Exp Brain Res (1999) 129:592–604

© Springer-Verlag 1999

R E S E A R C H A RT I C L E

Chris J.J.E. van Groeningen · Evert-Jan Nijhof Fred M. Vermeule · Casper J. Erkelens

Relation between torque history, firing frequency, decruitment levels and force balance in two flexors of the elbow

Received: 19 October 1998 / Accepted: 14 June 1999

Abstract By means of intramuscular electromyographic recordings, we studied the firing frequencies and recruitment/decruitment thresholds of individual motor units in two elbow flexors, the biarticular biceps brachii muscle and the monoarticular brachioradialis muscle. Subjects had to perform isometric contractions with increasing elbow flexion torque until a specific peak torque level was reached. The torque level was kept constant for 6 s during which firing frequencies were measured. Then the torque was decreased to a lower level and, after 3 s, firing frequencies were again measured for 6 s. By repeating this procedure, the torque level was decreased stepwise until the motor unit under study stopped firing. The last level before the unit stopped firing was considered to be the decruitment torque level. We measured the firing frequency at recruitment and decruitment, the torquefrequency relationship and the recruitment and decruitment torque thresholds after various levels of peak torque. In the biceps, both the firing frequencies at a specific torque level and the decruitment torque level itself were independent of the peak torque. In the brachioradialis, however, firing frequencies at a specific torque level decreased and decruitment torque levels increased after subjects generated higher peak torques. Thus, in this muscle firing frequencies as well as decruitment thresholds show hysteresis effects. The result indicates a shift of force from the brachioradialis muscle during recruitment to the biceps muscle during decruitment. This shift is smaller than was concluded from previous studies in which decruitment threshold levels for the brachioradialis muscle were assumed to be independent of force history. Moreover, we found that in both muscles decruitment firing frequencies were lower than recruitment frequencies and they were independent of the peak torque level. In order to analyse the effect of the peak torque C.J.J.E. van Groeningen · E.J. Nijhof (✉) · F.M. Vermeule C.J. Erkelens Perceptual Motor Integration Group, Helmholtz Institute, Utrecht University, PO Box 80000, 3508 TA Utrecht, The Netherlands e-mail: [email protected] Tel: +31-302-532-274, Fax: +31-302-522-664

level on the distribution of force over the two muscles, we performed a model study in which we simulated the activation-frequency relation of two elbow flexors: a biceps-like and brachioradialis-like muscle, each contributing equally to the elbow torque during recruitment. In addition, we analysed how the different behaviour of the biceps and the brachioradialis during decruitment alters their contribution to the total torque production and how this redistribution is caused. The model study shows that the shift in contribution to the total torque is not constant during the relaxation phase and is not caused by a simple mechanism like a shift of activation from one muscle to another. Furthermore, changes limited to the muscle in which hysteresis is present do not seem to be sufficient to explain the experimental results. Key words Motor unit · Recruitment · Decruitment · Firing frequencies · Biceps brachii · Brachioradialis · Model

Introduction From an anatomical point of view the motor apparatus is divided into muscles. Functionally, muscles are not the basis of motor performance. According to the idea of task groups (Loeb 1985), the functional approach is based on groups cooperating motor units (MUs), not necessarily all from the same muscle. From this viewpoint, the required joint torque1 is produced by a teamwork of muscles and the workload is divided between them. Therefore, it is interesting to know what the force output of an individual muscle is and how it changes with task and with time. Changes in muscle force distributions of synergistic muscles can be studied by analysing changes in recruitment and decruitment thresholds of MUs. This is feasi1 The term “torque” is used to indicate the measurable quantity (in Nm) that is the result of all contributions of all muscles about a particular joint. The term “force” (in N) is restricted to the (inaccessible) output of an individual motor unit or muscle.

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ble since the order of MU recruitment and decruitment is more or less fixed and recruitment and decruitment are organized according to MU size (Henneman 1957). Hence, at the instant of recruitment or decruitment of a particular MU, all units consisting of fewer muscle fibres than the unit under study are active and all units consisting of more fibres are inactive. If in two given situations the measured torque is different at the instant of recruitment or decruitment of this MU, the change must be due to a difference in firing frequency, to a change in force production in synergists of the muscle, or to intrinsic muscle properties such as twitch potentiation or muscle fatigue. Hence, if changes in firing frequency and intrinsic properties are known, shifts in the contribution to the total torque production can be determined. The central nervous system uses various strategies to change the force output of a muscle, depending on the number of MUs in the muscle (Kukulka and Clamann 1981; Clamann 1993). Elbow muscles have many MUs and the recruitment-decruitment strategy plays an important role at levels of force up to about 80% of the maximum force output in the biceps (Kukulka and Clamann 1981). Force levels higher than 80% are primarily generated by means of frequency control. However, the firing frequencies of MUs already change considerably at force levels just above their usual recruitment threshold. By studying recruitment and decruitment thresholds, a shift in force distribution was found from the monoarticular elbow muscles – brachioradialis, brachialis, and the lateral and medial heads of the triceps brachii – during isometric contractions to the biarticular elbow muscles – biceps brachii and the long head of the triceps brachii – during isometric relaxations (Denier van der Gon et al. 1985; van Groeningen and Erkelens 1994; van Groeningen 1995; van Groeningen et al., submitted). The same authors studied the firing frequency behaviour of active MUs. They found that at torques around the muscle’s decruitment level, mono- and biarticular muscles behave differently. It turned out to be difficult to draw decisive conclusions from those data. Firstly, the firing frequencies were measured during changing torque levels. Although the levels were changed slowly, the firing frequencies were considerably affected by changes in force output just above recruitment and decruitment thresholds. Secondly, just after recruitment double or even triple spikes occurred, and just prior to decruitment MU firing became quite irregular. Both circumstances affect a correct determination of the firing frequency. We tried to solve these problems here with an improved experimental setup. In the present work we are going to focus on the firing behaviour of MUs of the brachialis and the biceps after different force histories. As was said, at torque levels around decruitment, mono- and biarticular muscles behave differently. Although MUs in both types of muscles have their firing frequencies decreased if output torque is lowered, the torque level at decruitment is different. MUs in the biarticular biceps and in the biarticular head of the triceps (caput longum) cease firing at a decruit-

ment level that is always lower than the recruitment threshold. In the monoarticular elbow muscles – brachioradialis, brachialis, and lateral and medial heads of the triceps – it is not clear beforehand at which torque level a unit stops firing. As was shown by Denier van der Gon et al. (1985) for the brachialis – but likely also for the brachioradialis – the decruitment torque threshold of a particular MU can be higher than its recruitment threshold. Related to this we are going to address the following question: What happens in the previously mentioned case if the torque output is increased to a level above recruitment of one of those monoarticular muscles but below decruitment and then decreased again? In addition, we performed a very simple model study to evaluate the obtained results in terms of a shift in activation between the biceps and brachioradialis muscle. With the model we also tried to make a distinction between the possible activation schemes responsible for the experimental results.

Materials and methods The experiments were performed on four male subjects aged between 25 and 43 years who had given informed consent. None of them had any known history of neurological or motor disorder. Intramuscular electromyograms (iEMGs) were recorded in the elbow flexor muscles biceps brachii (BIC) and brachioradialis (BRAD). Apparatus During the experiments, subjects were seated in a dentist’s chair with their right arm abducted at 80° and supported under the elbow joint. Their wrist was tightly fixed in a cast. By means of strain gauges, torques exerted by the forearm were measured with 0.02 Nm resolution in three independent directions: flexion/extension and pronation/supination of the forearm and exorotation/endorotation of the humerus. During all the trials, the forearm was extended at 100° and fixed tightly to the holder in a semiprone position.2 The reader who requires more detailed information is referred to Tax et al. (1989). iEMG recording and analysis In order to examine MU activity in the muscles involved, iEMGs were recorded by means of nylon-coated fine-wire electrodes. Bipolar recordings were amplified, band-pass filtered (320 Hz– 32 kHz) and stored on tape for offline analysis. Simultaneously, the torque data were recorded on the same tape. In order to determine the exact firing frequency, it was essential that no spurious spikes were counted or that spikes were missed. Therefore care was taken that the activity of only one MU was recorded by the electrodes at low torque levels and only a few at higher levels. We obtained this by carefully manipulating the very position of the wires while the subject repeatedly contracted and relaxed the muscles. During this procedure spikes were displayed on an oscilloscope. During the offline data analysis, the EMG and torque recordings as stored on tape were played back. The EMG signals were sampled at a frequency of 20 kHz and the torques as exerted by the subjects during a spike were noted. For most of the lower 2

Full extension of the elbow was defined as 180°.

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Fig. 2 Example of the experimental results for the biceps caput longum. The upper trace shows part of the spike trains of several biceps MUs, with one easily distinguishable unit having long spikes, i.e., the unit under study. The lower trace shows the torque produced by the subject. Notice the extra decrease in firing frequency immediately after the torque step as is indicated by the arrows and the recovery in 2–3 s. The periods in which the firing frequencies were measured are indicated by the bars under the torque trace

Fig. 1 Simplified scheme of the experimental procedure. Shown is the way subjects had to change the torque in the experiments for the different muscles. The grey intervals indicate when firing frequencies were measured; Recr indicates the recruitment level. Upper panel biceps brachii muscle, lower panel brachioradialis muscle torque levels, only one MU was active and its firing frequency could easily be measured by automatically counting the spikes. At higher levels of torque, different simultaneously firing MUs made simple counting impossible. In this case, the spike shape was analysed by means of principal vector decomposition (Fukunaga and Koontz 1970; Glaser 1971). A spike was attributed to an MU by means of cluster analysis. By this procedure we were able to track reliably the MU under study and determine its firing frequency at higher torque levels as well. Experimental protocol In each trial we tested only one particular MU of the BIC or BRAD. For this, an MU recruitment threshold was determined by repeatedly, slowly increasing the flexion torque until the MU started to fire. When the recruitment threshold was reached, the subject had to increase the torque further until a level was reached at which so many MUs were active that analysis of firing frequency became impossible. We shall refer to this level as the “limit torque level”. Then we divided the torque interval between the recruitment threshold and the limit torque level into steps, where the step size was chosen to be the same in the various trials. Hence the number of steps varied according to the difference between limit torque level and recruitment threshold. The way the subjects had to change the torque is schematically shown in Fig. 1. The subjects were asked to raise the torque to an initial level and to maintain this level as accurately as possible for 6 s. Then they were asked to lower the torque to a subsequent level during the next 3 s. This new level had to be maintained for another 6 s. This procedure was repeated until the particular MU stopped firing. The initial and also highest torque level in the trial

will be called the peak level and the last level before the MU stopped defines the decruitment threshold. The 6-s periods were used to measure the firing frequency at a particular level of torque. The intermediate periods of 3 s were necessary because MU firing frequency is influenced by a rapid decrease in force (as indicated by the arrows in Fig. 2). After 2–3 s the firing frequencies were stabilized again. During some pilot experiments – and as will be shown later – the BIC and the BRAD muscle were found to react differently to different peak levels. Therefore the two procedures for these muscles were individually optimized and differ slightly as is depicted in Fig. 1. We found during the pilots that the decruitment levels of the BIC were always lower than the recruitment levels. So we skipped the first part of the protocol and started the actual recordings at a torque level slightly below recruitment. As is shown in the upper panel, the series of levels the subjects had to generate after the peak level were all the same. For the BRAD units, we measured the full range from peak level down to decruitment (lower panel). Here, the difference in torque was the same for all levels. In this way, it took the same number of steps and thus the same amount of time in both muscles for the decruitment level to be reached. Validation protocol Two validation experiments were performed for both muscles. The purpose of the first experiment was to check for possible effects of fatigue or twitch potentiation on the firing frequencies. Two subjects had to maintain a typical torque at a level one step above the recruitment level for several minutes. Note that this period is much longer than the duration of the standard experiments, which last less than 1 min. The test period was divided into blocks of 15 s, during which the average firing frequency of the MU was determined. The second validation experiment was performed in order to compare our results with the contraction-relaxation experiments previously performed by Denier van der Gon et al. (1985). These authors used slightly different torque history profiles and measured firing frequencies during torque change. The subjects were asked to raise the torque slowly to different peak levels between the recruitment threshold and the peak torque level, maintain this

595 level for a certain period and decrease torque again to zero. All trials lasted the same time because the periods of constant torque were changed to compensate for the different times needed to reach the peak level. Frequencies were determined by counting the number of spikes during periods of 1 s. Data analysis Every experiment was repeated at least 5 times for each MU. The measured firing frequencies and torques were averaged per step; series with different peak torque levels were handled separately. In this way different frequencies were obtained for different torques and different torque histories. The lowest initial torque level for MUs of both muscles was the recruitment threshold. The decruitment threshold was defined as the torque at the last level at which an MU was still firing.

Results Special care was taken to ensure that only one clearly distinguishable motor unit was visible in the recordings at the peak torque levels we used during the standard experiments. In this way we were able to measure frequencies after four to six different peak levels per MU. The peak Fig. 3A–D The relation between firing frequency, elbow torque, and performed peak torque level of a biceps brachii MU (A,C) and a brachioradialis MU (B,D). The upper two panels show the frequencytorque relation for different levels of peak torque. In the lower two panels the same data are replotted as the frequencypeak torque relation for different levels of elbow torque. The legends in the upper two panels indicate the different levels of peak torque and in the lower panels the different levels of elbow torque

torque levels were in the range of 1.6 times the recruitment threshold for a BRAD unit with a relatively high recruitment threshold (16%MVC), and up to more than 10 times for a BIC unit with a low threshold (1.6%MVC). The average recruitment thresholds of the units were 7±5%MVC for both muscles. Typically we investigated five to seven levels of torque lower than the peak level. A typical result of an experiment for a BIC unit is shown in Fig. 2. The upper trace shows part of the spike trains of several MUs with one easily distinguishable unit having large spikes, i.e., the unit under study. The lower trace shows the last two torque levels in a series of six as produced by the subject. Notice the extra decrease in firing frequency immediately after the torque step as is indicated by the arrows and the recovery in 2–3 s. The periods in which the firing frequencies were measured are indicated by the bars under the torque trace. Firing frequencies In the upper two panels of Fig. 3, the relations between the firing frequency and elbow torque are shown for a

596 Fig. 4 Firing frequencies at the decruitment torque level after the generation of different peak torque levels. Different units are indicated by different symbols. Left panel biceps brachii muscle, right panel brachioradialis muscle

Fig. 5 Decruitment thresholds of the same units as in Fig. 4. Thresholds are normalized with respect to the recruitment threshold of each unit. Symbols correspond to the same units as in Fig. 4. Left panel biceps brachii muscle; right panel brachioradialis muscle

typical BIC unit (Fig. 3A) and a typical BRAD unit (Fig. 3B) after the subject generated different peak torque levels (indicated by the different symbols and expressed as %MVC) according to the protocols of Fig. 1. Note that for the BIC unit frequency-torque curves after different peak torque levels overlap, whereas the BRAD shows a clear downward shift of these curves with increasing peak torque. Furthermore it can be seen that the BIC unit shows different decruitment thresholds but these thresholds are not correlated with the peak torque level. For the BRAD, decruitment thresholds increase with increasing peak torque level. In the lower two panels of Fig. 3, the same data are replotted where parameter and abscissa are exchanged to show more clearly the effect of the peak torque level on the firing frequencies. The firing frequencies of the BIC unit were independent of the performed peak torque level but increase with elbow torque (Fig. 3C). For the BRAD unit, the firing frequencies at a specific elbow torque level decreased when the performed peak torque level was increased (Fig. 3D). Figure 4 shows for a larger number of MUs the influence of the peak torque on the firing frequencies at the

decruitment level in more detail. It can be seen that the peak torque had no effect on the decruitment frequencies, as was already noted from Fig. 3. The average recruitment frequency of the BIC MUs was found to be 13±1 Hz and the average decruitment frequency was 7± 2 Hz. For the BRAD units these values were 14±1 Hz and 8±2 Hz, respectively. Hence all decruitment frequencies were significantly lower than the recruitment frequencies. Decruitment thresholds Figure 5 shows the decruitment thresholds and the influence of the peak torque level on these thresholds. The decruitment thresholds of all units were normalized with respect to their recruitment thresholds. As was already concluded from Fig. 3, BIC decruitment thresholds are not systematically influenced by the peak torque level and are always less than the recruitment threshold. For the BRAD, the decruitment thresholds increase with the peak torque level and most units eventually become decruited at torque levels above the recruitment threshold. What can-

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not be seen in Fig. 5 is that the decruitment thresholds of MUs with low recruitment thresholds are always lower than those of units with high recruitment thresholds. This is even the case if the peak torque level is such that the decruitment thresholds of the low-threshold units are raised and those of the high-decruitment units are lowered. Thus, Henneman’s size principle is not violated. Validation experiments We performed the first validation experiment with two subjects to check for effects of fatigue on firing frequencies. In Fig. 6, the average firing frequencies for blocks

of 15 s are shown during the first 2 min for both muscles and both subjects tested. It is obvious that no significant changes in firing frequencies for either muscle could be observed. The second validation experiment was performed so that we could compare our results with the experiments previously described by Denier van der Gon et al. (1985). Their experiments showed the same results as the experiments described above. As shown in Fig. 7, the decruitment thresholds of the BIC (left panel, open circles) did not depend on the peak torque level, whereas the BRAD decruitment thresholds (right panel, open symbols) increased with increasing peak torque. Note that in both projects and for both muscles, recruitment levels (filled symbols) were independent of peak torque. Finally, in Fig. 8 the average firing frequencies are shown during a period of 1 s, starting 1/2 s before a certain torque level is reached. The various symbols denote the peak torque levels (as %MVC), where the open symbols indicate contraction and the filled symbols indicate relaxation. As in the standard experiments, firing frequencies during relaxation are independent of the peak torque level for the BIC (left panel) but change with changing peak torque for the BRAD (right panel). Furthermore it can be seen that for both muscles the firing frequencies are higher during contraction (filled symbols) than during relaxation (open symbols), as was the case in the experiments of Denier van der Gon et al. (1985). Model Muscle model

Fig. 6 Firing frequencies in the biceps (circles) and the brachioradialis (squares) muscles during blocks of 15 s in the first 2 min of a prolonged contraction. The torque levels were 7%MVC for the biceps and 7%MVC for the brachioradialis muscle for subject 1 (filled symbols) and 13% MVC and 8%MVC for subject 2 (open symbols)

Fig. 7 Results of the second validation experiment. Recruitment and decruitment thresholds after the generation of different peak torque levels. Left panel biceps brachii muscle, right panel brachioradialis muscle

We performed a model study to evaluate the experimentally found firing frequencies and thresholds of the biceps and brachioradialis muscle. In addition, we wanted to analyse the effects of these data on the shift in each muscle’s contribution to the total force. It should be stressed

598 Fig. 8 Results of the second validation experiment. Average firing frequencies during periods of 1 s around a certain torque level for contraction (filled symbols) and for relaxation (open symbols) for different peak torque levels (as %MVC), indicated by different types of symbols. Left panel biceps brachii muscle, right panel brachioradialis muscle

Fig. 9A–F Block diagram of the model. A Central activation. Contraction and relaxation vary linearly with time. B Muscles. Activation is directed to both muscle groups. C Activation to frequency conversion. Firing frequency for different MUs is calculated according to individual thresholds, contraction or relaxation, and muscle group. D Frequency to force conversion. Force for different MUs is calculated according to individual firing frequency and strength. E Muscle force. MU force is added per muscle to obtain muscle force. F Total force. The force of both muscles is added

that we did not want to develop a physiological model of the (fore)arm. The sole purpose of the model study was to obtain some very basic insights into the problem. For the model we assumed only two muscles to contribute to elbow flexion, a biceps-like muscle, hereafter called BIC, and a brachioradialis-like muscle, hereafter called BRAD. The BRAD is defined as a lumped, monoarticular elbow flexor muscle, consisting of both brachialis and brachioradialis muscle. As stated in the “Introduction”, it is likely that the brachialis behaves in the same way as the brachioradialis and thus both muscles can be lumped for the present analysis. All simulated contractions were isometric and quasistatic as in our experiments, so viscoelastic properties like the force-length and force-velocity relationships had no influence on thresholds and frequencies. A block diagram of the model is shown in Fig. 9. We define activation as the central motor command affecting

the motor neuron (MN) pools in the spinal cord, contraction as the phase in which the activation level increases, and relaxation as the phase in which the activation level decreases. During contraction the central motor activation signal A (where 0≤A≤1) was linearly increased to Apeak and during relaxation decreased to zero in order to produce frequencies and thresholds in a wide range of force outputs (Fig. 9A). A was directed to the BIC and the BRAD MN pools (Fig. 9B). For contraction, A was divided equally between the two MN pools; for relaxation the balance between the two pools could be changed to simulate a shift in activation. The BRAD and the BIC MN pools each consisted of N neurons, where we arbitrarily used N=500. MUs were activated at discrete intervals of the activation signal A until all units were active. MN firing frequency fi depended on the actual activation A and on a specific activation threshold Ti for MN i (i=1...N) (Fig. 9C). Firing frequencies ranged from fmin to fmax, where fmin=5 Hz and fmax=27.5 Hz as found in our experiments (and comparable to the range of 7–25 Hz as found by Andreassen and Rosenfalck 1980). The relation describing the non-linear relation between firing frequency and activation is assumed to have a form like:  f + ( f − f ) A – Ti max min A + A – T , if A ≥ Ti fi ( A) =  min 0 i 0 , if A < Ti

(1)

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where A0 is a constant. With a convenient choice of A0 (A0=0.2), this activation-frequency relationship results in a steep increase in firing frequency after recruitment, followed by a more gradually increasing frequency to the limit value of fmax as found by ter Haar Romeny (1983) and in our experiments. The exact way in which this saturation of frequencies is produced has only a minor influence on the outcome of the simulations and does not alter the general conclusions. The activation threshold Ti was assumed to increase linearly with MN i according to Henneman’s size-principle: Ti = i N

(2)

Next the force Fi of an MU was calculated in such a way that it varied linearly with the firing frequency fi of the MN (Fig. 9D). This simple relationship is justified by the following arguments. The number of MUs within a certain force interval decreases exponentially with the force output of the units in that interval (Milner-Brown et al. 1973). However, the product of the number of MUs in an interval and the total force output of all MUs in that interval is more or less independent of the interval threshold. Therefore it is not too much of a simplificaFig. 10A–D Force-frequency relations of one BIC and one BRAD unit with a Ti of 0.5. Shown are one force-frequency curve for increasing activation A (contraction) and several curves for decreasing A (relaxation) with different levels of Apeak. A BIC muscle, simulation 1; B BRAD muscle, simulation 1; C BIC muscle, simulation 2; D BRAD muscle, simulation 2

tion to assume that the force-frequency relation is the same for all MUs in this simulation. In order to obtain the total force within one muscle, Fmuscle, we summed the force outputs of all active MUs (Fig. 9E) and, finally, we added both muscle forces to obtain the total force output Fout (Fig. 9F). Fout was used to obtain the recruitment and decruitment thresholds and the force-frequency relationship of an MU. Simulations We have tested two possible explanations for the gradual change in the decruitment threshold of the brachioradialis muscle as found in our experiments: (1) a simple shift of the central motor command to the two muscles, or (2) a change in the MN pool of one or both muscles. In order to test the first hypothesis, we gradually changed the distribution of activation A between the muscles. Immediately after the start of the relaxation phase (i.e., after Apeak), the distribution was 50% to each muscle and at decruitment of the last MU 40% went to the BRAD and 60% to the BIC MN pool. Note that Fout at A=Ti corresponds to the recruitment threshold of MU i. The decruitment threshold, on the other hand, was de-

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fined as the Fout belonging to the lowest activation level during relaxation at which unit i was still active. Figures 10A and 10B show the force-frequency relations of a BIC and a BRAD unit during contraction (solid curves) and during relaxation after different levels of peak activation Apeak. From these figures we see that when the activation balance is changed, the force-frequency relation is affected by Apeak for both muscles, but in an opposite way. At the same time, this change in the force-frequency relation results in a change in decruitment thresholds for both muscles. However, in the experiments there were no significant changes in the biceps muscle. Moreover, for every Apeak, the BRAD stops firing at Fout levels that were higher than the recruitment threshold, which is the not case for the real brachioradialis muscle. This first simulation clearly does not describe our experimental findings since both muscles become affected by a redistribution of the activation, in contrast to our experiments (Fig. 3A,B). In the second simulation, BRAD units should have changing decruitment thresholds, whereas the decruitment thresholds of the BIC units should be more or less independent of Apeak. However, if we change the activation-frequency relation for one of the muscles, the forcefrequency relation of both muscles will change, since extra force produced by more active units in one muscle will result in a higher Fout at a certain firing frequency of a unit in the other muscle. For example, changes in the activation decruitment thresholds of the BRAD as the result of different Apeak will influence the force-frequency relation and the decruitment thresholds of the BIC units. In order to compensate for this coupling and thus to let the model muscles behave more physiologically, both muscles will have to be changed during relaxation. Furthermore, for both model muscles the firing frequencies must be lower during relaxation than during contraction, especially at decruitment. In the second simulation we changed the activation-frequency relation of the BRAD units until they more or less conform with the experimental results of the brachioradialis muscle, and we studied the way the BIC units behave as a result of this adaptation. First, contraction and relaxation phases were torn apart, where the contraction phase is described by: A – γ c Ti  f + ( fmax – fmin ) , if A ≥ Ti , fic ( A) =  min A0 + A – γ c Ti , if A < Ti 0

(3)

and the relaxation phase by:  f + ( f – f ) A – γ r Ti max min A + A – γ T , if A ≥ γ r Ti . fi r ( A) =  min 0 r i 0 , if A < γ r Ti

(4)

Since the threshold parameter γc in Eq. 3 is a constant smaller than 1 (γc=0.8), units start firing at a higher frequency than fmin, but, as can be deduced from Eq. 4, decruitment frequencies remain fmin. Equations 3 and 4 ensure lower force decruitment thresholds than recruitment thresholds as well as lower firing frequencies at decruit-

ment than at recruitment. The threshold parameter during the relaxation phase is defined as: , for BIC γ c Apeak – Ti  , γr =  , for BRAD γ 1+ β Apeak   c 

(5)

where γc is already defined in Eq. 3 and β is a constant (β =0.56). Equation 5 results in a decruitment threshold equal to the recruitment threshold for a strong BRAD unit with a recruitment threshold equal to Apeak. Weaker units with lower recruitment thresholds have correspondingly higher decruitment thresholds. If the activation threshold γcTi is changed abruptly for the BRAD units at the start of the relaxation phase, their firing frequencies increase stepwise, resulting in an increase in Fout. In order to prevent this, parameter A0, which was constant during contraction and for the BIC, was changed for the BRAD during the relaxation phase according to: A0r, BRAD = A0

Apeak – γ r Ti Apeak – Ti

(6)

It can be easily verified that if we substitute Eq. 6 into Eq. 4, this latter equation transforms back to Eq. 1 for the case A=Apeak. Hence, the decreased activation decruitment thresholds γrTi have no influence at high activation levels and gradually increase their influence with decreasing activation. With this model we investigated the effect of different peak values of the central motor command on the firing frequencies and the decruitment thresholds for both the BIC and the BRAD. We also calculated the differences in muscle force output between the recruitment and the decruitment of unit i. Finally, we investigated the effect of the gradual change of the BRAD decruitment threshold (cf. Eq. 5) on the shift of force production from the BRAD to the BIC. This is compared with the case when BRAD MUs have decruitment thresholds fixed at a level higher than the recruitment threshold. In Fig. 10C,D, the results of the second simulation are shown. In both muscles, firing frequencies at a specific force level are lower during relaxation than during contraction. This can be understood since more units are active during the relaxation phase (γr30%MVC). Although not analysed in this way by the cited authors, their reported data (Fig. 7A; De Luca et al. 1996) allow us to calculate similar threshold ratios as shown in our Fig. 5 but now for the FDI. The decruitment/recruitment ratios of three FDI MUs after a peak force of 50 %MVC were found to be 1.0, 1.3 and 1.5, i.e., all larger than 1. Other FDI MUs that did not showed any decrease in firing frequency (Fig. 6; De Luca et al. 1996) had ratios of 0.95, 0.93 and 0.91, i.e., all smaller than 1. Whether the conclusion that the threshold ratios are larger than 1 exclusively for units that decrease their firing frequencies and are smaller than 1 for units with quasiconstant firing frequencies is a general one remains unclear due to the limited number of data points. Our two muscles showed no decrease in firing frequency during sustained contraction (Fig. 6), probably due to our relatively low recruitment thresholds (≈7%MVC). Note that extrapolation of the data of De Luca et al. (1996) (Fig. 7B) to such a small threshold value also predicts that firing frequency decrease should be very small indeed. Since the TDI had no synergists for the task of De Luca et al. (1996), they concluded that a decrease in firing frequency during a constant-force contraction had to be attributed to an increase in twitch force. Whether potentiation plays a role in our units cannot be concluded or excluded since any change in firing frequency or twitch potentiation of an MU of one muscle can be compensated for by MUs of the synergist. Conclusions The torque history has quite different influences on the biceps brachii muscle as compared to the brachioradialis muscle. For the biceps both firing frequencies at a particular torque level and decruitment level are independent of torque history. The firing frequencies of the brachioradialis muscle at a particular torque level decrease with increasing torque history, whereas the decruitment level simultaneously increases. It has not been possible to give a satisfactory explanation for these shifts.

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