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Regularity Aspects in Inverse Musculoskeletal Biomechanics
Mittuniversitetet, Institutionen för teknik och hållbar utveckling (-2013).ORCID iD: 0000-0001-5317-2779
Mittuniversitetet, Institutionen för teknik och hållbar utveckling (-2013).
Mittuniversitetet, Institutionen för naturvetenskap, teknik och matematik (-2012).
2008 (English)In: NUMERICAL ANALYSIS AND APPLIED MATHEMATICS / [ed] Simos, TE; Psihoyios, G; Tsitouras, C, American Institute of Physics (AIP) , 2008, p. 368-371Conference paper, Published paper (Refereed)
Abstract [en]

Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling, which is unrealistic but the error maybe small enough to be accepted for specific applications. These results are a start to ensure better results of inverse musculoskeletal simulations from a numerical point of view.

Place, publisher, year, edition, pages
American Institute of Physics (AIP) , 2008. p. 368-371
Series
AIP conference proceedings, ISSN 0094-243X ; 1048
Keywords [en]
Least Squares Problem; Optimization; Inverse problem; Forward dynamics
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:gih:diva-7830DOI: 10.1063/1.2990935ISI: 000259567000087Scopus ID: 2-s2.0-54049098396ISBN: 978-0-7354-0576-9 (print)OAI: oai:DiVA.org:gih-7830DiVA, id: diva2:1801153
Conference
International Conference on Numerical Analysis and Applied Mathematics, Sep 16-20, 2008, Psalidi, Greece
Available from: 2009-09-29 Created: 2023-09-29

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Lund, MarieStåhl, FredrikGulliksson, Mårten

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