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New methods for movement technique development in cross-country skiing using mathematical models and simulation
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.ORCID iD: 0000-0001-5317-2779
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: urn:nbn:se:miun:diva-10041ISBN: 978-91-86073-53-4 (print)OAI: oai:DiVA.org:miun-10041DiVA, id: diva2:272471
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
List of papers
1. Regularity Aspects in Inverse Musculoskeletal Biomechanics
Open this publication in new window or tab >>Regularity Aspects in Inverse Musculoskeletal Biomechanics
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
Series
AIP conference proceedings, ISSN 0094-243X ; 1048
Keywords
Least Squares Problem; Optimization; Inverse problem; Forward dynamics
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-9938 (URN)10.1063/1.2990935 (DOI)000259567000087 ()2-s2.0-54049098396 (Scopus ID)978-0-7354-0576-9 (ISBN)
Conference
International Conference on Numerical Analysis and Applied Mathematics, Sep 16-20, 2008, Psalidi, Greece
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2016-09-23Bibliographically approved
2. Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics
Open this publication in new window or tab >>Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics
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
Series
FSCN-rapport ; R-09-80
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-9937 (URN)
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2018-05-09Bibliographically approved
3. A Musculoskeletal Full‐body Simulation of Cross‐Country Skiing
Open this publication in new window or tab >>A Musculoskeletal Full‐body Simulation of Cross‐Country Skiing
2008 (English)In: Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, ISSN 1754-3371, Vol. 222, no P1, p. 11-22Article in journal (Refereed) Published
Abstract [en]

This paper presents a measurement-driven, musculoskeletal, full-body simulation model for biomechanical analysis of the double-poling (DP) technique in cross-country skiing. DP is a fast and powerful full-body movement; therefore, it is interesting to examine whether inverse dynamics using static optimization is working for a musculoskeletal full-body model with high accelerations, a large range of motion, and realistic loads. An experiment was carried out to measure motion and pole force of a skier on a double-poling ergometer. Using the measurement data, a simulation model was implemented in the AnyBody Modeling System (AnyBody Technology A/S, Denmark). Experimental results of motion and pole force from the DP ergometer, and also simulation results of relative muscle force profiles, are presented. These results agree with results found in literature when the kinematics and external kinetics are similar. Consequently, it should be possible to use computer simulations of this type for cross-country skiing simulations. With a simulation model, it is possible to perform optimization studies and to ask and answer ‘what if’ questions. Solutions to such problems are not easy to obtain by traditional testing alone.

Place, publisher, year, edition, pages
London: The Institution of Mechanical Engineers, 2008
Keywords
biomechanics, double poling, ergometer, inverse dynamics
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-9934 (URN)10.1243/17543371JSET10 (DOI)000207664600003 ()2-s2.0-84990348576 (Scopus ID)
Projects
Nationellt vintersportcentrum
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2018-02-08Bibliographically approved
4. Which are the Antagonists to the Pectoralis MajorMuscle in 4th Gear, Free‐style Technique, Cross‐Country Skiing?
Open this publication in new window or tab >>Which are the Antagonists to the Pectoralis MajorMuscle in 4th Gear, Free‐style Technique, Cross‐Country Skiing?
2008 (English)In: Science and Nordic Skiing, Oxford: Meyer & Meyer Sport, 2008, p. 110-118Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Oxford: Meyer & Meyer Sport, 2008
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-9935 (URN)978-1-84126-229-1 (ISBN)
Conference
Science and Nordic Skiing
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2016-06-20Bibliographically approved
5. Using Double‐Poling Simulations to Study the Load Distribution between Teres Major and Latissimus Dorsi
Open this publication in new window or tab >>Using Double‐Poling Simulations to Study the Load Distribution between Teres Major and Latissimus Dorsi
2007 (English)In: Science and Nordic Skiing, Oxford: Meyer & Meyer Sport, 2007, p. 81-89Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Oxford: Meyer & Meyer Sport, 2007
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-9936 (URN)978-1-84126-229-1 (ISBN)
Conference
Science and Nordic Skiing
Available from: 2009-09-29 Created: 2009-09-29 Last updated: 2016-06-20Bibliographically approved

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Lund Ohlsson, Marie

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