1. Isometric muscle force and the surface electromyogram (EMG) were si
mulated from a model that predicted recruitment and firing times in a
pool of 120 motor units under different levels of excitatory drive. Th
e EMG-force relationships that emerged from simulations using various
schedules of recruitment and rate coding were compared with those obse
rved experimentally to determine which of the modeled schemes were pla
usible representations of the actual organization in motor-unit pools.
2. The model was comprised of three elements: a motoneuron model, a m
otor-unit force model, and a model of the surface EMG. Input to the ne
uron model was an excitatory drive function representing the net synap
tic input to motoneurons during voluntary muscle contractions. Recruit
ment thresholds were assigned such that many motoneurons had low thres
holds and relatively few neurons had high thresholds. Motoneuron firin
g rate increased as a linear function of excitatory drive between recr
uitment threshold and peak firing rate levels. The sequence of dischar
ge times for each motoneuron was simulated as a random renewal process
. 3. Motor-unit twitch force was estimated as an impulse response of a
critically damped, second-order system. Twitch amplitudes were assign
ed according to rank in the recruitment order, and twitch contraction
times were inversely related to twitch amplitude. Nonlinear force-firi
ng rate behavior was simulated by varying motor-unit force gain as a f
unction of the instantaneous firing rate and the contraction time of t
he unit. The total force exerted by the muscle was computed as the sum
of the motor-unit forces. 4. Motor-unit action potentials were simula
ted on the basis of estimates of the number and location of motor-unit
muscle fibers and the propagation velocity of the fiber action potent
ials. The number of fibers innervated by each unit was assumed to be d
irectly proportional to the twitch force. The area of muscle encompass
ing unit fibers was proportional to the number of fibers innervated, a
nd the location of motor-unit territories were randomly assigned withi
n the muscle cross section. Action-potential propagation velocities we
re estimated from an inverse function of contraction time. The train o
f discharge times predicted from the motoneuron model determined the o
ccurrence of each motor-unit action potential. The surface EMG was syn
thesized as the sum of all motor-unit action-potential trains. 5. Two
recruitment conditions were tested: narrow (limit of recruitment <50%
maximum excitation) and broad recruitment range conditions (limit of r
ecruitment >70% maximum excitation). Three rate coding conditions were
tested: 1) low-threshold units attained greater firing rates than hig
h-threshold units, 2) all units were assigned the same peak firing rat
e, and 3) peak firing rates were matched for each unit to the stimulus
frequency required for maximum tetanic force. 6. The relation between
EMG and force was linear when recruitment operated over a broad force
range, and peak firing rates were not the same for all units. When re
cruitment was complete at low force levels (<57% maximum) the EMG-forc
e relation, in all cases, was nonlinear and unlike that observed exper
imentally. 7. For the conditions that yielded linear EMG-force relatio
nships, the relation between EMG and excitatory drive and between forc
e and excitatory drive were both nonlinear. Because the shape of those
nonlinear relationships were similar, when EMG was plotted as a funct
ion of force, a linear relation resulted. 8. When recruitment operated
over a broad range and the peak firing rates were similar for all mot
or units, the EMG-force relation exhibited a slightly parabolic shape.
As excitatory drive increased and the mean firing rates of the units
converged toward the same value, rhythmic bursting was evident in the
EMG. The bursting was associated with an augmentation of EMG amplitude
, which induced a degree of concavity on an otherwise linear EMG-force
relationship. 9. Unexpectedly, the maximum force capacity of the mode
led muscle was not achieved in conditions where peak firing rates were
set for each unit equivalent to the stimulus rate required for maximu
m tetanic force. The natural variability in interspike intervals combi
ned with nonlinear force-firing rate curves for each unit diminished f
orce from what would have been exerted had units discharged with const
ant interspike intervals. 10. The relation between the twitch force of
a unit and the muscle force at which the unit was recruited was linea
r. However, the force added by the recruitment of a new unit was not a
constant fraction of the muscle force. The force contributed by newly
recruited units, relative to muscle force, declined hyperbolically as
muscle force increased. This occurred because low-threshold units gen
erated a larger proportion of their maximum force capacity when discha
rging at the threshold rate as compared with high-threshold units.