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Models of recruitment and rate coding organization in motor-unit pools.
Abstract
1. Isometric muscle force and the surface electromyogram (EMG) were simulated from a model that predicted recruitment and firing times in a pool of 120 motor units under different levels of excitatory drive. The EMG-force relationships that emerged from simulations using various schedules of recruitment and rate coding were compared with those observed experimentally to determine which of the modeled schemes were plausible representations of the actual organization in motor-unit pools. 2. The model was comprised of three elements: a motoneuron model, a motor-unit force model, and a model of the surface EMG. Input to the neuron model was an excitatory drive function representing the net synaptic input to motoneurons during voluntary muscle contractions. Recruitment thresholds were assigned such that many motoneurons had low thresholds and relatively few neurons had high thresholds. Motoneuron firing rate increased as a linear function of excitatory drive between recruitment threshold and peak firing rate levels. The sequence of discharge 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 assigned according to rank in the recruitment order, and twitch contraction times were inversely related to twitch amplitude. Nonlinear force-firing rate behavior was simulated by varying motor-unit force gain as a function of the instantaneous firing rate and the contraction time of the unit. The total force exerted by the muscle was computed as the sum of the motor-unit forces. 4. Motor-unit action potentials were simulated on the basis of estimates of the number and location of motor-unit muscle fibers and the propagation velocity of the fiber action potentials. The number of fibers innervated by each unit was assumed to be directly proportional to the twitch force. The area of muscle encompassing unit fibers was proportional to the number of fibers innervated, and the location of motor-unit territories were randomly assigned within the muscle cross section. Action-potential propagation velocities were estimated from an inverse function of contraction time. The train of discharge times predicted from the motoneuron model determined the occurrence of each motor-unit action potential. The surface EMG was synthesized 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 recruitment > 70% maximum excitation).(ABSTRACT TRUNCATED AT 400 WORDS)
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“Firing rates were excluded from further analysis when the coefficient of variation in mean firing rate was greater than 30% or when the number of firings was lower than two, i.e., one firing (Fuglevand et al., 1993).”
From Effect of resistance training and fish protein intake on motor unit firing pattern and motor function of elderly (2018) · cites this paper as Fuglevand et al., 1993
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“Additionally, resistance from synovial fluid (viscous fluid between moving bony surfaces), was modeled as a resistive torque, τ−, proportional to the joint velocity, q̇; τ− = q̇τSF , where, the scaling factor τSF was to be determined in the identification process.”
BackgroundSparse Optimal Motor Estimation (SOME) for Extracting Commands for Prosthetic Limbs
Li, Y., Smith, L. H., Hargrove, L. J., Weber, D. J., & Loeb, G. E. (2012) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2012.2218286 · Cited by 7
“In order to bracket the possibilities of different modulation patterns of MUs [18], we created and tested three different simulations: saturation recruitment model, continuous modulation model and “onion skin” recruitment model, each has five slow MUs (labeled – ) and five fast MUs (labeled”
MethodMeigal, A. Y., Rissanen, S. M., Zaripova, Y. R., Miroshnichenko, G. G., & Karjalainen, P. A. (2015) · Human Physiology · doi:10.1134/s0362119715050102 · Cited by 7
Roles of Motor-Unit Recruitment in Producing Force Variability of Simulated Muscle Contractions
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“The recruitment thresholds of the 120 motor neurons in the pool were determined from an exponential function that assigned many neurons to have relatively low thresholds and progressively fewer neurons to have higher thresholds (Fuglevand et al., 1993).”
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Intent-Related Differences in Surface EMG of Maximum Eccentric and Concentric Contractions
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Supraspinal control of motoneurons after paralysis enabled by spinal cord stimulationPreprint
Capogrosso, M., Balaguer, J.-M., Prat-Ortega, G., Verma, N., Yadav, P., Sorensen, E., de Freitas, R., Ensel, S., Borda, L., Donadio, S., et al. (2024) · Research Square · doi:10.21203/rs.3.rs-3650257/v1 · Cited by 7
“To estimate the force from the motoneuron pool firing rate, we used the model proposed in 30 .”
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Zero, A. M., Fanous, J., & Rice, C. L. (2025) · Journal of Neurophysiology · doi:10.1152/jn.00173.2025 · Cited by 6
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Kunugi, S., Holobar, A., Kodera, T., Toyoda, H., & Watanabe, K. (2022) · Journal of Electromyography and Kinesiology · doi:10.1016/j.jelekin.2022.102720 · Cited by 6
Li, Y., Zheng, Y., Xu, G., et al. (2024) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2024.3364716 · Cited by 6
“The spike trains of individual MUs were obtained using the MU recruitment and rate coding model proposed previously [25].”
MethodNishikawa, Y., Holobar, A., Watanabe, K., KOMATSUZAKI, T., CHIHARA, T., Sakamoto, J., Kawagoe, T., Nagayasu, H., Mori, K., Kawano, K., et al. (2024) · European Journal of Applied Physiology · doi:10.1007/s00421-024-05553-9 · Cited by 6
“Further analysis did not include MUs with CVs greater than 30% during the submaximal ramp-up task or during sustained contractions (Fuglevand et al. 1993).”
Navallas, J., Mariscal, C., Malanda, A., et al. (2024) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2024.3452308 · Cited by 6
“2) MU Firing Rate: Apart from MU recruitment, another strategy of the neuromuscular system to increase the exerted force is the increase of the firing rate of the MUs [31].”
BackgroundWang, W., He, L., Wang, J., Pan, M., Yi, J., Cheng, N., & Liu, T. (2024) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2024.3480235 · Cited by 6
“The recruitment threshold excitation (RTE) and the contraction time of MU i are distributed according to the principle in [31].”
MethodNoninvasive analysis of motor unit behavior in pathological tremor
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“For an already active unit, the discharge frequency increases as the difference between the current excitation level of the muscle and the recruitment threshold of this motor unit increases.(27,28) In fact, for this analysis, the key point is not the discharge rate of the motor unit when it was first recruited but the…”
BackgroundAppropriate index parameters may serve a useful purpose in motor unit number estimation
Zhou, P. (2022) · Clinical Neurophysiology · doi:10.1016/j.clinph.2022.05.002 · Cited by 6
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“, the sEMG envelope, which is smoothed rectified EMG by itself, and muscle force) needs not be linear (Fuglevand et al., 1993; Hof, 1997), especially in broad force range.”
BackgroundPrediction of 1-year change in knee extension strength by neuromuscular properties in older adults
Hirono, T., Takeda, R., Nishikawa, T., & Watanabe, K. (2023) · GeroScience · doi:10.1007/s11357-023-01035-6 · Cited by 6
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“P is modeled as a linear function of recruitment threshold over the recruitment range RR=130 [10].”
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“Some models (Fuglevand et al. 1993; Heckman 1994; Heckman and Binder 1991) allow the calculation of the force developed by whole muscles using known firing properties of motoneurones and known mechanical properties of MUs.”
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“As seen in the upper dashed box, the dynamics from EMGSOL to the active ankle torque were modeled using a critically damped, second-order lowpass system [18], [19].”
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“Number of simulated motor units decreased exponentially with their size [10].”
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“The MU firing pattern was computed by the model proposed in [7] with the parameters adapted to the biceps brachii muscle.”
BackgroundMethodMotor-Unit Ordering of Blindly-Separated Surface-EMG Signals for Gesture Recognition
Orlandi, M., Zanghieri, M., Schiavone, D., et al. (2022) · Lecture notes in networks and systems · doi:10.1007/978-3-031-16281-7_49 · Cited by 6
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“(3-56)”
Le, H., Panhuis, M. I. H., Spinks, G. M., & Alıcı, G. (2025) · Robotics · doi:10.3390/robotics14060083 · Cited by 5
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Zero, A. M., & Rice, C. L. (2025) · European Journal of Applied Physiology · doi:10.1007/s00421-025-05872-5 · Cited by 7
“Surface detected potentials are preferentially influenced by the closest (more superficial) MUs relative to the recording electrodes (Fuglevand et al. 1993a; Merletti et al. 2008).”
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“Descending neural drive is directly reflected in populational MU firing rates, as human motor control commands that lead to muscle force, joint torque, and joint motion is encoded by motor units’ recruitment and firing rates [16].”
BackgroundNonlinear spatio-temporal filter to reduce crosstalk in bipolar electromyogram
Mesin, L. (2024) · Journal of Neural Engineering · doi:10.1088/1741-2552/ad2334 · Cited by 5
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“The new motoneuron pool model could replace math-ematically developed motoneuron pool models including passive dendrites under static conditions (24, 26, 31) and also serve to provide an effective way of incorporating cell type-specific electrical properties into reduced motoneuron models in a…”
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“MUFRs were determined from an average of 10 continuous inter-spike intervals at 0, 25, 50, 75, 100% TTF and only those trains with inter-spike interval coefficients of variance below 30% (Fuglevand et al. 1993) were accepted for further analysis.”
MethodFeedforward modulation of gamma motor neuron activity can improve motor command accuracy
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“In summary, the model combines several previously published models of spinal neuron activity [20, 21], muscle force [22, 23], muscle dynamics [24], and type Ia afferent feedback [16] to reflect the activity of an antagonist muscle pair affecting the movement of a limb in 1 ◦ of freedom.”
Thome, G. R., Costa, R. A., Marquezi, M. L., Aparecido, J. M. L., Durigan, J. L. Q., Amorim, C. F., & Liebano, R. E. (2021) · Journal of Bodywork and Movement Therapies · doi:10.1016/j.jbmt.2021.07.035 · Cited by 5
Nishikawa, Y., Watanabe, K., Holobar, A., Takahashi, T., Maeda, N., Maruyama, H., Tanaka, S., & Hyngstrom, A. S. (2021) · Sensors · doi:10.3390/s21196615 · Cited by 5
“We used only < 30% CV for further analysis [24].”
MethodMotor Unit Identification in the M Waves Recorded by High-Density Electromyogram
Kalc, M., Škarabot, J., Divjak, M., Urh, F., Kramberger, M., Vogrin, M., & Holobar, A. (2022) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2022.3224962 · Cited by 5
“Their firing patterns were generated as per the model of [28], with the parameters adapted to the biceps brachii muscle.”
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“given the skewed size distribution of the motor unit pool [4].”
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Raikova, R., Krutki, P., & Celichowski, J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0162385 · Cited by 5
“Muscle models composed of MUs [12, 13, 14] give deeper and new insight into the processes of generation and control of the muscle force.”
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Kirk, E. A., & Rice, C. L. (2021) · Experimental Brain Research · doi:10.1007/s00221-021-06168-8 · Cited by 5
“Under voluntary control, tension in the muscle, and its corresponding force, are mediated by motor unit (MU) recruitment and firing rate (FR) modulation from descending synaptic inputs (Heckman and Binder 1991; Fuglevand et al. 1993; Devanne et al. 1997).”
BackgroundMonophasic and biphasic relaxation during motor unit tetanic contractions of variable fusion degree.
Celichowski, J., Pogrzebna, M., & Krutki, P. (2006) · PubMed · Cited by 5
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Simulation of EMG signals for Aging muscle
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“Motor unit firing frequency is characterized by four parameters, namely, minimum firing frequency, peak firing frequency, force and firing frequency relationship and inter-pulse interval (IPI) of the firing action potentials [14].”
BackgroundAge-Related Modifications to the Magnitude and Periodicity of Neuromuscular Noise
Singh, N. B., König, N., Arampatzis, A., et al. (2013) · PLoS ONE · doi:10.1371/journal.pone.0082791 · Cited by 5
“Studies conducted primarily on the upper-extremity muscles have revealed an association between force fluctuations and; the recruitment patterns of muscle motor units (MMUs) [8,9,13,14], and the variability in the discharge rate of action potentials [14–19].”
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“Motor units were included in the population sample if they had a minimum of five contigu - ous action potentials of consistent shape (as viewed in a sequential overlay) per MU train, with an interspike interval coefficient of variation of no more than 30% (Fuglevand et al. 1993 ; Roos et al. 1999 ).”
Onion skin is not a universal firing pattern for spinal motoneurons: simulation study
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“The FR of each MU first increased proportionally with the excitation drive up to a peak value, and then the FR remained unchanged despite further increases in the excitation drive [39].”
InfluentialCharacterization of motor unit activities during isometric elbow flexion with different speeds
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“Discharge rates also tend to increase with force, up to a certain limit, after which additional force is primarily achieved via further recruitment [7, 8].”
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“The recruitment thresholds, activated number, and firing frequency were determined by the rate coding model in [27], consistent with the first simulation.”
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Chen, C., Zhao, J., Yu, Y., Sheng, X., & Zhu, X. (2024) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2024.3509859 · Cited by 4
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“The spike trains of individual MUs were obtained using the MU recruitment and rate coding model proposed previously [24].”
Neuromusculoskeletal modeling of spasticity: A scoping review
da Silva, V. A., da Silva, R. L., Withers, J. W., Massenz, K. J. V., Orselli, M. I. V., Menegaldo, L. L., & Manffra, E. F. (2025) · PLoS ONE · doi:10.1371/journal.pone.0320153 · Cited by 6
“The Gaussian cumulative distribution function proposed by Fuglevand et al. [66] models the α -motoneuron pool [40,42,52,55] as an input-output relationship.”
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BackgroundMethodInfluentialValidation of a Virtual Arm Model for Movement Control and Rehabilitation
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“Early observation confIrmed that the intrinsic disturbance of neural noise is the source of kinematic variability [Fuglevand et al. 1993; Jones et al. 2002; Moritz et al. 2005].”
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“Anti-fatigue” control for over-actuated bionic arm with muscle force constraints
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A masked least-squares smoothing procedure for artifact reduction in scanning-EMG recordings
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“The cross-sectional areas of MU territories were modeled fitting an exponential function [6] between the area of the smallest MU, 1.”
MethodInfluentialHerold, J. L., Kirches, C., & Schlöder, J. P. (2018) · European Journal of Applied Physiology · doi:10.1007/s00421-018-3983-z · Cited by 4
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Yi, C., Jiang, F., Lu, G., Yang, C., Ding, Z., Zhu, J., & Liu, J. (2021) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48506.2021.9561535 · Cited by 4
“That is, information is encoded by clusters of neural cells rather than single neural cells [16], which”
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A fast gradient convolution kernel compensation method for surface electromyogram decomposition
Lin, C., Cui, Z., Chen, C., Liu, Y., Chen, C., & Jiang, N. (2024) · Journal of Electromyography and Kinesiology · doi:10.1016/j.jelekin.2024.102869 · Cited by 5
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“Fuglevand et al. (1993) proposed a gain for modification of the amplitude of the successive contractions within the tetanus, which depends on the preceding IPIs and MU contraction time.”
BackgroundMuscle force simulation by using two motor-unit recruitment strategies
Cao, H., Marin, F., Boudaoud, S., et al. (2008) · Computer Methods in Biomechanics & Biomedical Engineering · doi:10.1080/10255840802296723 · Cited by 4
“For the Strategy 2, the recruitment thresholds (RTi) of the ith MU is modeled as an exponential in the form (Fuglevand et al. 1993): RTi ¼ eðln RR=NÞi; ð2Þ where RR is the range of recruitment threshold desired, which is set to be 80% MVC, N is the total number of MUs, and i is an index identifying…”
MethodSpatio-temporal representation of multichannel EMG firing patterns and its clinical applications
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An integrative model of the surface EMG in pathological tremor
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Hierarchical neural control of human postural balance and bipedal walking in sagittal plane
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Ali, A. H. (2013) · PEARL (University of Plymouth) · doi:10.24382/1817 · Cited by 3
Estimation of the number of motor unit action potentials in the surface electromyogram
Zhou, P., & Rymer, W. Z. (2003) · International IEEE/EMBS Conference on Neural Engineering · doi:10.1109/cne.2003.1196838 · Cited by 4
Prat-Ortega, G., Ensel, S., Donadio, S., Borda, L., Boos, A., Yadav, P., Verma, N., Ho, J. C., Frazier-Kim, S., Fields, D. P., et al. (2024) · medRxiv · doi:10.1101/2024.02.14.24302709 · Cited by 4
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Engelhardt, L., Sachse, R., Burgkart, R., et al. (2025) · International Journal for Numerical Methods in Biomedical Engineering · doi:10.1002/cnm.70036 · Cited by 3
“The twitch contraction time T i defines the time until the peak twitch force F i in the ascending phase of a single twitch response is reached [129, 130].”
Klotz, T., & Rohlén, R. (2025) · Journal of Neural Engineering · doi:10.1088/1741-2552/adf886 · Cited by 4
“The columns of the extended and whitened mixing matrix ˜ h ul are given by ˜ h ul = V ˜ H : , u (: , l ) = V [ h 1 u ( l + R − 1 ) , ... , h 1 u ( l ) , ... , h Mu ( l + R − 1 ) , ... , h Mu ( l )] T , (A.2) with 0 ⩽ l ⩽ L + R − 1.”
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Metadata
- Authors
- Fuglevand, A. J., Winter, D. A., & Patla, A. E.
- Affiliations
- University of Waterloo (CA)
- Venue
- Journal of Neurophysiology
- Publisher
- American Physiological Society
- Published
- 1993-12-01
- Volume
- 70
- Issue
- 6
- Pages
- 2470-2488
- ISSN
- 0022-3077 (ISSN-L)
- 1522-1598
- OpenAlex
- W1809394698
- Cited by
- 988
- References
- 0
- Citations by year
- 2026: 41 · 2025: 47 · 2024: 64 · 2023: 49 · 2022: 38 · 2021: 55 · 2020: 43 · 2019: 44 · 2018: 45 · 2017: 37 · 2016: 37 · 2015: 41 · 2014: 34 · 2013: 38 · 2012: 39
- FWCI
- 4.88
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Neurophysiology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Muscle activation and electromyography studies
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Muscle Physiology and Disorders
- Life Sciences › Neuroscience › Cognitive Neuroscience › Motor Control and Adaptation
- Keywords
- motor unit recruitment, rate coding, surface electromyogram, EMG-force relationship, motor unit action potentials, action potential propagation velocity, recruitment threshold, motor unit territory, isometric force, voluntary muscle contraction
- MeSH terms
- Animals, Computer Simulation, Electromyography, Humans, Isometric Contraction, Models, Neurological, Motor Neurons, Muscles, Synaptic Transmission, Muscle Spindles, Recruitment, Neurophysiological
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