJOINT MOTOR EQUIVALENCE The interaction of the performance variable and the projec- quantified by computing for each subject the slope of change tion component (Fig. 6) was nonsignificant during the early between the two stiffness conditions (Low-K ⫽ 4.9 N/m; portion of the reach except for the second phase. After 40% of High-K ⫽ 12.5 N/m) for both ME and Non-ME components. the reach (⬃320 ms based on an average MT of ⬃800 ms), the The slopes were then compared by repeated-measures differences in the projection component were dependent on the ANOVA (see METHODS). The slope (m) for the ME component performance variable from 41% to 80% of the reach trajectory, was always larger than the slope for the Non-ME component and this interaction was close to significant thereafter. The ME for all phases of the reach trajectory (Table 3). component of the joint difference projection was approxi- mately equal for 3D pointer-tip path and 3D hand orientation. UCM Variance Analysis However, as illustrated in Fig. 6, the Non-ME component was The analysis of variance components found no consistent larger for 3D pointer-tip path, indicating that the difference in main effects of target type, stiffness, performance variable, or joint configurations between the nonperturbed and perturbed interactions of these factors with the variance component conditions led to a greater deviation of the 3D pointer-tip path across phases of the reach. The only consistent effect was that from nonperturbed reaches than was the case for 3D hand VUCM was larger than VORT for all phases of reaching, (all P ⬍ orientation, regardless of the target type. 0.05). Figure 8 presents these results, collapsed across target The interaction of stiffness and projection component (Fig. type, performance variable, and stiffness condition (0-K, 7) was nonsignificant through the first 40% of the reach. Low-K, and High-K). Throughout the remainder of the reach, stiffness or perturba- tion strength significantly affected the projection component, as indicated in Fig. 7. The stronger perturbation caused by the DISCUSSION stiffer band led to an increase in both the ME and Non-ME The present study investigated the extent to which motor components compared with the low-stiffness condition, but the equivalence is used to produce relatively stable values of Downloaded from on February 28, 2015 ME component increased more, as suggested by the significant variables most directly related to performance success in the stiffness by component interaction. This difference was further face of a perturbation of reaching. If a larger component of the Fig. 4. Time series (⫾SD) of the hand’s orientation to coordinates of the cylindrical target (pitch, roll, and yaw) for reaching to both the spherical and cylindrical targets for a subject showing smaller changes in orientation (A) and a subject showing larger changes in orientation (B). J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org MULTIJOINT MOTOR EQUIVALENCE 1431 Fig. 4—Continued Downloaded from on February 28, 2015 difference in the joint configuration between perturbed and Results of the present study supported most of our hypoth- nonperturbed trials had no effect on the pointer-tip path and/or eses. Although the elbow perturbation led to significant differ- hand orientation, variables most related to success of the ences in the anterior-posterior terminal pointer-tip location pointing task, then this would provide stronger evidence for compared with nonperturbed reaches, the differences were motor equivalence than has been provided in previous studies. relatively small, ⬃6 mm between the 0-K and High-K condi- This is a statistical question that required an appropriate tions. Perfect compensation for the perturbing force of the band method, for which we used a variation of the UCM method of is probably unrealistic given the nature of the task. Indeed, the analysis. The method was first introduced earlier in a study of ME component of the JDV, related to both the pointer-tip’s postural stability in response to support surface perturbations path and the hand’s orientation, was found to be significantly (Scholz et al. 2007). greater than the non-ME component throughout the reach. Table 1. Movement time, peak velocity, and time of peak velocity MT Peak Velocity Target Stiffness Mean, s STDEV, s Mean, m/s % of Reach Sphere 0-K 0.732 ⫾ 0.08 0.088 ⫾ 0.04 1.48 ⫾ 0.11 40.43 ⫾ 1.94 Low-K 0.749 ⫾ 0.10 0.080 ⫾ 0.01 1.49 ⫾ 0.11 40.08 ⫾ 1.70 High-K 0.774 ⫾ 0.10 0.085 ⫾ 0.03 1.43 ⫾ 0.09 36.56 ⫾ 1.68 Cylinder 0-K 0.788 ⫾ 0.10 0.082 ⫾ 0.02 1.46 ⫾ 0.10 36.61 ⫾ 1.43 Low-K 0.821 ⫾ 0.11 0.084 ⫾ 0.02 1.44 ⫾ 0.09 35.10 ⫾ 1.26 High-K 0.824 ⫾ 0.11 0.089 ⫾ 0.02 1.47 ⫾ 0.11 34.54 ⫾ 1.32 Averages ⫾ SE across subjects of movement time (MT) and its standard deviation (STDEV) and peak velocity and the percentage of the reach at which the peak of velocity occurred are presented. 0-K, Low-K, and High-K refer to no elastic band, low-stiffness band, and high-stiffness band crossing the elbow joint. J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org 1432 MULTIJOINT MOTOR EQUIVALENCE Table 2. Targeting error Stiffness x-Coordinate y-Coordinate z-Coordinate CE 0-K 0.0043 ⫾ 0.0020 ⫺0.0104 ⫾ 0.0032 ⫺0.0008 ⫾ 0.0014 Low-K 0.0022 ⫾ 0.0021 ⫺0.0130 ⫾ 0.0034 ⫺0.0020 ⫾ 0.0016 High-K 0.0002 ⫾ 0.0020 ⫺0.0160 ⫾ 0.0037 ⫺0.0022 ⫾ 0.0016 VE 0-K 0.0055 ⫾ 0.0016 0.0064 ⫾ 0.0018 0.0040 ⫾ 0.0005 Low-K 0.0062 ⫾ 0.0019 0.0068 ⫾ 0.0024 0.0062 ⫾ 0.0026 High-K 0.0044 ⫾ 0.0002 0.0051 ⫾ 0.0006 0.0043 ⫾ 0.0005 Averages ⫾ SE across subjects of targeting error (meters) for each target coordinate are presented. Data are also averaged across target type due to a nonsignificant effect of target type. CE, constant error; VE, variable error. 0-K, Low-K, and High-K refer to no elastic band, low-stiffness band, and high-stiffness band crossing the elbow joint. Quantification of the joint configuration differences between to either the pointer-tip path or the hand orientation. For the perturbed and nonperturbed conditions revealed that most of spherical target, the projection components (i.e., ME vs. Non- that difference did not contribute to differences in the pointer- ME) were not that different when computed relative to pointer- tip path or the hand orientation. Moreover, as predicted, the tip path versus hand orientation (Fig. 5, left). If anything, the magnitude of motor equivalence depended on the strength of Non-ME component related to the stabilization of hand orien- the perturbation, but only after ⬃40% of the reach trajectory, tation was greater early in the reach. For reaching to the at approximately the time that elbow joint motion was affected cylindrical target, for which the pointer had to be oriented to by the perturbation (Fig. 2). The strongest perturbation insert it properly, the perturbation had a substantially larger (High-K condition) resulted in a larger ME component than the effect on control of 3D position (higher Non-ME component) weaker perturbation (Low-K), while the perturbation magni- than for control of 3D orientation. Motor equivalence related to Downloaded from on February 28, 2015 tude had a weaker effect on the Non-ME component of the hand orientation was always larger than that for pointer-tip JDV. This result is consistent with motor equivalence results path regardless of the target type, a somewhat unexpected computed at the termination of pointing in a recent report of the finding. Note that the ME and Non-ME variables were quan- effect of reaching at different movement speeds (Scholz et al. tified per DOF in corresponding subspaces, so by itself, the 2011). number of constraints could not affect the proportion of ME Contrary to one of our hypotheses, however, the target type value. The larger Non-ME values computed with respect to the had no affect on the amount of motor equivalence with respect pointer-tip path suggest that in perturbed trials the subjects Fig. 5. Time series (⫾SE) of the motor equivalent (ME, solid lines) and non-motor equivalent (Non-ME, dashed lines) compo- nents of the joint difference vector (JDV). Results are presented for each target (left and right) and in relation to the 2 performance variables (top and bottom). J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org MULTIJOINT MOTOR EQUIVALENCE 1433 Fig. 6. Average (⫾SE) of ME and Non-ME components for each performance variable at each 10% of the reach trajectory; F ratios and P values are based on the 4-way repeated- measures ANOVA performed over each 10% of the reach. The interaction performance vari- able [3-dimensional (3D) position vs. 3D ori- entation] by projection component (i.e., ME vs. Non-ME) was significant for the phases indicated. Downloaded from on February 28, 2015 were less concerned with keeping the end point trajectory although the differences were not huge, amounting at most to consistent compared with keeping the end-effector orientation 4% of the cycle. Despite this delay, most of the change in the consistent. JDV due to the perturbation was motor equivalent and had no The inequality ME ⬎ Non-ME is far from being trivial. effect on the progression of the movement. Indeed, although In the course of the unperturbed movement, the joint config- both the ME and Non-ME components increased with greater uration changed to move the end point from the starting perturbation strength, the ME component’s increase was sig- location to the target. If in the case of the perturbation the nificantly greater than that of the Non-ME component. entire time course of the movement slowed down, then we The direct mechanical effects of the perturbation produced would expect the Non-ME component of JDV to be substan- by the elastic band crossing the elbow joint were not limited to tial. This is because at a given percentage of the movement changing the trajectory of the elbow joint because of the cycle the joint configurations for the 0-K and, for example, the mechanical joint coupling. Its effects on joint motion were High-K conditions would differ in large part because of dif- complex, being both joint configuration and velocity dependent ferent pointer-tip positions. Although there was no difference (see Zatsiorsky 2002). Even during the first time interval, that in peak velocity among the conditions (Table 1), the timing of is, from the time of movement initiation to 10% of MT (⬃80 the peak was affected by the perturbation, occurring earlier in ms), the deviation of the joint configuration (JDV) from its the perturbed conditions than in the 0-K condition. This effect unperturbed trajectory was significantly larger within the ME can also be seen in the representative velocity plots in Fig. 3, subspace compared with the Non-ME subspace. Since it was Fig. 7. Average (⫾SE) for ME and Non-ME components for each stiffness condition for each 10% of the reach trajectory. F ratios and P values are based on the 4-way repeated-measures ANOVA performed over each 10% of the reach. The interaction stiffness (Low-K vs. High-K) by projection component (i.e., ME vs. Non-ME) was significant for the phases indicated. J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org 1434 MULTIJOINT MOTOR EQUIVALENCE Table 3. Slope of change in ME and Non-ME components % of Reach mME mNon-ME Statistical Test 41–50% 0.00258 ⫾ 0.00045 0.00134 ⫾ 0.00027 F1,7 ⫽ 12.470, P ⫽ 0.010 51–60% 0.00370 ⫾ 0.00049 0.00147 ⫾ 0.00044 F1,7 ⫽ 39.743, P ⬍ 0.0001 61–70% 0.00467 ⫾ 0.00063 0.00183 ⫾ 0.00056 F1,7 ⫽ 53.227, P ⬍ 0.0001 71–80% 0.00527 ⫾ 0.00077 0.00211 ⫾ 0.00064 F1,7 ⫽ 40.226, P ⬍ 0.0001 81–90% 0.00560 ⫾ 0.00086 0.00223 ⫾ 0.00070 F1,7 ⫽ 32.417, P ⬍ 0.001 91–100% 0.00570 ⫾ 0.00089 0.00226 ⫾ 0.00074 F1,7 ⫽ 29.352, P ⬍ 0.001 Mean ⫾ SE slopes (m) of the change of motor equivalent (ME) and non-motor equivalent (Non-ME) projection of the joint angle configuration between the Low-K and High-K conditions, based on each 10% of the reach, are presented. The slope for ME was always significantly larger. impossible for the subject to predict when a perturbation would face of perturbations. Martin et al.’s (2009) model contains emerge, this time is too short for any conscious correction of components responsible for planning goal states and for move- the ongoing movement. There are two interpretations for this ment initiation and timing, formulated at the level of the finding. First, the movement could be associated with a time performance variables (e.g., hand position and/or orientation). profile of muscle activations that favored certain responses to The model also contains biomechanical dynamics of the effec- unexpected mechanical perturbations organized to keep the end tor system as well as an associated muscle-joint model that point trajectory relatively immune to the perturbation. These takes into account the impedance properties of muscles based are similar to “preflexes,” a term introduced by Dickinson and on a simplified version of Gribble et al. (1998). According to colleagues (2000) to designate peripheral responses of the the Martin et al. (2009) model, the descending motor command muscles and tendons tuned in advance by the CNS. Second, to the muscle-joint system is a set of equilibrium joint angles Downloaded from on February 28, 2015 there could be nonlocal, reflexlike corrections at a latency of and velocity vectors. The neuronal dynamics of the model under 70 ms sometimes referred to as preprogrammed reac- generates the time courses of these equilibrium joint angles tions, triggered reactions, or long-loop reflexes (cf. Chan et al. based on an input signal that specifies the time course of the 1979; Gielen et al. 1988). This latter explanation sounds less plausible because the first time interval was only 80 ms long, performance variable. In other words, this dynamics achieves which seems too short to incorporate mechanically meaningful the transformation from task space into joint space. It does so corrections in response to an unexpected smooth perturbation by coupling the equilibrium joint velocities such that joint produced by the elastic band. velocity vectors that leave the performance variable unchanged Results of the motor equivalence analysis suggest two dif- are decoupled from joint velocity vectors that change the ferent effects of “feedback” from mechanoreceptors. Tradition- performance variable. This accounts for many of the signature ally, feedback would operate to stabilize the elbow joint features of movement tasks that have been reported previously against the band’s perturbation, given that the perturbation based on UCM analyses (Martin et al. 2009). An alternative most directly affected elbow movement. However, the results perspective, however, is that the descending commands do not of the pointer-tip path and hand orientation indicate stabiliza- specify joint angles or velocity vectors per se, but act to tion of these more global performance variables, consistent predetermine through threshold position control the spatial with idea that cross-limb reflex pathways are crucially involved frame of reference in which the neuromuscular system is in producing interlimb synergies (Ross and Nichols 2009). In constrained to work (Raptis et al. 2010; see below). Neverthe- addition, an additional type of “feedback,” referred to as less, the back-coupling in the Martin et al. (2009) model affects “back-coupling,” that operates differently is likely. Back-cou- primarily the subspace of joint space where goal-equivalent pling has been proposed in a model of reaching by Martin et al. joint configurations lie (i.e., the UCM) and explains motor (2009) as a mechanism that adjusts the referent trajectory of the equivalence: Deviations of the real from the equilibrium joint end point to ensure equifinality of the actual trajectory in the trajectory lead to an update of the equilibrium joint trajectory Fig. 8. Mean (⫾SE) of each component of joint configuration variance (VUCM and VORT) computed at each phase of the reach and averaged across target type, performance variable, and stiffness. F ratios and P values are based on the 4-way repeated- measures ANOVA performed over each 10% of the reach. Only the main effect of variance component (VUCM vs. VORT) was significant for the phases indicated. DOF, degree of freedom. J Neurophysiol • VOL 106 • SEPTEMBER 2011 • www.jn.org MULTIJOINT MOTOR EQUIVALENCE 1435 within the UCM. The result is the generation of a new, of the pointer-tip and hand orientation, from their average motor-equivalent plan. trajectories observed in unperturbed trials. These reasoning and This last point also suggests possible links of the data to the conclusions have to be viewed as tentative since no explicit idea of control with referent configurations (reviewed in Feld- model of the arm reaction to different bands was studied. man et al. 2007; Feldman and Levin 2009). Within this idea, A final point of interest is the results of the UCM variance the central controller is presumed to set a time profile of a analysis, performed here across repetitions of each condition, referent configuration of the body defined as a configuration at i.e., within each combination of target type and stiffness which all the muscles are at their threshold for activation. Thus condition (0-K, Low-K, and High-K), performed for each the reaching tasks investigated here may have been guided performance variable (Fig. 8). Unlike the motor equivalence primarily by changes in the referent position and referent analysis, this analysis yielded no effects of, or interactions orientation of the hand with respect to the environment, among, stiffness conditions or performance variables. In all whereas individual DOFs were involved in the task or not cases, VUCM was substantially and significantly higher than depending on their capacity to minimize the difference be- VORT, the component of joint configuration variance that tween the actual hand position and orientation and their refer- would induce variability of the 3D pointer-tip position or hand ent prototypes specified by the brain. Referent configurations orientation. This result is consistent with the results of many may be unattainable because of external forces and anatomic previous studies (Freitas and Scholz 2009; Freitas et al. 2010; constraints, which may explain why reaches were somewhat Latash et al. 2002, 2003; Reisman and Scholz 2006; Reisman short of the target when working against the high band stiff- et al. 2002; Scholz and Schoner 1999; Scholz et al. 2000; ness; in such cases, the body is predicted to come to equilib- Tseng et al. 2002; Yang et al. 2007), further supporting the rium with nonzero levels of muscle activation. UCM control hypothesis (Latash et al. 2007; Martin et al. Within a recent development of this general idea, neural 2009; Schöner et al. 2008). Thus, despite differences among control of natural movements is organized into a hierarchy the conditions in the strength of perturbation, within a condi- Downloaded from on February 28, 2015 (Latash 2010a, 2010 b); at each level of the hierarchy, neural tion a similar variance structure emerged. The same mecha- signals can be adequately described as a set of referent values nisms may be at play when investigating deviations of the joint for salient variables. During a reaching movement, control at configuration induced by different levels of perturbation, but the highest level defines referent values for such variables as the response is much stronger. This is probably due to the fact position and orientation of the end-effector. Movement is that feedback pathways are more strongly activated by external driven by a disparity between actual and referent values of perturbations. those variables. At lower levels, the relatively low-dimensional input is transformed into a higher-dimensional set of referent Conclusions values for appropriate variables formulated at a joint or muscle This study provides additional quantitative evidence for level. This mapping is organized in a synergic way: Families of motor equivalence, here in response to mechanical perturba- referent configurations at a lower level may be facilitated as tions during reaching. Evidence for motor equivalence was long as they correspond to the required referent configuration present throughout the entire reach, not only at or near move- at the higher level. ment termination. Moreover, the stronger the perturbation was, In our experiment, salient variables were 3D pointer-tip path the stronger was the evidence for motor equivalence once the and hand orientation (for the cylindrical target). Referent bands were clearly engaged. The results are consistent with a values for those variables mapped onto a redundant set of recent model of neural control in which the space of the motor referent values (trajectories) in the joint space. This mapping elements is decoupled into motor equivalent and non-motor was organized in a synergic way as demonstrated by the fact equivalent subspaces, allowing for flexible patterns of coordi- that most variance in the joint space was compatible with the nation while resisting deviations to the values of variables most same pointer-tip or hand position (orientation). This organiza- related to task success. The results may also be compatible tion naturally channels effects of perturbations, internal or with the hypothesis of hierarchical control with referent con- external, into the subspace of joint configurations compatible figurations at each level, and synergic mappings between with the end point trajectory [similarly to results of a recent control levels of the hierarchy. study by Gorniak et al. (2009)]. Note that the elastic bands generated position-dependent forces. As a result, end point coordinates in the terminal GRANTS position would be expected to differ between the two stiffness Support for this work was provided by National Institute of Neurological conditions if no correction of the referent configuration at the Disorders and Stroke Grants R01 NS-35032, awarded to M. L. Latash, and R01 upper level of the hierarchy were implemented. Table 2 does NS-050880, awarded to J. P. 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