{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T05:04:04Z","timestamp":1790053444126,"version":"4.0.1"},"reference-count":58,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Physiol."],"abstract":"<jats:sec>\n                    <jats:title>Introduction<\/jats:title>\n                    <jats:p>\n                      Muscle hysteresis reflects nonlinear changes in electromyographic (EMG) activity during isolated changes in the length and force of individual muscles. However, previous studies have primarily considered changes in individual muscle state variables, whereas the hysteresis behavior associated with\n                      <jats:italic>simultaneous<\/jats:italic>\n                      changes in muscle length and force, remains insufficiently understood. Therefore, this study aimed to develop a mathematical model of EMG responses to simultaneous changes in muscle force and length using population-averaged experimental data from the authors\u2019 previously published study. Characterizing the history-dependent relationship among muscle activation, force, and length may contribute to adaptive control strategies for robot-aided rehabilitation, with potential applications in the assessment of motor dysfunction and rehabilitation personalization.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>\n                      A mathematical model was developed to describe the intensity of EMG signals from human elbow flexor muscles during\n                      <jats:italic>simultaneous<\/jats:italic>\n                      changes in muscle force and length. EMG signals and muscle state parameters were obtained from ten participants during a combination of externally controlled joint movements and active force generation under visual biofeedback. The framework of time-averaged derivatives of muscle state parameters was used to derive algorithms for estimating the activation intensity of synergistic muscles during motor tasks.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      The T-model (\u201cthermodynamic\u201d model) was developed based on the functional interdependence of three key parameters: muscle length, force, and the intensity of incoming activation. Algorithms were proposed to predict the activation intensity of synergistic muscles performing motor tasks involving simultaneous changes in muscle force and length. The results show that the use of time-averaged derivatives of muscle state parameters provides a close approximation of central motor commands, with COD values \u22650.9389 across the tested conditions. The analysis demonstrates that the amplitude of hysteresis effects increases with\n                      <jats:italic>coinciding<\/jats:italic>\n                      changes in muscle force and length and decreases when these changes are\n                      <jats:italic>opposing<\/jats:italic>\n                      .\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>\n                      The modeling results demonstrate that hysteresis in agonist muscle groups is strongly dependent on the interaction between\n                      <jats:italic>simultaneous<\/jats:italic>\n                      changes in muscle force and length. These findings highlight the importance of considering coupled force\u2013length dynamics in the analysis of neuromuscular control and provide a basis for further applications of muscle hysteresis analysis in motor control and rehabilitation.\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.3389\/fphys.2026.1904516","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T04:25:51Z","timestamp":1790051151000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A \u201cthermodynamic\u201d model of synergistic interaction of human elbow flexor muscles during simultaneous change in their length and force"],"prefix":"10.3389","volume":"17","author":[{"given":"Alexander","family":"Kostyukov","sequence":"first","affiliation":[{"name":"Department of Movement Physiology, Bogomoletz Institute of Physiology, National Academy of Sciences of Ukraine","place":["Kyiv, Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andriy","family":"Gorkovenko","sequence":"additional","affiliation":[{"name":"Department of Movement Physiology, Bogomoletz Institute of Physiology, National Academy of Sciences of Ukraine","place":["Kyiv, Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elena","family":"Kolosova","sequence":"additional","affiliation":[{"name":"Department of Movement Physiology, Bogomoletz Institute of Physiology, National Academy of Sciences of Ukraine","place":["Kyiv, Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"B4","doi-asserted-by":"publisher","first-page":"2761","DOI":"10.1152\/jn.00052.2018","article-title":"Synergies in coordination: a comprehensive overview of neural, computational and behavioral approaches","volume":"120","author":"Bruton","year":"2018","journal-title":"J. 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