{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:06:57Z","timestamp":1787029617822,"version":"build-2736575974"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T00:00:00Z","timestamp":1675382400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Fund of the Republic of Serbia, PROMIS","award":["#6062528"],"award-info":[{"award-number":["#6062528"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The ultimate goal of rehabilitation engineering is to provide objective assessment tools for the level of injury and\/or the degree of neurorehabilitation recovery based on a combination of different sensing technologies that enable the monitoring of relevant measurable variables, as well as the assessment of non-measurable variables (such as muscle effort\/force and joint mechanical stiffness). This paper aims to present a feasibility study for a general assessment methodology for subject-specific non-measurable elbow model parameter prediction and elbow joint stiffness estimation. Ten participants without sensorimotor disorders performed a modified \u201cReach and retrieve\u201d task of the Wolf Motor Function Test while electromyography (EMG) data of an antagonistic muscle pair (the triceps brachii long head and biceps brachii long head muscle) and elbow angle were simultaneously acquired. A complete list of the Hill\u2019s muscle model and passive joint structure model parameters was generated using a genetic algorithm (GA) on the acquired training dataset with a maximum deviation of 6.1% of the full elbow angle range values during the modified task 8 of the Wolf Motor Function Test, and it was also verified using two experimental test scenarios (a task tempo variation scenario and a load variation scenario with a maximum deviation of 8.1%). The recursive least square (RLS) algorithm was used to estimate elbow joint stiffness (Stiffness) based on the estimated joint torque and the estimated elbow angle. Finally, novel Stiffness scales (general patterns) for upper limb functional assessment in the two performed test scenarios were proposed. The stiffness scales showed an exponentially increasing trend with increasing movement tempo, as well as with increasing weights. The obtained general Stiffness patterns from the group of participants without sensorimotor disorders could significantly contribute to the further monitoring of motor recovery in patients with sensorimotor disorders.<\/jats:p>","DOI":"10.3390\/s23031709","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T02:06:43Z","timestamp":1675649203000},"page":"1709","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Elbow Joint Stiffness Functional Scales Based on Hill\u2019s Muscle Model and Genetic Optimization"],"prefix":"10.3390","volume":"23","author":[{"given":"Marija","family":"Radmilovi\u0107","sequence":"first","affiliation":[{"name":"Institute Mihailo Pupin, University of Belgrade, Volgina 15, 11060 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5177-4386","authenticated-orcid":false,"given":"Djordje","family":"Urukalo","sequence":"additional","affiliation":[{"name":"Institute Mihailo Pupin, University of Belgrade, Volgina 15, 11060 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7506-4995","authenticated-orcid":false,"given":"Milica M.","family":"Jankovi\u0107","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11120 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Suzana Dedijer","family":"Dujovi\u0107","sequence":"additional","affiliation":[{"name":"Clinic for Rehabilitation \u201cDr. Miroslav Zotovi\u0107\u201d, Faculty of Medicine, University of Belgrade, 11000 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tijana J. Dimki\u0107","family":"Tomi\u0107","sequence":"additional","affiliation":[{"name":"Clinic for Rehabilitation \u201cDr. Miroslav Zotovi\u0107\u201d, Faculty of Medicine, University of Belgrade, 11000 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2945-8010","authenticated-orcid":false,"given":"Maja","family":"Trumi\u0107","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11120 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9029-4465","authenticated-orcid":false,"given":"Kosta","family":"Jovanovi\u0107","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11120 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.medengphy.2017.12.005","article-title":"Kinematic Measures for Upper Limb Robot-Assisted Therapy Following Stroke and Correlations with Clinical Outcome Measures: A review","volume":"53","author":"Tran","year":"2018","journal-title":"Med. Eng. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1177\/154596802401105171","article-title":"The Fugl-Meyer Assessment of Motor Recovery After Stroke: A Critical Review of its Measurement Properties","volume":"16","author":"Gladstone","year":"2002","journal-title":"Neurorehabil. Neural Repair"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1177\/1747493017711816","article-title":"Agreed Definitions and A Shared Vision for New Standards in Stroke Recovery Research: The Stroke Recovery and Rehabilitation Roundtable Taskforce","volume":"12","author":"Bernhardt","year":"2017","journal-title":"Int. J. Stroke"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bernaldo de Quir\u00f3s, M., Douma, E.H., van den Akker-Scheek, I., Lamoth, C.J.C., and Maurits, N.M. (2022). Quantification of Movement in Stroke Patients under Free Living Conditions Using Wearable Sensors: A Systematic Review. Sensors, 22.","DOI":"10.3390\/s22031050"},{"key":"ref_5","first-page":"784","article-title":"Standardized Measurement of Sensorimotor Recovery in Stroke Trials: Consensus-Based Core Recommendations from the Stroke Recovery and Rehabilitation Roundtable","volume":"31","author":"Kwakkel","year":"2017","journal-title":"Int. J. Stroke"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Borzelli, D., Pastorelli, S., d\u2019Avella, A., and Gastaldi, L. (2023). Virtual Stiffness: A Novel Biomechanical Approach to Estimate Limb Stiffness of a Multi-Muscle and Multi-Joint System. Sensors, 23.","DOI":"10.3390\/s23020673"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102074","DOI":"10.1016\/j.bspc.2020.102074","article-title":"A Review of The Key Technologies for sEMG-Based Human-Robot Interaction Systems","volume":"62","author":"Li","year":"2020","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1950040","DOI":"10.1142\/S0219519419500404","article-title":"Continuous Motion and Time-Varying Stiffness Estimation of the Human Elbow Joint Based on SEMG","volume":"19","author":"Li","year":"2019","journal-title":"J. Mech. Med. Biol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1109\/TNSRE.2020.3027501","article-title":"A Complex Stiffness Human Impedance Model with Customizable Exoskeleton Control","volume":"28","author":"He","year":"2020","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2808","DOI":"10.1152\/jn.2002.87.6.2808","article-title":"Voluntary Control of Static Endpoint Stiffness During Force Regulation Tasks","volume":"87","author":"Perreault","year":"2002","journal-title":"J. Neurophysiol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s00221-004-1864-7","article-title":"Multijoint Dynamics and Postural Stability of the Human Arm","volume":"157","author":"Perreault","year":"2004","journal-title":"Exp. Brain Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ajoudani, A., Fang, C., Tsagarakis, N.G., and Bicchi, A.A. (October, January 28). A reduced-Complexity Description of Arm Endpoint Stiffness with Applications to Teleimpedance Control. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS 2015), Hamburg, Germany.","DOI":"10.1109\/IROS.2015.7353495"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1177\/0278364917744035","article-title":"Reduced-Complexity Representation of the Human Arm Active Endpoint Stiffness for Supervisory Control of Remote Manipulation","volume":"37","author":"Ajoudani","year":"2017","journal-title":"Int. J. Robot. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/LRA.2017.2731524","article-title":"Online Model Based Estimation of Complete Joint Stiffness of Human Arm","volume":"3","author":"Fang","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.jbiomech.2019.01.017","article-title":"Stiffness Modulation of Redundant Musculoskeletal Systems","volume":"85","author":"Stanev","year":"2019","journal-title":"J. Biomech."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wu, Y., Zhao, F., Kim, W., and Ajoudani, A. (2020). An Intuitive Formulation of the Human Arm Active Endpoint Stiffness. Sensors, 20.","DOI":"10.3390\/s20185357"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1109\/TBME.2019.2935182","article-title":"EMG-Based Real-Time Linear-Nonlinear Cascade Regression Decoding of Shoulder, Elbow, and Wrist Movements in Able-Bodied Persons and Stroke Survivors","volume":"67","author":"Liu","year":"2019","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"53","DOI":"10.2298\/SJEE1501053J","article-title":"Hill's and Huxley's Muscle Models: Tools for Simulations in Biomechanics","volume":"12","year":"2015","journal-title":"Serbian J. Electr. Eng."},{"key":"ref_19","unstructured":"Robleto, R. (1997). An Analysis of the Musculotendon Dynamics of Hill-Based Models. [Master\u2019s thesis, Texas Tech University Libraries]."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2387","DOI":"10.1109\/TBME.2006.880883","article-title":"Real-Time Myoprocessors for a Neural Controlled Powered Exoskeleton Arm","volume":"53","author":"Cavallaro","year":"2006","journal-title":"IEEE Trans. Bio-Med. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/10255840008908000","article-title":"Musculoskeletal Model of the Upper Limb Based on the Visible Human Male Dataset","volume":"4","author":"Garner","year":"2001","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1016\/0021-9290(88)90249-7","article-title":"Estimated Mechanical Properties of Synergistic Muscles Involved in Movements of a Variety of Human Joints","volume":"21","author":"Winters","year":"1988","journal-title":"J. Biomech."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Desplenter, T., and Trejos, A. (2018). Evaluating Muscle Activation Models for Elbow Motion Estimation. Sensors, 18.","DOI":"10.3390\/s18041004"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1007\/s10439-005-3320-7","article-title":"A Model of the Upper Extremity for Simulating Musculoskeletal Surgery and Analyzing Neuromuscular Control","volume":"33","author":"Holzbaur","year":"2005","journal-title":"Ann. Biomed. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/S0021-9290(00)00051-8","article-title":"The Isometric Functional Capacity of Muscles that Cross the Elbow","volume":"33","author":"Murray","year":"2000","journal-title":"J. Biomech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"e46","DOI":"10.1016\/j.cmpb.2013.11.003","article-title":"A Passive Movement Method for Parameter Estimation of a Musculoskeletal Arm Model Incorporating a Modified Hill Muscle Model","volume":"114","author":"Yu","year":"2014","journal-title":"Comput. Methods Progr. Biomed."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1007\/s10439-008-9461-8","article-title":"Model-Based Sensorimotor Integration for Multi-Joint Control: Development of a Virtual Arm Model","volume":"36","author":"Song","year":"2008","journal-title":"Ann. Biomed. Eng."},{"key":"ref_28","first-page":"1985741","article-title":"An Improved EMG-Driven Neuromusculoskeletal Model for Elbow Joint Muscle Torque Estimation","volume":"2021","author":"Bingshan","year":"2021","journal-title":"Appl. Bionics Biomech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"102657","DOI":"10.1016\/j.bspc.2021.102657","article-title":"Motion Estimation of Elbow Joint From sEMG using Continuous Wavelet Transform and Back Propagation Neural Networks","volume":"68","author":"Huang","year":"2021","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Lemerle, S., Grioli, G., Bicchi, A., and Catalano, M.G. (2019, January 4\u20138). A Variable Stiffness Elbow Joint for Upper Limb Prosthesis. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS 2019), Macau, China.","DOI":"10.1109\/IROS40897.2019.8970475"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"126","DOI":"10.2165\/00007256-199418020-00005","article-title":"The Study of Human Body Segment Parameters in Biomechanics","volume":"18","author":"Pearsall","year":"1994","journal-title":"Sports Med."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0014-4886(89)80005-6","article-title":"Forced Use of Hemiplegic Upper Extremities to Reverse the Effect of Learned Nonuse Among Chronic Stroke and Head-Injured Patients","volume":"104","author":"Wolf","year":"1989","journal-title":"Exp. Neurol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1820","DOI":"10.1016\/j.apmr.2015.06.004","article-title":"Optimal Normalization Tests for Muscle Activation of the Levator Scapulae, Pectoralis Minor, and Rhomboid Major: An Electromyography Study Using Maximum Voluntary Isometric Contractions","volume":"96","author":"Cestelein","year":"2015","journal-title":"Arch. Phys. Med. Rehabil."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF00864215","article-title":"Normalization of Electromyogram in the Neck-Shoulder Region","volume":"67","author":"Nieminen","year":"1993","journal-title":"Eur. Appl. J. Physiol. Occup. Physiol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.jelekin.2004.09.006","article-title":"Normalization Procedures Using Maximum Voluntary Isometric Contractions for the Serratus Anterior and Trapezius Muscles During Surface EMG Analysis","volume":"15","author":"Ekstrom","year":"2004","journal-title":"J. Electromyogr. Kinesiol."},{"key":"ref_36","unstructured":"Halaki, M., and Ginn, K. (2012). Computational Intelligence in Electromyography Analysis\u2014A Perspective on Current Applications and Future Challenges, InTech. Chapter 7."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1016\/S0021-9290(03)00152-0","article-title":"A One-Parameter Neural Activation to Muscle Activation Model: Estimating Isometric Joint Moments from Electromyograms","volume":"36","author":"Manal","year":"2003","journal-title":"J. Biomech."},{"key":"ref_38","first-page":"136","article-title":"The Heat of Shortening and the Dynamic Constants of Muscle","volume":"126","author":"Hill","year":"1938","journal-title":"Proc. R. Soc."},{"key":"ref_39","unstructured":"He, J. (1988). A Feedback Control Analysis of the Neuro-Musculo-Skeletal System of a Cat Hindlimb. [Ph.D. Dissertation, The University of Maryland]."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1115\/1.3138535","article-title":"The Influence of Muscle Model Complexity in Musculoskeletal Motion Modeling","volume":"107","author":"Audu","year":"1985","journal-title":"J. Biomech. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/TASSP.1978.1163055","article-title":"Dynamic Programming Algorithm Optimization for Spoken Word Recognition","volume":"26","author":"Sakoe","year":"1978","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1109\/LRA.2020.2969952","article-title":"An Input Observer-Based Stiffness Estimation Approach for Flexible Robot Joints","volume":"5","author":"Fagiolini","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"7036","DOI":"10.1109\/LRA.2022.3178467","article-title":"Force\/Torque-Sensorless Joint Stiffness Estimation in Articulated Soft Robots","volume":"7","author":"Grioli","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Proch\u00e1zka, A., Uhl\u00ed\u0159, J., Rayner, P.W.J., and Kingsbury, N.G. (1998). Signal Analysis and Prediction, Springer, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-1768-8"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.1109\/TNSRE.2020.3038051","article-title":"An EMG-Driven Musculoskeletal Model for Estimating Continuous Wrist Motion","volume":"28","author":"Zhao","year":"2020","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF02259118","article-title":"Time-Varying Stiffness of Human Elbow Joint During Cyclic Voluntary Movement","volume":"88","author":"Bennett","year":"1992","journal-title":"Exp. Brain Res."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1299\/jbse.21-00088","article-title":"Human elbow motor learning skills of varying loads: Proof of internal model generation using joint stiffness estimation","volume":"16","author":"Shin","year":"2021","journal-title":"J. Biomech. Sci. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s00221-003-1443-3","article-title":"Functional Significance of Stiffness in Adaptation of Multijoint Arm Movements to Stable and Unstable Dynamics","volume":"151","author":"Franklin","year":"2003","journal-title":"Exp. Brain Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s002210100797","article-title":"Relationship Between Cocontraction, Movement Kinematics and Phasic Muscle Activity in Single-Joint Arm Movement","volume":"140","author":"Suzuki","year":"2021","journal-title":"Exp. Brain Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1152\/jn.1987.58.3.525","article-title":"Voluntary Control of Motor Units in Human Antagonist Muscles: Coactivation and Reciprocal Activation","volume":"58","author":"Mambrito","year":"1987","journal-title":"J. Neurophysiol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1161\/STROKEAHA.118.023531","article-title":"Systematic Review on Kinematic Assessments of Upper Limb Movements After Stroke","volume":"50","author":"Schwarz","year":"2019","journal-title":"Stroke"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/3\/1709\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:23:32Z","timestamp":1760120612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/3\/1709"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,3]]},"references-count":51,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["s23031709"],"URL":"https:\/\/doi.org\/10.3390\/s23031709","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,3]]}}}