Rehabilitation Research and Development Center, Veterans Affairs Palo Alto Health Care System, Palo Alto, California 94304-1200; and Neuromuscular Biomechanics Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
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ABSTRACT |
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Valero-Cuevas, Francisco J..
Predictive Modulation of Muscle Coordination Pattern Magnitude
Scales Fingertip Force Magnitude Over the Voluntary Range.
J. Neurophysiol. 83: 1469-1479, 2000.
Human
fingers have sufficiently more muscles than joints such that every
fingertip force of submaximal magnitude can be produced by an infinite
number of muscle coordination patterns. Nevertheless, the nervous
system seems to effortlessly select muscle coordination patterns when
sequentially producing fingertip forces of low, moderate, and maximal
magnitude. The hypothesis of this study is that the selection of
coordination patterns to produce submaximal forces is simplified by the
appropriate modulation of the magnitude of a muscle coordination
pattern capable of producing the largest expected fingertip force. In
each of three directions, eight subjects were asked to sequentially
produce fingertip forces of low, moderate, and maximal magnitude with
their dominant forefinger. Muscle activity was described by fine-wire
electromyograms (EMGs) simultaneously collected from all muscles of the
forefinger. A muscle coordination pattern was defined as the vector
list of the EMG activity of each muscle. For all force directions,
statistically significant muscle coordination patterns similar to those
previously reported for 100% of maximal fingertip forces were found
for 50% of maximal voluntary force. Furthermore the coordination
pattern and fingertip force vector magnitudes were highly correlated
(r > 0.88). Average coordination pattern vectors
at 50 and 100% of maximal force were highly correlated with each
other, as well as with individual coordination pattern vectors in the
ramp transitions preceding them. In contrast to this consistency of EMG
coordination patterns, predictions using a musculoskeletal computer
model of the forefinger show that force magnitudes 50% of maximal
fingertip force can be produced by coordination patterns drastically
different from those needed for maximal force. Thus when modulating
fingertip force magnitude across the voluntary range, the number of
contributing muscles and the relative activity among them was not
changed. Rather, the production of low and moderate forces seems to be simplified by appropriately scaling the magnitude of a coordination pattern capable of producing the highest force expected.
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INTRODUCTION |
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Task-specific motor strategies have been
hypothesized to simplify the coordination of redundant musculature to
reduce delays and improve performance in the nervous system
(Bernstein 1967). However, in the case of the redundant
musculature of the fingers, little attention has been paid to the basic
question of how a muscle coordination pattern is selected from a large
pool of valid alternatives to achieve a specific submaximal fingertip
force magnitude. The coordination of finger musculature is redundant because fingers have sufficiently more muscles than joints. As a
result, every fingertip force of submaximal magnitude can in theory be
produced by an infinite number of different, yet functionally equivalent, muscle coordination patterns (Chao and An
1978
; Valero-Cuevas et al. 1998
). Even the
common task of grasping, lifting, and placing objects requires
selecting an appropriate sequence of muscle coordination patterns to
modulate fingertip force magnitudes between zero (when the fingertips
first come in contact with or releases the object) and the magnitude
necessary to lift the object. Thus the control of finger musculature
during grasping could be simplified by a motor strategy that did not
require adopting a different muscle coordination pattern for each level
of submaximal fingertip force magnitude. One such simplifying motor
strategy would be to implement a muscle coordination pattern capable of
producing the largest expected fingertip force and scale down this
pattern to produce fingertip forces of lower magnitudes. Unfortunately
the lack of direct methods for recording descending motor commands has
made it difficult both to describe complete muscle coordination
patterns for finger musculature and to identify motor strategies during fingertip force production. Luckily there are practical tools that can
describe these patterns indirectly, as intramuscular electromyograms (EMGs) can characterize descending motor commands to
multiple finger muscles (Basmajian and De Luca 1985
).
To date, no EMG study has reported subject-independent muscle
coordination patterns for the modulation of fingertip force magnitude
over the voluntary range, which has been interpreted as evidence that
the control of redundant finger musculature may be idiosyncratic and
variable. EMG has been used to study the activity of different muscles
during the production of low fingertip forces (Close and Kidd
1969; Long et al. 1970
; Maier and
Hepp-Reymond 1995a
,b
) and of moderate and maximal voluntary
fingertip forces (MVF) of the thumb (Chao et al. 1989
;
Cooney et al. 1985
). The lack of consistent coordination
patterns in these studies is not necessarily evidence of idiosyncratic
motor strategies during ramp-and-hold force tasks. Various experimental
limitations may have rendered the experimental task ambiguous or
introduced variability into the EMG recordings. Because the digits have
three flexion mechanical degrees-of-freedom, the distal phalanx can
impart a torque to an object in contact with it (i.e., fingertip
torque) independently of the force it produces. Thus previous force
measurement techniques may confound the interpretation of EMGs because
the compliant and high-friction interface between the bare finger pad
and dynamometer allow production of fingertip torque, which is not
measured, and latitude in the direction of force application. In
addition, finger (Mathiowetz et al. 1985
;
Weightman and Amis 1982
) and wrist (O'Driscoll
et al. 1992
) posture affect finger mechanics and muscle fiber
length, which influence muscle force and EMG output (Zajac
1992
). Similarly, the high EMG scatter reported for fingertip
forces of low magnitude (Maier and Hepp-Reymond 1995a
)
underscores that factors particular to low force production may obscure
the detection of motor strategies. These include the nonlinearities at
the low end of the force-EMG curve (Basmajian and De Luca
1985
; Lawrence and De Luca 1983
) and the
stronger variability in the relationship between EMG and force caused
by other modulating factors such as the influence of peripheral
receptors (Garnett and Stephens 1981
). Such factors may
explain the inconsistency in reported maximal tip and key pinch forces
[19 to 106 N (Mathiowetz et al. 1985
; Weightman
and Amis 1982
)] and EMG patterns (Close and Kidd
1969
; Long et al. 1970
; Maier and
Hepp-Reymond 1995a
). Furthermore these studies did not
simultaneously record from all muscles of the digit in question and
therefore do not describe complete muscle coordination patterns. In a
previous study designed to isolate fingertip force magnitude from
direction and fingertip torque while standardizing forefinger posture
(Valero-Cuevas et al. 1998
), we reported
subject-independent muscle coordination patterns for maximal voluntary
fingertip forces. This consistency of coordination patterns is evidence
of intersubject consistency of motor strategies for static
ramp-and-hold force production. The analysis of these coordination
patterns, using a three-dimensional musculoskeletal computer model of
the forefinger, indicated that these coordination patterns were
mechanically advantageous. This suggests that mechanical principles may
govern the selection of muscle coordination patterns. However, we did
not study muscle coordination patterns for low and moderate forces.
Another indirect method to elucidate motor strategies in redundant
systems such as the fingers is musculoskeletal computer modeling
(Chao and An 1978). Musculoskeletal computer models can numerically predict coordination patterns that fulfill specific functional requirements during the simulated performance of a task.
Similarly, musculoskeletal models of redundant systems can explicitly
predict a variety of valid muscle coordination patterns for a specific
task. The predicted variability among these functionally equivalent
muscle coordination patterns then can provide valuable insight into the
nature and extent of the redundancy of control of finger musculature.
To date, no three-dimensional musculoskeletal model that includes all
finger muscles has been used to explore the redundancy of finger motor control.
This study examines the hypothesis that the selection of muscle
coordination patterns to span a broad range of fingertip force magnitudes is simplified by appropriately modulating the coordination pattern capable of producing the largest expected force. Simultaneous EMG recordings from all seven muscles of the forefinger are used to
estimate muscle coordination patterns during the sequential production
of fingertip force from 0 to 50% MVF, from 50 to 100% MVF, and from
100 to 50% MVF. A three-dimensional, seven-muscle musculoskeletal
computer model is used to predict the variability among muscle
coordination patterns that can produce forces 50% of maximal
magnitude. The hypothesis was tested for three fingertip force
directions by comparing the variability among EMG coordination patterns
that subjects used to span the voluntary range of fingertip force
magnitude with the variability among different coordination patterns
predicted by the model to produce fingertip forces
50% of maximal
magnitude. The hypothesis would be supported if similar EMG
coordination patterns were used by the subjects to span the voluntary
range of fingertip force magnitude, yet the model showed that
substantially different coordination patterns could have been used to
produce fingertip forces of
50% MVF magnitude. If confirmed, this
hypothesis would be an example of a task-specific motor program for the
coordination of redundant muscles.
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METHODS |
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Subjects
Eight right handed individuals (6 female, 2 male; age 27 ± 6 yr; mean ± SD) with no history of hand injury or dysfunction participated. Before participation, each subject read and signed a consent form approved by the Medical Committee for Protection of Human Subjects in Research at Stanford University.
Experimental production of fingertip forces
In a manner similar to that previously reported
(Valero-Cuevas et al. 1998), subjects produced fingertip
forces by ramping from 0 to 50% MVF, to 100% MVF and back to 50% MVF
while maintaining their forefingers in a standardized posture, Fig.
1. Subjects placed their forearm in a
trough, wrapped their dominant right hand around a fixed dowel to
isolate forefinger function. Subjects generated three maximal
forefinger forces in the dorsal, palmar, and distal, directions in
randomized order while maintaining the standard posture. The
standardized finger posture was defined as neutral
ad-abduction, 45° flexion at metacarpophalangeal and proximal
interphalangeal joints, and 10° flexion at distal interphalangeal joint. The forefinger did not rest against the middle finger. The wrist
was held in full extension and neutral radial deviation by the trough
and dowel without requiring straps. Subjects wore custom thimbles made
of thermoplastic splinting material (MaxD, North Coast Medical, Morgan
Hill, CA) with 5-mm brass balls that defined the directions of force
production. A 6-axis dynamometer (Gamma F/T Transducer, ATI Industrial
Automation, Garner, North Carolina; 0.1 N resolution in force axes) was
positioned and rigidly held by a 6-DOF robot arm (Puma 260, Stäubli-Unimate, Faverges, France; 0.5-mm position accuracy) such
that one ball at a time came in contact with the low-friction surface
of the dynamometer. The friction characteristics of the contact
required finger force to be directed within 16° of the surface normal
for the ball in contact not to slip. Fingertip torque had to be zero
for the thimble not to rotate about the contact point. In each 10-s
trial, subjects were asked to sequentially achieve and hold three
fingertip force plateaus (50, 100, and 50% of MVF, in that order) for
2 s under concurrent visual and auditory feedback of the 50% MVF
and 100% MVF targets (see diagram in Table 1). Two sessions were run
on separate days. In the first session, the experimental set-up was adjusted to the dimensions of the subject's hand, and a test trial was
done for each direction to estimate the starting 100% MVF target. The
programmable robot arm quickly positioned and rigidly held the
force-sensing surface against the appropriate aspect of the fingertip,
and subjects performed a battery of three trials in each of the three
directions in randomized order. Subjects were encouraged verbally to
exceed the 100% MVF target in every trial to maximize their force
production. If exceeded, the 100% MVF targets were increased
automatically for that direction and the new maximal value used in all
subsequent trials. The maximal force values recorded in the first
session were used as the starting targets for the second session and
also were adjusted upward if exceeded during the second session. In the
second session on the following day, fine-wire EMG was recorded
simultaneously from all muscles of the forefinger while subjects
repeated the battery of trials in a new randomized sequence.
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Electromyography
Fine-wire intramuscular electrodes were placed in all muscles
and muscle slips acting on the forefinger using previously reported techniques (Burgar et al. 1997). The muscles of the
forefinger are flexor digitorum profundus (FDP),
flexor digitorum superficialis (FDS), extensor indicis
proprius (EI), extensor digitorum communis (EC),
first lumbrical (LUM), first dorsal interosseous
(DI), and first palmar interosseous (PI). EMGs were 100 Hz to 20 kHz band-pass filtered, amplified, full-wave rectified and
smoothed (t = 20 ms), and digitized at 200 s/S. The EMG
signals from each muscle were normalized by dividing by the largest EMG
level found during maximal voluntary contractions of that muscle.
Maximal voluntary contractions of individual muscles were done
immediately before and after fingertip force production with the
forefinger braced in the same posture used for fingertip force
production (Burgar et al. 1997
; Valero-Cuevas et
al. 1998
). This normalization allowed the description of the
level of EMG activity of each muscle as a value between 0 and 1. The
presence of multiple fine-wire electrodes does not significantly affect
fingertip force production (Burgar et al. 1997
).
Definition of fingertip force vectors and EMG coordination pattern vectors
For every sample of every trial (200 S/s over 10 s make 2,000 sample points per trial), the three force components recorded by the force-sensing surface were assembled into a three-dimensional fingertip force vector {fx, fy, fz}T. Similarly, the seven EMG signals from individual muscles were assembled into a "coordination pattern vector" {FP, FS, EI, EC, LUM, DI, PI}T.
Correlation between force and coordination pattern vector magnitudes
The Euclidean magnitude (defined as the square root of the sum of squares of the elements of the vector) of every fingertip force and muscle coordination pattern vector was calculated at every sample of every trial. In this way, as shown in Fig. 4B, the time histories of the vector magnitudes of fingertip force and muscle coordination pattern were obtained for each trial. The Pearson product-moment correlation coefficient between these two time histories was calculated and averaged across trials. Similarly, the correlation coefficient between the time histories of fingertip force vector magnitude and EMG level for each muscle was calculated and averaged across trials.
Definition of force plateaus and transition regions
Force plateaus were defined at the first 50% MVF level, at the 100% MVF level, and at the second 50% MVF level of each trial (Fig. 2). Each plateau was defined as a 750-ms window centered on each of the three periods in which force was held level. For each trial, transition regions a, b and c were defined, respectively, from time 0 to the beginning of the first 50% plateau; from the end of the first 50% to the beginning of the 100% plateau; and from the end of the 100% to the beginning of the second 50% plateau (see the legend in Table 1).
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The average fingertip force vector within each plateau was defined by
averaging each of the three fingertip force components: {fxavg, fyavg,
fzavg}T. Similarly, the
average muscle coordination pattern vector within each plateau was
defined as the average normalized EMG signals from each muscle,
{FPavg, FSavg,
EIavg, ECavg, LUMavg, DIavg,
PIavg}T (Valero-Cuevas
et al. 1998).
Correlation between fingertip force vectors at different levels of fingertip force magnitude
To determine the consistency of force direction during
modulation of force magnitude, the degree of alignment between average fingertip force vectors at different force plateaus was quantified by
the square root of the dot product of their unit vectors. This measure
of alignment is provided by the correlation coefficient between two
unit vectors (Klecka 1989; Strang 1980
),
denoted by a value between 0 (perpendicular) and 1 (parallel). These
correlation coefficients are labeled 1:2, 1:3, and 2:3 in the top half
of Table 1.
The consistency of fingertip force vector direction between transition regions and subsequent force plateaus was calculated similarly. First, the unit vector of the fingertip force vector at each digitized sample in the transition region was calculated. Second, the square root of the dot product of each of these unit vectors with the unit vector of the average fingertip force vector at the subsequent force plateau was calculated and averaged for each transition region of every trial. And third, these average correlation coefficients were averaged across subjects and force directions. These correlation coefficients are labeled a:1, b:2 and c:3 in the top half of Table 1.
Correlation between muscle coordination pattern vectors at different levels of fingertip force magnitude
When the excitation of a muscle is represented as a value between 0 and 1 along an axis, a muscle coordination pattern vector can be thought of as a point in seven-dimensional "muscle space." Then, every muscle coordination pattern vector can be thought of as having a magnitude and direction in seven-dimensional muscle space. Therefore the correlation coefficient (i.e., degree of alignment) between average muscle coordination pattern vectors at different force plateaus also was calculated by the square root of the dot product of their unit vectors. As was done for fingertip force vectors in the preceding text, the correlation coefficients between muscle coordination pattern vectors at different force plateaus were calculated and labeled 1:2, 1:3, and 2:3 in the bottom half of Table 1. Similarly, the correlation coefficients of muscle coordination pattern vectors in a transition region with the average muscle coordination pattern vector in the subsequent plateau were calculated, averaged, and labeled a:1, b:2 and c:3 in the bottom half of Table 1.
Statistical analysis of muscle coordination patterns at each force plateau
For each force plateau in each force direction, average muscle
coordination pattern vectors from all subjects were pooled, and
repeated-measures ANOVA was used to test for differences among EMG
signals from individual muscles (Valero-Cuevas et al.
1998). When a significant difference was found, Turkey-Kramer
post hoc pairwise comparisons were used to test for significant
groupings of EMG signals within the average coordination patterns
vectors. In this way, a muscle coordination pattern for each force
direction was described statistically in absolute terms as the ranking
of muscles by EMG level (Valero-Cuevas et al. 1998
).
This ranking succinctly conveys the coordination pattern by indicating
the statistical differences in excitation levels among muscles.
Prediction of muscle coordination patterns capable of producing 50% of maximal fingertip force magnitude
A previously validated three-dimensional, seven-muscle,
four-joint musculoskeletal computer model of the forefinger was used to
predict different muscle coordination patterns that can produce 50% of
maximal biomechanically possible fingertip force (Valero-Cuevas et al. 1998). The model is a matrix equation that relates
coordination pattern vectors to fingertip force vectors. The model was
used to predict different muscle coordination patterns that can produce 50% of maximal fingertip force, consistent with the 50% MVF force plateaus and finger posture of the experimental part of this study.
The model uses computational geometry to identify coordination patterns
that can produce maximal and submaximal fingertip forces in a specific
direction as previously described by Valero-Cuevas et al.
(1998). Briefly, the excitation of a muscle is modeled as a
value between 0 and 1 along an axis. By assembling as many orthogonal
axes are there are muscles, a modeled muscle coordination pattern
vector also can be thought of as a point in seven-dimensional muscle
space. Furthermore every possible muscle coordination pattern vector is
contained in the positive seven-dimensional hyper-cube of sides of
length one. Its 128 vertices define the boundary of the hyper-cube. A
functional specification of fingertip force direction and fingertip
torque magnitude is interpreted geometrically as a constraint plane
that contains all possible coordination patterns that satisfy the
functional constraint. Thus, the region of the hyper-cube that
satisfies all constraints is the intersection of all such hyper-planes
with the hyper-cube. Computational geometry algorithms (Avis and
Fukuda 1992
) identify 46 vertices that describe the region of
the hyper-cube containing all possible muscle coordination patterns
that produce fingertip forces with zero medial-lateral force and zero
fingertip torque components. These functional constraints on fingertip
force direction and torque are equivalent to those imposed on subjects
when producing palmar, dorsal, and distal fingertip forces. Multiplying
all 46 coordination pattern vertices through the musculoskeletal model
matrix equations resulted in 46 fingertip force vectors
(Chvátal 1983
). Twelve of the 46 fingertip force
vectors define the boundary of the feasible force polyhedron that
specifies the biomechanical limit on fingertip force magnitudes (Fig.
3A) (Chvátal
1983
; Valero-Cuevas et al. 1998
). The distance from the origin to a point on the boundary of the feasible force polyhedron in a given three-dimensional direction is proportional to
the maximal fingertip force that can be produced in that direction (Fig. 3A). Because every point along a face of the boundary
is uniquely defined by the weighted sum of the vertices that define that edge, every maximal fingertip force (i.e., point on the boundary) also is produced by a unique muscle coordination pattern (Chao and An 1978
; Kuo and Zajac 1993
; Spoor
1983
; Valero-Cuevas et al. 1998
). In contrast,
points internal to the boundary can be produced by different vector
sums of vertices. Thus a geometric interpretation of redundancy of
control of finger musculature is that every submaximal force, i.e.,
point internal to the boundary, can be achieved by more than one vector
sum of force vertices. Figure 3, B-D, shows three such
solutions for palmar force using force vertices from the boundary. The
coordination pattern that achieves each of the vector sums of force
vertices then is found by applying the same vector sum to the unique
coordination patterns associated with the force vertices used (see Fig.
3, B-D). A combination of two force vertices is considered
biomechanically valid if the coefficients of their vector sum and the
resulting muscle excitations are positive values between 0 and 1 (i.e.,
fingertip forces and tendon tensions act only in their positive sense).
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This geometric interpretation of redundancy of finger musculature
control was used to predict different muscle coordination patterns that
can produce fingertip force magnitudes of 50% of maximal in the
dorsal, palmar, and distal directions. For each force direction, an
ordered lexicographic search tested all possible combinations of 2 of
the 46 force vertices to find valid coordination patterns that can
produce 50% of maximal force.
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RESULTS |
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Correlation between fingertip force vectors at different levels of fingertip force magnitude
The direction of fingertip force vectors remained consistent while subjects varied the magnitude of fingertip force vectors over the voluntary range. The correlation coefficient between average fingertip force vectors at different plateaus was in excess of 0.99 (comparisons labeled 1:2, 1:3, and 2:3 in the top half of Table 1) and in excess of 0.97 (comparisons labeled a:1, b:2, and c:3 in the top half of Table 1) between force vectors in the transition regions and the average fingertip force vector in the subsequent force plateau. Figure 4A shows a three-dimensional view of the time history of fingertip force vector for one representative fingertip force in the distal direction.
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Correlation between muscle coordination pattern vectors at different levels of fingertip force magnitude
Similarly, the coordination pattern vectors maintained a consistent seven-dimensional direction in muscle space while producing fingertip forces of different magnitudes. Average coordination pattern vectors were correlated highly between plateaus (in excess of 0.96; see comparisons labeled 1:2, 1:3, and 2:3 in the bottom half of Table 1) as were coordination pattern vectors in the transition regions with the average coordination pattern vector in the subsequent force plateau (in excess of 0.95; see comparisons labeled a:1, b:2, and c:3 in the bottom half of Table 1). The high correlation between measured coordination pattern vectors at different force magnitudes suggests subjects altered the vector magnitude of the motor command, whereas the vector direction of the motor command remained consistent.
Correlation between force and coordination pattern vector magnitudes
The vector magnitudes of coordination patterns and fingertip forces were highly correlated (0.89 ± 0.06, 0.88 ± 0.05, and 0.91 ± 0.07 for dorsal, palmar, and distal forces, respectively; column labeled CP in Fig. 5). Figure 4, B and C, shows the time histories of fingertip force and coordination pattern magnitudes for the trial shown in Fig. 4A. The correlation of some muscles with fingertip force magnitude was statistically similar to that of the coordination pattern with force (gray box plots in Fig. 5, P < 0.05). Other muscles had a statistically lower correlation with fingertip force magnitude (white box plots in Fig. 5, P < 0.05).
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Doubling or halving fingertip force magnitude between force plateaus was associated with a similar change in average coordination pattern vector magnitudes. For all force directions, the ratio of average fingertip force vector magnitudes between the 100 and 50% force plateaus was 2.07 ± 0.51. The corresponding ratio for coordination pattern vector magnitudes was 1.86 ± 0.62. Comparing across force directions, the average fingertip force ratios were lowest for palmar force (1.93 ± 0.32) and highest for distal force (2.18 ± 0.78; P < 0.05). This difference also was found in coordination pattern vector ratios, which were significantly higher for distal force (2.06 ± 0.64) than for palmar and dorsal forces (1.64 ± 0.56 and 1.80 ± 0.58, respectively; P < 0.05).
EMG signals from individual muscles also reflected the changes in fingertip force magnitude. For dorsal force, the ratio of average EMG signal between the 100 and 50% force plateaus ranged between 1.61 ± 0.41 for dorsal interosseous to 2.31 ± 1.13 for lumbrical, which were significantly different (P < 0.05). For palmar force, palmar interosseous had the lowest ratio (1.16 ± 0.30) and extensor muscles the highest ratios (2.30 ± 1.8 and 2.25 ± 1.76, respectively, P < 0.05). Last, for distal force, extensor muscles had the lowest ratios (1.53 ± 0.79 and 1.50 ± 1.33, respectively) and dorsal interosseous with the highest (2.43 ± 1.3; P < 0.05). Note that the muscles with the lowest ratios for palmar and distal forces are also among the muscles that are excited the least in these force directions (see Table 2).
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Statistical analysis of muscle coordination patterns at each force plateau
Subject-independent muscle coordination patterns were found for
fingertip force production in all three directions at the 50% MVF
plateaus. For all force directions (Table 2), the statistical rankings
of average EMG levels among muscles seen at both 50% force plateaus
were similar to each other and consistent with coordination patterns
reported in an earlier study for 100% MVF (Valero-Cuevas et al.
1998). Although there were instances of individual muscles
changing rank order among force plateaus, only in four cases did a
muscle become part of a statistically different grouping (see solid
lines between columns in Table 3). The
remaining six instances of rank changes did not affect the statistical
ranking of muscle groups.
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Prediction of muscle coordination patterns capable of producing 50% of maximal fingertip force magnitude
The musculoskeletal model of the forefinger predicted that
dramatically different muscle coordination patterns can produce fingertip force magnitudes of 50% of maximal in the three force directions studied. In all, 72 valid coordination patterns were identified for dorsal force, 99 for palmar force, and 73 for distal force. All valid coordination patterns for 50% of maximal force for
each force direction were summarized as excitation level histograms for
each muscle in each force direction (see Fig.
6). The excitation level histograms show
that some muscles can have more variability than others when producing
fingertip force magnitudes of
50% of maximal in all three force
directions. In particular, extensor, and lumbrical muscles
can be excited between 63 and 100% of their excitation range; and
dorsal and palmar interosseous muscles between 27 and 63% of their excitation range. In contrast, flexor muscles can
only be excited over 25% of their excitation range for dorsal and
palmar forces and over a broader range for distal force.
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DISCUSSION |
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There is much kinematic and kinetic evidence suggesting that the
control of manipulation is simplified by memory and sensory-modulated scaling of stereotypical profiles of hand displacement and grasp force
(Cole and Johansson 1993; Forssberg et al. 1991
,
1992
, 1995
; Gordon et al. 1992
; Johansson
1996
). This study provides evidence that the control of the
redundant musculature of the forefinger also is simplified when
sequentially producing fingertip forces of different magnitudes by
scaling a coordination pattern capable of producing the largest
expected force. Because modulating fingertip force magnitudes is
essential to dexterous manipulation (Murray et al.
1994
), this scaling strategy also may simplify the control of
the manipulation skills common to daily living. However, to truly
investigate everyday manipulation strategies, additional studies are
needed that extend the methodology presented here to multiple fingers.
This study is unique in examining complete muscle coordination patterns for a finger while fingertip force magnitude is modulated independently of other functional factors. An experimental paradigm was used in which subjects modulated fingertip force magnitude over the entire voluntary range while force direction, finger posture, and amount of fingertip torque were held constant. This justified interpreting changes in EMG muscle coordination pattern vectors as the encoding of descending motor commands that modulated force magnitude.
The limitations of EMG data should be taken into account when
interpreting the results. EMG is an indirect, yet practical, estimate
of the neural drive to a muscle that has a strong stochastic component
(Basmajian and De Luca 1985). Moreover, the relationship between EMG and force is known to change with force magnitude and
muscle type (Basmajian and De Luca 1985
; Lawrence
and De Luca 1983
) and excitation history
(Bigland-Ritchie et al. 1983
; Burke et al.
1976
; Zajac and Young 1980
). Also, muscle fiber
shortening due to stretching of passive musculo-tendon elements in
isometric contractions further affect relationship between force and
EMG (Zajac 1989
). Thus the relationship between EMG and
muscle force cannot be considered linear over the entire range of
activation. The cumulative effect of these EMG-related artifacts is to
add to the variability in the direction and magnitude of the excitation pattern vectors assembled. Therefore the consistency among EMG coordination patterns for 50 and 100% force plateaus may only be
interpreted as an indication of motor command similarity not equality
(Tables 2 and 3). These changes in the relationship between EMG and
force at different levels of activation also may explain in part the
discrepancy between curves in Fig. 4B as well as the
hysteresis for the ramp-up and ramp-down phases in Fig. 4C.
Also, muscles that are excited at lower levels (i.e., EI and EC for
distal force, Tables 2 and 3) will naturally have lower correlation
coefficients with force because the influence of the stochastic
component of EMG will be greater. Last, these EMG-related artifacts
also may explain why the correlation between coordination pattern
vectors is lower than the correlation between fingertip force vectors
(Table 1).
The vector magnitude and vector direction of a coordination pattern can change in one of three ways when adjusting fingertip force magnitude. First, both the vector magnitude and direction of the coordination pattern can change. Second, the vector direction, but not magnitude, of the coordination pattern can change. These two cases can be achieved by altering the number of active muscles and the relative excitation among them as fingertip force magnitude is adjusted And third, the hypothesis of this study, the vector magnitude, but not direction, of the coordination pattern can change. A single joint musculoskeletal model with two agonist and one antagonist muscles can be used to show examples of all three cases.
Some studies have proposed that different coordination patterns are
used to produce different magnitudes of a given fingertip force vector
(Chao et al. 1989; Cooney et al. 1985
;
Maier and Hepp-Reymond 1995a
). These EMG studies
proposed that the number of active muscles varies with fingertip force
magnitude with primary muscles active throughout the force range,
secondary muscles contributing to the intermediate range, and tertiary
muscles contributing only at the highest range of force magnitude.
However, their results were not conclusive because they did not find
statistically significant muscle coordination patterns at each force
level, probably because the experimental paradigms of these studies did
not isolate force magnitude from force direction or control the posture
of the digit studied. Thus the reported differences in number of active
muscles for low, moderate, and high force magnitudes reported by
Cooney et al. (1985)
and Chao et al.
(1989)
may be due to changes in force direction or digit
posture, which would require different muscle-coordination patterns.
The ramp-and-hold study of fingertip forces of low magnitude by
Maier and Hepp-Reymond (1995a)
qualitatively reported a
constant set of muscles active in each subject that were thought to be
the primary muscles for that subject. However, moderate- and high-force
magnitudes were not collected. Moreover, the high EMG scatter reported
for all subjects underscores that artifacts particular to low force
production may obscure the detection of motor strategies. These include
the nonlinearities at the low end of the force-EMG curve
(Basmajian and De Luca 1985
; Lawrence and De Luca
1983
), and the stronger variability in the relationship between
EMG and force caused by other modulating factors such as the influence
of peripheral receptors (Garnett and Stephens 1981
).
This study presents several lines of evidence that scaled versions of a
given muscle coordination patterns are used to produce different
magnitudes of a given fingertip force vector. First, the high
correlation between vector magnitude of fingertip forces and
coordination patterns (Fig. 5) suggests that the magnitude of the
descending motor command is correlated tightly with fingertip force
magnitude. In this study, the correlation of fingertip force with
coordination pattern vector magnitude is as high, and often higher,
than correlations with individual muscles (Fig. 5). In fact, the
correlation coefficients of EMG from individual muscle with fingertip
force in this study are generally higher than those reported in
previous studies of finger musculature (Chao et al. 1989; Cooney et al. 1985
; Maier and
Hepp-Reymond 1995a
). It is likely that the strict mechanical
definition of the experimental task (see METHODS) played a
major role in obtaining a strong correlation of EMG and force.
Furthermore the consistency of EMG signals in this study was probably
enhanced by studying force magnitudes spanning the voluntary range
(reducing EMG artifacts particular to low force production) and using
fine-wire electrodes (less susceptible than needle electrodes to muscle
fiber migration artifacts during muscle contraction).
Second, the consistent vector direction of coordination pattern shows
that the relative level of excitation among muscles remained uniform
during the modulation of fingertip force magnitude over the voluntary
range. Whether or not the vector directions of coordination patterns at
each force magnitude are identical is beyond the resolution of the
intramuscular EMG data (Basmajian and De Luca 1985) and
may not be a realistic expectation for biological signals. Nevertheless
the results show both in relative and absolute terms, a high
consistency of descending motor command during the modulation of
fingertip force magnitude. In relative terms, the lower half of Table 1
shows a high correlation between seven-dimensional coordination pattern
vectors in muscle space both in the low-force range (0-50% MVF,
comparison a:1) and the high-force range (50-100% MVF, comparisons
b:2 and c:3). Furthermore doubling fingertip force magnitude between 50 and 100% MVF plateaus produced a ratio for coordination pattern vector
magnitudes close to two. In absolute terms, Tables 2 and 3 show
statistically significant muscle coordination patterns for 50% MVF
levels that are similar to each other and consistent with coordination
patterns reported by us for 100% MVF (Valero-Cuevas et al.
1998
). Previous studies of submaximal forces have not found
subject-independent, statistically significant muscle coordination
patterns (Close and Kidd 1969
; Maier and
Hepp-Reymond 1995a
). Although there are instances in these
results of individual muscles changing rank order (see horizontal lines
between columns in Table 3), these changes do not affect the
statistical ranking of muscle groups. A detailed description of the
biomechanical interpretation of these coordination patterns has been
published (Valero-Cuevas et al. 1998
).
And third, in contrast to the observed consistency of coordination
patterns, the previously validated musculoskeletal model here predicts
that 50% of maximal fingertip force can be produced by coordination
patterns that are drastically different from those needed for 100%
MVF. The model predicts extensor, interosseous, and
lumbrical muscles can be excited at very different levels and still produce a well-directed fingertip force of 50% MVF. Because the tendons of the extensor, lumbrical, and
palmar interosseous muscles insert into a common network
(Zancolli and Cozzi 1992
), the particularly broad
latitude in their excitation may be due to different individual muscle
forces producing the same net torque at the joints spanned by this
network. Because there is conceivably an infinite number of
coordination patterns capable of producing 50% MVF, the excitation
ranges shown here are necessarily an underestimate. Finding additional
valid coordination patterns can only increase the excitation ranges
shown and strengthen the conclusions of this study.
The fact that this study focused on the performance of learned finger
tasks that are strictly defined does not make these conclusions
inapplicable to the control of grasping in general. Recent and distant
learning and memory are instrumental in the predictive control of the
kinematics and kinetics of reaching and grasping (Forssberg et
al. 1992; Johansson 1996
). Thus the expectation
of producing large fingertip force magnitudes, and the recent memory of
previous trials, may have contributed to the consistency of muscle
coordination patterns at submaximal force magnitudes. This study
suggests that the control of muscle coordination during learned
grasping may also be predictive. Additional studies of muscle
coordination patterns used for unknown and unexpected force magnitude
targets in naïve subjects need to be done to reveal the extent
to which distant learning and memory affect motor control strategies in
finger musculature.
The rapid and consistent adjustment of fingertip forces is
essential for dexterous manipulation. Individual digits are the building blocks of manipulation function (Murray et al.
1994), and thus simplifying the control of individual digits
naturally simplifies the control of dexterous manipulation in general.
Also, well-directed fingertip forces with no associated fingertip
torque are necessary to grasp small and/or slippery objects
(Murray et al. 1994
), and fingertip forces that can
grasp slippery objects also can grasp a high-friction objects but not
vice versa. It is, of course, possible that humans change the control
strategy as the mechanical constraints of the task become relaxed
(e.g., by the presence of friction or a broader contact surface that allows the production of fingertip torque). Nevertheless using a
stringent mechanical definition of the task in this study was useful to test the hypothesis that scaling of muscle coordination patterns is a simplifying strategy to control the redundant
musculature of the digits. It is likely that the forefinger and other
digits also can use this control strategy to scale the magnitude of
fingertip forces under more relaxed mechanical conditions and other
force directions. This study is the first to provide evidence of motor strategies at the level of the coordination of redundant finger muscles
and reveals a neural process that may be instrumental to
dexterous manipulation.
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ACKNOWLEDGMENTS |
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The author thanks Dr. Charles G. Burgar and M. E. Johanson, MS, PT, for placing EMG electrodes and Joseph Towles, MS, and Drs. Felix Zajac, Zoia Lateva, and Peter Lum for insightful comments on the earlier drafts of this manuscript.
The Rehabilitation R and D Service of the Department of Veterans Affairs (VA) supported this work.
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FOOTNOTES |
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Address for reprint requests: F. J. Valero-Cuevas, Neuromuscular Biomechanics Laboratory, 222 Upson Hall, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853.
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 29 June 1999; accepted in final form 30 November 1999.
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REFERENCES |
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