EMG-torque dynamics at different contraction levels in human ankle muscles

Journal of Electromyo raphy and Kinesiology Vol. 3, No. 2, pp 6F 4 Ltd 0 1993Butterworth-Heinemann 1050~6411/93/020067-11

EMG-Torque

Dynamics at Different Contraction Human Ankle Muscles

Levels in

Thomas Sinkjaer, Egon Toft, Knud Larsen, Steen Andreassen Department of Medical Informatics and Image Analysis, Aalborg Denmark

University, Fredrik Bajersvej 70,

DK-9220 Aalborg,

Summary: The electrically elicited muscle twitch has been used to identify

mechanical muscle properties in relaxed muscles. We attempted to characterize the mechanical muscle properties in an active muscle. Each subject was seated and his/her left foot was strapped to a platform. The ankle torque and electromyogram (EMG) of the ankle extensors and flexors were measured while the subject was asked to match the ankle torque to a pseudo randomized rectangular tracking signal. A system identification technique was used to determine the impulse response from EMG to torque at various contraction levels. The amplitude of the impulse response decreased markedly with the contraction level when the amplitude of the tracking signal was constant, whereas the amplitude of the impulse response increased with the amplitude of the tracking signal. An explanation for these findings could be seen in the results from the properties of individual motor units. Our results suggest that the rate modulation that occurs during rapid changes in the force in an already isometric contracted muscle is very efficient in generating force in the newly recruited motor units, but inefficient in motor units approaching tetanus. Key Words: EMG-Torque-Muscle-Impulse

February

units.

cation, it is possible to consider the muscle as a transducer that relates EMG (in units of p,V) to torque (in units of Nm). The transducer is characterized by its impulse response, which states the time course of the transducer’s torque output in response to a very brief EMG input. Since a muscle is not a linear transducer, the impulse response will be the best linear approximation to the true non-linear impulse response. A number of special cases have been well described in the literature, for example the impulse response during maintained or slowly varying contractions. During maintained contractions, the integrated EMG and the force are almost proportiona13J3J4J6~zo~*3~2s. A linear relationship indicates that the gain of the conversion from EMG to force is independent of

During a motor task, a muscle is converting neural input into force output. As concerning the central nervous system, this conversion has two important characteristics: the gain and the speed. If the rectified surface electromyogram (EMG) is used as an index of the neural input to the muscle, then the gain, defined as the ratio between torque output and EMG input, can be assessed as the increment in the force, produced by a certain increment in the EMG. According to the theory of linear system identifiAccepted Address

response-Motor

4, 1993

correspondence and reprint requests to Thomas Sinkjaer, Ph.D., Department of Medical Informatics and Image Analysis, Aalborg University, Fredrik Bajersvej 7D, DK-9220 Aalborg, Denmark.

67

T. SINKJER

68

the contraction level. Milner-Brown et a1.17-19and Milner-Brown and Stein20 explained this linear relationship through the complex interaction of the rate modulation of already recruited motor units and the mechanical and electrical properties of motor units recruited according to the size principle12. In contrast to this, Woods et a1.26 found that the twitch, elicited by a single supramaximal stimulation of the innervating nerve, declined with an increasing contraction level and fell to zero at maximal voluntary contraction (MVC). This indicates that the gain decreases with the contraction level. The contraction time (CT) and the half relaxation time (HRT) are usually used to describe the speed of the force development. Since these parameters depend on the activation history of the muscle6*9, it is uncertain to what extent a muscle can maintain its speed during a motor task. In this study, we use a mathematical system identification technique to identify the impulse response of the ankle extensors in normal subjects from the EMG to the ankle torque, and the impulse response of the ankle flexors from the EMG to the angle torque, in a motor task where a subject is asked to track a force signal. The impulse response will be used to assess the extent to which the speed of the force development in a muscle is changed at different levels of voluntary contraction. The EMGtorque relation from the impulse response will also be used to assess the extent to which the gain of the conversion from EMG to force depends on the contraction level. MATERIALS

AND METHODS

This study included 18 subjects (age 24-38). Ten of the subjects were well-trained athletes. In each of the different experiments, four to 10 subjects participated. All subjects gave their informed consent. Experimental Set-up During a recording session, the subject was seated in a chair with his/her left foot strapped to a platform. The torque from the ankle flexor and extensor muscles was measured by a strain gauge attached to the platform21. All experiments were performed under isometric conditions, with the knee and ankle angles at approximately 100”. The axis of rotation of the platform was aligned with the axis of rotation of the ankle joint. The angle Journal

of Electromyography

& Kinesiology Vol. 3, No. 2, 1993

ET AL. of the ankle was measured between the sole of the foot and the shaft of the tibia. The skin temperature was 35” C, maintained by a lamp and a sensor on the skin over the investigated muscles. Data Collection Bipolar EMG surface electrodes with an electrode spacing of 2 cm were placed parallel to the tibia on the skin, overlying the anterior tibia1 muscle. Another pair of electrodes was placed over the soleus muscle, parallel to the achilles tendon, below the gastrocnemius muscle. Each recording surface of the bipolar electrode was 3 x 5 mm. The signals were band-pass filtered (20 Hz to 2 kHz), fullwave rectified, and processed with a first order low pass filter (20 Hz). The rectified EMG signals and the platform torque were stored on an Intel RMX286 microcomputer for later analysis. Tracking Signal A pseudo-randomized rectangular wave, as used by Genadry et al.” was displayed on an oscilloscope (Figure 1). The subject was asked to match the ankle torque, which was displayed on the oscilloscope, to this tracking signal. In each recording, the tracking signal was varied around a given mean. The amplitude of the fluctuations (the modulation depth) was typically +2.5%, &lo%, and +20% MVC. The average frequency of the square waves was 0.8 Hz. The mean of the torque exerted by the subject during tracking is called the contraction level. Data Analysis Ten seconds of the EMG and the ankle torque were sampled with a sampling frequency of 250 Hz, corresponding to a sampling interval of T, = 4 ms. This gave a total of N = 2500 samples. The mean of the sampled EMG was subtracted, giving the sampled EMG signal emg(n), for N = 1 . . . N. Similarly, the subtraction of the mean torque from the torque signal resulted in the sampled torque signal torque(N), for n = 1 . . . N. It is assumed that the muscle ‘converts’ the EMG input into the torque output in a linear way, at least for small fluctuations in the EMG and the torque around the ‘operating point’, determined by the contraction level. Foroutput, that the this means mally , torque (n), can be calculated by convolving the

69

MECHANICAL MUSCLE PROPERTIES Platform

EMG

torque

input,

emg(n)

with the impulse

response

h(m): M-l

torque(n)

=

T; 2 h(m).emg(n-m);n

= l..N.

m=O

0’O'*

I

II11111

I

3

5

6

7

8

9

10

M is the number of samples in the impulse response, h(m). M was chosen to be 125, corresponding to a

5

a

Rectified

and filtered

duration of 500 ms duration of the impulse response. Standard methods are available to provide deconvolutions, i.e. estimates of h(m), given torque(n) and emg(n). An unbiased estimate can be obtained from the matrix equation:

AT-EMC

200

1

100 n “0

1

2

3

Rectified

0

1JJu4A-d. -1 2

0

100

b

200

4

5 5

6

and filtered

7

4

5 s

300

400

500

4

5

9

6

7

8

7

8

.AhLA1 9

10

10 5 E z

0 -5 0

C

1

2

3

6

9

h = T,-l. C,-,l. C,,

10

SOL-k.

-3

8

Ins

’

(1)

1

_

4

10

s

FIG. 1. Examples of a lo-second tracking command and recorded signals during the contraction of the ankle flexors. a, From top to bottom, the tracking command and the recorded ankle joint torque, rectified and filtered anterior tibia1 EMG (ATEMG), and rectified and filtered soleus EMG (SOL-EMG). b, The twitch-like EMG/torque impulse response. c, Measured and predicted ankle torque The predicted ankle torque was found by convolving the EMG-signal in a with the model in b. The subject relaxed in his ankle extensors. Background torque 13 Nm (22% MVC) and modulation depth *6 Nm (10% MVC). MVC = 60 Nm.

(2)

matrix where C,, represents the auto-correlation for emg(n) and C,, represents the cross:correlation matrix for emg(n) and torque(n) Figure lb gives an example of an estimated impulse response for the ankle flexors at a background contraction level of 20% MVC and a modulation depth of +lO% MVC, using Eqn (2). The impulse response resembled an electrically elicited muscle twitch, and since the electrical stimulation can be considered as brief, the twitch is identical to an impulse response in this special case. We used the twitch parameters; the contraction time (CTJ, the half relaxation time (HRT,,), the amplitude and the area (the area under the curve in Figure lb) to characterize the impulse response. To assess the reproducibility of the impulse response, a subject was asked to follow the same pseudo-randomized tracking signal nine times. The subject kept a background torque of 20% MVC (12 Nm) and a modulation depth of +-lo% MVC (6 Nm) in the ankle flexors in all trials. All twitch parameters could be reproduced with a coefficient of variation of 5-10% in the repeated trials. As this seemed quite satisfactory, we did not further assess the reproducibility of the twitch parameters, to avoid unnecessary fatiguing of the subjects. We checked the validity of the transfer function by convolving it with the rectified EMG signal. This estimate can be compared to the measured torque. A typical example is shown in Figure lc. RESULTS MVC and Electrically Elicited Twitch As first part of the experiment, the subject’s MVC was determined to be the maximal torque Journal

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& Kinesiology Vol. 3, No. 2, 1993

T. SINKJBR ET AL.

70

around the ankle joint, produced by a contraction that was maintained for 1 second. The highest of three repeated measurements was chosen as the MVC. In the flexors, the MVC ranged from 30-72 Nm (mean 45 Nm, SD + 7.3 Nm), and in the extensors the MVC ranged from 85-200 Nm (mean 131 Nm, SD k 32.0 Nm). At very high contractions in the extensors, it turned out to be difficult to strap the foot to the platform firmly enough to have a reliable measurement of the MVC. It is possible that at least some of the subjects might not have achieved MVC in the extensors. These difficulties also prevented us from using contraction levels above 50% MVC in the extensors. Twitches were elicited from the ankle flexors (six subjects) and extensors (six subjects) by electrical stimulation using a surface stimulation electrode (DISA 13L22), over the deep peroneal and the tibia1 nerve, respectively. The measured twitch parameters CT,, HRT,, and amplitude are given in Table 1. The MVC for the six subjects was within the MVC of the other subjects. Relationship Between EMG and Torque during Maintained Contraction The soleus EMG was used as an index of the electromyographic activity of the ankle extensors. The close link between the soleus EMG and the ankle torque was verified during the maintained contraction (Figure 2). The ankle torque was proportional to the soleus EMG and the slope of the regression line was used as an EMG-torque conversion factor. The mean slope (2 1s~) in the extensors in Figure 2 was 0.79 ? 0.26 Nm pV_’ (five subjects). As an example, a soleus EMG of 100 l,r,V, multiplied by 0.79 Nm kV_l, gives a background torque of 79 Nm. Figure 2 shows similar data for the flexor muscles, where the EMG from the anterior tibia1 muscle is used as an index of the electromyographic activity of the ankle flexors. The TABLE 1. Mean 2 1 SD for contraction time (CT,), ha/f relaxation time (HRT,) and maximal amplitude (AMP,) in electrically elicited muscle twitches in six subjects

0 Flexors Extensors

70.5 + 11.l 97.6 2 11.3

HRT, (ms)

AMP, (Nm)

59.6 ” 12.3 76.2 2 13.2

3.6 2 2.4 17.6 k 2.6

Journal of Electromyography & KinesiologyVol. 3, No. 2, 1993

Extensors

Pf 0

100

200

300

400

EMG FIG. 2. Relationship between rectified and filtered EMG and torque during maintained contraction. Data points are given for the extensors (five subjects) and flexors (five subjects). The subject’s data are represented by different symbols. The averaged best linear fit is shown for both the extensors and the flexors.

mean slope (+ 1s~) of the flexors was 0.09 + 0.01 Nm pV_’ (five subjects). On average, the EMG-torque conversion factor was nine times higher for the extensors than for the flexors, indicating that the extensors generate nine times more torque than the flexors at the same EMG level. EMG-torque Impulse Response at Different Background Torques Figure 3 gives examples of EMG-torque impulse responses for the ankle flexors in one subject at different background torques. The impulse responses were identified while the subject was tracking a signal with a modulation depth of ?lO% MVC. Both the amplitude and the area of the impulse response increased from lO-19% MVC, but otherwise decreased with the background torque. Figure 4 shows average measurements of area, amplitude, CT, and HRT, of the impulse responses for the flexors in all subjects. Assuming linearity, the EMG-torque conversion factor is equal to the area of the impulse response. The EMG-torque conversion factor [Nm p.V-‘1 is a measure of the muscle gain, i.e. its ability to convert EMG [PV] into torque [Nm], during a maintained contraction. Similarly, the area of the impulse response

MECHANICAL MUSCLE PROPERTIES

71

Nm/(mVms)

Flexors 250

0

20

40

60

80

%MVC

i’L 19% MVC

0.25

0.8

0.6

0.4 0 0.2 0

200

400

600

ms

FIG. 3. Examples of rectified and filtered EMG-torque impulse responses for a subject at different levels of contraction in the ankle flexors. The contraction level is indicated to the right of each trace. Modulation depth -clO% MVC and WC = 45 Nm.

[Nm pV_l], is a measure of the muscle gain during the tracking task. The EMG-torque conversion factor and the area of the impulse response are plotted in Figure 4a. The area is larger than the EMG-torque conversion factor for low contraction levels. This indicates that the gain of the EMG to

I

0.0 0

I

1

40

60

I

I

80

%MVC 180 -

160 -

140 -

,pp

HRTh

120 -

*+q 1

100 ----

FIG. 4. Rectified and filtered EMG-torque impulse response for the flexors averaged for all the subjects at different contraction levels expressed in % WC. a, Area under the EMG-torque impulse response curve. b, amplitude. c, CT,, and HRT,. In a the full and broken lines represent the mean EMG-torque conversion factor 21 SE derived from Figure 2. In c the best linear fits of the CT,, and the HHT,, are shown together with the CT, and the HRT, found from the eiectrically elicited twitch. CT,,: broken line. HRT,,: full line. N: number of subjects. Modulation depth ?lO% MVC. Mean +ls~ is shown.

1

20

----- ~

80 -

3

-

CTh

CTt

60 -

HRTt

N=6

40

I__!___

0

6 I 20

6

6 I 40

6

6 1 60

6

5 I 80

%MVC Contraction

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T. SINKJAZR ET AL.

torque conversion is larger during the tracking task, when the torque is fluctuating rapidly, than during maintained contraction. At higher contraction levels, the area of the impulse response decreases. A regression line for the data points between 20% and 80% MVC crossed the abscissa at approximately 100% MVC, indicating that the muscle completely loses its capacity to modulate the torque at MVC. A similar regression line for the amplitude also crossed the abscissa at approximately 100% MVC (Figure 4b). The CTh and the HRT, are relatively independent of the contraction level, but both are larger than the CT, and the HRT,, measured from the electrically elicited twitches (Figure 4~). CT, was 21-43% larger than CT,, when measured from the range of CT, in Figure 4. HRTh was 75-125% larger than HRT,. This indicates that a contracting muscle is slower than a relaxed muscle. For the extensors, Figure 5 shows the same parameters as in Figure 4. Compared to the flexors, the maximal values of the area and the amplitude for the impulse responses are a factor 4.5 higher for the extensors (Figures 5a and 5b) and the CTh and the HRTh are longer for the extensors than for the flexors (Figure 5~). CTh and HRT,, measured from the impulse response, exceeded CT, and HRT,.

Extensors

____ ___ ___ I +57

1000

___________________

800

z

400

<

200 1 I

I

01

0

I

20

a

I

I

40

60

%MVC

EMG-torque Impulse Response at Different Modulation Depths To assess the effect of the modulation depth on the parameters of the EMG-torque impulse response, a series of experiments was made in which the background torque was hxed at 30% MVC and the modulation depth was varied from +2.5 to +25%. Only well-trained subjects participated in these experiments. Findings were similar in the flexors (Figure 6) and in the extensors (Figure 7): the area and the amplitude of the impulse response increased with the modulation depth until it reached a plateau at about 15% MVC. The CT, and the HRTh decreased with the modulation depth, but FIG. 5. Rectified and filtered EMG-torque impulse response for the extensors averaged for all subjects at different contraction levels expressed in % WC. a, Area under the EMG-torque impulse response curve. b, Amplitude. c, CT,, and HRT,,. In a the full and broken lines represent the mean EMG-torque conversion factor ?l SE derived from Figure 2. In c the best linear fits of the CT,, and the HRT, are shown together with the CT, and the HRT, found from the electrically elicited twitch. CT,: broken line. HRT,: full line. N: number of subjects. Modulation depth 210% MVC. Mean rls~ is shown. Journal of Electromyography

& Kinesiology

Vol.

3, No.

2, 1993

01 0

I

I

I

20

180

r

160

-

I

I

60

HRTh

T 140-

1

E

t

1

%MVC

b

‘;;

I

40

--120-

_c--

---

_c--

-I

0

iki

100 CTt

t; 80

60

HRTt N=

40 0

C

5 I

5

5 1

20

5 40

%MVC Contraction

level

4 I

I 60

MECHANICAL

MUSCLE

73

PROPERTIES

remained larger than CT, and HRT,, measured from the electrically elicited twitches.

Flexors

DISCUSSION In the active ankle extensor and flexor muscles, have attempted to characterize the mechanical isometric muscle properties using a linear ‘small signal’ model on a highly non-linear muscle system. Before discussing our results concerning the contractile properties of single motor units, we would like to stress some of the limitations of our technique.

we

01

I 0

I

I

10

I

I

30

20 %MVC

1.5

-

1.0

-

0.5

-

0.01 0

I

I

I

I

10

Soleus and Anterior Tibia1 EMG as Indexes of the Electromyographic Activity

I

I

20

30

%MVC

200 -

Earlier investigations have shown how the anterior tibial, the extensor hallucis longus, the extensor digitalis longus, and the antagonistic peroneus longus and brevis muscles have contributed to the torque around the ankle joint when the common peroneal nerve was stimulated by an external bipolar electrode21. Having carefully positioned the stimulation electrode, it was possible to recruit a major fraction of the deep peroneal nerve in many subjects, without stimulating the superficial peroneal nerve (and thereby activating the antagonistic peroneus longus and brevis muscles). The major finding was that the elicited muscle twitches were only forcible when the anterior tibia1 muscle was stimulated21 thus being a useful index for the electromyographic activity in the ankle flexors. When the knee is flexed, and, in particular, when the extensor torque is below 50% MVC, the gastrocnemius muscles only develop a relatively small fraction of the total ankle torque13+24. Having carefully positioned an external stimulation electrode above the tibia1 nerve at the popliteal fossa, it was possible to elicit a muscle twitch in the gastrocnemius muscles. Such an electrical stimulation gives rise to a clearly visual contraction of the gastrocnemius muscles but only a small twitch contraction at the ankle joint. When the electrical stimulation of the tibia1 nerve activates the soleus muscle, a prominent muscle twitch can be detected24.

80 c+

CT+ HRit

llo N=lO

10

0

4

0

7

4

5

10

9 20

% WC Modulation

depth

9

7

5 30

FIG. 6. Rectified and filtered EMG-torque impulse response for the flexors averaged for all subjects at different modulation depths. a, Area. b, Amplitude. c, CT, and the HRT,,. In c the best linear fits of CT,, and HRTh are shown together with the CT+ and HRT, found from the electrically elicited twllch in Table 1. CT,,: broken line. HRT,: full line. N: number of subjects. Background contraction 30% WC. Mean f 1 SE is shown. Journal

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T. SINKhER ET AL.

74 Extensors 1800

r

01

I

0

I

I

10

20

I 30

20

30

I

%MVC

a-

6-

4-

2-

0,, 0

10

At contraction levels below 50% MVC, the EMG activity in the gastrocnemius muscles is often very low compared to the possible maximal effort13J4, which further suggests that the soleus EMG is a useful index of the electromyographic activity in the ankle extensors during sustained contractions and when the knee is flexed. The interpretation of our findings is based on the assumption that the intensity of the surface EMG is related to the activity of the muscle, as demonstrated by various authors13,20,24. Other factors, such as the nature of the tissue interposed between the sources and the skin, can influence the measurements. Since both muscles (anterior tibia1 and soleus) are situated below the subcutaneous layer and all subjects were slim and had only a minimal thickness of the subcutaneous fat-layer, we have assumed these properties to be of less importance. Differences in the non-muscle ‘filter-function’, however, might result in errors. During rapid contractions, such as the chosen tracking task, the gastrocnemius muscle may receive relatively more activation than the soleus muscle, and may thereby influence the measured ankle torque significantly. In one subject, we calculated the normalized cross-correlation function between the measured soleus EMG and the gastrocnemius EMG during a tracking task and found a highly significant correlation. This implies that the EMG co-varies in the two muscles, making the soleus muscle an appropriate index for the electromyographic activity in the extensor muscles during the tracking task in this study.

%MVC

Comparison Between Muscles The EMG that we measured is the signal detected by a bipolar electrode on the anterior tibia1 or the soleus muscle, generated in the pick-up volume of such electrodes. In all subjects, we have used a simple procedure to decide on the position of the EMG electrodes. The distinct separation between the slopes of the EMG-to-torque regression lines for the soleus and anterior tibia1 muscles and the small inter-subject variation in the EMG-to-torque

120 -

F

CTt

80

HRTt

N=4

40

0

4

4

4 I 10

4

4

5

20 %MVC

Modulation depth

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I 30

FIG. 7. Rectified and filtered EMG-torque impulse response for the extensors averaged for all subjects at different modulation depths. a, Area. b, Amplitude. c, CT, and the HRT,,. In c the best linear fits of CT,, and HRT,, are shown together with the CT, and HRT, found from the electrically elicited twitch in Table 1. CT,,: broken line. HRT,: full line. N: number of Subjects. Background contraction 30% WC. Mean * 1 SE is shown.

MECHANICAL

MUSCLE

regression lines for each muscle (see Figure 2) suggest that slightly different electrode locations will not affect the main findings of this study. The ankle extensors are considerably stronger than the flexors. On average, we found that the MVC is about three times larger in the extensors than in the flexors. This may be an underestimation of the difference between the extensors and the flexors, due to the previously mentioned problems with fixation of the foot during maximal voluntary contraction of the extensors. The extensors are also stronger than the flexors in the sense that the EMG-torque conversion factors on average are nine times larger in the extensors than in the flexors (Figure 2): At an EMG level of 100 pV, the extensors produce 79 Nm and the flexors produce 9 Nm. These EMG-torque conversion factors can be compared directly to the area of the estimated impulse response as done in Figures 4a and 5a. The EMG cross-talk between neighbour muscles might influence this factor. Particularly cross-talk from the gastrocnemius muscle to the soleus EMG might underestimate the EMG-torque conversion factor of the extensors24. Differences in the non-muscle filter transfer function, however, might result in errors. Depending on the contraction level, the area of the impulse response is 4.5-8 times larger in the extensors than in the flexors. The extensors are slower than the flexors. This is to be expected from the higher density of fast fibres in the flexors4. This is reflected in the parameters CT, and HRT,, measured from the twitch elicited electrically in the relaxed muscle. CT, and HRT, are 39% and 32% larger in the extensors than in the flexors, respectively. These differences also apply to the active muscles: for all contraction levels and modulation depths, the parameters CTI, and HRTh, measured from the impulse response, are larger in the extensors than in the flexors. Dependence on Contraction Level and Modulation Depth We shall now summarize some of our findings in the following four points. These findings are compared to the findings of properties in single motor units in the next sectio’n: (a) In the flexors, at contraction levels of 10-40% MVC, the area of the impulse response is larger than the EMG-torque conversion factor

PROPERTIES

75

(Figure 4a). This means that the gain of the muscle is larger during the dynamic tracking task than during maintained contraction. (b) At higher contraction levels, the gain of the muscles decreases (Figures 4a and 5a). At least in the flexors, the reduction in gain with contraction level is similar to the reduction in twitch amplitude found by Woods et al.26 in response to supramaximal nerve stimulation during voluntary contraction. Also, Toft et al.23,24 and Vredenbregt and Rauz5 found that the gain decreased with the contraction level during brief increases of the EMG, elicited by the stretch reflex. Active muscles are slower than relaxed muscles. (cl At a modulation depth of 10%) CT,, measured from the impulse response, is 21-43% longer than CT,, measured in the relaxed muscle. HRTh is 75-125% longer than HRT, (Figures 4c and 5~). At smaller modulation depth, CT, can be up to 70% longer than CT,, and HRT, up to 160% longer than HRT, (Figures 6c and 7c). Cd)When the modulation depth is increased, the muscles get faster. Experiments were performed at a contraction level of 30% MVC. When the modulation depth was increased to 30% MVC, both CT, and HRTh declined. CT, almost decreased down to CT,. Apparently, a muscle can regain its speed when it is required to make a large and rapid change of contraction. Similar results can be extracted from Genadry et al.l’, who used a technique similar to the one used in this study. Comparison to the Contractile Properties of Single Motor Units It is tempting to build a model of force modulation, taking into account the known properties of force generation in single motor units and the properties of the motor neuron pool. However, such a model would require experimental verification beyond the data collected in this study, and we shall therefore limit this discussion to two properties of force generation in single motor units that together provide a plausible explanation for most of our findings. The first observation is that the gain of the force production in a single motor unit varies with the rate of activation of the motor unit. Milner-Brown et al.19 gave an example of a small group of motor Journal

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T.SINKSER ETAL.

units in the first dorsal interosseus which increased the gain (area under the twitch per stimulus) by a factor of 4.6, when the stimulus rate was increased from 10 to 20 Hz. Burke et a1.6 gave examples of increases in the gain with factors ranging from 2.5 to 4.5 for motor units in the cat’s medial gastrocnemius muscle. Similar increases in the gain were reported by Kernel1 and Sjiiholm15 in the first lumbrical muscle of the cat. At higher stimulus rates, the motor units approach a fused tetanus and the gain falls to zero. The second observation concerns the prolongation of CT and HRT in motor units activated at intervals shorter than the CT. Long CT and HRT have been demonstrated in potentiated6 and fatigued muscles3,5,Q, but actually the prolonged CT and HRT can be observed from the second twitch in a train of twitches, provided that the stimulus intervals in the train are shorter than the twitch contraction time of the motor uniP*. The motor units can be divided into three populations: 1. Motor units that are not recruited at the present level of contraction. For these motor units we arbitrarily define the gain (area under the twitch) to be one. 2. Motor units that are firing at or above their minimum firing rate during voluntary contraction, but below the firing rate where they approach a fused tetanus. For this population the gain is higher than one, and then contraction time CT is longer than the contraction time of motor units in population 1. 3. Motor units that are firing so rapidly that they are approaching a fused tetanus. These motor units can not generate significantly more force, if the firing rate is increased, and the gain is therefore close to zero. We will now try to relate these observations to the four findings (a, b, c, and d above) mentioned in the previous section. At low contraction levels, it appears likely that a large fraction of the recruited motor units are belonging to population 2, rather than to population 3. This is in agreement with the large gain at low contraction levels that we found in particular in the flexors (finding a). As the contraction level increases, it appears likely that the fraction of recruited motor units belonging to population 3 grows, and the gain of the whole muscle must therefore decline (finding b). At any contraction level, the modulation of force during Journal

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the tracking task is accomplished by a combination of recruitment of motor units from population 1 and rate modulation of units in population 2. Motor units in population 3 are possibly also rate modulated, but this is unimportant since they can not significantly contribute to the force production. Since both units in population 1 and 2 contribute to the force modulation, the whole contraction time of the muscles will be a weighted average of the contraction time for population 1 and the contraction time for population 2. This is in accordance with the longer contraction time in the active muscle (finding c). At any contraction level there is a certain number of motor units in population 2. Rate modulation of this limited population can only contribute to force modulation up to a certain limit, and increasing the depth of modulation therefore necessitates a larger recruitment of units from population 1. Accordingly, we must expect the contraction time to go down, which is in agreement with finding d. The interpretation made above is quite similar to the model of the motor unit recruitment and the rate modulation proposed by Mimer-Brown et a1.19. The addition to their model is the assumption that motor units, firing so rapidly that they are approaching a fused tetanus, can not generate significantly more force if the firing rate is increased. As mentioned above, this assumption is supported experimentally by the results of Milner-Brown et a1.19 and together it provides an explanation to all our findings. In summary, our results suggest that the rate modulation that occurs during rapid changes in isometric force contractions in an already contracted muscle is very efficient in generating force in the newly recruited motor units, but inefficient in already recruited motor units. REFERENCES 1. Andreassen

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Journal of Electromyography & Kinesiology Vol. 3, No. 2, 1993