Abstract
We present parameter estimation results for a full three-dimensional model of the human body with nearly 100 degrees of freedom. This task could only be achieved by the use of sophisticated numerical techniques not only for optimization but also for the model setup. We have developed an object-oriented biomechanical modeling library based on a special form of natural coordinates that does not only serve to establish the full set of equations of motion of highly complex biome-chanical systems, but also to efficiently compute all the derivative information that is required in the parameter estimation context. Our parameter estimation algorithm is based on a multiple shooting state discretization and uses a generalized Gauss–Newton method. Eight experiments are combined in a multiple experiment setting. Inconsistent initial values are treated by a special form of non-stiff Baumgarte relaxation.
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Bock, H.G., ‘Numerical treatment of inverse problems in chemical reaction kinetics’, in Modelling of Chemical Reaction Systems, volume 18 of Springer Series in Chemical Physics, Ebert, K.H., Deuflhard, P. and Jäger, W. (eds.), Springer, Heidelberg, 1981.
Deng, Y.C., ‘Human neck-upper-torso model response to dynamic loading’, Ph.D. Thesis, University of California, Berkley, 1985.
García de Jalón, J. and Bayo, E., Kinematic and Dynamic Simulation of Multibody Systems, Springer, 1994.
Gruber, K., Denoth, J., Stuessi, E. and Ruder, H., ‘The wobbling mass model’, in International Series on Biomechanics, Jonsson, B. (ed.), Vol. 6B, 1987, pp. 1095–1099.
Hahn, U., Entwicklung mehrgliedriger Modelle zur realistischen Simulation dynamischer Prozesse in biologischen Systemen, Diploma Thesis, Eberhard-Karls-Universität Tübingen, 1993.
Kraus, C., Winckler, M. and Bock, H.G., ‘Modeling mechanical DAE using Natural Coordinates’, Mathematical and Computer Modelling of Dynamical Systems, Swets & Zeitlinger, Vol. 7, No. 2, 2001, pp. 145–158.
Schlöder, J.P., ‘Numerische Methoden zur behandlung hochdimensionaler aufgaben der parameteridentifizierung’, Bonner Mathematische Schriften, 187, 1988.
Schulz, V.H., Bock, H.G. and Steinbach, M.C., ‘Exploiting invariants in the numerical solution of multipoint boundary value problems for DAEs’, SIAM Journal of Science and Computer 19, 1998, 440–467.
v. Schwerin, R., MultiBody System SIMulation – Numerical Methods, Algorithms and Software, Springer, 1999.
v. Schwerin, R. and Winckler, M.J., A Guide to the Integrator Library MBSSIM, Version 1.00 IWR-Preprint 94-75, University of Heidelberg, 1994.
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Kraus, C., Bock, HG. & Mutschler, H. Parameter Estimation for Biomechanical Models Based on a Special Form of Natural Coordinates. Multibody Syst Dyn 13, 101–111 (2005). https://doi.org/10.1007/s11044-005-4081-7
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DOI: https://doi.org/10.1007/s11044-005-4081-7