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Superposition of motor programs—I. Rhythmic forearm movements in man
SUPERPOSITION OF MOTOR PROGRAMS-I, RHYTHMIC FORWARD MUV~MENTS IN MAN A.G. FBLDMAN Institute of Problems of Infarmation Transmission, Academy of Sciences, Ermaiova L9, 103oSI Moscow, U.SS.R. Abstract-_lhe so-called invariant ~b~racteristi~s of the elbow muscles are described, An invariant characteristic is a curve on a plot of elbow static. moment vs angle. An invar~a~t ~haracterist~c shows the elbow displacements in response to different amplitudes of toad change when the subjecr is told not to compensate, or not to intervene voluntary to correct the dcfkction of the arm. If an ~n~~~~a~onof the invariant characteristic is known, the degree of central tonic coactivation of antagonistic motoneurones can be estimated. The idea was utilized when analysing rhythmic movements (2-6 Hz) of the forearm that were carried out against a spring resistance (2-10Nm). When the spring was suddenly switched off, the d&e&on of forearm rose. The subject was told not to correct the deflection and not to interrupt the swingings. The mean changes of both muscle torque and joint angle were determined in the experiments so that it was possible to estimate the inclination of the invariant characteristic used at a given frequency. Judging by the results, central tonic coactivation of elbow flexors and extensors occurs and increases to maximum as the frequency of movement increases. In addition, the reciprocai activation of antagonistic mu&es is we3 known to occur upon execution of this movement. ft canbe concluded that both the reciprocal and the unjdire~t~o~al central c~~rna~ds to ~tagonjs~i~ motoneuroues occur simultaneously. The fun~tionaS significance~ as well as a scheme of supe~~sition, of these motor commands are discussed. ft is suggested that the commands are universal. i.e. the nervous system operates by using them during the performance of any movement.
TW~EACTIVITY of antagonistic muscles changes reciprocaify, especially during rhythmic movements. This is known as the law of the reciprocal inhibition discovered by SHERRINGTON (1906). An overlapping of e~~~omyo~arns (E?vK&f recorded from the muscles is not a serious objection to the law provided that the contrary change of the EMGs rakes place. But a unidirectional change of activity of the muscles, in paris sometimes ticular, their tonic coactivation observed, for instance, during jumps in the cat (ZOMLEWR,X,43& & LEVINE, 1977) as well as during voluntary efforts in human subjects (AIZERMAN,ANDREEVA, KANDJX & TENNENBAUM,1974). For the stability of posture and movement to be guaranteed this coacrivation must often occur (FELDMAN,1979). SIGIIRKNGTON (1906) supposed the reciprocal and unid~r~t~ona~ commands that are given to antagonistic muscles would exclude eaeb other. This point of view has not been ~hai~eng~d until recently* But it is possible that the nervous system can combine the commands in a proper manner depending upon mntar task. The present study was undertakes to check the hypothesis for rhythmic movements in an elbow joint. Why does EMG analysis of rhythmic movements make it possible to demonstrate so easily the reciproca! activation of antagonistic muscles but reveal very
seems to be that the component of coactivation is a tonic one in this case and is easily masked by the rhythmic reciprocal component. A scheme of the masking is represented in Fig. 1. Let us assume that the intensity of tfie central influence on a moto~euro~ pool of a given muscle changes rhythmically from +m to -m (A). The iaff uence with intensity f m is determined as an influence that can recruit m motoneurones. The influence with intensity -m is determined as an influence that can inhibit m working motoneuranes. In addition, the central inflow is capable of switching on tonically n motor units of the muscle (Bj. Consider a case n < m. To obtain a number of the actually recruited motor units, an algebraic sum of these influences must be calculated. If the sum is negative at some intervals of time, one must befieve the number to be zero at that time. As a res,&, a picture of the ‘EMG’ arises in which the tonic component is completely absent (C). Not knowing the genesis of the picture it is impossible to say whether there is a su~r~sit~on of two central programs or not. This example shows that EMG is not a reliable basis to judge the composition of motor program. A method which makes it possible to reveal the coactivating component in the eentrai program of the rhythmic movements ia an elbow joint is based essentially on experimental determination of the so-called invariant characteristics (KS) of muscles. Operating by these ~h~a~ter~stj~~ the nervous system brings about shifts of the e~u~~~br~urnpoint of the muscie&de of their co~~~iv~~~~~~ The reason
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EXPERIMENTAL
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PROCEDURES
Experimental demonstration of the ICs and analysis of rhythmic movements in the elbow joint was carried out using an apparatus shown in Fig. 2. The subject put his right forearm on the upper plate of the apparatus, clasping his hand round a vertical handle. The apparatus permitted flexion and extension of the forearm about the elbow in the horizontal plane. The elbow angle was measured with a variable resistance (D). A long steel lever (C) was fastened to a ball-bearing situated on the axis of rotation (0) of the platform. The lever was also attached to a rigid steel ring (A) connected in a diametrical point to the lower plate of the platform. The ring was the sensitive element of a strain gauge. Depending on the type of experiment (demonstration of the ICs or analysis of rhythmic movements), weights or springs, respectively. were roped on to electromagnetic locks (F) fixed to the lever C. The strain gauge was sensitive to the horizontal component of the load only because the vertical component of the pressure exerted on the lever C was compensated by a roller (B). For the registration of the ICs it is essential only that, in statics, the readings of the strain gauge are proportional to the load torque (P) which is equal to muscle torque (M) in that case. In general, the readings are proportional to deformation of the ring A. Let Q and R be the torques applied to the ring in its diametrical points. The torques arc created by the lever C and the rest of the platform. We consider Q = R because the inertia of the ring is negligible as compared with the inertia of the elements acting on it. Hence, the deformation of the ring is proportional to Q = R. The equations of motion of the lever and of the whole platform are of the form:
m+pLcLL FIG. I. Central tonic influences on the motoneuronal are masked in the electromyogram by the rhythmic
pool
ones (scheme). (A) The intensity of central influence on the motoneuronal pool changes rhythmically from +m to --m. The influence with intensity +m is defined as an influence that can recruit m motoneurones. The influence with intensity -m is defined as an influence that can inhibit m working motoneurones. (B) n Motoneurones are recruited by the tonic excitatory inflow. (C) The number of active motoneurones when both types of inflows are combined. A case n < m is shown. Abscissa: time (t).
load
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of it, the
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(FELDMAN 1966a,h, 1974; 1979; BIZZI, Po~rr & MORASSCI.1976). Therefore, the experimental study of ICs utilized during the performance of a movement seems to be an essential stage in the analyIc$ = P - Q. I;p; = P - M sis of its construction. II) To summarize briefly the conception of ICs, note that there are many controllable parameters of motoneuronal pool activity; for instance, a number of active motor units, the threshold and the gradient of their recruitment, the frequency of firing and so on. But it seems as if only one can be set by the nervous system independently from the others, as well as from muscle length and tension. This parameter is the threshold, i.e. the muscle length at which the tonic firing of motor units arises (MATTHEWS, 1959a,b; ASATRYAN & FELDMAN, 1965; FELDMAN, 1966a; FELDMAN & ORLOVSKY, 1972; HOUK, 1976; NICHOLS & HOUK, 1976). If the threshold is fixed, the tonic motoneuronal activity, i.e. a number of the motor units recruited as well as the muscle force is a single-valued and increasing function of the length. This function is an IC. With some reservation, ICs are similar to the tension-extension curves characterizing the tonic FIG. 2. The apparatus for the mechanographic analysis of stretch reflex in the decerebrate cat (MATTHEWS human forearm movements. A, sensitive element of strain 1959u,b; FELDMAN & ORLOVSKY, 1972). The indepengauge; B, roller compensating a vertical component of dently controllable parameter indicated above is idenpressure exerted on the lever C to which load is applied; D. tical with the threshold of the reflex. goniometer; E. range of the goniometer; F, electromagnetic Methods of experimental study of KS in normal locks to fasten a spring or another load to lever C: 0. axis of rotation of the platform. subjects have been described elsewhere (ASATRYAN& ment
arises
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Control of rhythmic movements
83
5
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FIG. 3. Two families of the invariant characteristics of the elbow muscles. Abscissa: elbow angle; ordinate: static muscle torque being positive for flexors and negative for extensors. The registration of each invariant characteristic began from the solid circle. (A) Family of KS of the flexors (above dashed line) and of the extensors (below); dashed line: passive muscle torque vs angle. (B) KS recorded against the background of maximal tonic coactivation of flexor and extensor muscles.
where ;d is the angle acceleration; I, 1, are the inertia of the whole platform (I = 0.11 kg. m2) and of its lever (I, = 0.03 kg. m2). For comparison, the inertia of the forearm is equal to about 0.05 kg.m2. Muscle torque M is considered to be positive if it tends to carry out flexion. Positive direction for a load of torque P is opposite to that for M. From the equation (I), the readings of the strain gauge are proportional to Q = M + (I - I,)$
= P - I,$.
(2)
This formula confirms that muscle torque is displayed on the meter, if 4 = 0. When the load torque P is equal to zero, the meter shows an angle acceleration ;f;. Furthermore, if the oscillations of the forearm are close to harmonic ones, the mean strain gauge readings measured for a period are proportional to the mean muscle torque as well as to load torque because the mean value of 0 is equal to zero in that case [see (2)]. The strain gauge was calibrated in terms of moment of forces (Nm) by load application to the lever C while the platform was motionless. Inoariant
characteristics
of forearm
muscles
In order to describe the ICs of the elbow muscles in their totality, such variables as the muscle moment (M) and the elbow angle (4) will be used. The shape of the ICs depends essentially on the number of the active muscles. Figure 3(A) shows one family of ICs recorded by the unloading method in man (ASATRYAN & FELDMAN,1965; FELDMAN,1979). A dashed line in Fig. 3(A) is the M - 4 characteristic of the passive muscles. The ICs of elbow flexors are situated above the line while those of extensors are below. When an IC of the flexors was recorded, the extensors, judging by the EMG, were not active and vice versa. Each of the ICs shows the elbow displacements in response to different amplitudes of load change when the subject was told not to intervene vohmtarily to correct the deflection of the arm. For instance, to
determine the upper left-hand IC, a monotonous series of experiments was carried out. In each trial, the elbow flexors were loaded and the subject set a predetermined elbow angle. A solid circle of the IC shows the respective initial combination of static M and 6. After a sudden decrease of the load the forearm transferred to another equilibrium position, if the instruction indicated above (‘not to correct’) was used. As a result, a new combination of static M and @Jwas taken up. It gave another point of the IC. The magnitude of the change in load was varied from trial to trial so that it was possible to determine several points of the IC (open circle). To find out another IC of the family the subject was told to set another initial elbow angle and an analogous series of unloading trials was repeated. It has been shown that the IC preserves its shape despite rather wide time-space variations in the load change procedure (ASATRYAN& FELDMAN,1965; FELDMAN,1979). Therefore, the term invariant characteristic is well founded. Note that ICs of the family in Fig. 3(A) branch off from different points characteristic of relaxed muscles (dashed line). This means that the transition from one IC of the flexors, for instance, to another is performed by means of the change of the threshold angle at which the motor units begin to recruit. For electromyographic evidence of this point see elsewhere (FELDMAN,1979). Let us donote the thresholds by &, where k = 1 for the flexors and k = 2 for the extensors. It is worth noting that the 1, and /?* are independently controllable parameters. Figure 3(B) shows another family of ICs each of which was recorded by the load change method when the subject carried out maximal tonic coactivation of all elbow muscles. The slope of the ICs of the B family is essentially greater than that of the A family. Hence, the stiffness of the muscle-load system increases under the cocontraction. Using the data on the independently controllable parameters /Ii and flZ, let us describe schematically the conversion of the A family into the B family. It should be noted
x4
FIG. 4. The change m the number of the active elbow muscles (A and B) as well as of the shape of invariant characteristics (C) due to regulation of difference between tonic stretch reflex thresholds of the flexors (/I,) and extensors (pz). Abscissa: elbow angle. Ordinates: active muscle torque (C), index of activation (A and B) of the flexors (up) and of the extensors (down); this index equal 1 or 0 depending on whether the respective group of muscles has motor units recruited or not. For further explanation see text
that the elbow flexors are active, if 4 > pi, while the extensors are active if 4 < /&. Let the index of activation of the flexors (extensors) equal 1 or 0 depending on whether the condition of activation of the flexors (extensors) is fulfilled or not. These indexes are shown in Fig. 4(A) and (B). It can be seen that if sz < Pi
(3)
the areas of activity of the flexors (F) and of the extensors (E) do not overlap (Fig. 4A), that is, inequality (3) is a necessary and sufficient condition for the absence of their tonic coactivation. If 111 > Pi
(4)
the F and E areas overlap (Fig. 4B). The more the difference between f12 and bi. the greater the area of the overlapping. Thus, the inequality (4) is a necessary condition of the coactivation. One can assume that the IC of the A family is converted into the IC of the B family as the difference between /I2 and pi increases. The conversion is illustrated in Fig. 4(C). Three ICs of the flexors (2-4) with pi = 91 , 77. and 54’ as well as one IC of the extensors (1) with /Iz = 159’ were taken from the A family of Fig. 3. The passive muscle torque was subtracted from the ICs. The dashed lines denoted by 1 + 2. 1 + 3 and 1 + 4 are algebraic sums of the respective ICs. The slope of the total ICs increases with increasing B2 - pi. Note that the /I2 - pi = 105” for the curve indicated by 1 + 4 but it is not a limit. To reach a limiting value of the slope, which is equal to that of ICs of the B family, fi, - [
The reciprocal activation of flexor and extensor motoneurones is well known to occur during rhythmical movements. The question is whether there is some joint central activation of the groups of motoneurones. To answer this question, the slope of the IC used must be estimated experimentally. Studies were performed on five normal subjects aged from 25 to 30yr. Similar qualitative data were obtained for all of them. In each trial, the subject set the elbow angle (100-105’) while overcoming the spring resistance to flexion (6-7 Nm). Then he was carrying out the rhythmic movements in the elbow joint at a some stable frequency (1-7 Hz). When the spring was suddenly switched off, the deflection of the forearm rose. The subject was told not to correct the deflection as well as not to interrupt the oscillations. It is worth mentioning that the instruction ‘not to correct’ is a fine point of the method of determination of the ICs. The experiments were repeated three to six times for one and the same frequency of movements. Readings of the goniometer and the strain gauge were displayed both orthogonally and continuously (Fig. 5). The subject could not see the display.
RESULTS Figure 5(A-C) shows orthogonal recordings of the goniometer and strain gauge readings during 2-5 cycles of movements at a low (2.3), moderate (4.1) and maximal (6.2 Hz) frequencies, It should be noted that the maximum (6.2 Hz) is not an absolute one (7-8 Hz, e.g. Fig. 7), as the inertia of the movable part of the apparatus sets the upper limits of the frequency. It means that the ‘central generator’ is not quite autonomous from the afferent inflow. The trajectory of movement displayed in the coordinates M and 4 is a
85
Control of rhythmic movements C
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FIG. 5. Effects of unloading during forearm rhythmic movements (A-D) and after their cessation (E and F). (A-C, E and F) Orthogonal recordings of readings of strain gauge (ordinate, Nm) and of goniometer (abscissa, degrees); the numbers show the frequency of oscillations (Hz). (D) Continuous recordings, of muscle moment M and of angle 4. Unloading in (E) and (F) was performed immediately after cessation of movements with frequency of 2.3 and 6.2 Hz, respectively. straightforward segment [Fig. 5(A-C)]. After unloading of the forearm, it is shifted below and left as both the mean muscle torque and joint angle decrease. Figure 5(D) shows a continuous recording of M and 4 at a frequency of 6.2 Hz. Transition to a new position of the forearm is accomplished for 200-300 ms. Rhythmic movement lasts without visible change of both phase and frequency (P < 0.05). It shows independence of the generator process from afferent influences created by the unloading. Under zero load the strain gauge readings are proportional to acceleration 4 [see (2) for P = 01. The fact that the trajectory of movement displayed in the orthogonal coordinates is a straightforward segment [Fig. 5(A-C)] means that 4 is proportional to I#J.This is a characteristic property of the harmonic oscillations. In this case the mean values of M and r$ coincide with the coordinates of the middle of the segment. Using this property let us estimate the inclination of the ICs used. The mean deflection of the forearm (A4) caused by the unloading decreases with increasing frequency and is equal to 23.5, 11.6 and 8.3” respectively for 2.3, 4.1 and 6.2 Hz, while the mean torque being changed (AM) by 5.8, 6.3, 6.7 Nm. AM should be divided by AI$ to measure the slope of the ICs used. Obviously, it increases with increasing frequency (14.2 f 0.7, 31.2 k 5.1, 46.5 k 9.3Nm/radian). This is confirmed also by the fact that the slope of the trajectory of movement [Fig. S(A-C)] behaves in a similar manner. It is of interest to compare the mean forearm deflections evoked by the unloading during the rhythmic movements and the corresponding stable posture. To do it, the subject was asked to stop the rhythmic movement, preserving the mean position of the forearm but not relaxing the muscles. Soon the spring was switched off. The same instruction ‘not to correct the
deflection of forearm’ was given to the subject. Figure 5(E and F) shows the effect of forearm unloading after stopping the oscillations with frequencies of 2.3 Hz (E) and 6.2 Hz (F). The deflections of the forearm are equal to 24.2” and 5.7”. The inclinations (AMlAb) of the ICs are equal to 13.5 + 0.6 and 57.7 + 9.5 Nm/ radian, being close to those observed during movements with a corresponding frequency (P < 0.05). This comparison shows that in spite of dynamic conditions during rhythmic movements the slope of the static, i.e. invariant characteristic, can be estimated rather exactly by the unloading method. The data obtained allow one to answer the question whether the central tonic coactivation of antagonistic motoneurones occurs during rhythmic movements or not. To verify this, consider again the A family of ICs for the same subject (Fig. 3A). Let us determine for any IC the decrease of 4 when the muscle torque is changed from 67 Nm to 0. The decrease proves to be greater than 40” while the greatest decrease in 4 under the same load change during rhythmic movements was equal to 23.5’. Hence it follows that during rhythmic movements (2-6 Hz) those ICs were used the slope of which was dictated by the central tonic coactivation of the antagonistic muscles. The data described above also show that the coactivation increases with increasing frequency up to maximum because the slope (46.6Nm/radian) of the IC used at 6.2 Hz approaches the limiting value (4&102Nm/radian) defined on the basis of the B family in Fig. 3(B).
DISCUSSION The present data confirm the hypothesis that the central tonic coactivation of fiexor and extensor motoneurones is performed during rhythmic forearm
movement together with their rhythmic reciprocal activation. Thus, the superposition of two motor programs takes place during such movements. Rapid active change of forearm posture in man has been shown to be performed by means of transfer of an IC (FELDMAN. 1966a,b). The inclination of the IC was noticeably greater than that of the ICs of the A family in Fig. 3(A). Hence it follows that the nervous system does employ the coactivation in that case as well. The reciprocal activation of the muscles is welt known to take place during such movements (WAC.H~~OLDEK& ALTENRERGER,1926; WAC.HHOLDER,1928; HUFSC‘HMIDT& HI_Y:S~HMIDT.1954: TANAKA, 1974: Kors, 1975). Consequently, the superposition of two central programs also takes place during rapid change of posture. Thus, the data described above do not support Sherrington’s view that the processes of the reciprocal and the joint activation of antagonistic muscles are alternatives (SHERRINGTON, 1906). These processes seem to be universal+ that is, the nervous system operates by them in a proper manner for any movement. Let us consider a scheme of superposition of these moior commands during rhythmical movements. Figure 6 shows a plane of the controllable parameters /I, (abscissa) and /12 (ordinate) normalized so that their minimal and maximal values are equal to 0 and 1. respectively. The normalized values are denoted by p, and &. A formula of the normalization is as foilows; jjrk= (P, - Bk )/(/I: -- B,, ).
k = 152
(5)
where & . /?; are minimal and maximal values of Pk. It is worth mentioning that /II and pZ are the elbow angles at which tonic recruitment of motor units of flexors and extensors begins, respectively. The multitude of the available meanings of PI and flZ is a square (Fig. 6). A condition of the coactivation is expressed by the inequality (4). For simplicity, let us assume that the minimal values of /I, and & are coincident (fiIm = b;) and so are the maximal ones (/ji = 8;). Then the condition for coactivation in terms of normalized variables preserves its form: $2 > PI.
0
V
(6)
I I
7%
FIG. 6. Superposition of the reciprocal and joint central commands on the antagonistic muscles during rhythmical movements (scheme). For explanations see text.
This area of values is \ltuated abobe a diagonal pa~bing through the point 0 of the square in Fig. 6. ‘~-he more the point (p,. pZ) rises above the diagonal. the stronger is the inequality (6) and. cotlsequcnt~~, the coactivation. Let us suppose now that the point moves along the diagonal or in parallel, Then /i, and /jL increase or decrease simultaneously. In this c;~sc. the reciprocal change of activity of antagonistic muscles happens because, if /I, and [iZ, for instance. increase, the condition of activ~itiol~ of the elbow flexors (4 > fi,) becomes weaker or is violated and that of the extensors (4 < /j,) becomes stronger. Figuratively. selecting a line parallel to the diagonal. the nervous system ensures the muscle stiffness required while the movement itself is performuct by displacement of the point along the line. According to the data obtained. we can believe that as frequency increases the higher is the line which is selected. This is symbolized by the numbers (Hz) near the linca in the diagram (Fig. 6). But one should make this conclusion more precise. From our own experience we know that it is possible to produce rhythmic movements with low frequency both during high and low coactivation of muscles. But it is impossible to produce rhythmic movements with maximal frequency during low coactivation. To take these facts into account, one should consider that. in order to produce the movement with a frequency, for instnncc, of 2 Hz. the nervous system can select either the line marked by 2 in Fig. 6 or an) line situated above and parallel to it. So. for a given frequency of the movement, the parametric operational area IS a triangle limited by the left and the upper sides of the square and a line marked by the respective number in Fig. 6. ft is worth empbasizing that displacemenr of the point (B,. /3,) caused by one of the central programs turns out to be perpendicular to that caused by another. So. the reciprocal and joint commands seem to be, in a mathematical sense, the orthogonal basis for the construction of any motor program. Hence, any combination of I{, and p2 can be provided by the proper combination of the central commands. In particular, one of the parameters can be changed independently of another in this way. So, it is possible to control activity of the muscles individually (for instance, to change activity of the flexors, preserving activity of the extensors) by means of superposition of the central commands, each of which evident]! controls the groups non-individually. A proof of the proper mathematical theorem is given in Theoretical Appendix. The superposition of the motor programs seems to be very expedient for different reasons. It should be mentioned that the natural frequency of the muscle load system is dependent on static stiffness of the muscles, i.e. on the slope of the IC (FEI.DMAN. 1979). Therefore, in performing the tonic coactivation. the nervous system seems to bring the natural frequency into accord with that predetermined by the centrat
Control of rhythmic movements
87
2.0
I,.3
75
) 0.55 4.6
1 5.6
FIG. 7. Decrease of maximal amphtude with increasing frequency of oscillation. Marks: surface EMGs of triceps and biceps brachii muscles (tric. bit), elbow angle (I#$,frequencies of movements (numbers above oscillograms, Hz). On the right: a pIot of maximal amplitude (ordinate) attainable under a given frequency (abscissa).
generator which accomplishes reciprocal activation of the antagonistic muscles. The fact that the dope of the ICs changed with the rhythm of movements is evidence for the control of the natural frequency (Fig. S[A-Cl). If rhythmic movement is a harmonic (sinusoidal) one, as took place in this study, the muscle torque is known to be proportional to the amplitude of displacement as we11 as to the square of frequency. Besides, the increase of the force of the muscles occurs in the phase of their extension [Fig. .5(D)]. So, when the frequency is near to maximum the amplitude of movement must be limited to prevent extreme muscle extension that can cause trauma (RACK & WESTBURY, 1969). The limitation of the amplitude movement is automaticaIly provided by su~rposition of the two motor commands. Actually, Fig. 6 shows that the operational areas in which the point @,, &) can be
shifted by the reciprocal program narrows with increasing frequency. This means that maximal amplitude of the movement itself must decrease with increasing frequency. The reader can learn this from his own experience. This fact is documented in Fig. 7. The subject was performing (out of the apparatus) the rhythmic movements of the forearm trying to reach a maximum amplitude at a frequency which gradually increased up to a limiting value (7.1 Hz). It can be seen in Fig. 7 that the amplitude does decrease (see also A~ZERMAN er al., 1974). Thus, the effect can be easily accounted for by the superposition of motor commands. As it is seen from Fig. 7, the amplitudes of burst activity of the flexor and extensor increased with increasing frequency, This fact is considered to be an electromyographic sign of the increasing tonic coactivation of antagonistic muscles.
RE~RENCES AIZERMANM. A., ANDREEVA K. A., KANDELE. L. 8~ TENNENBAUM L. A. (1974) Mechanisms in rhe Control of Muscle Activity (Norm and Pathology). Publ. House ‘Nauka’, Moscow. (In Russian.) ASATRYAND. G. & FELDMANA. G. (1965) Functional tuning of the nervous system with control of movement or
maintenance of a steady posture--I. Mechanographic analysis of the work of the joint on execution of a postural task. Biophysics IO, 925-935. BIZZI E., POLITA. 8r MO~A~SCI P. (1976) Mechanisms underlying achievement of final head position. J. N~~r~~~~~~i~~. 39, 435-444. FELDMANA. G. (19%) Functional tuning of the nervous system with control of movement or maintenance of a steady posture-II. Controllable parameters of the muscle. Biophysics 11, 565-578. FELDMAN A. G. (19666) Functional tuning of the nervous system with control of movement or maintenance of a steady posture--III. Mechanographic analysis of the execution by man of the simplest motor tasks. Biophl~sics II, 766775. FELDMANA. G. (1974) Control of length of the muscle. Biopkysies 19, 766-771. FELDMANA. G. (1979) Centraf and Re$ex ~~ec~a~is~ in rhe Control of movements. Publ. House ‘Nauka’, Moscow. (In Russian.) FELDMANA. G. & ORLOVSKY G. N. (1972) The influence of different descending systems on the tonic stretch reflex in the cat. Expl Neural. 37, 481494. HUF%HMIDTH. J. & HUFSCHMIDT T. (1954) Antagonist inhibition as the earliest sign of a sensory-motor reaction. Nature, Land. 174,607-619. HOW J. C. (1976) An assessment of stretch reflex function. Frog. Brain Res. 44, 303-314. KOTSY. M. (1975) Org~ni~u~~o~of Volu~rury ~4o~ement. Publ. House ‘Nauka’, Moscow. (In Russian.} v.s.[‘.
5!,-
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A. G. FELDMAN
MATT~WS P. B. C. (1959~) The dependence of tension upon extension in the stretch reflex of the soleus mubclc ,II the decerebrate cat. J. Ph,~.siol.. Land. 147. 521-546. MATTHE~S P. B. C. (1959b) A study of certam factors influencing the stretch reflex of the decerebrate cat. J. Phr,t~d, I.,& 147. 547 564. NI~.F~OI.ST. R. & HO~IK J. C. (1976) Improvement in linearity and regulation of stiffness that results from action? (II‘stretch r&x. J. Nruwph~xiol. 39. I I9 142. RA(.K P. M. H. & WFSTR~JRY D. R. (1969) The effect of length and stimulus rate on tension in the isometric cat saleus muscle. J. Physiol., Lord 204, 443460. SHERKINGTO~ C. S. (1906) Intryrcrrire Action of rhr Nrrrous System. Yale University Press. TANAKA R. (1974) Reciprocal la inhibition during voluntary movements in man. Expl Bruin RCA. 21, 529-540. WA(‘HHot.Dt:a K. (1928) Willkiirliche Haltung und Bewegung insbesondere im Lichte electrophysiologischer Untersuchungen. Ergrhn. Physiol. 26, 56% 775. WA(.HfioLoFR K. & ALTENHURGER H. (1926) Beitrgge zur Physiologie der willkiirlichen Bewegung-m IO. Einzelbewegungen. Pf1iiyer.t Art+. ga. Physiol. 214, 642-661. ZOMLWER bl.R.. ZAJA~. F. E. & LEVINE W. S. (1977) Kinematics and muscular activity of cats during maximum height jumpy. Brtrin. Rtz\. 126, 563- 566. (Accepted
THEORETICAL
APPENDIX
A THI:OREMhas been mentioned that the nervous system, by combining the reciprocal and joint activation programs. can determine the different (if any) combinations of activities of synergistic and antagonistic muscles controlling a mechanical degree of freedom and can, in particular, alter the activity of one muscle group independently of another. While proving this. we also show that these programs are not absolutely independent, i.e. changes in one of them can restrict the variation in the other. The proof of this theorem is based on the supposition that the motoneuronal pool of the given muscle group is controlled monoparametrically by determining the static threshold [jI, of the stretch reflex (k = I for flexors and li = 2 for extensors; subscript k is omitted. if the action of one group only. for clearness. of flexors is considered). It is worth noting that the alternative hypothesis (that several independent parameters control the muscle group) does not reject the theorem completely but somewhat narrows Its limits. For instance. if the static threshold of each of the synergistic muscles turns out to be controlled independentI>. the theorem must be referred to any antagonistic muscle pair (flexor ~extensor). Besides. the dynamic sensitivity of the stretch reflex determined by the activity of the dynamic y-motoneurones could be an additional parameter controlling the r-motoneuronal pool of the given muscle.
‘t
In the case, regulation of the static thresholds allows one to determine any type of static activity of the pair, but not all types of its dynamic activity. To prove the theorem, it is necessary, first of all, to explain why regulation of the parameter /I allows one effectively to control the activity of one muscle and. ultimately, its length and tension. Figure .X(A) shows the determination of the so-called equilibrium point of the tricomponent system (motoneuronal pool&muscle-load). The solid line beginning from the threshold point /I is a characteristic of the tonic stretch reflex. The dashed line is a characteristic of the load. which need not be external but can be set by the antagonistic muscles. The point a where the lines intersect is an cquilibrium point of the system. Coordinates of this point are equilibrium meanings of the joint angle and the torque. It is worth noting that a certain number of motoneurones recruited corresponds to each point of the solid line so that. on principle, this number can be found out for the equilibrium point as well. Evidently, in order to move the load to another position, it is necessary to shift the equilibrium point. The change of the static threshold /I is the most effective method of hringing about the shift: this is shown in Fig. 8(B). There are considered to be three regimes of muscle work. In the isometric regime, the load characteristic is a vertical line I. In the Isotonic regime, the load characteristic is a horizontal
--ALM (A)
P
?I Muv 1979)
9
--_-O
P3
(B)
2
5--z-
3 --B
d
C
\O
->8'
43 I I’
I ,'
FIG. 8. Equilibrium ponts of the tricomponent system (load-muscle-motoneurones). (A) Definition of equilibrium points (EP) (a); solid line: characteristic of the tonic stretch reflex (static muscle torque versus joint angle); p: its threshold: dashed line: some load characteristic; I’. 6: equilibrium torque and angle, respectively. (B) Change of the threshold of the reflex (,f?’ -+ /12) as an effective method of the shift of EP: a: initial EP: b-d: final EPs during isometric (1). isotonic (2) and intermediate (3) regimes of the muscle contraction: l-3: load characteristics of these regimes; P,, & (k = l-3): equilibrium torques and angles for respective EPs.
89
Control of rhyth imic movements
line 2. In the remaining cases, the load characteristic is some line 3 not coinciding with lines I or 2. The initial equilibrium point for all of the regimes was chosen to be identical (a) so that the system is in equilibrium at +r = 42 when the muscle torque equals P,. One can see that when the threshold is attered f@’+ 8’) the system transfers to a new equilibrium point fb, c or d, depending on the regime). The shift of this point leads to a change in the equilibrium torque (PZ - PI) in the isometric regime, of the joint angle t#r -&) in the isotonic regime, of both the torque [Pa --* P3) and the angfe f& -+ 4p,) in the intermcdiatc regime. It is evident that the physiological range of the change of the muscle torque and joint angle can be achieved provided there is a sufficiently wide range of the parameter p. It is worth noting that the shift of the equilibrium point is nat only a necessary but a sufficient condition of the initiation of active movement. Based upon it, one can describe the dynamics and, as web, the main electromyographic events during an active change of posture (see for details, Feldman, 1974; f 979). To prove the theorem, we consider again the multitude of permissible meanings of the parameters normalized by (5) and denoted by fir and 8,. This multitude presents a square (Fig, 9A). Note that the correlation
where A& (k = 1, 2) is an increase of &. is executed on both a diagonal of the square passing tbrougb point D and any line gorng in paraliel. In accord with the explanation given before, the correlation (7) and direction of the diagonal symbolize the program of reciprocal activation. It is worth making a reservation that the coefficients before A& in (5) and in the following correlation (8) are taken to be equal to 1, although their actual meanings are not known. Nevertheless, this reservation does not put the limits on the theorem to be proved. The correlation
is executed on the other diagonal of the square and on any jine going in parallel. ‘This correlation and the direction of the diagonal symbolize the program of the joint activation. By definition, simultaneous inhibition of both muscle groups is a particular manifestation of the program of joint activation. Let e, and eZ be the unit vectors directed in parallci to the diagonals of the square (Fig. 9A). Let also B = (B, ~&) be a vector characterizing a current state of the controlling system and &, indicate this vector when both programs are not used a&ail. The exact meaning of & is not known. Figure 9fg) shows that
(Cl
FSG. 9. Vector representation of the motor programs on the plane of the controlling parameters ?, and Pa which are the normalized threshold of activation of flexors and extensors, respectively. (A) Vector Ip0 shows a state of the system when both motor programs are off; e, and e, : unit vectors symbolizing these programs+ (13)Expansion of the voluntary program B into basis e, and e2 ; a, and aZ : variables showing a degree of utilizing of the motor programs. (C) Multitude of permissible meanings of or and aa when &, = (l,O)+
of a limb. One of the possible generalizations is described elsewhere (hmsf~~, WY). Now, let us determine the available meanings of aI and a2. Consider. for simplicity, a case /lo i= (1, 0) which means full relaxation of the muscle under zero action of both programs. BY (91,
BY- 1 = (a~ -
a,).$/2
(9)
The parameters Br , fit2change from 0 to t and therefore, by (1017
where u1 and aa are scalar variables determinative the contribution of the program of the reciprocal (at) and joint (aA) activation. These variables are considered to be the time functions which are chosen by the nervous system in relation on motor tasks. The formula (9) proves to be right for any fr,. We have shown that any state of the system can be considered as a result of successive or simultaneous apphcations of two central programs under consideration. The principle of superposition of motor programs in the form of the vector eq (9) can be generatized for the control
Geometrically, the inequalities (1 I) determine a square with diagonals going along the axis of the coordinates (Fig. 9Cf. There is a single-vaiued corresponding between its points and points of the square on the plane of the parameters Dr. B2,so that the first square transfers into the second by means of turning by n/4. One may see in Fig. 9(C) that the independence of two programs cannot be absolute because the possibie mean-
b - B0 = alet + a2e2
:I. G. Et-1 I)\I.\\
90 ings of one of the variables (LI, or u2) arc limited increase in the other. In particular,
activation of the muscles occurs (uIz = , reduced to
21. the program 01
reclprocitg
is
assumption
that the reciprocal and joint
mands arc aitcrnativcs utely unjustilicd
zero
bq an
when the maximal joint ((I, = 0)
(SHI.KKtI\G’Tos.
Therefore activation
the com-
1906) ib not abwl-
because they do prove to bc alternative
111
the extreme c;w~s. In this connection nnc ma! suggest that
TW~EACTIVITY of antagonistic muscles changes reciprocaify, especially during rhythmic movements. This is known as the law of the reciprocal inhibition discovered by SHERRINGTON (1906). An overlapping of e~~~omyo~arns (E?vK&f recorded from the muscles is not a serious objection to the law provided that the contrary change of the EMGs rakes place. But a unidirectional change of activity of the muscles, in paris sometimes ticular, their tonic coactivation observed, for instance, during jumps in the cat (ZOMLEWR,X,43& & LEVINE, 1977) as well as during voluntary efforts in human subjects (AIZERMAN,ANDREEVA, KANDJX & TENNENBAUM,1974). For the stability of posture and movement to be guaranteed this coacrivation must often occur (FELDMAN,1979). SIGIIRKNGTON (1906) supposed the reciprocal and unid~r~t~ona~ commands that are given to antagonistic muscles would exclude eaeb other. This point of view has not been ~hai~eng~d until recently* But it is possible that the nervous system can combine the commands in a proper manner depending upon mntar task. The present study was undertakes to check the hypothesis for rhythmic movements in an elbow joint. Why does EMG analysis of rhythmic movements make it possible to demonstrate so easily the reciproca! activation of antagonistic muscles but reveal very
seems to be that the component of coactivation is a tonic one in this case and is easily masked by the rhythmic reciprocal component. A scheme of the masking is represented in Fig. 1. Let us assume that the intensity of tfie central influence on a moto~euro~ pool of a given muscle changes rhythmically from +m to -m (A). The iaff uence with intensity f m is determined as an influence that can recruit m motoneurones. The influence with intensity -m is determined as an influence that can inhibit m working motoneuranes. In addition, the central inflow is capable of switching on tonically n motor units of the muscle (Bj. Consider a case n < m. To obtain a number of the actually recruited motor units, an algebraic sum of these influences must be calculated. If the sum is negative at some intervals of time, one must befieve the number to be zero at that time. As a res,&, a picture of the ‘EMG’ arises in which the tonic component is completely absent (C). Not knowing the genesis of the picture it is impossible to say whether there is a su~r~sit~on of two central programs or not. This example shows that EMG is not a reliable basis to judge the composition of motor program. A method which makes it possible to reveal the coactivating component in the eentrai program of the rhythmic movements ia an elbow joint is based essentially on experimental determination of the so-called invariant characteristics (KS) of muscles. Operating by these ~h~a~ter~stj~~ the nervous system brings about shifts of the e~u~~~br~urnpoint of the muscie&de of their co~~~iv~~~~~~ The reason
X2
w
A. G.
A
m
0
-m
FELDMAN. 1965; FELDMAN. 196611; 1979) and marized
briefly
O-t
arc hum-
below.
EXPERIMENTAL
t
B
n
FEl.I)MAI\
PROCEDURES
Experimental demonstration of the ICs and analysis of rhythmic movements in the elbow joint was carried out using an apparatus shown in Fig. 2. The subject put his right forearm on the upper plate of the apparatus, clasping his hand round a vertical handle. The apparatus permitted flexion and extension of the forearm about the elbow in the horizontal plane. The elbow angle was measured with a variable resistance (D). A long steel lever (C) was fastened to a ball-bearing situated on the axis of rotation (0) of the platform. The lever was also attached to a rigid steel ring (A) connected in a diametrical point to the lower plate of the platform. The ring was the sensitive element of a strain gauge. Depending on the type of experiment (demonstration of the ICs or analysis of rhythmic movements), weights or springs, respectively. were roped on to electromagnetic locks (F) fixed to the lever C. The strain gauge was sensitive to the horizontal component of the load only because the vertical component of the pressure exerted on the lever C was compensated by a roller (B). For the registration of the ICs it is essential only that, in statics, the readings of the strain gauge are proportional to the load torque (P) which is equal to muscle torque (M) in that case. In general, the readings are proportional to deformation of the ring A. Let Q and R be the torques applied to the ring in its diametrical points. The torques arc created by the lever C and the rest of the platform. We consider Q = R because the inertia of the ring is negligible as compared with the inertia of the elements acting on it. Hence, the deformation of the ring is proportional to Q = R. The equations of motion of the lever and of the whole platform are of the form:
m+pLcLL FIG. I. Central tonic influences on the motoneuronal are masked in the electromyogram by the rhythmic
pool
ones (scheme). (A) The intensity of central influence on the motoneuronal pool changes rhythmically from +m to --m. The influence with intensity +m is defined as an influence that can recruit m motoneurones. The influence with intensity -m is defined as an influence that can inhibit m working motoneurones. (B) n Motoneurones are recruited by the tonic excitatory inflow. (C) The number of active motoneurones when both types of inflows are combined. A case n < m is shown. Abscissa: time (t).
load
system
and,
as a consequence
of it, the
move-
(FELDMAN 1966a,h, 1974; 1979; BIZZI, Po~rr & MORASSCI.1976). Therefore, the experimental study of ICs utilized during the performance of a movement seems to be an essential stage in the analyIc$ = P - Q. I;p; = P - M sis of its construction. II) To summarize briefly the conception of ICs, note that there are many controllable parameters of motoneuronal pool activity; for instance, a number of active motor units, the threshold and the gradient of their recruitment, the frequency of firing and so on. But it seems as if only one can be set by the nervous system independently from the others, as well as from muscle length and tension. This parameter is the threshold, i.e. the muscle length at which the tonic firing of motor units arises (MATTHEWS, 1959a,b; ASATRYAN & FELDMAN, 1965; FELDMAN, 1966a; FELDMAN & ORLOVSKY, 1972; HOUK, 1976; NICHOLS & HOUK, 1976). If the threshold is fixed, the tonic motoneuronal activity, i.e. a number of the motor units recruited as well as the muscle force is a single-valued and increasing function of the length. This function is an IC. With some reservation, ICs are similar to the tension-extension curves characterizing the tonic FIG. 2. The apparatus for the mechanographic analysis of stretch reflex in the decerebrate cat (MATTHEWS human forearm movements. A, sensitive element of strain 1959u,b; FELDMAN & ORLOVSKY, 1972). The indepengauge; B, roller compensating a vertical component of dently controllable parameter indicated above is idenpressure exerted on the lever C to which load is applied; D. tical with the threshold of the reflex. goniometer; E. range of the goniometer; F, electromagnetic Methods of experimental study of KS in normal locks to fasten a spring or another load to lever C: 0. axis of rotation of the platform. subjects have been described elsewhere (ASATRYAN& ment
arises
I---’
Control of rhythmic movements
83
5
E
z
0
-5
FIG. 3. Two families of the invariant characteristics of the elbow muscles. Abscissa: elbow angle; ordinate: static muscle torque being positive for flexors and negative for extensors. The registration of each invariant characteristic began from the solid circle. (A) Family of KS of the flexors (above dashed line) and of the extensors (below); dashed line: passive muscle torque vs angle. (B) KS recorded against the background of maximal tonic coactivation of flexor and extensor muscles.
where ;d is the angle acceleration; I, 1, are the inertia of the whole platform (I = 0.11 kg. m2) and of its lever (I, = 0.03 kg. m2). For comparison, the inertia of the forearm is equal to about 0.05 kg.m2. Muscle torque M is considered to be positive if it tends to carry out flexion. Positive direction for a load of torque P is opposite to that for M. From the equation (I), the readings of the strain gauge are proportional to Q = M + (I - I,)$
= P - I,$.
(2)
This formula confirms that muscle torque is displayed on the meter, if 4 = 0. When the load torque P is equal to zero, the meter shows an angle acceleration ;f;. Furthermore, if the oscillations of the forearm are close to harmonic ones, the mean strain gauge readings measured for a period are proportional to the mean muscle torque as well as to load torque because the mean value of 0 is equal to zero in that case [see (2)]. The strain gauge was calibrated in terms of moment of forces (Nm) by load application to the lever C while the platform was motionless. Inoariant
characteristics
of forearm
muscles
In order to describe the ICs of the elbow muscles in their totality, such variables as the muscle moment (M) and the elbow angle (4) will be used. The shape of the ICs depends essentially on the number of the active muscles. Figure 3(A) shows one family of ICs recorded by the unloading method in man (ASATRYAN & FELDMAN,1965; FELDMAN,1979). A dashed line in Fig. 3(A) is the M - 4 characteristic of the passive muscles. The ICs of elbow flexors are situated above the line while those of extensors are below. When an IC of the flexors was recorded, the extensors, judging by the EMG, were not active and vice versa. Each of the ICs shows the elbow displacements in response to different amplitudes of load change when the subject was told not to intervene vohmtarily to correct the deflection of the arm. For instance, to
determine the upper left-hand IC, a monotonous series of experiments was carried out. In each trial, the elbow flexors were loaded and the subject set a predetermined elbow angle. A solid circle of the IC shows the respective initial combination of static M and 6. After a sudden decrease of the load the forearm transferred to another equilibrium position, if the instruction indicated above (‘not to correct’) was used. As a result, a new combination of static M and @Jwas taken up. It gave another point of the IC. The magnitude of the change in load was varied from trial to trial so that it was possible to determine several points of the IC (open circle). To find out another IC of the family the subject was told to set another initial elbow angle and an analogous series of unloading trials was repeated. It has been shown that the IC preserves its shape despite rather wide time-space variations in the load change procedure (ASATRYAN& FELDMAN,1965; FELDMAN,1979). Therefore, the term invariant characteristic is well founded. Note that ICs of the family in Fig. 3(A) branch off from different points characteristic of relaxed muscles (dashed line). This means that the transition from one IC of the flexors, for instance, to another is performed by means of the change of the threshold angle at which the motor units begin to recruit. For electromyographic evidence of this point see elsewhere (FELDMAN,1979). Let us donote the thresholds by &, where k = 1 for the flexors and k = 2 for the extensors. It is worth noting that the 1, and /?* are independently controllable parameters. Figure 3(B) shows another family of ICs each of which was recorded by the load change method when the subject carried out maximal tonic coactivation of all elbow muscles. The slope of the ICs of the B family is essentially greater than that of the A family. Hence, the stiffness of the muscle-load system increases under the cocontraction. Using the data on the independently controllable parameters /Ii and flZ, let us describe schematically the conversion of the A family into the B family. It should be noted
x4
FIG. 4. The change m the number of the active elbow muscles (A and B) as well as of the shape of invariant characteristics (C) due to regulation of difference between tonic stretch reflex thresholds of the flexors (/I,) and extensors (pz). Abscissa: elbow angle. Ordinates: active muscle torque (C), index of activation (A and B) of the flexors (up) and of the extensors (down); this index equal 1 or 0 depending on whether the respective group of muscles has motor units recruited or not. For further explanation see text
that the elbow flexors are active, if 4 > pi, while the extensors are active if 4 < /&. Let the index of activation of the flexors (extensors) equal 1 or 0 depending on whether the condition of activation of the flexors (extensors) is fulfilled or not. These indexes are shown in Fig. 4(A) and (B). It can be seen that if sz < Pi
(3)
the areas of activity of the flexors (F) and of the extensors (E) do not overlap (Fig. 4A), that is, inequality (3) is a necessary and sufficient condition for the absence of their tonic coactivation. If 111 > Pi
(4)
the F and E areas overlap (Fig. 4B). The more the difference between f12 and bi. the greater the area of the overlapping. Thus, the inequality (4) is a necessary condition of the coactivation. One can assume that the IC of the A family is converted into the IC of the B family as the difference between /I2 and pi increases. The conversion is illustrated in Fig. 4(C). Three ICs of the flexors (2-4) with pi = 91 , 77. and 54’ as well as one IC of the extensors (1) with /Iz = 159’ were taken from the A family of Fig. 3. The passive muscle torque was subtracted from the ICs. The dashed lines denoted by 1 + 2. 1 + 3 and 1 + 4 are algebraic sums of the respective ICs. The slope of the total ICs increases with increasing B2 - pi. Note that the /I2 - pi = 105” for the curve indicated by 1 + 4 but it is not a limit. To reach a limiting value of the slope, which is equal to that of ICs of the B family, fi, - [
The reciprocal activation of flexor and extensor motoneurones is well known to occur during rhythmical movements. The question is whether there is some joint central activation of the groups of motoneurones. To answer this question, the slope of the IC used must be estimated experimentally. Studies were performed on five normal subjects aged from 25 to 30yr. Similar qualitative data were obtained for all of them. In each trial, the subject set the elbow angle (100-105’) while overcoming the spring resistance to flexion (6-7 Nm). Then he was carrying out the rhythmic movements in the elbow joint at a some stable frequency (1-7 Hz). When the spring was suddenly switched off, the deflection of the forearm rose. The subject was told not to correct the deflection as well as not to interrupt the oscillations. It is worth mentioning that the instruction ‘not to correct’ is a fine point of the method of determination of the ICs. The experiments were repeated three to six times for one and the same frequency of movements. Readings of the goniometer and the strain gauge were displayed both orthogonally and continuously (Fig. 5). The subject could not see the display.
RESULTS Figure 5(A-C) shows orthogonal recordings of the goniometer and strain gauge readings during 2-5 cycles of movements at a low (2.3), moderate (4.1) and maximal (6.2 Hz) frequencies, It should be noted that the maximum (6.2 Hz) is not an absolute one (7-8 Hz, e.g. Fig. 7), as the inertia of the movable part of the apparatus sets the upper limits of the frequency. It means that the ‘central generator’ is not quite autonomous from the afferent inflow. The trajectory of movement displayed in the coordinates M and 4 is a
85
Control of rhythmic movements C
B
A 4.1
2.3
D
Nm 120”
6.2
80”
IO
5” 0
Fd
F
E
1 ::‘* a0
.
?
loo’
d 00
IOC?
FIG. 5. Effects of unloading during forearm rhythmic movements (A-D) and after their cessation (E and F). (A-C, E and F) Orthogonal recordings of readings of strain gauge (ordinate, Nm) and of goniometer (abscissa, degrees); the numbers show the frequency of oscillations (Hz). (D) Continuous recordings, of muscle moment M and of angle 4. Unloading in (E) and (F) was performed immediately after cessation of movements with frequency of 2.3 and 6.2 Hz, respectively. straightforward segment [Fig. 5(A-C)]. After unloading of the forearm, it is shifted below and left as both the mean muscle torque and joint angle decrease. Figure 5(D) shows a continuous recording of M and 4 at a frequency of 6.2 Hz. Transition to a new position of the forearm is accomplished for 200-300 ms. Rhythmic movement lasts without visible change of both phase and frequency (P < 0.05). It shows independence of the generator process from afferent influences created by the unloading. Under zero load the strain gauge readings are proportional to acceleration 4 [see (2) for P = 01. The fact that the trajectory of movement displayed in the orthogonal coordinates is a straightforward segment [Fig. 5(A-C)] means that 4 is proportional to I#J.This is a characteristic property of the harmonic oscillations. In this case the mean values of M and r$ coincide with the coordinates of the middle of the segment. Using this property let us estimate the inclination of the ICs used. The mean deflection of the forearm (A4) caused by the unloading decreases with increasing frequency and is equal to 23.5, 11.6 and 8.3” respectively for 2.3, 4.1 and 6.2 Hz, while the mean torque being changed (AM) by 5.8, 6.3, 6.7 Nm. AM should be divided by AI$ to measure the slope of the ICs used. Obviously, it increases with increasing frequency (14.2 f 0.7, 31.2 k 5.1, 46.5 k 9.3Nm/radian). This is confirmed also by the fact that the slope of the trajectory of movement [Fig. S(A-C)] behaves in a similar manner. It is of interest to compare the mean forearm deflections evoked by the unloading during the rhythmic movements and the corresponding stable posture. To do it, the subject was asked to stop the rhythmic movement, preserving the mean position of the forearm but not relaxing the muscles. Soon the spring was switched off. The same instruction ‘not to correct the
deflection of forearm’ was given to the subject. Figure 5(E and F) shows the effect of forearm unloading after stopping the oscillations with frequencies of 2.3 Hz (E) and 6.2 Hz (F). The deflections of the forearm are equal to 24.2” and 5.7”. The inclinations (AMlAb) of the ICs are equal to 13.5 + 0.6 and 57.7 + 9.5 Nm/ radian, being close to those observed during movements with a corresponding frequency (P < 0.05). This comparison shows that in spite of dynamic conditions during rhythmic movements the slope of the static, i.e. invariant characteristic, can be estimated rather exactly by the unloading method. The data obtained allow one to answer the question whether the central tonic coactivation of antagonistic motoneurones occurs during rhythmic movements or not. To verify this, consider again the A family of ICs for the same subject (Fig. 3A). Let us determine for any IC the decrease of 4 when the muscle torque is changed from 67 Nm to 0. The decrease proves to be greater than 40” while the greatest decrease in 4 under the same load change during rhythmic movements was equal to 23.5’. Hence it follows that during rhythmic movements (2-6 Hz) those ICs were used the slope of which was dictated by the central tonic coactivation of the antagonistic muscles. The data described above also show that the coactivation increases with increasing frequency up to maximum because the slope (46.6Nm/radian) of the IC used at 6.2 Hz approaches the limiting value (4&102Nm/radian) defined on the basis of the B family in Fig. 3(B).
DISCUSSION The present data confirm the hypothesis that the central tonic coactivation of fiexor and extensor motoneurones is performed during rhythmic forearm
movement together with their rhythmic reciprocal activation. Thus, the superposition of two motor programs takes place during such movements. Rapid active change of forearm posture in man has been shown to be performed by means of transfer of an IC (FELDMAN. 1966a,b). The inclination of the IC was noticeably greater than that of the ICs of the A family in Fig. 3(A). Hence it follows that the nervous system does employ the coactivation in that case as well. The reciprocal activation of the muscles is welt known to take place during such movements (WAC.H~~OLDEK& ALTENRERGER,1926; WAC.HHOLDER,1928; HUFSC‘HMIDT& HI_Y:S~HMIDT.1954: TANAKA, 1974: Kors, 1975). Consequently, the superposition of two central programs also takes place during rapid change of posture. Thus, the data described above do not support Sherrington’s view that the processes of the reciprocal and the joint activation of antagonistic muscles are alternatives (SHERRINGTON, 1906). These processes seem to be universal+ that is, the nervous system operates by them in a proper manner for any movement. Let us consider a scheme of superposition of these moior commands during rhythmical movements. Figure 6 shows a plane of the controllable parameters /I, (abscissa) and /12 (ordinate) normalized so that their minimal and maximal values are equal to 0 and 1. respectively. The normalized values are denoted by p, and &. A formula of the normalization is as foilows; jjrk= (P, - Bk )/(/I: -- B,, ).
k = 152
(5)
where & . /?; are minimal and maximal values of Pk. It is worth mentioning that /II and pZ are the elbow angles at which tonic recruitment of motor units of flexors and extensors begins, respectively. The multitude of the available meanings of PI and flZ is a square (Fig. 6). A condition of the coactivation is expressed by the inequality (4). For simplicity, let us assume that the minimal values of /I, and & are coincident (fiIm = b;) and so are the maximal ones (/ji = 8;). Then the condition for coactivation in terms of normalized variables preserves its form: $2 > PI.
0
V
(6)
I I
7%
FIG. 6. Superposition of the reciprocal and joint central commands on the antagonistic muscles during rhythmical movements (scheme). For explanations see text.
This area of values is \ltuated abobe a diagonal pa~bing through the point 0 of the square in Fig. 6. ‘~-he more the point (p,. pZ) rises above the diagonal. the stronger is the inequality (6) and. cotlsequcnt~~, the coactivation. Let us suppose now that the point moves along the diagonal or in parallel, Then /i, and /jL increase or decrease simultaneously. In this c;~sc. the reciprocal change of activity of antagonistic muscles happens because, if /I, and [iZ, for instance. increase, the condition of activ~itiol~ of the elbow flexors (4 > fi,) becomes weaker or is violated and that of the extensors (4 < /j,) becomes stronger. Figuratively. selecting a line parallel to the diagonal. the nervous system ensures the muscle stiffness required while the movement itself is performuct by displacement of the point along the line. According to the data obtained. we can believe that as frequency increases the higher is the line which is selected. This is symbolized by the numbers (Hz) near the linca in the diagram (Fig. 6). But one should make this conclusion more precise. From our own experience we know that it is possible to produce rhythmic movements with low frequency both during high and low coactivation of muscles. But it is impossible to produce rhythmic movements with maximal frequency during low coactivation. To take these facts into account, one should consider that. in order to produce the movement with a frequency, for instnncc, of 2 Hz. the nervous system can select either the line marked by 2 in Fig. 6 or an) line situated above and parallel to it. So. for a given frequency of the movement, the parametric operational area IS a triangle limited by the left and the upper sides of the square and a line marked by the respective number in Fig. 6. ft is worth empbasizing that displacemenr of the point (B,. /3,) caused by one of the central programs turns out to be perpendicular to that caused by another. So. the reciprocal and joint commands seem to be, in a mathematical sense, the orthogonal basis for the construction of any motor program. Hence, any combination of I{, and p2 can be provided by the proper combination of the central commands. In particular, one of the parameters can be changed independently of another in this way. So, it is possible to control activity of the muscles individually (for instance, to change activity of the flexors, preserving activity of the extensors) by means of superposition of the central commands, each of which evident]! controls the groups non-individually. A proof of the proper mathematical theorem is given in Theoretical Appendix. The superposition of the motor programs seems to be very expedient for different reasons. It should be mentioned that the natural frequency of the muscle load system is dependent on static stiffness of the muscles, i.e. on the slope of the IC (FEI.DMAN. 1979). Therefore, in performing the tonic coactivation. the nervous system seems to bring the natural frequency into accord with that predetermined by the centrat
Control of rhythmic movements
87
2.0
I,.3
75
) 0.55 4.6
1 5.6
FIG. 7. Decrease of maximal amphtude with increasing frequency of oscillation. Marks: surface EMGs of triceps and biceps brachii muscles (tric. bit), elbow angle (I#$,frequencies of movements (numbers above oscillograms, Hz). On the right: a pIot of maximal amplitude (ordinate) attainable under a given frequency (abscissa).
generator which accomplishes reciprocal activation of the antagonistic muscles. The fact that the dope of the ICs changed with the rhythm of movements is evidence for the control of the natural frequency (Fig. S[A-Cl). If rhythmic movement is a harmonic (sinusoidal) one, as took place in this study, the muscle torque is known to be proportional to the amplitude of displacement as we11 as to the square of frequency. Besides, the increase of the force of the muscles occurs in the phase of their extension [Fig. .5(D)]. So, when the frequency is near to maximum the amplitude of movement must be limited to prevent extreme muscle extension that can cause trauma (RACK & WESTBURY, 1969). The limitation of the amplitude movement is automaticaIly provided by su~rposition of the two motor commands. Actually, Fig. 6 shows that the operational areas in which the point @,, &) can be
shifted by the reciprocal program narrows with increasing frequency. This means that maximal amplitude of the movement itself must decrease with increasing frequency. The reader can learn this from his own experience. This fact is documented in Fig. 7. The subject was performing (out of the apparatus) the rhythmic movements of the forearm trying to reach a maximum amplitude at a frequency which gradually increased up to a limiting value (7.1 Hz). It can be seen in Fig. 7 that the amplitude does decrease (see also A~ZERMAN er al., 1974). Thus, the effect can be easily accounted for by the superposition of motor commands. As it is seen from Fig. 7, the amplitudes of burst activity of the flexor and extensor increased with increasing frequency, This fact is considered to be an electromyographic sign of the increasing tonic coactivation of antagonistic muscles.
RE~RENCES AIZERMANM. A., ANDREEVA K. A., KANDELE. L. 8~ TENNENBAUM L. A. (1974) Mechanisms in rhe Control of Muscle Activity (Norm and Pathology). Publ. House ‘Nauka’, Moscow. (In Russian.) ASATRYAND. G. & FELDMANA. G. (1965) Functional tuning of the nervous system with control of movement or
maintenance of a steady posture--I. Mechanographic analysis of the work of the joint on execution of a postural task. Biophysics IO, 925-935. BIZZI E., POLITA. 8r MO~A~SCI P. (1976) Mechanisms underlying achievement of final head position. J. N~~r~~~~~~i~~. 39, 435-444. FELDMANA. G. (19%) Functional tuning of the nervous system with control of movement or maintenance of a steady posture-II. Controllable parameters of the muscle. Biophysics 11, 565-578. FELDMAN A. G. (19666) Functional tuning of the nervous system with control of movement or maintenance of a steady posture--III. Mechanographic analysis of the execution by man of the simplest motor tasks. Biophl~sics II, 766775. FELDMANA. G. (1974) Control of length of the muscle. Biopkysies 19, 766-771. FELDMANA. G. (1979) Centraf and Re$ex ~~ec~a~is~ in rhe Control of movements. Publ. House ‘Nauka’, Moscow. (In Russian.) FELDMANA. G. & ORLOVSKY G. N. (1972) The influence of different descending systems on the tonic stretch reflex in the cat. Expl Neural. 37, 481494. HUF%HMIDTH. J. & HUFSCHMIDT T. (1954) Antagonist inhibition as the earliest sign of a sensory-motor reaction. Nature, Land. 174,607-619. HOW J. C. (1976) An assessment of stretch reflex function. Frog. Brain Res. 44, 303-314. KOTSY. M. (1975) Org~ni~u~~o~of Volu~rury ~4o~ement. Publ. House ‘Nauka’, Moscow. (In Russian.} v.s.[‘.
5!,-
1
XX
A. G. FELDMAN
MATT~WS P. B. C. (1959~) The dependence of tension upon extension in the stretch reflex of the soleus mubclc ,II the decerebrate cat. J. Ph,~.siol.. Land. 147. 521-546. MATTHE~S P. B. C. (1959b) A study of certam factors influencing the stretch reflex of the decerebrate cat. J. Phr,t~d, I.,& 147. 547 564. NI~.F~OI.ST. R. & HO~IK J. C. (1976) Improvement in linearity and regulation of stiffness that results from action? (II‘stretch r&x. J. Nruwph~xiol. 39. I I9 142. RA(.K P. M. H. & WFSTR~JRY D. R. (1969) The effect of length and stimulus rate on tension in the isometric cat saleus muscle. J. Physiol., Lord 204, 443460. SHERKINGTO~ C. S. (1906) Intryrcrrire Action of rhr Nrrrous System. Yale University Press. TANAKA R. (1974) Reciprocal la inhibition during voluntary movements in man. Expl Bruin RCA. 21, 529-540. WA(‘HHot.Dt:a K. (1928) Willkiirliche Haltung und Bewegung insbesondere im Lichte electrophysiologischer Untersuchungen. Ergrhn. Physiol. 26, 56% 775. WA(.HfioLoFR K. & ALTENHURGER H. (1926) Beitrgge zur Physiologie der willkiirlichen Bewegung-m IO. Einzelbewegungen. Pf1iiyer.t Art+. ga. Physiol. 214, 642-661. ZOMLWER bl.R.. ZAJA~. F. E. & LEVINE W. S. (1977) Kinematics and muscular activity of cats during maximum height jumpy. Brtrin. Rtz\. 126, 563- 566. (Accepted
THEORETICAL
APPENDIX
A THI:OREMhas been mentioned that the nervous system, by combining the reciprocal and joint activation programs. can determine the different (if any) combinations of activities of synergistic and antagonistic muscles controlling a mechanical degree of freedom and can, in particular, alter the activity of one muscle group independently of another. While proving this. we also show that these programs are not absolutely independent, i.e. changes in one of them can restrict the variation in the other. The proof of this theorem is based on the supposition that the motoneuronal pool of the given muscle group is controlled monoparametrically by determining the static threshold [jI, of the stretch reflex (k = I for flexors and li = 2 for extensors; subscript k is omitted. if the action of one group only. for clearness. of flexors is considered). It is worth noting that the alternative hypothesis (that several independent parameters control the muscle group) does not reject the theorem completely but somewhat narrows Its limits. For instance. if the static threshold of each of the synergistic muscles turns out to be controlled independentI>. the theorem must be referred to any antagonistic muscle pair (flexor ~extensor). Besides. the dynamic sensitivity of the stretch reflex determined by the activity of the dynamic y-motoneurones could be an additional parameter controlling the r-motoneuronal pool of the given muscle.
‘t
In the case, regulation of the static thresholds allows one to determine any type of static activity of the pair, but not all types of its dynamic activity. To prove the theorem, it is necessary, first of all, to explain why regulation of the parameter /I allows one effectively to control the activity of one muscle and. ultimately, its length and tension. Figure .X(A) shows the determination of the so-called equilibrium point of the tricomponent system (motoneuronal pool&muscle-load). The solid line beginning from the threshold point /I is a characteristic of the tonic stretch reflex. The dashed line is a characteristic of the load. which need not be external but can be set by the antagonistic muscles. The point a where the lines intersect is an cquilibrium point of the system. Coordinates of this point are equilibrium meanings of the joint angle and the torque. It is worth noting that a certain number of motoneurones recruited corresponds to each point of the solid line so that. on principle, this number can be found out for the equilibrium point as well. Evidently, in order to move the load to another position, it is necessary to shift the equilibrium point. The change of the static threshold /I is the most effective method of hringing about the shift: this is shown in Fig. 8(B). There are considered to be three regimes of muscle work. In the isometric regime, the load characteristic is a vertical line I. In the Isotonic regime, the load characteristic is a horizontal
--ALM (A)
P
?I Muv 1979)
9
--_-O
P3
(B)
2
5--z-
3 --B
d
C
\O
->8'
43 I I’
I ,'
FIG. 8. Equilibrium ponts of the tricomponent system (load-muscle-motoneurones). (A) Definition of equilibrium points (EP) (a); solid line: characteristic of the tonic stretch reflex (static muscle torque versus joint angle); p: its threshold: dashed line: some load characteristic; I’. 6: equilibrium torque and angle, respectively. (B) Change of the threshold of the reflex (,f?’ -+ /12) as an effective method of the shift of EP: a: initial EP: b-d: final EPs during isometric (1). isotonic (2) and intermediate (3) regimes of the muscle contraction: l-3: load characteristics of these regimes; P,, & (k = l-3): equilibrium torques and angles for respective EPs.
89
Control of rhyth imic movements
line 2. In the remaining cases, the load characteristic is some line 3 not coinciding with lines I or 2. The initial equilibrium point for all of the regimes was chosen to be identical (a) so that the system is in equilibrium at +r = 42 when the muscle torque equals P,. One can see that when the threshold is attered f@’+ 8’) the system transfers to a new equilibrium point fb, c or d, depending on the regime). The shift of this point leads to a change in the equilibrium torque (PZ - PI) in the isometric regime, of the joint angle t#r -&) in the isotonic regime, of both the torque [Pa --* P3) and the angfe f& -+ 4p,) in the intermcdiatc regime. It is evident that the physiological range of the change of the muscle torque and joint angle can be achieved provided there is a sufficiently wide range of the parameter p. It is worth noting that the shift of the equilibrium point is nat only a necessary but a sufficient condition of the initiation of active movement. Based upon it, one can describe the dynamics and, as web, the main electromyographic events during an active change of posture (see for details, Feldman, 1974; f 979). To prove the theorem, we consider again the multitude of permissible meanings of the parameters normalized by (5) and denoted by fir and 8,. This multitude presents a square (Fig, 9A). Note that the correlation
where A& (k = 1, 2) is an increase of &. is executed on both a diagonal of the square passing tbrougb point D and any line gorng in paraliel. In accord with the explanation given before, the correlation (7) and direction of the diagonal symbolize the program of reciprocal activation. It is worth making a reservation that the coefficients before A& in (5) and in the following correlation (8) are taken to be equal to 1, although their actual meanings are not known. Nevertheless, this reservation does not put the limits on the theorem to be proved. The correlation
is executed on the other diagonal of the square and on any jine going in parallel. ‘This correlation and the direction of the diagonal symbolize the program of the joint activation. By definition, simultaneous inhibition of both muscle groups is a particular manifestation of the program of joint activation. Let e, and eZ be the unit vectors directed in parallci to the diagonals of the square (Fig. 9A). Let also B = (B, ~&) be a vector characterizing a current state of the controlling system and &, indicate this vector when both programs are not used a&ail. The exact meaning of & is not known. Figure 9fg) shows that
(Cl
FSG. 9. Vector representation of the motor programs on the plane of the controlling parameters ?, and Pa which are the normalized threshold of activation of flexors and extensors, respectively. (A) Vector Ip0 shows a state of the system when both motor programs are off; e, and e, : unit vectors symbolizing these programs+ (13)Expansion of the voluntary program B into basis e, and e2 ; a, and aZ : variables showing a degree of utilizing of the motor programs. (C) Multitude of permissible meanings of or and aa when &, = (l,O)+
of a limb. One of the possible generalizations is described elsewhere (hmsf~~, WY). Now, let us determine the available meanings of aI and a2. Consider. for simplicity, a case /lo i= (1, 0) which means full relaxation of the muscle under zero action of both programs. BY (91,
BY- 1 = (a~ -
a,).$/2
(9)
The parameters Br , fit2change from 0 to t and therefore, by (1017
where u1 and aa are scalar variables determinative the contribution of the program of the reciprocal (at) and joint (aA) activation. These variables are considered to be the time functions which are chosen by the nervous system in relation on motor tasks. The formula (9) proves to be right for any fr,. We have shown that any state of the system can be considered as a result of successive or simultaneous apphcations of two central programs under consideration. The principle of superposition of motor programs in the form of the vector eq (9) can be generatized for the control
Geometrically, the inequalities (1 I) determine a square with diagonals going along the axis of the coordinates (Fig. 9Cf. There is a single-vaiued corresponding between its points and points of the square on the plane of the parameters Dr. B2,so that the first square transfers into the second by means of turning by n/4. One may see in Fig. 9(C) that the independence of two programs cannot be absolute because the possibie mean-
b - B0 = alet + a2e2
:I. G. Et-1 I)\I.\\
90 ings of one of the variables (LI, or u2) arc limited increase in the other. In particular,
activation of the muscles occurs (uIz = , reduced to
21. the program 01
reclprocitg
is
assumption
that the reciprocal and joint
mands arc aitcrnativcs utely unjustilicd
zero
bq an
when the maximal joint ((I, = 0)
(SHI.KKtI\G’Tos.
Therefore activation
the com-
1906) ib not abwl-
because they do prove to bc alternative
111
the extreme c;w~s. In this connection nnc ma! suggest that