{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:45:45Z","timestamp":1776793545186,"version":"3.51.2"},"reference-count":83,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T00:00:00Z","timestamp":1654646400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003130","name":"fonds wetenschappelijk onderzoek","doi-asserted-by":"publisher","award":["1S82320N"],"award-info":[{"award-number":["1S82320N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["G079216N"],"award-info":[{"award-number":["G079216N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009338","type":"journal-article","created":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T13:29:30Z","timestamp":1654694970000},"page":"e1009338","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":37,"title":["An approximate stochastic optimal control framework to simulate nonlinear neuro-musculoskeletal models in the presence of noise"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6180-8730","authenticated-orcid":true,"given":"Tom","family":"Van Wouwe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6854-9444","authenticated-orcid":true,"given":"Lena H.","family":"Ting","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4255-8673","authenticated-orcid":true,"given":"Friedl","family":"De Groote","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2022,6,8]]},"reference":[{"key":"pcbi.1009338.ref001","first-page":"1","article-title":"Optimal control modeling of human movement.","author":"BR Umberger","year":"2018","journal-title":"Handb Hum Motion."},{"key":"pcbi.1009338.ref002","author":"CL Dembia","journal-title":"OpenSim Moco: Musculoskeletal optimal control"},{"key":"pcbi.1009338.ref003","author":"E Todorov","year":"2002","journal-title":"Optimal feedback control as a theory of motor coordination"},{"key":"pcbi.1009338.ref004","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.jbiomech.2009.12.012","article-title":"Optimality principles for model-based prediction of human gait","volume":"43","author":"M Ackermann","year":"2010","journal-title":"J Biomech"},{"key":"pcbi.1009338.ref005","first-page":"20202432","article-title":"Perspective on musculoskeletal modelling and predictive simulations of human movement to assess the neuromechanics of gait.","volume":"288","author":"F De Groote","year":"2021","journal-title":"Proceedings Biol Sci."},{"key":"pcbi.1009338.ref006","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2019.0402","article-title":"Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies.","volume":"16","author":"A Falisse","year":"2019","journal-title":"J R Soc Interface."},{"key":"pcbi.1009338.ref007","doi-asserted-by":"crossref","first-page":"e1003869","DOI":"10.1371\/journal.pcbi.1003869","article-title":"Beyond Muscles Stiffness: Importance of State-Estimation to Account for Very Fast Motor Corrections.","volume":"10","author":"F Crevecoeur","year":"2014","journal-title":"PLoS Comput Biol."},{"key":"pcbi.1009338.ref008","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1152\/jn.01089.2011","article-title":"Influence of the behavioral goal and environmental obstacles on rapid feedback responses","volume":"108","author":"JY Nashed","year":"2012","journal-title":"J Neurophysiol"},{"key":"pcbi.1009338.ref009","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0165-0270(98)00063-6","article-title":"On the optimal control of behaviour: a stochastic perspective","volume":"83","author":"CM Harris","year":"1998","journal-title":"J Neurosci Methods"},{"key":"pcbi.1009338.ref010","doi-asserted-by":"crossref","first-page":"8135","DOI":"10.1523\/JNEUROSCI.0770-19.2019","article-title":"Robust Control in Human Reaching Movements: A Model-Free Strategy to Compensate for Unpredictable Disturbances","volume":"39","author":"F Crevecoeur","year":"2019","journal-title":"J Neurosci"},{"key":"pcbi.1009338.ref011","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1038\/29528","article-title":"Signal-dependent Noise determines Motor Planning","volume":"394","author":"C Harris","year":"1998","journal-title":"Nature"},{"key":"pcbi.1009338.ref012","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.tics.2012.09.008","article-title":"The computational and neural basis of voluntary motor control and planning","author":"SH Scott","year":"2012","journal-title":"Trends in Cognitive Sciences"},{"key":"pcbi.1009338.ref013","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1038\/nn1309","article-title":"Optimality principles in sensorimotor control","volume":"7","author":"E. 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