JOURNALOF NEUROPHYSIOLOGY Vol. 67, No. 6, June 1992. Printed
Organizing Principles for Single Joint Movements: V. Agonist-Antagonist Interactions GERALD TAURAS
L. GOTTLIEB, J. LIUBINSKAS,
L. LATASH, DANIEL GYAN C. AGARWAL
Departments of Physiology, Neurological Sciences,and Physical Medicine and Rehabilitation, Rush Medical College, Chicago 60612; and College of Kinesiology and Departments of Electrical Engineering and Computer Science and Bioengineering, University of Illinois, Chicago, Illinois 60680 During much of a movement, agonist and antagonist muscles are simultaneously active, implying that except 1. Normal human subjectsmadediscreteelbow flexionsin the of acceleration, the horizontal plane under different task conditions of initial or final during the first tens of milliseconds position, inertial loading, or instruction about speed.We mea- forces that produce these movements must be attributed to sured joint angle, acceleration, and electromyographic signals the summed contraction of both agonist and antagonist (EMGs) from two agonistand two antagonistmuscles. muscles. Nevertheless, it is a simple and common matter to 2. For many of the experimentaltasks,the latency of the antag- demonstrate a high correlation between electromyographic onist EMG burst wasstrongly correlated with parametersof the ( EMG) signs of activation in a single ( agonist) muscle and first agonistEMG burst definedby a singleequation, expressedin kinetic measures of the trajectory such as peak inertial terms of the agonist’shypothetical excitation pulse. Latency is torque or kinetic energy under diverse conditions (Bouisset proportional to the ratio of pulseduration to pulseintensity, making it proportional to movement distanceand inertial load and and Goubel 1968, 1973; Gottlieb et al. 1989a). When the inversely proportional to planned movement speed.However, load remains constant, similar correlations have been demmeasures as well (cf. theserulesare not sufficient to define the timing of every possible onstrated with various kinematic Gottlieb et al. 1989b for references). singlejoint movement. 3. For movementsdescribedby the speed-insensitive strategy, In terms of features of the movement task, the behavior the quantity of both antagonistand agonistmuscleactivity canbe of an equivalent antagonist muscle has proven much more uniformly associatedwith selectedkinetic measuresthat incorpo- difficult to characterize. Physical principles only tell us that rate muscleforce-velocity relations. the strength of the decelerating torques should be propor4. For movementscollectively describedby the speed-sensitive tional to factors such as the kinetic energy generated by the strategy,(i.e., that havedirect or indirect constraintson speed),no accelerating contraction. However, this is a mild constraint singlerule can describeall the combinationsof agonist-antagonist because the same distance can be moved with a long, gentle coordination that are usedto perform thesediversetasks. deceleration or a brief, vigorous one. Often, the area of the 5. Estimatesof joint viscosity were made by calculating the amount of velocity-dependent torque used to terminate move- antagonist burst covaries with the torque required to decelments on target. These estimatesare similar to those that have erate the limb. Increasing movement speed (Corcos et al. previously been made of limb viscosity during postural mainte- 1989; Hoffman and Strick 1990) or inertial load (Gottlieb nance.They imply that a significantcomponentof muscleactivity et al. 1989a; Lestienne 1979) increases antagonist activity, must be usedto overcometheseforces. even though the latter procedure usually reduces speed. 6. Theseand previous results are all consistentwith a dual- Ghez and Gordon ( 1987) showed that the strength of antagstrategyhypothesisfor thosesingle-jointmovementsthat aresuffi- onist contraction controls the torque rise time rather than ciently fast to require pulse-likemuscleactivation patterns. The its peak during isometric pulse contractions. The average major featuresof suchpatterns (pulseintensities,durations, and latencies)are determined by central commandsprogrammedin decelerating torque for movements of different speeds and advanceof movementinitiation. The selectionbetweenspeed-in- loads is also positively correlated with the degree of antagosensitiveor speed-sensitive rulesof motoneuron pool excitation is nist activity (Karst and Hasan 1987), but those experiimplicitly specifiedby the nature of speedconstraintsof the move- ments were not clear on the effects of changing movement ment task. distance. Movement distance is usually strongly and positively correlated with peak velocity, acceleration, and both accelerating and decelerating torques. It is experiments in INTRODUCTION which movement distance varies that have produced conRapid, self-terminated movements of a limb about a sin- flicting results on the relationship between antagonist burst gle joint are associated with two or more bursts of activity in area and movement distance. For example, Wadman et al. the muscles that generate the movement. A burst of excita- ( 1979) found no relationship. Some (Brown and Cooke tion activates agonist muscles and generates the initial, ac- 198 1; Cheron and Godaux 1986; Gottlieb et al. 1989a; celerating torque. The second, antagonist muscle burst gen- Marsden et al. 1983) found an inverse relation, whereas others found a proportional one (Hoffman and Strick erates an opposing torque to decelerate and arrest the limb at its target. 1990; Mustard and Lee 1987; Sherwood et al. 1988). SUMMARY
0022-3077192 $2.00 Copyright 0 1992 The American Physiological Society
Wierzbicka et al. ( 1986) showed how the strength of antagonist contraction could be used to control movement time, whereas movement distance could then be independently controlled by the strength of the agonist contraction. They also emphasized the differences in force production during lengthening versus shortening contractions (Katz 1939) as a possible explanation of the fall in antagonist EMG while the forces it generates appears to be increasing. Those movements that demonstrated a proportional antagonist relationship with torque or one of its kinematic correlates for varying movement distance were generally isochronous. That fact, and the findings of Ghez and Gordon ( 1987) and Wierzbicka et al. ( 1986), highlight the necessity of considering the timing of antagonist action, not merely its strength. The latency of the antagonist burst is always proportional to movement time (Corcos et al. 1989; Gottlieb et al. 1989a; Lestienne 1979; Wadman et al. 1979). The latency is constant under isochronous conditions, even when movement distance varies (Hoffman and Strick 1990; Sherwood et al. 1988). The experiments reported here quantitatively characterize the latency and intensity of antagonist muscle activation in terms of physical parameters of the movement task. We found that the latency of the antagonist is often closely coupled to parameters that characterize the degree to which the agonist muscle is activated. This leads to very simple rules for single joint movement planning. We also found that the degree of antagonist activity can be quantitatively associated with joint torques if the force-velocity properties of muscle are considered, but only for those movements we have characterized as controlled by the speed-insensitive (SI) strategy. Consideration of force-velocity properties also improves our description of the degree of agonist activity. For movements in which distance and accuracy are fixed and only movement speed (or movement time) is manipulated, the same rules can describe antagonist latency but not its degree of activity. Considering all the task elements that can influence movement speed, we find no single, simple rule to specify the degree of activation of the muscles in tasks characterized as speed-sensitive (SS). METHODS
Apparatus and general instructions Seatedsubjectsadductedthe right shoulder90” and restedthe forearmon a horizontal manipulandumthat allowedfreerotation about the elbow. They viewed a computer monitor that displayed a cursor, the horizontal location of which wasdeterminedby the angleof the elbow. A narrow marker on the screenlocated the starting position of the limb. A second,broader marker was a target, centeredat the desiredangular position. Zero degreeswas defined with the forearm and upper arm forming a right angle. Extension wastoward -90°, and flexion approached+90”. Subjects madeblocks of 1l- 15 similar movementswith each condition of positionand loadingon the manipulandum.An audio tone lasting2 s signaledthe subjectto makean elbow flexion from the starting position to the target. These methods are describedin greaterdetail in Gottlieb et al. ( 1989a). Joint angleand accelerationwere transducedand low-passfilteredat 30 Hz. Joint velocity wascomputedfrom the acceleration. Inertial torque wascomputedby multiplying the measuredacceleration by the sum of the manipulandum’s moment of inertia
(0.086 Nm s2/rad) and the estimatedlimb moment of inertia ( -0.095 Nm s2/rad with < 10%varianceacrossour subjectpopulation) on the basisof body segmentparameters(Miller and Nelson 1976). EMG surface electrodes(Liberty Mutual Myoelectrodes)weretapedover the belliesof the bicepsbrachii, brachioradialis, and triceps (lateral and long heads)muscles.EMGs were amplified ( X 1,600)and band-passfiltered (60-500 Hz). All measured signalswere digitized with 12-bit resolution at a rate of 1,OOO/s. After obtaining informed consentaccordingto Medical Center approved protocols,various experimentswereperformed. The different experimentswere conducted over an extended period of time with different subjects.They can be mostconcisely describedasconsistingof four series,the first two conforming to the protocolsfor the SI strategyand the secondto the SSstrategy. SeriesI required flexion movementsof 18, 36, 54, or 72Oto a target 9” wide from an initial position at -36” (extension). These movementswereperformedasquickly and accurately aspossible with one of four different weightsattachedto the manipulandum. Moments of inertia of the device under the four conditions were 0.28, 0.80, 1.31, and 1.83 Nm s2/rad. Someof the resultsof this serieson six subjectswere reported in Gottlieb et al. ( 1989a). SeriesII alsorequired flexion movementsof 18, 36, 54, or 72”, but to a target fixed at 35” flexion. This was accomplishedby varying the starting angle.Movements were madeasquickly and accurately aspossible.Nine subjectstook part in this series. SeriesIII had subjectsperform 54” movementswith a weighted manipulandum (moment of inertia 0.741 Nm s2/rad). The addedweight increasedthe torque neededboth to accelerateand arrest the manipulandum. This produced larger EMG signals (Gottlieb et al. 1989a;Lestienne1979). The subjectfirst moved as quickly and accurately as possible.Movement time (MT) was calculated from the velocity signalafter eachmovement and reported to the experimenter. Movements with longer times were obtainedby askingthe subjectto move more slowlyand providing verbal feedbackuntil the desiredMT was obtained. During the experiment, verbal MT feedbackwas provided after eachmovement. MT wasincreasedby -50, 100,and 150mson successive blocks of 15 movements. Four subjectseach performed four blocks of 15 movements. SeriesIVrequired subjectsto move four different distancesasin seriesI. They repeatedthat seriesfour times,eachwith a different instruction influencing movement speed. Speed ranged from fairly slowwhenmadeat the subjects’choiceto asfast aspossible. Some results from these experimentswere reported previously (Gottlieb et al. 1990a).We report the resultsof further analysisof thosedata here.
Analysis We canpartition the net torque producedby all the musclesat a joint into three componentsgiven by Eq. 1. Theseare 1) torque exertedon external physicalloads,2) an inertial torque that acceleratesthe limb and manipulandum,and 3) an intrinsic force that is dissipatedwithin the muscles 7=7
The external torque includes those applied to all mechanical loads,except the manipulandum,including the isometriccondition. The parameter J includesthe inertia of the limb and the manipulandumbecausethe location of the torque measurement transducerdid not allow us to measurethe component of torque that acceleratedthe device. We will assumethat the third component is related to movement velocity so that, asa simplifying approximation
This approximation is clearly not a completeaccounting of the heatproducedby muscleactivation and shorteningnor of muscle mechanicalimpedancein general.Elastic,energystorageelements arealsoneglected’(Feldman 1986;Flash 1987;Joyce et al. 1969; Latashand Gottlieb 1991b) . This is a useful first approximation of the processesunderlying Hill’s force-velocity relation (Hill 1938). We have previously usedpeakvaluesof inertial torque (Corcos et al. 1989, 1990;Gottlieb et al. 1989a,1990a)asthe mechanical correlateof musclecontraction relatedto the myoelectrical measure, integrated EMG. Although peak inertial torque is better correlatedthan kinematic measuresover a wider rangeof movement conditions, it lacks any theoretical rationale as a general correlateof integratedEMG. Inspection of the inertial torque trajectory over the courseof a seriesof rapid movementsof different distancesshowsthat peak acceleratingtorque often tendsto saturate with continued increasesin movement distance and load (e.g., Figs.2 and 3 in Gottlieb et al. 1989a). When a task variable (e.g., distance)and the EMG burst both increase,we expect that there shouldbe a mechanicalmeasureof musclecontraction that doesthe same.One that has been usedpreviously is power (7 d0/dt, Gottlieb 1991), which can be integrated to give kinetic energy (Bouissetand Goubel 1973). Here we will consider an alternative, the mechanicalimpulseasdefined by Eq. 3 t2
To evaluate the degreeof muscleexcitation, we usedthe integrated, rectified EMG. The integration interval for the agonist musclewasdefinedfrom the first sustainedriseof the EMG above baselineto the first zero crossingof the acceleration(i.e., peak velocity). This encompassed the first agonistburst (a,,>. For the antagonistmuscle,integration beganat the sametime asfor the agonistand extendedto the projected end of deceleration,determined by linearly extrapolating the decelerationto zero from the point at which it had fallen to 50% of its negative (deceleration) peak.This kinematically definedinterval encompasses the antagonist burst ( Qant) , and the rationalefor its useisgiven in Gottlieb et al. 1989a.This avoidsthe needto defineburst durationsfrom the EMG records.Suchdefinitionsaredifficult or impossibleto determine consistentlyacrosssubjectsand tasks. The latency of the antagonistburst (t,,,) wasmeasuredon a computer monitor. The highly amplified EMG signalsfor each movement were rectified and smoothedwith a narrow ( lo-ms) rectangularaveragingwindow and displayed.The first detectable antagonistactivity begins20-30 msafter agonistonset.This activity scaleswith the agonist (Corcos et al. 1989; Gottlieb et al. 1989a)and continuesuntil the onsetof a larger,abrupt increasein activity, 50-250 mslater. This increaseis usually identifiableasa distinct discontinuity in the EMG record (seeFig. 4) and marks what we will refer to as“the antagonistburst.” If it wasnot identifiable, the record wasrejectedfrom analysis. Measurementsweremadefrom bicepsand brachioradialisagonists and lateral and long headsof triceps (antagonists). The quantitiespresentedin Figs. l-3 and 6-8 beloware all taken from biceps(Q,) an lateral triceps ( Qant,t,,) for consistency.Similar resultswereobtained from the other musclepair.
The integration interval covers the region of positive acceleration from movement onset( tl = 0) to the first zero crossingof RESULTS acceleration,which correspondsto the time of maximum moveThe principal focus of this study is to characterize properment velocity. In the experimentswe will discusshere,the external torque component is alwayszero. For a symmetricalmovement ties of antagonist muscle behavior. To do this, we will not (which in this caserequireshalf the distancebe traversedbefore torque reversal), substituting Eq. 1 and 2 into Eq. 3 and letting = 0 simplifiesto 7external 600 __t_
d6 Impulse = J r x 1 (UL
Note that the inertial term in Eq. 4 is equivalent to the momentum that ismaximum at peakvelocity. In consideringthe work of the antagonistmuscle,this momentum is completely dissipated when the limb returns to zero velocity, sothis component is the samefor agonistand antagonist(assuminglittle or no overshooting or terminal oscillation, which is characteristicof the movementsmadein our manipulandum). The signof the secondterm dependsupon whether we are calculating the impulsegenerated by the agonist(+ ) or antagonist(- ) muscle.Viscous forcesimpedeaccelerationby the agonistbut assistdecelerationby the antagonist.We will not arguethat impulseis an optimal mechanical measurein any theoretical senseor that the trajectory is planned to minimize its value. Equation 4 simply showsthat impulseis a particularly simple quantity to evaluate for the partitioning of torquesas in Eq. 1 and 2 that may provide a better description than inertial torque alone.
!Ig 400 W 5 >
0 t 300 250 200 50
ANTAGONIST LATENCY(ms) ’ We have neglected the elastic work because its inclusion requires a more complex modeling approach. The elastic term should be K( 6 - 0,,,), where etestis the hypothetical rest length at which the activated muscle would generate zero force. Not only is 6,,, a third unknown parameter value to estimate, but both experimental data (Joyce et al. 1969; Latash and Gottlieb 199 1b) and theoretical models of muscle (e.g., equilibrium point models, Feldman 1986; Flash 1987) suggest that t9,, cannot be assumed constant during time-varying contractions or movements.
Movement time as function of the latency of the antagonist EMG burst for 1 subject. Each symbol is the average of-1 0 movements. Thin solid lines l are regression curves for movements of the same distance with different inertial loads. Thin dotted lines are regression curves of movements over 4 different distances with the same inertial load. The heavy solid line is the regression curve of the pooled data (MT = 35.9 + 1.69i ant, Y = 0.96 ) . Note that the slopes of the regression lines are steeper when load varies than when distance varies. FIG. 1.
present the results in the sequence by which the series are enumerated above. Instead, we will organize the data around the two primary characteristics of antagonist activity, its timing and its strength of activation.
Timing of antagonist muscle activity The timing of the antagonist EMG burst was examined for movements under both SI (series Z) and SS (series ZZZ) conditions. We began in series Z by reanalyzing experiments that were described in Gottlieb et al. 1989a, where movements over four different distances with four different inertial loads were studied. The patterns of EMG and inertial torque for all these movements can be described as behavior under the SI strategy. Data from one subject, showing MT versus tant, are shown in Fig. 1. The overall regression curve is MT = 35.9 + 1.69t,,,, r = 0.96. We have also plotted the dependence of antagonist latency on quantity of agonist activity ( Qap) in Fig. 2. The antagonist latency is slightly better correlated with the area of the agonist burst (t ant = 52.4 + l.O03Q,, r = 0.98) than with MT. Figures 1 and 2 also show the linear regression lines that were calculated under two different partitionings of the data. First we computed the four regression lines for movements of one distance with different loads and then of four different distances with the same load. All correlation coefficients were >0.93, and most were >0.95. We would expect that, were movement time completely determined by the latency of the antagonist burst (which itself would depend on movement-specific parameters), then the slopes of the regression curves relating tant and MT would be independent of the task. Figure 1 confirms the well-known fact that Qant begins approximately at or before the midpoint of the 300
INTEGRATEDAGONIST EMG (Q ) ag FIG. 2. The latency of the antagonist EMG burst as a function of the area of the agonist EMG burst. Each symbol is the average of - 10 movements. Thin solid lines are regression curves for movements of the same distance with different inertial loads. Thin dotted lines are regression curves of movements over 4 different distances with the same inertial load. The heavy solid line is the regression curve of the pooled data ( tant= 52.4 + l.O03Q,, r = 0.98). There is no significant difference between the slopes of the regression curves computed in the 2 ways.
AND AGARWAL ?-
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