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 . . . . . . . . . . . . . . . . . . . . . . 115
4.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
viContents
5 Enhancements for the RPMS-therapy 123
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2 Quantification of Patient Parameters . . . . . . . . . . . . . . . . . . . . . 125
5.2.1 Spasticity Quantification . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2.2 Identification of Muscle Fatigue . . . . . . . . . . . . . . . . . . . . 129
5.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3 Position Controlled Movement Induction . . . . . . . . . . . . . . . . . . . 133
5.3.1 Simplified Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.3.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.4 EMG-Driven Position Control . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.4.1 Stimulation Artifacts and Signal Preprocessing . . . . . . . . . . . . 139
5.4.2 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.4.3 Patient Cooperative Therapy Mode . . . . . . . . . . . . . . . . . . 149
5.4.4 Experiment and Results . . . . . . . . . . . . . . . . . . . . . . . . 149
5.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6 Conclusion 154
6.1 Major Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.2 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
A Derivations and Auxiliary Results 158
A.1 Derivations concerning the SLS-Algorithm . . . . . . . . . . . . . . . . . . 158
TA.2 Positive Semidefiniteness of M =aa . . . . . . . . . . . . . . . . . . . . . 159
A.3 Update Equations Interpreted as PT -Filter . . . . . . . . . . . . . . . . . 1591
A.3.1 Continuous Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
A.3.2 Discrete Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
A.4 Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
A.4.1 Normalized Mean Square Error (NMSE) . . . . . . . . . . . . . . . 160
A.4.2 Relative Model Error . . . . . . . . . . . . . . . . . . . . . . . . . . 161
A.5 Calculation of the Moments of Inertia for the Index Finger Phalanges . . . 161
B The Sensorimotor System and Sensorimotor Deficits 163
B.1 Relevant Neuromuscular Anatomy and Physiology . . . . . . . . . . . . . . 163
B.1.1 The Nervous System and Functional Nerve Cell Classes . . . . . . . 163
B.1.2 The Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
B.1.3 Neuronal Signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
B.1.4 Skeletal Muscle Anatomy. . . . . . . . . . . . . . . . . . . . . . . . 166
B.1.5 Skeletal Muscle Physiology: Innervation, Activation and Contraction 166
B.1.6 Skeletal Muscle Force Generation . . . . . . . . . . . . . . . . . . . 168
B.2 Surface Electromyography . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
B.3 Motor Control and Sensorimotor Integration . . . . . . . . . . . . . . . . . 173
B.3.1 The Brain Motor Centers and Descending Motor Pathways . . . . . 173
viiContents
B.3.2 The Hierarchical Structure of Motor Control System . . . . . . . . 174
B.3.3 Muscle Sensors: The Proprioceptors . . . . . . . . . . . . . . . . . . 175
B.3.4 Reflexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
B.4 Paresis and Spasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
C The Fingertester 180
Bibliography 182
viiiNotations
Abbreviations
APRB Amplitude modulated pseudo random binary
ATP Adenosine triphosphate
CNS Central nervous system
DIP Distal interphalangeal
DOF Degree of freedom
EDC Extensor digitorum communis
EIP Extensor indices proprius
EM Error model
EMG Electromyography
EvMA Estimation of voluntary muscle activity
FDP Flexor digitorum profundus
FDS Flexor digitorum superficialis
GN Gauss-Newton
GS Gradient search
ITAE Integral time multiplied absolute error
LM Levenberg-Marquardt
LMS Least mean squares
LP Linearly parameterized
l.p.e. Linear persistent excitation/linearly persistently exciting
l.o.l. Location of lesion
LTI Linear time invariant
LAP Linear adaptive prediction
m. Musculus
MA Moving average
MAP Muscle action potential
MCP Metacarpophalangeal
MIL Matrix inversion lemma
MLP Multi layer perceptron
MU Motor unit
MVC Maximum voluntary contraction
NARX Nonlinear autoregressive with exogenous input
NFIR Nonlinear finite impulse response
NLP Nonlinearly parameterized
NMSE Normalized mean square error
ixNotations
NRBF Normalized radial basis function
n.l.p.e. Nonlinear local persistent excitation
PCA Principle component analysis
PID Proportional-integral-derivative
PIP Proximal interphalangeal
PSD Power spectral density
RBF Radial basis function
RLS Recursive least squares
RMS Root mean square
SNLP Separable nonlinearly parameterized
t.s.l. Time since lesion
wRMS Weighted RMS
WSS Wide sense stationary
ZDVC Zero degree voluntary contraction
Conventions
Scalars, Vectors, and Matrices
Scalars are denoted by upper and lower case letters in italic type. Vectors are denoted
by underlined lower case letters in italic type, as the vector x is composed of elements x .i
Matrices are denoted by underlined upper case letters in italic type, as the matrix M is
th thcomposed of elements M (i row, j column).ij
x or X Scalar
x Vector
X Matrix
TX Transposed of X
−1X Inverse of X
+X Pseudoinverse of X
f(·) Scalar function
f(·) Vector function
xˆ Estimated or predicted value of x
x˜ Estimation error: x˜=x−xˆ
x Average value of x
k·k p-normp
∂f(x)
∇f(x) = Gradient vector
∂x
x