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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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Choi, J. W., Jung, W. M., Kim, J. M., Song, C., Kim, W. H., & Kim, H. S. (2025) · Biomedical Engineering Letters · doi:10.1007/s13534-025-00498-0 · Cited by 3
“This makes EMG a valuable tool for design - ing optimized and individualized exercise strategies [6].”
Fanous, J., Zero, A. M., & Rice, C. L. (2026) · Journal of Applied Physiology · doi:10.1152/japplphysiol.00851.2025 · Cited by 3
Mao, J., Li, H., Yu, J., Wu, H., López, M. B., & Zhao, Y. (2024) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2024.107191 · Cited by 3
Matching dynamically varying forces with multi-motor-unit muscle models: a simulation study
Murtola, T., & Richards, C. T. (2025) · Royal Society Open Science · doi:10.1098/rsos.241401 · Cited by 2
Sidharth, N., & Venugopal, G. (2023) · Proceedings of the Institution of Mechanical Engineers Part H Journal of Engineering in Medicine · doi:10.1177/09544119221149234 · Cited by 4
“The mean Tfs values, m are calculated every second.(8) The stochastic nature of motor neuron firing is implemented using equation (13).”
BackgroundMethodInfluentialDevelopment of a High-SNR Stochastic sEMG Processor in a Multiple Muscle Elbow Joint
Chang, H., Kyeong, S., Na, Y., et al. (2023) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2023.3281410 · Cited by 3
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Foot-dominance does not influence force variability during ankle dorsiflexion and foot adduction
Sahinis, C., Amiridis, I. G., Varvariotis, N., et al. (2024) · Journal of Sports Sciences · doi:10.1080/02640414.2024.2379699 · Cited by 3
“The resulting fluctuations in the force produced by the motor unit will only impact the CoV for force at low forces when it adds significantly to the net force (Fuglevand et al., 1993).”
Siddiqi, A., Arjunan, S. P., & Kumar, D. (2018) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-018-1788-1 · Cited by 3
Šavc, M., & Holobar, A. (2021) · IEEE Access · doi:10.1109/access.2021.3078644 · Cited by 3
“The EMG signals in this study were synthesized using a collection of MUAPs extracted at different stages of biceps brachii (BB) muscle shortening, a model of MU firing rates [28], and carefully selected excitation and muscle short-”
MethodAntagonist surface electromyogram decomposition and the case of the missing motor units
Haynes, E. M. K., & Kim, C. (2021) · Journal of Neurophysiology · doi:10.1152/jn.00435.2021 · Cited by 3
A modelling study on transmission of the central oscillator in tremor by a motor neuron pool
Gallego, J. Á., Dideriksen, J. L., Farina, D., et al. (2011) · doi:10.1109/iembs.2011.6090375 · Cited by 3
“For a given tremor frequency, differences among motor units grow larger with the amount of voluntary contraction, reaching to a level where their distribution becomes exponential, as for the recruitment threshold [13].”
Web-based neuromuscular simulator applied to the teaching of principles of neuroscience
Elias, L. A., & Kohn, A. F. (2013) · Research on Biomedical Engineering · doi:10.4322/rbeb.2013.026 · Cited by 3
“Different multi-scale models have already been developed for the study of the neuromuscular system (Bashor, 1998; Fuglevand et al., 1993; Raphael et al., 2010; Winters, 1995).”
MethodEffects of the physiological parameters on the signal-to-noise ratio of single myoelectric channel
Ma, H. T., & Zhang, Y. (2007) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/1743-0003-4-29 · Cited by 3
“Simulation parameters were chosen according to previous studies [21], as shown in Table 2, while other parameters are the same as in Table 1.”
Muscle fatigue estimation with twitch force derived from sEMG peaks
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Mazzoni, A., Petrini, F. M., Rigosa, J., et al. (2015) · BMC Neuroscience · doi:10.1186/1471-2202-16-s1-p163 · Cited by 3
“The model builds on previous studies [1,2] i) to define a common drive to motoneurons proportional to the target force and ii) to define a relationship between the motoneurons firing rate and the resulting muscular force.”
Towards in-silico robotic post-stroke rehabilitation for mice
Vannucci, L., Pasquini, M., Spalletti, C., Caleo, M., Micera, S., Laschi, C., & Falotico, E. (2019) · IEEE International Conference on Cyborg and Bionic Systems (CBS) · doi:10.1109/cbs46900.2019.9114483 · Cited by 3
“integrated using the discrete time equations of [19] with a non-linear scaling factor from [23] that prevents the activation to grow indefinitely:”
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“The simulation of the surface electromyographic (EMG) signal aims at better understanding the physiological issues, interpreting real data or testing algorithms for information extraction [1], [2].”
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A New Muscle Architecture Model With Non-Uniform Distribution Of Muscle Fiber Types
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“The model used a prior model of muscle motor unit pools [18] to estimate contraction times to failure during isometric contractions across different contraction forces (% MVC).”
MethodAvrillon, S., Hug, F., Enoka, R. M., Caillet, A. H., & Farina, D. (2024) · eLife · doi:10.7554/elife.97085.2 · Cited by 3
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Spike-Based Neuromorphic Model of Spasticity for Generation of Affected Neural Activity
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“The twitch model converts the spike neural signals produced by the motoneuron pool into a continuous digital signal [42].”
The Physiological Control of Motoneuron Activity
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The NEUROiD neuromusculoskeletal movement simulation platform
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“the LMMSE estimator of the j th pulse train ̂̄tj(n) = cytjC yyy(n) (4)”
MethodHuang, C., Chen, M., Lu, Z., Klein, C. S., & Zhou, P. (2023) · Bioengineering · doi:10.3390/bioengineering10040469 · Cited by 2
“For each motor unit (the ith motor unit), the twitch force simulation was adopted from the Fuglevand model [12], which followed a second-order critically damped impulse response (Equation (2)).”
BackgroundMethodInfluentialBabcock, C. D., Volk, V. L., Zeng, W., et al. (2023) · Computer Methods in Biomechanics & Biomedical Engineering · doi:10.1080/10255842.2023.2280772 · Cited by 2
“These motor neuron cell diameters ranged from 49.8 to 99.7 l m (Sreenivasa et al. 2016) in an exponential relation (Fuglevand et al. 1993), with this model successfully showcasing spatial recruitment and rate coding capabilities (Figure 1).”
InfluentialDecomposition strategy for surface EMG with few channels: a simulation study
Wu, W., Jiang, L., & Yang, B. (2024) · Journal of Neural Engineering · doi:10.1088/1741-2552/ad4913 · Cited by 2
“The recruitment of a population of MUs was based on the model proposed by Fuglevand et al [41], recruitment thresholds with range between 0% and 50% of maximal excitation level.”
MethodChen, W., Wang, S., Bao, J., Yu, C., Jiang, Q., Song, J., Zheng, Y., Hao, Y., & Xu, K. (2024) · Journal of Neural Engineering · doi:10.1088/1741-2552/ad5935 · Cited by 2
“Instead, it modulated the frequency at which muscle responses occurred, thereby influencing the movement state, which may be related to the temporal summation of muscle contractions [38–40].”
BackgroundInfluence of stimulation frequency on early and late phase rate of torque and velocity development
Paris, M. T., Zero, A. M., & Rice, C. L. (2024) · Journal of Applied Physiology · doi:10.1152/japplphysiol.00076.2024 · Cited by 2
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“1) Initial estimate of twitch responses: Each twitch response ( a 0 ) was modeled as an impulse response of a second-order system [22] (4): where A c is the peak amplitude, T c is the contraction time and u is the excitation input, i.e. , a MU spike train.”
BackgroundSimultaneous and proportional control of wrist and finger force via motor unit activity
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Skiadopoulos, A., & Knikou, M. (2025) · PLoS ONE · doi:10.1371/journal.pone.0317218 · Cited by 3
“Additionally, the exponential distribution of recruitment thresholds across the motoneuron pool [13], discharge probability of multiple motoneurons/interneurons [2], intrinsic threshold of motoneurons [14], input resistance [15, 16], relative share of synaptic inputs whereas a moto-neuron that…”
InfluentialAnalysis of Wearable Force Myography Responses to Varied Perceived Exertion Levels During Power Grip
Baklouti, S., Rezgui, T., Chaker, A., et al. (2025) · IISE Transactions on Occupational Ergonomics and Human Factors · doi:10.1080/24725838.2025.2488333 · Cited by 2
“…intensifies, larger, high-threshold motor units are recruited, but their contribution to overall force output diminishes because fewer additional units are available, and the system relies more on increasing the firing rates of already active units (Enoka & Duchateau, 2017; Fuglevand et al., 1993).”
Messaoudi, N., Bekka, R. E., & Belkacem, S. (2021) · Polish Journal of Medical Physics And Engineering · doi:10.2478/pjmpe-2021-0011 · Cited by 2
Kohn, A. F. (2008) · Cited by 2
Implementing a surface EMG model with accurate parameters and a force output
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“[14] A. J. Fuglevand, D. A. Winter, and A. E. Patla, “Models of recruitment and rate coding organization in motor-unit pools,” J Neurophysiol, vol. 70, no. 6, pp. 2470-2488, December 1, 1993, 1993.”
BackgroundMethodInfluentialMotor Unit Contractions Evoked by Stimulation with Variable Interpulse Intervals
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Simulation Analysis on the MUAPs Classification Using a Combined Detection Method
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“Relating to the firing process of each motor unit, the inter-pulse intervals can be simulated as the gaussian distribution[14].”
Prediction of Tetanic Force of Muscle Motor Units Evoked by Irregular Stimulation Patterns
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A Finite Element Approach for the Modelling of Skeletal Muscle Fatigue
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“[13–19], that calculate muscle force by summing up the force produced by individual muscle fibres under consideration of fatigue effects.”
BackgroundMotor-Unit Pool Model of Continuous and Discrete Force Variability
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“The force model developed by Fuglevand et al.51 has been adapted in this study.”
MethodOn the Crosstalk in Motor Unit Spike Train Identification from High-Density Surface Electromyograms
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“In the simulation study, the Fuglevand motor neuron pool model [30] and a surface EMG model [31] were followed.”
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Influence of Fibres Inclination on the Degree of Gaussianity of Simulated Surface EMG Signals
Messaoudi, N., Bekka, R. E., & Belkacem, S. (2020) · International Conference on Bioinformatics and Biomedical Technology (ICBBT) · doi:10.1145/3405758.3405781 · Cited by 2
“The MUAP is the sum of the SFAPs belonging to this motor unit [5].”
BackgroundInfluentialHolobar, A., & Frančič, A. (2020) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/embc44109.2020.9175479 · Cited by 2
“MU firing patterns during the voluntary contraction were generated by the model described in [5], whereat we adapted the parameters to the properties of Biceps Brachii muscle.”
MethodThe physiology and simulation of alpha motoneurons in the human spinal cord
Jones, K. E. (1995) · Summit (Simon Fraser University) · Cited by 2
Novel Methods in SEMG-Force Estimation
Hashemi, J. (2013) · QSpace (Queen's University Library) · Cited by 2
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Hip posture affects the firing properties of motor units in the tibialis anterior muscle
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“Another study assigned threshold level and twitch force of each MU to compute the force generated by the muscles for various rate coding schemes [4].”
InfluentialMotor Neuron Loss Detection Based on EMG Probability Density Function Shape Descriptors
Navallas, J., Biurrun, L., Mariscal, C., et al. (2025) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2025.3599103 · Cited by 1
“Firing rates were modeled according to [37].”
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“A MU pool model generated synthetic firing patterns under pseudorandom neural drive, incorporating MU recruitment and rate-coding mechanisms detailed in previous studies [17].”
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“The distribution of time constants in the system allows for both fast and slow twitches (Henneman et al., 1965; Fuglevand et al., 1993).”
Multi-Channel Surface Electromyography for Simultaneous and Proportional Control of Prostheses
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“[5] proposed a MU pool-based model that included both surface electromyogram (sEMG) and force predictions under isometric conditions, in comparison with experimental recordings.”
BackgroundResultMechanics of doublet firings in motor unit pools
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“[11] itemized some important nonlinearities in the force response of motor units due to activation history, for example, posttetanic potentiation [24] or fatigue [22].”
BackgroundMethodTowards a genioglossus surface EMG model of obstructive sleep apnea
Chua, E. C.-P., McSharry, D. G., McNicholas, W. T., et al. (2009) · doi:10.1109/iembs.2009.5332517 · Cited by 1
Optimization of input parameters of an EMG-force model in constant and sinusoidal force contractions
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“RTi of the ith MU is modeled as follows [10]:”
Methodsustained submaximal contractions An integrative model of motor unit activity during
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Chapter 8 Stiffness of Contracting Human Muscle Measured with Supersonic Shear Imaging
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Spike Sorting: Application to Motor Unit Action Potential Discrimination
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“The Fuglevand’s model [7] was used to generate MU firing patterns at constant 10 % muscle excitation level.”
MethodChandra, S., Afsharipour, B., Rymer, W. Z., et al. (2022) · Frontiers in Neurology · doi:10.3389/fneur.2021.789442 · Cited by 1
“There is a finite lag after the neural activation of muscle fibers before there is detectable force generation by the muscle-tendon system (2, 3).”
BackgroundHigher Order Statistics Analyses Based on the Mathematical Model of Surface Electromyography
Zhao, Y. C., Li, D., & Zhang, J. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-39182-8_47 · Cited by 1
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Generation of sEMG for Post-stroke Spasticity with Spike-based Neuromorphic Models*
Jin, Y., Chen, Z., Jin, S. C., et al. (2024) · IEEE International Conference on Real-time Computing and Robotics (RCAR) · doi:10.1109/rcar61438.2024.10670730 · Cited by 1
Ornelas-Kobayashi, R., Gomez-Orozco, I., Gogeascoechea, A., van Asseldonk, E. H. F., & Sartori, M. (2024) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2024.3467692 · Cited by 1
“Based on the characteristics of the motor task [4], distinct mechanisms influence MN activity to modulate the neural drive, including cortically-originated changes in the CSI [5], [6], [7], regulation of CSI strength ( i.e., proportion of common vs independent inputs) [8], and synaptic…”
BackgroundRohlén, R., Lubel, E., & Farina, D. (2024) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2024.107002 · Cited by 1
Zero, A. M., & Rice, C. L. (2024) · Journal of Neurophysiology · doi:10.1152/jn.00274.2024 · Cited by 1
Tailoring neuromuscular dynamics: A modeling framework for realistic sEMG simulation
Costa‐García, Á., Shimoda, S., & Murai, A. (2025) · PLoS ONE · doi:10.1371/journal.pone.0319162 · Cited by 1
“To achieve this goal, the force response of each motor neuron was computed for each fire rate from 8 to 42 Hz [8].”
Sex Differences in Motor Unit Behavior in Patients With Parkinson's Disease
Nishikawa, Y., Watanabe, K., Holobar, A., Takahashi, T., Maeda, N., Maruyama, H., & Hyngstrom, A. S. (2025) · European Journal of Neuroscience · doi:10.1111/ejn.70191 · Cited by 1
“Here, we excluded units with motor unit discharge rates with CVs above 30%, as previously reported by Fuglevand et al. 1993 (Fuglevand et al. 1993).”
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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