Motor Control and Motor Redundancy in the Upper ... - Semantic Scholar
Motor Control and Motor Redundancy in the Upper Extremity: Implications for Neurorehabilitation Boris I. Prilutsky,1 PhD, David Ashley, MS,1 Leslie VanHiel, MSPT,2 Linda Harley, MS,1 Jason S. Tidwell,2 and Deborah Backus, PT, PhD2,3 School of Applied Physiology, Georgia Institute of Technology, Atlanta, Georgia; 2Crawford Research Institute, Shepherd Center, Atlanta, Georgia; 3Department of Rehabilitation Medicine, Emory University School of Medicine, Atlanta, Georgia
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A fundamental feature of musculoskeletal design of the upper extremity is kinematic and muscle redundancy that has profound consequences for arm control in healthy people and individuals with spinal cord injury (SCI) at the cervical level (tetraplegia). After reviewing basic facts related to arm redundancy and associated complexities of arm motor control, our experimental data demonstrate that individuals with motor complete (n = 5) or incomplete (n = 1) SCI at C5-C7 can learn to perform a complex multijoint task of tracking target forces by the arm. We conclude that individuals with SCI can benefit from musculoskeletal redundancy and alternative control strategies to accomplish complex multi-joint tasks. Key words: force tracking, joint moments, muscle activity, musculoskeletal redundancy, spinal cord injury at cervical level, tetraplegia, upper extremity
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etraining upper extremity function in individuals with tetraplegia poses a unique problem. Depending on the extent of the injury, or how complete the SCI is, an individual may experience varying degrees of motor control deficits. In a complete injury, the essential problem is the inability to activate the muscles in the arm and hand adequately to elicit movement; there is also a lack of meaningful somatosensory feedback to help guide the movement. In sensory and motor incomplete injuries, the motor control problem becomes more complex. Muscles may be innervated and even demonstrate adequate strength, but there is often a lack of control of these muscles. Common motor control problems in the upper extremity after tetraplegia include abnormal reflexes and tonal influences, spasticity, co-contraction, and ineffective timing throughout movements. Typically, therapies for the upper extremity in individuals with tetraplegia focus on restoring strength and not necessarily on retraining the control of the muscles. This approach does not address the needs of approximately onethird of the population of individuals with incomplete tetraplegia.1 Information about how an individual with tetraplegia performs upper extremity motor tasks can provide important insight into how the musculoskeletal and neural control systems interact to control the arm and hand. Such information could then be used to apply existing interventions and technologies, or develop new ones, to facilitate greater function and control of the arm and hand in individuals with tetraplegia.
Kinematic Redundancy The human body has more kinematic degrees of freedom (DoF) than are strictly necessary to perform a movement or exert an external force. As a result, the hand can be positioned in a specific location of a horizontal plane with many different combinations of angles at the shoulder, elbow, and wrist joints (Figure 1A). This is because the arm in the horizontal plane has more kinematic degrees of freedom (1 flexion-extension DoF per joint, that is, 3 DoF in total) than the 2 dimensions of the horizontal plane. In more realistic everyday situations, our arm operating in a 3-dimensional space has access to 7 DoF (3 in shoulder: flexion-extension, adduction-abduction, internal-external rotations; 2 in elbow: flexion-extension, pronation-supination; and 2 in wrist: flexion-extension, adduction-abduction). A great variety of arm configurations available to move the arm in a required place (see example in Figure 1A) beg a question: How and why does the central nervous system select a specific combination of joint angles to reach an object or target or exert a force in a specified direction? This question is the essence of the so-called degrees-of-freedom problem formulated by Bernstein.2
Top Spinal Cord Inj Rehabil 2011;17(1):7–15 2011;17(1):7–7 © 2011 Thomas Land Publishers, Inc. www.thomasland.com doi: 10.1310/sci1701-7
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Figure 1. Schematic of an arm model, experimental setup, and examples of recordings. (A) A 2-dimensional diagram of a 3-joint arm model with 6 muscles: 1, anterior deltoid (AND); 2, posterior deltoid (POD); 3, brachioradialis (BR); 4, triceps brachialis short head (TS); 5, biceps brachii (BI); 6, triceps brachialis long head (TL); 7, flexor carpi radialis (FCR): and 8, extensor carpi radialis (ECR). The open and shaded arm configurations demonstrate how the same position of the arm endpoint can be achieved with different joint angles. The arm endpoint is located in the center of a circle that corresponds to the trajectory of a moving force target; the target is indicated by the small circle (moving target). The cross indicates the cursor position, which is controlled by the participant pushing on the instrumented handle (see B and C). Positions of the moving target and the cursor are determined by the target force direction and cursor force direction angles, respectively. The instrumented handle in the center of the target trajectory records horizontal forces (Fx, Fy) and a torque (Tz) with respect to the (long) vertical axis of the handle (see B and C). (B) Experimental setup. The participant sits in front of a computer screen with the arm suspended and holds an instrumented handle. The participant is instructed to track a moving target on the screen with a cursor that is controlled by application of horizontal force on the handle. (C) Instrumented handle that permits recordings of the 2 components of the force vector in the horizontal plane (Fx, Fy) and the torque around the vertical axis of the handle (Tz) (see A). (D) Examples of recorded forces and EMG exerted by a participant from the control group during 5 consecutive cycles of force tracking task. The first 3 plots are the forces and torque (Fx, Fy , and Tz) exerted on the handle; thin smooth lines indicate the target force; the thick lines indicate the force and torque exerted by the participant. The next 3 plots are the joint moments at the shoulder (Ms), elbow (Me), and wrist (Mw) calculated from the recorded forces and torque and arm configuration (see Data analysis); positive values correspond to flexion moment. The next 4 plots show rectified (dark lines) and low-pass filtered (white lines) EMG of antagonist muscles, AND – POD, BR – TS, BI – TL, FCR – ECR. The bottom plot shows target force (thin line) and cursor force (thick line) directions.
Although the complete answer to this question is presently not available, it has been recognized that despite the kinematic redundancy and, as a consequence, availability of many motor strategies to perform skilled movements, healthy people utilize very limited motor patterns during arm reaching 3,4 and prehension 5 tasks. The limited kinematic patterns observed in arm reaching are called kinematic invariant characteristics. They include (1) straight-line hand trajectory; (2) bellshaped hand velocity profile; (3) power law, describing the relation between hand velocity and curvature of hand trajectory; and (4) Fitts’s law, describing the trade-off between speed and accuracy during reaching movements. The first invariant characteristic, the straight-line hand trajectory, can be observed during point-to-point reaching arm movements. In these tasks, the hand tends to move along a nearly straight line connecting initial and final hand locations in space. Joint angles during reaching to different points in space are variable and have complex non-linear patterns.3 Bell-shaped hand velocity profile is a robust kinematic feature of reaching movements according to which the hand velocity changes smoothly from zero at the initial hand position to the peak velocity in middle of reaching and back to zero velocity at the target hand position. The symmetry of this bell-shaped velocity profile can be distorted by unanticipated external perturbations of the arm or extreme requirements for accuracy. Practicing arm reaching movements in a novel force-field environment leads to restoring symmetry and smoothness of the hand velocity profile.6 When
we perform arm movements along curved trajectories to avoid obstacles or during drawing or writing, the arm endpoint velocity is coupled with curvature of endpoint trajectory.7,8 This coupling (power law) is expressed by the following empirical equation: v = k · C1/3, where v is the limb endpoint tangential velocity, r is the radius of curvature C of endpoint trajectory, and k is a coefficient. Finally, Fitts’s law describes the relation between task accuracy requirements or difficulty (ie, target width along movement trajectory, W, and the distance to the target, D) on the one hand and movement time (MT) on the other hand: MT = a + b · log2 (2D/W), where a and b are empirical constants. According to Fitts’s law, the more difficult the pointing task is (the smaller and further away the target), the longer it takes to reach it. Although this empirical relation can be explained based on the information theory of physical communication systems,9 it is not immediately clear how this kinematic law is related to the other kinematic invariant features of arm skilled movements. It turns out that all of the kinematic invariants described above can be predicted and explained by an assumption that during arm reaching movements, people select such kinematic patterns that minimize the arm endpoint variance in the final position.10 The main source of this variability was proposed to be signal-dependent noise of motor commands to muscles. Thus, reducing the overall magnitude of motor commands results in smaller variability of arm endpoint in the final arm position as well as in the 4 kinematic invariant characteristics.10
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Muscle Redundancy Another important design feature of the upper extremity is that the arm has more muscles or muscle parts (which are called muscle compartments or actons11) than kinematic DoF (for review, see ref. 12). According to estimates of Morecki et al,11 there are 66 muscle compartments (actons) in the human arm that serve 22 joints and 30 DoF. Therefore, on average, 3 actons serve one joint (=66/22) and 2.2 actons serve 1 DoF (=66/30). Each acton can produce several moments of force with respect to anatomical joint axes (for reviews on muscle moment arms, see refs. 13 and 14). The long head of the biceps brachii, for instance, can produce 5 moments of force that tend to (1) flex, (2) abduct, and (3) internally rotate the upper arm at the shoulder as well as (4) flex and (5) supinate the forearm at the elbow. The total number of joint moments that actons can produce (or the number of functions of actons) in the human arm is 264. Thus in the human arm, the number of acton functions per joint and DoF is 12 (= 264/22) and 8.8 (= 264/30), respectively. One important consequence of the multiple functions of actons and muscles at the joints is that when a muscle is activated to produce a desired (primary) moment with respect to a DoF, it also typically generates additional undesired (secondary) moments of force with respect to other DoF, which must be counterbalanced by other actons/muscles. The latter actons/muscles also develop undesired (tertiary) moments of force with respect to other DoF, and so forth. Thus, the task of activating muscles to produce desired joint moments and movements seems overwhelmingly complex. Despite the muscle redundancy, muscle activity patterns seem rather stereotyped in skilled arm tasks and can be characterized by several invariant characteristics: (1) synergistic muscle activation or broad tuning of muscle activity around preferred movement direction, that is, the direction in which muscle demonstrates its maximum electromyographic (EMG) activity15,16; (2) reciprocal muscle activation, that is, relatively low coactivation of anatomical antagonists17; and (3) specific activation of 2-joint muscles, that is, EMG activity of a 2-joint muscle (or a muscle that controls 2 DoF) is greater when the muscle can contribute to the motion at both joints as an anatomical agonist (eg, biceps brachii, elbow flexor and supinator), is typically more active during movements that require simultaneous elbow flexion and supination.15,18 The assumption discussed previously that during skilled arm movements the nervous system is minimizing the signal-dependent noise of motor commands (or a non-linear function of muscle force
magnitude) leads to reasonable predictions of muscle EMG patterns.19,20 Implications of Musculoskeletal Redundancy for Rehabilitation The considerations about the complexities of arm control in intact upper extremities suggest that individuals with SCI at C5-C7 levels, leading to loss or altered functions of several muscle groups, would experience overwhelming difficulties in performing accurate multi-joint tasks by the affected arm. On the other hand, there is the possibility that kinematic and muscle redundancy of the upper extremity can offer the individual with tetraplegia alternative motor strategies of task performance that can be discovered during repeated attempts to execute the task. To test this possibility experimentally, we asked a group of 6 participants with complete and incomplete C5-C7 SCI (Table 1) to track a moving target on a computer screen by exerting external force by the arm. A group of age-matched uninjured right-handed participants (n = 7) served as control (Table 1). All participants gave informed consent for participating in the study. The experimental protocol was approved by the Institutional Review Boards of Shepherd Center and Georgia Tech. Tracking task and data collection Each participant was instructed to sit comfortably in a wheelchair (SCI group) or a chair (control group) in front of a computer screen. The participant’s right arm was positioned in the horizontal plane and suspended from above using a long rubber band (Figure 1B). The hands of participants with SCI were attached to a vertically fixed handle (Figure 1C) by a grasping cuff (Sammons Preston, Bolingbrook, Illinois). Uninjured participants did not use the grasping cuff. The handle was instrumented with a 6-component force transducer (ATI Mini; Assurance Technologies, Inc., Bartlett, Illinois). Participants’ arm angles were adjusted to be in the range of 20 o to 40o, 40 o to 60o, and 25 o to 45o for shoulder (q1), elbow (q2), and wrist (q3) joints, respectively (Figure 1A). Joint angles were measured by a mechanical goniometer. The instrumented handle recorded the 2 force components in the horizontal plane (Fx, Fy) and a torque (Tz) with respect to the handle vertical axis (Figure 1A) at sampling frequency of 1 kHz. These signals were fed into a computer and used to control the position of a cursor on the computer screen (Figures 1 A and B). The participant was instructed to track a moving target on screen (5-mm circle)
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Table 1. Participant information Participants
Upper arm length, cm
Forearm length, cm
M M F M M M
22.3 27.3 26.0 25.7 28.4 30.0 26.6±2.6
25.2 25.1 22.9 24.2 29.1 27.8 25.7±2.3
C5-C6, incomplete C7, complete C7, complete C6-C7, complete C6-C7, complete C5-C6, complete
5 6 48 22 7 20 18±17
M M M M M F F
33.5 26.0 29.3 27.0 26.0 27.5 27.0 27.9±2.3
28.5 25.5 27.4 26.0 25.5 22.0 25.5 25.8±2.0
– – – – – – –
– – – – – – –
Age, years
Gender
SCI group 1 2 3 4 5 6 Mean ±SD
35 38 22 29 23 30 30±6
Control group 1 2 3 4 5 6 7 Mean ±SD
26 32 23 20 20 23 23 27±9
with the cursor (5-mm cross; Figure 1A) as closely as possible by exerting force on the handle and trying to maintain the same arm position. The target was moving counterclockwise along a circle of 11 cm in diameter (or 40 N in force scale) with a frequency of 0.2 Hz. Each participant performed over 300 tracking cycles with 1-minute rest periods after each 8 cycles. Surface EMG was recorded synchronously with the forces and torque at a sampling rate of 1 kHz (Konigsberg Instruments Inc, Pasadena, California) from 8 arm muscles [Figure 1B: anterior deltoid (AND-1), posterior deltoid (POD2), brachioradialis (BR-3), short head of triceps (TS-4), long head of biceps (BI-5), long head of triceps (TL6), flexor carpi radialis (FCR-7), and extensor carpi radialis (ECR-8)]. Before and 1 minute after the force tracking experiment, the participant was asked to exert a maximum force on the handle in 8 directions in the horizontal plane (from 0o to 360o every 45o; Figure 1A) to measure maximum voluntary EMG activity. Data analysis After the experiments, all recorded raw EMGs were rectified and low-pass filtered (Butterworth 4th order, zero lag filter, cutoff frequency 15 Hz) to obtain linear envelopes (Figure 1D). The envelopes were normalized to the maximum envelope values found in maximum force production tests. Joint moments (ie, the resultant moments produced by all muscles around each joint,
Injury
Time since injury, mo
assuming negligibly small contribution of passive tissues at the joint) were computed as M = JTF, where F = [Fx, Fy, Tz]T, vector of recorded handle forces and torque; M = [Ms, Me, Mw]T, vector of shoulder, elbow, and wrist moments; and JT, the transposed Jacobian matrix (for details see ref. 21). Tracking performance, exerted joint moments, and EMG were analyzed using the following linear and circular (directional) measures: (1) tracking error, normalized distance between target and cursor positions at each degree of target force direction averaged over a tracking cycle (Figures 1A and 2); (2) time delay between target force direction and cursor force direction at each degree of target force direction (Figures 1A and 2) averaged over each cycle; (3) normalized EMG envelope peak in each tracking cycle (Figure 1D); (4) peak of joint moment in each tracking cycle (Figure 1D); (5) EMG preferred direction (in degrees) for each muscle, that is, the resultant of EMG vectors represented by the EMG magnitude and direction (for each degree from 0o to 360o); (6) EMG spatial focus of muscle preferred direction, that is, measure of variance of the EMG preferred direction22; (7) joint moment preferred direction (in degrees) for each joint; and (8) joint moment spatial focus. Statistical methods of analysis included circular and linear correlation and regression, Rayleigh test (directedness), chi-square (comparison of circular distributions), and t test. Significance level was set at .05.
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Figure 2. Normalized tracking error and time delay between the target and cursor force directions (see Figures 1A and 1D) as functions of tracking force cycle. Each dot corresponds to the mean value averaged over each cycle and across all participants in the group; the continuous line is an exponential regression line. (A) The normalized errors of participants with SCI. (B) The normalized errors of control participants. (C) The time delay of participants with SCI. (D) The time delay of control participants.
Results and Discussion The group with SCI was able to perform the multijoint tracking task with reasonable performance. Specifically, the normalized tracking error was ~40% initially and decreased to 20% after 300 to 400 tracking cycles (Figure 2A). As predicted, the control group performed significantly better. The initial and final normalized mean errors were 23% and 12%, respectively (Figure 2B; P < .05). Both groups demonstrated a strong and significant correlation between the tracking error and the delay (r > 0.9, P < .05; Figures 2C and D), suggesting that the performance improvement was achieved in both groups by decreasing the delay between the target and cursor force directions (ie, by increasing the contribution of feed-forward cursor control). Both groups of participants exhibited similar patterns of joint moments (Figure 3). Flexor and extensor joint moments in both groups had statistically significant preferred directions (P < .05; Figure 3), although the shoulder and elbow preferred directions in the group with SCI differed by 30o to 45o from the control group (P < .05). Moment peaks in each joint were significantly smaller in the group with SCI compared to the control group (P < .05; Figure 3), suggesting weakness in these
muscles to generate force. Normalized EMG peaks of BR, BI, and ECR were higher in participants with SCI compared to control (P < .05; Figure 4), indicating a significantly higher level of effort needed in these muscles by the participants with SCI to execute the task. However, the more proximal muscles (AND and POD) showed equal or less effort when compared to the controls. Thus, the included muscle groups controlling the elbow and wrist could contribute to an alternate motor strategy through changes in direction and increased magnitude of effort (assuming some changes in arm configuration) to substitute for the weaker triceps and wrist/finger flexors. On the other hand, the included proximal shoulder muscles contributed to this alternate strategy mostly through changes in direction of effort. The tracking task required co-activation of antagonists, which was evident from broad EMG tuning curves (example in Figure 1D) around the EMG preferred directions in both groups. In the muscles of the SCI group with reliable EMG recordings (AND, POD, BR, BI, and ECR), EMG peaks and spatial focus increased with practice (P < .05), whereas in the control group the EMG peak magnitude decreased (P < .05). Perhaps those in the control group were able to find
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Figure 3. Joint moment magnitude as a function of exerted cursor force direction (from 0o to 360o; see Figure 1A) in polar coordinates. The joint moment magnitude at a given force direction corresponds to the distance from the center of the big circle to the point on the moment line. Lines with small open circles correspond to the mean moments of the SCI group; lines with small open squares, to the control group. The small filled circles and squares indicate preferred directions for joint moments of the SCI and control groups, respectively.
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Figure 4. Normalized EMG activity of 5 arm muscles as a function of exerted cursor force direction (from 0o to 360o; see Figure 1A) in polar coordinates. The normalized EMG magnitude at a given force direction corresponds to the distance from the center of the big circle to the point on the EMG line. Lines with small open circles correspond to the mean normalized EMG of the SCI group; lines with small open squares, to the control group. The small filled circles and squares indicate preferred directions for EMG of the SCI and control groups, respectively.
a way to use their muscles more efficiently, requiring less effort, while those in the SCI group learned how to better activate their muscles. The obtained results primarily demonstrated that (1) individuals with C5-C7 SCI were able to perform a complex multi-joint force tracking task with weakened or absent elbow extensors and wrist flexors, (2) the participants with SCI improved their performance and increased the EMG activity of functioning muscles with practice, and (3) the participants with SCI demonstrated synergistic activity, a typical invariant feature of muscle activation. This synergistic activity was shown by the broad EMG tuning curves in functioning muscles (coactivation) and signs of a negative correlation between EMG preferred directions of shoulder flexor and extensor muscles (reciprocal activation). The ability of the participants with SCI to perform the difficult force tracking task may have resulted from exploiting
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musculoskeletal redundancy that permitted alternative motor strategies involving additional kinematic DoF and different muscle groups. These findings suggest the potential effectiveness of practicing and discovering alternative movement patterns during rehabilitation for improved upper extremity function and motor control, even in individuals with complete SCI. Detailed arm kinematic and intramuscular activity recordings (for example, see refs. 23 and 24) may be needed in the future to understand the exact mechanisms of executing and controlling multi-joint upper extremity tasks by individuals with C5-C7 SCI. Acknowledgments We thank the participants of this study and acknowledge support of the Shepherd Center and the Center for Human Movement Studies at Georgia Tech.
REFERENCES 1. National Spinal Cord Injury Statistics Center. Annual Report for the Model Spinal Cord Injury Systems. Birmingham, AL: University of Alabama; 2010. 2. Bernstein NA. The Co-ordination and Regulation of Movements. Oxford: Pergamon Press; 1967. 3. Morasso P. Spatial control of arm movements. Exp Brain Res. 1981;42:223-227. 4. Soechting JF, Buneo CA, Herrmann U, Flanders M. Moving effortlessly in three dimensions: does Donders’ law apply to arm movement? J Neurosci. 1995;15:6271-6280. 5. Terekhov AV, Pesin YB, Niu X, Latash ML, Zatsiorsky VM. An analytical approach to the problem of inverse optimization with additive objective functions: an application to human prehension. J Math Biol. 2010;61:423-453. 6. Shadmehr R, Mussa-Ivaldi FA. Adaptive representation of dynamics during learning of a motor task. J Neurosci. 1994;14:3208-3224. 7. Lacquaniti F, Terzuolo C, Viviani P. The law relating the kinematic and figural aspects of drawing movements. Acta Psychol (Amst). 1983;54:115-130. 8. Viviani P, Terzuolo C. Trajectory determines movement dynamics. Neuroscience. 1982;7:431-437. 9. Fitts PM. The information capacity of the human motor system in controlling the amplitude of movement. J Exp Psychol. 1954;47:381-391. 10. Harris CM, Wolpert DM. Signal-dependent noise determines motor planning. Nature. 1998;394:780784. 11. Morecki A, Ekiel J, Fidelus K. Cybernetic Systems of Limb Movements in Man, Animals and Robots. New York: John Wiley & Sons; 1984. 12. Zatsiorsky VM, Prilutsky BI. Biomechanics of Skeletal Muscles. Champaign, IL: Human Kinetics. In Press 13. Dostal WF, Soderberg GL, Andrews JG. Actions of hip muscles. Phys Ther. 1986;66:351-361.
14. Pandy MG. Moment arm of a muscle force. Exerc Sport Sci Rev. 1999;27:79-118. 15. Buchanan TS, Rovai GP, Rymer WZ. Strategies for muscle activation during isometric torque generation at the human elbow. J Neurophysiol. 1989;62:12011212. 16. van Bolhuis BM, Gielen CC. A comparison of models explaining muscle activation patterns for isometric contractions. Biol Cybern. 1999;81:249-261. 17. Darainy M, Ostry DJ. Muscle co-contraction following dynamics learning. Exp Brain Res. 2008;190:153163. 18. Sergio LE, Ostry DJ. Coordination of mono- and biarticular muscles in multi-degree of freedom elbow movements. Exp Brain Res. 1994;97:551-555. 19. Haruno M, Wolpert DM. Optimal control of redundant muscles in step-tracking wrist movements. J Neurophysiol. 2005;94:4244-4255. 20. Prilutsky BI, Zatsiorsky VM. Optimization-based models of muscle coordination. Exerc Sport Sci Rev. 2002;30:32-38. 21. Zatsiorsky VM. Kinetics of Human Motion. Champaign, IL: Human Kinetics; 2002. 22. Batschelet E. Circular Statistics in Biology. London: Academic Press; 1981. 23. Koshland GF, Galloway JC, Farley B. Novel muscle patterns for reaching after cervical spinal cord injury: a case for motor redundancy. Exp Brain Res. 2005;164:133-147. 24. Mulroy SJ, Farrokhi S, Newsam CJ, Perry J. Effects of spinal cord injury level on the activity of shoulder muscles during wheelchair propulsion: an electromyographic study. Arch Phys Med Rehabil. 2004;85:925-934.
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A fundamental feature of musculoskeletal design of the upper extremity is kinematic and muscle redundancy that has profound consequences for arm control in healthy people and individuals with spinal cord injury (SCI) at the cervical level (tetraplegia). After reviewing basic facts related to arm redundancy and associated complexities of arm motor control, our experimental data demonstrate that individuals with motor complete (n = 5) or incomplete (n = 1) SCI at C5-C7 can learn to perform a complex multijoint task of tracking target forces by the arm. We conclude that individuals with SCI can benefit from musculoskeletal redundancy and alternative control strategies to accomplish complex multi-joint tasks. Key words: force tracking, joint moments, muscle activity, musculoskeletal redundancy, spinal cord injury at cervical level, tetraplegia, upper extremity
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etraining upper extremity function in individuals with tetraplegia poses a unique problem. Depending on the extent of the injury, or how complete the SCI is, an individual may experience varying degrees of motor control deficits. In a complete injury, the essential problem is the inability to activate the muscles in the arm and hand adequately to elicit movement; there is also a lack of meaningful somatosensory feedback to help guide the movement. In sensory and motor incomplete injuries, the motor control problem becomes more complex. Muscles may be innervated and even demonstrate adequate strength, but there is often a lack of control of these muscles. Common motor control problems in the upper extremity after tetraplegia include abnormal reflexes and tonal influences, spasticity, co-contraction, and ineffective timing throughout movements. Typically, therapies for the upper extremity in individuals with tetraplegia focus on restoring strength and not necessarily on retraining the control of the muscles. This approach does not address the needs of approximately onethird of the population of individuals with incomplete tetraplegia.1 Information about how an individual with tetraplegia performs upper extremity motor tasks can provide important insight into how the musculoskeletal and neural control systems interact to control the arm and hand. Such information could then be used to apply existing interventions and technologies, or develop new ones, to facilitate greater function and control of the arm and hand in individuals with tetraplegia.
Kinematic Redundancy The human body has more kinematic degrees of freedom (DoF) than are strictly necessary to perform a movement or exert an external force. As a result, the hand can be positioned in a specific location of a horizontal plane with many different combinations of angles at the shoulder, elbow, and wrist joints (Figure 1A). This is because the arm in the horizontal plane has more kinematic degrees of freedom (1 flexion-extension DoF per joint, that is, 3 DoF in total) than the 2 dimensions of the horizontal plane. In more realistic everyday situations, our arm operating in a 3-dimensional space has access to 7 DoF (3 in shoulder: flexion-extension, adduction-abduction, internal-external rotations; 2 in elbow: flexion-extension, pronation-supination; and 2 in wrist: flexion-extension, adduction-abduction). A great variety of arm configurations available to move the arm in a required place (see example in Figure 1A) beg a question: How and why does the central nervous system select a specific combination of joint angles to reach an object or target or exert a force in a specified direction? This question is the essence of the so-called degrees-of-freedom problem formulated by Bernstein.2
Top Spinal Cord Inj Rehabil 2011;17(1):7–15 2011;17(1):7–7 © 2011 Thomas Land Publishers, Inc. www.thomasland.com doi: 10.1310/sci1701-7
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Figure 1. Schematic of an arm model, experimental setup, and examples of recordings. (A) A 2-dimensional diagram of a 3-joint arm model with 6 muscles: 1, anterior deltoid (AND); 2, posterior deltoid (POD); 3, brachioradialis (BR); 4, triceps brachialis short head (TS); 5, biceps brachii (BI); 6, triceps brachialis long head (TL); 7, flexor carpi radialis (FCR): and 8, extensor carpi radialis (ECR). The open and shaded arm configurations demonstrate how the same position of the arm endpoint can be achieved with different joint angles. The arm endpoint is located in the center of a circle that corresponds to the trajectory of a moving force target; the target is indicated by the small circle (moving target). The cross indicates the cursor position, which is controlled by the participant pushing on the instrumented handle (see B and C). Positions of the moving target and the cursor are determined by the target force direction and cursor force direction angles, respectively. The instrumented handle in the center of the target trajectory records horizontal forces (Fx, Fy) and a torque (Tz) with respect to the (long) vertical axis of the handle (see B and C). (B) Experimental setup. The participant sits in front of a computer screen with the arm suspended and holds an instrumented handle. The participant is instructed to track a moving target on the screen with a cursor that is controlled by application of horizontal force on the handle. (C) Instrumented handle that permits recordings of the 2 components of the force vector in the horizontal plane (Fx, Fy) and the torque around the vertical axis of the handle (Tz) (see A). (D) Examples of recorded forces and EMG exerted by a participant from the control group during 5 consecutive cycles of force tracking task. The first 3 plots are the forces and torque (Fx, Fy , and Tz) exerted on the handle; thin smooth lines indicate the target force; the thick lines indicate the force and torque exerted by the participant. The next 3 plots are the joint moments at the shoulder (Ms), elbow (Me), and wrist (Mw) calculated from the recorded forces and torque and arm configuration (see Data analysis); positive values correspond to flexion moment. The next 4 plots show rectified (dark lines) and low-pass filtered (white lines) EMG of antagonist muscles, AND – POD, BR – TS, BI – TL, FCR – ECR. The bottom plot shows target force (thin line) and cursor force (thick line) directions.
Although the complete answer to this question is presently not available, it has been recognized that despite the kinematic redundancy and, as a consequence, availability of many motor strategies to perform skilled movements, healthy people utilize very limited motor patterns during arm reaching 3,4 and prehension 5 tasks. The limited kinematic patterns observed in arm reaching are called kinematic invariant characteristics. They include (1) straight-line hand trajectory; (2) bellshaped hand velocity profile; (3) power law, describing the relation between hand velocity and curvature of hand trajectory; and (4) Fitts’s law, describing the trade-off between speed and accuracy during reaching movements. The first invariant characteristic, the straight-line hand trajectory, can be observed during point-to-point reaching arm movements. In these tasks, the hand tends to move along a nearly straight line connecting initial and final hand locations in space. Joint angles during reaching to different points in space are variable and have complex non-linear patterns.3 Bell-shaped hand velocity profile is a robust kinematic feature of reaching movements according to which the hand velocity changes smoothly from zero at the initial hand position to the peak velocity in middle of reaching and back to zero velocity at the target hand position. The symmetry of this bell-shaped velocity profile can be distorted by unanticipated external perturbations of the arm or extreme requirements for accuracy. Practicing arm reaching movements in a novel force-field environment leads to restoring symmetry and smoothness of the hand velocity profile.6 When
we perform arm movements along curved trajectories to avoid obstacles or during drawing or writing, the arm endpoint velocity is coupled with curvature of endpoint trajectory.7,8 This coupling (power law) is expressed by the following empirical equation: v = k · C1/3, where v is the limb endpoint tangential velocity, r is the radius of curvature C of endpoint trajectory, and k is a coefficient. Finally, Fitts’s law describes the relation between task accuracy requirements or difficulty (ie, target width along movement trajectory, W, and the distance to the target, D) on the one hand and movement time (MT) on the other hand: MT = a + b · log2 (2D/W), where a and b are empirical constants. According to Fitts’s law, the more difficult the pointing task is (the smaller and further away the target), the longer it takes to reach it. Although this empirical relation can be explained based on the information theory of physical communication systems,9 it is not immediately clear how this kinematic law is related to the other kinematic invariant features of arm skilled movements. It turns out that all of the kinematic invariants described above can be predicted and explained by an assumption that during arm reaching movements, people select such kinematic patterns that minimize the arm endpoint variance in the final position.10 The main source of this variability was proposed to be signal-dependent noise of motor commands to muscles. Thus, reducing the overall magnitude of motor commands results in smaller variability of arm endpoint in the final arm position as well as in the 4 kinematic invariant characteristics.10
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Muscle Redundancy Another important design feature of the upper extremity is that the arm has more muscles or muscle parts (which are called muscle compartments or actons11) than kinematic DoF (for review, see ref. 12). According to estimates of Morecki et al,11 there are 66 muscle compartments (actons) in the human arm that serve 22 joints and 30 DoF. Therefore, on average, 3 actons serve one joint (=66/22) and 2.2 actons serve 1 DoF (=66/30). Each acton can produce several moments of force with respect to anatomical joint axes (for reviews on muscle moment arms, see refs. 13 and 14). The long head of the biceps brachii, for instance, can produce 5 moments of force that tend to (1) flex, (2) abduct, and (3) internally rotate the upper arm at the shoulder as well as (4) flex and (5) supinate the forearm at the elbow. The total number of joint moments that actons can produce (or the number of functions of actons) in the human arm is 264. Thus in the human arm, the number of acton functions per joint and DoF is 12 (= 264/22) and 8.8 (= 264/30), respectively. One important consequence of the multiple functions of actons and muscles at the joints is that when a muscle is activated to produce a desired (primary) moment with respect to a DoF, it also typically generates additional undesired (secondary) moments of force with respect to other DoF, which must be counterbalanced by other actons/muscles. The latter actons/muscles also develop undesired (tertiary) moments of force with respect to other DoF, and so forth. Thus, the task of activating muscles to produce desired joint moments and movements seems overwhelmingly complex. Despite the muscle redundancy, muscle activity patterns seem rather stereotyped in skilled arm tasks and can be characterized by several invariant characteristics: (1) synergistic muscle activation or broad tuning of muscle activity around preferred movement direction, that is, the direction in which muscle demonstrates its maximum electromyographic (EMG) activity15,16; (2) reciprocal muscle activation, that is, relatively low coactivation of anatomical antagonists17; and (3) specific activation of 2-joint muscles, that is, EMG activity of a 2-joint muscle (or a muscle that controls 2 DoF) is greater when the muscle can contribute to the motion at both joints as an anatomical agonist (eg, biceps brachii, elbow flexor and supinator), is typically more active during movements that require simultaneous elbow flexion and supination.15,18 The assumption discussed previously that during skilled arm movements the nervous system is minimizing the signal-dependent noise of motor commands (or a non-linear function of muscle force
magnitude) leads to reasonable predictions of muscle EMG patterns.19,20 Implications of Musculoskeletal Redundancy for Rehabilitation The considerations about the complexities of arm control in intact upper extremities suggest that individuals with SCI at C5-C7 levels, leading to loss or altered functions of several muscle groups, would experience overwhelming difficulties in performing accurate multi-joint tasks by the affected arm. On the other hand, there is the possibility that kinematic and muscle redundancy of the upper extremity can offer the individual with tetraplegia alternative motor strategies of task performance that can be discovered during repeated attempts to execute the task. To test this possibility experimentally, we asked a group of 6 participants with complete and incomplete C5-C7 SCI (Table 1) to track a moving target on a computer screen by exerting external force by the arm. A group of age-matched uninjured right-handed participants (n = 7) served as control (Table 1). All participants gave informed consent for participating in the study. The experimental protocol was approved by the Institutional Review Boards of Shepherd Center and Georgia Tech. Tracking task and data collection Each participant was instructed to sit comfortably in a wheelchair (SCI group) or a chair (control group) in front of a computer screen. The participant’s right arm was positioned in the horizontal plane and suspended from above using a long rubber band (Figure 1B). The hands of participants with SCI were attached to a vertically fixed handle (Figure 1C) by a grasping cuff (Sammons Preston, Bolingbrook, Illinois). Uninjured participants did not use the grasping cuff. The handle was instrumented with a 6-component force transducer (ATI Mini; Assurance Technologies, Inc., Bartlett, Illinois). Participants’ arm angles were adjusted to be in the range of 20 o to 40o, 40 o to 60o, and 25 o to 45o for shoulder (q1), elbow (q2), and wrist (q3) joints, respectively (Figure 1A). Joint angles were measured by a mechanical goniometer. The instrumented handle recorded the 2 force components in the horizontal plane (Fx, Fy) and a torque (Tz) with respect to the handle vertical axis (Figure 1A) at sampling frequency of 1 kHz. These signals were fed into a computer and used to control the position of a cursor on the computer screen (Figures 1 A and B). The participant was instructed to track a moving target on screen (5-mm circle)
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Table 1. Participant information Participants
Upper arm length, cm
Forearm length, cm
M M F M M M
22.3 27.3 26.0 25.7 28.4 30.0 26.6±2.6
25.2 25.1 22.9 24.2 29.1 27.8 25.7±2.3
C5-C6, incomplete C7, complete C7, complete C6-C7, complete C6-C7, complete C5-C6, complete
5 6 48 22 7 20 18±17
M M M M M F F
33.5 26.0 29.3 27.0 26.0 27.5 27.0 27.9±2.3
28.5 25.5 27.4 26.0 25.5 22.0 25.5 25.8±2.0
– – – – – – –
– – – – – – –
Age, years
Gender
SCI group 1 2 3 4 5 6 Mean ±SD
35 38 22 29 23 30 30±6
Control group 1 2 3 4 5 6 7 Mean ±SD
26 32 23 20 20 23 23 27±9
with the cursor (5-mm cross; Figure 1A) as closely as possible by exerting force on the handle and trying to maintain the same arm position. The target was moving counterclockwise along a circle of 11 cm in diameter (or 40 N in force scale) with a frequency of 0.2 Hz. Each participant performed over 300 tracking cycles with 1-minute rest periods after each 8 cycles. Surface EMG was recorded synchronously with the forces and torque at a sampling rate of 1 kHz (Konigsberg Instruments Inc, Pasadena, California) from 8 arm muscles [Figure 1B: anterior deltoid (AND-1), posterior deltoid (POD2), brachioradialis (BR-3), short head of triceps (TS-4), long head of biceps (BI-5), long head of triceps (TL6), flexor carpi radialis (FCR-7), and extensor carpi radialis (ECR-8)]. Before and 1 minute after the force tracking experiment, the participant was asked to exert a maximum force on the handle in 8 directions in the horizontal plane (from 0o to 360o every 45o; Figure 1A) to measure maximum voluntary EMG activity. Data analysis After the experiments, all recorded raw EMGs were rectified and low-pass filtered (Butterworth 4th order, zero lag filter, cutoff frequency 15 Hz) to obtain linear envelopes (Figure 1D). The envelopes were normalized to the maximum envelope values found in maximum force production tests. Joint moments (ie, the resultant moments produced by all muscles around each joint,
Injury
Time since injury, mo
assuming negligibly small contribution of passive tissues at the joint) were computed as M = JTF, where F = [Fx, Fy, Tz]T, vector of recorded handle forces and torque; M = [Ms, Me, Mw]T, vector of shoulder, elbow, and wrist moments; and JT, the transposed Jacobian matrix (for details see ref. 21). Tracking performance, exerted joint moments, and EMG were analyzed using the following linear and circular (directional) measures: (1) tracking error, normalized distance between target and cursor positions at each degree of target force direction averaged over a tracking cycle (Figures 1A and 2); (2) time delay between target force direction and cursor force direction at each degree of target force direction (Figures 1A and 2) averaged over each cycle; (3) normalized EMG envelope peak in each tracking cycle (Figure 1D); (4) peak of joint moment in each tracking cycle (Figure 1D); (5) EMG preferred direction (in degrees) for each muscle, that is, the resultant of EMG vectors represented by the EMG magnitude and direction (for each degree from 0o to 360o); (6) EMG spatial focus of muscle preferred direction, that is, measure of variance of the EMG preferred direction22; (7) joint moment preferred direction (in degrees) for each joint; and (8) joint moment spatial focus. Statistical methods of analysis included circular and linear correlation and regression, Rayleigh test (directedness), chi-square (comparison of circular distributions), and t test. Significance level was set at .05.
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Figure 2. Normalized tracking error and time delay between the target and cursor force directions (see Figures 1A and 1D) as functions of tracking force cycle. Each dot corresponds to the mean value averaged over each cycle and across all participants in the group; the continuous line is an exponential regression line. (A) The normalized errors of participants with SCI. (B) The normalized errors of control participants. (C) The time delay of participants with SCI. (D) The time delay of control participants.
Results and Discussion The group with SCI was able to perform the multijoint tracking task with reasonable performance. Specifically, the normalized tracking error was ~40% initially and decreased to 20% after 300 to 400 tracking cycles (Figure 2A). As predicted, the control group performed significantly better. The initial and final normalized mean errors were 23% and 12%, respectively (Figure 2B; P < .05). Both groups demonstrated a strong and significant correlation between the tracking error and the delay (r > 0.9, P < .05; Figures 2C and D), suggesting that the performance improvement was achieved in both groups by decreasing the delay between the target and cursor force directions (ie, by increasing the contribution of feed-forward cursor control). Both groups of participants exhibited similar patterns of joint moments (Figure 3). Flexor and extensor joint moments in both groups had statistically significant preferred directions (P < .05; Figure 3), although the shoulder and elbow preferred directions in the group with SCI differed by 30o to 45o from the control group (P < .05). Moment peaks in each joint were significantly smaller in the group with SCI compared to the control group (P < .05; Figure 3), suggesting weakness in these
muscles to generate force. Normalized EMG peaks of BR, BI, and ECR were higher in participants with SCI compared to control (P < .05; Figure 4), indicating a significantly higher level of effort needed in these muscles by the participants with SCI to execute the task. However, the more proximal muscles (AND and POD) showed equal or less effort when compared to the controls. Thus, the included muscle groups controlling the elbow and wrist could contribute to an alternate motor strategy through changes in direction and increased magnitude of effort (assuming some changes in arm configuration) to substitute for the weaker triceps and wrist/finger flexors. On the other hand, the included proximal shoulder muscles contributed to this alternate strategy mostly through changes in direction of effort. The tracking task required co-activation of antagonists, which was evident from broad EMG tuning curves (example in Figure 1D) around the EMG preferred directions in both groups. In the muscles of the SCI group with reliable EMG recordings (AND, POD, BR, BI, and ECR), EMG peaks and spatial focus increased with practice (P < .05), whereas in the control group the EMG peak magnitude decreased (P < .05). Perhaps those in the control group were able to find
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Figure 3. Joint moment magnitude as a function of exerted cursor force direction (from 0o to 360o; see Figure 1A) in polar coordinates. The joint moment magnitude at a given force direction corresponds to the distance from the center of the big circle to the point on the moment line. Lines with small open circles correspond to the mean moments of the SCI group; lines with small open squares, to the control group. The small filled circles and squares indicate preferred directions for joint moments of the SCI and control groups, respectively.
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Figure 4. Normalized EMG activity of 5 arm muscles as a function of exerted cursor force direction (from 0o to 360o; see Figure 1A) in polar coordinates. The normalized EMG magnitude at a given force direction corresponds to the distance from the center of the big circle to the point on the EMG line. Lines with small open circles correspond to the mean normalized EMG of the SCI group; lines with small open squares, to the control group. The small filled circles and squares indicate preferred directions for EMG of the SCI and control groups, respectively.
a way to use their muscles more efficiently, requiring less effort, while those in the SCI group learned how to better activate their muscles. The obtained results primarily demonstrated that (1) individuals with C5-C7 SCI were able to perform a complex multi-joint force tracking task with weakened or absent elbow extensors and wrist flexors, (2) the participants with SCI improved their performance and increased the EMG activity of functioning muscles with practice, and (3) the participants with SCI demonstrated synergistic activity, a typical invariant feature of muscle activation. This synergistic activity was shown by the broad EMG tuning curves in functioning muscles (coactivation) and signs of a negative correlation between EMG preferred directions of shoulder flexor and extensor muscles (reciprocal activation). The ability of the participants with SCI to perform the difficult force tracking task may have resulted from exploiting
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musculoskeletal redundancy that permitted alternative motor strategies involving additional kinematic DoF and different muscle groups. These findings suggest the potential effectiveness of practicing and discovering alternative movement patterns during rehabilitation for improved upper extremity function and motor control, even in individuals with complete SCI. Detailed arm kinematic and intramuscular activity recordings (for example, see refs. 23 and 24) may be needed in the future to understand the exact mechanisms of executing and controlling multi-joint upper extremity tasks by individuals with C5-C7 SCI. Acknowledgments We thank the participants of this study and acknowledge support of the Shepherd Center and the Center for Human Movement Studies at Georgia Tech.
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