Coordination and Inhomogeneous Activation of

1. In this study we have recorded the activ- ity of motor units of the important ... flexor muscles under varying conditions ( 1,7, ...... Basel, Karger, 198 1, vol. 9, p.
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JOURNALOF NEUROPHYSIOLOGY Vol. 60, No. 5, November 1988. Printed

in U.S.A.

Coordination and Inhomogeneous Activation of Human Arm Muscles During Isometric Torques E. J.

VAN

ZUYLEN,

c. c. A. M. GIELEN,

AND

J. J. DENIER

VAN

DER

GON

Departmentof Medical and PhysiologicalPhysics,Universityof Utrecht, NL 3584C Utrecht, The Netherlands

SUMMARY

AND CONCLUSIONS

1. In this study we have recorded the activity of motor units of the important muscles acting across the elbow joint during combinations of voluntary isometric torques in flexion/extension direction and supination/ pronation direction at different angles of the elbow joint. 2. Most muscles are not activated homogeneously; instead the population of motor units of muscles can be subdivided into several subpopulations. Inhomogeneous activation of the population of motor units in a muscle is a general finding and is not restricted to some multifunctional muscles. 3. Muscles can be activated even if their mechanical action does not contribute directly to the external torque. For example, m. triceps is activated during supination torques and thus compensates for the flexion component of the m, biceps. On the other hand, motor units in muscles are not necessarily activated if their mechanical action contributes to a prescribed torque. For example, there are motor units in the m. biceps that are activated during flexion torques, but not during supination torques. 4. The relative activation of the muscles depends on the elbow angle. Changing the elbow angle affects the mechanical advantage of different muscles differently. In general, muscles with the larger mechanical advantage receive the larger input. 5. We have calculated the relative contributions of some muscles to isometric torques. These contributions depend on the combination of the torques exerted. 6. Existing theoretical models on muscle coordination do not incorporate subpopula0022-3077/B

tions of motor units and therefore need to be amended. INTRODUCTION

.One of the important aims of research on motor control is to acquire an understanding of the coordinated activation of synergistic and antagonistic muscles. In general more than one muscle contributes to a torque in a particular movement direction such as flexion of the elbow joint. Consequently, many attempts have been made to find out in what ratio m. biceps, m. brachialis, and m. brachioradialis contribute to flexion torques. The contribution of each muscle to a particular torque generally depends among other things on its activation, its mechanical advantage, and on its length-tension relationship. Different authors have given conflicting descriptions of the relative activation of arm flexor muscles under varying conditions ( 1,7, 19, 23). A particular solution to the problem of redundancy has been proposed by Bouisset (2, 3) who introduced the concept of the “muscle equivalent.” According to this concept there is a constant relationship between the activation levels of the synergistic muscles. Bouisset thereby lumps synergistic muscles together as a single functional unit. In previous studies (17, 18) it has been shown that the activation of various motor units in the long head of the m. biceps brachii may depend in different ways on combined isometric contractions in flexion and supination direction. The results demonstrated the existence of at least three different subpopulations of motor units, each with a different homogeneous activation. The recruitment order within one subpopulation is fixed and

$1.50 Copyright 0 1988 The American Physiological Society

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may well be in agreement with the “size principle” (20, 2 1). Other evidence for a selective activation of motor units in a single muscle has been presented by Hoffer et al. (22) who found three discrete groups of motoneurons within the motoneuron pool of the cat sartorius muscle each being activated during different phases of normal locomotion. Comparable findings have been reported for human finger muscles (12, 13, 28, 3 1). If subpopulations of motor units are found to exist in more muscles, then clearly a modification of the concept of the “muscle equivalent” is required since groups of subpopulations, rather than groups of muscles, seem to act together for a particular motor task. The existence of subpopulations also stressesthe inadequacy of surface electrodes for making a detailed study of muscle activation and it might explain some of the discrepancies in the results of the various authors mentioned above. One of the aims of this study was to verify the existence of subpopulations of motor units in muscles other than the m. biceps. Some muscles contribute to torques in different directions (e.g., m. biceps: flexion and supination; m. pronator teres: flexion and pronation). Major parts of these muscles are activated when torques in either of these directions are exerted. It was found that the recruitment thresholds of motor units of the m. biceps depend on a linear combination of isometric flexion and supination torques (18). This has consequences for the distribution of activation of the other muscles involved (4,28,29). When, for example, a supination torque is added to a flexion torque the activation of the m. biceps is increased. As a consequence the flexion torque exerted by the m. biceps increases. To keep the external flexion torque constant the activation of another flexor muscle (e.g., m. brachialis) has to be decreased or the activation of the m. triceps has to be increased. This suggests that the activation of a single muscle cannot be understood solely from the anatomy of this single muscle and from its tendon insertion and origin. Instead one has to consider the contribution of all muscles acting across this joint. Recent data of Buchanan et al. (4) support this hypothesis, that will be further examined in this study. When the angle between two limb segments is changed, the mechanical advantage

ET AL.

of the muscles acting across this joint changes differently for each muscle. The length-tension relationship of muscles as a function of the joint angle differs too (34). Therefore, the relative contribution of muscles to torque around a particular joint is likely to change as a function ofjoint angle. This means that the relative activation of muscles should also depend on joint angle (11, 23). To investigate this issue, motor unit activity has been recorded during isometric contractions at different joint angles. Several theoretical models have been proposed to explain the concerted action of muscles in particular motor tasks (8, 9, 14- 16, 26). However, most of these models have not been adequately verified, because there is a lack of data on the activation of these muscles. This paper provides additional material on the basis of which the various theoretical concepts that have been proposed can be evaluated. METHODS

Experimental

set-up

Data were obtained in ~40 experiments from 8 normal subjects who gave informed consent. The right arm of the subject was in a horizontal plane. The forearm was held in a neutral position between full supination and full pronation. The angle between the frontal plane and the upper arm was -25”. The elbow joint angle could be varied between 40 and 180” (full extension). The wrist was tightly clamped in a force-measuring device with the help of a plaster cast. Torques in flexion/ extension, supination/pronation, and exorotation/intrarotation (valgus/varus) direction were measured independently without cross talk and simultaneously in all three directions. Torques were measured by means of strain gauges using a modification of a device described earlier by ter Haar Romeny et al. ( 18). With this device torques could be measured with a precision < 10 rnN* m in each direction. Motor-unit activity was measured with intramuscular fine wire electrodes (material: Karma, nylon coated, 25pm diam., Californian Fine Wire Co.). In each experiment intramuscular wire electrodes were inserted into several muscles (usually 3-4). In this way motor-unit activity in different muscles could be studied simultaneously. The wires were inserted by means of a hollow needle (0.4-mm diam., four wires per insertion) that was subsequently withdrawn. After amplification the EMG signal was bandpass filtered from 320 Hz to 32 kHz. Often up to four motor units could be dis-

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the subjectabout the torquesexerted in the three directions. In eachtrial the subjectwasinstructed to increasean isometrictorque slowly in a particular direction (e.g., flexion) to a prescribedlevel. While keeping this torque constant the subject then had to gradually increasetorque in another direction (e.g.,supination).This procedurewasrepeated for about eight different torque levels in eachdirection. The contractions were performed at a slow rate to prevent phasicrecruitment from interfering with the results(6, 13, 33). The speed of the contraction wastypically ~2% of the maximum voluntary contraction per secondin eachdirection. In all experimentstorquesin exorotation and intrarotation direction hadto be kept at zero. Experimental protocol The sequencein which the torques had to be inThe recruitment behavior of motor units in m. creasedaswell asthe prescribedtorque levelswere brachialis,m. brachioradialis,m. biceps(the long varied in random order. Betweensubsequentconhead, as well as the short head in a few experi- tractions the subjectwasallowedto relax the arm ments), m. supinator, m. pronator teres, and m. musclesfor at least0.5 min (10). triceps(long head, medialhead,and lateral head) When all relevant combinationsof torqueshad wasinvestigated.During the experimentstorques beentestedseveraltimes,the elbowjoint anglewas in the three directionstogetherwith the intramus- slowly changedby the experimenter. During the cular EMG signalswererecordedon an FM instru- movement motor unit activity wascontinuously mentation recorder (Honeywell type 101, band- monitored so that, if possible,activity from the width from DC up to 5 kHz) for off-line analysis. samemotor units could be studied in other arm Cursorson an oscilloscopeprovided feedbackto positions.Different elbow angleswere attained in

tinguished in one bipolar recording. If there was any doubt about the precise location of the recorded motor units, the muscle containing the wires was identified by electrical stimulation via the same wires before the wires were removed at the end of the experiment. The maximum voluntary torques for the different subjects ranged from 55 to 75 No m in flexion direction, from 40 to 60 N. m in extension direction, from 8 to 12 No m in supination direction and from 7 to 10 N m in pronation direction. The recruitment thresholds of motor units recorded in this study range up to 40% of thesevaluesin the various directions. l

BICEPS

EMC

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.1

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FIG. 1. Typical example of a recording and analysis of motor-unit activity in combination with exerted torques. On the left side of this figure in the upper trace the EMG signal recorded in the long head of the m. biceps is shown as a function of time. The middle and lower traces represent actively exerted torque in supination and flexion direction. First, the subject increases the torque exerted in supination direction and motor-unit activity can be seen in the EMG trace. Next the supination torque is kept approximately constant and the flexion torque is increased. The recruitment of 3 motor units is indicated in each torque trace with corresponding symbols. On the right the same symbols are used in a 2-dimensional plane to indicate the combination of torques in flexion and supination direction at which the 3 motor units are recruited.

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ET AL.

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2.5 FIG. 2. Examples of motor-unit behavior recorded in the m. biceps. Each point indicates the combination of torques at which a motor unit was recruited. Different symbols indicate different motor units. A: motor units that are

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FIG. 3. Recruitment thresholds in flexion direction (FR) and in supination direction (&) for type A motor units of the m. biceps (summing units). Symbols containing a dot are used to indicate results for motor units of the short head of the m. biceps. Different symbols indicate different elbow angles. 0: 100”. *: 130”. o: 160”. The ratio between the recruitment thresholds (SR/FR) tends to increase with increasing elbow angle.

a randomorder. At a new arm position the subject wasfirst askedto relax the arm musclescompletely and passivelyexertedtorqueswere measured.The actively exerted torques were calculated by correctingfor the passivetorques. Subjectswere specificallyinstructedto relax the musclesat the wrist and shoulderjoint. This instruction was intended to eliminate co-contraction of muscles,thereby reducing variability of muscle activation at a particular combination of flexion/extension and supination/pronation torques.

Data analysis During the off-line analysis,we measuredthe combination of torques in the flexion/extension direction and in the supination/pronation direction at which a particular motor unit startedfiring. The left part of Fig. 1 showsa typical exampleof

the recordingof an EMG signalfrom the long head of the m. bicepsandthe correspondingactively exerted torques during a combined isometric contraction in flexion and supinationdirection. In the EMG signalthe recruitment of three motor units can be clearly observed.In the torque tracesthe combinationof torquesat which thesemotor units are recruited is indicated by different symbols.In the right part of Fig. 1 the combinationsof these torques are plotted in a two-dimensionalplane with torque in flexion/extension direction on the abscissaand torque in supination/pronation direction on the ordinate. The recruitment thresholdsobtained for contractions with different combinations of torque were plotted in similar figuresfor all motor units. This givesplotswith symbolsthat indicatehowthe recruitment threshold of a particular motor unit dependson the torquesexertedin the different di-

recruited when torques in both flexion and supination direction are exerted: summing units. Closed symbols represent results from a motor unit recorded in the long head of the m. biceps; open symbols represent results from a motor unit recorded in the short head. For the latter motor unit the recruitment thresholds for flexion (FR) and supination (SR) are indicated. These results were obtained at an elbow angle of 110”. B: motor units from the long head of the m. biceps that are recruited only when a particular torque in flexion direction is exerted: flexion units. These results were obtained at an elbow angle of 100”.

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rections. The resulting data points can be described as if they are scattered around sets of straight lines with junctions at or near the axes. We therefore assume that the recruitment of the motor units for particular combinations of torques depends on a linear combination of the exerted torques. The slope of the lines may change abruptly at or near the intersection with the axes that correspond to the main torque directions. This finding corresponds to earlier findings described by ter Haar Romeny et al. ( 17, 18). For torques in flexion and supination direction the recruitment lines describing the linear relation between combinations of torques where the motor unit is recruited can now be described by the equation F/FR + S/!& = 1

(0

or, after rewriting, by the equation S=&-

(SR/FR)F

(2)

where FR and SR represent the recruitment thresholds of the motor unit for flexion (F) and supination (S), respectively. F, FR and S, SR have to be replaced by E, ER and P, PR when the direction of the contraction is extension instead of flexion or pronation instead of supination. The data obtained at different elbow angles have been pooled in groups from 55 to 85” (average 70”), 85 to 115” (average loo”), 115 to 145” (average 130”) and 145 to 175”, which is near full extension (average 160”). The data obtained from corresponding muscles of all subjects were pooled by using the absolute torque exerted by each subject. This procedure was allowed because the behavior of motor units did not clearly differ between subjects (See also DISCUSSION). We took great care to ensure that during the analysis of data of a motor unit, only recruitment thresholds of that particular motor unit were included. This was achieved by continuously monitoring the shape of the action potentials on a large oscilloscope screen with the help of a window trigger and a delay-line. It was not always possible to record from the same motor unit at different elbow angles because sometimes a change in elbow angle changed the shape of the action potential to such a degree that we were not sure of its identity (24). In such a case we resumed the experiment by studying another motor unit. The number of times a particular motor-unit behavior was observed is given in each table and figure, if relevant. For calculations, for instance concerning the relative activation of muscles, we have indicated the number of motor units included at the various elbow angles. These numbers may be different because of the problems mentioned with respect to the identification of motor units at different elbow angles. All population statistics are represented as the mean and the stan-

ET AL.

dard error of the mean. Statistical differences between averages were tested using a t test. RESULTS

M. biceps In Fig. 2 examples are presented of motorunit behavior observed in the long head of the m. biceps. Two types of motor-unit behavior were found in this muscle: units for which recruitment threshold depends on flexion torque only (“flexion units”) and units for which recruitment threshold depends on torques in both flexion and supination direction (“summing units”). These types of motor units have also been found by ter Haar Romeny et al. ( 18). An illustration of the recruitment behavior of summing units is shown in Fig. 2A. Extension torques do not affect the recruitment threshold of these motor units, nor do pronation torques. If the sequence in which the torques are increased is changed, the combinations of torques at which a particular motor unit is recruited shows the same linear relation as the data points obtained with the original sequence. Also, when in control experiments, torques in different directions were raised simultaneously, the motor units were recruited at a combination of torques situated around the recruitment line of this motor unit. In Fig. 3 a summary is presented of all motor units of the type shown in Fig. 2A (n = 18). The data points in Fig. 3 give the values for FR and SR for different elbow angles. All data points for a certain elbow angle scatter around an approximately straight line, which in good approximation passes through the origin. In a linear least squares fit the intercept at the ordinate did not differ significantly from the origin. This indicates that the ratio between the recruitment thresholds in flexion and supination direction for a given elbow angle is independent of the recruitment threshold of the motor units. Therefore the recruitment behavior of the motor units of this type can be summarized by the ratio SR/ FR. Similarly, the recruitment behavior for torques in other directions can be summarized by the ratios PR/FR, SR/FR, and PR/ER for each motor unit. For an elbow angle of 100” the average ratio between the recruitment thresholds SR/FR is 0.18 t 0.01 (SE), which is in agreement with the results of ter

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(NM)

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FIG. 4. Examples of the recruitment behavior of motor units of the m. brachialis and m. brachioradialis. Each point indicates the combination of torques at which a motor unit was recruited. Different symbols represent data from different motor units. A: recruitment threshold for flexion is independent of the exerted level of pronation, but increases with increasing supination torque. Motor units recorded from the m. brachialis at an elbow angle of 100”. B: recruitment threshold for flexion is increased by additional supination or pronation torques. Motor units recorded from the m. brachioradialis at an elbow angle of 65”. C: recruitment threshold for flexion is independent of exerted supination or pronation torques. Motor units recorded from the m. brachialis at an elbow angle of 90”.

Haar Romeny et al. (18). The averaged results are summarized in Table 1. It appears from Fig. 3 that for elbow angles exceeding 100” the ratio SR/FR tends to increase. This can also be concluded from the data in Table 1. The behavior of the recruitment thresholds for flexion and supination torques (SR and FR) at different elbow angles will be described in more detail in the subsection Behavior at other elbow angles.

Figure 2B shows two examples of the recruitment behavior of flexion units. The motor units of this type (n = 5) are not included in Fig. 3 because it was not possible to recruit these motor units by exerting a supination torque only. Units of this type were consistently found in the lateral part of the long head of the m. biceps. In this study flexion recruitment thresholds for these motor units ranged from 0.7 to 20 Nom.

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0 FIG. 5. Recruitment thresholds of motor units in the m. brachialis and m. brachioradialis for different elbow angles. 0: 70°. 0: 100’. *: 130°, q : 160'. Symbols with a dot refer to motor units recorded in the m. brachioradialis. A:

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FIG. 6. Examples of motor-unit behavior of the m. supinator. Flexion increases the recruitment threshold for supination, whereas extension hardly affects the threshold. Each point indicates the combination of torques at which a motor unit was recruited. Different symbols refer to different motor units. Results obtained at an elbow angle of 90”.

In this study we have not investigated motor units at medial locations in the long head of the m. biceps. Because a previous study ( 18) has shown that the medial site of the long head of m. biceps contains motor units the recruitment threshold of which depends on the supination torque only, we have not found any “supination units” in this study. In two experiments we recorded the behavior of motor units of the short head of the m. biceps. Only summing units were found. The data for these experiments are shown in Fig. 3 with symbols containing a dot. The recruitment behavior of these units did not clearly differ from the behavior of motor units found in the long head of the m. biceps. This finding

is consistent with the results of ter Haar Romeny et al. (18). AL brachialis/m. brachioradialis In Fig. 4 examples are presented of the behavior of motor units recorded in the m. brachialis and m. brachioradialis. Three subpopulations of motor units can be distinguished in both muscles. For two types of motor units the recruitment threshold for different combinations of torque in flexion and supination/pronation direction is shown in Fig. 4, A and B (n = 19). The recruitment threshold for flexion is raised when supination torques are exerted simultaneously. These motor units differ only with respect to their behavior dur-

recruitment threshold for flexion (FR) and apparent recruitment threshold for supination (-&) for the motor units of type A and B shown in Fig. 4, A and B. The absolute value for the ratio (SR/FR) tends to increase slightly for elbow angles > 100”. B: recruitment threshold for flexion (FR) and apparent recruitment threshold for pronation (-PR) for the motor units of type B shown in Fig. 4B. Results were obtained from only a few motor units.

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FIG. 7. Summary of the apparent recruitment threshold for flexion (-FR) and for the recruitment threshold for supination (SR) for motor units of the m. supinator. Different symbols indicate results obtained at different elbow angles. 0: 70”. 0: 100”. a: 130”. q : 160”. The ratio between the recruitment thresholds of these motor units is similar at the different elbow angles.

ing combinations of flexion and pronation torques. In Fig. 54 the results for all motor units of these types recorded in the m. brachialis and m. brachioradialis (indicated with dotted symbols) are presented for different elbow angles for the combination of flexion and supination torques. As illustrated in Fig. 54 no difference could be found between the behavior of motor units of this type for flexion and supination torques (see also DISCUSSION). The average results for the ratio between the recruitment thresholds are given in Table 1. There is a significant (P < 0.0 1) tendency for these motor units to have greater absolute values for the ratio SR/FR for elbow angles exceeding 100”. This tendency is in agreement with earlier observations ( 16). It is important to note that the apparent values for SR are negative. This means that the recruitment threshold for flexion for a motor unit of this type will increase when a torque in supination direction is added. Or in other words, it implies that when a motor

ET AL.

unit is recruited by exerting a flexion torque, it may stop firing when a supination torque is added. This decruitment threshold may be different from the recruitment threshold as reported earlier (10). In this study only recruitment thresholds have been included. The recruitment threshold for flexion of the motor units presented in Fig. 4A does not depend on the exerted pronation torque (n = 10). For motor units of the type shown in Fig. 4B the recruitment threshold for flexion increases when pronation torques are exerted simultaneously (n = 6). The results for the latter type are summarized in Fig. 5B. In some recordings the recruitment threshold for flexion was lowered during pronation (n = 3). We did not analyze these recordings any further because there was evidence that the subjects did not act according to the instructions. When pronation torques were combined with flexion torques these subjects complained about pain at the processus styloides radii. These subjects might have coactivated their muscles, thereby reducing the external torques and the flexion recruitment threshold of these motor units. It was impossible for the subjects to recruit these motor units by exerting a pronation torque only. In both muscles another subpopulation of motor units was found. Units of this type behaved similarly to the so-called flexion units that were recorded in the m. biceps (vt = 11). Supination and pronation torques do not have an effect on the recruitment threshold for flexion. Examples of these units are presented in Fig. 4C. Flexion recruitment thresholds ranged from 5 to 22 No m. In this case, too, a number of motor units showed reduced recruitment thresholds for flexion when pronation torques were exerted simultaneously (n = 5). The same mechanism as mentioned for the other motor units of the m. brachialis may be responsible for this behavior. M. supinator Figure 6 shows an example of the behavior of motor units in the m. supinator. The recruitment threshold for supination increases slightly when flexion torques are added. Extension torques do not significantly affect the recruitment threshold for supination. The results for the combination of supination and

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1. Averaged data for the ratio of the recruitment thresholds for motor-unit subpopulations of the d$erent muscles forfour dQ&erent elbow angles

TABLE

Muscle M. biceps Type A

M. brach. Br. rad. Type A+B

M. brach. Br. rad. TYPeB

M. supinator

Behavior

Ratio

SR FR

(-SR) FR

(--PR) FR

SR (-FR)

M. triceps Type A+B

ER

M. triceps Type A

ER

M. triceps Type A+B

M. pron. Teres Type A+B

M. pron. Teres TYPeB

70”

SR

PR

SR (-FR)

PR FR

(-SR) (FR)

100”

130”

160”

0.18 (0.0 1) n= 14

0.28 b (0.03) n= 9

0.5 1c (0.06) n=9

-0.72 b (0.05) n=9

-0.89 (0.08) n= 5

-0.60 (0.20) n= 3

-0.49 (0.03) n=21

-0.38 (0.04) n= 2

-0.44 (0.07) n=3

-0.049 a (0.004) n=4

-0.069 (0.002) n=7

-0.058 b (0.002) n= 4

0.54 (0.12) n= 2

0.42 (0.03) n = 20

0.57 b (0.04) n=9

1.10” (0.12) n=2

0.74 (0.03) n= 12

1.16b (0.03) n= 4

-0.2 1a (0.04) n= 2

-0.13 (0.0 1) n=9

-0.25 b (0.04) n=6

0.058” (0.007) n=3

0.078 (0.002) n=9

-0.18 (0.02) n=3

-0.18 (0.03) n=4

-0.06 1 (0.009) n= 2

0.1 15b (0.006) n=4

-0.38 b (0.03) n=3

The standard error in the mean is given between parentheses. Superscripts indicate significant differences (P < 0.0 1) between data obtained at different elbow angles: a 70 and 1OO”,b 100 and 130”, ’ 130 and 160”.

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FIG. 8. Behavior of motor units of the m. triceps. Closed symbols give results for motor units recorded in the long head of this muscle. Each point indicates the combination of torques at which a motor unit was recruited. Different symbols refer to data from different motor units. A: motor units activated during extension as well as supination and pronation torques. Flexion increases the recruitment threshold for supination but hardly influences the recruitment threshold for pronation. The motor unit that is indicated with aJi//eti circle has been recorded in the long head of the m. triceps. The other motor unit was recorded in the lateral head of the m. triceps. Both recordings were obtained at an elbow angle of 100”. B: motor units activated during extension as well as supination torques. Pronation torques have no effect on the extension recruitment threshold. Results from the long head of the m. triceps at an elbow angle of 90”. C: extension units recorded in the long head of the m. triceps at an elbow angle of 135”. Neither supination nor pronation torques influence the recruitment threshold for extension.

flexion torques for all recorded motor units (n = 7) are summarized in Fig. 7 and Table 1. The slope of the recruitment lines does not depend on the recruitment threshold. No indication for the existence of different subpop-

ulations of motor units has been found in this muscle. M. triceps In the m. triceps three different subpopulations of motor units could be distinguished.

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20

30 -FR

FIG. 9. Summary of the results for the recruitment thresholds for motor units of the m. triceps. Different symbols indicate different elbow angles. 0: 70’. 0: 100”. a: 130”. q : 160”. Symbols with a dot give results for motor units recorded in the lateral or medial head of the m. triceps. Open symbols indicate motor units recorded in the long head of this muscle. A: recruitment threshold for extension (ER) and for supination (&) of the motor units of type A and B shown in Fig. 8, A and B. The ratio between the recruitment thresholds (SR/ER) tends to be greater at an elbow angle of 130” than at an elbow angle of 100”. B: recruitment threshold for extension (ER) and for pronation (PR) of the motor units of type A shown in Fig. 8A. The ratio between the recruitment thresholds (PR/ER) tends to be greater at an elbow angle of 130” than at an elbow angle of 100”. C: apparent recruitment threshold for flexion (-FR) and the recruitment threshold for supination (SR) for type A and B motor units of the m. triceps shown in Fig. 8, A and B. The absolute value of the ratio between the recruitment thresholds (SR/FR) tends to increase for elbow angles different from 100”.

For one type of motor unit the recruitment threshold depends on torque in extension direction only; for the other two types the recruitment threshold depends on torque in extension and supination direction (see Fig. 8).

For the type of motor unit shown in Fig. 8A (n = 15) the recruitment threshold for extension is lowered when supination or pronation torques are added. Increasing the exerted torque in flexion direction raises the recruit-

1536

VAN

ZUYLEN

ET

AL.

2.5

A

v

4 4 v 4 v

4

I I

t

30

I I

I I

EXTENSION

(NM)

30

4 1

I I

I I

I I

I I

FLEXION

%

.+

(NM)

4 4 4

4 4 4

0

4

0

4 4 4

t

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I I

I 8

EXTENSION

I I

4 Y I .

I I

I I FLEXION

(NM) 4

4

4

I I (NM)

1 20

m

c

zY

0

0

0

2.5 FIG. 10. Examples of the behavior of motor units of the m. pronator teres. Each point indicates the combination of torques at which a motor unit was recruited. Different symbols refer to data from different motor units. A: motor

ACTIVATION

OF HUMAN

ment threshold for supination torques. Flexion torques affect the recruitment threshold for pronation torques only slightly. So, although m. triceps makes a torque contribution in extension direction only, these motor units are activated during supination and pronation torques, even when combined with torques in flexion direction. The activation during supination and pronation of motor units in m. triceps can be understood as a compensation for the (undesired) flexion component due to the activation of m. biceps and m. pronator teres, respectively. For some of the larger motor units of this subpopulation the recruitment threshold for supination or pronation was too high to be built up by the subject in a slow and reliable way. Therefore, the recruitment lines had to be extrapolated to obtain the recruitment threshold. In Fig. 8B motor units are shown for which the recruitment threshold for extension is not affected when a pronation torque is added to an extension torque (n = 7). For a number of other motor units (n = 6) it was not possible to decide to which subpopulation (shown in Fig. 8, A or B) they belonged because of a lack of data for the combination of pronation and extension torques. Figure 8C shows an example of motor units in a subpopulation that is activated only when a particular amount of extension torque is exerted (n = 4). The recruitment thresholds of these “extension units” ranged from5to 12N.m. In Fig. 9A the recruitment thresholds for extension and supination for motor units of the type shown in Fig. 8, A and B, are summarized. The resulting data points for different elbow angles are situated roughly on straight lines passing through the origin. The average ratio between the recruitment thresholds for supination and extension is given in Table 1 for different elbow angles. This ratio is slightly higher at elbow angles different from 100”. In Fig. 9B and Table 1 the recruitment

ARM

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1537

thresholds for extension and pronation are summarized for the type of motor units shown in Fig. 8A. Finally in Fig. 9C the recruitment thresholds for supination together with the apparent recruitment threshold for flexion (-FR) are summarized for the motor units shown in Fig. 8, A and B. The data of the medial head, the long head, and the lateral head of the m. triceps are all presented together by using different symbols in Fig. 9. There seemed to be no differences in the recruitment behavior of the motor units in the subpopulations in the three heads of the m. triceps during isometric contractions. A4. pronator teres For all motor units found in m. pronator teres the recruitment threshold depends on torques in both flexion and pronation direction. For the units shown in Fig. 10 neither supination nor extension affects the recruitment threshold (n = 9). The other type of motor units is shown in Fig. 1OB. For these motor units (n = 6) the recruitment threshold for flexion is raised when supination torques are added to a flexion torque. When pronation torques are involved the recruitment behavior of these motor units is similar to that of the motor-unit type shown in Fig. 1OA. The results are summarized in Fig. 11 and Table 1. The ratio between the recruitment thresholds in pronation and flexion direction for the units shown in Fig. 10, A and B, is given in Fig. 1 IA. The ratio is -0.078 at an elbow angle of 100” and increases with increasing elbow angle (see Table 1). Figure 11B shows the ratio between the apparent supination threshold and the flexion threshold of the motor units shown in Fig. 1OB. Discrete or continuous motor-unit properties? An important question with regard to the coordination of muscle activation is whether

units activated during fiexion torques as well as pronation torques. Neither supination torques nor extension torques influence the recruitment threshold. These results were obtained at an elbow angle of 90”. For the motor unit with the larger recruitment thresholds, the combination of extension and pronation torques could not be tested because the shape of the action potential changed such that we were not sure of its identity for this combination of torques. B: Motor units activated during flexion torques and pronation torques but for these motor units supination torques raise the recruitment threshold for flexion.

VAN ZUYLEN

1538

ET AL.

4 0

5

B FR

4

4

0

4

+ -s, /’ 0

3 - SR 2

4

0

1

0 0

FIG. 11. Summary of the results for the recruitment thresholds for motor units recorded from the m. pronator teres. Different symbols indicate different elbow angles. 0: 70”. 0: 100”. a: 130°. q : 160”. A: recruitment threshold for flexion (FR) and for pronation (PR) of the motor units shown in Fig. 10, A and B. The ratio between the recruitment thresholds (PR/FR) tends to increase with increasing elbow angle. B: recruitment threshold for flexion (FR) and the apparent recruitment threshold for supination (-SR) for the type A and B motor units of the pronator teres shown in Fig. 10, A and B. Only a few data were obtained but the absolute value of the ratio between the recruitment thresholds (SR/FR) at 135” is higher than at 100°.

ACTIVATION

OF

HUMAN

127 lo8642A 90

180

(DEG)

10 8 6 4

0

90 ( DEG )

C 8642-

(lg ...*

! 7 t . .. *-: ! I I I f 1’1 11 1 ’ ’ ’ 1’0 -go

(DEG)

FIG. 12. Histograms for the number of motor units found with a particular slope for the line fitted to the recruitment thresholds for m. biceps (A), m. brachialis and m. brachioradialis (B), and m. triceps (C). All data were obtained at an elbow angle of 100”. In A and B the angle ar refers to the angle with the flexion/supination quadrant; in C the angle -CY refers to angle of the line in the flexion/pronation quadrant.

motor units can be classified in a few subpopulations, each with a distinct homogeneous activation, or whether motor-unit properties demonstrate a broad and continuous, rather than a discrete, distribution. To address this question we have compiled a set of histograms that for an elbow angle of 100” flexion show for each muscle the number of motor units with a particular slope for the line that connects the recruitment thresholds for tor-

ARM

MUSCLES

1539

ques in flexion, extension, supination, and pronation direction (Fig. 12). The data in Fig. 12A clearly show that a discrete set of motor-unit properties is found in m. biceps. The units with a slope near 170” were all classified as belonging to the so-called type of summing units. The motor units whose recruitment line has a slope near 90” were classified as flexion units. The somewhat broader distribution of angles near 90” is due to the fact that the angle is calculated from the arctangent of the ratio of recruitment thresholds in supination and flexion direction. Due to the nonlinear character of the arctangent-function the same experimental error in the recruitment thresholds has a different effect on the error in the angle of the recruitment lines for different slopes. The data for m. brachialis and m. brachioradialis are shown in Fig. 12B, which suggests a bimodal, rather than a unimodal, distribution. However, if one accepts the suggestion of two populations of motor units, the motorunit properties within each population do not have a narrow, peaked distribution. The data suggest some variation in motor-unit properties within each population. The rather broad distribution within a subpopulation is certainly present in Fig. 12C, which shows data for m. triceps. The angle of the recruitment line for those motor units, which could be recruited by torques in pronation direction, varied in the range from -60 to -20”. A few motor units were found (angle -90”) that could not be recruited by torques in pronation direction. However, these units could easily be recruited by torques in extension direction and therefore seem to belong to another subpopulation of motor units. Behavior at other elbow angles On several occasions we were able to record from a particular motor unit at different elbow angles (see METHODS). For all motor units in a particular subpopulation the recruitment behavior changed as a function of elbow angle in an identical way. We never observed that a motor unit classified in a particular subpopulation at a given elbow angle had to be classified in another subpopulation if elbow angle changed. Consequently, if for instance a motor unit in the m. biceps recorded at an elbow angle of 100” was classi-

VAN ZUYLEN

1540

ET AL.

0 0

4

I I

t

25

* .

4

I I

EXTENSION

1 I

*

I I

(NM) (NM) *

4

h

FIG. 1 3.

Behav ior of a motor unit recorded in the short head of the m. biceps at different elbow angles. a: 110”. 0: 170”. The same motor u nit as in Fig. 2A with the largest recruitment th resholds is shown . The recruitment threshold for flexion decreases with increasing elbow angle. The recruitment threshold for supination hardly depends on elbow angle. The motor unit is classified as a summing unit independent of the elbow angle. 140”

*:

fied as a summing unit, this unit behaved as a summing unit at all other elbow angles. For the m. biceps, m. brachialis, m. brachioradialis, m. pronator teres, and m. supinator several motor units could be analyzed at different elbow angles. For the m. biceps an ex.ample is given in Fig. 13. The recruitment threshold for supination of this motor unit is about the same at all elbow angles, whereas the recruitment threshold for flexion tends to be lower at increasing elbow angles. The data in Fig. 13 for an elbow angle of 110” are the same as those shown in Fig. 2A. The averaged results are pooled for three muscles and presented in Fig. 14. The results of these muscles are normalized by arbitrarily choosing the recruitment threshold at 100” equal to one. Figure 14A shows that the recruitment threshold for flexion of motor units in flexor muscles decreases as the elbow angle increases from

100 to 160”. This is in agreement with the fact that the mechanical advantage and exerted force of all flexor muscles decreases for greater elbow angles (34). Therefore, a larger activation of all muscles is required to generate the same torque at elbow angles near extension, which in turn causes a lower recruitment threshold. Second, the recruitment threshold of motor units of the m. biceps is relatively lower than the recruitment thresholds of motor units of the other flexor muscles at elbow angles different from 100’. This means that for elbow angles towards flexion or extension the activation of the m. biceps increases relatively faster than the activation of the other flexor muscles. As shown in Fig. 14B the recruitment threshold of motor units of m. supinator decreases and therefore, the activation of the m. supinator for supination torques increases

ACTIVATION

0

W >

0.6..

G 4 2

0.51

BICEPS

(n

+PRONATOR

‘.

( n = 3 )b

I

1

100 ELBOW

I--z 20

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1

70

‘.

= 5 ) TERES

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OF

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ANGLE

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(“)

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(“)

FIG. 14. Recruitment threshold as a function of eibow angle. The value for the recruitment threshold at an elbow angle of 100” was arbitrarily normalized to unity for all motor units. The standard error in the mean is -5% of the actual value for all data points. A: average flexion recruitment threshold for m. biceps, m. brachialis/brachioradialis, and m. pronator teres. The recruitment threshold of motor units of all muscles is highest at 100”. The recruitment threshold for flexion of the m. biceps is relatively lower than the recruitment threshold of the other flexor muscles at elbow angles different from 100”. B: average supination recruitment threshold for m. supinator and m. biceps summing units. The recruit-

ARM

MUSCLES

1541

relative to the activation of m. biceps at elbow angles different from 100”. The recruitment threshold of motor units in the m. pronator teres for pronation torques is lowest at 100”. This indicates that the relative activation during pronation for this muscle is at its maximum at this elbow angle. The ratio of recruitment thresholds for different torque directions is shown in Table 1 for different types of motor units in all muscles. Clearly elbow angle has a significant effect (P < 0.0 1) on the relative activation for nearly all motor-unit types. In the few conditions where the effect was not significant, this may have been caused by the small number of motor units. However, even though the effect could not be demonstrated to be significant in these conditions, the effect was in agreement with extrapolation of the results at other elbow angles. Relative contributions of muscles We set out to determine, among other things, the relative contribution of different muscles to isometric torques. By using the averaged data on the ratio between the recruitment thresholds shown in Table 1 we are able to do this within certain limits. We assume that the torque exerted by all activated motor units of a particular subpopulation is the same along the recruitment line of a motor unit of that subpopulation. The same part of the motor units of the subpopulation is active at all combinations of torque on this line. In the APPENDIX we explain in detail the procedure we used. In Table 2 the results are summarized. This table shows that the contribution made by the m. biceps and the m. pronator teres to flexion torques is about 38% and 6%, respectively at an elbow angle of 100”. According to these data the m. brachialis and the m. brachioradialis together with the m. extensor carpi radialis longis are responsible for the remaining 56% of the flexion torque during pure flexion at an elbow angle of 100”.

merit threshold of motor units of the m. supinator is relatively lower than the recruitment threshold of motor units of the m. biceps at elbow angles different from 100”. Recruitment thresholds for pronation of the m. pronator teres are also shown, relative to the value obtained at an elbow angle of 100”.

VAN ZUYLEN

1542 TABLE 2.

Relative contributions of the m. biceps and the m. pronator teres to torques in d@erent directions Flexion

M. biceps

100”

Supination 130”

43%

38%

Flexion M. pronator teres

100”

130”

35%

26%

Pronation

100”

130”

100”

130”

6.3%

5.9%

20%

13%

The separate contributions of m. brachialis and m. brachioradialis to flexion could not be estimated in more detail because both muscles behave in a similar way. In agreement with the conclusions derived from Fig. 14, Table 2 shows that the relative contribution of the biceps at an elbow angle of 130” is larger than at 100”. The contribution of the m. biceps to supination torques decreases from -35% at an elbow angle of 100” to 26% at an elbow angle of 130’. Consequently, the contribution of the m. supinator increases from 65 to 74%. This finding is in agreement with the following findings. In the first place the relative activation of the m. biceps decreases compared to the activation of the m. supinator (see Fig. 14). Second, at 130” the mechanical advantage for supination of the m. biceps is lower, whereas that of the m. supinator is the same at both elbow angles. Finally, the tension exerted by the m. biceps is lower due to the length-tension relationship (34) (see also DISCUSSION). DISCUSSION

Different subpopulations of motor units were found in most muscles investigated in this study, each having its own characteristic activation. Comparable findings have already been reported for the m. biceps (17, 18). Our findings concerning the m. biceps fit in with these results. In addition we have shown that the existence of subpopulations of motor units in a single muscle, is not an exception. It is a general observation that is not exclusive for a “multifunctional” muscle such as the m.

ET AL.

biceps. Actually, the m. supinator is the only muscle in which no evidence was found for the existence of different subpopulations. However, it should be mentioned that the number of experiments on m. supinator was rather small so that we may not have obtained a representative sample of motor units in m. supinator. General comments It should be stressed that no differences were found between subjects. For instance the motor units of the long head of the m. triceps with the largest and with the smallest ratio SR/FR presented in Fig. 7A were recorded in the same subject. Therefore, in all figures data from different subjects have been pooled. The ratio SR/FR of motor units in a subpopulation did not depend on the recruitment threshold. This means that the recruitment order of motor units of a particular type remains approximately constant for all combinations of exerted torques; this suggests a rather homogeneous activation of all motor units belonging to one subpopulation. For each subpopulation we found motor units with high- and low-recruitment thresholds. Even though the sample of units was sometimes rather small the recruitment thresholds of motor units were equally distributed for all subpopulations, and no evidence was found that a particular subpopulation consisted exclusively of low- or high-threshold units. Figures 3, 5, 7, 9, 11, and 12, which summarize the data, indicate that within a subpopulation there is a scatter in the ratio between the recruitment thresholds. This scatter is somewhat greater than is expected on the basis of the experimental error alone. Part of this scatter might have been caused by the fact that results are pooled for groups of elbow angles each with slightly different ratios between the recruitment thresholds. A matter of serious concern was that external torques in the shoulder and wrist might have influenced the recruitment threshold of motor units. For example, it is known that torques in exorotation or endorotation direction do influence the recruitment threshold of motor units in m. biceps (18). Subjects were not always capable of keeping torques in these directions exactly at zero. We made certain by thoroughly checking all the

ACTIVATION

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HUMAN

torques that could be measured with our equipment that no systematic errors had been made in this way. Moreover, recordings were excluded from further analysis in which irregularities in the speed of the contraction were larger than 5% of maximal voluntary force per second. These recordings were excluded because the irregularities might have influenced the recruitment threshold of motor units ( 10, 12). Usually, the activity of several motor units was measured in a single bipolar recording. It should be stressed that in general in each recording motor units were recorded that belong to one single subpopulation with the same ratio for the recruitment threshold in different torque directions. This was observed for all muscles and is consistent with findings in the m. biceps (18). These results suggest that the muscle territory of motor units of a particular subpopulation overlap. They suggest also that the muscle territory of different types of motor units occupies different regions in muscles. This fits in with the fact that the motor-unit territory in a muscle is restricted to a small part of the muscle (5). Correspondingly, Desmedt (13) found that motor units in different parts of the first dorsal interosseus muscle receive a different activation. The data from the m. brachialis and m. brachioradialis were presented in the same figures. The behavior of motor units of these muscles was very similar. The mechanical action of both muscles is approximately the same in the neutral position of the forearm which we used in our experiments. The conclusions of Buchanan et al. (4) were similar to our own in that they did not find differences in the activation of m. brachialis and m. brachioradialis for any combination of torques investigated. The recruitment order and the recruitment thresholds of motor units are reproducible if the recruitment behavior of motor units is studied at a particular elbow angle. This is also true when motor units of different muscles are studied simultaneously. Minor exceptions to this rule have only been observed when motor units with almost the same threshold are studied (12). However, in studying the recruitment order of motor units of different muscles or of different subpopula-

ARM

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1543

tions within a single muscle, one finds that major reversals of recruitment order occur when contractions in different directions are combined. Comparable findings have been reported for the m. biceps ( 18), for the m. first dorsal interosseus (13) and for the m. adductor pollicis brevis and m. extensum digitorum longum (28, 3 1) although the results for the first dorsal interosseus muscle were contradicted in another study (30). Contributions of dzfirent muscles From the data obtained for the individual motor units we were able to calculate the relative contribution of a number of muscles to the isometric torques. First of all, the relative contribution of the different muscles appears to be independent of the level of exerted torque. This statement is an extension of the notion of the flexor equivalent of Bouisset (2, 3) in the case of pure flexion. We have verified our observation only for torques up to 40% of the maximum voluntary torque. Presumably, at large torques the activation ratio will not remain constant because the torque output of some subpopulations will saturate before that of others. The values found for the contributions of the different muscles during flexion torques are well within the range reported by Jsrgensen and Bankov (23). Hasan and Enoka (19) reported that there was a wide variety in the synergistic coactivation of the flexor muscles. This variety, however, is not present at all in our study and might have been caused by their use of surface electrodes to compare muscle activity at different arm positions. Surface electrodes are not able to selectively record from different subpopulations within one muscle. Furthermore, movement artefacts caused by the movement of the muscles relative to the surface electrodes cannot be ruled out. Second, the notion of the flexor equivalent (2, 3) does not have general validity. When torques in two directions are combined the relative activation of flexor muscles is changed (see Figs. 2,4,6,8, and 10). The relative activation of muscles is also found to be different at different elbow angles (see Fig. 14). Third, we found that muscles that become

1544

VAN

ZUYLEN

relatively less effective when the elbow angle is changed receive a relatively lower activation. Three examples will be discussed. With regard to the muscles that contribute to supination torques, only the length and the mechanical advantage of the m. biceps are changed when the elbow angle changes from 100 to 130” (34). The torque exerted by the m. supinator at a particular activation level remains unaffected because changing the elbow angle has no biomechanical effect on this muscle. Second, the recruitment threshold of m. biceps motor units increases, whereas the recruitment threshold of the motor units of the m. supinator decreases (see Fig. 14). This difference is significant (P < 0.0 l), indicating that the relative activation of the m. supinator increases whereas that of the m. biceps decreases. This means that the more effective muscle receives a larger activation. From Table 2 it appears that the contribution of the m. biceps to supination does indeed tend to decrease from 35 to 26%. Therefore, these two findings in fact corroborate each other. During pronation torques the change of length and mechanical advantage of the m. pronator teres give rise to a situation similar to that described above when the elbow angle is changed from 100 to 130’. The m. pronator teres becomes relatively less effective in exerting pronation torques, whereas the m. pronator quadratus remains unaffected. In addition the relative activation of m. pronator teres decreases (see Fig. 14). As a result of these effects the contribution of the m. pronator teres to pronation torques decreases. This can also be concluded from Table 2: the contribution of the m. pronator teres to pronation torques tends to decrease from 20 to 13%. The flexion recruitment threshold of all flexor muscles is lower at an elbow angle of 130” than it is at 100”. This is due to the fact that the torque in flexion direction of all flexor muscles decreases as a result of a smaller mechanical advantage and of the force-length relation (34). This decrease is smallest for the m. biceps. Furthermore, from Fig. 14 we can see that the activation of the m. biceps is also greater at 130” relative to the activation of m. brachialis and m. brachioradialis because the recruitment threshold of motor units in m. biceps for flexion decreases significantly more (P < 0.0 1) than the recruitment threshold of the other flexor muscles.

ET

AL.

These two findings imply that the relative contribution of the m. biceps to flexion torques increases. Table 2 shows that the contribution of the m. biceps to flexion does indeed increase slightly, namely from 38 to 44%. Synergism In a recent paper Buchanan et al. (4) state that “synergies between muscles are better defined in relation to a particular task, which would here be exemplified by torque generation in a particular direction.” In our study for instance it appears that two muscles, which are a classical example of antagonistic muscles, can be synergists during a particular task. For example, motor units in major parts of m. triceps and m. biceps are active simultaneously during supination, even when an amount of flexion or extension is added. Furthermore, as mentioned above, the muscle that becomes relatively more effective receives a relatively larger activation than the other muscles involved. We therefore conclude that the activation of a particular (part of a) muscle is determined by a mechanism that takes into account the mechanical actions of all muscles situated around a particular joint. Buchanan et al. (4) suggest that one might expect muscles with broad attachment sites (such as the m. brachialis) to be activated during a large range of different torque combinations. We did not find any such tendency. On the contrary, the activation of m. brachialis increases only when flexion torque is increased. Neither supination nor pronation nor extension increases the activation of this muscle. In the second place the m. brachioradialis and m. brachialis, which are quite different with respect to their attachment sites, are activated quite similarly. Another factor that contradicts the suggestion of Buchanan et al. (4) is that the major part of the m. biceps, which has quite narrow attachment sites, is activated during combinations of extension and supination, flexion and supination, and flexion and pronation. Another example is that motor units in major parts of the m. triceps are also activated during extension and during supination or pronation even combined with flexion torques. This activation is the same for the medial and lateral head, which have large attachment sites, and

ACTIVATION

OF

HUMAN

for the long head. It can be understood as a compensation of undesired flexion torques exerted by the m. biceps or the m. pronator teres during supination torques and pronation torques, respectively. In the literature several explanations have been suggested to account for the activation of muscles in a redundant motor system. Most of these explanations are based on the assumption that the observed behavior represents some optimum solution for the control of the biomechanical system (8,9, 14, 15,26, 32). The predictions concerning the muscle activation that result from these models are in contradiction with results from our study and from the literature (4). When, for example, supination torques are exerted, m. supinator, m. biceps, and m. triceps (that only exerts a torque in extension direction) are activated. This is in contradiction with the criterion of minimum muscle force (8, 32), which predicts activation of the m. supinator only. Minimum muscle fatigue (15) implies that muscles are activated homogeneously because muscle fatigue increases more than proportionally with muscle activation. This is in contradiction with our discovery of subpopulations of motor units each with a different activation in almost every arm muscle that we studied. Recently, Gielen and van Zuylen (16) presented a model that basically is a modified version of the tensor theory of Pellionisz and Llinas (27). In this model it is assumed that the activation of muscles is the result of a linear combination of the eigenvectors of a transformation between afferent muscle receptor signals and efferent muscle activation signals. This assumption leads to a linear relationship for the recruitment threshold of motor units as a function of torque in particular directions. The predicted linear relationships are similar to the straight-line fits found in this paper. Quantitatively, the predictions for the ratio of recruitment thresholds for torques in different directions are in good agreement with the values found for the largest subpopulation in each muscle, shown in Table 1. Furthermore, the changes in recruitment threshold as a function of elbow angle reported in this study were very accurately predicted by Gielen and van Zuylen. An explanation to account for the existence of subpopulations has been suggested

ARM

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1545

by Loeb (25). He suggested that the Central Nervous System activates “task groups” that may consist of parts of (different) muscles to linearize the motor output. Hoffer et al. (22) found three discrete groups of motoneurons (subpopulations) in the motoneuron pool of the cat sartorius muscle. These groups were activated in different phases during normal locomotion. Further experiments that take into account the fact that subpopulations exist are necessary to discriminate between the various hypotheses.

APPENDIX: DETERMINATION RELATIVE CONTRIBUTIONS MUSCLES TO FLEXION, AND PRONATION

OF THE OF ARM SUPINATION,

In this appendix we outline the procedure used to calculate the relative contributions of the m. biceps to flexion and supination torques and of the m. pronator teres to flexion and pronation torques. First let us consider the activations of muscles at an elbow angle of 100” when a pure supination torque of X No m is exerted as is indicated in Fig. 15. Motor units of the m. supinator, of the m. triceps (type A and B, shown in Fig. 8, A and B, respectively), and of the m. biceps [type A and type C: only activated during supination ( 1S)] will be activated. When a supination torque is exerted, the torque component of the m. biceps in flexion direction and of the m. triceps in extension direction will cancel each other. Therefore:

FBi.A+ FBi,C+

ETLA

+ ET~.B = 0

(3)

In this formula FBi,Arepresents the flexion torque component of the type A motor units of the m. biceps and so on. Now let us consider the activation of motor units while a pure extension torque of ETot = -X/ 0.42 N. m is exerted. At this extension torque the same population of type A and type B motor units of the m. triceps is activated as for the supination torque of X N. m. This follows from the fact that the average ratio between the recruitment thresholds for extension and supination for these motor units is 0.42 (see Table 1). However, during extension torques type C motor units of the m. triceps are activated as well, so ET~,A + ETr.B + ETLC

-X =GN-m .

(4)

I n our study we found only a small nu mber of m. triceps motor units of type C (4 out of 32). We

1546

VAN

ZUYLEN

X/O.42 EXTENSION

ET AL.

FLEXION (A.U.)

(A.

U. 1

x/o.

18

fj

FIG. 15. Schematic drawing for calculating the contribution of the m. biceps to flexion and supination torques at an elbow angle of 100”. The line marked B represents the recruitment line of a m. biceps summing motor unit that recruits at a level of X N . m supination torque. The slope of B equals the average slope of m. biceps summing units. The line denoted by T represents the recruitment line of a m. triceps summing unit that also recruits at a level of X N. m supination torque. The slope is equal to the average slope of m. triceps summing units.

assumethat we have studieda representativepart of the total population of all m. triceps motor units. Thereforea goodestimatefor the tricepsextensiontorque during pure supination of X Nom is -(32 - 4) X N . m %A + ETr.B = -*- 32 0.42 = -2.lXN.m

(5)

and with Equation 3:

We know that the mechanicaladvantageof the m. bicepsfor flexion is 5.9 * 0.2 timeslargerthan for supination( 18).Therefore at a level of X Nom supinationthe relative contribution of the m. bicepsto this supinationtorque is: %A

+ s&C =- 2* lx $ i $ 100% = S To: 5.9 x

350/ 0

(7)

The remaining65% of the supination torque is delivered by the m. supinator. Note that X, indicatingthe exertedtorque iseliminatedfrom Equa-

tion 7. This meansthat the relative contribution of the different musclesdoesnot dependon the level of the contraction. When pure flexion is exertedwith FTot= X/O. 18 Nom the samepopulation of type A motor units of the m. bicepswill be activated asin the casedescribed by Equation 3. This can be concluded from the data in Table 1 and from Fig. 15.Type C units of the m. biceps(supinationmotor units; see description of m. biceps)are not activated now, but insteadmotor units of the m. bicepstype B areactivated. We assumethat both typesof motor units occur with roughly the samefrequency and that asa consequencethe total torque exertedby the whole m. bicepsis the same,i.e., 2.1X. This will be a fairly good estimateof FBI,*+ FBi,B,becausethe number of motor units of type B and C isquite smallanyway (Ref 18and this study). So FBi.A + FBi.B= - 2.1x * 100% = 38% FTot x/o. 18

(8)

This result implies that the m. bicepscontributes38%of the flexion torque at an elbowangle of 100”.The sameline of reasoningcan be applied for an elbow angle of, for instance, 13OO. The resultsare presentedin Table 2.

ACTIVATION

OF HUMAN

The samereasoningalsoholdsfor the m. pronator teres.We have to take into accountthat during the combination of pronation and extensiononly 15 out of 26 motor units of m. triceps that were analyzedduring this combination of torqueswere activated during pronation as well as extension torques(type A motor units). This meansthat now a correction of 15126X 100%hasto be included in the calculation of the extensiontorque exerted by the m. triceps during pure pronation in order to counteractthe flexion torque of the m. pronator teres.The mechanicaladvantageof the m. pronator teresin flexion direction is ~4.0 times higher than in pronation direction. The resultsare shown in Table 2. The m. pronator quadratuswill be responsiblefor the restof the pronation torques.The accuracy of the estimatedcorrection (15/26) and

ARM

MUSCLES

1547

of the ratio of the mechanicaladvantages(4.0) is somewhatlessthan in the former analysisof the contributions of the m. biceps.Therefore,the estimate of the contributions of the m. pronator teres can only be a rough estimate.However, this inaccuracy doesnot influence the conclusionthat the relative contribution of the m. pronator teresto pronation decreases with increasingelbowangle. ACKNOWLEDGMENTS

This study was supported by the Netherlands Organisation for Pure Research (Z.W.O.). Received 10 September 1987; accepted in final form 17 June 1988.

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