Computer simulation of the motoneuron pool-muscle complex. I. Input system and motoneuron pool.

The aim of the present study was to simulate the input system and the motoneuron (MN) pool of the MN pool-muscle complex (MNPMC). Input fibers, which can originate from command centers in the central nervous system or from sensory organs, activate the MN pool. They generate sequences of action potentials, the frequency of which is proportional to a time-dependent activation factor (which is an input to the model). Different connection patterns between the input fibers and motor units (MUs) are allowed. For simplicity and since no precise experimental data are available, 70 input fibers and 4 boutons per fiber and MN are simulated (this corresponds approximately to the monosynaptic group-Ia input of the cat medial gastrocnemius muscle). Each bouton generates the same conductance change in the postsynaptic membrane. The MNs are modeled with a single compartment and a homogeneous membrane. According to experimental data, the membrane leakage conductance and capacitance are MU dependent. Since the precise relation is unknown: (a) the computed relation between MU contraction force and the MN leakage conductance was taken from a steady-state MNPMC model, and (b) the capacitance was assumed to be proportional to the leakage conductance. The MN membrane includes time- and voltage-dependent ionic channels (fast and slow K(+) and low- and high-threshold Ca(2+) channels). The density and time constant of the slow K(+) channels and the density of the Ca(2+) channels were fitted to approximate afterhyperpolarization characteristics and frequency-injected current relations of type-identified cat MNs. If the membrane reaches a voltage threshold the MNs generate action potentials, which were simulated by voltage pulses. The activation of the MN pool of the human first dorsal interosseus muscle was simulated with injected and synaptic currents in order to illustrate the size principle, synaptic noise, and other features of muscle activation. It is concluded that the present model reproduces the main properties of the input-output relations of different MN types within a muscle. Together with the simulation of the muscle force and the surface EMG, which will be published in subsequent papers, it will be a powerful tool for reproducing experiments on the motor system and investigating functional mechanisms of motor control.

A model for steady isometric muscle activation.

The present model of the motoneuronal (MN) pool-muscle complex (MNPMC) is deterministic and designed for steady isometric muscle activation. Time-dependent quantities are treated as time-averages. The character of the model is continuous in the sense that the motor unit (MU) population is described by a continuous density function. In contrast to most already published models, the wiring (synaptic weight) between the input fibers to the MNPMC and the MNs (about which no detailed data are known) is deduced, whereas the input-force relation is given. As suggested by experimental data, this relation is assumed to be linear during MU recruitment, but the model allows other, nonlinear relations. The input to the MN pool is defined as the number of action potentials per second in all input fibers, and the excitatory postsynaptic potential (EPSP) conductance in MNs evoked by the input is assumed to be proportional to the input. A single compartment model with a homogeneous membrane is used for a MN. The MNs start firing after passing a constant voltage threshold. The synaptic current-frequency relation is described by a linear function and the frequency-force transformation of a MU by an exponential function. The sum of the MU contraction forces is the muscle force, and the activation of the MUs obeys the size principle. The model parameters were determined a priori, i.e., the model was not used for their estimation. The analysis of the model reveals special features of the activation curve which we define as the relation between the input normalized by the threshold input of the MN pool and the force normalized by the maximal muscle force. This curve for any muscle turned out to be completely determined by the activation factor, the slope of the linear part of the activation curve (during MU recruitment). This factor determines quantitatively the relation between MU recruitment and rate modulation. This property of the model (the only known model with this property) allows a quantification of the recruitment gain (Kernell and Hultborn 1990). The interest of the activation factor is illustrated using two human muscles, namely the first dorsal interosseus muscle, a small muscle with a relatively small force at the end of recruitment, and the medial gastrocnemius muscle, a strong muscle with a relatively large force at the end of recruitment. It is concluded that the present model allows us to reproduce the main features of muscle activation in the steady state. Its analytical character facilitates a deeper understanding of these features.

Contribution of a Ia muscle afferent activation to the rise of H reflexes and somatosensory evoked potentials in man.

Electrical stimuli were applied to the tibial nerve in the popliteal fossa in man in order to investigate how information is transferred from group I muscle afferents to motoneurons and to the somatosensory cortex. For control purposes, identical stimuli were applied to the skin beside the electrode above the nerve. The somatosensory evoked potential (SEP) to skin stimulation alone had a peak latency which was 5 ms longer than the SEP to transcutaneous nerve stimulation. Influences by stimulation of the skin above the nerve could thus be excluded. The threshold intensity to evoke a liminal H reflex was at least two times higher than the threshold for a SEP. In most of the subjects, there was a correlation between the H reflex and the SEP size. If two identical stimuli were applied to the posterior tibial nerve with an interval of 1 s, the second H reflex was 30% smaller than the first one (postactivation depression). The corresponding SEPs were, however, only slightly reduced. Postactivation depression was probably caused by general intrinsic properties of synapses of group I muscle afferents. The results of this investigation indicate that: (1) a large volley in group I muscle afferents is necessary to evoke a liminal H reflex, whereas transmission from muscle afferents to the somatosensory cortex is very efficient; (2) these feedback signals to motoneurons and the somatosensory cortex are used independently.

Simulation of the surface EMG of an active muscle.

A model of the motoneuronal (MN) pool-muscle system was developed. The model consists of four modules: (1) the input to the MN pool, (2) the MN pool, (3) the muscle and (4) the surface electromyogram (EMG). A control parameter activates the input fibers and determines the activity level of the muscle. A single compartment model with a homogenous membrane was used to model the MNs. The trajectory between spikes is determined by two voltage-gated K(+)- and two voltage-gated Ca(2+)-channels. The size of the MNs is adjusted by the size of the leakage conductance. The model muscle is of circular cross section and with parallel fibers. The motor unit (MU) territories are of circular shape and their area is proportional to the MU contraction force. Action potentials propagated along the muscle fibers are approximated by a dipole with a current source and current sink. The potential evoked by the dipole at the recording site is computed. The surface EMG is obtained by summing up (1) the potentials of all fibers of the MU and (2) the MU action potentials of all active MUs. Numerical results show that the MUs are recruited with increasing contraction force and that the active MUs modulate their firing frequency similar as in real muscles. The model will be used for investigation of the motor system in man.

Influence of different properties of a reaction time task on the pre-movement gating of input from Ia afferents to motoneurons.

The monosynaptic reflex (H reflex) is facilitated before movement onset in human subjects who are performing a conditioned plantar flexion of the ankle in a reaction time task. The aim of this study was to investigate how tightly this gating of Ia spindle input is coupled with the conditioned muscle contraction. Test H reflexes were elicited at various times during the reaction time (RT) in order to test the efficacy of Ia volleys on the soleus motoneurons. Tactile, auditory and visual go stimuli were used. The RT to a tactile stimulus was about the same as the RT to an auditory stimulus although distance and therefore conduction time from the site of stimulation to the cerebral cortex was much larger for the tactile than for the auditory modality. The RT to visual stimulation was about 20 ms longer than to the other two modalities. Although central latencies depended clearly on the stimulus modality the duration of the H reflex facilitation, i.e. the interval between the onset of the facilitation and the onset of the voluntary muscle contraction, was always the same. Similarly, the reflex facilitation was insensitive to the succeeding contrast of a visual go stimulus. The subjects were also examined in visual RT tasks in which different advance information about the laterality and the execution of the contraction was given. By combination the following four RT situations were realized: (1) simple, go, (2) choice, go, (3) simple, go-no go and (4) choice, go-no go.(ABSTRACT TRUNCATED AT 250 WORDS)

Superposition of H reflexes on steady contractions in man.

1. The aim of the investigation was to study the influence of steady isometric contractions on H reflexes of human soleus muscle. 2. Stimulating and recording conditions were hardly affected by plantar flexions which subjects maintained in a force matching task. 3. If the interval between a preceding control and the test stimulus was less than 8 s the test H reflex was depressed in the relaxed subject. The depression was diminished or removed if the test reflex was superimposed on a background activity. The interval between control and test H reflex was at least 8 s in the following experiments. 4. H reflexes were nearly independent of steady plantar flexions on which they were superimposed. In some subjects, there was a slight increase with increasing torque. During dorsal flexions, H reflexes in all subjects were inhibited with increasing torque. 5. The relationship between test H reflexes, control H reflexes and background activity was evaluated by varying pseudo-randomly stimulus intensity and steady flexion torque. The surface defined by this three-dimensional relation approximated a plane suggesting linear properties of the H reflex. In some subjects threshold intensity decreased slightly with torque, in others it was constant. 6. In response to a warning signal, human subjects initiated steady plantar or dorsal flexions in both feet and, at the same time, they started to concentrate on a light at the onset of which they performed a unilateral ballistic plantar contraction as fast as possible. The relations between H reflex and maintained flexion force during the warning period of the reaction time task were identical to those during force matching, showing that the behavioural context did not modulate the relations. 7. The relations were also the same if reflexes were evoked bi- or unilaterally, illustrating the absence of a mutual modification of simultaneously evoked H reflexes. 8. The relation was the same with ipsilateral matching and relaxed contralateral muscles as with bilateral matching. If the ipsilateral side stayed flaccid contralateral matching increased H reflexes by about 20% above control values. 9. It was concluded that various factors can combine to produce an increase of H reflexes with torque, the most important of them being the use of short intervals between H reflexes. We have various evidence from the present experiments for believing that, in the relaxed subjects, the subliminal fringe was small and that although stimulus intensities below threshold could evoke an afferent volley, the effect of this on low-threshold motor units was prevented by presynaptic inhibition at the Ia terminals.

Relation between electromyogram and torque of isometric reflex contractions in man.

Human subjects maintained isometric plantar or dorsal flexions of the ankle in a matching task. H-reflexes of different sizes were superimposed on the steady activity. The peak-to-peak amplitude of the reflexes was measured on the electromyogram (EMG) of the soleus muscle. The size of the corresponding muscle contractions was determined on the isometric torque signal in relation to the maintained flexion force. The EMG-torque relation which was defined as the reflex muscle contraction as a function of the EMG reflex signal approximated a square root function for a given steady contraction level. It was not modulated by steady dorsal flexions, but it decreased continuously with stronger plantar steady torques. This dependence was caused by the silent period following the reflex discharge. Since the reflex discharge and the silent period were near in time to the duration of the contraction, the silent period had a direct effect on the reflex contraction amplitude.

Ia afferents of the antagonist are inhibited presynaptically before the onset of a ballistic muscle contraction in man.

The aim of the present investigation was to study whether the pre-movement inhibition of the H reflex in the antagonist of a ballistic voluntary contraction was due to a reduced activity of the motoneuronal pool of the antagonist, or to a reduced excitatory effect of the afferent volley reaching these motoneurons. Human subjects performed visually conditioned ballistic dorsal flexions of the ankle. The inhibition of the H reflex in the antagonist (soleus muscle) was similar if the muscle was initially relaxed or if there was a preexisting level of motor discharge. Since the soleus muscle was inhibited before movement onset in parallel with the H reflex inhibition, the relation between the level of a background activity and the size of superimposed H reflexes was studied. The finding that H reflexes were only slightly reduced in size with decreasing steady EMG levels could not explain the pre-movement inhibition, and it was concluded than an increased presynaptic inhibition of Ia terminals was the source of the H reflex inhibition.

Superposition of ballistic on steady contractions in man.

In a visual reaction time task, human subjects superimposed isometric ballistic contractions on a maintained activity in the soleus or anterior tibial muscle. Since there were good reasons to believe that the supraspinal motor commands for the ballistic contractions were independent of those for the background activity, the interaction between the motor commands for the ballistic and for the steady contractions could be studied at the spinal level. If ballistic and steady contractions were in the same direction, the EMG burst and torque changes associated with the ballistic contraction were nearly constant irrespective of the maintained steady flexion force. This was true if a muscle was activated to about 5% of its maximum force as the soleus muscle during plantar flexions and if it was activated to about 40% of its maximum force as the anterior tibial muscle during dorsal flexions. If ballistic and steady contractions were in opposite directions the torque changes related to the ballistic contraction increased linearly with the background activity. This relation was caused by a reduction in antagonist activity starting about 50 ms before the agonist EMG burst and not by an increased agonist burst, the latter remaining independent of background activity. These results imply that the input-output relationship of the motoneuronal pool is nearly linear. The functional basis of this relation is the size principle which is valid during continuous and ballistic contractions. The number of motor units recruited for the ballistic contraction is adjusted according to their force such that the contraction amplitude remains constant.

Origin of the specific H reflex facilitation preceding a voluntary movement in man.

1. In a reaction time situation, the monosynaptic spinal reflex (H reflex) is facilitated before the onset of an electromyographic (EMG) response. The aim of the present investigation was to test if the facilitation can be attributed either to a subliminal depolarization of motoneurones or to an increase of the excitatory effect of the afferent volley reaching the motoneurones. 2. At the onset of an acoustic warning signal, human subjects were required to concentrate on a reaction time task and, in addition, to initiate a steady isometric plantar flexion of medium intensity in both feet. In response to a following visual stimulus, they carried out a ballistic plantar flexion randomly with the right or left foot. At different times after the visual reaction signal, H reflexes were elicited bilaterally. 3. The facilitation of the H reflex was similar in the presence and absence of a steady activation. In addition, the facilitations were similar in absolute amplitude and duration when the stimuli evoking the H reflexes were at threshold intensities, or at an intensity which produced control H reflexes of 60% maximum amplitude. 4. In a second series of experiments, no H reflexes were elicited but the strength of the steady plantar flexion was varied. Premotor time, i.e. the interval between the onset of the visual stimulus and the EMG response, and reaction time, i.e. the interval between the onset of the visual stimulus and the mechanical response, were computed. Neither parameter depended significantly on the intensity of steady flexion and they were the same with steady flexion as without. 5. The rectified EMG records and the torque records were aligned by the end of premotor time. Three-dimensional displays of average activity as a function of time and steady activation level were computed. No activation before premotor and reaction time was detected which could have been related to the H reflex facilitation. 6. The present results suggest that all motoneurones, in particular those being activated during the voluntary contraction, can contribute to the H reflex facilitation before movement onset and that the basis of this facilitation is an enhanced excitatory effect of the afferent volley elicited by the H reflex stimulus. Mechanisms leading to the facilitation could be removal of presynaptic inhibition at I a terminals or facilitation of interneurones intercalated in polysynaptic components of the reflex pathways.

Contributions of the motor cortex and the cerebellum to a simple learned movement in the monkey.

Monkeys were trained to perform isometric plantar flexions of the foot in a simple reaction time situation. In test sessions, the contralateral hindlimb area of the motor cortex was cooled by a cryode placed on the dura until somatosensory evoked potentials disappeared. Movement amplitude decreased to about 70% of initial size; reaction time which was measured on the EMG, and torque signals increased slightly; and the evoked response in the dentate nucleus of the cerebellum remained unchanged. An extensive lesion in the motor cortex by coagulation reduced the movement amplitude to 10% of its preoperational size, but again, did not change reaction time significantly. It is concluded that the motor cortex is not essential for the execution of this overtrained simple movement.

Relation between the specific H reflex facilitation preceding a voluntary movement and movement parameters in man.

In a reaction-time situation, the monosynaptic spinal reflex (H reflex) is facilitated before the onset of an electromyographic (e.m.g.) response. The aim of the present investigation was to study aspects of this facilitation. Human subjects were required to perform isometric plantarflexions of the foot in response to a visual stimulus. The movement was always on the same side in the simple reaction-time situation, and randomly with the right or left foot in the choice reaction-time situation. Stimuli to evoke H reflexes were applied bilaterally 40-400 ms after the onset of the visual stimulus. Pre-motor time, i.e. the interval between the onset of the visual stimulus and the e.m.g. response, and reaction time, i.e. the interval between the onset of the visual stimulus and the response on the torque recording, were computed. In both reaction-time situations, there was a significant facilitation of the ipsilateral H reflex 100-160 ms before e.m.g. onset and, in some subjects, a small facilitation of the contralateral H reflex. The specific facilitation, i.e. the difference between the facilitation on the ipsi- and contralateral side relative to the movement, was not significantly different on the right and left side. Pre-motor time was divided into the interval from the light onset until the onset of the specific facilitation, and the interval from the onset of the facilitation until the onset of the voluntary response. Both intervals increased, and the slope and the amplitude of the facilitation decreased with increasing pre-motor time and reaction time. The specificity of the H reflex facilitation in a choice reaction-time situation implies that the interval from light onset until the onset of the facilitation includes stimulus identification and response selection, and the interval from the onset of the facilitation until the e.m.g. response preparation of the motor system for the required movement. The present results suggest that the specific facilitation of the H reflex before a movement is caused by removal of presynaptic inhibition at I a terminals or by activation of interneurones intercalated in polysynaptic components of the H reflex rather than by a subthreshold activation of motoneurones.

Effects of electrical stimulation of low-threshold muscle afferents on visual reaction time.

Human subjects performed plantar flexions of the foot in visual reaction time (RT) situations. In the simple RT task, the same foot had to be moved during the whole session, in the choice RT task, the right or left foot was moved in a random sequence. Low-threshold muscle afferents which evoked a monosynaptic H reflex were electrically activated on both sides at various intervals after the onset of the light stimulus. In both RT situations. RT was shortened equally by the electrical stimulation. The intersensory facilitation in the choice RT task provided support for the preparation enhancement model, since the subjects could not react to the electrical stimulus alone.

Detection of reaction time by an adaptive filter based on the least squares fit.

An adaptive filter based on the least squares fit between a template and individual records was developed. It has been applied to compute reaction times of a voluntary movement. Its performance was tested by comparing these reaction times with the latency of the EMG responses. Different properties of the least squares fit technique and Woody's filter technique (Woody 1967) are discussed.

Peripheral and transcortical loops activated by electrical stimulation of the tibial nerve in the monkey.

Peripheral and supraspinal loops activated by electrical stimulation of the tibial nerve were studied in alert monkeys. Weak conditioning stimuli below the threshold for muscle contraction and strong conditioning stimuli which elicited a direct motor response and an H-reflex were applied to the tibial nerve, while soleus EMG was recorded. The motoneuronal excitability was measured with a test H-reflex for different intervals between conditioning and test stimuli. A facilitation of the motoneuronal pool occurred with a latency of about 50 ms for weak, as well as strong, conditioning stimuli. The facilitation was superimposed on a long-lasting inhibition which was more pronounced when strong stimuli were used. The shape of the excitability curve of the motoneurons after strong conditioning stimuli was studied before and after various lesions. The shape of the curve did not change after an ipsilateral cerebellectomy except that the facilitation was more pronounced. A few days after pyramidotomy, the facilitation diminished in size but it recovered to its initial size after 3 months. Spinal hemisection did not abolish the facilitation. We concluded from these results that a peripheral loop was activated when conditioning stimuli above the threshold for a direct motor and reflex response were applied. The facilitation might be mediated by the muscle contraction and following activation of muscle afferents. Superimposed on thus loop is a previously demonstrated transcortical loop of similar latency.

Effects of dorsal cord stimulation on stretch reflexes.

The effects of dorsal cord stimulation on phasic and tonic stretch reflex activity in extensor muscles were studied in decerebrate cats. The tonic stretch response was depressed in both fore- and hindlimb (stimulation at levels C1 and T8, respectively) and this often persisted for 5-20 min after the end of 1-10 min of dorsal cord stimulation. Depression of the phasic stretch response was only consistently seen in the forelimb during stimulation (C1) and this rarely outlasted the period of stimulation. These results support the idea that dorsal cord stimulation can reduce muscle tone but provide no explanation for the long-lasting effects of chronic, continuous stimulation in spastic man.

A transcortical loop demonstrated by stimulation of low-threshold muscle afferents in the awake monkey.

1. The hypothesis that a transcortical loop can be activated by electrical stimulation of low-threshold muscle afferents was tested. The effect of these afferents on the excitability of motoneurones was measured with the monosynaptic spinal reflex (H-reflex).2. Four monkeys were trained to maintain a constant tonic activity in the soleus muscle so that the amplitude of evoked H-reflexes was constant. The intensity of conditioning stimuli was just subthreshold for direct or reflex electromyographic responses. The intensity of the test stimuli was adjusted to evoke an H-reflex of maximal amplitude. The amplitude of the H-reflex was recorded for different intervals between conditioning and test stimuli (10-1000 msec).3. The excitability curve obtained showed three components: (1) an early excitatory process, F1, at intervals of 10-20 msec, (2) a late excitatory process, F2, at intervals of 40-80 msec and (3) a short latency depression of about 400 msec duration, on which F1 and F2 were superimposed.4. F2 was selectively abolished during cooling of the contralateral motor cortex, after an irreversible lesion of the motor cortex, and after pyramidotomy; however, F1 and the inhibition remained unchanged.5. The conduction time from the tibial nerve to the somatosensory cortex (SI), the cortical delay between SI and motor cortex, and the conduction time from motor cortex to the soleus muscle were measured in an anaesthetized animal. The sum of these values as an estimate of the transcortical loop time was 5 msec shorter than the latency of F2.6. It is concluded that a transcortical loop can be activated by electrical stimulation of low-threshold muscle afferents and, by analogy, also by mechanical perturbations applied during a motor task.