Prince of Wales Medical Research Institute, University of New South Wales, Randwick, New South Wales 2031; and School of Physiotherapy, University of Sydney, Lidcombe, New South Wales 2141, Australia
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ABSTRACT |
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Herbert, R. D. and S. C. Gandevia. Twitch Interpolation in Human Muscles: Mechanisms and Implications for Measurement of Voluntary Activation. J. Neurophysiol. 82: 2271-2283, 1999. An electrical stimulus delivered to a muscle nerve during a maximal voluntary contraction usually produces a twitchlike increment in force. The amplitude of this "interpolated twitch" is widely used to measure voluntary "activation" of muscles. In the present study, a computer model of the human adductor pollicis motoneuron pool was used to investigate factors that affect the interpolated twitch. Antidromic occlusion of naturally occurring orthodromic potentials was modeled, but reflex effects of the stimulus were not. In simulations, antidromic collisions occurred with probabilities of between ~16% (in early recruited motoneurons) and nearly 100% (in late recruited motoneurons). The model closely predicted experimental data on the amplitude and time course of the rising phase of interpolated twitches over the full range of voluntary forces, except that the amplitude of interpolated twitches was slightly overestimated at intermediate contraction intensities. Small interpolated twitches (4.7% of the resting twitch) were evident in simulated maximal voluntary contractions, but were nearly completely occluded when mean peak firing rate was increased to ~60 Hz. Simulated interpolated twitches did not show the marked force drop that follows the peak of the twitch, and when antidromic collisions were excluded from the model interpolated twitch amplitude was slightly increased and time-to-peak force was prolonged. These findings suggest that both antidromic and reflex effects reduce the amplitude of the interpolated twitch and contribute to the force drop that follows the twitch. The amplitude of the interpolated twitch was related to "excitation" of the motoneuron pool in a nonlinear way, so that at near-maximal contraction intensities (>90% maximal voluntary force) increases in excitation produced only small changes in interpolated twitch amplitude. Thus twitch interpolation may not provide a sensitive measure of motoneuronal excitation at near-maximal forces. Increases in the amplitude of interpolated twitches such as have been observed in fatigue and various pathologies may reflect large reductions in excitation of the motoneuron pool.
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INTRODUCTION |
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A central question in human muscle physiology
concerns how well the brain can "drive" muscles during maximal
voluntary contractions. To answer this question it is necessary to
determine whether the motoneuron pool has been excited sufficiently by
volition to evoke all the force the relevant muscles can produce. This
can be done by comparing the increment in muscle force produced when an
electrical stimulus is delivered to a muscle during a voluntary
contraction with the force increment produced when the same stimulus is
delivered to the resting muscle (e.g., Allen et al.
1998; Bellemare and Bigland-Ritchie 1984
; Merton 1954
). When
the stimulus consists of only a single pulse, the method is called
twitch interpolation, and the force increment is referred to as the
interpolated twitch. The amplitude of the interpolated twitch declines
with increasing contraction intensity, so it has been used to measure
the level of excitation of motoneurons (also referred to as
"voluntary activation" or "neural drive") (see Gandevia
et al. 1995
for review). The method has also been used to
estimate, by extrapolation, the muscle force that could be produced if
voluntary activation were complete (e.g., Bellemare and
Bigland-Ritchie 1984
; De Serres and Enoka 1998
; Merton 1954
; Phillips et al.
1992
; Rutherford et al. 1986
). Twitch
interpolation has been used to investigate limitations to muscle force
production (usually under isometric conditions) (e.g., Allen et
al. 1995
; Belanger and McComas 1981
;
Merton 1954
; cf. Gandevia et al. 1998),
mechanisms of fatigue (e.g., Bigland-Ritchie et al.
1983a
,b
; McKenzie et al. 1992
), the nature
of weakness associated with various pathologies (e.g., Allen et
al. 1993
, 1997
; McComas et al.
1983
; Rice et al. 1992
; Rutherford et al. 1986
; Thomas et al. 1998
), and neural
adaptations associated with training voluntary isometric muscle
strength (Herbert et al. 1998
; Jones and
Rutherford 1987
).
When, in a maximal voluntary contraction, a subject manages to
completely occlude the interpolated twitch, interpretation is usually
straightforward: the level of excitation of motoneurons must have been
sufficient to extract all of the force that the muscle could have
produced ("maximal muscle force") (cf. Allen et al.
1998 for a discussion of factors that may sometimes obscure interpolated twitches even when activation is truly maximal). Usually,
however, subjects cannot completely occlude the twitch. In this case,
the amplitude of the interpolated twitch is often used to infer the
level of motoneuronal excitation. If quantitative inferences are to be
made about excitation of motoneurons, it is necessary to know how
interpolated twitch amplitude and excitation are related. It is not
currently possible to measure excitation of the motoneuron pool any
more directly than with the twitch interpolation method, so the
relationship between interpolated twitch amplitude and excitation
cannot be determined experimentally. Thus it is not certain what level
of motoneuron excitation can be inferred from any particular
interpolated twitch amplitude, nor how much of a change in excitation
can be inferred from a change in interpolated twitch amplitude.
Sometimes the interpolated twitch method is used to make inferences
about maximal muscle force. Interpolated twitches are measured as
subjects intentionally contract to a range of submaximal intensities,
and the relationship between interpolated twitch amplitude and
voluntary force is extrapolated to the force at which the interpolated
twitch would have been completely occluded (Bellemare and
Bigland-Ritchie 1984; De Serres and Enoka
1998
; Merton 1954
; Phillips et al.
1992
; Rutherford et al. 1986
). This force is
thought to correspond to maximal muscle force. Again, it is difficult
to test the validity of these estimates of maximal muscle force because
there is no completely satisfactory method for determining maximal
muscle force. One comparison is between the force produced by tetanic
stimulation and maximal voluntary force (Bigland and Lippold
1954
; Merton 1954
). However, this may be
unsatisfactory because it is usually not possible to be certain that
all of the agonists and none of the antagonist muscles are being
stimulated supramaximally, and synergistic muscles will not usually be
stimulated optimally.
The mechanisms that determine the amplitude of the interpolated twitch
are complex and incompletely understood (Merton 1951). An interpolated stimulus evokes action potentials that propagate orthodromically and antidromically in nonrefractory motor and sensory axons. Orthodromic potentials in motor axons produce a near-synchronous twitch from muscle units. Antidromic potentials in
motor axons may also influence the amplitude of the twitch, even at
short latencies, because some collide with voluntarily produced
potentials and reduce the rate of motoneuron discharge immediately
after the stimulus. Other antidromic potentials reach the motoneuron
soma and produce hyperpolarization (Brock et al. 1952
)
and may propagate along recurrent branches terminating on Renshaw
cells, evoking inhibitory postsynaptic potentials in motoneurons. Motoneuron discharge after the interpolated stimulus may also be
influenced by short-latency reflex effects of stimulated sensory axons
and longer-latency reflex effects, including those due to the
mechanical effects of the twitch (such as the decrease in spindle
afferent discharge that accompanies unloading of muscle spindles).
Presumably all the mechanisms described above can influence the period
of prolonged "inhibition" (i.e., the electromyographic "silent
period"), which follows the interpolated twitch.
The aim of the present study was to investigate properties of the
interpolated twitch. We sought to determine the relationship between
interpolated twitch amplitude and both motoneuronal excitation and
muscle force, because knowledge of these relationships might enable
quantitative inferences to be made about motoneuronal excitation or
maximal muscle force when the interpolated twitch is not occluded. We
also sought to examine factors that influence the amplitude of the
interpolated twitch. Of particular interest was whether antidromic
potentials reduce the amplitude of the interpolated twitch compared
with the hypothetical situation in which antidromic conduction does not
occur. In addition we examined the effect of motor-unit discharge rates
and contractile properties on interpolated twitch amplitude. These
questions are not easily investigated experimentally, so a computer
modeling approach was used. Some of the results have been presented in
preliminary form (Herbert and Gandevia 1998).
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METHODS |
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Terminology
Throughout the text we refer to maximal voluntary
contraction, by which is meant the greatest muscle force that can
be produced voluntarily, maximal voluntary excitation, by
which is meant the level of excitation of the motoneuron pool required
to excite all motoneurons to their peak voluntary firing frequencies,
and maximal muscle force, by which is meant the greatest
force the muscle can produce (i.e., with tetanic stimulation at 100 Hz). Excitation is used to mean "effective synaptic current"
(Heckman and Binder 1988), which was assumed to be
distributed uniformly to the motoneuron pool.
Experimental data
Experimental data were obtained from three subjects (healthy
males, 29-44 yr of age) to assist in construction of the model and
assignment of parameter values. Subjects were seated with the forearm
resting on a bench, and brackets held the forearm halfway between full
pronation and supination (Fig.
1A). Force produced by the
adductor pollicis muscle was measured with a transducer (XTran, 250 N)
firmly coupled to the proximal phalanx of the thumb, as described
previously (Herbert and Gandevia 1996). The force signal
was sampled at 5 kHz.
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Twitch and force-frequency data were obtained by delivering stimulus trains at supramaximal intensities (constant current, 160-280 mA) to the ulnar nerve through a pair of surface electrodes (diameter 2 cm; interelectrode spacing ~4 cm) placed longitudinally over the ulnar nerve anteriorly and just proximal to the wrist. Care was taken to avoid inadvertent stimulation of the median nerve. Before each stimulus train, subjects performed a single, brief, maximal voluntary contraction to potentiate the adductor pollicis. Five seconds later, a stimulus train of 1-s duration was delivered. One minute of rest was allowed between each train. Stimulus frequencies were delivered in the following order: 1, 5, 10, 20, 50, 100, 100, 50, 20, 10, 5, and 1 Hz. The force produced by 100-Hz trains averaged 60.3% of maximal voluntary force. In additional trials, an extra stimulus was interpolated on constant frequency trains of 10 or 20 Hz. The results of these experiments were used to build the model, and so are given in the following methods.
In addition, interpolated twitches were obtained during contractions at a range of intensities. These data were used to test model predictions. Before each test contraction, subjects performed a single, brief maximal voluntary contraction. Five seconds later the subject contracted to a target proportion of maximal voluntary force using feedback of force on an oscilloscope. Target forces were 10% increments from 0 to 100% maximal voluntary force (MVC), presented in random order. A single supramaximal stimulus was delivered to the ulnar nerve during the force plateau of the contraction. At least 1 min of rest was given between contractions.
Model structure and modeling strategy
We modified the model of a motoneuron pool described in detail
by Fuglevand et al. (1993) (see also Fuglevand
1989
; Fuglevand and Bigland-Ritchie 1993
) so
that it could simulate interpolated twitches of the adductor pollicis
muscle. The model consists of a pool of 120 motoneurons with varying
excitation thresholds. When the motoneuron pool is excited, motoneurons
excited above threshold begin to fire at a specified initial firing
frequency. As excitation is increased above threshold, the firing rate
of each motoneuron increases linearly with excitation according to an
excitation-firing rate relationship analogous to the steady-state current-frequency relationship observed when single motoneurons are
injected with current, up to a predetermined maximal firing frequency.
A normally distributed random component is added to interspike
intervals to simulate physiological variability in the instantaneous
firing frequency. Then, once the firing pattern of each motoneuron has
been determined, its force output is determined as follows. The twitch
responses of motor units to a single stimulus are distributed so that
the speeds and forces of twitches of early-recruited motor units are
less than those of later recruited units. The force response to a train
of stimuli is determined by summing twitch responses after scaling them
according to the duration of the preceding interspike interval. The
force of all motor units is then summed to give muscle force.
It is desirable, particularly in complex models with many parameters, that the structure of a model and the values of its parameters are determined without reference to the final outputs of the model. Thus values were assigned to parameters in a way that maximized goodness-of-fit to simple muscle behaviors observed experimentally (such as the response of the resting muscle to a single stimulus). The values of these parameters were then fixed. Values were assigned to more parameters as progressively more complex muscle behaviors were examined (see Fig. 2 and below for details). Data on the most complex behaviors (motor-unit firing patterns in voluntary contractions) were obtained from the literature. Once a good fit had been obtained to a complex set of muscle behaviors, values for all parameters were fixed, and the model was used to predict the effect of interpolated stimuli delivered during voluntary contractions of different strengths.
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Model construction I: the resting twitch
The shape of the single twitch obtained from the resting
adductor pollicis muscle could not be accurately modeled as the sum of
motor unit twitches if motor-unit twitches were modeled as the impulse
response of a critically damped second-order system (as used by
Fuglevand et al. 1993). If the duration of the rising phase was matched to experimental data, the falling phase was much too
slow (Fig. 3A). Consequently
only the rising phase of the motor-unit twitch was modeled as described
by Fuglevand et al. (1993)
, that is
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Model construction II: trains of stimuli
There have been few attempts to model the isometric forces
produced by time-varying rates of stimulation in motor units or whole
muscles [see Bobet and Stein (1999) and Ding et
al. (1998)
for references and descriptions of 2 successful
models]. The approach used here is a modification of that used by
Fuglevand et al. (1993)
.
When trains of stimuli are delivered to a motoneuron, motor-unit
twitches do not sum linearly (e.g., Burke et al. 1976;
Hartree and Hill 1921
). The additional force produced by
a single pulse in a stimulus train is a function of stimulation rate
and history and may be more or less than the force produced in a
resting twitch. The steady-state gain of a
constant-frequency train of stimuli can be obtained from the
force-frequency relationship, because the gain at any frequency is
simply the ratio of force and frequency. For the present study,
steady-state gains obtained from the force-frequency relationship were
used to scale the amplitude of each motor-unit twitch according to the
duration of the preceding interspike interval. The model assumed that
the relationship between normalized force (per cent of maximum) and
normalized frequency (frequency × contraction time) was the same
for all motor units (Fuglevand et al. 1993
; Kernell et al. 1983
; cf. Heckman and Binder
1991
), and that forces from different motor unit summed
linearly, so motor-unit gains were obtained from the experimentally
obtained relationship between whole muscle force and normalized
frequency. The experimentally obtained relationship was closely fitted
by
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Simulations of force responses to constant-frequency trains of stimuli
at a range of frequencies (1, 5, 10, 20, 50, and 100 Hz) closely
reproduced experimental measures of mean steady-state muscle force.
However, the amplitude of the simulated force fluctuations tended to be
too large when the muscle was stimulated at all but the lowest
frequencies. Consequently motor-unit twitches were filtered with a
causal, critically damped, second-order low-pass filter. It was
necessary to apply lower filter cutoffs at higher frequencies. (On the
basis of experiments with brief interpulse intervals at low forces, we
established that filter cutoffs should vary with stimulation frequency,
not force.) To fit the force fluctuations well, filter cutoffs needed
to decline progressively more slowly with increasing frequency, and
thus they were modeled as
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Model construction III: simulated voluntary contractions
To simulate voluntary muscle force we used the approach
described by Fuglevand (1989) and Fuglevand et
al. (1993)
. Thus it was assumed that all motoneurons received a
common level of excitation during a voluntary contraction. The
threshold level of excitation required to cause the motoneuron to
discharge was distributed so that many small units had low thresholds
and relatively few units had high thresholds. The range of recruitment
thresholds (in multiples of the threshold of the first-recruited unit)
was RR, and the minimum rate of discharge, attained when
units were excited to their threshold, was MFR. Above
threshold, all motoneurons increased their firing frequencies linearly
with increasing excitation, and the ratio of change in firing rate to
excitation (ge) was the same for all
motoneurons. A normally distributed random component (with coefficient
of variation V) was added to interspike intervals. Motoneurons increased their rate of firing to a predetermined maximum.
In the model by Fuglevand et al. (1993)
, maximal firing frequencies were set as linear functions of excitation thresholds. As
excitation thresholds are highly skewed, this produced a positively skewed distribution of peak firing rates (PFRs), but the best available
experimental data suggest that PFRs of the adductor pollicis muscle are
close to normally distributed (Bellemare et al. 1983
).
Consequently, PFRs were assigned in a way that ensured a normal
distribution (each PFRi was a
j/121st fractile of the normal distribution, where
j is an integer between 1 and 120). Four normal
distributions of PFRs were considered. In the first (a
"progressive" distribution), early-recruited units attained the
lowest PFRs, late-recruited units attained the highest PFRs, and PFR
increased in strict order of recruitment (i.e., j = i). In the second ("regressive") distribution, the reverse
occurred: PFRs declined in strict order of recruitment (j = 121
i). In the third ("random") distribution, PFRs
were assigned randomly from a normal distribution. In the last
distribution ("progressive/random"), PFRs were assigned partly in a
progressive way and partly randomly (by calculating PFRs using both the
progressive and random methods, and then taking the average of the 2 results for each unit). Maximal voluntary excitation was defined as the
level of excitation required to make all motoneurons fire at their
specified PFRs, and maximal voluntary force was the force produced with
this level of excitation (Fuglevand et al. 1993
).
Thus seven model parameters determined the firing patterns of
motoneurons during simulated voluntary contractions. They were RR, the range of recruitment thresholds,
MFR, the minimal firing rate,
ge, the rate of increase of firing rate with
excitation, and V, the coefficient of variation of
interspike intervals, with three parameters used to describe the
distribution of firing frequencies (the mean and standard deviation of
the distribution, and the order in which PFRs were distributed). All
motoneurons were assigned an MFR of 8 Hz, because this
approximates the minimal mean continuous firing rate usually observed
during voluntary contractions (e.g., Monster and Chan
1977). The mean and standard deviation of the distribution of
PFRs were assigned values of 29.9 and 8.6, respectively [giving a
range between 9.3 and 50.2 Hz (Bellemare et al. 1983
); Fig. 4B]. The parameter
ge was assigned a value of 1 (meaning an
increase of 1 Hz per unit of excitation, where the unit of excitation
is the threshold excitation of the 1st recruited unit). This
approximates the average gain in steady-state firing frequency observed
when single motoneurons are injected with current (Kernell 1965
). (The steady state might not be attained in brief
voluntary contractions but, nonetheless, provides the best available
estimate of ge. Simulations using this value
can reproduce physiological firing patterns.) The coefficient of
variation V was assigned a value of 0.2 (e.g.,
Person and Kudina 1972
; Stålberg and Thiele 1973
). The remaining two parameters, RR and the
order in which PFRs were distributed, were determined by assessment of
the performance of the model with values of RR of 10, 20, 25, and 30, and with progressive, regressive, random, and
progressive/random distributions. One additional simulation was
performed in which a regressive recruitment strategy was used and the
minimum PFR was increased to 18 Hz by setting the mean and standard
deviation of the distribution of PFRs to 35 and 7, respectively. This
was done to simulate the narrower range of maximal firing frequencies
observed in some individual subjects (Bellemare et al.
1983
).
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The best combination of values for these parameters was determined by
exciting the motoneuron pool to different levels and examining their
effects on the rate of increase in motoneuron firing frequency with
force, and on the force threshold of the last recruited motoneuron.
Experimental data suggest that some or all motoneurons increase their
firing frequencies progressively more slowly with increasing muscle
force, and that an acceleration of firing rates with increasing force
is rarely or never seen in early recruited motoneurons (e.g.,
Kanosue et al. 1979; Monster and Chan
1977
). In the adductor pollicis muscle, most units are recruited by 50% maximal voluntary force (although this may be an
underestimate, because it is difficult to be certain that the last
recruited motor unit has been observed) (Kukulka and Clamann 1981
). When RR was set at 10, the rate of
increase in motoneuron firing frequencies progressively increased,
rather than declined, with force. On the other hand, if
RR was set at 25 or 30, the force threshold of the
last-recruited unit was too high (always
75% maximal voluntary
force), particularly with the regressive and random distributions. Thus
RR was set to 20. With an RR of 20, the
force threshold of the last recruited unit was 67, 71, 75, and 90%
maximal voluntary force for the progressive, progressive/random, random, and regressive distributions, respectively. Even if the minimum
PFR was increased to 18 Hz, the regressive recruitment strategy
produced nonphysiological outputs. In this simulation, the force
threshold of the last-recruited unit was 85% of maximal voluntary
force, and firing rates of all recruited units increased linearly until
~90% of maximal voluntary force, whereupon the firing frequency
increased extremely rapidly. The progressive model was used in all
subsequent simulations because this model caused all motoneurons to be
recruited at relatively low forces, much as is observed experimentally
(Kukulka and Clamann 1981
). With this model 95% of
motoneurons were recruited at forces <56% maximal voluntary force
(Fig. 4A). At submaximal forces, the right-hand tail of
the distribution of firing frequencies was compressed toward lower
frequencies, exactly as shown by Bigland-Ritchie et al.
(1992)
for the tibialis anterior muscle.
Model predictions: interpolated twitches
To simulate interpolated twitches obtained from contractions of
varying intensities, the motoneuron pool was sequentially excited in
increments of 10% from 0 to 100% of the maximal excitation level.
Each level of excitation was sustained for 750 ms, and muscle force was
determined every millisecond. To simulate a supramaximal stimulus, the
muscle was excited with an interpolated stimulus at 500 ms, when muscle
force had reached a plateau. The stimulus caused all nonrefractory
motoneurons to fire synchronously. Motoneurons were considered to be
refractory and therefore were not excited by the stimulus if they had
discharged in the preceding 5 ms (Borg 1983). For
simplicity, stimulation-contraction delays were ignored. After the
stimulus, motoneurons fired as they would have if the stimulus had not
been delivered, except that in some units action potentials were
extinguished by collision with antidromically conducting potentials
generated by the stimulus (Fig. 1B). This was modeled by
preventing those units that were not refractory at the time of the
stimulus from firing for a period equal to trefr + 2d/cvi
after the stimulus, where trefr
is the refractory period of motor axons, d is the
distance from the stimulation site to the spinal cord, and
cvi is the conduction velocity of the
motor axon supplying unit i. Axonal
conduction velocities were linearly related to the rank order of their
twitch tensions (cf. Jami and Petit 1985
). The range of
motor axon conduction velocities was 35-65 ms
1, and,
except where indicated, d was set to 80 cm (the
approximate distance of the site of stimulation of adductor pollicis
from the spinal cord). Thus the period trefr + 2d/cvi varied from 30 to 51 ms.
The amplitude of the interpolated twitch
(Aint) was found by subtraction of the
background force immediately preceding the stimulus from the force
maxima occurring in a time window following the stimulus. This window
was 20 ms longer than the contraction time of the slowest motor unit.
Voluntary activation was calculated as 100 × (1 Aint/Atw), where
Atw is the amplitude of a control twitch
evoked from a resting muscle (e.g., Bigland-Ritchie et al.
1983b
; McKenzie et al. 1992
). The same
procedures were used to calculate voluntary activation scores from
experimental data.
In some simulations we examined the effects of interpolating two stimuli with a 20-ms interstimulus interval. Voluntary activation was measured in the same way as above except that a longer time window was used to detect the peak of the interpolated twitch, and the interpolated twitch was normalized to the amplitude of the resting muscle's force response to paired stimuli. Antidromic collisions could occur following either stimulus.
Probability of refractoriness and of antidromic collision
To aid analysis, analytic expressions were developed to determine both the probability that an axon would be refractory at the time of stimulus and the probability that an antidromic collision would occur.
The probability of an axon being refractory at the time of the
stimulus, Prefr, is the probability of an action
potential having traversed the site of stimulation in a period
trefr preceding the stimulus (Fig.
7A). In motor units excited above threshold, the probability
density is constant for a period 1/f preceding the stimulus
(where f is the mean firing frequency of the unit), but
tapers to zero at periods greater than 1/f before the
stimulus. The "shoulder" of this function is one-half of the
distribution of interspike intervals. As interspike intervals are
normally distributed, the shoulder has a standard deviation of
V/f and a peak amplitude of f/(V × ), and the area under the shoulder is 0.5 (Defares et al. 1973
; Roscoe 1975
). The
total area under the entire frequency distribution from time t
=
to t = 0 is thus
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A similar approach can be used to determine the probability of
antidromic collision. The probability of antidromic collision in an
axon that has been excited above its threshold and is not refractory at
the time of stimulus (Pac) is the probability
that an action potential would have traversed the site of stimulation (had the axon not been stimulated) within a period of
trefr + 2dp/cvi following the
stimulus. In these nonrefractory axons, the probability density of an
action potential in the period following the stimulus is zero between
the time of stimulus and t = trefr, then
constant until t = 1/f, and then tapers to zero
(Fig. 7B). Thus provided trefr + 2dp/cvi 1/f
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If the motor unit is firing very rapidly, or if the distance to the
spinal cord is great, or if the axon conducts slowly, trefr + 2dp/cvi can become
>1/f. Then
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Testing the effects of antidromic collisions, motor-unit contractile properties, and PFRs
In most simulations, both orthodromic and antidromic effects of the interpolated stimulus were studied. However, to determine the effects of antidromic collisions on interpolated twitch amplitude, the model was sometimes run without antidromic collisions (Fig. 1B). When the simulation was implemented this way, the sole effect of the stimulus was to interpolate an extra potential in motor axons of nonrefractory units.
To examine the effects of peripheral changes in contractile properties
and variations in central drive on interpolated twitch amplitude, we
changed the distribution of motor-unit contraction times, PFRs of
motoneurons, or both. Motor-unit contraction times were reduced (the
contractile properties of the muscle were made "faster") by
reducing the contraction time of the slowest motor unit
(T1) from 110 to 90 ms. The
contraction times of all other motor units were referenced to this
motor unit (Fuglevand et al. 1993), so the effect was to
scale down the contraction times of all motor units. This reduced the
contraction time of the whole muscle resting twitch from 69 to 55 ms
(or by ~2 SDs) (Bellemare et al. 1983
). To examine the
effects of an increase in firing rate, the mean PFR was increased from
29.9 Hz in increments of 8.2 Hz. This number was chosen because the
first increment (to 38.1 Hz) maintains the normalized firing frequency
of the whole muscle (mean PRF × whole muscle twitch contraction
time) when contraction time is reduced to 55 ms.
One set of simulations investigated the effect of occasional brief
interpulse intervals (or "doublets") that are sometimes observed
experimentally (Bawa and Calancie 1983), by causing a random selection of 10% of all discharges to occur with an interpulse interval of 5 ms. The actual frequency of doublets is not known with
any certainty, and there is no data on the frequency of doublets in
human adductor pollicis during maximal voluntary contractions. A
frequency of 10% probably represents the highest plausible frequency.
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RESULTS |
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In METHODS we showed that the model provided a good fit to a range of experimental observations (Figs. 2-4). Here we present the predictions of the model. The results of a simulation in which interpolated stimuli were delivered to the muscle as it was sequentially excited to increasing proportions of maximal voluntary excitation are shown in Figs. 5 and 6A. The amplitude of the interpolated twitch declined with increasing excitation (and contraction intensity) as observed experimentally. The stimulus evoked twitches in all motor units at rest, but interpolated twitches were only discernible in the largest motor units at high contraction intensities (Fig. 5B). Randomness in interspike intervals did not produce a discernible degree of trial-to-trial variability in the force of simulated voluntary contractions or interpolated twitches, so the results from only one simulation are shown in this and subsequent figures.
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When interpolated twitches were measured in experimental subjects during contractions to submaximal target intensities, both interpolated twitch amplitudes and times-to-peak were nearly linearly related to voluntary force (R2 = 0.93 and 0.97, respectively; Fig. 6, B and C). Simulated amplitudes and times-to-peak were also linearly related to voluntary force (R2 > 0.99) and closely approximated experimental data, although the amplitude of simulated interpolated twitches tended to overestimate experimental measures (mean overestimation of 12% of resting twitch, range 2-34%; Fig. 6, B and C). The relationship between simulated voluntary force and interpolated twitch amplitude was essentially unchanged by adding doublets to 10% of all discharges, or by using paired stimuli instead of a single interpolated stimulus (Fig. 6C). Force fell less, after the interpolated twitch, in simulated records compared with experimental records (Fig. 6A).
With simulated maximal voluntary excitation of the adductor pollicis
motoneuron pool (the level of excitation required to make all
motoneurons fire at their assigned peak rates, see
METHODS), the amplitude of interpolated twitches was 4.7%
of the resting twitch (Fig. 6A), giving a simulated
voluntary activation of 95.3%. Very similar values were obtained when
doublets were added to 10% of all discharges (activation, 95.2%) and
when paired stimuli were used (activation, 94.2%). These values are
all close to the median voluntary activation of 90.3% for the adductor
pollicis, and well within the range of voluntary activation of
individual subjects (81.2-100%) (Herbert and Gandevia
1996). The time-to-peak of the simulated interpolated twitch in
a maximal voluntary contraction was 26 ms, slightly longer than the 19 ms (measured from time of force onset) observed in an experimental
subject whose resting twitch had a similar contraction time to that
used in the simulation (Fig. 6, A and B).
The force produced by simulated stimulus trains at 100 Hz ("maximal
muscle force") was 9.6% greater than the force produced in simulated
maximal voluntary contractions (Fig. 6D). To investigate how
well maximal muscle force could be estimated from the relationship between experimental interpolated twitch amplitude and voluntary force,
the linear regression of these variables was extrapolated to the
abcissa (Fig. 6D). This predicted a maximal muscle force of
97.9% of maximal voluntary force, an underestimation of maximal muscle
force of 10.7%. The confidence intervals associated with this estimate
(95% CI 88.2 to 111.4%) included simulated maximal voluntary force,
but the limits of the confidence interval were wide. Nonlinear
regression [using 3rd-order polynomial regression or a power
transformation of interpolated twitch amplitude, as described by
De Serres and Enoka (1998)] provided less accurate estimates of maximal muscle force (131.6 and 181.3% respectively), with even wider confidence intervals.
The probability of the interpolated stimulus arriving when an axon was
refractory increased with firing frequency. For any single motoneuron
that had been voluntarily excited above threshold, this probability
increased from 3.2% at 8 Hz to 20.8% at 52 Hz (Fig.
7C), assuming a refractory
period of 5 ms. If, instead, the refractory period was assumed to be
2.5 ms, the probability of refractoriness ranged from 1.6 to 10.4%
over the same range of frequencies. The latter figure (2.5 ms) is
likely to be closer to the true value (see Fig. 2 in Borg
1983). However, the degree of supramaximality probably varies
with motor-unit size, so it is difficult to be certain which motor
units will discharge in their relatively refractory periods. In
practice, varying the refractory period from 2.5 to 5 ms had little
effect on interpolated twitch amplitude.
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In motoneurons excited above threshold but not refractory at the time of the stimulus, the probability of antidromic collision ranged from 16.3% in the first recruited motoneuron at its lowest firing frequency up to 99.8% in the last recruited motoneuron at its maximum firing frequency (Fig. 7C). The probability of antidromic collision was relatively insensitive to the "refractory" period (see also METHODS).
To assess the effect of antidromically conducting action potentials, interpolated twitches were compared when the model was run with and without extinction of potentials in nonrefractory motor axons after the stimulus (Fig. 1B). Without antidromic potentials, the amplitude and duration of interpolated twitches was slightly increased at all voluntary forces (Fig. 8) and, with high-intensity contractions, there was a conspicuous lack of the fall in force after the twitch (Fig. 8A). During simulated maximal voluntary contractions, the amplitude of the interpolated twitch was increased to 8.7% of resting twitch (i.e., 91.3% activation) when there were no antidromic collisions, compared with 4.7% of the resting twitch (95.3% activation) when antidromic collisions occurred. This indicates that antidromic potentials slightly reduce the amplitude and duration of interpolated twitches and are responsible for at least some of the drop in force that occurs after the peak of the twitch. Because the effect of antidromic collisions on interpolated twitch amplitude was rather small, movement of the site of stimulation proximally from 0.8 m (i.e., wrist) to 0.4 m (i.e., elbow) from the spinal cord (a procedure that would reduce the number of antidromic collisions) only increased the amplitude of the interpolated twitch by 0.9% (to 5.6% of the resting twitch).
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When simulations were performed in which motoneurons fired at the peak
rates described in the literature for maximal voluntary efforts
(Bellemare et al. 1983), small interpolated twitches
were still observed. This suggests that subjects might attain higher PFRs than the "pooled" rates measured experimentally when, in experiments, the twitch is completely occluded. In the model, an
increase of 8.2 Hz in mean PFR (to 38.1 Hz) increased muscle force to
4.4% above that observed during a simulated maximal voluntary contraction and reduced interpolated twitch amplitude to 2.9% (i.e.,
increased voluntary activation to 97.1%). Further increases in mean
PFR by increments of 8.2 Hz increased voluntary force to 107.0% (at
46.3 Hz), 108.0% (at 54.5 Hz), and 108.7% (at 62.7 Hz) of maximal
voluntary force, and increased voluntary activation to 98.4, 98.6, and
99.0%, respectively. Conversely, a reduction in whole muscle
contraction time of ~2 SDs (or from 69 to 55 ms) reduced muscle force
to 92.3% maximal voluntary force and increased interpolated twitch
amplitude from 4.7 to 8.5% of the resting twitch (i.e., voluntary
activation decreased from 95.3 to 91.5%). In one simulation, the
contraction time of the muscle was reduced by ~2 SDs, but PFRs were
increased to a mean of 38.1 Hz, so that the normalized frequency of the
whole muscle remained constant. This resulted in an interpolated twitch
amplitude of 4.8%, very similar to the 4.7% obtained with the default
parameter values.
The relationship between the level of "excitation" of the motoneuron pool and muscle force was sigmoidal (Fig. 9C). Force initially increased rapidly with excitation, but above ~50% of the level of excitation required to excite motoneurons to frequencies observed during maximal efforts, very large increases in excitation were required to produce small increases in force. This finding was robust, because it occurred with all plausible combinations of model parameters. Implications of the finding are considered in the DISCUSSION. The relationship between excitation and interpolated twitch amplitude was complementary (Fig. 9C). Interpolated twitch amplitude declined rapidly at low levels of excitation, but above ~50% of maximal voluntary excitation, decreases in interpolated twitch amplitude were very small. This was because all of the motoneuron pool was recruited, and most motor units had attained near-tetanic firing frequencies, at relatively low levels of excitation and force (Fig. 9, A and B). Thus at higher levels of excitation, the stimulus was only able to evoke additional force from the small number of motor units contracting at subtetanic frequencies.
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DISCUSSION |
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In the present study a computer model based on experimental data from human adductor pollicis was used to simulate transients in muscle force produced by an interpolated stimulus. The model involved simplifying assumptions, and its implementation required that values were assigned to some parameters for which exact values were not available. Nevertheless, it incorporated realistic analogues of mechanisms known to influence muscle force, such as the orderly recruitment of motoneurons. Because there was unlikely to be a unique set of parameters that optimally fitted experimental data, we optimized the process of assigning values to parameters by first assigning values to those parameters that influenced the simplest muscle responses (e.g., resting twitch, response to stimulus trains of constant frequency), and then sequentially assigning values to parameters that determined more complex behaviors (e.g., irregular trains of stimuli, voluntary contractions). This approach minimized redundancy. The resulting model fitted complex muscle behaviors well and provided good predictions of the force responses to interpolated twitches over the full range of contraction intensities.
A primary aim of the present study was to investigate factors that
influence the amplitude of the interpolated twitch. The time course and
amplitude of the rising phase of simulated interpolated twitches
obtained during maximal contractions closely resembled experimental
data. However, the size of simulated interpolated twitches in
submaximal contractions was slightly greater than observed
experimentally. This may be because the model did not incorporate all
consequences of the stimulus at spinal cord level, such as
hyperpolarization of motoneuron somata, possible recurrent inhibition,
and the inhibitory and disfacilitatory effects of stimulation of muscle
afferents. Assuming the site of the stimulus was 0.8 m from the
spinal cord and a maximal conduction velocity of 65 ms1, and ignoring synaptic delays, these
effects could not influence adductor pollicis muscle forces until ~30
ms after the twitch (cf. Leis et al. 1991
), and so would
have no effect on the rising phase of interpolated twitches obtained
during maximal contractions (which had times to peak force of ~19
ms). When the effects of antidromic collisions in motoneurons were
eliminated (Fig. 1B), the amplitude of the interpolated
twitch was slightly greater at all contraction intensities, especially
between 40 and 80% maximal voluntary force. These data suggest that
both antidromic collisions and the spinal (including reflex) effects of
the stimulus can reduce the amplitude of the interpolated twitch at
submaximal intensities, and that antidromic collisions slightly reduce
the amplitude of interpolated twitches in maximal contractions.
A conspicuous feature of the force response to an interpolated twitch
during a voluntary contraction is the large drop in force after the
twitch. The precise mechanisms producing the drop in force are not
known, but a number of studies have investigated the mechanisms that
produce the accompanying electromyographic silence. Merton
(1951) observed that the depth and duration of the silent
period was closely associated with the size and duration of the
interpolated twitch, and he argued that the later part of the
electrical silence must therefore be due to afferent consequences of
the twitch. More recent studies have shown that a silent period can be
induced by the stimulation of afferent axons (Leis et al. 1991
; McClelland 1973
). In our simulations,
which ignored the spinal effects of the stimulus, there was little or
no decline in force after the twitch. This suggests that the primary
mechanism producing the drop in force is of spinal origin. Moreover,
when the model was run without antidromic collisions, the interpolated twitch became less peaked because force declined only slowly after the
force maxima (Fig. 8). This suggests that antidromic collisions, as
well as spinal mechanisms, contribute to the force drop after the
stimulus. These findings are not surprising, because the interpolated stimulus advances the arrival of one potential in nonrefractory axons
but may delay the arrival of the subsequent one (if an antidromic collision occurs; see Figs. 1B and 7). In real contractions,
further delays may be produced when antidromic potentials that do not undergo collision "reset" membrane potential at the motoneuron soma.
Currently it is not possible to measure neural drive to the motoneuron
pool more directly than with the interpolated twitch, as conventional
measures of voluntarily generated electromyogram (EMG) cannot indicate
if activation is truly "maximal." Simulations by Heckman and
Binder (1991) showed that the relationship between excitation
of a cat motoneuron pool and muscle force is sigmoidal and, as muscle
force is known to be near-linearly related to interpolated twitch
amplitude, this implies that interpolated twitch amplitude is
nonlinearly related to excitation. In the present study we showed that
the relationship between excitation of a human motoneuron pool and
interpolated twitch amplitude is also sigmoidal (Fig. 9C). This occurs because most motor units are recruited
at low forces and attain near-tetanic frequencies at low levels of
excitation, and because the firing rates of early recruited motor units
plateau, rather than continue to increase markedly with force (Fig.
4A; e.g., Kanosue et al. 1979
;
Monster and Chan 1977
; cf. Erim et al.
1996
). The mechanisms that cause motor-unit firing frequencies to plateau are not known but may reflect nonhomogenous excitation of
the motoneuron pool at high forces (Binder et al. 1996
,
1998
; Heckman and Binder 1993
), the
action of neuromodulators (Binder et al. 1996
;
Hounsgaard et al. 1988
; see also Brownstone et
al. 1992
), or shunting of the synaptic current by active
synaptic conductances located on proximal parts of dendrites
(Binder et al. 1996
; see also Jones and Bawa
1997
). The sigmoidal shape of the relationship between
motoneuronal excitation and interpolated twitch amplitude means that
large increases in motoneuronal excitation produce only small
reductions in interpolated twitch amplitude during high-intensity
contractions. Twitch interpolation is therefore not a sensitive measure
of excitation at high forces. [A similar conclusion was drawn by
Dowling et al. (1994)
, although their conclusion was
based on observations of the relationship between interpolated twitch
and voluntary force; cf. Allen et al. (1998)
.] These
data imply that it may not be possible, in experiments, to distinguish
between contractions of 60 and 100% of maximal voluntary excitation.
Surface EMG is linearly or near-linearly related to muscle force
(Woods and Bigland-Ritchie 1983
), so it too probably
provides insensitive measures of excitation at high forces. The lack of
sensitivity of EMG is compounded by the high-frequency component in the
EMG signal, which makes it more difficult to quantify than force
(Allen et al. 1998
).
The relationship between effective synaptic current and muscle force
simulated by Heckman and Binder (1991) has been redrawn in Fig. 9D for comparison with our simulated
relationship between excitation and force in Fig. 9C.
The difficulty in comparing these data are that Heckman and Binder
considered the effect of increasing effective synaptic current up to
levels where muscle force was maximal, whereas we considered the effect
of increasing "excitation" up to levels required to attain the
firing frequencies observed in maximal voluntary contractions. In our
simulations, force was essentially maximal at ~60% of maximal
voluntary excitation. It is probable therefore that the maximal level
of effective current investigated by Heckman and Binder is equal to
~60% of the maximal voluntary excitation in our simulations. When
the Heckman and Binder data are drawn with the crest of the sigmoid at
the same level of excitation (95 nA
60% maximal voluntary
excitation) the two curves essentially superimpose.
The plateau of the relationship between excitation and force (or interpolated twitch amplitude) at levels above ~60% maximal voluntary excitation may seem paradoxical. This may be because it is tempting to draw an analogy between excitation and "motor commands." However, the concept of excitation used here is a notional one that may not, and is unlikely to, be directly related to a parameter that can be measured in volunteer subjects. Hence it would be speculative to attempt to relate excitation to the concepts of "effort" and corollary "motor commands" that are used in the literature on proprioception. There is no a priori reason to expect psychophysical "commands" to be linearly related to excitation of motoneurons. Increasing excitation from 60 to 100% of maximal voluntary excitation affects only a very small number of motoneurons: those recruited at high thresholds. This and other processes (such as nonhomogeneous distribution of commands) may cause the total excitatory drive summed across all motor units to be nonlinearly related to commands to generate force.
A more linear relationship between excitation and force would arise if
less excitation was required to excite late-recruited units to maximal
firing frequencies. This could occur if excitation thresholds were less
skewed than in our model, or if the rate of increase in firing rate
with excitation was greater for late-recruited units. The consequence
would be that the sigmoid would have less curvature, but with any
reasonable assumptions the relationship remains sigmoidal (see Figs. 3,
4, and 6 in Heckman and Binder 1991). Thus modification
of the relationship between excitation and motor-unit firing
frequencies may alter quantitative estimates of the sensitivity of the
interpolated twitch to excitation of the motoneuron pool, but would not
qualitatively change our conclusion about the insensitivity of the
interpolated twitch to excitation at high forces. Nor would it change
other conclusions that depend on the relationship between interpolated
twitch amplitude and force rather than on the relationship between
interpolated twitch amplitude and excitation.
For the adductor pollicis, comparison of experimental maximal voluntary
force and 100-Hz force does not provide a valid experimental measure of
activation. This is evident from the comparison of our experimental
measures of voluntary force and 100-Hz force. Force produced by 100-Hz
trains averaged 60.3% of maximal voluntary force. Maximal voluntary
force was bigger than stimulated force, even though the stimulus was
supramaximal and excited most or all of the intrinsic agonist muscles,
because in stimulated contractions the rest of the hand was relaxed. In
maximal voluntary contractions, other muscles (those not innervated by
the ulnar nerve) may act synergistically to optimize force production
by the thumb adductors (for example, synergistic muscles hold the thumb
more internally rotated during maximal voluntary contractions) (see
Merton 1954). In general, comparison of maximal
voluntary force and 100-Hz force will not provide a valid measure of
voluntary activation if nonstimulated muscles act synergistically to
enhance measured muscle force.
Several studies have shown reduced levels of voluntary activation in
fatigue and in some populations with pathology (e.g., Allen et
al. 1993, 1997
; Bigland-Ritchie et al.
1983
; McComas et al. 1983
; McKenzie et
al. 1992
; Rice et al. 1992
; Rutherford et
al. 1986
). If, as the predictions of our model suggest,
measures of voluntary activation obtained with the twitch interpolation method are insensitive to excitation, observations of even small reductions in voluntary drive must indicate significant failures of
excitation to the motoneuron pool. Theoretically, such reductions may
arise when there is a mismatch between the level of excitation to the
motoneuron pool and the contractile properties of motor units. In the
present simulations, voluntary activation was maintained when the
normalized firing frequency (mean PFR × whole
muscle twitch contraction time) was kept constant, for example, when a
reduction in contraction time from 69 to 55 ms was matched by an
increase in mean PFR from 30 to 38 Hz. An alternative mechanism is that
fatigue could reduce the gain of the relationship between excitation
and motoneuron firing frequency (for example, by reducing the level of
synaptic "noise").
In experiments, it is usual to see small interpolated twitches during
maximal voluntary efforts. A small proportion of these twitches may
actually be random fluctuations in voluntary force that coincide with
the stimulus, but most are "real" interpolated twitches produced by
the stimulus (an analysis of the experimental data shows that, for
adductor pollicis, random force fluctuations in the plateau of maximal
voluntary contractions is such that artifactual "twitches" with
amplitudes of >5% of the resting twitch would be expected follow the
stimulus in <10% of contractions, yet interpolated twitches >9.7%
of the resting twitch are observed in 50% of maximal voluntary
contractions). Interestingly, most subjects can fully activate the
muscle (i.e., completely occlude the twitch) in some maximal efforts
(Allen et al. 1995; Herbert and Gandevia
1996
). If the predictions of our model are correct, this cannot
occur unless the distribution of PFRs is shifted toward higher values
than those observed by Bellemare et al. (1983)
. The
production of 200-Hz doublets in 10% of discharges of motoneurons (probably an extreme scenario) had little effect on the amplitude of
interpolated twitches. However, interpolated twitch amplitude could be
reduced to 1.0% (i.e., voluntary activation could be increased from
95.3 to 99.0%) by an increase in the mean firing frequency of all
motoneurons from 29.9 to 62.7 Hz. Firing frequencies of this magnitude
are unlikely to be sustained in maximal voluntary efforts
(Bellemare et al. 1983
), but perhaps could be attained transiently.
It is concluded that the amplitude of the interpolated twitch is influenced by reflex and antidromic effects. At forces greater than ~90% of maximal voluntary force, interpolated twitch amplitude is insensitive to motoneuron pool excitation, so real changes in interpolated twitch amplitude must indicate large changes in motoneuronal excitation.
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ACKNOWLEDGMENTS |
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The authors acknowledge helpful discussions with Prof. David Burke, Drs. Janet Taylor and Richard Fitzpatrick, and R. Gorman. We are grateful to Dr. Marc Binder for comments on the manuscript.
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FOOTNOTES |
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Address for reprint requests: S. C. Gandevia, Prince of Wales Medical Research Institute, High St., Randwick, New South Wales 2031, Australia.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 24 September 1998; accepted in final form 24 June 1999.
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REFERENCES |
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