1Kawato Dynamic Brain Project,
Osu, Rieko and
Hiroaki Gomi.
Multijoint muscle regulation mechanisms examined by measured
human arm stiffness and EMG signals. Stiffness properties of the musculo-skeletal system can be controlled by regulating muscle activation and neural feedback gain. To understand the regulation of
multijoint stiffness, we examined the relationship between human arm
joint stiffness and muscle activation during static force control in
the horizontal plane by means of surface electromyographic (EMG)
studies. Subjects were asked to produce a specified force in a
specified direction without cocontraction or they were asked to keep
different cocontractions while producing or not producing an external
force. The stiffness components of shoulder, elbow, and their
cross-term and the EMG of six related muscles were measured during the
tasks. Assuming that the EMG reflects the corresponding muscle
stiffness, the joint stiffness was predicted from the EMG by using a
two-link six-muscle arm model and a constrained least-square-error regression method. Using the parameters estimated in this regression, single-joint stiffness (diagonal terms of the joint-stiffness matrix)
was decomposed successfully into biarticular and monoarticular muscle
components. Although biarticular muscles act on both shoulder and
elbow, they were found to covary strongly with elbow monoarticular muscles. The preferred force directions of biarticular muscles were
biased to the directions of elbow monoarticular muscles. Namely, the
elbow joint is regulated by the simultaneous activation of
monoarticular and biarticular muscles, whereas the shoulder joint is
regulated dominantly by monoarticular muscles. These results suggest
that biarticular muscles are innervated mainly to control the elbow
joint during static force-regulation tasks. In addition, muscle
regulation mechanisms for static force control tasks were found to be
quite different from those during movements previously reported. The
elbow single-joint stiffness was always higher than cross-joint
stiffness (off-diagonal terms of the matrix) in static tasks while
elbow single-joint stiffness is reported to be sometimes as small as
cross-joint stiffness during movement. That is, during movements, the
elbow monoarticular muscles were occasionally not activated when
biarticular muscles were activated. In static tasks, however,
monoarticular muscle components in single-joint stiffness were
increased considerably whenever biarticular muscle components in
single- and cross-joint stiffness increased. These observations suggest
that biarticular muscles are not simply coupled with the innervation of
elbow monoarticular muscles but also are regulated independently
according to the required task. During static force-regulation tasks,
covariation between biarticular and elbow monoarticular muscles may be
required to increase stability and/or controllability or to distribute
effort among the appropriate muscles.
The human musculo-skeletal system has springlike
properties that enable posture stabilization and interaction with the
environment. Stiffness properties are determined by both the muscle's
inherent springlike properties and neural feedback systems, and the
stiffness can be controlled by regulating muscle activation and neural
feedback gain. Although many attempts have been made to measure human
multijoint arm stiffness, only a few researchers have tackled the
contribution of multiple muscle activation to multijoint stiffness
(Flash and Mussa-Ivaldi 1990 The contributions of monoarticular and biarticular muscle stiffness to
each term of the stiffness matrix is worth examining because they may
play an important role in altering the shape or orientation of the
stiffness ellipse, which represents an elastic force that resists
displacement of the hand in any direction in the horizontal plane. It
has been reported that the stiffness ellipse size can vary while shape
or orientation cannot (Dolan et al. 1993 Stiffness ellipse alteration, however, was found to be limited in
isometric tasks because the magnitude of cross-joint stiffness was
always much smaller than the magnitude of single-joint stiffness (Gomi and Osu 1998 This paper examines the relation between joint stiffness and muscle
activities during multijoint static force-regulation tasks in the
horizontal plane at shoulder level. We predict the joint stiffness from
the surface electromyographic (EMG) signals of six muscles that
correspond to idealized muscles in the two-link arm model by using the
constrained least-square-error regression method. Using the estimated
parameters, we examine the muscle-regulation mechanisms, especially,
the regulation of biarticular muscles, in the light of task dependency.
The estimation of such parameters is practical because we can predict
stiffness matrix from surface EMG signals without directly measuring
them. Note that the analysis of the spatial characteristics of
stiffness was presented elsewhere (Gomi and Osu 1998 Experiment
Four subjects, aged 23-34 yr old, took part in this study
(subjects A and B: right-handed males,
subject C: ambidextrous female, subject D:
right-handed female). The subjects were seated on a chair in front of
the parallel link drive air-magnet floating manipulandum (PFM) with
their shoulders fixed to the back of the chair by straps (see Fig.
1). The handle position of the PFM was controlled by a high gain position servo. The right forearm of the
subjects was fixed to a molded plastic cuff tightly coupled to the
handle of the PFM and supported in the direction of gravity by a beam.
The wrist joint of the subjects was fixed by the cuff and only the
exertion of the shoulder and elbow joint torque in the horizontal plane
were permitted. The right hand of each subject was kept at a specified
position by the PFM during the experiment.
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
; Tsuji et al.
1996
). Linear relationships between single-muscle activation
and the corresponding muscle stiffness or single-joint stiffness have
been reported (Cannon and Zahalak 1982
; Joyce and
Rack 1969
; Kearney and Hunter 1990
). The
relationship observed between single-muscle and single-joint stiffness
possibly can be extended to the relationship between multijoint
stiffness and multiple-muscle activation. Accordingly, each term of
joint-stiffness matrix can be decomposed into the stiffness components
contributed by each muscle's stiffness, which we will call
"effective muscle stiffness."
; Flash
and Mussa-Ivaldi 1990
; Hogan 1985
;
Mussa-Ivaldi et al. 1985
; Tsuji et al.
1995
). Lacquaniti, Carrozzo, and Borghese (1993)
, however, showed that stiffness can be modified during catching tasks, suggesting that stiffness may change with environmental interaction. In addition, Gomi and Osu (1998)
showed
that the stiffness ellipses also can be altered voluntarily by
regulating muscle activation in isometric contraction tasks. The shape
and orientation of a hand-stiffness ellipse is influenced most strongly by the ratio of single-joint stiffness (diagonal terms of the joint-stiffness matrix) and cross-joint stiffness (off-diagonal terms
of the joint-stiffness matrix that govern interjoint-interaction between the shoulder and elbow joints). Because single-joint stiffness is composed of both monoarticular and biarticular effective muscle stiffness, whereas cross-joint stiffness is only composed of
biarticular effective muscle stiffness, the regulation of monoarticular
and biarticular muscles activation should play an important role in regulating the shape of the stiffness ellipse.
). On the contrary, during movement,
drastic changes in the elliptical orientations were observed,
especially in the presence of external constraints such as a handle
that can only be moved in one direction along the x axis
(Gomi and Kawato 1995
, 1996a
). In the middle of this
constrained movement, the magnitude of the elbow single-joint stiffness
became as small as the magnitude of the cross-joint stiffness. This
indicates that the regulation of monoarticular and biarticular muscles
during movement is quite different from that in isometric task. These different formations in the joint-stiffness matrix between static and
dynamic tasks suggest adaptive changes in muscle regulation according
to the task requirements.
).
METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Fig. 1.
Parallel link drive air-magnet floating manipulandum (PFM) system and
experimental setup for measuring human arm mechanical impedance.
x axis indicates right direction and y
axis indicates frontal direction away from body. Origin is shoulder
position. Force vector in horizontal plane was displayed on the
computer monitor. Electromyogram (EMG; rectified and averaged) levels
of 6 muscles were shown by bar graph to maintain muscle activation
level in each experimental set.
A computer monitor behind the PFM displayed the current force vector applied by the hand to the handle and a small circle indicating the target force. Subjects were asked to keep the head of the force vector on the target during each experimental set to preserve a constant external force. The current rectified and filtered surface EMG signals (moving average: 0.5 s) of six muscles were displayed in a bar graph (current EMG bar graph) during the experimental set. A reference line was marked on the current EMG bar graph. The reference line was the rectified and filtered surface EMG signals (moving average: 0.5 s) of six muscles that was determined by requesting target force exertion before each experimental set. The subjects were asked to keep the current EMG bar graph the same as the reference line on the EMG bar graph so that the muscle activities would be constant during each set.
The hand of each subject was placed in the following five positions:
proximal center (PC: [x, y] = [0.0, 0.35] m),
middle center (MC: [0.0, 0.45] m), distal center (DC: [0.2, 0.55]
m), proximal left (PL: [0.2, 0.35] m), and proximal right (PR:
[0.2, 0.35] m]). Two types of tasks were given to the subjects.
FORCE-REGULATION TASKS WITHOUT COCONTRACTION. The subjects were asked to produce a specified force (5, 10, 15, or 20 N) in a specified direction [8 directions (5 N) or 16 directions (10, 15, 20 N) in the hand's x-y plane at even intervals] without cocontraction.
POSTURE MAINTENANCE AND FORCE-REGULATION TASKS WITH DIFFERENT COCONTRACTIONS. The subjects were asked to maintain different contractions while producing, or not producing, an external force. The specified tasks were to keep the current force vector 0: 1) without cocontraction, 2) with a quarter cocontraction, 3) half, 4) full cocontraction, 5) with cocontraction only in the shoulder, 6) with cocontraction only in the elbow, or 7) to produce a 5-N force in a specified direction (4 directions in the horizontal plane) with moderate cocontraction.
The tasks requested of each subject were as follows. All subjects: PC (5, 10, 15 N); DC (10 N); 1-6 at PC, MC, DC, and 7 at PC. Subject A was also: PC (20 N), MC (5, 10, 15 N), PL, PR (10 N), 1-6 at PL, PR, and 7 at MC. Subject B was also PC (20 N) and MC (10 N); subject D was also MC (10 N). To estimate impedance parameters, the hand was pushed slightly and pulled back (6-8 mm) within a brief period (0.3 s) in eight randomized directions (3 trials for each of 8 directions in each experimental set). The rising time of the positional displacement (duration between perturbation onset and the peak displacement) was 0.17 s. The displacement amplitude was almost the same for all tasks due to the positional perturbation. The subjects were asked not to intervene voluntarily during the perturbation, and all visual feedback on the monitor (i.e., current force vector and current EMG bar graph) was frozen. The hand position, force, and EMG signals were recorded. The applied external forces were decomposed into arm dynamics and muscle-generated force. Details of the arm impedance estimation method are provided in elsewhere (Gomi and Kawato 1995Estimation of joint-stiffness from EMG levels
A human arm on the horizontal plane can be modeled as a two-link manipulator with four monoarticular muscles and two biarticular muscles. The relation between joint-stiffness and EMG levels was estimated by the arm model and a least-square-error method as described in the following text.
Joint stiffness R is expressed as a differential operator
that relates the small variation of joint torque to the small
angular displacement q. The relation between joint stiffness
R and muscle stiffness S can be defined as
follows (see APPENDIX B for details).
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(1) |
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(2) |
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(3) |
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(4) |
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(5) |
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(6) |
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(7) |
Assuming that muscle activities ui are
proportional to EMG levels, we examined whether we could reconstruct
the joint stiffness matrix R from measured EMG levels. A
constrained optimization method (the sequential quadratic programming
method in MATLAB software) was used to estimate the parameters that
satisfied Eqs. 6 and 7. The averaged values of
off-diagonal terms of the measured joint stiffness matrix were used as
cross-joint stiffness Rcj because the stiffness
matrix under static conditions (i.e., posture maintenance and
force-regulation tasks) was nearly symmetric (Gomi and Osu
1998; Mussa-Ivaldi et al. 1985
; Tsuji et
al. 1995
) as assumed in the model.
We obtained preferred hand-force direction for each muscle by
calculating the maximum correlation angle between the positive range of
the cosine function (/2 ~
/2) and the EMG levels under force-regulation tasks in all 16 directions.
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RESULTS |
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Regression performance
Because a nonlinear increase in EMG signal with muscle force has
been reported in high muscle activation, we separated the data
according to the contraction level (Basmajian and De Luca 1985). We performed the estimation using the following three
data groups. The first group contains data under force-regulation tasks without cocontraction and rest condition (a), both at the proximal center posture. The second group contains data under the same condition
as in the first group but at all postures. The third group contains
data under posture maintenance and force-regulation tasks with
different amounts of cocontraction and the maximum hand force in the
force-regulation tasks, (subjects A and B: 20 N,
16 directions; subjects C and D: 15 N, 16 directions).
The correlation coefficients between the measured and reconstructed
stiffness for each subject were 0.966, 0.951, 0.966, and 0.939 for the
first data group. The correlation coefficients for the second data
group were 0.951, 0.932, 0.921, and 0.879. The deterioration in
estimation accuracy compared with the first data group might be
ascribed to the difference in moment arms among the postures
(van Zuylen et al. 1988). The correlation coefficients for the third data group were 0.943, 0.933, 0.940, and 0.931. Figure
2 compares each term of the measured and
reconstructed stiffness values of subject A using the first
data group. The estimation of single-joint stiffness was better than
that of cross-joint stiffness for all subjects.
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Table 1 summarizes the estimated
parameters and their 90% confidence intervals as well as the ratios of
the confidence intervals to the estimated parameters for the three data
groups (subject A). The parameters are different for the
three data groups. The differences between the first and third data
groups and between the second and third data groups are conspicuous
compared with those between the first and second groups. The parameter
difference cannot be ascribed to the different moment arms among the
postures because both the second and third data group include data from all postures. Three possible explanations could account for these differences. The first is that conducting the EMG recordings on different days may have resulted in the failure of daily normalization. The second is that there may have been contributions by muscles other
than those measured in the present experiment. The third is that there
actually may be nonlinearity between the EMG levels and muscle
stiffness. Because the normalization appears to be accurate as
indicated by the values of correlation coefficients shown in
APPENDIX A, only the second and third reasons appear feasible. Parameters a5,
a7, and a9, which are
related to the biarticular flexor (biceps brachii), were considerably
smaller under cocontraction than under force regulation for three
subjects (subjects A, B, and C). The difference
in parameters cannot be ascribed to the nonlinear contribution of other
muscles (the 2nd reason) because there is only one biarticular flexor
in the human arm. The nonlinear contribution of different heads of the
biceps could hardly explain the parameter difference as well because only small differences have been reported between the activities of two
heads of the biceps during isometric contraction (Basmajian and
De Luca 1985). The difference suggests that the contribution of
the biceps' EMG levels to the biarticular flexor muscle stiffness (p5 in Eq. 4) is decreased when
the biceps are strongly activated.
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Relation between effective muscle stiffness and joint stiffness
Figure 3A shows the relation between joint stiffness and effective muscle stiffness aiuj (EMG levels weighted by their corresponding estimated parameters) in tasks without cocontraction for subject A. All the other subjects showed a similar tendency. A sign was given to each joint-stiffness value according to the sign of the joint torque (a positive sign was given to flexor torque) related to that stiffness. Figure 3A, top, shows the relation between Rss and the shoulder monoarticular effective muscle stiffness. The sign for the shoulder torque was given to Rss. Figure 3A, middle, shows the relation between Rcj and biarticular effective muscle stiffness. The sign for the elbow torque was given to Rcj. Figure 3A, bottom, shows the relation between Ree and the elbow monoarticular effective muscle stiffness. The sign for the elbow torque was given to Ree.
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When muscles are working as agonists, that is, when the joint torque is positive for flexor muscles and when the joint torque is negative for extensor muscles, a strong correlation can be observed between effective muscle stiffness and joint stiffness. The relation is roughly linear, but in some cases, especially in the biceps brachii in subjects A and B, an accelerating increase in effective muscle stiffness can be observed when muscles are strongly activated by high joint torque (see the panels at the right column of the second row in Fig. 3A). These responses were not so clear for subjects C and D, which is possibly because they did not execute the tasks with the 20 N hand force. This nonlinearity in the biarticular flexor is one of the reasons of lower reliability in predicting cross-joint stiffness compared with that of single-joint stiffness.
Even when muscles are working as antagonists, a correlation can often
be found between joint stiffness and effective muscle stiffness,
especially in the elbow monoarticular muscles and the biarticular
flexor. The slope is, however, lower when muscles are working as
antagonists than when they are working as agonists. This observation
indicates that a part of the net joint stiffness in force-regulation
tasks can be ascribed to antagonist activation. Joint stiffness in
force-regulation tasks is correlated strongly to joint torque
(Gomi and Osu 1998). The present results indicate that
coactivation (and hence stiffness) also increases as the joint torque
increases even under relaxed conditions without instructions to
cocontract. Coactivation under force-regulation tasks was reported to
be observed in the sagittal plane (Flanders and Soechting
1990
).
Figure 3B shows the relation between joint stiffness and effective muscle stiffness in posture maintenance tasks with different levels of cocontraction. The panel arrangements are the same as in Fig. 3A. Open circles and solid line denote the monoarticular effective muscle stiffness and their regression lines, respectively. Plus signs and dashed line denote the biarticular effective muscle stiffness and their regression lines, respectively. In all muscles, the effective muscle stiffness linearly increased as the corresponding joint stiffness increased.
Variations in effective muscle stiffness depending on posture and force direction
In Fig. 4, the ratios between shoulder monoarticular flexor and extensor effective stiffness in shoulder single-joint stiffness are compared among proximal left, center, and right postures. Figure 4, top, represents the contribution of each muscle stiffness to shoulder joint stiffness in a posture maintenance task (e: shoulder cocontraction) for subject A; bottom represents the ratios between monoarticular flexor and extensor effective stiffness in shoulder joint stiffness at the corresponding postures. As shown in the figure, the muscles that contribute most to shoulder stiffness change with the posture. At proximal left, the monoarticular flexor contributes to shoulder stiffness more than the monoarticular extensor. At proximal right, however, the reverse is true. At proximal center, both the monoarticular flexor and monoarticular extensor contribute to shoulder joint stiffness. These phenomena can be explained by the muscles' length-tension relation. At proximal left, the shoulder monoarticular flexor is shortened and the shoulder monoarticular extensor lengthened compared with the positions of proximal center or proximal right, so there is necessarily more activation in the flexor and less activation in the extensor to hold the arm at the specified posture. On the other hand, when the shoulder monoarticular flexor is lengthened and the shoulder monoarticular extensor shortened at proximal right, there is necessarily less activation in the flexor and more activation in the extensor to keep the arm at the specified posture. If muscle stiffness is proportional to muscle activation, the contribution of the shoulder monoarticular flexor and extensor to shoulder stiffness is expected to vary with postures.
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Identical explanations are possible for the contribution difference of elbow monoarticular muscles between proximal center and distal center for subject A. At proximal center, the elbow monoarticular flexor is shortened and the elbow monoarticular extensor lengthened compared with the distal center position. More activation in the flexor and less activation in the extensor was observed at the proximal position compared with the distal position, which is also consistent with the length-tension relationship.
Figure 5 shows the variations of effective muscle stiffness against hand-force directions for subject A (left: extensor, right: flexion). Figure 5, A and B, shows the effective muscle stiffness values of shoulder monoarticular (solid thick curve) and biarticular muscles (dotted thick curve) in the shoulder joint stiffness for 15 N forces. C and D and E and F show corresponding effective muscle stiffness in the cross-joint and elbow joint stiffness, respectively. The corners of the dash-dot thin octagons in the first and second rows represent normalized absolute shoulder torque plotted against the hand-force direction (torque vector). The corners of the dashed thin octagons in the second and third rows represent normalized absolute elbow torque plotted against the hand-force direction. The octagons on the left denote extension torque, and those on the right denote flexion torque. In the hand-force direction where the shoulder torque vector and elbow torque vector overlap (see the 2nd row), the shoulder and elbow torque are in the same direction [both in extension direction (C) or both in flexion direction (D)]. As shown (A and B), biarticular muscles contribute to single-joint stiffness (dotted thick curves) more extensively in the flexion directions (8-12) than in the extension directions (1-4, and 16). Biarticular muscles contribute to elbow joint stiffness more strongly than they do to shoulder joint stiffness [see dotted thick curves in graphs (A, B, E, and F)]. In general, stiffness mainly is composed of agonist activations, but in the elbow joint, antagonist activations also contribute to stiffness (e.g., the elbow monoarticular flexor and extensor, biarticular flexor). The contribution of antagonists was observed most frequently in the elbow joint in force directions 1-6, where the elbow torque was negative. All the other subjects showed a similar tendency.
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In force directions 5, 6, 7, 13, 14, and 15, the directions of
the shoulder torque and elbow torque oppose each other or either elbow
torque alone, or shoulder torque alone, is exerted. The activation of
biarticular muscles should not effective in such directions
(Karst and Hasan 1991). However, biarticular muscles, especially the biarticular flexor, were activated in some of these directions (13, 14, and 15; Fig. 5D). The activation of the
shoulder monoarticular extensor would have been greater than the
activation needed to generate the extension torque that meets the task
requirements because the shoulder flexion torque generated by the
biarticular flexor was canceled out.
The solid and dotted arrows in the graphs denote the preferred force direction (defined in METHODS) of monoarticular and biarticular muscles at 15 N force, respectively. The preferred force direction of the elbow and shoulder monoarticular muscles (solid arrows) roughly corresponds to the force direction where the maximum torque is required at the corresponding joint. However, the biarticular muscles' preferred force direction (dotted arrows) was not located in the middle of the shoulder and elbow monoarticular muscles' preferred force direction (Fig. 5, C and D), but closer to the elbow monoarticular muscles' preferred direction (Fig. 5, E and F). Table 2 shows the absolute difference of the preferred direction between monoarticular muscles and biarticular muscles. For all subjects, the differences between shoulder monoarticular muscles and biarticular muscles were larger than those between elbow monoarticular muscles and biarticular muscles. The biarticular flexor's preferred direction was almost the same as the elbow monoarticular flexor's preferred direction. The mean and the standard deviation of correlation coefficients between EMG levels and the fitted cosine function at the preferred direction for four subjects were as follows: 0.99 and 0.013 for shoulder monoarticular muscles, 0.95 and 0.039 for biarticular muscles, and 0.96 and 0.029 for elbow monoarticular muscles.
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In force-regulation tasks (5 N) with cocontraction, both
monoarticular muscles and biarticular muscles were activated in all four directions. The shoulder joint stiffness was high in the force
direction toward or away from the shoulder joint (directions 5 and 13),
although it was low in those tasks without cocontraction (directions 5 and 13 in Fig. 5). Although the directional differences in joint
stiffness were decreased by cocontraction, the contribution of
different muscles to stiffness differed with the force direction. Without cocontraction, the stiffness ellipses in directions 5 and 13 were thinner than those in other directions, i.e., the hand is more
compliant in a direction perpendicular to the force (Gomi and
Osu 1998; McIntyre et al. 1996
). Cocontraction
can stabilize the hand even in these compliant pushing or pulling force directions.
Difference in contribution of biarticular and monoarticular muscles to single-joint stiffness
Next, we examined the contribution of each muscle to single-joint stiffness. Figure 6A shows the relationships between biarticular and monoarticular effective muscle stiffness in shoulder and elbow single-joint stiffness (subject C, force-regulation tasks without cocontraction). Because the preferred directions of elbow mono- and biarticular muscles were similar to each other, as observed in the preceding section, the biarticular and monoarticular effective muscle stiffness at elbow is expected to be highly correlated to each other. The mean ± SD of correlation coefficients between them for four subjects were 0.78 ± 0.15 for elbow extensor, 0.84 ± 0.085 for elbow flexor. Biarticular muscles contribute little to shoulder joint stiffness but contribute much to elbow joint stiffness for all subjects. The slopes of regression lines between the elbow mono- and biarticular effective muscle stiffnesses were greater than one for both extensor and flexor (mean ± SD for 4 subjects, extensor: 3.00 ± 1.24, flexor: 1.80 ± 0.83), indicating that monoarticular muscle contributions to joint stiffness were greater than biarticular muscle contribution. On the other hand, in the tasks with cocontraction (Fig. 6B), the slope of the regression line was decreased (mean ± SD: 1.15 ± 0.62) compared with that in the tasks without cocontraction. The decrease in the slope indicates that the contribution of biarticular muscles increased in cocontraction tasks, which resulted in increasing posture stability.
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Reflex contribution to stiffness
It has been reported that stretch reflex mainly responds to
stretching velocity, thus stretch reflex contributes little to stiffness, especially if the stretch is small and quick (Kearney and Hunter 1983; Matthews and Stein 1968
;
Stein et al. 1995
). However, muscle spindle sensitivity
seems to change with perturbation amplitude and/or velocity
(Kearney and Hunter 1983
). To examine the effect of
reflex components on stiffness estimation in the current setup, we
observed the correlation between the rectified EMG signals of elbow
monoarticular muscles and the kinematic components of elbow joint
(position, velocity, and acceleration) during perturbation (0.6-s
period beginning 0.2 s before perturbation onset). Both in elbow
flexion (force directions 9-13) and extension (force direction 1-5)
tasks, the EMG signals of elbow single-joint flexor muscles of the four
subjects were better correlated to perturbation velocity (0.18 ± 0.024 for flexion, 0.16 ± 0.032 for extension) than to position
(0.018 ± 0.016 for flexion,
0.040 ± 0.016 for extension)
or acceleration (0.033 ± 0.038 for flexion, 0.085 ± 0.023 for extension). These results suggests that, at the perturbation amplitude and velocity examined here, reflex components contribute little to stiffness; they mainly contribute to viscosity.
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DISCUSSION |
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Joint stiffness predicted from EMG signals
The roughly linear relationship of muscle activation and muscle
stiffness has been observed in human muscles and in isolated cat
muscles (Cannon and Zahalak 1982; Joyce and Rack
1969
; Kearney and Hunter 1990
). On the basis of
these observations, we tried to extend this linear characteristic to
model the relationships between the EMG level of multiple muscles and
multijoint stiffness. The success of the model for various conditions
indicates that our simple model can predict joint stiffness from EMG
measurements and permits the contribution of each muscle to joint
stiffness to be estimated. The success of the model also confirmed the
assumption that muscle stiffness is proportional to EMG level.
However, results in Fig. 3 suggest that there is nonlinearity in the
relation between the rectified averaged surface EMG levels and joint
stiffness, especially in biceps brachii, which degraded estimation
accuracy. Joint stiffness tends to saturate when the muscles are
strongly activated by cocontraction or by a high joint torque.
According to Basmajian and De Luca (1985), the
relationship between EMG signal amplitude and force output for small
hand muscles such as the first dorsal interosseous and the adductor
pollicis always has been found to be quasilinear, whereas in larger
muscles such as the biceps brachii, triceps brachii, deltoid, and
soleus, the signal amplitude increases more than the force. Such
nonlinearity may be explained partially by a change in the regulation
of muscle tension according to the muscle tension magnitude. At a low
contraction level, the force mainly is increased by motor unit
recruitment, whereas at a higher contraction level, the rising firing
frequency increases the muscle tension (Kanosue et al.
1979
). The effect of muscle fatigue, another possible factor of
the nonlinearity (Basmajian and De Luca 1985
) may be
negligible in this kind of experimental paradigm as demonstrated in
Cannon and Zahalak (1982)
.
Reflexes could be another source of modeling error. Because of the
low-pass-filter characteristics of nerve impulses and muscle force
(Mannard and Stein 1973), a part of the stiffness
components could be attributed to reflex despite the minor correlation
between the EMG and angular position shown in the preceding section.
The magnitude of the reflex contribution to total stiffness is
controversial. Sinkjaer and Hayashi (1989)
estimated
that 30 to >50% of wrist stiffness can be attributed to reflexes by
abolishing the stretch reflex through ischemia. Similar values were
obtained from the results of Bennett (1994)
for
the elbow. On the other hand, Soechting, Dufresne, and
Lacquaniti (1981)
and Lacquaniti, Licata, and Soechting (1982)
argued that the EMG attributed to reflex response is low (5-10%). Lacquaniti et al. (1982)
suggested that
reflex contributes mainly to viscosity rather than stiffness.
Furthermore, De Serres and Milner (1991)
mentioned that
they could find no evidence to suggest that reflex responses contribute
significantly to joint stiffness. Different estimations of the
influence of the reflex response on stiffness may be attributed to the
perturbation properties.
We may need to include the nonlinearities and reflex effects if
musculo-skeletal dynamics are to be modeled more accurately. However,
the compact model introduced in this study is sufficient to
characterize the major factors relating joint stiffness to muscle
activation. This simple model is advantageous because we can use
surface EMG signals to predict arm stiffness instead of using direct
measurements (Osu et al. 1997).
Regulation of biarticular muscle activities
The role and regulation mechanism of biarticular muscles have been
one of the major topics in human arm-movement studies, especially
because the activation of biarticular muscles has been revealed to play
an important role in the formation of hand-stiffness stability
(Hogan 1985; Mussa-Ivaldi et al. 1985
).
From the viewpoint of muscle kinematics, biarticular muscles should be effective only in the force directions where the torque directions at both the shoulder and elbow are same because each biarticular muscle rotates the both joints in the same direction. If this rule is adopted in the CNS, biarticular muscles should not be activated in force directions 5, 6, 7, 13, 14, and 15 where the shoulder and elbow rotations are opposite. However, the biarticular flexor often was activated in force directions 13, 14, and 15, and the biarticular extensor often was activated in force directions 5, 6, and 7, except for subject B. In addition, the biarticular muscles' preferred force directions were biased to those of the elbow monoarticular muscles rather than those of shoulder monoarticular muscles. The higher correlation between bi- and monoarticular effective muscle stiffness in the elbow than in the shoulder indicates that biarticular muscle activations covary more with the elbow monoarticular muscles than with the shoulder monoarticular muscles (Fig. 6). In the shoulder joint, biarticular muscles did not always activate simultaneously with monoarticular muscles but sometimes were inactivated when monoarticular muscles were activated. These observations suggest that the CNS activates biarticular muscles mainly to control the elbow joint rather than the shoulder joint. As a result of the elbow-oriented regulation of biarticular muscles, the shoulder antagonists should cancel the shoulder torque generated by biarticular muscles. This cancellation of shoulder torque typically was observed for all subjects in force direction 13 (see Fig. 5). In this force direction, the shoulder monoarticular extensor was activated to cancel the torque generated by the biarticular flexor because no shoulder torque was required.
The biarticular muscles' preference of elbow joint to shoulder joint
could be ascribed to their different moment arm for each joint.
According to Meek et al. (1990), the effective moment
arm of the biceps for the elbow flexion is larger than that for the shoulder flexion. This means that the biceps can rotate the elbow joint
more effectively than the shoulder joint. This relation regarding the
size of the effective moment arm is consistent with the parameters
estimated here in tasks without cocontraction (parameters a5 and a7). The biased
moment arms of biarticular muscles resulted in the smaller contribution
of biarticular muscles to shoulder stiffness than to elbow stiffness
observed in Fig. 6A. It may be reasonable to assume that
biarticular muscles are intended for the joint for which they can more
effectively generate torque (Buchanan et al. 1986
).
However, it is not quite certain whether this principle holds true for
the triceps long head or for all biarticular muscles.
Another possibility to explain the preference of biarticular muscles is
the synergy between biarticular muscles and elbow monoarticular muscles
that has been reported in several studies. Wadman, Denier van
der Gon, and Derksen (1980), Buchaman et al. (1986)
, and Flanders and Soechting (1990)
reported a synergistic relationship between biceps and brachioradialis
or brachialis. Buchaman et al. (1986)
reported synergy
between triceps long head and medial head for extensors. On the other
hand, uncoupled activations of these muscles also have been reported.
Jamison and Caldwell (1993)
reported the reciprocal
activation of biceps and brachioradialis during supination/pronation
isometric torque productions. The reciprocal inhibitory projection has
been found between the biceps and brachioradialis (Miyasaka et
al. 1995
; Naito et al. 1996
). For the same pair
of muscles to show both a synergistic relationship together with a
reciprocal inhibitory relationship, some mechanism should exist to
control alternative muscle regulations according to the torque
requirements. The independent operation of each head of triceps also is
suggested in several studies. Buchaman et al. reported different
directionality in the three heads of triceps brachii. Flanders
and Soechting (1990)
reported quite different directional
tuning between the long head and medial head of the triceps. The
present study also found a difference in preferred direction between
the long head and lateral head of triceps (see Fig. 5 and Table 2).
Although the three head of the triceps brachii share the same tendon,
their activations are not coupled and may be controlled separately by
the CNS.
Task-dependent regulation of muscle activation
Task-dependent change in muscle regulation is another key topic in
the field of human motor control. In isometric static force-regulation tasks, the ratio of single-joint stiffness to cross-joint stiffness changed with the force and/or cocontraction levels. However, the ratio
was limited to a local range, i.e., single-joint stiffness was always
higher than cross-joint stiffness (Gomi and Osu 1998). The limitation in the ratio of single- to cross-joint stiffness observed in isometric tasks results from the covaried activations of
monoarticular and biarticular muscles. Cross-joint stiffness is
composed of biarticular effective muscle stiffness, whereas single-joint stiffness is composed of both biarticular and
monoarticular effective muscle stiffness. In the present isometric
conditions, monoarticular muscles always were activated whenever
biarticular muscles were activated (see Fig. 6). Note that
monoarticular muscle activation was not always accompanied by
biarticular muscle activation. From the constraints given by Eqs.
6 and 7, the parameter for each biarticular muscle's
activation to cross-joint stiffness (a9,
a10) is smaller than the average of the
parameters for its activation to single-joint stiffness
(a5 and a7,
a6 and a8). The constraints mean that the biarticular effective muscle stiffness in
cross-joint stiffness will not greatly exceed the biarticular effective
muscle stiffness in single-joint stiffness unless the moment arm of a
particular biarticular at the shoulder joint muscle is quite different
from that at the elbow joint. Thus single-joint stiffness as a whole
always exceeds cross-joint stiffness due to the constraints and the
covaried activations in isometric conditions.
Contrary to the observations in isometric conditions, it has been
reported (Karst and Hasan 1991) that during some
movements, biarticular muscles were activated vigorously, whereas the
monoarticular muscle were less activated. If it is possible to assume
that the muscle activation is proportional to the muscle stiffness
during movements, the elbow single-joint stiffness will decrease
compared with cross-joint stiffness. In addition, direct observation of the decrease in elbow single-joint stiffness during a constrained movement has been reported (Gomi and Kawato 1995
,
1996a
). The regulation of muscle activation in static
conditions seems to be quite different from that during movements.
Tax et al. (1989, 1990a
,b
) and van Groeningen and
Erkelens (1994)
showed that recruitment thresholds in
biarticular muscles are higher in isometric conditions than during
movement. Their observations are consistent with our prediction that in
static tasks, the activation of monoarticular muscles is facilitated whereas during movement, the activation of biarticular muscles is facilitated.
The advantage of activating both mono- and biarticular muscles at the elbow-joint in static tasks may be ascribed to the increases in stability and/or controllability that are required in the force-regulation tasks. Additionally, the CNS may try to distribute effort among muscles to avoid fatiguing a particular muscle. A more detailed examination of the task-dependent difference in muscle activation pattern is required to reveal the principle on which the CNS regulates multiple muscle systems.
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APPENDIX |
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A. Normalization of EMG signals
The EMG signals measured on different days were normalized and scaled by the following method. We measured the EMG signals during applications of a 15 N hand force at the position where the shoulder joint angle was 45° and the elbow joint angle was 90° on each experimental day for each subject (see Fig. A1). The directions of the hand force were 135° (the direction opposite the elbow rotational center, direction 1 in Fig. A1), 315° (the direction of the elbow rotational center, direction 2), 225° (the direction parallel to the upper arm, direction 3), 45° (the direction parallel to the upper arm, direction 4), the direction of the shoulder rotational center (direction 5), the direction opposite the shoulder rotational center (direction 6), the direction between the shoulder rotational center and elbow rotational center (direction 7), and the opposite direction between shoulder rotational center and elbow rotational center (direction 8). The EMG signals rectified and averaged for each force direction were called "reference EMG level." The reference EMG level on one experimental day was used as the "standard EMG level" and EMG signals of the other days were normalized to the standard EMG level by using the reference EMG level measured on the corresponding day. These EMG signals normalized to standard EMG level were then scaled for each muscle by the value of maximum voluntary contraction.
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The correlation coefficients between the standard EMG level and the EMG level reconstructed from reference EMG level for each day were 0.984, 0.969, and 0.978 for subject A, 0.987 and 0.983 for subject B, 0.988, 0.969, and 0.990 for subject C, and 0.991 and 0.994 for subject D.
Estimation method
Equation 1 can be derived from the following
relationship among joint torque and muscle tension, muscle stiffness,
and muscle length. Muscle tension T can be determined from
muscle stiffness S and the stretch length of each muscle
(L0 L) as follows.
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(A1) |
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(A2) |
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(A3) |
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(A4) |
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(A5) |
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(A6) |
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(A7) |
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(A8) |
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ACKNOWLEDGMENTS |
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We thank Drs. M. Kawato of ERATO and ATR, H. Imamizu of ERATO, K. Kawano of CREST, and M. Honda, K. Ishii, and Y. Tohkura of Nippon Telegraph and Telephone for continuing encouragement and N. Imamura, H. Nagaoka of KOBELCO and T. Yoshioka of CSK Corporation for technical support.
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FOOTNOTES |
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Address for reprint requests: R. Osu, Kawato Dynamic Brain Project, ERATO, JST, c/o ATR 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto, 619-0288, Japan.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 19 February 1998; accepted in final form 2 December 1998.
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REFERENCES |
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