Advances in system identification, neuromuscular modeling and repetitive peripheral magnetic stimulation [Elektronische Ressource] / Michael Bernhardt

Informations

• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 21
• Langue: English
• Poids de l'ouvrage: 10 Mo

Extrait

Lehrstuhl fu¨r Steuerungs- und Regelungstechnik
Technische Universit¨at Mu¨nchen
Univ.-Prof. Dr.-Ing. (Univ. Tokio) Martin Buss
Advances in System Identification,
Neuromuscular Modeling and Repetitive
Peripheral Magnetic Stimulation
Michael Bernhardt
Vollst¨andiger Abdruck der von der Fakult¨at fu¨r Elektrotechnik und Informationstechnik
der Technischen Universit¨at Mu¨nchen zur Erlangung des akademischen Grades eines
Doktor-Ingenieurs (Dr.-Ing.)
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. Thomas Eibert
Pru¨fer der Dissertation:
1. Univ.-Prof. Dr.-Ing. (Univ. Tokio) Martin Buss
2. Univ.-Prof. Dr.-Ing. Dr.-Ing. h.c. Dierk Schr¨oder, i.R.
Die Dissertation wurde am 19.01.2009 bei der Technischen Universit¨at Mu¨nchen einge-
reicht und durch die Fakult¨at fu¨r Elektrotechnik und Informationstechnik am 17.07.2009
angenommen.Foreword
This thesis is the result of almost four years of research done at the Institute of Automatic
Control Engineering and within the Research Group for Sensorimotor Integration, both
at the Technische Universit¨at Mu¨nchen. The research was funded in part by the DFG
(German Research Foundation) within the project ”Induction of adaptively controlled
compound movements of arm and fingers by multichannel repetitive peripheral magnetic
stimulation (RPMS) – early rehabilitation of central paresis”. This work would not have
been possible without the help of many different persons to which I would like to express
my gratitude.
First of all, I thank my doctoral advisers Professor Martin Buss and Professor Albrecht
Struppler. Martin Buss provided an excellent environment for open-minded and interdis-
ciplinary research and had always complete confidence in me. Professor Struppler is an
extraordinary researcher and man who gave me scientific and personal advice whenever I
needed it.
Myworkwassupportedbymanyhighlymotivatedstudentassistantsorbachelor/master
students: BastianBuchholz, CorneliusBuchkremer, DennisDumke,MichaelEibl,Andreas
Gasser, DanielGurdan, Qichen Huang, Yang Ji, Sebastian Kibler, Inga Krause, Yuanyuan
Li, Adrian Lindner, Daniel Meißner, Nik Neusser, Bastian Schmitz, Thomas Spittler, and
Lena Springer. Thank you for your contribution.
During my graduate studies at TUM and during my stay at the Swiss Federal Institute
of Technology Zurich I collaborated with Professor Robert Riener and Dr. Martin Frey
who were my scientific mentors at that time and whom I thank for teaching me so much.
I would like to thank Professor Shohreh Amini and my colleagues Martin Kuschel and
Chih-ChungChenforproofreadingthethesis. FurthermoreIthankmycollaboratorsinthe
Research Group for Sensorimotor Integration Barbara Gebhard and Bernhard Angerer for
helping me with many practical issues, for giving scientific advice and for encouraging me
as friends. I am also indebted to all my colleagues at the Institute of Automatic Control
Engineering and particularly to my office mates Georgios Lidoris, Moritz Große-Wentrup
and Johannes Dold who provided a really joyful atmosphere and helped me with many
smaller and bigger problems.
Finally I want to express my deep gratitude to my parents, my fianc´ee Mehrnoush and
my sister Eva for their strong affection and constant support. Mehrnoush completes my
life with joy and diversion.
Munich, January 2009 Michael Bernhardt
iiiContents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions and Outline of this Thesis . . . . . . . . . . . . . . . . . . . 3
2 Parameter Adaptation and Stable Error Models 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Fundamentals and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Identification Structure, Error Models and Model Equations . . . . 9
2.2.2 The Neural Observer . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Parameter Identification Algorithms. . . . . . . . . . . . . . . . . . 13
2.3 A Modified Levenberg-Marquardt Algorithm . . . . . . . . . . . . . . . . . 18
2.3.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.2 Simulative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Error Models for Linear Parameterization. . . . . . . . . . . . . . . . . . . 21
2.4.1 Error Model A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.2 Error Model A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.3 Error Model A3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Error Models for Nonlinear Parameterization . . . . . . . . . . . . . . . . . 29
2.5.1 Error Model B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.2 Error Model B2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6 Error Models for Separable Nonlinear Parameterization . . . . . . . . . . . 37
2.6.1 Error Model C1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6.2 Error Model C2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 Neuromuscular and Biomechanical Modeling 46
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Fundamentals and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1 Neuromuscular Excitation with RPMS . . . . . . . . . . . . . . . . 47
3.2.2 Bones, Joints, Muscles and Tendons . . . . . . . . . . . . . . . . . . 51
3.2.3 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Force Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 Tendon Leverage of the Index Finger Extension . . . . . . . . . . . 54
vContents
3.3.2 Tendon Leverage of the Index Finger Flexion. . . . . . . . . . . . . 55
3.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Force Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.2 Physiological Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.3 Dynamic Force Response to a Single Stimulus . . . . . . . . . . . . 60
3.4.4 Dynamic Force Response to Repetitive Stimuli . . . . . . . . . . . . 62
3.4.5 Motor Unit Recruitment . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4.6 Complete Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.5 Length-Velocity-Dependencies . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.1 Simulative Quantification . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 Segment Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6.1 Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.2 The Nonlinearities N (α ) and N (α˙ ) . . . . . . . . . . . . . . . . 731 2 2 2
3.6.3 Relaxation Characteristics . . . . . . . . . . . . . . . . . . . . . . . 74
3.6.4 Model Identification and Verification . . . . . . . . . . . . . . . . . 77
3.6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.7 Spastic Joint Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.7.1 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.7.2 Qualitative Model Verification . . . . . . . . . . . . . . . . . . . . . 84
3.7.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 System Identification During RPMS 87
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Identification under Isometric Conditions . . . . . . . . . . . . . . . . . . . 88
4.2.1 Model Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2.2 Identification Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2.3 System Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.4 Simulative Identification . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.5 Experimental Identification . . . . . . . . . . . . . . . . . . . . . . 98
4.2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3 Identification under Nonisometric Conditions . . . . . . . . . . . . . . . . . 104
4.3.1 Model Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.2 Identification Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.3 System Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.4 Simulative Identification . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.5 Experimental Identification . . . . . . . . . . . . .