{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T04:02:43Z","timestamp":1778126563157,"version":"3.51.4"},"reference-count":128,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T00:00:00Z","timestamp":1754870400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T00:00:00Z","timestamp":1754870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2021.04840.BD"],"award-info":[{"award-number":["2021.04840.BD"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04436\/2020"],"award-info":[{"award-number":["UIDB\/04436\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04436\/2020"],"award-info":[{"award-number":["UIDB\/04436\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005765","name":"Universidade de Lisboa","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005765","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Multibody Syst Dyn"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The definition of the musculotendon model is a critical step in the implementation of musculoskeletal models. However, the redundant nature of the muscle force-sharing problem and the diversity of functions available for modeling muscle parameters make the computational validation of new models and formulations a challenging aspect, as no standard reference data is available. The present work proposes a collaborative benchmark framework for validating musculoskeletal models implemented using a multibody dynamics formulation. Based on the use of simplistic biomechanical models, five benchmark cases are introduced to progressively guide the implementation and validation of muscle contraction dynamics and musculotendon models. Specifically, the first case validates the muscle contraction dynamics model. The second case focuses on modeling musculotendon units (MTUs) with via-points. The third case addresses the muscle force-sharing problem, while the fourth and fifth cases evaluate the ability of the implemented models to predict the neutralizing actions of antagonist muscles and to handle biarticular muscle modeling, respectively. In order to facilitate the implementation of the benchmark cases, this work details the steps required for developing a muscle contraction dynamics model, modeling MTUs within a multibody framework, and solving the muscle redundancy problem using static optimization. The proposed cases were solved using two distinct multibody formulations, namely Cartesian coordinates (CC) and fully Cartesian coordinates with a generic rigid body (FCC-GRB). The main MTU outcomes for each benchmark problem are presented, with detailed results provided as supplementary material. The proposed cases serve as an effective platform for the validation of skeletal muscle modeling methodologies.<\/jats:p>","DOI":"10.1007\/s11044-025-10096-8","type":"journal-article","created":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T06:45:38Z","timestamp":1754894738000},"page":"1057-1100","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Validation of skeletal muscle models in multibody dynamics: A collaborative collection of benchmark cases"],"prefix":"10.1007","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8200-005X","authenticated-orcid":false,"given":"S\u00e9rgio B.","family":"Gon\u00e7alves","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6093-2083","authenticated-orcid":false,"given":"Mariana","family":"Rodrigues\u00a0da\u00a0Silva","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1162-5618","authenticated-orcid":false,"given":"Filipe","family":"Marques","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7013-4202","authenticated-orcid":false,"given":"Paulo","family":"Flores","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7056-4555","authenticated-orcid":false,"given":"Miguel","family":"Tavares\u00a0da\u00a0Silva","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,11]]},"reference":[{"key":"10096_CR1","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s00223-014-9915-y","volume":"96","author":"W.R. Frontera","year":"2015","unstructured":"Frontera, W.R., Ochala, J.: Skeletal muscle: a brief review of structure and function. Calcif. Tissue Int. 96, 183\u2013195 (2015). https:\/\/doi.org\/10.1007\/s00223-014-9915-y","journal-title":"Calcif. Tissue Int."},{"key":"10096_CR2","doi-asserted-by":"publisher","DOI":"10.5040\/9781492595298","volume-title":"Biomechanics of Skeletal Muscles","author":"V.M. Zatsiorsky","year":"2012","unstructured":"Zatsiorsky, V.M., Prilutsky, B.I.: Biomechanics of Skeletal Muscles. Human Kinetics, Champaign (2012)"},{"key":"10096_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11914-014-0244-x","volume":"13","author":"K.G. Avin","year":"2015","unstructured":"Avin, K.G., Bloomfield, S.A., Gross, T.S., Warden, S.J.: Biomechanical aspects of the muscle-bone interaction. Curr. Osteoporos. Rep. 13, 1\u20138 (2015). https:\/\/doi.org\/10.1007\/s11914-014-0244-x","journal-title":"Curr. Osteoporos. Rep."},{"key":"10096_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.pharmthera.2023.108357","volume":"243","author":"Y. Yoshimoto","year":"2023","unstructured":"Yoshimoto, Y., Oishi, Y.: Mechanisms of skeletal muscle-tendon development and regeneration\/healing as potential therapeutic targets. Pharmacol. Ther. 243, 108357 (2023). https:\/\/doi.org\/10.1016\/j.pharmthera.2023.108357","journal-title":"Pharmacol. Ther."},{"key":"10096_CR5","doi-asserted-by":"publisher","DOI":"10.1177\/23259671211020731","volume":"9","author":"M.C.P. Vila Pouca","year":"2021","unstructured":"Vila Pouca, M.C.P., Parente, M.P.L., Jorge, R.M.N., Ashton-Miller, J.A.: Injuries in muscle-tendon-bone units: a systematic review considering the role of passive tissue fatigue. Orthop. J. Sports Med. 9, 232596712110207 (2021). https:\/\/doi.org\/10.1177\/23259671211020731","journal-title":"Orthop. J. Sports Med."},{"key":"10096_CR6","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s12551-020-00610-x","volume":"12","author":"D. Shishmarev","year":"2020","unstructured":"Shishmarev, D.: Excitation-contraction coupling in skeletal muscle: recent progress and unanswered questions. Biophys. Rev. 12, 143\u2013153 (2020). https:\/\/doi.org\/10.1007\/s12551-020-00610-x","journal-title":"Biophys. Rev."},{"key":"10096_CR7","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s12551-013-0135-x","volume":"6","author":"J.C. Calder\u00f3n","year":"2014","unstructured":"Calder\u00f3n, J.C., Bola\u00f1os, P., Caputo, C.: The excitation\u2013contraction coupling mechanism in skeletal muscle. Biophys. Rev. 6, 133\u2013160 (2014). https:\/\/doi.org\/10.1007\/s12551-013-0135-x","journal-title":"Biophys. Rev."},{"key":"10096_CR8","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s11831-019-09393-1","volume":"28","author":"M. Silva","year":"2021","unstructured":"Silva, M., Freitas, B., Andrade, R., Carvalho, \u00d3., Renjewski, D., Flores, P., Espregueira-Mendes, J.: Current perspectives on the biomechanical modelling of the human lower limb: a systematic review. Arch. Comput. Methods Eng. 28, 601\u2013636 (2021). https:\/\/doi.org\/10.1007\/s11831-019-09393-1","journal-title":"Arch. Comput. Methods Eng."},{"key":"10096_CR9","doi-asserted-by":"publisher","first-page":"4915","DOI":"10.1007\/s11831-022-09757-0","volume":"29","author":"I. Roupa","year":"2022","unstructured":"Roupa, I., Silva, M.R., Marques, F., Gon\u00e7alves, S.B., Flores, P., Silva, M.T.: On the modeling of biomechanical systems for human movement analysis: a narrative review. Arch. Comput. Methods Eng. 29, 4915\u20134958 (2022). https:\/\/doi.org\/10.1007\/s11831-022-09757-0","journal-title":"Arch. Comput. Methods Eng."},{"key":"10096_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2022.105046","volume":"177","author":"L. Saraiva","year":"2022","unstructured":"Saraiva, L., Silva, M.R., Marques, F., Silva, M.T., Flores, P.: A review on foot-ground contact modeling strategies for human motion analysis. Mech. Mach. Theory 177, 105046 (2022). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2022.105046","journal-title":"Mech. Mach. Theory"},{"key":"10096_CR11","doi-asserted-by":"publisher","first-page":"1897","DOI":"10.1007\/s11831-022-09856-y","volume":"30","author":"M.R. Silva","year":"2023","unstructured":"Silva, M.R., Marques, F., Silva, M.T., Flores, P.: A comprehensive review on biomechanical modeling applied to device-assisted locomotion. Arch. Comput. Methods Eng. 30, 1897\u20131960 (2023). https:\/\/doi.org\/10.1007\/s11831-022-09856-y","journal-title":"Arch. Comput. Methods Eng."},{"key":"10096_CR12","doi-asserted-by":"publisher","first-page":"1953","DOI":"10.1016\/j.jbiomech.2016.04.008","volume":"49","author":"V. Carbone","year":"2016","unstructured":"Carbone, V., van der Krogt, M.M., Koopman, H.F.J.M., Verdonschot, N.: Sensitivity of subject-specific models to Hill muscle\u2013tendon model parameters in simulations of gait. J. Biomech. 49, 1953\u20131960 (2016). https:\/\/doi.org\/10.1016\/j.jbiomech.2016.04.008","journal-title":"J. Biomech."},{"key":"10096_CR13","doi-asserted-by":"publisher","first-page":"1463","DOI":"10.1016\/j.jbiomech.2012.02.023","volume":"45","author":"D.C. Ackland","year":"2012","unstructured":"Ackland, D.C., Lin, Y.-C., Pandy, M.G.: Sensitivity of model predictions of muscle function to changes in moment arms and muscle\u2013tendon properties: a Monte-Carlo analysis. J. Biomech. 45, 1463\u20131471 (2012). https:\/\/doi.org\/10.1016\/j.jbiomech.2012.02.023","journal-title":"J. Biomech."},{"key":"10096_CR14","first-page":"136","volume":"126","author":"A.V. Hill","year":"1938","unstructured":"Hill, A.V.: The heat of shortening and the dynamic constants of muscle. Proc. Royal Soc. B, Biol. Sci. 126, 136\u2013195 (1938)","journal-title":"Proc. Royal Soc. B, Biol. Sci."},{"key":"10096_CR15","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1146\/annurev-bioeng-061008-124941","volume":"11","author":"R.R. Neptune","year":"2009","unstructured":"Neptune, R.R., McGowan, C.P., Fiandt, J.M.: The influence of muscle physiology and advanced technology on sports performance. Annu. Rev. Biomed. Eng. 11, 81\u2013107 (2009). https:\/\/doi.org\/10.1146\/annurev-bioeng-061008-124941","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"10096_CR16","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/s11044-020-09747-9","volume":"50","author":"K.A. Inkol","year":"2020","unstructured":"Inkol, K.A., Brown, C., McNally, W., Jansen, C., McPhee, J.: Muscle torque generators in multibody dynamic simulations of optimal sports performance. Multibody Syst. Dyn. 50, 435\u2013452 (2020). https:\/\/doi.org\/10.1007\/s11044-020-09747-9","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR17","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1016\/j.jbiomech.2011.04.040","volume":"45","author":"R.H. Miller","year":"2012","unstructured":"Miller, R.H., Umberger, B.R., Caldwell, G.E.: Limitations to maximum sprinting speed imposed by muscle mechanical properties. J. Biomech. 45, 1092\u20131097 (2012). https:\/\/doi.org\/10.1016\/j.jbiomech.2011.04.040","journal-title":"J. Biomech."},{"key":"10096_CR18","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.gaitpost.2017.07.119","volume":"58","author":"M. B\u0142a\u017ckiewicz","year":"2017","unstructured":"B\u0142a\u017ckiewicz, M., Wiszomirska, I., Kaczmarczyk, K., Naemi, R., Wit, A.: Inter-individual similarities and variations in muscle forces acting on the ankle joint during gait. Gait Posture 58, 166\u2013170 (2017). https:\/\/doi.org\/10.1016\/j.gaitpost.2017.07.119","journal-title":"Gait Posture"},{"key":"10096_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2020.109971","volume":"110","author":"R. Haddara","year":"2020","unstructured":"Haddara, R., Harandi, V.J., Lee, P.V.S.: Anterior cruciate ligament agonist and antagonist muscle force differences between males and females during perturbed walking. J. Biomech. 110, 109971 (2020). https:\/\/doi.org\/10.1016\/j.jbiomech.2020.109971","journal-title":"J. Biomech."},{"key":"10096_CR20","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/s10439-020-02594-x","volume":"49","author":"W.H. Clark","year":"2021","unstructured":"Clark, W.H., Pimentel, R.E., Franz, J.R.: Imaging and simulation of inter-muscular differences in triceps surae contributions to forward propulsion during walking. Ann. Biomed. Eng. 49, 703\u2013715 (2021). https:\/\/doi.org\/10.1007\/s10439-020-02594-x","journal-title":"Ann. Biomed. Eng."},{"key":"10096_CR21","doi-asserted-by":"publisher","DOI":"10.1186\/s12984-024-01458-y","volume":"21","author":"M. Abdullah","year":"2024","unstructured":"Abdullah, M., Hulleck, A.A., Katmah, R., Khalaf, K., El-Rich, M.: Multibody dynamics-based musculoskeletal modeling for gait analysis: a systematic review. J. NeuroEng. Rehabil. 21, 178 (2024). https:\/\/doi.org\/10.1186\/s12984-024-01458-y","journal-title":"J. NeuroEng. Rehabil."},{"key":"10096_CR22","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.jbiomech.2019.07.042","volume":"94","author":"J. Li","year":"2019","unstructured":"Li, J., Lu, Y., Miller, S.C., Jin, Z., Hua, X.: Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles. J. Biomech. 94, 230\u2013234 (2019). https:\/\/doi.org\/10.1016\/j.jbiomech.2019.07.042","journal-title":"J. Biomech."},{"key":"10096_CR23","doi-asserted-by":"publisher","unstructured":"Luis, I., Afschrift, M., De Groote, F., Gutierrez-Farewik, E.M.: Evaluation of musculoskeletal models, scaling methods, and performance criteria for estimating muscle excitations and fiber lengths across walking speeds. Front. Bioeng. Biotechnol. 10 (2022). https:\/\/doi.org\/10.3389\/fbioe.2022.1002731","DOI":"10.3389\/fbioe.2022.1002731"},{"key":"10096_CR24","doi-asserted-by":"publisher","first-page":"2782","DOI":"10.1016\/j.jbiomech.2011.08.024","volume":"44","author":"T.A. Correa","year":"2011","unstructured":"Correa, T.A., Pandy, M.G.: A mass\u2013length scaling law for modeling muscle strength in the lower limb. J. Biomech. 44, 2782\u20132789 (2011). https:\/\/doi.org\/10.1016\/j.jbiomech.2011.08.024","journal-title":"J. Biomech."},{"key":"10096_CR25","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.jbiomech.2015.11.006","volume":"49","author":"L. Modenese","year":"2016","unstructured":"Modenese, L., Ceseracciu, E., Reggiani, M., Lloyd, D.G.: Estimation of musculotendon parameters for scaled and subject specific musculoskeletal models using an optimization technique. J. Biomech. 49, 141\u2013148 (2016). https:\/\/doi.org\/10.1016\/j.jbiomech.2015.11.006","journal-title":"J. Biomech."},{"key":"10096_CR26","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/1-4020-3393-1_7","volume-title":"Advances in Computational Multibody Systems. Computational Methods in Applied Sciences","author":"J. Ambr\u00f3sio","year":"2005","unstructured":"Ambr\u00f3sio, J., Silva, M.T.: A biomechanical multibody model with a detailed locomotion muscle apparatus. In: Ambr\u00f3sio, J.A.C. (ed.) Advances in Computational Multibody Systems. Computational Methods in Applied Sciences, pp.\u00a0155\u2013184. Springer, Dordrecht (2005). https:\/\/doi.org\/10.1007\/1-4020-3393-1_7"},{"key":"10096_CR27","unstructured":"Silva, M.T.: Human motion analysis using multibody dynamics and optimization tools (2003)"},{"issue":"3","key":"10096_CR28","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/S11044-019-09685-1","volume":"47","author":"M. Ezati","year":"2019","unstructured":"Ezati, M., Ghannadi, B., Mcphee, J.: A review of simulation methods for human movement dynamics with emphasis on gait. Multibody Syst. Dyn. 47(3), 265\u2013292 (2019). https:\/\/doi.org\/10.1007\/S11044-019-09685-1","journal-title":"Multibody Syst. Dyn."},{"issue":"3","key":"10096_CR29","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/S11044-022-09852-X","volume":"58","author":"M. Febrer-Nafr\u00eda","year":"2022","unstructured":"Febrer-Nafr\u00eda, M., Nasr, A., Ezati, M., Brown, P., Font-Llagunes, J.M., McPhee, J.: Predictive multibody dynamic simulation of human neuromusculoskeletal systems: a review. Multibody Syst. Dyn. 58(3), 299\u2013339 (2022). https:\/\/doi.org\/10.1007\/S11044-022-09852-X","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00366-009-0139-0","volume":"26","author":"M. Gonz\u00e1lez","year":"2010","unstructured":"Gonz\u00e1lez, M., Gonz\u00e1lez, F., Luaces, A., Cuadrado, J.: A collaborative benchmarking framework for multibody system dynamics. Eng. Comput. 26, 1\u20139 (2010). https:\/\/doi.org\/10.1007\/s00366-009-0139-0","journal-title":"Eng. Comput."},{"key":"10096_CR31","first-page":"1153","volume-title":"Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2013","author":"R. Masoudi","year":"2013","unstructured":"Masoudi, R., Uchida, T., Vilela, D., Luaces, A., Cuadrado, J., McPhee, J.: A library of computational benchmark problems for the multibody dynamics community. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2013, pp.\u00a01153\u20131162 (2013)"},{"key":"10096_CR32","unstructured":"IFToMM technical committee for multibody dynamics, library of computational benchmark problems (2022). Available at https:\/\/www.iftomm-multibody.org\/benchmark\/"},{"key":"10096_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/10255840008915251","volume":"3","author":"B.A. Garner","year":"2000","unstructured":"Garner, B.A., Pandy, M.G.: The obstacle-set method for representing muscle paths in musculoskeletal models. Comput. Methods Biomech. Biomed. Eng. 3, 1\u201330 (2000). https:\/\/doi.org\/10.1080\/10255840008915251","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"10096_CR34","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s11044-015-9451-1","volume":"36","author":"A. Scholz","year":"2016","unstructured":"Scholz, A., Sherman, M., Stavness, I., Delp, S., Kecskem\u00e9thy, A.: A fast multi-obstacle muscle wrapping method using natural geodesic variations. Multibody Syst. Dyn. 36, 195\u2013219 (2016). https:\/\/doi.org\/10.1007\/s11044-015-9451-1","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR35","doi-asserted-by":"publisher","first-page":"1931","DOI":"10.1016\/j.jbiomech.2010.03.018","volume":"43","author":"P. Favre","year":"2010","unstructured":"Favre, P., Gerber, C., Snedeker, J.G.: Automated muscle wrapping using finite element contact detection. J. Biomech. 43, 1931\u20131940 (2010). https:\/\/doi.org\/10.1016\/j.jbiomech.2010.03.018","journal-title":"J. Biomech."},{"key":"10096_CR36","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.cmpb.2008.05.005","volume":"92","author":"A. Audenaert","year":"2008","unstructured":"Audenaert, A., Audenaert, E.: Global optimization method for combined spherical\u2013cylindrical wrapping in musculoskeletal upper limb modelling. Comput. Methods Programs Biomed. 92, 8\u201319 (2008). https:\/\/doi.org\/10.1016\/j.cmpb.2008.05.005","journal-title":"Comput. Methods Programs Biomed."},{"key":"10096_CR37","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s00422-002-0326-1","volume":"87","author":"F. Gao","year":"2002","unstructured":"Gao, F., Damsgaard, M., Rasmussen, J., Christensen, S.T.: Computational method for muscle-path representation in musculoskeletal models. Biol. Cybern. 87, 199\u2013210 (2002). https:\/\/doi.org\/10.1007\/s00422-002-0326-1","journal-title":"Biol. Cybern."},{"key":"10096_CR38","volume-title":"Computer-Aided Analysis of Mechanical Systems","author":"P. Nikravesh","year":"1988","unstructured":"Nikravesh, P.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, New York (1988)"},{"key":"10096_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2022.105134","volume":"180","author":"I. Roupa","year":"2023","unstructured":"Roupa, I., Gon\u00e7alves, S.B., Silva, M.T.: Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body. Mech. Mach. Theory 180, 105134 (2023). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2022.105134","journal-title":"Mech. Mach. Theory"},{"key":"10096_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.mechmachtheory.2025.105955","volume":"209","author":"S.B. Gon\u00e7alves","year":"2025","unstructured":"Gon\u00e7alves, S.B., Roupa, I., Flores, P., Tavares da Silva, M.: Kinematic and dynamic analysis of spatial multibody systems with fully Cartesian coordinates and a generic rigid body. Mech. Mach. Theory 209, 1\u201335 (2025). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2025.105955","journal-title":"Mech. Mach. Theory"},{"key":"10096_CR41","doi-asserted-by":"publisher","first-page":"106080_1","DOI":"10.1016\/j.mechmachtheory.2025.106080","volume":"214","author":"S.B. Gon\u00e7alves","year":"2025","unstructured":"Gon\u00e7alves, S.B., Roupa, I., Flores, P., Tavares da Silva, M.: Kinematic and inverse dynamic analysis using mixed and fully Cartesian coordinates with a generic rigid body. Mech. Mach. Theory 214, 106080_1\u2013106080_25 (2025). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2025.106080","journal-title":"Mech. Mach. Theory"},{"key":"10096_CR42","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/978-3-319-30614-8_10","volume-title":"Multibody Dynamics. Computational Methods in Applied Sciences","author":"A.R. Oliveira","year":"2016","unstructured":"Oliveira, A.R., Gon\u00e7alves, S.B., de Carvalho, M., Silva, M.T.: Development of a musculotendon model within the framework of multibody systems dynamics. In: Font-Llagunes, J. (ed.) Multibody Dynamics. Computational Methods in Applied Sciences, pp.\u00a0213\u2013237. Springer, Cham (2016) https:\/\/doi.org\/10.1007\/978-3-319-30614-8_10"},{"key":"10096_CR43","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1016\/j.jbiomech.2014.12.034","volume":"48","author":"V. Carbone","year":"2015","unstructured":"Carbone, V., Fluit, R., Pellikaan, P., van der Krogt, M.M., Janssen, D., Damsgaard, M., Vigneron, L., Feilkas, T., Koopman, H.F.J.M., Verdonschot, N.: TLEM 2.0 - a comprehensive musculoskeletal geometry dataset for subject-specific modeling of lower extremity. J. Biomech. 48, 734\u2013741 (2015). https:\/\/doi.org\/10.1016\/j.jbiomech.2014.12.034","journal-title":"J. Biomech."},{"key":"10096_CR44","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1016\/S0021-9290(99)00122-0","volume":"32","author":"M.D. Klein Breteler","year":"1999","unstructured":"Klein Breteler, M.D., Spoor, C.W., Van Der Helm, F.C.T.: Measuring muscle and joint geometry parameters of a shoulder for modeling purposes. J. Biomech. 32, 1191\u20131197 (1999). https:\/\/doi.org\/10.1016\/S0021-9290(99)00122-0","journal-title":"J. Biomech."},{"key":"10096_CR45","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1016\/S0021-9290(97)00011-0","volume":"30","author":"H.E.J. Veeger","year":"1997","unstructured":"Veeger, H.E.J., Yu, B., An, K.N., Rozendal, R.H.: Parameters for modeling the upper extremity. J. Biomech. 30, 647\u2013652 (1997). https:\/\/doi.org\/10.1016\/S0021-9290(97)00011-0","journal-title":"J. Biomech."},{"key":"10096_CR46","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/0021-9290(92)90270-B","volume":"25","author":"F.C.T. Van der Helm","year":"1992","unstructured":"Van der Helm, F.C.T., Veeger, H.E.J., Pronk, G.M., Van der Woude, L.H.V., Rozendal, R.H.: Geometry parameters for musculoskeletal modelling of the shoulder system. J. Biomech. 25, 129\u2013144 (1992). https:\/\/doi.org\/10.1016\/0021-9290(92)90270-B","journal-title":"J. Biomech."},{"key":"10096_CR47","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-28750-8","volume-title":"Dynamic Modeling of Musculoskeletal Motion: A Vectorized Approach for Biomechanical Analysis in Three Dimensions","author":"G.T. Yamaguchi","year":"2001","unstructured":"Yamaguchi, G.T.: Dynamic Modeling of Musculoskeletal Motion: A Vectorized Approach for Biomechanical Analysis in Three Dimensions. Kluwer Academic, Boston (2001)"},{"key":"10096_CR48","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.clinbiomech.2006.10.003","volume":"22","author":"M.D. Klein Horsman","year":"2007","unstructured":"Klein Horsman, M.D., Koopman, H.F.J.M., van der Helm, F.C.T., Pros\u00e9, L.P., Veeger, H.E.J.: Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity. Clin. Biomech. 22, 239\u2013247 (2007). https:\/\/doi.org\/10.1016\/j.clinbiomech.2006.10.003","journal-title":"Clin. Biomech."},{"key":"10096_CR49","doi-asserted-by":"publisher","first-page":"2601","DOI":"10.1016\/J.JBIOMECH.2010.05.005","volume":"43","author":"E. Desailly","year":"2010","unstructured":"Desailly, E., Sardain, P., Khouri, N., Yepremian, D., Lacouture, P.: The convex wrapping algorithm: a method for identifying muscle paths using the underlying bone mesh. J. Biomech. 43, 2601\u20132607 (2010). https:\/\/doi.org\/10.1016\/J.JBIOMECH.2010.05.005","journal-title":"J. Biomech."},{"key":"10096_CR50","doi-asserted-by":"publisher","first-page":"13073","DOI":"10.1007\/S11071-024-09754-X","volume":"112","author":"Y. Tang","year":"2024","unstructured":"Tang, Y., Guo, J., Tian, Q., Hu, H.: Dynamic modeling of three-dimensional muscle wrapping based on absolute nodal coordinate formulation. Nonlinear Dyn. 112, 13073\u201313093 (2024). https:\/\/doi.org\/10.1007\/S11071-024-09754-X","journal-title":"Nonlinear Dyn."},{"key":"10096_CR51","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/S11044-020-09733-1","volume":"49","author":"J. Guo","year":"2020","unstructured":"Guo, J., Huang, H., Yu, Y., Liang, Z., Ambr\u00f3sio, J., Zhao, Z., Ren, G., Ao, Y.: Modeling muscle wrapping and mass flow using a mass-variable multibody formulation. Multibody Syst. Dyn. 49, 315\u2013336 (2020). https:\/\/doi.org\/10.1007\/S11044-020-09733-1","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR52","doi-asserted-by":"publisher","first-page":"1876","DOI":"10.1016\/J.JBIOMECH.2010.03.022","volume":"43","author":"F. De Groote","year":"2010","unstructured":"De Groote, F., Van Campen, A., Jonkers, I., De Schutter, J.: Sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors. J. Biomech. 43, 1876\u20131883 (2010). https:\/\/doi.org\/10.1016\/J.JBIOMECH.2010.03.022","journal-title":"J. Biomech."},{"key":"10096_CR53","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1177\/1464419311415954","volume":"225","author":"A. Pereira","year":"2011","unstructured":"Pereira, A., Silva, M.T., Martins, J.M., de Carvalho, M.: Implementation of an efficient muscle fatigue model in the framework of multibody systems dynamics for analysis of human movements. Proc. Inst. Mech. Eng. Part K, J. Multi-Body Dyn. 225, 359\u2013370 (2011). https:\/\/doi.org\/10.1177\/1464419311415954","journal-title":"Proc. Inst. Mech. Eng. Part K, J. Multi-Body Dyn."},{"key":"10096_CR54","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.1249\/01.mss.0000176684.24008.6f","volume":"37","author":"T.S. Buchanan","year":"2005","unstructured":"Buchanan, T.S., Lloyd, D.G., Manal, K., Besier, T.F.: Estimation of muscle forces and joint moments using a forward-inverse dynamics model. Med. Sci. Sports Exerc. 37, 1911\u20131916 (2005)","journal-title":"Med. Sci. Sports Exerc."},{"key":"10096_CR55","first-page":"76","volume":"29","author":"R.R. Neptune","year":"2001","unstructured":"Neptune, R.R., Kautz, S.A.: Muscle activation and deactivation dynamics: the governing properties in fast cyclical human movement performance? Exerc. Sport Sci. Rev. 29, 76\u201381 (2001)","journal-title":"Exerc. Sport Sci. Rev."},{"key":"10096_CR56","first-page":"359","volume":"17","author":"F.E. Zajac","year":"1989","unstructured":"Zajac, F.E.: Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17, 359\u2013411 (1989)","journal-title":"Crit. Rev. Biomed. Eng."},{"key":"10096_CR57","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1115\/1.2894094","volume":"114","author":"M.G. Pandy","year":"1992","unstructured":"Pandy, M.G., Anderson, F.C., Hull, D.G.: A parameter optimization approach for the optimal control of large-scale musculoskeletal systems. J. Biomech. Eng. 114, 450\u2013460 (1992). https:\/\/doi.org\/10.1115\/1.2894094","journal-title":"J. Biomech. Eng."},{"key":"10096_CR58","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1123\/JAB.20.4.367","volume":"20","author":"T.S. Buchanan","year":"2004","unstructured":"Buchanan, T.S., Lloyd, D.G., Manal, K., Besier, T.F.: Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command. J. Appl. Biomech. 20, 367\u2013395 (2004). https:\/\/doi.org\/10.1123\/JAB.20.4.367","journal-title":"J. Appl. Biomech."},{"key":"10096_CR59","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/S0021-9290(96)00188-1","volume":"30","author":"C.C. Raasch","year":"1997","unstructured":"Raasch, C.C., Zajac, F.E., Ma, B., Levine, W.S.: Muscle coordination of maximum-speed pedaling. J. Biomech. 30, 595\u2013602 (1997). https:\/\/doi.org\/10.1016\/S0021-9290(96)00188-1","journal-title":"J. Biomech."},{"key":"10096_CR60","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1080\/1025584031000091678","volume":"6","author":"B.R. Umberger","year":"2003","unstructured":"Umberger, B.R., Gerritsen, K.G.M., Martin, P.E.: A model of human muscle energy expenditure. Comput. Methods Biomech. Biomed. Eng. 6, 99\u2013111 (2003). https:\/\/doi.org\/10.1080\/1025584031000091678","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"10096_CR61","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1177\/0954411911429401","volume":"226","author":"Y.C. Lin","year":"2012","unstructured":"Lin, Y.C., Dorn, T.W., Schache, A.G., Pandy, M.G.: Comparison of different methods for estimating muscle forces in human movement. Proc. Inst. Mech. Eng. H 226, 103\u2013112 (2012). https:\/\/doi.org\/10.1177\/0954411911429401","journal-title":"Proc. Inst. Mech. Eng. H"},{"key":"10096_CR62","doi-asserted-by":"publisher","unstructured":"Quental, C., Azevedo, M., Ambr\u00f3sio, J., Gon\u00e7alves, S.B., Folgado, J.: Influence of the Musculotendon Dynamics on the Muscle Force-Sharing Problem of the Shoulder\u2014a Fully Inverse Dynamics Approach. J. Biomech. Eng. 140 (2018). https:\/\/doi.org\/10.1115\/1.4039675","DOI":"10.1115\/1.4039675"},{"key":"10096_CR63","doi-asserted-by":"publisher","first-page":"2344","DOI":"10.1016\/S0006-3495(02)75580-X","volume":"82","author":"J.Z. Liu","year":"2002","unstructured":"Liu, J.Z., Brown, R.W., Yue, G.H.: A dynamical model of muscle activation, fatigue, and recovery. Biophys. J. 82, 2344\u20132359 (2002). https:\/\/doi.org\/10.1016\/S0006-3495(02)75580-X","journal-title":"Biophys. J."},{"key":"10096_CR64","doi-asserted-by":"publisher","first-page":"3046","DOI":"10.1016\/j.jbiomech.2008.07.013","volume":"41","author":"T. Xia","year":"2008","unstructured":"Xia, T., Frey Law, L.A.: A theoretical approach for modeling peripheral muscle fatigue and recovery. J. Biomech. 41, 3046\u20133052 (2008). https:\/\/doi.org\/10.1016\/j.jbiomech.2008.07.013","journal-title":"J. Biomech."},{"key":"10096_CR65","doi-asserted-by":"publisher","DOI":"10.3389\/FPHYS.2024.1366172","volume":"15","author":"F. Michaud","year":"2024","unstructured":"Michaud, F., Beron, S., Lugr\u00eds, U., Cuadrado, J.: Four-compartment muscle fatigue model to predict metabolic inhibition and long-lasting nonmetabolic components. Front. Physiol. 15, 1366172 (2024). https:\/\/doi.org\/10.3389\/FPHYS.2024.1366172","journal-title":"Front. Physiol."},{"key":"10096_CR66","doi-asserted-by":"publisher","DOI":"10.3389\/FPHYS.2023.1167748","volume":"14","author":"F. Michaud","year":"2023","unstructured":"Michaud, F., Frey-Law, L.A., Lugr\u00eds, U., Cuadrado, L., Figueroa-Rodr\u00edguez, J., Cuadrado, J.: Applying a muscle fatigue model when optimizing load-sharing between muscles for short-duration high-intensity exercise: a preliminary study. Front. Physiol. 14, 1167748 (2023). https:\/\/doi.org\/10.3389\/FPHYS.2023.1167748","journal-title":"Front. Physiol."},{"key":"10096_CR67","doi-asserted-by":"publisher","DOI":"10.1002\/WSBM.1457","volume":"11","author":"O. R\u00f6hrle","year":"2019","unstructured":"R\u00f6hrle, O., Yavuz, U., Klotz, T., Negro, F., Heidlauf, T.: Multiscale modeling of the neuromuscular system: coupling neurophysiology and skeletal muscle mechanics. Wiley Interdiscip. Rev., Syst. Biol. Med. 11, e1457 (2019). https:\/\/doi.org\/10.1002\/WSBM.1457","journal-title":"Wiley Interdiscip. Rev., Syst. Biol. Med."},{"key":"10096_CR68","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/S11044-021-09781-1","volume":"52","author":"M.H. Gfrerer","year":"2021","unstructured":"Gfrerer, M.H., Simeon, B.: Fiber-based modeling and simulation of skeletal muscles. Multibody Syst. Dyn. 52, 1\u201330 (2021). https:\/\/doi.org\/10.1007\/S11044-021-09781-1","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR69","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/S11044-023-09876-X","volume":"57","author":"J. Guo","year":"2023","unstructured":"Guo, J., Wang, J., Chen, J., Ren, G., Tian, Q., Guo, C.: Multibody dynamics modeling of human mandibular musculoskeletal system and its applications in surgical planning. Multibody Syst. Dyn. 57, 299\u2013325 (2023). https:\/\/doi.org\/10.1007\/S11044-023-09876-X","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR70","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1177\/09544119221122062","volume":"236","author":"F. Ortes","year":"2022","unstructured":"Ortes, F., Jinha, A., Herzog, W., Ziya Arslan, Y.: Sensitivity of muscle force response of a two-state cross-bridge model to variations in model parameters. Proc. Inst. Mech. Eng. H 236, 1513\u20131520 (2022). https:\/\/doi.org\/10.1177\/09544119221122062","journal-title":"Proc. Inst. Mech. Eng. H"},{"key":"10096_CR71","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/S0096-4174(18)30128-8","volume":"7","author":"A.F. Huxley","year":"1957","unstructured":"Huxley, A.F.: Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255\u2013318 (1957). https:\/\/doi.org\/10.1016\/S0096-4174(18)30128-8","journal-title":"Prog. Biophys. Biophys. Chem."},{"key":"10096_CR72","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/J.JBIOMECH.2018.11.021","volume":"83","author":"A.J. van Soest","year":"2019","unstructured":"van Soest, A.J., Knoek, Casius, L.J.R., Lemaire, K.K.: Huxley-type cross-bridge models in largeish-scale musculoskeletal models; an evaluation of computational cost. J. Biomech. 83, 43\u201348 (2019). https:\/\/doi.org\/10.1016\/J.JBIOMECH.2018.11.021","journal-title":"J. Biomech."},{"key":"10096_CR73","doi-asserted-by":"publisher","DOI":"10.1016\/J.JBIOMECH.2023.111657","volume":"155","author":"J.M. Wakeling","year":"2023","unstructured":"Wakeling, J.M., Febrer-Nafr\u00eda, M., De Groote, F.: A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years. J. Biomech. 155, 111657 (2023). https:\/\/doi.org\/10.1016\/J.JBIOMECH.2023.111657","journal-title":"J. Biomech."},{"key":"10096_CR74","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1115\/1.2891126","volume":"112","author":"G.I. Zahalak","year":"1990","unstructured":"Zahalak, G.I., Ma, S.P.: Muscle activation and contraction: constitutive relations based directly on cross-bridge kinetics. J. Biomech. Eng. 112, 52\u201362 (1990). https:\/\/doi.org\/10.1115\/1.2891126","journal-title":"J. Biomech. Eng."},{"key":"10096_CR75","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7631818","volume":"2018","author":"T.T. Dao","year":"2018","unstructured":"Dao, T.T., Tho, M.C.H.B.: A systematic review of continuum modeling of skeletal muscles: current trends, limitations, and recommendations. Appl. Bionics Biomech. 2018, 7631818 (2018). https:\/\/doi.org\/10.1155\/2018\/7631818","journal-title":"Appl. Bionics Biomech."},{"key":"10096_CR76","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1007\/S10237-016-0850-X","volume":"16","author":"O. R\u00f6hrle","year":"2017","unstructured":"R\u00f6hrle, O., Sprenger, M., Schmitt, S.: A two-muscle, continuum-mechanical forward simulation of the upper limb. Biomech. Model. Mechanobiol. 16, 743\u2013762 (2017). https:\/\/doi.org\/10.1007\/S10237-016-0850-X","journal-title":"Biomech. Model. Mechanobiol."},{"key":"10096_CR77","doi-asserted-by":"publisher","DOI":"10.3389\/FBIOE.2023.1153692","volume":"11","author":"W. Zeng","year":"2023","unstructured":"Zeng, W., Hume, D.R., Lu, Y., Fitzpatrick, C.K., Babcock, C., Myers, C.A., Rullkoetter, P.J., Shelburne, K.B.: Modeling of active skeletal muscles: a 3D continuum approach incorporating multiple muscle interactions. Front. Bioeng. Biotechnol. 11, 1153692 (2023). https:\/\/doi.org\/10.3389\/FBIOE.2023.1153692","journal-title":"Front. Bioeng. Biotechnol."},{"key":"10096_CR78","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/0021-9290(71)90035-2","volume":"4","author":"Y.C. Fung","year":"1971","unstructured":"Fung, Y.C.: Comparison of different models of the heart muscle. J. Biomech. 4, 289\u2013295 (1971). https:\/\/doi.org\/10.1016\/0021-9290(71)90035-2","journal-title":"J. Biomech."},{"key":"10096_CR79","doi-asserted-by":"publisher","first-page":"19","DOI":"10.5194\/ms-7-19-2016","volume":"7","author":"F. Romero","year":"2016","unstructured":"Romero, F., Alonso, F.J.: A comparison among different Hill-type contraction dynamics formulations for muscle force estimation. Mech. Sci. 7, 19\u201329 (2016). https:\/\/doi.org\/10.5194\/ms-7-19-2016","journal-title":"Mech. Sci."},{"key":"10096_CR80","first-page":"399","volume":"136","author":"A. Hill","year":"1949","unstructured":"Hill, A.: The abrupt transition from rest to activity in muscle. Proc. Royal Soc. B 136, 399\u2013420 (1949)","journal-title":"Proc. Royal Soc. B"},{"key":"10096_CR81","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1098\/rspb.1950.0035","volume":"137","author":"A.V. Hill","year":"1950","unstructured":"Hill, A.V.: The series elastic component of muscle. Proc. R. Soc. Lond. B, Biol. Sci. 137, 273\u2013280 (1950)","journal-title":"Proc. R. Soc. Lond. B, Biol. Sci."},{"key":"10096_CR82","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1038\/166415a0","volume":"166","author":"A.V. Hill","year":"1950","unstructured":"Hill, A.V.: Mechanics of the contractile element of muscle. Nature 166, 415\u2013419 (1950)","journal-title":"Nature"},{"key":"10096_CR83","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/978-1-4613-9030-5_5","volume-title":"Multiple Muscle Systems","author":"J.M. Winters","year":"1990","unstructured":"Winters, J.M.: Hill-based muscle models: a systems engineering perspective. In: Multiple Muscle Systems, pp.\u00a069\u201393. Springer, Berlin (1990)"},{"key":"10096_CR84","doi-asserted-by":"publisher","first-page":"976","DOI":"10.1177\/0954411916659894","volume":"230","author":"F. Heinen","year":"2016","unstructured":"Heinen, F., Lund, M.E., Rasmussen, J., De Zee, M.: Muscle-tendon unit scaling methods of Hill-type musculoskeletal models: an overview. Proc. Inst. Mech. Eng. H 230, 976\u2013984 (2016). https:\/\/doi.org\/10.1177\/0954411916659894","journal-title":"Proc. Inst. Mech. Eng. H"},{"key":"10096_CR85","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1115\/1.1531112","volume":"125","author":"D.G. Thelen","year":"2003","unstructured":"Thelen, D.G.: Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. J. Biomech. Eng. 125, 70\u201377 (2003). https:\/\/doi.org\/10.1115\/1.1531112","journal-title":"J. Biomech. Eng."},{"key":"10096_CR86","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1016\/S0045-7825(97)00162-X","volume":"151","author":"J.A.C. Martins","year":"1998","unstructured":"Martins, J.A.C., Pires, E.B., Salvado, R., Dinis, P.B.: A numerical model of passive and active behavior of skeletal muscles. Comput. Methods Appl. Mech. Eng. 151, 419\u2013433 (1998). https:\/\/doi.org\/10.1016\/S0045-7825(97)00162-X","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10096_CR87","unstructured":"Kaplan, M.L.: Efficient Optimal Control of Large-Scale Biomechanical Systems. PhD Thesis (2000)"},{"key":"10096_CR88","doi-asserted-by":"publisher","unstructured":"Millard, M., Uchida, T., Seth, A., Delp, S.L.: Flexing computational muscle: Modeling and simulation of musculotendon dynamics. J. Biomech. Eng. 135 (2013). https:\/\/doi.org\/10.1115\/1.4023390\/371394","DOI":"10.1115\/1.4023390\/371394"},{"key":"10096_CR89","doi-asserted-by":"publisher","first-page":"2068","DOI":"10.1109\/TBME.2016.2586891","volume":"63","author":"A. Rajagopal","year":"2016","unstructured":"Rajagopal, A., Dembia, C.L., DeMers, M.S., Delp, D.D., Hicks, J.L., Delp, S.L.: Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans. Biomed. Eng. 63, 2068\u20132079 (2016). https:\/\/doi.org\/10.1109\/TBME.2016.2586891","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"10096_CR90","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s11044-022-09843-y","volume":"56","author":"M.R. Silva","year":"2022","unstructured":"Silva, M.R., Marques, F., Silva, M.T., Flores, P.: A comparison of spherical joint models in the dynamic analysis of rigid mechanical systems: ideal, dry, hydrodynamic and bushing approaches. Multibody Syst. Dyn. 56, 221\u2013266 (2022). https:\/\/doi.org\/10.1007\/s11044-022-09843-y","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR91","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/978-3-030-88751-3_9","volume-title":"Multibody Mechatronic Systems. MuSMe 2021. Mechanisms and Machine Science","author":"M.R. Silva","year":"2022","unstructured":"Silva, M.R., Marques, F., Silva, M.T., Flores, P.: Modelling spherical joints in multibody systems. In: Pucheta, M., Cardona, A., Preidikman, S., Hecker, R. (eds.) Multibody Mechatronic Systems. MuSMe 2021. Mechanisms and Machine Science, vol.\u00a0110, pp.\u00a085\u201393. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-88751-3_9"},{"key":"10096_CR92","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-16190-7","volume-title":"Concepts and Formulations for Spatial Multibody Dynamics","author":"P. Flores","year":"2015","unstructured":"Flores, P.: Concepts and Formulations for Spatial Multibody Dynamics. Springer, Cham (2015)"},{"key":"10096_CR93","volume-title":"Planar Multibody Dynamics: Formulation, Programming with MATLAB\u00ae, and Applications","author":"P.E. Nikravesh","year":"2019","unstructured":"Nikravesh, P.E.: Planar Multibody Dynamics: Formulation, Programming with MATLAB\u00ae, and Applications. CRC Press, Boca Raton (2019)"},{"key":"10096_CR94","volume-title":"ECCOMAS Thematic Conference on Multibody Dynamics 2023","author":"S.B. Gon\u00e7alves","year":"2023","unstructured":"Gon\u00e7alves, S.B., Roupa, I., Tavares da Silva, M.: On the analysis of fully Cartesian coordinates \u2013 a comparison between a reduced and full-defined modelling approach in spatial mechanisms. In: ECCOMAS Thematic Conference on Multibody Dynamics 2023, Lisbon, Portugal (2023)"},{"key":"10096_CR95","volume-title":"MMT Symposium","author":"S.B. Gon\u00e7alves","year":"2024","unstructured":"Gon\u00e7alves, S.B., Flores, P., Silva, M.T.: On the modeling of musculotendon units with fully Cartesian coordinates and a generic rigid body. In: MMT Symposium, Guimar\u00e3es, Portugal (2024)"},{"key":"10096_CR96","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1615\/CritRevBiomedEng.v25.i4-5.20","volume":"25","author":"D. Tsirakos","year":"1997","unstructured":"Tsirakos, D., Baltzopoulos, V., Bartlett, R.: Inverse optimization: functional and physiological considerations related to the force-sharing problem. Crit. Rev. Biomed. Eng. 25, 371\u2013407 (1997). https:\/\/doi.org\/10.1615\/CritRevBiomedEng.v25.i4-5.20","journal-title":"Crit. Rev. Biomed. Eng."},{"key":"10096_CR97","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/S0021-9290(00)00191-3","volume":"34","author":"J. Rasmussen","year":"2001","unstructured":"Rasmussen, J., Damsgaard, M., Voigt, M.: Muscle recruitment by the min\/max criterion - a comparative numerical study. J. Biomech. 34, 409\u2013415 (2001). https:\/\/doi.org\/10.1016\/S0021-9290(00)00191-3","journal-title":"J. Biomech."},{"key":"10096_CR98","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1016\/0021-9290(94)00145-T","volume":"28","author":"G.T. Yamaguchi","year":"1995","unstructured":"Yamaguchi, G.T., Moran, D.W., Si, J.: A computationally efficient method for solving the redundant problem in biomechanics. J. Biomech. 28, 999\u20131005 (1995). https:\/\/doi.org\/10.1016\/0021-9290(94)00145-T","journal-title":"J. Biomech."},{"key":"10096_CR99","doi-asserted-by":"publisher","first-page":"1108","DOI":"10.1177\/0954411914556790","volume":"228","author":"R. Dumas","year":"2014","unstructured":"Dumas, R., Moissenet, F., Lafon, Y., Cheze, L.: Multi-objective optimisation for musculoskeletal modelling: application to a planar elbow model. Proc. Inst. Mech. Eng. H 228, 1108\u20131113 (2014). https:\/\/doi.org\/10.1177\/0954411914556790","journal-title":"Proc. Inst. Mech. Eng. H"},{"key":"10096_CR100","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.crme.2012.01.002","volume":"340","author":"A. Bensghaier","year":"2012","unstructured":"Bensghaier, A., Romdhane, L., Benouezdou, F.: Multi-objective optimization to predict muscle tensions in a pinch function using genetic algorithm. C. R., M\u00e9c. 340, 139\u2013155 (2012). https:\/\/doi.org\/10.1016\/j.crme.2012.01.002","journal-title":"C. R., M\u00e9c."},{"key":"10096_CR101","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s11044-006-9019-1","volume":"16","author":"C.L. Bottasso","year":"2006","unstructured":"Bottasso, C.L., Prilutsky, B.I., Croce, A., Imberti, E., Sartirana, S.: A numerical procedure for inferring from experimental data the optimization cost functions using a multibody model of the neuro-musculoskeletal system. Multibody Syst. Dyn. 16, 123\u2013154 (2006). https:\/\/doi.org\/10.1007\/s11044-006-9019-1","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR102","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1016\/0021-9290(81)90035-X","volume":"14","author":"R.D. Crowninshield","year":"1981","unstructured":"Crowninshield, R.D., Brand, R.A.: A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14, 793\u2013801 (1981). https:\/\/doi.org\/10.1016\/0021-9290(81)90035-X","journal-title":"J. Biomech."},{"key":"10096_CR103","doi-asserted-by":"publisher","unstructured":"Shourijeh, M.S., Mehrabi, N., McPhee, J.: Forward Static Optimization in Dynamic Simulation of Human Musculoskeletal Systems: a Proof-of-Concept Study. J. Comput. Nonlinear Dyn. 12 (2017). https:\/\/doi.org\/10.1115\/1.4036195\/474412","DOI":"10.1115\/1.4036195\/474412"},{"key":"10096_CR104","doi-asserted-by":"publisher","first-page":"3459","DOI":"10.1016\/j.jbiomech.2014.09.013","volume":"47","author":"M.M. Morrow","year":"2014","unstructured":"Morrow, M.M., Rankin, J.W., Neptune, R.R., Kaufman, K.R.: A comparison of static and dynamic optimization muscle force predictions during wheelchair propulsion. J. Biomech. 47, 3459\u20133465 (2014). https:\/\/doi.org\/10.1016\/j.jbiomech.2014.09.013","journal-title":"J. Biomech."},{"key":"10096_CR105","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1016\/j.jbiomech.2005.02.010","volume":"39","author":"D.G. Thelen","year":"2006","unstructured":"Thelen, D.G., Anderson, F.C.: Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. 39, 1107\u20131115 (2006). https:\/\/doi.org\/10.1016\/j.jbiomech.2005.02.010","journal-title":"J. Biomech."},{"key":"10096_CR106","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1016\/J.JBIOMECH.2004.11.027","volume":"39","author":"G. Li","year":"2006","unstructured":"Li, G., Pierce, J.E., Herndon, J.H.: A global optimization method for prediction of muscle forces of human musculoskeletal system. J. Biomech. 39, 522\u2013529 (2006). https:\/\/doi.org\/10.1016\/J.JBIOMECH.2004.11.027","journal-title":"J. Biomech."},{"key":"10096_CR107","doi-asserted-by":"publisher","DOI":"10.1115\/1.1392310","volume":"123","author":"F.C. Anderson","year":"2001","unstructured":"Anderson, F.C., Pandy, M.G.: Dynamic optimization of human walking. J. Biomech. Eng. 123, 381 (2001). https:\/\/doi.org\/10.1115\/1.1392310","journal-title":"J. Biomech. Eng."},{"key":"10096_CR108","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1080\/10255849908907988","volume":"2","author":"F.C. Anderson","year":"1999","unstructured":"Anderson, F.C., Pandy, M.G.: A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2, 201\u2013231 (1999). https:\/\/doi.org\/10.1080\/10255849908907988","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"10096_CR109","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s11044-016-9529-4","volume":"38","author":"C. Quental","year":"2016","unstructured":"Quental, C., Folgado, J., Ambr\u00f3sio, J.: A window moving inverse dynamics optimization for biomechanics of motion. Multibody Syst. Dyn. 38, 157\u2013171 (2016). https:\/\/doi.org\/10.1007\/s11044-016-9529-4","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR110","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1007\/978-3-030-43195-2_52","volume-title":"International Symposium on Computer Methods in Biomechanics and Biomedical Engineering","author":"R. Mateus","year":"2019","unstructured":"Mateus, R., Jo\u00e3o, F., Veloso, A.P.: Differences between static and dynamical optimization methods in musculoskeletal modeling estimations to study elite athletes. In: International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, pp.\u00a0624\u2013631. Springer, Berlin (2019). https:\/\/doi.org\/10.1007\/978-3-030-43195-2_52"},{"key":"10096_CR111","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1097\/COC.0b013e31817f9e00","volume":"34","author":"F.C. Anderson","year":"2001","unstructured":"Anderson, F.C., Pandy, M.G.: Static and dynamic optimization solutions for gait are practically equivalent. J. Biomech. 34, 153\u2013161 (2001). https:\/\/doi.org\/10.1097\/COC.0b013e31817f9e00","journal-title":"J. Biomech."},{"key":"10096_CR112","volume-title":"MMT Symposium","author":"M. Rodrigues da Silva","year":"2024","unstructured":"Rodrigues da Silva, M., Sousa, M.F., Marques, F., Gon\u00e7alves, S.B., da Silva, M.T., Flores, P.: Modeling and analysis of the ankle joint complex with muscles. In: MMT Symposium, Guimar\u00e3es, Portugal (2024)"},{"key":"10096_CR113","doi-asserted-by":"publisher","DOI":"10.1016\/J.JBIOMECH.2023.111623","volume":"154","author":"S.D. Uhlrich","year":"2023","unstructured":"Uhlrich, S.D., Uchida, T.K., Lee, M.R., Delp, S.L.: Ten steps to becoming a musculoskeletal simulation expert: a half-century of progress and outlook for the future. J. Biomech. 154, 111623 (2023). https:\/\/doi.org\/10.1016\/J.JBIOMECH.2023.111623","journal-title":"J. Biomech."},{"key":"10096_CR114","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1152\/JAPPLPHYSIOL.00296.2024","volume":"137","author":"L.S. Persad","year":"2024","unstructured":"Persad, L.S., Wang, Z., Pino, P.A., Binder-Markey, B.I., Kaufman, K.R., Lieber, R.L.: Specific tension of human muscle in vivo: a systematic review. J Appl Physiol. 137, 945\u2013962 (2024). https:\/\/doi.org\/10.1152\/JAPPLPHYSIOL.00296.2024","journal-title":"J Appl Physiol."},{"key":"10096_CR115","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1002\/JOR.22023","volume":"30","author":"B.J. Fregly","year":"2012","unstructured":"Fregly, B.J., Besier, T.F., Lloyd, D.G., Delp, S.L., Banks, S.A., Pandy, M.G., D\u2019Lima, D.D.: Grand challenge competition to predict in vivo knee loads. J. Orthop. Res. 30, 503\u2013513 (2012). https:\/\/doi.org\/10.1002\/JOR.22023","journal-title":"J. Orthop. Res."},{"key":"10096_CR116","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/S12984-021-00806-6","volume":"18","author":"F. Michaud","year":"2021","unstructured":"Michaud, F., Lamas, M., Lugr\u00eds, U., Cuadrado, J.: A fair and EMG-validated comparison of recruitment criteria, musculotendon models and muscle coordination strategies, for the inverse-dynamics based optimization of muscle forces during gait. J. NeuroEng. Rehabil. 18, 1\u201315 (2021). https:\/\/doi.org\/10.1186\/S12984-021-00806-6","journal-title":"J. NeuroEng. Rehabil."},{"key":"10096_CR117","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/S11044-024-09997-X","volume":"64","author":"M. Lavaill","year":"2024","unstructured":"Lavaill, M., Pizzolato, C., Bolsterlee, B., Martelli, S., Pivonka, P.: Benchmark and validation of state-of-the-art muscle recruitment strategies in shoulder modelling. Multibody Syst. Dyn. 64, 105\u2013120 (2024). https:\/\/doi.org\/10.1007\/S11044-024-09997-X","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR118","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1177\/0954411911431516","volume":"226","author":"M.E. Lund","year":"2012","unstructured":"Lund, M.E., de Zee, M., Andersen, M.S., Rasmussen, J.: On validation of multibody musculoskeletal models. Proc. Inst. Mech. Eng. H 226, 82\u201394 (2012). https:\/\/doi.org\/10.1177\/0954411911431516","journal-title":"Proc. Inst. Mech. Eng. H"},{"key":"10096_CR119","doi-asserted-by":"publisher","DOI":"10.3390\/APP11052037","volume":"11","author":"B.J. Fregly","year":"2021","unstructured":"Fregly, B.J.: A conceptual blueprint for making neuromusculoskeletal models clinically useful. Appl. Sci. 11, 2037 (2021). https:\/\/doi.org\/10.3390\/APP11052037","journal-title":"Appl. Sci."},{"key":"10096_CR120","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1007\/S11517-013-1099-5","volume":"51","author":"B. Bolsterlee","year":"2013","unstructured":"Bolsterlee, B., Veeger, D.H.E.J., Chadwick, E.K.: Clinical applications of musculoskeletal modelling for the shoulder and upper limb. Med. Biol. Eng. Comput. 51, 953\u2013963 (2013). https:\/\/doi.org\/10.1007\/S11517-013-1099-5","journal-title":"Med. Biol. Eng. Comput."},{"key":"10096_CR121","doi-asserted-by":"publisher","DOI":"10.1016\/J.CLINBIOMECH.2022.105682","volume":"96","author":"S.B. Gon\u00e7alves","year":"2022","unstructured":"Gon\u00e7alves, S.B., Lama, S.B.C., da Silva, M.T.: Three decades of gait index development: a comparative review of clinical and research gait indices. Clin. Biomech. 96, 105682 (2022). https:\/\/doi.org\/10.1016\/J.CLINBIOMECH.2022.105682","journal-title":"Clin. Biomech."},{"key":"10096_CR122","doi-asserted-by":"crossref","unstructured":"Schiehlen, W.: History of benchmark problems in multibody dynamics. In: Multibody Dynamics: Computational Methods and Applications, pp.\u00a0357\u2013368 (2014)","DOI":"10.1007\/978-3-319-07260-9_15"},{"key":"10096_CR123","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/S11044-016-9514-Y","volume":"37","author":"O.A. Bauchau","year":"2016","unstructured":"Bauchau, O.A., Betsch, P., Cardona, A., Gerstmayr, J., Jonker, B., Masarati, P., Sonneville, V.: Validation of flexible multibody dynamics beam formulations using benchmark problems. Multibody Syst. Dyn. 37, 29\u201348 (2016). https:\/\/doi.org\/10.1007\/S11044-016-9514-Y","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR124","doi-asserted-by":"publisher","unstructured":"Callejo, A., Dopico, D.: Direct sensitivity analysis of multibody systems: a vehicle dynamics benchmark. J. Comput. Nonlinear Dyn. 14 (2019). https:\/\/doi.org\/10.1115\/1.4041960\/400837","DOI":"10.1115\/1.4041960\/400837"},{"key":"10096_CR125","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/S11044-023-09896-7","volume":"58","author":"M. Ruggiu","year":"2023","unstructured":"Ruggiu, M., Gonz\u00e1lez, F.: A benchmark problem with singularities for multibody system dynamics formulations with constraints. Multibody Syst. Dyn. 58, 181\u2013196 (2023). https:\/\/doi.org\/10.1007\/S11044-023-09896-7","journal-title":"Multibody Syst. Dyn."},{"key":"10096_CR126","first-page":"511","volume-title":"Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference, ENOC-2005","author":"A.L. Schwab","year":"2005","unstructured":"Schwab, A.L., Meijaard, J.P., Papadopoulos, J.M.: A multibody dynamics benchmark on the equations of motion of an uncontrolled bicycle. In: Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference, ENOC-2005, Eindhoven University of Technology, The Netherlands, August 7\u201312, 2005, pp.\u00a0511\u2013521 (2005)"},{"key":"10096_CR127","doi-asserted-by":"publisher","first-page":"660","DOI":"10.1080\/00423114.2021.1959038","volume":"61","author":"Y. Bezin","year":"2023","unstructured":"Bezin, Y., P\u00e5lsson, B.A., Kik, W., Schreiber, P., Clarke, J., Beuter, V., Sebes, M., Persson, I., Magalhaes, H., Wang, P., Klauser, P.: Multibody simulation benchmark for dynamic vehicle\u2013track interaction in switches and crossings: results and method statements. Veh. Syst. Dyn. 61, 660\u2013697 (2023). https:\/\/doi.org\/10.1080\/00423114.2021.1959038","journal-title":"Veh. Syst. Dyn."},{"key":"10096_CR128","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1080\/00423114.2021.1942079","volume":"61","author":"Y. Bezin","year":"2023","unstructured":"Bezin, Y., P\u00e5lsson, B.A.: Multibody simulation benchmark for dynamic vehicle-track interaction in switches and crossings: modelling description and simulation tasks. Veh. Syst. Dyn. 61, 644\u2013659 (2023). https:\/\/doi.org\/10.1080\/00423114.2021.1942079","journal-title":"Veh. Syst. Dyn."}],"container-title":["Multibody System Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11044-025-10096-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11044-025-10096-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11044-025-10096-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:36:47Z","timestamp":1777369007000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11044-025-10096-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,11]]},"references-count":128,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10096"],"URL":"https:\/\/doi.org\/10.1007\/s11044-025-10096-8","relation":{},"ISSN":["1384-5640","1573-272X"],"issn-type":[{"value":"1384-5640","type":"print"},{"value":"1573-272X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,11]]},"assertion":[{"value":"30 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}