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Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.ORCID iD: 0000-0001-5317-2779
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
2009 (English)Report (Other academic)
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. The simulation method is explained in detail. 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. Despite this unrealistic behavior the error maybe small enough to be accepted for specific applications. These results is a starting point start for achieving better results of inverse musculoskeletal simulations from a numerical point of view.

Place, publisher, year, edition, pages
Sundsvall, 2009. , p. 10
Series
Rapportserie FSCN, ISSN 1650-5387 ; 2009:52
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-9937OAI: oai:DiVA.org:miun-9937DiVA, id: diva2:240713
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2016-06-20Bibliographically approved
In thesis
1. New methods for movement technique development in cross-country skiing using mathematical models and simulation
Open this publication in new window or tab >>New methods for movement technique development in cross-country skiing using mathematical models and simulation
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate Thesis is devoted to the presentation and discussion of some new contributions in applied mathematics directed towards scientific computing in sports engineering. It considers inverse problems of biomechanical simulations with rigid body musculoskeletal systems especially in cross-country skiing. This is a contrast to the main research on cross-country skiing biomechanics, which is based mainly on experimental testing alone. The thesis consists of an introduction and five papers. The introduction motivates the context of the papers and puts them into a more general framework. Two papers (D and E) consider studies of real questions in cross-country skiing, which are modelled and simulated. The results give some interesting indications, concerning these challenging questions, which can be used as a basis for further research. However, the measurements are not accurate enough to give the final answers. Paper C is a simulation study which is more extensive than paper D and E, and is compared to electromyography measurements in the literature. Validation in biomechanical simulations is difficult and reducing mathematical errors is one way of reaching closer to more realistic results. Paper A examines well-posedness for forward dynamics with full muscle dynamics. Moreover, paper B is a technical report which describes the problem formulation and mathematical models and simulation from paper A in more detail. Our new modelling together with the simulations enable new possibilities. This is similar to simulations of applications in other engineering fields, and need in the same way be handled with care in order to achieve reliable results. The results in this thesis indicate that it can be very useful to use mathematical modelling and numerical simulations when describing cross-country skiing biomechanics. Hence, this thesis contributes to the possibility of beginning to use and develop such modelling and simulation techniques also in this context.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2009
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 41
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-10041 (URN)978-91-86073-53-4 (ISBN)
Presentation
2009-11-11, Q221, Mid Sweden Univ, Campus Östersund, Östersund, 13:00 (English)
Supervisors
Available from: 2009-10-15 Created: 2009-10-15 Last updated: 2016-06-20Bibliographically approved

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Lund Ohlsson, MarieGulliksson, Mårten

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