Knee extensors are mixed muscles containing both fast (FMU) and slow motor units (SMU). It has been hypothesized that, at high angular velocities (150-360 deg/s), FMU contributes primarily to knee joint moment development, while at low angular velocities (30-120 deg/s), both FMU and SMU contribute to force generation. It was hypothesized that the maximum isometric moment in m. quadriceps, registered on the isokinetic dynamometer “BIODEX System 4Pro”at speeds of 30-150 deg/s, represents the sum of the moments from SMU and FMU, while in the range of 150-360 deg/s, it is primarily generated by FMU. The maximum isometric moment created by the FMU was calculated using a linear equation, as the force-velocity relationship becomes linear at high velocities. During knee extension at a constant angular velocity, the maximum number of RMUs, according to the model, is activated up to an angular velocity of 240 deg/s: (knee amplitude motion 90 deg) / (time developing maximum force 0.37s) = 240 deg/s. The maximum number of MMUs is recruited 1.09 s after the onset of knee extension, which corresponds to an angular velocity of 90 deg/based on the results of isokinetic dynamometry and a mathematical model, FMU and SMU forces were calculated for highly skilled athletes of different sports. For athletes of various specializations, the SMU force does not exceed 24 N/kg, while the FMU force ranges from 52-83 N/kg. The main result of this study demonstrates an acceptable level of agreement between the model and experimental calculations of the SMU and FMU contributions to knee extension force. Based on the obtained model characteristics, individual "boundaries" of SMU and FMU involvement can be determined.
| Published in | American Journal of Sports Science (Volume 14, Issue 1) |
| DOI | 10.11648/j.ajss.20261401.11 |
| Page(s) | 1-7 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Modeling, Isometric Force, Modeling, Motor Units Force, Muscle, Fibers Cross-sectional Areas
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APA Style
Voronov, A., Shpakov, A., Tomilovskaya, E., Voronova, A., Sokolov, N. (2026). Model of Force Calculation of Fast and Slow Motor Units of Knee Extensor Muscles in Isometric Mode. American Journal of Sports Science, 14(1), 1-7. https://doi.org/10.11648/j.ajss.20261401.11
ACS Style
Voronov, A.; Shpakov, A.; Tomilovskaya, E.; Voronova, A.; Sokolov, N. Model of Force Calculation of Fast and Slow Motor Units of Knee Extensor Muscles in Isometric Mode. Am. J. Sports Sci. 2026, 14(1), 1-7. doi: 10.11648/j.ajss.20261401.11
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Download@article{10.11648/j.ajss.20261401.11,
author = {Andrey Voronov and Alexey Shpakov and Elena Tomilovskaya and Anastasia Voronova and Nikolay Sokolov},
title = {Model of Force Calculation of Fast and Slow Motor Units of Knee Extensor Muscles in Isometric Mode},
journal = {American Journal of Sports Science},
volume = {14},
number = {1},
pages = {1-7},
doi = {10.11648/j.ajss.20261401.11},
url = {https://doi.org/10.11648/j.ajss.20261401.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajss.20261401.11},
abstract = {Knee extensors are mixed muscles containing both fast (FMU) and slow motor units (SMU). It has been hypothesized that, at high angular velocities (150-360 deg/s), FMU contributes primarily to knee joint moment development, while at low angular velocities (30-120 deg/s), both FMU and SMU contribute to force generation. It was hypothesized that the maximum isometric moment in m. quadriceps, registered on the isokinetic dynamometer “BIODEX System 4Pro”at speeds of 30-150 deg/s, represents the sum of the moments from SMU and FMU, while in the range of 150-360 deg/s, it is primarily generated by FMU. The maximum isometric moment created by the FMU was calculated using a linear equation, as the force-velocity relationship becomes linear at high velocities. During knee extension at a constant angular velocity, the maximum number of RMUs, according to the model, is activated up to an angular velocity of 240 deg/s: (knee amplitude motion 90 deg) / (time developing maximum force 0.37s) = 240 deg/s. The maximum number of MMUs is recruited 1.09 s after the onset of knee extension, which corresponds to an angular velocity of 90 deg/based on the results of isokinetic dynamometry and a mathematical model, FMU and SMU forces were calculated for highly skilled athletes of different sports. For athletes of various specializations, the SMU force does not exceed 24 N/kg, while the FMU force ranges from 52-83 N/kg. The main result of this study demonstrates an acceptable level of agreement between the model and experimental calculations of the SMU and FMU contributions to knee extension force. Based on the obtained model characteristics, individual "boundaries" of SMU and FMU involvement can be determined.},
year = {2026}
}
TY - JOUR T1 - Model of Force Calculation of Fast and Slow Motor Units of Knee Extensor Muscles in Isometric Mode AU - Andrey Voronov AU - Alexey Shpakov AU - Elena Tomilovskaya AU - Anastasia Voronova AU - Nikolay Sokolov Y1 - 2026/01/07 PY - 2026 N1 - https://doi.org/10.11648/j.ajss.20261401.11 DO - 10.11648/j.ajss.20261401.11 T2 - American Journal of Sports Science JF - American Journal of Sports Science JO - American Journal of Sports Science SP - 1 EP - 7 PB - Science Publishing Group SN - 2330-8540 UR - https://doi.org/10.11648/j.ajss.20261401.11 AB - Knee extensors are mixed muscles containing both fast (FMU) and slow motor units (SMU). It has been hypothesized that, at high angular velocities (150-360 deg/s), FMU contributes primarily to knee joint moment development, while at low angular velocities (30-120 deg/s), both FMU and SMU contribute to force generation. It was hypothesized that the maximum isometric moment in m. quadriceps, registered on the isokinetic dynamometer “BIODEX System 4Pro”at speeds of 30-150 deg/s, represents the sum of the moments from SMU and FMU, while in the range of 150-360 deg/s, it is primarily generated by FMU. The maximum isometric moment created by the FMU was calculated using a linear equation, as the force-velocity relationship becomes linear at high velocities. During knee extension at a constant angular velocity, the maximum number of RMUs, according to the model, is activated up to an angular velocity of 240 deg/s: (knee amplitude motion 90 deg) / (time developing maximum force 0.37s) = 240 deg/s. The maximum number of MMUs is recruited 1.09 s after the onset of knee extension, which corresponds to an angular velocity of 90 deg/based on the results of isokinetic dynamometry and a mathematical model, FMU and SMU forces were calculated for highly skilled athletes of different sports. For athletes of various specializations, the SMU force does not exceed 24 N/kg, while the FMU force ranges from 52-83 N/kg. The main result of this study demonstrates an acceptable level of agreement between the model and experimental calculations of the SMU and FMU contributions to knee extension force. Based on the obtained model characteristics, individual "boundaries" of SMU and FMU involvement can be determined. VL - 14 IS - 1 ER -
Laboratory of Sports Training Problems, Federal Science Center of Physical Culture and Sport (VNIIFK), Moscow, Russia;Russian Federation State Scientific Center, Institute of Biomedical Problems of the Russian Academy of Sciences, Moscow, Russia
Laboratory of Sports Training Problems, Federal Science Center of Physical Culture and Sport (VNIIFK), Moscow, Russia;Russian Federation State Scientific Center, Institute of Biomedical Problems of the Russian Academy of Sciences, Moscow, Russia
Russian Federation State Scientific Center, Institute of Biomedical Problems of the Russian Academy of Sciences, Moscow, Russia
Laboratory of Sports Training Problems, Federal Science Center of Physical Culture and Sport (VNIIFK), Moscow, Russia
Laboratory of Sports Training Problems, Federal Science Center of Physical Culture and Sport (VNIIFK), Moscow, Russia;Russian Federation State Scientific Center, Institute of Biomedical Problems of the Russian Academy of Sciences, Moscow, Russia
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