Neuromuscular dynamics in the context of motor redundancy

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Content NEUROMUSCULAR DYNAMICS IN THE CONTEXT OF MOTOR
REDUNDANCY
by
Cornelius Raths (Kornelius R´ acz)
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(NEUROSCIENCE)
August 2012
Copyright 2012 Cornelius Raths (Kornelius R´ acz)
F¨ ur Włodek Bz´ owka (21.06.1979 - 26.12.2007)
ii
Acknowledgements
In the spring of 2007, having completed three lab rotations, I met with Professor Ger-
ald Loeb to break to him my decision to join his lab, in which I had done my second
lab rotation, working on the machine learning problem of predicting elbow angles from
should coordinates. My overly idealistic plan for my dissertation project was to develop
a neural hand prosthesis, having worked on the development of Brain-Computer Inter-
faces for my Master’s thesis in Computer Science. Professor Loeb correctly pointed out
that the neural control of the hand was poorly understood (and additionally, I was hardly
familiar with what was understood), rendering the development of such a prosthesis
premature. To alleviate my shortcomings and enable me to potentially embark on this
project in the long-term future, he introduced me to Francisco Valero-Cuevas, who was
soon going to join the Biomedical Engineering Department at USC. Having completed a
successful and very instructive fourth lab rotation in the summer of 2007, and been very
much involved in the establishment of the new Brain-Body Dynamics Lab, I decided to
join.
I have always admired Francisco for his intuition: where it took me hours to come
up with an idea of how to analyze or interpret data, he suggested an excellent solution
within minutes, if not seconds. Many times, this has reinvigorated my enthusiasm for
the projects described in this dissertation. Furthermore, I would like to thank him for
his kind and generous attitude, allowing me to complete two Master of Science degrees
iii
in addition to the PhD, and the many pleasant conversations we had, sometimes outside
the scope of our immediate work.
Naturally, I extend my thanks to the person to whom I owe having met Francisco:
Professor Gerald Loeb, who did however serve on my Guidance Committee. While
Francisco was a great source of encouragement for my ideas and plans, Professor Loeb
was antipodal in that in our numerous and lengthy discussions (or should I say, lessons),
he challenged them, based on scientific principle and experience. The challenges were
never general, always addressing details, but also providing ideas to overcome demon-
strated shortcomings. When it comes to muscle physiology, his knowlege is unmatched.
Another important source of scientific challenge, but also of means to ”get things
done”, joined our lab in the summer of 2008: Jason Kutch, then a post-doc, now a pro-
fessor in the Biokinesiology division. I had first met Jason at a workshop on mathematics
and biosciences at Ohio State University earlier that year, when he had just completed
his PhD. His combined mathematics and physiology background allowed Jason more
than anybody to identify appropriate ways to model and simulate scientific phenomena
and to test hypotheses. Without his ideas, much of the work presented here would not
have been possible. I am grateful that he served on my Dissertation committee.
Speaking of interdisciplinarity, I would also like to express my gratitude to Profes-
sor Madhusudan Venkadesan, Francisco’s PhD student at Cornell University until 2007
and now a Professor at the National Centre for Biological Sciences in Bangalore, India.
Although we talked only briefly at a noise and balance workshop in Banff, Alberta,
Canada, these conversations proved to be some of the most important of my entire PhD.
While the idea that motor variability in terms of muscle and endpoint force reflects
fatigue mitigation mechanisms and is not simply uncorrelated noise came to me previ-
ously, it was thanks to Madhu that I started thinking of using differential equations to
model fatigue and recovery and combine these models with optimization.
iv
While I was not short of projects and work, a conversation between Francisco and
Professor Nina Bradley, of the Biokinesiology Division, in 2009, would lead to a very
fruitful collaboration on the motor development of domestic chick. This project taught
me a lot about the use of statistics in life science research and I am deeply grateful to
Nina for her devotion to precision both methodologically and in terms of expressing sci-
entific findings. Naturally, I would also like to thank her to have served on my Guidance
and Dissertation Committees, in fact, as the chair on the latter.
Besides faculty, I am indebted first of all to Sudarshan Dayanidhi, who joined the
lab and graduated at the same time as I. During those 5 years in between, we became
close friends and I will never forget that he attended my wedding in China in the fall of
2010, and served as one of the best men. Besides this, he has always found the time for
a discussion on physiology or science in general, being an excellent Physical Therapist,
and to participate in one of my experiments. I hope that my presence in the lab was half
as useful to his work as my presence was to his.
Those 5 years I also shared with Manish Kurse, who had accompanied Francisco
from Cornell, having joined the lab the year before. Manish helped me tremendously
in modeling isometric motor task, with his excellent background in mechanics and opti-
mization. Furthermore, I will always kindly remember his cheerful personality.
Besides, I would like to thank Josh Inouye, for having designed and built the second
generation of the TIM grasping device. Moreover, his productivity, work ethic and
determination towards his work have been inspirational. I would also like to thank Dan
Brown, formerly at Cornell and whom unfortunately I have never met, for having built
the first generation of the TIM and having mathematically modeled the motor task of
simultaneous tripod grasp and thumb oscillation.
None of university research would be possible without the contribution of admin-
istrators, who make sure that stipends are paid, equipment is purchased and forms are
v
filled out. In this regard, I would like to mention the great work done by Adriana Cis-
neros, at the RTH Business Center, and Vanessa Clark, at the Neuroscience Graduate
Program. But most of all, I would like to thank Linda Bazilian, especially for helping
me stay at USC when there was a chance of my having to drop out due to university
regulations. I am grateful to the Neuroscience Program as a whole for having provided
this awesome opportunity and having accepted me into the program.
Finally, I owe much of the happiness of the last 6 years to Jingyang Zhong, whom
I met on August 2, 2006, when we both started our PhDs in Neuroscience and whom I
married on September 29, in Hangzhou, China. Facing similar challenges in our PhDs,
but fortunately (!) pursuing very different interests scientifically, we found in each other
sources of constant and unconditional support.
Kornelius R´ acz
Los Angeles, 2012
vi
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables xi
List of Figures xii
Abstract xvi
Chapter 1: Introduction, Background and Prior Work 1
1.1 Motor Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Muscle Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Experimental Evidence: Leveraging Muscle Redundancy for Fatigue
Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Modeling and Simulation: Muscle Redundancy and Muscle Fatigue . . 10
Chapter 2: Fatigue Dynamics Have Profound Consequences for
Muscle Coordination and Theories of Motor Control 14
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Modeling a redundant neuromuscular system . . . . . . . . . . 19
2.3.2 Mathematical modeling of fatigue . . . . . . . . . . . . . . . . 25
2.3.3 Simulating muscle activation dynamics in isometric knee exten-
sion subject to optimization . . . . . . . . . . . . . . . . . . . 27
2.3.4 Parameter search . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.1 Eureqa-extracted dynamics of muscle fatigue and recovery . . . 30
2.4.2 Running the nominal model subject to optimized activation . . . 32
2.4.3 Parameter search results . . . . . . . . . . . . . . . . . . . . . 34
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
vii
Chapter 3: Biomechanics Rather Than Neurophysiology Explains the Abol-
ishment of Alternating Activation of Synergistic Muscles in Submaximal
Fatiguing Isometric Contractions 45
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.1 Modeling a redundant neuromuscular system . . . . . . . . . . 48
3.3.2 Muscle necessity analysis . . . . . . . . . . . . . . . . . . . . 50
3.3.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.4 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.5 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.1 Muscle necessity analysis . . . . . . . . . . . . . . . . . . . . 54
3.4.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 54
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Chapter 4: Temporal Analysis Reveals a Continuum, Rather Than a Separa-
tion, of Task Relevance 63
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.1 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.2 Data preprocessing . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.4 Identification and modeling of the mechanical requirements of
the task and its nullspace . . . . . . . . . . . . . . . . . . . . . 72
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.1 Principal component analysis of simulated normal forces . . . . 74
4.4.2 Principal component analysis of experimental forces . . . . . . 76
4.4.3 Detrended Fluctuation Analysis of time series projected onto
principal components . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Chapter 5: An Involuntary Stereotypical Grasp Strategy Pervades Voluntary
Dynamic Multifinger Manipulation 90
5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1 Experimental procedure . . . . . . . . . . . . . . . . . . . . . 92
5.3.2 Mechanical Analysis . . . . . . . . . . . . . . . . . . . . . . . 97
viii
5.3.3 Equations of motion for a 2-D system of three links connected
via a common hinge . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3.5 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4.1 Analytical Solution and Simulations . . . . . . . . . . . . . . . 107
5.4.2 Principal component associated with the modeled ideal perfor-
mance of the task. . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.3 Summary of experimental PCA result and comparison with the
modeled ideal performance of the task . . . . . . . . . . . . . . 110
5.4.4 Experimental PCA result and comparison with the modeled ideal
performance of the task . . . . . . . . . . . . . . . . . . . . . . 110
5.4.5 Comparison with the modeled imperfect performance and the
experimentally grounded task . . . . . . . . . . . . . . . . . . 113
5.4.6 Comparison with the simple static hold control tasks . . . . . . 116
5.4.7 Comparison with the alternating index/middle finger normal force
task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.4.8 Comparison with voluntarily oscillated grasp force . . . . . . . 120
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.5.1 Ruling out potential confounds . . . . . . . . . . . . . . . . . . 123
5.5.2 Grasp Mode variability reveals fundamental challenges to con-
trolling dynamic multifinger manipulation . . . . . . . . . . . . 126
Chapter 6: Prenatal Motor Development Under Different Incubation Periods
Affects Postural Control in Domestic Chick 129
6.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.3.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.3.2 Incubation Conditions . . . . . . . . . . . . . . . . . . . . . . 133
6.3.3 Acceleration of embryogenesis through light exposure . . . . . 133
6.3.4 Quiet Stance Training . . . . . . . . . . . . . . . . . . . . . . 133
6.3.5 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3.6 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.3.7 Center of pressure dynamics analysis: classical approach . . . . 139
6.3.8 Center of pressure dynamics analysis: perturbation response . . 141
6.3.9 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . 142
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.4.1 Quiet stance experiment . . . . . . . . . . . . . . . . . . . . . 144
6.4.2 Stance perturbation experiment . . . . . . . . . . . . . . . . . 145
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
ix
Chapter 7: Summary and Conclusions 155
Bibliography 159
x
List of Tables
Table 4.1: List of relevant constraints in static grasp . . . . . . . . . . . . . . 74
Table 5.1: Explanation of tests and simulations used to support hypothesis . . 98
xi
List of Figures
Figure 1.1: Levels of redundancy . . . . . . . . . . . . . . . . . . . . . . . . 3
Figure 1.2: Hyperbolic relationship between force and endurance . . . . . . . 5
Figure 1.3: EMG recorded from 12 finger muscles . . . . . . . . . . . . . . . 9
Figure 1.4: Muscle activation pattern vector direction . . . . . . . . . . . . . 9
Figure 1.5: Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 1.6: Quadriceps EMG of 1 h of isometric knee extension . . . . . . . . 11
xii
Figure 2.1: Muscles contributing to isometric knee extension . . . . . . . . . 24
Figure 2.2: Model MVC decline . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 2.3: Model MVC recovery . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 2.4: Model fatigue dynamics . . . . . . . . . . . . . . . . . . . . . . 32
Figure 2.5: Model recovery dynamics . . . . . . . . . . . . . . . . . . . . . 32
Figure 2.6: Sum of squared activation muscle dynamics . . . . . . . . . . . . 34
Figure 2.7: Sum of activation muscle dynamics . . . . . . . . . . . . . . . . 35
Figure 2.8: Constant activation proportions dynamics . . . . . . . . . . . . . 36
Figure 2.9: Constant muscle forces dynamics . . . . . . . . . . . . . . . . . 37
Figure 2.10: Objective functions error comparison . . . . . . . . . . . . . . . 38
Figure 2.11: Objective functions switching dynamics comparison . . . . . . . 39
Figure 3.1: Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 53
Figure 3.2: Muscle necessity analysis result at 15% MVC . . . . . . . . . . . 55
Figure 3.3: Muscle necessity analysis result at 41% MVC . . . . . . . . . . . 56
Figure 3.4: Vasti muscles sensitivity analysis . . . . . . . . . . . . . . . . . . 57
Figure 3.5: Rectus femoris sensitivity analysis result . . . . . . . . . . . . . . 58
Figure 3.6: Representative EMG recordings at 2.5% MVC . . . . . . . . . . 59
Figure 3.7: Representative EMG recordings at 10% MVC . . . . . . . . . . . 60
Figure 3.8: Representative EMG recordings at 15% MVC . . . . . . . . . . . 61
xiii
Figure 4.1: Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure 4.2: Task simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Figure 4.3: Normal force modes . . . . . . . . . . . . . . . . . . . . . . . . 77
Figure 4.4: Representative data for simple grasp . . . . . . . . . . . . . . . . 79
Figure 4.5: Representative data for grasp with visual feedback . . . . . . . . 80
Figure 4.6: Distribution of data principal components . . . . . . . . . . . . . 81
Figure 4.7: Proportions of variance explained . . . . . . . . . . . . . . . . . 82
Figure 4.8: Representative plot of projected data . . . . . . . . . . . . . . . . 83
Figure 4.9: DFA scaling exponent distribution . . . . . . . . . . . . . . . . . 86
Figure 5.1: Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 94
Figure 5.2: Force space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Figure 5.3: Sample time histories . . . . . . . . . . . . . . . . . . . . . . . . 105
Figure 5.4: Overview of the 3 force variability modes . . . . . . . . . . . . . 108
Figure 5.5: Results summary . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Figure 5.6: Results of the original task . . . . . . . . . . . . . . . . . . . . . 114
Figure 5.7: Results of the original task simulation . . . . . . . . . . . . . . . 115
Figure 5.8: Results of the simulation with signal-dependent noise added . . . 117
Figure 5.9: Results of the original task with device attached to ground . . . . 118
Figure 5.10: Results of the static hold task . . . . . . . . . . . . . . . . . . . 119
Figure 5.11: Results of the alternating forces task . . . . . . . . . . . . . . . 121
xiv
Figure 6.1: The incubator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Figure 6.2: Chick on force platform . . . . . . . . . . . . . . . . . . . . . . 136
Figure 6.3: Sample center-of-pressure data . . . . . . . . . . . . . . . . . . . 137
Figure 6.4: Sample perturbation response . . . . . . . . . . . . . . . . . . . 143
Figure 6.5: Mean distance distribution . . . . . . . . . . . . . . . . . . . . . 145
Figure 6.6: Mean speed distribution . . . . . . . . . . . . . . . . . . . . . . 146
Figure 6.7: Sway area distribution . . . . . . . . . . . . . . . . . . . . . . . 147
Figure 6.8: Sample pre- and post-perturbation center-of-pressure data . . . . . 148
Figure 6.9: 2nd peak magnitude distribution . . . . . . . . . . . . . . . . . . 149
Figure 6.10: 2nd peak to 1st peak magnitude ratio distribution . . . . . . . . . 150
Figure 6.11: 2nd peak to perturbation magnitude ratio distribution . . . . . . 151
Figure 6.12: Post-perturbation sway area distribution . . . . . . . . . . . . . 152
Figure 6.13: Individual chick performances . . . . . . . . . . . . . . . . . . 153
Figure 6.14: Absence of learning effects . . . . . . . . . . . . . . . . . . . . 154
xv
Abstract
Motor redundancy in neuromuscular systems exists on multiple levels. The term ”motor
redundancy” represents the availability of infinitely many different solutions to perform
a motor task. This dissertation is concerned with three particular of those levels: muscle
redundancy, wrench redundancy and posture redundancy, which are successively more
general forms of redundancy, each of which will be explained in detail.
The first level corresponds to the phenomenon that for a given constant vector of sub-
maximal limb endpoint force in isometric tasks, an infinite multitude of muscle coor-
dination patterns exists. The motor control research community refers to this kind of
redundancy as muscle redundancy, and traditionally, the selection of a particular mus-
cle coordination pattern has been considered a computational problem for the nervous
system. Mathematically, the possible muscle activations span an n-dimensional space
- n being the number of independently controlled muscles - and the mapping between
this space and that of isometrically generated endpoint forces is projective, therefore
giving rise to a null space. The null space comprises those muscle activation vectors
that do not have an effect on the endpoint forces, due to the mutual cancellations of gen-
erated forces. Specifically, the space of endpoint force vectors is 6-dimensional, con-
sisting of three linear and three rotational components, leaving n-6 degrees of freedom.
In the present work, I am studying a potential benefit of muscle redundancy, namely
xvi
the mitigation of muscle fatigue through the dynamic switching between muscle acti-
vation patterns. Based on my results, I am proposing to abandon the view of muscle
redundancy as a computational problem for the nervous system, since in the presence
of muscle fatigue even the alleged simplification of this problem, that is, dimension
reduction through muscle synergies requires awareness of the full dimensionality of the
motor task. Instead, future research should focus on how the nervous system responds
flexibly to the challenge of time-variance due to fatiguing and actually leverages muscle
redundancy.
The second level of motor redundancy is concerned with the phenomenon that in
addition to the redundancy of muscles, infinitely many different combinations of end-
point forces and moments all achieve successful task performance. Again, this redun-
dancy has been considered a computational problem for the nervous system and various
ways of how it simplifies the selection of a particular wrench have been proposed. Note
that the selected solution in terms of endpoint forces constrains the muscle coordina-
tion solution space, in which a particular solution has to be found. Hence, wrench
redundancy is a generalization of muscle redundancy. In the case of three-finger grasp,
for instance, different fingertip force vector combinations result in an absence of net
forces and moments applied to a grasped object, due to mutual cancellation of forces
and moments applied by the fingertips. For example, one way to vary the applied forces
is to squeeze the object harder and still succeed at the motor task of static grasp. I refer
to this kind of redundancy as wrench redundancy: the same 6-dimensional wrench
vector applied to an object can be produced by a multitude of force vectors individ-
ually acting on the object. Wrench redundancy can possibly help to mitigate effects
of fatigue, namely through the dynamic shifting between endpoint force vector com-
binations, just like shifting between coordination patterns achieves this at the muscle
level. In the present work, however, I am pursuing a different path of research: In
xvii
the first study, looking at the normal force dynamics in static tripod grasp, I will show
how mathematically independent wrench space dimensions are actually controlled in
quite different ways, reflecting their specific roles in achieving dexterous manipulation.
This work shows that a purely spatial analysis of endpoint force variability is not suf-
ficient and that temporal correlations can reveal important aspects of motor control. In
particular, the dynamics of forces indicate a hierarchy of task dimensions in terms of
task-relevance and contradict the view held by some that task variables can be separated
into task-relevant and -irrelevant (i.e. the Uncontrolled Manifold Hypothesis). Accord-
ing to this view, large variability in a mechanically task-irrelevant dimension reflects
the lack of control of this dimension by the nervous system. Based on these results, I
am proposing to abandon the view of wrench redundancy as a purely spatial problem
and to espouse the use of time series analysis to determine neural control strategies. In
the second study of wrench dynamics, I will show how in a non-redundant dexterous
manipulation task, where all wrench dimensions are task-relevant due to simultaneous
force and motion requirements, the control of different task dimensions is likely cou-
pled through neurophysiological pathways, whose separation during evolution has been
incomplete. Specifically, I will show how different wrench space dimensions of the
motor task, though mathematically independent, are nevertheless coupled in the perfor-
mance of the task, thus limiting the ability to match the perfect mechanical solution
of the task. We see here an important interaction between the wrench and the muscle
level: when the wrench level becomes non-redundant, the muscle level also seems to
hit a boundary and reveals limitations in the independence of control of muscles across
fingers.
Finally, the third level is concerned with postural redundancy, meaning that dur-
ing the performance of a motor task the task goal can be achieved with different limb
configurations, described in terms of joint angles. Once again, this level of redundancy
xviii
is a generalization of the previous level and potentially extends the potential benefits of
the former: a selected posture that enables motor task performance will constrain the
admissible endpoint force space, which in turn will constrain the muscle coordination
space. One common task taking advantage of postural redundancy is quiet stance. Dur-
ing quiet bipedal stance, two-legged animals are usually swaying or shifting from one
posture to another, the former of which can be attributed to motor noise and the latter of
which is likely a fatigue mitigation strategy. In this dissertation, I will present results of
an analysis of postural control in one-day old domestic chicks (Gallus gallus) that reveal
differences in prenatal motor development, which were induced by different amounts of
light exposure during incubation.
In summary, it can be said that the nervous system is remarkable in that it is capable
of monitoring and reconciling continuously multiple levels of redundancy during perfor-
mance of common motor tasks, in particular, since the kinematic degrees of freedom of
limbs are not controlled directly by the brain. Instead, their actuation is achieved through
a complex mapping starting with the degrees of freedom found at the brain level, where
the task is likely represented very differently from joint angles. Importantly however,
not even the three levels studied and discussed here are exhaustive: at one end, muscle
redundancy specializes to the little studied motor unit redundancy, whereby different
subsets of motor units in a single muscle generate the same muscle force. Motor units
represent the control subunits that make up and provide graded control of muscle activ-
ity. At the other end of the redundancy spectrum, postural redundancy generalizes to
behavioral redundancy, that is, using different strategies to achieve a task, for instance,
walking vs. running, etc. Personally, I found that the separation of motor control into
different levels of redundancy espoused here to be uncommon in the literature and the
field, although it has helped me tremendously in forming hypotheses, designing experi-
ments and attributing causes of failure in motor tasks to specific neuromuscular factors,
xix
and would certainly help the field of motor control research as well. I hope that the
following work induces the reader to consider adopting this hierarchical view of motor
redundancy, which is different from, and can potentially exist alongside other, hierar-
chical views of the neuromuscular system.
xx
Chapter 1
Introduction, Background and Prior
Work
1.1 Motor Redundancy
Manipulating objects with the fingertips (dexterous manipulation) is an awe-inspiring
sensorimotor ability that is essential to the activities of daily living. Multifinger
dexterous manipulation arises from dynamical interactions among muscles within
and across fingers to produce accurate fingertip forces (and motions). Arguably,
the simplest of dexterous manipulation tasks is the static grasp of rigid objects: it
nevertheless requires the accurate orchestrations of forces across the two or three
fingertips involved [Cutkosky, 1985, Raibert and Craig, 1981, Yoshikawa, 1990,
Goddard et al., 1992, Murray et al., 1994], having selected an appropriate posture,
such that the grasped object does not move or turn. Many investigators have studied
finger biomechanics (e.g., [Berme et al., 1977, Minami et al., 1983, An et al., 1985,
Schuind et al., 1992, Valero-Cuevas et al., 1998, Sancho-Bru et al., 2001]), neuromus-
cular control (e.g. [Cole and Abbs, 1986, Darling et al., 1988, Burstedt et al., 1999,
Zatsiorsky et al., 2000, Venkadesan and Valero-Cuevas, 2008, Winges et al., 2009,
Keenan et al., 2009]), and the role of brain function during their use
(e.g., [Binkofski et al., 1999, Ehrsson et al., 2000, Talati et al., 2005]). In addi-
tion, the coordination of two, three or more fingers as they hold an object is the
1
subject of multiple studies (e.g., [Johansson and Birznieks, 2004, Winges et al., 2009,
Latash and Zatsiorsky, 2009]).
Understanding redundancy (i.e., how the nervous system selects and implements
a specific posture, a specific wrench and a specific muscle coordination pattern from
among the many possible options that all achieve successful motor task performance)
has been the central problem of neuromuscular control for at least four decades
(e.g., [Bernstein, 1967, Chao and An, 1978, Hogan, 1985, Valero-Cuevas et al., 1998,
Todorov and Jordan, 2002, Seth and Pandy, 2007]). I illustrate the different levels of
redundancy with a simple example (Figure 1.1): quiet stance. With regards to postural
redundancy: the task of standing quiet and upright can be achieved by many leg joint
angle configurations, where some might be more suited than other for specific purposes,
such as resisting perturbations, for instance, or reducing the level of stress on the joints
and muscles. With regards to wrench redundancy: during standing, the body weight can
be shifted from one leg to the other, allowing for infinitely many weight distributions
that produce the same functional outcome. Lastly, with regards to muscle redundancy:
again, the forces necessary to stabilize the legs in quiet stance can be achieved by dif-
ferent muscle coordination patterns, and once again, different patterns provide different
benefits.
The complexity of the human hand, the system, whose redundancy we study in chap-
ters 4 and 5, far exceeds that of the legs and apparently exacerbates the problem of redun-
dancy for dexterous manipulation due to the large number of muscles and kinematic
degrees of freedom involved. The triple challenge of task complexity, anatomical com-
plexity and muscle redundancy has delayed a rigorous understanding of how we coordi-
nate finger musculature for dexterous manipulation. Moreover, understanding how the
redundancy problem is solved in the context of dexterous manipulation remains a critical
limitation to our understanding of the mechanisms of impairment and clinical treatment
2
Posture redundancy
Wrench redundancy
Muscle redundancy
Kinematic redundancy
Motor unit redundancy
Figure 1.1: The three levels of redundancy studied in this work and embedded into the
next more general and more specific levels of redundancy, respectively. The most spe-
cific level is muscle redundancy, i.e. the availability of infinitely many different muscle
coordination patterns producing the same endpoint force. This kind of redundancy is
embedded into wrench redundancy, i.e. the availability of infinitely many different end-
point force vectors satisfying the motor task constraints. Wrench redundancy, in turn,
specializes posture redundancy, i.e. the availability of infinitely many different static
postures in an isometric task, for each of which endpoint force vectors can be found
that satisfy the constraints of the motor task. Also shown are the next more special and
general levels of redundancy, respectively.
of hand disability (some reviews include [Spoor, 1983, Schieber and Santello, 2004,
Valero-Cuevas et al., 2009a, Latash and Zatsiorsky, 2009]). I am careful to explicitly
delineate the aspects of redundancy I will address in the following chapters of this dis-
sertation.
More general than the selection of a static posture, the choice of a particular motion
pattern (i.e. a sequence of postures) constitutes the next higher level of redundancy.
3
On the other hand, more specific than the selection of a particular muscle coordination
pattern, we have at the single-muscle level the so-called motor unit redundancy: since
a muscle is composed of a large number of muscle fibers, different activation patterns
of the associated motor units can generate the same submaximal single-muscle output
force (a maximal force would obviously involve all fibers of a muscle). The dynamic
phenomenon associated with motor unit redundancy is also known as motor unit rotation
or substitution [Sale, 1987, Westgaard and De Luca, 1999], hypothesized to spread the
work load.
1.2 Muscle Fatigue
For the purposes of this work, I adopt the definition of muscle fatigue as the
exercise-induced reversible decline of the maximum force a muscle can gener-
ate [V ollestad, 1997]. In the performance of submaximal motor tasks, this decline
in performance is not immediately apparent, but eventually muscle fatigue will lead
to the inability to maintain the force required for the task. This phenomenon is
referred to as exhaustion [Bigland-Ritchie et al., 1986]. Fatigue is a phenomenon
mostly [Merton, 1954] occurring in the muscle itself rather than the central nervous sys-
tem, i.e. in the neurons and the brain, and has therefore been studied almost exclusively
in isolated muscle tissue. Since the central aspects of fatigue are poorly understood, and
since I believe that the plant should be understood before the controller, I focus on the
peripheral aspects of fatigue and disregard central aspects.
At the task level, in submaximal activity, the fatigue state cannot be directly observed
but only estimated through the interpolation of occasional maximal contractions. After
exercise, there is usually a phase of recovery that is nearly complete within minutes and
4
sometimes a much slower component [Edwards et al., 1977, Allen et al., 2008]. Usu-
ally recovery of maximum force is virtually complete by 30 minutes, and it is possi-
ble to perform repeated fatigue runs with nearly similar time courses after this recov-
ery [Allen et al., 2008].
Studies at the physiological level, in turn, indicate that different fatigue mechanisms,
which are not fully understood, but involve the depletion of Ca
2+
and ATP, cascade so
as to give rise to a hyperbolic relationship between force (Figure 1.2) and endurance
time [Enoka and Stuart, 1992], which indicates the onset of exhaustion. In the follow-
ing, I will explain the known mechanisms briefly and specifically highlight differences
between the two major fiber types found in human muscle. 682 J. DUL. G. E. JOHNSON, R. SHIAVI and M. A. TOWNSEND
Force W
Fig. 5. Measured relationship between external froce and activity endurance time for diKerent human
muscle groups during static-isometric contractions. The relationship predicted with the Minimum-Fatigue
criterion (not shown) coincides with the solid regression line (From Monod 1972).
the medial gastrocnemius is bifunctional and capable
of both knee flexion and ankle extension, its reflex
connections and electrical activity show it to be largely
concerned with ankle extension during stepping’.
In Fig. 6, the predictions are compared with direct
force measurement data. The force in the soleus is
given as a function of the force in the medial gas-
trocnemius for several activities. The symbol (A) relates
to measured instantaneous forces during standing and
(0) to measured peak forces during walking and other
movements. The lines are the predictions from the
minimum-fatigue criterion (equation 12), from several
non-linear MINISUM criteria from the literature
(equation 14) and, for comparison, for several linear
Postural Walk Run
criteria that have been used in the literature. According
to our previous investigation the linear criteria predict
that only the medial gastrocnemius is active, since this
muscle is larger than the soleus (larger maximum force
and larger cross-sectional area) and has a moment arm
that, if at ail different, is probably larger than that of
the soleus.
The non-linear criteria from the literature predict
that there is a linear relationship between the force in
the soleus and the force in the gastrocnemius. The
minimum-fatigue criterion predicts that these forces
are non-linearly related according to the equation FIo,
= 5.08 (F9,,,)0.42. (equation 8, Appendix)
It turns out that only the prediction from th:
Gallop Jump
-
MG force (kg wt 1
Fig. 6. Measured vs predicted load sharing between two cat muscles during standing and locomotion.
(Measurements from Walmsley et al.. 1978). 1. Minimum-fatigue criterion; 2. Quadratic criterion: IF:,
3. Quadratic criteria: I(F,/,4,)*, Z(F,/F,,,)‘; 4. Cubic criterion: T(FJA$; 5. Linear criteria: ZF,,
xF,;lA,, xF,;lF,,,.
Figure 1.2: The relationship between force requirement and endurance time is
hyperbolic, indicating that fatigue benefits can be achieved by reducing force in
a muscle, which makes activation pattern shifts a reasonable option (Diagram
from [Dul et al., 1984]).
5
Cross-bridge cycling in myocytes, which generates the force produced by muscles
through contraction, can only occur in the presence of Ca
2+
, which is released from the
Sarcoplasmatic Reticulum (SR) in response to a muscle action potential (AP) and then
pumped into the SR again. Since the time constants of Ca
2+
release (< 20 ms) and
re-uptake (80 - 200 ms, [Baker et al., 1995]) differ greatly, the net result of sustained
muscle contraction - especially under a fused tetanus - is a depletion of available Ca
2+
.
The amount of available Ca
2+
is further reduced due to the gradual depletion of ATP,
since ATP is needed for Ca
2+
re-uptake into the SR through the pumps as well as the
release of cross-bridges.
To maintain a constant force level under fatigue, the activation of the muscle has
to be increased, which will increase the rate of Ca
2+
and ATP depletion even more,
leading to a ”vicious circle”. Importantly, the muscle fibers, which the muscle is com-
posed of, fatigue at different rates and can be categorized into slow-fatiguing (aero-
bic) [Bevan, 1991], or slow-twitch, and fast-fatiguing (anaerobic), or fast-twitch, types.
According to the size principle [Henneman, 1957], fast-fatiguing fibers being larger than
slow-fatiguing ones, they are recruited at higher activation levels. Therefore, tasks with
very low force requirements can be performed virtually infinitely, with very limited
amounts of fatiguing [Sjogaard et al., 1986].
The slow-twitch fibers owe their endurance to the following qualities: a) a high
oxidative capacity due to a large number of mitochondria [Bezanilla et al., 1972,
Essen et al., 1975], b) a much greater amount of Ca
2+
stored in rested muscle
(70% of maximum capacity vs. 20% [Bhagat and Wheeler, 1973] in fast-fatiguing
fibers) and c) a smaller Ca
2+
release time constant (1/3 of that of fast-twitch mus-
cles [Bianchi and Narayan, 1982]). Furthermore, the rate and amount of SR Ca
2+
6
release per AP is approximately three times higher in fast-twitch fibers than in slow-
twitch fibers [Baylor and Hollingworth, 2003]. A feature of fast muscle but also a draw-
back, from a fatigue point of view, is that it can consume ATP, and thereby produce ADP
and P
i
(Phosphate) much faster than it can regenerate it, hence the above difference in
time constants applies to the consumption (fast) and regeneration (slow) of ATP as well.
Lastly, this difference between slow and fast fibers is also attributable
to the higher density of both DHPR/voltage sensors and Ca
2+
release chan-
nels in fast-twitch fibers [Lamb and Walsh, 1987, Lamb, 1992, Margreth et al., 1993,
Delbono and Meissner, 1996]. The rapid contraction of fast-twitch fibers requires the
presence both of fast MHC (type II) isoforms and fast Ca
2+
release. Slow-twitch fibers,
on the other hand, have fewer Ca
2+
binding sites on troponin C and the SR pumps,
and thus, a lower rate and amount of Ca
2+
release suffices for contraction, particu-
larly given the much slower contraction rate of the predominant MHC isoform (type I)
present [Bortolotto et al., 2000, Bottinelli and Reggiani, 2000]. Thus SR and contractile
properties in a given fiber are generally well matched [Trinh and Lamb, 2006].
In conclusion, an appropriate modeling of fatigue needs to take into account oxygen-
dependence and differential rates of fatigue among fibers and the proportions of these
fibers present in contributing muscles: in the slow-twitch fiber-dominated muscle, time-
variance of the EMG-to-muscle force relationship is hardly attributable to fatigue. Iso-
metric tasks involving muscles with a high proportion of fast-twitch fibers, on the other
hand, will be strongly affected by fatigue, unless they have low force requirements,
in which case only the non-fatiguable slow-twitch fibers in that muscle are activated.
In consequence, as the fast-twitch-fiber-dominated muscle progressively fatigues, the
activation of that muscle has to be increased (Figure 1.3) to maintain a constant mus-
cle force. In turn, the resulting recruitment of additional motor units gives rise to the
increase in EMG occurring when muscles sustain force at a given submaximal level.
7
Somewhat surprisingly however, the discharge rate of originally active motor
units can decrease during prolonged submaximal contractions, since twitch time
constants increase with fatigue, despite the fact the overall excitatory drive to the
motor neuron pool increases as fatigue develops [Garland et al., 1994]. It is the
increased excitatory drive and the concurrent increased recruitment that is measured
by the EMG, but not the (decreased) discharge rates of individual motor units. The
reduction of discharge rate in motor units is normally well-matched to the slow-
ing of relaxation that occurs with muscle activation (increase of twitch time con-
stant), such that the stimulation rate remains just sufficient to give a fused tetanus of
close to maximum force possible at that point in time [Bigland-Ritchie et al., 1983,
BiglandRitchie and Woods, 1984, Balog et al., 1994]. This phenomenon is often called
”muscle wisdom” [Enoka and Stuart, 1992, Gandevia, 2001]. There exists evidence
that the reduction in motor unit activation is mediated through group III/IV affer-
ents reflex inhibition [Garland and McComas, 1990, Gandevia, 1990, Garland, 1991,
Hayward et al., 1991] as their discharge rates decline during the initial phase of fatigue,
and muscle spindle afferents later in fatigue [Gandevia, 1990, Macefield et al., 1991].
1.3 Experimental Evidence: Leveraging Muscle Redun-
dancy for Fatigue Mitigation
At the level of muscle redundancy, there currently exists one study involving tripod
grasp, [Santos et al., 2010] that has investigated the neuromuscular system’s ability to
traverse the muscle solution space, for a constant endpoint force output. Subjects were
asked to produce a constant submaximal normal force output, while minimizing tangen-
tial force, with three fingers in a grasp posture until exhaustion. Fine-wire EMG was
recorded from 10 muscles and subsequently, the relative muscle activation contributions
8
0
1.5
0
1.0
0
0.5
0
1.0
0
1.5
0 50 100 150
0
2.0
0
1.0
0
1.5
0
1.0
0
1.5
0
1.0
0 50 100 150
0
1.0
FDI
FPI
2DI
2PI
ABPB
FPB
ED2
ED3
EPL
FDS2
FDS3
FPL
Time (s) Time (s)
EMG (normalized to MVC EMG)
Figure 3
extrinsic muscles intrinsic muscles
T1 T2 T3 T4
Task
failure
T1 T2 T3 T4
Task
failure
Figure 1.3: All 12 muscles measured in [Santos et al., 2010] show an increase in EMG
activity as the muscles gradually fatigue, while producing the same isometric force out-
put.
0
1
2
3
T1 T2 T3 T4
0.96
0.97
0.98
0.99
1.00
T1 vs. T2
0.90
0.95
1.00
1.05
020 40 60 80 100
Time epoch comparison
Normalized trial duration (%)
Trial epoch
A
B
C
*
*
MAP vector magnitude
Cosine of the angle b/w
MAP vector @ t= 1 vs. t>1
Cosine of the angle b/w
MAP vector pairs
T1 vs. T3 T1 vs. T4
Figure 5
*P < 0.05
Figure 1.4: The activation pattern of the 12 muscles does not change, despite the overall
increase in EMG, as evidenced by an only minimal change in the activation pattern
direction vector (diagram from [Santos et al., 2010]).
9
were computed to determine if the activation pattern changed. The results indicate that
although the activations of all contributing muscles increased as time passed, the rela-
tive contributions did not change. We will show in Chapter 3, for the simpler task of
isometric knee extension, how a target force of only 15% MVC already constrains the
solution space such that dynamic muscle activation becomes severely limited.
The dynamics of muscle coordination in the context of isometric knee extension
have been extensively studied by Kouzaki, Shinohara and others [Kouzaki et al., 2002,
Kouzaki et al., 2004, Kouzaki and Shinohara, 2006]. The authors showed that involun-
tary alternation between synergist quadriceps muscles, rectus femoris and vastus lat-
eralis, occurs during very low-level sustained knee extension, between 4 and 11 times
during the one hour long trial. Subjects were asked to generate an extremely low iso-
metric 2.5% MVC force for 1 hour, whereupon MVC force was measured again, to
determine if fatigue had occurred. Interestingly, the reduction in MVC was inversely
correlated with the frequency of alternation, indicating that alternation did provide the
benefit of reducing fatigue, for instance, by enabling recovery of the temporarily silent
muscle. While these results are very encouraging, the authors have not provided a for-
mal generative mechanism or model to explain and interpret those results.
1.4 Modeling and Simulation: Muscle Redundancy and
Muscle Fatigue
Modeling of isometric force sharing under fatigue minimization was first done in Dul
et al. [Dul et al., 1984]. Their minimum-fatigue criterion was formulated as the maxi-
mization of the endurance time across a group of synergistic muscles. The endurance
time is a function of both the force generated by the muscle (inversely proportional)
10
679 ALTERNATE MUSCLE ACTIVITY OF SYNERGISTS
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Figure 1.5: The experimental setup for the isometric knee extension task described
in [Kouzaki et al., 2002].
alternation in muscle activation, it is likely that fatigued mus-
cles may recover from fatigue during their silent phases,
leading to an attenuation of muscle fatigue. Hence, we hypoth-
esized that the frequency of alternate muscle activity is asso-
ciated with the degree of muscle fatigue.
METHODS
Subjects. Data from 41 healthy subjects during a sustained knee
extension at 2.5% MVC force were examined. In addition to the
existing data set of 19 subjects in previous studies (17–19), the new
data set was obtained from 22 subjects. The age, height, and body
mass of the 41 subjects (means! SD) were 26.1! 2.5 yr, 171.6!
6.7 cm, and 67.4 ! 8.6 kg, respectively. They gave their written,
informed consent for the study after receiving a detailed explanation
of the purposes, potential benefits, and risks associated with partici-
pation in the study. All procedures used in this study were in
accordancewiththeDeclarationofHelsinkiandwereapprovedbythe
Committee for Human Experimentation at the Department of Life
Sciences, The University of Tokyo.
General procedure and equipments. The basic setup for the knee
extension procedure has been described in our laboratory’s previous
studies (17–19). Subjects were in a seated position with the hip and
kneejointanglesflexed90°(fullextension"0°).Thetrunkandthigh
were strapped to a chair. The knee extension force was measured by
astraingaugeforcetransducer(model274II,Minebea,Tokyo,Japan),
which was coupled with a strain amplifier and attached by a strap to
the dorsal aspect of the lower leg just above the medial malleolus.
Bipolar surface electromyogram (EMG) was recorded from skin
surface over the muscle belly of rectus femoris (RF), vastus lateralis
(VL), and vastus medialis (VM) and biceps femoris long head (BF),
using Ag-AgCl electrodes with a diameter of 5 mm and an interelec-
trode distance of 20 mm. After careful abrasion of the skin, the
electrodes were placed on the skin over the muscle belly of the
respective muscles. The common reference electrode was placed on
the iliac crest. The electrodes were connected to a preamplifier and a
differential amplifier having a bandwidth of 5 Hz to 1 kHz (model
1253A, NEC Medical Systems, Tokyo, Japan). All electric signals
were stored on hard disk of a personal computer at a sampling rate of
1 kHz using a 16-bit analog-to-digital converter (PowerLab/16SP,
ADInstruments, Sydney, Australia).
Experimental protocol. Subjects performed MVCs before and im-
mediately after (#1 s) a sustained contraction. The MVC task in-
volved a gradual increase in knee extension force exerted by the
quadriceps muscle from baseline to maximum in 3–4 s and then
sustained at the maximum for 2 s. The knee extension force was
displayed in real-time on an oscilloscope. The onset of the task was
based on a verbal count given at 1-s intervals. Vigorous encourage-
ment was provided from the investigator when the force began to
plateau. Each subject performed at least three MVC trials with
subsequent trials performed if the differences in the peak force of two
MVCs were$5% (10), and the trial with the highest peak force was
chosen for analysis. After a sufficient rest period (%10 min), the
subject sustained a contraction of the knee extensor muscles at 2.5%
MVC force for 1 h. The force and the target were displayed as
horizontal lines on an oscilloscope in front of the subject to provide
visual feedback. Subjects were instructed not to alter joint angles or
force directions during the sustained contraction. No verbal feedback
or encouragement was provided during the sustained contraction to
avoid intentional changes in muscle activation strategy. Furthermore,
our laboratory has confirmed that the alternate muscle activity cannot
be achieved voluntarily by altering joint angles or force directions
(18).
Data analyses. During the MVC tasks, simultaneous recordings of
forceandEMGsignalswereanalyzedover1-speriodsofsteadyforce
output. The mean value of force was calculated for 1 s in each MVC
task. The EMG signals were full-wave rectified and averaged for 1 s
to calculate the average EMG (AEMG) in each MVC task.
Alternate muscle activity was observed in EMG activity between
RF and a set of VL and VM during the sustained contraction (Fig. 1).
To quantify the alternate muscle activity between synergist muscles,
we focused on marked changes in the EMG sequences between the
kneeextensormuscles.EMGofBF(antagonistmuscle)wassmalland
constantacrossthesustainedcontraction,andthusitwasnotincluded
in further analyses.
An alternate muscle activity between synergist muscles was de-
fined and counted according to previously established methods (18).
Briefly, EMG signals during the sustained contraction were full-wave
rectifiedandaveragedover15stoyieldAEMGevery15s.Calculated
AEMG of each muscle head was smoothed by five-point moving
average and differentiated (dAEMG/dt); an outlier was defined as
dAEMG/dt that exceeds! 3 SD of the first eight sample points; the
extracted outliers were classified into positive and negative outliers;
the alternate muscle activity was defined as the case in which the
positive and negative outliers overlapped between the synergist mus-
cles; and the number of the alternate muscle activity was counted in
eachmusclecombination,i.e.,betweenRFandVL(RF-VL),between
RF and VM (RF-VM), and between VL and VM (VL-VM) through-
out the sustained contraction. The total number (frequency) and
combinations of alternate muscle activity were determined by this
Fig. 1. Representative data demonstrating alternate
muscleactivityduringsustainedkneeextensionat2.5%
of maximal voluntary contraction (MVC) force. Knee
extensionforce,electromyograms(EMG)ofrectusfem-
oris (RF), vastus lateralis (VL), vastus medialis (VM),
and biceps femoris long head (BF) are shown.
716 ALTERNATE MUSCLE ACTIVITY AND MUSCLE FATIGUE
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Figure 1.6: During one hour of 2.5 % MVC force production, alternations between
synergistic muscles were observed (diagram from [Kouzaki and Shinohara, 2006]).
and its percentage of slow-fatiguing aerobic fibers (proportional), based on observa-
tions and curve fitting. Not surprisingly, the optimal activation of muscles in an iso-
metric knee flexion task, according to a nonlinear (i.e. maximization of a mininum)
11
optimization scheme, tended to favor force production in muscles with a higher per-
centage of slow fibers and muscles with large volumes, predicting nonetheless syn-
ergistic activation among muscles. Finally, the predicted time to failure and the pre-
dicted forces agree with values from the literature, underlining the physiological correct-
ness of this optimization criterion further confirmed elsewhere [Prilutsky et al., 1997,
Prilutsky and Zatsiorsky, 2002]. These studies found that fatigue, along with stress,
energy expenditure and perceived effort [Prilutsky and Zatsiorsky, 2002], were the best
predictors in static optimization schemes The major drawback of modeling studies
in fatigue-minimization in isometric tasks are their staticness, as they predict a sin-
gle fatigue-minimizing activation pattern that is held until failure, and do not con-
sider by design dynamic changes in the pattern as the isometric task progresses that
could improve performance and time to failure. Therefore, so far no model has been
able to reproduce the activation pattern [Kouzaki et al., 2002]. In Chapter 2, I will
address the problem of static optimization, based on the incorrect assumption of time-
invariance of the neuromuscular system and show in particular, how the concept of
synergies strongly conflicts with the control of a time-varying system. Synergies,
in short, are understood as the rigid co-activation of muscles, basically treating a
group of muscles as one muscle and thereby simplifying the muscle redundancy prob-
lem [Bizzi et al., 2002, d’Avella et al., 2003]. .
With respect to redundancy at the wrench level, there are currently no studies which
directly investigating possible dynamic strategies in a fatiguing, isometric, and submax-
imal task or consider the specifics of muscle fatigue and recovery dynamics. Instead,
studies at this level of redundancy focus on the effect of fatigue on the variability along
different task-relevant and task-irrelevant dimensions of a motor task, in the context
of the Uncontrolled Manifold Hypothesis [Scholz and Schner, 1999]. Two studies by
Danion et al. [Danion et al., 2000, Danion et al., 2001] explicitly looked at the effects
12
of fatigue on a redundant task. The first study involved two fatiguing force production
exercises, one at the distal and one at the proximal phalanges, both with four fingers and
single fingers. While force enslaving [Zatsiorsky et al., 2000] across fingers remained
unaffected by fatigue at the phalanx involving the exercise, enslaving increased at the
other phalanx. Furthermore, the difference between the MVC generated by all four
fingers in unison and the larger sum of single-finger MVCs increased. These results
indicate a neural level reorganization that aims to ”preserve” a force production syn-
ergy across fingers. The other study involved fatiguing exercises at the same distal and
proximal sites by the index finger only. This resulted in reduced enslavement of the
index finger in an all-finger force production task, and a reduction in its contribution
to the total sum of forces, leading the same authors to reach the opposite conclusion:
that fatigue leads to a reorganization at the neural level that ”progressively removes” the
fatigued finger from a synergy (so that in can be ”reintegrated into the synergy” faster
due to a swift recovery).
Another study, by [Singh et al., 2010] found that unfatigued fingers in multi-finger
force production tasks adaptively increase their force variability, so as to match the
fatigue-induced increase in variability in the fatigued finger. This adaptive behavior
helps to maintain a balance of variability, i.e. a synergy and to protect the task-relevant
dimensions from fatigue effects. While the authors certainly admit the benefits of redun-
dancy in fatigue mitigation, they fail to investigate the specific dynamics of wrench
along the task-irrelevant directions.
In conclusion, the findings of these studies therefore necessitate further investigation
into wrench redundancy and the opportunities for the nervous system to mitigate the
effects of fatigue at this level of control.
13
Chapter 2
Fatigue Dynamics Have Profound
Consequences for
Muscle Coordination and Theories of
Motor Control
2.1 Abstract
In submaximal motor tasks, the nervous system is believed to be confronted with the
computational challenge of selecting a particular from infinitely many distinct mus-
cle coordination patterns. Muscle redundancy, as this phenomenon is known, has led
researchers to hypothesize either the minimization of cost functions to find a solution,
or control strategies such as muscle synergies, whereby muscles are co-activated in a
stereotypical fashion, thus reducing computational complexity.
Here, we investigate the consequences of these hypotheses in the light of the hith-
erto oft-overlooked interplay between muscle coordination and fatigue. Simulations of
submaximal isometric knee extension with realistic fatigue and recovery show that the
nervous system continuously needs to respond to the complex changes in force produc-
tion capability experienced by muscles, to lengthen the time to failure.
First, we find that adherence to a synergy in activation space or muscle force space
requires either non-synergy-like muscle activations or muscle forces, respectively. We
14
conclude that synergies can only be enforced in a single space (muscle activations or
forces). This challenges the hypothesis that synergies can serve to simplify and guide
the selection of muscle coordination patterns.
Secondly, the adherence to a synergy leads to early task failure, if compared to other
strategies of pattern selection (for instance, energy minimization), which do not restrict
dynamics in any space. This result indicates the disadvantage of suppressing changes in
the levels and proportions of muscle activations or force when enforcing the constraints
of the task.
Thirdly, and somewhat surprisingly, we find that intuitive cost functions, some of
which have been proposed in the literature and are based on physiological considera-
tions, actually prevent muscle recovery. We conclude that one needs to recognize the
impact of fatigue on redundancy when proposing optimization strategies.
Together, the results not only cast doubt on the utility of synergies and highlight a
major disadvantage, but challenge their association with computational benefits. There-
fore, the results encourage abandoning the view of redundancy as a computational chal-
lenge, and instead encourage us to study associated opportunities in the mitigation of
muscle fatigue and to find relevant and appropriate objective functions capable of repro-
ducing the dynamics in time-variant neuromuscular systems.
2.2 Introduction
The problem of motor redundancy has been a longstanding one in motor control
research [Bernstein, 1967, Tresch and Jarc, 2009], ever since it had been observed that
in repeatedly performed motor tasks, humans never seem to use the exact same coordi-
nation pattern of joints to achieve the task goal [Bernstein, 1967]. Redundancy refers
to the multitude of muscle activation or muscle force patterns that all give rise to the
15
same endpoint force vector in submaximal and otherwise underspecified tasks, due to
the mutual cancellation of muscle actions. The perceived computational ”problem” of
motor redundancy now is that the nervous system is confronted with having to choose
one from many possible muscle coordination patterns.
Having observed that despite motor output variability (be it kinematic or
kinetic), muscle activation patterns are similar across repetitions of a motor task
and across people, scientists have proposed the existence of an underlying opti-
mizing principle as a means to determine a unique solution [Chao and An, 1978,
Crowninshield and Brand, 1981, Dul et al., 1984, Prilutsky and Zatsiorsky, 2002]. This
solution minimizes or maximizes a proposed objective function, which is selected
based on various neurophysiological or energetic considerations. It has been shown
in numerous studies that experimentally observed muscle coordination patterns can
(at least nominally) be found through the optimization of different objective func-
tions [Crowninshield and Brand, 1981, Dul et al., 1984, Anderson and Pandy, 2001].
However, these studies fail to address the possibility that there exist sufficiently many
constraints to the task (e.g. high force, resistance to perturbations, posture) to uniquely
determine a solution [Loeb, 2000], regardless of the objective function. Furthermore,
optimization is commonly employed to compute a single static solution, based on the
often implicit assumption that the neuromuscular system does not undergo changes over
time, during repeated or continuous task performance. However, allowing for time-
variance in the system might actually help to further constrain the search space of poten-
tial objective functions, since the ability to reproduce experimentally observed muscle
activation patterns provides another selection criterion.
Assuming that there exists an underlying principle of optimization in the selec-
tion of muscle coordination, scientists have proposed for the purpose of computa-
tional simplicity the concept of muscle synergies. Subject to a synergy, muscles
16
are always co-activated in specific patterns [Bizzi et al., 2002, d’Avella et al., 2003,
Chhabra and Jacobs, 2006, Tresch and Jarc, 2009]. The combination of different dis-
tinct synergies enables variable and dynamic muscle coordinations, while simulta-
neously reducing the number of variables in optimization. One criticism of syner-
gies is firstly the assumption that high dimensionality poses a computational prob-
lem [Bizzi et al., 2002], an assumption that remains to be supported by evidence. Sec-
ondly, while allowing for motor variability, synergies constrain the muscle activation or
force spaces in specific ways, which greatly restricts potential beneficial or even nec-
essary variability [Kutch and Valero-Cuevas, 2012]. Numerous studies have shown that
the role of an individual muscle relative to another (synergist or antagonist) depends on
posture [Hasan and Enoka, 1985], torque [Caldwell and Van Leemputte, 1991] or direc-
tion of force application [Theeuwen et al., 1994], and in fact, synergists like gastrocne-
mius medialis and soleus can become functional antagonists [Schieppati et al., 1990,
Kutch and Valero-Cuevas, 2011].
In the present work, we firstly explore the potential consequences of one way in
which neuromuscular systems are time-varying: muscle fatigue, which we understand
as the exercise-induced decline of the maximum force of a muscle. The primary effect
of fatigue is to reduce the proportionality between muscle activation, measured through
EMG, and muscle force [Dideriksen et al., 2010]. Hence, to maintain a given force
level, the activation of each fatigued muscle has to be increased, to recruit more motor
units or increase the firing rate of already recruited ones. Since synergistic muscles
fatigue at different rates, due to the demands of the task and the proportion of fatigable
vs non-fatigable fibers [Johnson et al., 1973, Housh et al., 1995, Loeb and Ghez, 2000],
we hypothesize that the increase in activation occurs at different rates across muscles.
17
Specifically, we hypothesize that including fatigue-based time-variance in modeling
exposes an important drawback of adhering to a single initial solution, and simply scal-
ing it up to maintain a force, in the presence of reduced muscle output as it fatigues.
This strategy will lead to comparatively early failure, and exposes the requirement for
continuous optimization, or more generally, continuous adaptation. Besides, adding
time-variance to musculoskeletal models provides another constraint to identify valid
approaches to the finding of a solution.
Secondly, we show that due to the time-variance of the mapping from muscle acti-
vation to muscle force, only one domain (muscle force or activation) at a time can
be controlled synergistically, while the other varies dynamically, thus making obvi-
ous the inevitability of dynamical changes in either activity or force, with important
consequences to the study of computational complexity in motor function. Further-
more, we hypothesize that the restriction on the solution space imposed by synergies
will lead to a relatively early task failure. It is important to note that we consider
the adherence to a synergy to be equivalent to the adherence to a static optimal solu-
tion: if an ”optimal” synergy fails, then a random synergy is all the more likely to
fail, as the co-activation pattern in that case is not even adapted to the task. This
result suggests the need for and the benefits of dynamic activation strategies in sub-
maximal tasks, for which there exists evidence from isometric knee extension EMG
recordings [Sjogaard et al., 1986, Kouzaki, 2005, Kouzaki and Shinohara, 2006].
18
2.3 Methods
2.3.1 Modeling a redundant neuromuscular system
Assumptions
For the purposes of modeling a redundant motor task subject to fatiguing, we adopt
the definition of muscle fatigue as the exercise-induced decline of the maxi-
mum force a muscle can generate [V ollestad, 1997]. In turn, this requires an
increase of activation of that muscle to maintain the force, as has been observed pre-
viously [Dideriksen et al., 2010, Danna-Dos Santos et al., 2010, Rudroff et al., 2010].
Muscle recovery, on the other hand, occurs only in the total absence of activa-
tion [Dideriksen et al., 2011], while at very low muscle forces, the muscle neither
fatigues nor recovers, due to the reliance on slow-twitch fibers, also known as inde-
fatigable fibers [Loeb and Ghez, 2000].
We selected the task of isometric knee extension, because there exists prior evi-
dence, in the absence of a mathematical model, that the nervous system lever-
ages redundancy for the mitigation of fatigue [Sjogaard et al., 1986, Kouzaki, 2005,
Kouzaki and Shinohara, 2006]. Besides, from a modeling point of view, knee extension
has favorable properties: it allows for isolation of muscle redundancy and a relatively
clean separation from endpoint force vector redundancy, whereby different force vec-
tors can all achieve successful task performance. Specifically, the muscles actuating
knee extension (vasti and rectus femoris) are largely similar in terms of their mechan-
ical action - in particular, these muscles don’t add/abduct or rotate the leg. Therefore,
dynamic activation of RF and the Vasti in isometric knee extension is unlikely to give
rise to undesirable tangential endpoint force component, which helps to keep this vector
constant.
Furthermore, we assume the following:
19
Independence of muscles: The 31 muscles actuating the modeled limbs (actu-
ally 33, but see below) are assumed to be controlled independently. However, it
has been observed in numerous studies that the activations of muscles correlate to
some degree. Whether these correlations are a function of the particular motor
task [Kutch et al., 2008, Valero-Cuevas et al., 2009b] or the common input at a higher
center [Winges et al., 2006], is currently unclear. The only exception we make to this
assumption is that the three Vasti muscles are controlled together and basically treated as
one muscle [Hoffer et al., 1987a, Hoffer et al., 1987b]. This reduces the original number
of 33 muscles to 31.
Knowledge of muscle state is unaffected by noise and neural delays: since
the neural delays involved in transmitting information about the muscle state to a
central controller are negligible (on the order of ms) compared to the time scale of
fatiguing (on the order of 10s of seconds to minutes) and force modulation (isomet-
ric task), we do not include them in our model. Furthermore, we disregard noise,
either in the muscle activation signal or the endpoint force fluctuation (signal-dependent
noise [Jones et al., 2002]), based on the observation that the magnitudes of relative shifts
in muscle activation are much larger than the fluctuations about the mean force level
generated by a muscle. Nevertheless, noise and delays might influence the amplitude,
frequency or timing of activation pattern dynamics but are unlikely to prevent such high-
amplitude, low-frequency dynamics altogether.
Leg consisting of rigid, supported links with ball and hinge joints:
for an isometric task, this assumption has been shown to be sufficient and
valid [Valero-Cuevas et al., 1998]. This assumption allows us to use a simple three-
dimensional geometric model to model the mapping from joint torques to limb endpoint
forces. Furthermore, since we model a seated posture, with knee and hip flexed at right
angles, the leg is completely supported and no torques are necessary to maintain posture.
20
Linearity: It has been shown previously that in isometric force production,
the mapping from muscle activation to the endpoint wrench is approximately lin-
ear [Valero-Cuevas et al., 1998], which entails that the mapping from muscle activation
to limb endpoint force can be described by matrix multiplication. Force-velocity curves
do not play a role in isometric tasks and the force-length curve properties are captured
by the changes of the moment arms as the posture varies.
Post activation potentiation: Under activation, the maximum force a muscle can
generate initially increases [Brown and Loeb, 1998], before the onset of fatigue. We
assume here that the muscle has been activated accordingly and is capable of generating
its maximum force.
Mathematical modeling of isometric knee extension
The leg model consists of two joints, a ball joint at the hip and a hinge joint at knee, but
no ankle joint, since none of the knee extensors crosses this joint. The knee and hip joint
are both flexed at 90

. The two joints actuate a rigid two-link system, with the upper
and lower leg being 0.437 m and 0.37 m long, respectively [Ward et al., 2009]. The
particular endpoint coordinates and limb orientationx;y;z; at the lower end of the shin
are a function of the four joint angles~ q = [q
1
;q
2
;q
3
;q
4
] (i.e. hip add/abduction, rotation,
flexion/extension and knee flexion/extension) [Valero-Cuevas, 2009]. This relationship
is expressed by the geometric relationship (s(q) = sin(q), andc(q) = cos(q)):
~ x =
2
6
6
6
6
6
6
4
x
y
z

3
7
7
7
7
7
7
5
=
2
6
6
6
6
6
6
4
Gx(~ q)
Gy(~ q)
Gz(~ q)
G(~ q)
3
7
7
7
7
7
7
5
=
2
6
6
6
6
6
6
4
L
1
c(q
1
)c(q
2
)+L
2
[s(q
4
)(s(q
1
)s(q
2
)c(q
1
)c(q
3
)s(q
2
))+c(q
1
)c(q
2
)c(q
3
)]
L
1
s(q
2
)+L
2
[c(q
4
)s(q
2
)+c(q
2
)c(q
3
)s(q
4
)]
L
1
c(q
2
)s(q
1
)+L
2
[s(q
4
)(c(q
1
)s(q
3
)+c(q
3
)s(q
1
)s(q
2
))c(q
2
)c(q
4
)s(q
1
)]
c(q
1
)q
3
+s(q
1
)(q
2
+q
4
)
3
7
7
7
7
7
7
5
21
where the L
i
are the link lengths. The change in endpoint coordinates and ori-
entation, as a function of the change in joint angles can be expressed by the Jaco-
bian [Yoshikawa, 1990], i.e. the partial derivatives of the above geometric relationship:
_
~ x =J(~ q)
_
~ q =
2
6
6
6
6
6
6
6
4
@Gx(~ q)
@q
1
@Gx(~ q)
@q
2
@Gx(~ q)
@q
3
@Gx(~ q)
@q
4
@Gy(~ q)
@q
1
@Gy(~ q)
@q
2
@Gy(~ q)
@q
3
@Gy(~ q)
@q
4
@Gz(~ q)
@q
1
@Gz(~ q)
@q
2
@Gz(~ q)
@q
3
@Gz(~ q)
@q
4
@G(~ q)
@q
1
@G(~ q)
@q
2
@G(~ q)
@q
3
@G(~ q)
@q
4
3
7
7
7
7
7
7
7
5
_
~ q
The JacobianJ(~ q) is nonlinearly dependent on the posture~ q. The endpoint wrench~ w
in knee extension, i.e. the four-dimensional vector consisting of 3 forces and 1 moment
applied by the shin, is also related to the joint torques ~ by the Jacobian, taking its
inverse transpose:
~ w =J(~ q)
T
~
These torques, in turn, are generated about the hip and knee joints by the tendon
tensions
~
f, where
~
f is an n-dimensional vector and n the number of muscles (n = 31):
~ =R(~ q)
~
f =
2
6
6
6
4
r
11
::: r
1n
.
.
.
.
.
.
.
.
.
r
31
::: r
3n
3
7
7
7
5
~
f
Here, R(~ q) is the moment arm matrix and the r
ij
are the moment arms of the j-
th muscle acting about the i-th joint. Since muscle moment arms change with mus-
cle lengths, which in turn depend on the posture and thus the joint configuration, the
moment arm matrix is posture-dependent, but we simplify it to R. We used moment
arms for the 31 muscles for this particular posture (90

knee and hip flexion) based on
published values [Arnold et al., 2010]. In our model, the 31 muscles generate 4 joint
22
torques (hip add/abduction, rotation, flexion/extension and knee flexion/extension), cor-
responding to an underdetermined mapping from activation to torques.
Finally, the tendon tensions
~
f generated by the muscles are related to the muscle
activations~ a (0a
i
1) through a diagonal mappingF
0
:
F
0
~ a =
2
6
6
6
6
6
6
6
4
F
11
0 ::: 0
0 F
22
::: 0
.
.
.
.
.
.
.
.
.
.
.
.
0 0 ::: F
nn
3
7
7
7
7
7
7
7
5
~ a
where the entryF
i
i corresponds to the maximum muscle tension of thei-th muscle.
This value scales the individual muscle activations, which are between 0 and 1, to the
force generated by the muscle. The diagonality of this mapping reflects the above men-
tioned assumption of independent muscle control. The maximum muscle tension values
are computed as the product of the physiological cross-sectional areas (PCSA) of the
muscles and the muscle stress, the values of which can be found in [Arnold et al., 2010].
If we allow for fatigue dynamics, which we describe in the next section, the matrix
F
0
becomes time-varying, since the maximum tension a muscle can generate will
decrease or increase depending on its activation level, as per our adopted definition
of fatigue, hence F
0
(t). Initially, muscles are assumed to be unfatigued and capable
of producing maximum force [Brown and Loeb, 1998]. Incorporating muscle fatigue
and recovery dynamics in this way reflects the assumption of immediate knowledge of
muscle state (above).
In conclusion, the linear mapping from muscle activations a to the 4-dimensional
endpoint wrenchw, applied by the ventral aspect of the lower leg, in an isometric knee
extension task, can be described by the product of the 3 above matrices:
23
Rectus femoris
Adductor brevis
Adductor longus
Gemelli
Gluteus medius 1
Iliacus
Pectineus
Piriformis
Psoas
Tensor fascia latae
Quadratus femoris
Sartorius
Vasti
F
normal
Figure 2.1: Muscles contributing to knee extension and their vectors of force application
(if knee and hip are flexed at right angles), based on the linear model and selected by
various optimization functions (described below). Also shown is the direction of nor-
mal force application (black arrow), just above the malleolus. Note that some of these
vectors, those associated with adductors and abductors, point out of the plane.
w =J
T
RF
0
(t)a
In our modeling approach of knee extension, where 31 muscles actuate the hip and
knee joints to generate a wrench, the redundancy, i.e. the infinity of possible solutions,
can then be mathematically illustrated as follows:
24
w = J
T
RF
0
(t)a
w = J
T
RF
0
(t)a
= J
T
RF
0
(t) (y +z)
= J
T
RF
0
(t)y +J
T
RF
0
(t)z
= J
T
RF
0
(t)y +0
= J
T
RF
0
(t)y
where an 31-dimensional muscle activation vector a = y +z can be decomposed
into two vectors, one of whichz is an arbitrary vector from the null space of the matrix
J
T
RF , which has 31 4 = 27 basis vectors. Note that due to the [0; 1]-constraint
on the activations the solution space is constrained and moreover, because of the time-
dependence of F
0
(t), the solution space of the matrix is shrinking and expanding in
various dimensions as the muscles fatigue and recover.
2.3.2 Mathematical modeling of fatigue
To extract realistic fatigue and recovery dynamics, represented by a set of differential
equations, we implemented and ran a recently published model [Dideriksen et al., 2011]
of single-muscle force production and fatigue. This model extends a common motor
unit-based model of muscle force generation [Fuglevand et al., 1993] by dynamics of
muscle cell metabolite uptake and release rates, which in turn depend on the muscle acti-
vation level. Accumulation of metabolites decreases the twitch amplitude and increases
the twitch time constant of each motor unit. We simulated the decrease in MVC force,
25
and thus fatigue, by continuously activating the muscle activated at 10 different, but
constant levels, from 0.1 to 1.0, i.e. full activation, where full activation is the level of
activation necessary to achieve the maximum firing rate in all of the motor units of the
muscle. We simulated the time course of MVC force increase due to recovery, on the
other hand, by leaving an initially fully fatigued muscle deactivated for a sufficiently
long time. The fatigue and recovery profiles are shown in figures 2.2 and 2.3. Note
that the fully fatigued muscle is still capable of generating low amounts of force, which
reflects the contribution of indefatigable slow fibers [Loeb and Ghez, 2000]. The fatigue
dynamics at high forces initially match the activation-dependent exponential profile pro-
posed elsewhere [Freund and Takala, 2001]. The recovery, on the other hand, follows an
initial exponential increase, which is followed by a slow linear phase. The linear phase
represents the change in the amplitude in the H-reflex [Duchateau et al., 2002].
Based on these time series of muscle fatigue and recovery, we used the EUREQA
software [Schmidt and Lipson, 2009] to find possibly non-linear differential equations
dF
0
dt
=f(F
0
(t);a(t))a(t) and
dF
0
dt
=f(F
0
(t)) representing fatigue and recovery, respec-
tively. EUREQA implements a machine learning technique known as symbolic regres-
sion that uses genetic programming to evolve analytical expressions to model the avail-
able data. A population of models is evaluated iteratively to find a set of models that
best map the inputs to the outputs. This is unlike other machine learning techniques
that use a ”black box” approach to model input-output relationships because it avoids
overfitting in attempting to uncover the underlying physics by not espousing any one
specific form of the equations.. The optimization criterion we used to fit the dynamics
was the maximization of the R-squared goodness-of-fit metric, as this provided the best
trade-off between minimizing the fitting error and model complexity, i.e. the over-fitting
of the simulation time series.
26
2.3.3 Simulating muscle activation dynamics in isometric knee
extension subject to optimization
We integrated the previously obtained differential equations with a simple Euler scheme,
implemented in the MATLAB c
(Natick, MA) environment. The activation dynamics
at each time step, which we set to 10 s (i.e. small relative to time constants of muscle
fatigue and recovery), were found using the constrained optimization functions linprog()
and quadprog(), minimizing linear or quadratic objective functions, respectively. These
objective functions represent simple control strategies and ways to overcome or lever-
age, respectively, motor redundancy. The following constraints applied:
J
T
RF
0
(t)
x;y
a(t) = 0
J
T
RF
0
(t)

a(t) = 0
J
T
RF
0
(t)
z
a(t) = c
i.e. the normal force component of the vector generated at the leg endpoint needs to
be kept constant at c N (Figure 2.1), where c represents a percentage of MVC force,
while keeping tangential force componentsF
x
andF
y
and the endpoint torque at zero.
Furthermore, the 31 muscle activationsa(t) are constrained to fall in the [0; 1] interval,
i.e.:
0 a
i
(t) 1
27
We simulated activation dynamics based on the instantaneous minimization of six objec-
tive functions at each time point of simulation, static variations (muscle forces being
static) of which have been proposed previously [Prilutsky and Zatsiorsky, 2002]:
1)
P
i
a
i
(t)
2
(sum of activations squared)
2)
P
i
a
i
(t) (sum of activations)
3)
P
i
(F
i
(t)a
i
(t))
2
(sum of muscle forces squared)
4)
P
i
F
i
(t)a
i
(t) (sum of muscle forces)
5)
P
i

a

i
P
i
a

i

a
i
(t)
P
i
a
i
(t)

2
(constant activation proportions)
6) a
i
(t) =F

i
=F
i
(t) (constant muscle force)
where thea
i
andF
i
are initial muscle activations and muscle forces computed for the
unfatigued muscle, by minimization of objective function 1). Note that in 5), activation
proportions rather than actual activations are kept constant, since the latter would lead to
immediate task failure, i.e. activations need to increase from task beginning to compen-
sate for fatigue. Objective functions 5) and 6) represent synergistic strategies of task per-
formance, by either keeping all muscle activation contributions equal, as in 5) or keep-
ing the force produced by each muscle constant. In [Danna-Dos Santos et al., 2010], the
authors claim to have found evidence for the former strategy, while synergies can also
be understood as occurring at the muscle force level, as in 6), or yet another level of the
control hierarchy.
Running the muscle activation dynamics based on these objective functions, we
quantified the performance of each control strategy in terms of i) failure times, i.e. the
time point at which the 31 muscles were no longer capable of generating the forces nec-
essary to produce the isometric knee extension force, ii) cumulative error, that is, the
cumulative absolute difference between the generated force and the target forces, iii)
28
the number of changes in the order of individual muscle activation proportions, iv) the
number of changes in the order of individual muscle forces, v) the summed difference in
activation at the beginning and the time of failure and vi) the same as v), but for muscle
force. Synergies would aim to keep the latter four metrics at zero, due to ”hard-wired”
muscle co-activation, which intends to prevent any dynamics in activation or muscle
force. Specifically, we would expect objective function 5) to keep at zero the number
of activation order switches and objective function 6) the number of muscle force order
switches.
2.3.4 Parameter search
Since the model [Dideriksen et al., 2011] simulates the force, activation, fatigue and
recovery dynamics of the first dorsal interosseous (FDI) muscle, the extracted differ-
ential equations cannot be simply applied to any muscle of the human body without
some degree of adjustment. Therefore, to test the sensitivity of our obtained results
to parameters, we reran the above described simulations over a range of values. Most
importantly, we ran simulations at different submaximal activation levels, expressed as
percentages of normal force MVC. Gradually increasing the activation level has the
effect of reducing the volume of the solution space of admissible muscle coordination
patterns [Valero-Cuevas, 2009]. Specifically, we hypothesize that at high activation lev-
els, different optimization functions all converge to the same activation dynamics, due
to the lack of solutions. Furthermore, we tested different ratios of the dominant time
constants of fatigue and recovery, thus gradually approaching a scenario without muscle
recovery. Lastly, we explored the sensitivity to a parameter we refer to as the ”fatigue
threshold”, whereby muscles do not fatigue if their activation is below this value (Fig-
ure 2.2, at low activations) [Housh et al., 1995]. This reflects the contribution or pro-
portion of slow-twitch (or non-fatiguable) motor units, which are variable in the human
29
body [Johnson et al., 1973]. We hypothesize that since the above objective functions
do not explicitly take into account the muscle physiology, a change in this value will
not have an obvious effect on the computed muscle coordination patterns. The specific
parameters and value ranges tested are shown in table 2.3.4.
Parameter Range
MVC percentage 0.01 - 20 %

recovery
=
fatigue
0.5 - 10
Non-fatiguable activation level 0.01 - 0.3
2.4 Results
2.4.1 Eureqa-extracted dynamics of muscle fatigue and recovery
We first ran the motor-unit model [Dideriksen et al., 2011] at different activation levels,
to obtain curves of decrease and increase of maximum muscle force representing fatigue
and recovery (Figures 2.2 and 2.3).
Based on these curves, we ran Eureqa for approximately 9 hours on an Apple Mac-
book Pro with a 4-core 2.53 Ghz Intel Core i5 and selected a fit that achieved the best
trade-off between low error and complexity:
dF
0
dt
=
fatigue
F
0
(t)e
(2:451F
0
(t)
2
a(t)0:5933)
2
a(t)
where
fatigue
= 0:00905 for the nominal fatigue dynamics. Similarly, we ran
Eureqa on the muscle recovery curve for 4 hours to obtain:
dF
0
dt
=
recovery
erfc(15:18F
0
(t)
2
11:66F
0
(t))
30
20 60 100 140 180
0
0.2
0.5
0.7
1.0
Time [s]
MVC force

0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 2.2: Fatigue dynamics. Decline
in MVC force for various constant mus-
cle activations, based on the model
in [Dideriksen et al., 2010]. Note that at
low activation levels (a(t) 0:2), the
muscle almost doesn’t fatigue and that
even if fully activated, the muscles max-
imum force declines to a non-zero level.
These phenomena likely reflect the con-
tribution of slow-twitch fibers.
200 400 600 800 0
Time [s]
Figure 2.3: Recovery dynamics. Incline
in MVC force in the absence of muscle
activation. Note the much longer time
scale compared to muscle fatiguing. Also
note that an initial exponential increase in
MVC force is followed by a long linear
increase.
where erfc(x) represents the complementary error function, i.e. erfc(x) =
2
p

R
1
x
e
y
2
dy and
recovery
= 0:00448 for the nominal recovery dynamics (Figure 2.5).
Lastly, we extended the fatigue differential equation by a conditional operations,
whereby fatigue dynamics were suppressed if the activation level of the muscles was
below the fatigue thresholdh described above, i.e. a(t) h. Moreover, we extended
the recovery differential equation by another conditional operator to suppress recovery
if the activation was different from zero, i.ea(t) = 0:0.
31
Figure 2.4: Observed fatigue dynamics
dF
0
dt
in the simulations
of [Dideriksen et al., 2011], and the fit (red) obtained using Eureqa.
Figure 2.5: Observed recovery dynamics
dF
0
dt
in the simulations
of [Dideriksen et al., 2011], and the fit (red) obtained using Eureqa.
2.4.2 Running the nominal model subject to optimized activation
At each time step of simulation, wheredt = 10 s, we ran MATLAB’slinprog() and
quadprog() functions, minimizing the above described objective functions, subject
32
to the above mentioned constraints and using the current maximum muscle forcesF
0
i
(t).
Next, we computed the instantaneous fatigue or recovery increment or decrement from
the Eureqa-extracted differential equations (previous section). In Figures 2.6 and 2.7,
we observe a clear difference in muscle activation dynamics, based on the objective
function minimized. All objective functions rely mostly on the rectus femoris and the
vasti, as expected. None of the objective functions, however, gives rise to the activa-
tion of hamstring muscles, which are hip extensors. Their activation would be expected,
based on the fact that rectus femoris also acts as a hip flexor and this flexion needs to
be counteracted. However, it has been found [Andersen et al., 1985] that the hamstrings
remain silent in knee extension in this posture and that RF basically acts as a monoartic-
ular muscle. Here, the upward component of the rectus femoris is mostly counteracted
by its synergists, the vasti, and other muscles.
Importantly, synergy-based activation dynamics, i.e. keeping constant the propor-
tions of muscle activations or the force produced by each muscle, succeed at their
respective objectives (Figures 2.8 and 2.9). However, we observe that the former also
entails non-constant contributions of individual muscles in terms of force, while the lat-
ter entails non-constant contributions in terms of activation. In other words, synergy-
based objectives can only be met in one domain, while requiring dynamic changes
in others. Furthermore, the constant activations proportion objective function almost
immediately gives rise to a tangential force component, thus violating the task con-
straints (Figure 2.8).
Another important observation is that not only do different objective functions give
rise to different activation dynamics, but they also rely on vastly different numbers of
muscles. For instance, minimizing the sum of activations, a linear objective function,
involves only 4 muscles, while minimizing the sum of squared activations, a quadratic
objective function, involves 13 muscles (Figures 2.7 and 2.6).
33
0
2k
4k
Maximum muscle force
N
0
2
4
Endpoint force
N

Force
x
Force
y
Force
normal
0
0.5
1
Activation
0
0.1
0.2
Activation proportions
0 50 100 150
0
50
100
150
Muscle force
Time [min]
N
0 50 100 150
0
0.2
0.4
Muscle force proportions
Time [min]

Adductor brevis
Adductor longus
Gemelli
Gluteus medius 1
Iliacus
Pectineus
Piriformis
Psoas
Quadratus femoris
Rectus femoris
Sartorius
Tensor fascia latae
Vasti
6
0.3
200
Figure 2.6: Sum of squared activations objective function muscle activation and force
dynamics. Muscle activation and force dynamics are highly dynamic, quite different
from a static optimization approach that ignores time-variance due to muscle fatigue.
2.4.3 Parameter search results
Even more strikingly, relying on just 4 muscles at the lowest force levels, the sum of
activations objective function fails at the task significantly later than its quadratic coun-
terpart (Figure 2.10), and for that matter, all other objective functions. It does so con-
sistently across all levels of force. This can be attributed to the fact that minimizing
this criterion is actually the only one tested here that leverages the ability of muscles to
recover, here specifically the rectus femoris and the vasti (Figure 2.7), to a considerable
degree, reaching the maximum recovery rate at levels between 10 and 20 % of MVC
force (Figure 2.11). Note that at lower force levels, recovery is necessary to a lesser
34
1k
2k
3k
4k
Maximum muscle force [N]
2
4
6
Endpoint force [N]

Force
x
Force
y
Force
normal
0
0.5
1
Activation
0.2
0.4
0.6
0.8
Activation proportions
0 50 100 150
20
40
60
Muscle force [N]
Time [s]
0 50 100 150
0.2
0.4
0.6
0.8
Muscle force proportions
Time [s]

Iliacus
Quadratus femoris
Rectus femoris
Vasti
Figure 2.7: Sum of activations objective function muscle activation and force dynamics.
Note the rapid switching between rectus femoris and vasti muscles and the fact that this
strategy only relies on 4 muscles for successful task performance. The brief switching
off of rectus femoris allows it to recover slightly, before being reactivated.
degree, due to the fatigue threshold described above. The decline of recovery at higher
forces can be attributed to the lack of available muscle coordination patterns that achieve
the task, while the lower rate at low forces reflects the contribution of muscles activated
sufficiently low to avoid fatiguing.
35
0
2k
4k
Maximum muscle force
N
2
4
Endpoint force
N

Force
x
Force
y
Force
normal
0.5
1
Activation
0
0.1
0.2
Activation proportions
0 50 100 150
0
20
40
Muscle force
Time [min]
N
0 50 100 150
0
0.2
0.4
Muscle force proportions
Time [min]

Adductor brevis
Adductor longus
Gemelli
Iliacus
Pectineus
Piriformis
Psoas
Quadratus femoris
Rectus femoris
Sartorius
Tensor fascia latae
Vasti
0
0
6
0.3
60
0.6
Figure 2.8: Constant activation proportions objective function muscle activation and
force dynamics. Note that this objective functions leads to both a relatively early task
failure and a large task error in terms of normal force and one of the tangential compo-
nents of force. Finally, it involves complex dynamics in muscle force space.
All objective functions perform better than the constant muscle force objective func-
tion, in terms of failure time and better than the constant activation proportions objective
function, in terms of error rate (Figure 2.10). As a matter of fact, note that while the
constant activation proportions function seemingly fails later than all other activation
schemes, it consistently does so by violating the task constraint of zero tangential force
(Figure 2.8), thus giving rise to a large error rate at all MVC force percentage levels
(Figure 2.10). Interestingly, while succeeding at enforcing their respective synergy, syn-
ergies do however involve either activation or muscle switching and thus give rise to
”undesirable” computational complexity.
36
0
2k
4k
Maximum muscle force
0
2
4
Endpoint force

Force
x
Force
y
Force
normal
0
0.5
1
Activation
0.4
Activation proportions
0 50 100 150
0
20
40
Muscle force
Time [min]
0 50 100 150
0
0.2
0.4
Muscle force proportions
Time [min]
Adductor brevis
Adductor longus
Gemelli
Iliacus
Pectineus
Piriformis
Psoas
Quadratus femoris
Rectus femoris
Sartorius
Tensor fascia latae
Vasti
N
N
6
N
0
0.8
Figure 2.9: Constant muscle forces objective function muscle activation and force
dynamics. This objective function leads to a relatively early task failure and involves
complex dynamics in muscle activation space.
Lastly, varying the ratio of recovery and fatigue time constants and the fatigue
threshold have far smaller influence on the results, giving almost the same results for
all values in terms of the metrics computed here (results not shown). This is hardly
surprising, since only one of the objective functions, minimizing the sum of activations,
actually leverages muscle recovery dynamics. Thus, its dynamics are the only ones that
do show some effect of increasing the recovery time constant, specifically a reduction
in switching behavior and a reduction in the recovery rate.
37
0
50
100
150
Time [min]
Failure times

Sum of activations
Constant activation proportions
Constant muscle force proportions
0.05 0.1 0.15 0.2 0.25 0.3
0
5
10
15
Force [N] / minute
MVC normal force proportion
Error rate
Figure 2.10: Comparison of failure times and error rates over a range of target normal
force MVC proportions. While naturally, all dynamics fail progressively earlier as the
force demands of the task increase, the linear sum of activations objective functions
performs the longest. Note that while the synergistic constant activation proportion
objective function seemingly performs well in terms of time-to-failure, it has by far
the largest error rate, due to its inability to enforce the zero tangential force constraint
(Figure 2.8)
38
0
20
40
60
80
100
120
Count
Number of activation switches
0.1 0.2 0.3
0
20
40
60
80
100
120
Count
MVC normal force proportion
Number of muscle force switches
0
0.5
1
1.5
2
Sum of activation proportions changes
Sum of squared activations
Sum of activations
Sum of squared muscle forces
Sum of muscle forces
Constant activation proportions
Constant muscle force proportions
0.1 0.2 0.3
0
0.5
1
1.5
2
MVC normal force proportion
Sum of muscle force proportions changes
0.1 0.2 0.3
0
5
10
15
20
Force [N] / minute
MVC normal force proportion
Max force recovery rate
Figure 2.11: Comparison of activation and muscle force dynamics at different target
normal force MVC proportions. Note that as the target force level increases, only the
linear sum of activations objective functions increasingly relies on switching between
muscles in terms of both activations and force. At low force levels, this function is
actually less dynamic than most others, while achieving similar failure times and error
rates (Figure 2.10)
.
2.5 Discussion
In submaximal tasks, the reality of fatigue and recovery in neuromuscular systems and
the resultant time-variance of maximum muscle forces necessitates an adaptive response
by the nervous system to select muscle activations based on the instantaneous state of the
system, to maintain a desired output. This is contrary to the currently dominant think-
ing about optimization for neuromuscular systems, whereby a single optimal solution
is relied on for the entire duration of task performance [Prilutsky and Zatsiorsky, 2002].
Importantly, the need for dynamic muscle activations and forces doesn’t arise simply to
39
ensure increased activation to compensate for muscle fatigue [Dideriksen et al., 2010]:
since muscles fatigue differentially [Housh et al., 1995], the compensatory increase
in activation needs to be individually tuned. Mathematically, the activation pat-
tern can be represented by a vector, whose direction is determined by the individ-
ual muscle activation contributions and whose magnitude represents the overall acti-
vation [Valero-Cuevas et al., 1998, Valero-Cuevas, 2000]. Based on this interpretation,
the need for continuous adaptation is expressed by the need for both changes in direction
of the vector and increase in its magnitude. A single static optimal solution, on the other
hand, is expected to yield an optimal result only for the instantaneous state of the system
and thus proves suitable only in the prediction of muscle forces, when the relationship
between activation and force is ignored (e.g. [Prilutsky and Zatsiorsky, 2002]), or in the
prediction of activation in tasks of short duration.
Incorporating sophisticated state-of-the-art dynamics of fatigue and recov-
ery [Dideriksen et al., 2011] in a realistic linear model of isometric knee exten-
sion [Yoshikawa, 1990, Arnold et al., 2010], we simulated continuous optimization for a
variety of objective functions and showed that fatigue-induced time-variance inevitably,
regardless of the objective, leads to complex dynamics of activation and individual mus-
cle force contribution (Figures 2.6 and 2.7).
Importantly, synergy-based co-activation of muscles, such as maintaining constant
muscle activation proportions or individual muscle forces, is equivalent to adhering to
an initial solution found through static optimization. While synergies indeed succeed at
minimizing dynamics in their respective domains, the dynamics in the respective other
domains are clearly not synergy-like (Figure 2.8 and 2.9). However, combining the
contributions of individual muscles into a desired endpoint force output, the nervous
system cannot ignore any of the domains. Therefore, the results presented here for even
a simple motor task indicate that the computational benefits associated with synergies
40
are restricted to a single domain. However, the fact that humans are capable of perform-
ing motor tasks continuously or repeatedly show that the nervous system is capable of
processing time-varying relationship between high-dimensional muscle activation and
muscle force spaces.
How could the neuromuscular system still achieve simultaneous simplicity in the
muscle force and the activation dynamics? One possibility is that despite their dif-
ferential activation, contributing muscles all fatigue at the same rate, which in turn
requires equal increases in activation across muscles to compensate for the loss in
muscle force. Given the possibility that some muscles are activated at levels suf-
ficiently low to avoid fatiguing and thus make unnecessary the increase in activa-
tion [Housh et al., 1995], this seems highly unlikely. The other possibility is that the
mapping from muscle activation to muscle force, which is known to be complex and
time-variant [Dideriksen et al., 2010], is adjusted such that synergies can be maintained
in both domains simultaneously. Apart from the lack of evidence for such a complex
and unnecessary adjustment, it again requires knowledge of individual muscle states and
thus information about the full dimensionality of the problem.
Moreover, synergistic objective functions either lead to relatively early task failure,
as in the case of constant muscle forces, or they fail to meet the task constraints, as in
the case of constant activation proportions (Figure 2.10). Alternatively, this can be con-
sidered an immediate task failure. Since fatiguing depends functionally on the muscle
force, a constant muscle force strategy will leave resources in less activated muscles
unused and this strategy will fail by the time one of the muscles reaches full activation
and fatigue cannot be compensated any more. A constant activation proportion strategy,
on the other hand, cannot meet task constraints due to the above mentioned differential
fatiguing in muscles, almost immediately producing force in undesired directions. For
these reasons, lack of computational simplification and early failure, synergies (and thus
41
single static optimization) are at best unnecessary but at worst outright detrimental for
motor task performance.
It can be argued nevertheless, that shifting between synergies might help to alleviate
this problem. While there exists evidence for switching between specific activation
patterns [Akima et al., 2011], this strategy raises the question of how many synergies
are necessary to perform a task and where the difference lies between shifting between
synergies and dynamic activation.
Why have these necessary consequences of differential fatiguing seldom been
observed previously? One possibility is the lack of redundancy in previously stud-
ied tasks: for instance, the task posture or the force requirement might only admit a
very limited number of solutions [Loeb, 2000, Kutch and Valero-Cuevas, 2011] (Fig-
ure 3.2). While these solutions likely require differential activation of contributing mus-
cles, leading to differential fatiguing, the observed activation dynamics might approxi-
mate those of synergistic activation, i.e. a simple scaling up of the muscle coordination
pattern [Rudroff et al., 2010, Danna-Dos Santos et al., 2010], due to the limited resolu-
tion of surface EMG [Farina et al., 2004].
Unexpectedly, while it did enable relatively longer task performance, continuous
optimization of most objective functions tested here did not leverage the availability
of muscle recovery. Only minimizing the sum of activations function gave rise to the
required disabling of muscles. While, on the one hand, being one of the least com-
plex strategies, involving the fewest number of muscles, it also came closest to repro-
ducing the dynamics observed in [Kouzaki and Shinohara, 2006], namely the switching
between rectus femoris and the vasti (Figure 2.7). As we increased the force require-
ment, this switching gradually disappeared (Figure 2.11), reflecting the need to keep all
quadriceps muscles activated and reducing the space of available solutions. The ability
42
to leverage redundancy for optimal use of resources provides another important aspect
in the debate on optimization as a means to solve the redundancy problem.
There exists peripheral evidence for the underlying mechanisms that give rise to
activation shifts between muscles. Selective fatiguing through electric stimulation of
the vastus lateralis [Akima et al., 2002] and biceps brachii [Aymard et al., 1995] has
been shown to increase recruitment of synergists, while the selective fatiguing of first
dorsal interosseous has been shown to increase the -motoneuron excitability of the
non-fatigued neighboring abductor pollicis brevis [Duchateau and Hainaut, 1993]. The
former observations have been attributed to the decrease in inhibition of group Ia
afferents between synergists, with the inhibition between antagonists remaining unaf-
fected [Aymard et al., 1995], while the latter are due to the activation of group III and
IV afferents under fatigue, which in turn inhibit the fatigued muscle. Further evidence
suggests that an observed alternating activity between synergistic muscles, such as the
switching between rectus femoris and the vasti (as seen in the optimization of the sum
of activations function), when we optimized the sum of activations objective function,
serves to prolong task performance, as the switching frequency negatively correlated
with the post-trial decrease in MVC force [Kouzaki and Shinohara, 2006].
Concluding, our results encourage us to view redundancy as an opportunity for
mitigation of fatigue in neuromuscular systems, rather than a computational problem.
However, the results furthermore indicate that even if the neuromuscular system does
not leverage redundancy, a controller nevertheless needs to be fully aware of the high-
dimensional dynamics in muscle force and activation spaces and the time-varying rela-
tionship between the two. Future efforts at discovering a potential optimization principle
underlying muscle activations in motor tasks should therefore investigate the interplay
between redundancy and muscle recovery at submaximal forces. However, computa-
tional models are required to design experiments to ensure the availability of multiple
43
solutions in a given motor task, so as to avoid falsely concluding that synergies are a con-
sequence of nervous system control, as well as the drawbacks of the limited resolution
of EMG.
44
Chapter 3
Biomechanics Rather Than
Neurophysiology Explains the
Abolishment of Alternating Activation
of Synergistic Muscles in Submaximal
Fatiguing Isometric Contractions
3.1 Abstract
Several publications in the last two decades have demonstrated slow dynamic reweigh-
ing of muscle activation among synergists in fatiguing low-force isometric tasks. Fur-
thermore, some of these studies have found evidence that switching between synergists
serves as a fatigue mitigation mechanism, as the frequency of switching is inversely
related to the decrease in MVC force during the trial. Potentially, muscles that are
switched off can recover from fatigue to some degree. However, the switching between
synergists largely disappears at approximately 10% of MVC [Kouzaki et al., 2002], a
phenomenon hitherto not understood.
It is a well-known that at lower force levels, multiple muscle coordination patterns
can generate the same force output. Here, we show, based on the prediction of a real-
istic biomechanical model of isometric knee extension, that although multiple muscle
45
coordination solutions do exist at the 15% MVC force level, each of them requires all
synergists involved in knee extension to be activated, thus precluding muscle coordina-
tion patterns in which individual muscles are switched off.
We then used surface EMG to determine experimentally the muscle activations in
isometric knee extension and successfully reproduced the switching dynamics observed
in previous studies of isometric knee extension. We find that, as predicted by the model,
switching largely disappears between 10 % and 15 % of MVC force.
Hence, we provide a simple biomechanical rather than a complex neurophysiolog-
ical explanation for the abolishment of muscle switching at higher force levels. This
result has important implications for our understanding of how the nervous system deals
with muscle redundancy: specifically, we show that the assumption of neurophysiolog-
ical factors is unnecessary in the explanation of the abolishment of muscle switching.
This enables us to view control by the nervous system as being mainly constrained by
biomechanical factors, while being able to play an active role in the mitigation of fatigue.
3.2 Introduction
Involuntary low-frequency alternations in recruitment of different parts of the
quadriceps during submaximal isometric knee extension were first reported
in [Sjogaard et al., 1986]. Since then, such changes in muscle activation in isomet-
ric tasks have been reproduced in the same task [Kouzaki and Shinohara, 2006], as
well as observed in other isometric tasks such as elbow flexion [Semmler et al., 2000]
and ankle extension [Tamaki et al., 1998]. In particular, in the former two studies the
observed changes were statistically associated with a reduced decrease in post-trial
MVC [Kouzaki and Shinohara, 2006] or increased endurance [Semmler et al., 2000].
46
These results have important and hitherto overlooked implications for motor con-
trol, specifically the way in which the nervous system handles the redundancy prob-
lem [Bernstein, 1967], i.e. the seemingly infinite number of muscle activation patterns
that all generate the same endpoint force vector in submaximal tasks. The results indi-
cate that the nervous system is actually capable of leveraging redundancy for the mit-
igation of fatigue, i.e. employing the switching between synergists to mitigate fatigue
and extend the time to exhaustion in submaximal tasks.
Besides, these results cast doubt on the validity of using optimization to determine a
unique solution to the redundancy problem [Prilutsky and Zatsiorsky, 2002], since tradi-
tional approaches in biomechanics disregard the time-varying nature of neuromuscular
systems subject to fatigue and thus do not allow for dynamic muscle activation or at
least, the switching between solutions. This mismatch between prediction and observa-
tion also applies to the idea of muscle synergies [Tresch and Jarc, 2009], i.e. the rigid
co-activation of muscles, since synergies can be considered as static solutions to the
redundancy problem.
Importantly, however, the endurance-enhancing muscle switching between syn-
ergists has only been observed at very low forces, at no more than 10% of MVC
force [Kouzaki et al., 2002]. Why alternating recruitment has not been observed at
higher force levels, is currently unclear, but [Kouzaki et al., 2002] suggest that these
dynamics are related to the balance between neural inputs from peripheral afferents and
the voluntary drive. Specifically, inhibition between synergist muscles decline as volun-
tary contraction levels increase [Gritti and Schieppati, 1989, Schieppati et al., 1990].
Here, we test a simpler hypothesis for the observed abolishment of switching at
higher contraction intensities. In particular, we hypothesize that the neuromuscular sys-
tem simply requires all synergists, i.e. rectus femoris and the vasti, to produce the
desired force. To generate a specific endpoint force vectors, a subtle combination of
47
muscles whose individual vectors point in the approximate direction is required. While
at low forces, combinations exist that do not necessarily involve all synergists, at higher
force the neuromuscular system simply runs out of solutions of this kind. This predic-
tion is based on a simple linear and redundant, but realistic model of isometric knee
extension [Yoshikawa, 1990, Valero-Cuevas, 2009].
3.3 Methods
3.3.1 Modeling a redundant neuromuscular system
Assumptions
For the purposes of modeling a redundant motor task subject to fatiguing, we adopt the
definition of muscle fatigue as the exercise-induced decline of the maximum force
a muscle can generate [V ollestad, 1997]. In turn, this requires the increase of activa-
tion of that muscle to maintain the force generated by it, as has been observed pre-
viously [Dideriksen et al., 2010, Danna-Dos Santos et al., 2010, Rudroff et al., 2010].
Muscle recovery, on the other hand, occurs only in the total absence of activa-
tion [Dideriksen et al., 2011]. At very low muscle forces, the muscle neither fatigues
nor recovers, due to the reliance on slow-twitch fibers, also known as indefatigable
fibers [Loeb and Ghez, 2000].
We selected the task of isometric knee extension, because there exists prior
evidence that the nervous system leverages redundancy for the mitigation of
fatigue [Sjogaard et al., 1986, Kouzaki, 2005, Kouzaki and Shinohara, 2006]. Besides,
from a modeling point of view, knee extension has favorable properties: it allows for
isolation of muscle redundancy and a clear separation from endpoint force vector redun-
dancy, whereby different force vectors can all achieve successful task performance.
48
Specifically, the muscles actuating the knee (vasti and rectus femoris) are largely simi-
lar in terms of their mechanical action and additionally, these muscles don’t add/abduct
or rotate the leg. Therefore, dynamic activation of rectus femoris and the vasti in iso-
metric knee extension is unlikely to give rise to undesirable tangential endpoint force
component, which helps to keep this vector constant.
Furthermore, we assume the following:
Independence of muscles: Muscles actuating the modeled limbs are assumed to
be controlled independently. However, it has been observed in numerous studies that
the activations of muscles correlate to some degree. Whether these correlations are a
function of the particular motor task [Valero-Cuevas et al., 2009b, Kutch et al., 2008] or
the common input at a higher center [Winges et al., 2006], is currently unclear. The
only exception we make to this assumption is that the three vasti muscles are controlled
together and basically treated as one muscle [Eccles et al., 1957, Hoffer et al., 1987a,
Hoffer et al., 1987b].
Leg consisting of rigid, supported links with ball and hinge joints: for
an isometric finger task, this assumption has been shown to be sufficient and
valid [Valero-Cuevas et al., 1998]. This assumption allows us to use a simple three-
dimensional geometric model to model the mapping from joint torques to limb endpoint
forces. Furthermore, since we model a seated posture, with knee and hip flexed at right
angles, the leg is completely supported and no torques are necessary to maintain posture.
Linearity: It has been shown previously that in isometric force production,
the mapping from muscle activation to the endpoint wrench is approximately lin-
ear [Valero-Cuevas et al., 1998], which entails that the mapping from muscle activation
to limb endpoint force can be described by matrix multiplication. Force-velocity curves
do not play a role in isometric tasks and the force-length curve properties are captured
by the changes of the moment arms as the posture varies.
49
Mathematical modeling of isometric knee extension
The modeling of isometric knee extension has been described in the previous chapter,
in a section with the same title.
3.3.2 Muscle necessity analysis
We used the nominal matrixJ
T
R(~ q)F
0
to determine whether specific muscles, namely
the rectus femoris and the vasti are necessary for a given desired output force using
standard tools in computational geometry. The muscle redundancy problem can be
expressed as a set of linear inequalities [Chao and An, 1978, Spoor, 1983]. These
inequality constraints enforce firstly, that the activation for each muscle lie between
0 and 1, secondly, that the actual output normal force is equal to the desired force,
in terms of the percentage of MVC normal force, thirdly, the tangential components
of the endpoint force vector are zero and finally, that no torque is applied about the
endpoint. The inequality constraints define a region in muscle activation space called
the task-specific activation set: any point inside that set will produce the desired
output force [Kuo and Zajac, 1993, Valero-Cuevas et al., 1998, Valero-Cuevas, 2000,
Valero-Cuevas, 2005]. We computed the vertices defining the task-specific activation
set using a vertex enumeration algorithm [Avis and Fukuda, 1992]. We then found the
task-specific activation ranges to achieve the desired output force for each muscle by
projecting all vertices onto the 31 muscle coordinate axes to determine the minimum
and maximum task-specific activations. We used the necessity analysis of the nominal
model to determine a set of candidate muscles for the subsequent sensitivity analysis
(below). Since running vertex enumeration to test the robustness of muscle necessity
results is computationally too costly, we tested the necessity of a few individual muscles
only, which we identified by the low force at which they became necessary. Lastly, due
50
to the computational cost, we performed the necessity analysis on a reduced model with
15 muscles, including all muscles that have a moment about the knee plus some of the
hip muscles, mainly hip flexors and extensors.
3.3.3 Sensitivity analysis
To test how sensitive the muscle necessities of the most necessary muscles found
through vertex enumeration are to variations in task posture, muscle moment arms and
maximum muscle forces, we perturbed the column vectors of the matrixJ
T
R(~ q)F
0
, by
adding random vectors drawn from a zero-mean normal distribution. Since the action
matrix is formed by the product of the posture-dependent Jacobian inverse transpose,
the muscle moment arm matrix and the diagonal matrix of maximum muscle forces,
perturbing this product is equivalent to randomly varying these parameters in isolation.
To determine necessity of individual muscles, we ran MATLAB’slinprog() con-
strained linear optimization algorithm. Specifically, we minimized the sum of muscle
activations
P
c
i
a
i
subject to the above described muscle activation, torque and tangen-
tial constraints. However, all coefficients c
i
, except the one for the muscle of interest
(rectus femoris and vasti) were set to zero, therefore the objective function becomes sim-
plyc
i
a
i
. Thus, the objective is to minimize the contribution of the muscle of interest,
while allowing other muscles to contribute an arbitrary amount of force, as long as the
constraints are satisfied. If the contribution of the muscle of interest cannot be reduced
to zero, that muscle needs to be considered necessary under the given constraints.
Besides varying the perturbation intensity from zero (nominal model) to 20% of each
action matrix column vector’s length, we also varied the output normal force in terms
of the percentage of MVC normal force, which the particular perturbed model could
generate, to determine for each perturbation intensity the percentage at which a muscle
becomes necessary.
51
3.3.4 Data collection
Data were obtained from 3 young adult male subjects (ages 23, 32 and 33, all right-
dominant) during sustained knee extension at three different MVC percentage levels
(2.5%, 10% and 15%), below and just above the predicted level at which the vasti mus-
cles became necessary to perform the task.
We measured subjects’ MVC torque using a CYBEX Humac Norm system (Cybex,
Medway, MA). They were asked to produce maximum isometric knee extension torque
with their dominant leg and with hip and knee flexed at 90

for 5 seconds. This was
repeated 3 times and the maximum obtained value was used as the MVC torque. Based
on the MVC knee extension torque and the moment arm length, i.e. the distance between
knee and the location of force application just above the malleolus, we computed the
MVC normal force by dividing the torque by the moment arm length.
Subjects were seated in a chair, hip joint flexed at 90

and the knee of the dominant
leg flexed at slightly less than 90

. Subjects were not strapped to the chair, to ensure
that they voluntarily maintained that posture and could not rely on postural changes to
mitigate fatigue. However, the lower leg was immobilized between the force sensor and
the leg rest of the chair. Subjects exerted force with the ventral aspect of their lower
dominant leg just above the medial malleolus (Figure 3.1) against a 6-axis force trans-
ducer (JR3, Woodland, CA). Simultaneously, we recorded bipolar surface electromyo-
gram (EMG) using a Delsys system (Delsys, Boston, MA) from the muscle bellies of
rectus femoris (RF), vastus lateralis (VL), vastus medialis (VM), biceps femoris (BF)
and semitendinosus (ST), while the common reference electrode was placed on the skin
around the olecranon. Because of its deep location, we were unfortunately not able
to record from iliacus via surface EMG. EMG and force data were sampled at 1000
Hz using a 16-bit data acquisition system (National Instruments 6259) and stored and
analyzed on a computer.
52
Plastic tube
Force sensor
Surface EMG
(Rectus femoris)
Figure 3.1: Experimental setup. Subjects were seated on a chair, with the backrest set
to vertical, to help them maintain a posture of 90

hip flexion and near 90

knee flexion.
They exerted a force directed forward against a tube that was attached to a force sensor,
set to the appropriate height above ground. The dominant leg, with which subjects
exerted force, was immobilized between the tube and the leg rest. To prevent discomfort
caused by the force exertion, a strap was tied around the leg above the malleolus.
Subjects maintained the 2.5% MVC normal force for 1 hour, the 10% for 20 min-
utes, and the 15% MVC for 15 minutes or until exhaustion. Subjects were given visual
feedback on the normal force: a horizontal line on the screen representing the applied
normal force had to be aligned with a horizontal target force line, as closely as pos-
sible. While subjects did perform a short 1-minute learning trial, they were not given
directions during the actual trial.
53
3.3.5 Data analysis
3.4 Results
3.4.1 Muscle necessity analysis
The muscle necessity analysis reveals that first, the vasti become necessary, near 12%
MVC normal force and next, both rectus femoris and illiacus become necessary at 41%
(Figures 3.2 and 3.3). None of the other muscles that have a moment about the knee
joint, such as the hamstrings, for instance, become necessary at these force levels. In
fact, at 41% MVC, all muscles except the three mentioned above can be arbitrarily
activated and a suitable solution still be found. Therefore, for the subsequent sensitivity
analysis, we investigated the robustness of the necessity results for the vasti, rectus
femoris and iliacus.
3.4.2 Sensitivity analysis
Our sensitivity analysis based on randomized perturbations to the model of isometric
knee extension suggests that it is the vasti which are the determining factors in the
disappearance of muscle switching, since they become necessary at lower MVC normal
force levels than the rectus femoris.
3.4.3 Experimental results
Subjects’ MVC normal forces were found to be 440 N, 481 N and 951 N, respectively.
All three subjects were able to maintain the required force for the duration of the trial
at the 2.5 and 10% MVC target forces. When the task was performed until exhaustion,
the subjects only failed to maintain the required force at the very end. Exhaustion only
occurred when 15% MVC normal force was the target force.
54
ADDBREV ADDLONG ADDMAG GLEM GLUTMED ILIACUS PECT PERI PSOAS QUADFEM RF SAR SEMITEN TFL VAS
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Muscle activation
Figure 3.2: Muscle necessity analysis result at 15% of MVC normal force. The admissi-
ble activation ranges for necessary muscles are colored red. At this force level, the vasti
muscles (V AS) become necessary for any muscle coordination pattern, and thus cannot
be switched off for potential recovery from fatigue. Note that all other muscles can be
activated at any level and a suitable coordination pattern can still be found.
Plotting the EMG traces for the three force levels of 2.5%, 10% and 15% of MVC
normal force (Figures 3.6 - 3.8), we see a gradual change from very pronounced switch-
ing dynamics among the rectus femoris and the two vasti at low force, becoming less
pronounced as the force increases to a complete disappearance at the highest force level.
Instead, the high force is maintained by gradually increasing the activation of all syner-
gistic muscles, thus confirming our hypothesis that at least one of the synergists becomes
necessary at this force level. Thus, the switching off of a muscle would lead to violation
of the task constraints.
More specifically, the observed switching occurred mainly between the
rectus femoris and the two of the vasti muscles, possibly all three of
55
ADDBREV ADDLONG ADDMAG GLEM GLUTMED ILIACUS PECT PERI PSOAS QUADFEM RF SAR SEMITEN TFL VAS
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Muscle activation
Figure 3.3: Muscle necessity analysis result at 41 % of MVC normal force. The admis-
sible activation ranges for necessary muscles are colored red. Besides the vasti (V AS),
the rectus femoris (RF) and the illiacus (ILIACUS) become necessary, too, while all
other muscles can be activated at any level.
them [Akima et al., 2011], due to the common innervation of these mus-
cles [Hoffer et al., 1987a, Hoffer et al., 1987b, Eccles et al., 1957]. This con-
firms the observations in [Kouzaki et al., 2002, Kouzaki and Shinohara, 2006,
Akima et al., 2011], where the observed switching frequency among the vasti
was near zero. Moreover, the switching activity between muscles, when it occurred,
never began immediately or soon after the start of the trials, but 15 minutes into the trial
at medium force levels (Figure 3.7) and even later at the lowest force level (Figure 3.6,
25-30 minutes), suggesting that the switching is induced by fatigue.
Finally, the finding of our sensitivity analysis that the vasti become necessary at
lower force levels than the rectus femoris is reflected by the comparatively greater mod-
ulation of RF activation (Figures 3.6 and 3.7), i.e. the difference in activation between
56
0
0.1
0.2
0.3
0.4
0.5
0.05
0.1
0.15
0.2
0
0.2
0.4
0.6
0.8
1
MVC normal force proportion
Perturbation intensity
Vasti Necessity proportion
Figure 3.4: Sensitivity analysis for the vasti muscles. For a given MVC normal force
proportion between 0 and 0.5, the column vectors of the matrixJ
T
RF
0
were perturbed
by vectors of length 0 to 0.2 of the nominal vector length. For each perturbation length,
the perturbation was repeated 100 times and at each iteration the necessity of the vasti
was determined. The z-axis represents the proportion of iterations for which the vasti
were necessary. We see that the vasti become necessary at the lowest force level for the
unperturbed nominal model, near 0.12 of its MVC normal force.
”on” and ”off” phases is more pronounced in the latter. This confirms that more muscle
coordination patterns exist in the absence of RF activation than do in the absence of vasti
activation.
3.5 Discussion
In this work, we have found evidence for a simple biomechanical explanation for the
abolishment of muscle activation alternation among synergists. Specifically, our 31-
muscle model of isometric knee extension predicts the necessary activation of some of
57
0
0.1
0.2
0.3
0.4
0.5
0.05
0.1
0.15
0.2
0
0.2
0.4
0.6
0.8
1
RF Necessity proportion
MVC normal force proportion
Perturbation intensity
Figure 3.5: Sensitivity analysis for rectus femoris. Contrary to the vasti, in the nominal
model the rectus femoris becomes necessary at the highest MVC normal force propor-
tion, between 0.35 and 0.4, while in the most perturbed model, the RF can be necessary
at force levels as low as 0.1.
the involved muscles, which prevents their deactivation and thus the alternation among
synergists.
Alternating activation between synergistic muscles in fatiguing submaximal
isometric tasks is a phenomenon that has been observed in multiple stud-
ies [Sjogaard et al., 1986, Tamaki et al., 1998, Kouzaki et al., 2002]. it has been sug-
gested that the alternation serves as a endurance-enhancing mechanism, whereby deac-
tivated muscles recover some of their force-generating capability that decreased under
fatigue. The underlying physiological mechanisms giving rise to the alternation phe-
nomenon are currently unclear, but it has been hypothesized that muscle afferents send
fatigue-related information to the -motoneurons of all synergists via interneurons.
In particular, a potential mechanism is the fatigue-induced disinhibition of afferents
between synergists [Schieppati et al., 1990, Pascoe et al., 2006]. According to this inter-
pretation, the alternation between synergists occurs due to the reciprocal decrease in
58
Figure 3.6: Representative EMG recordings at 2.5% MVC normal force. The subject
maintained this force level for 60 minutes. Between 20 and 30 minutes into the trial, we
see activation rotation between the RF and the two vasti, becoming more pronounced as
the trial progresses. Two sample coordination patterns are highlighted: dashed rectan-
gle: RF activated, vasti deactivated, solid rectangle: RF deactivated, vasti activated
inhibition, but since muscles fatigue at different rates, they inhibit each other differ-
entially. Not surprisingly, the reason for the disappearance of alternation at approxi-
mately 10% MVC is even less understood. It has been found that the blood flow to
muscles is significantly reduced at 10% MVC [Sjgaard et al., 1988]. This in turn would
require larger activation of the muscle. It has been found [Gritti and Schieppati, 1989,
Schieppati et al., 1990] that besides fatigue, greater muscle contraction also as the effect
of disinhibition among synergists. Therefore, the constant disinhibition due the larger
activation overrides the effect of the periodic disinhibition due to fatigue.
59
Figure 3.7: Representative EMG recordings at 10% MVC normal force. The subject
maintained this force level for 20 minutes. The switching between RF and the vasti
now begins around 10 to 15 minutes into the trial, but is less pronounced. Two sample
coordination patterns are highlighted: dashed rectangle: RF activated, vasti deactivated,
solid rectangle: RF deactivated, vasti activated
While this interpretation might be true, we argue that it is too complex and incor-
rectly assumes that alternation would still occur if not for the abolishment of inhibition
between synergists by high muscle activation. Indeed, a larger desired output force
requires greater activation. but based on the experimentally confirmed biomechanical
model of isometric knee extension, we argue that the primary reason for the absence of
alternation between the rectus femoris and the vasti muscles is the necessity for vasti
activation. Given that rectus femoris occupies only 15% of the volume of the quadri-
ceps [Akima et al., 2007], it appears obvious that the knee extension force generated at
60
Figure 3.8: Representative EMG recordings at 15% MVC normal force. The subject
maintained this force level for 10 minutes. Assuming that switching serves as a fatigue
mitigation mechanism, we expect it to begin progressively earlier as the force level is
increased. However, no switching occurs at this force level.
higher levels needs to originate somewhere and cannot solely come from rectus. How-
ever, since the rectus femoris is not necessary at the low force levels studied here (Fig-
ure 3.3), this muscle could still be deactivated on its own, while the activation of the
vasti would be accordingly modulated to compensate. While modulation is indeed more
pronounced in RF (Figure 3.7), we hypothesize that disinhibition due to high activa-
tion [Gritti and Schieppati, 1989, Schieppati et al., 1990] still plays a role in preventing
the complete deactivation of rectus femoris at higher force levels.
The importance of biomechanics in the explanation of neural control strategies
seen here emphasizes the need for a controller capable of a flexible response to the
complex and interdependent requirements imposed by the mechanics of the task, the
61
redundancy of muscles and the time-variance due to muscles fatiguing at different
rates, proportional to their individual activation. Indeed, there exists some indica-
tion for a great degree of flexibility in the activation of synergistic and thus, redun-
dant, muscles. In [Schieppati et al., 1990], it was found that gastrocnemius and soleus
are not necessarily synergists under all conditions: as the force requirements of the
task increase, the inhibition between synergists disappears, thus altering the relative
function of the two muscles, which become more synergistic. Furthermore, selec-
tive fatigue of biceps brachii has been shown to increase the activation of unfa-
tigued synergists [Aymard et al., 1995], while the same has been shown in the quadri-
ceps [Akima et al., 2002], potentially due to the disinhibition mechanism described
above. In summary, these findings strongly argue against a rigid co-activation by mus-
cles, as suggested by optimization [Prilutsky and Zatsiorsky, 2002] and the muscle syn-
ergy concept [Tresch and Jarc, 2009]. Instead, they indicate that i) the biomechanical
requirements of the task, in particular the desired output force level, need to be taken
into consideration in trying to determine a muscle coordination pattern, and ii) the time-
varying nature imposed by fatigue on neuromuscular systems does not allow for a static
solution without violation of task constraints. On the other hand, the ability to respond
in a flexible way affords the nervous system a means to proactively leverage muscle
redundancy, specifically a dynamic activation of muscles, to enhance the endurance of
the system [Kouzaki and Shinohara, 2006].
62
Chapter 4
Temporal Analysis Reveals a
Continuum, Rather Than a Separation,
of Task Relevance
4.1 Abstract
The Uncontrolled Manifold and Principle of Minimal Intervention hypotheses propose
that the observed differential variability across task relevant (i.e., task goals) vs.
irrelevant (i.e., in the nullspace of those goals) variables is evidence of a separation
of task variables for efficient neural control strategies. Support for this comes from
spatial domain analyses of kinematic, kinetic and EMG variability. While proponents
admit the possibility of preferential as opposed strictly ”uncontrolled” variables,
such distinction has not been quantified or considered when inferring control action.
Here we extend analysis of task variability to the temporal domain and show that,
even for steady-state 3-finger static grasp, the variability in ”task-irrelevant” variables
exhibits a structure indicative of corrective action at par with that for ”task-relevant”
variables. The spatial fluctuations of fingertip forces show, as expected, greater ranges
of variability in ”task-irrelevant” variables (> 98% associated with changes in total
grasp force; vs. only< 2% in ”task-relevant” changes associated with acceleration of
the object). At some time scales, however, the temporal fluctuations of ”task-irrelevant”
variables can exhibit negative correlations clearly indicative of corrective control (Hurst
63
exponents < 0.5); and temporal fluctuations of ”task relevant” variables can exhibit
neutral and positive correlations clearly indicative of absence of corrective control
(Hurst exponents 0.5). We conclude that we must revise our understanding of task
relevance in the context of task variability, and that we must consider both spatial and
temporal features of all task variables when inferring control action and understanding
how the CNS handles task redundancy.
4.2 Introduction
In motor control research, redundancy has traditionally been viewed as its ”central
problem” [Bernstein, 1967]. Here, we understand the term ”redundancy” as the avail-
ability of infinitely many different solutions to the performance of a motor task, as
opposed to muscle redundancy, which refers to the multitude of muscle coordination
patterns producing the same endpoint force. The ”problem” in either type of redun-
dancy is selecting a unique solution. In multifinger grasp, which has been studied exten-
sively from a redundancy point of view [Park et al., 2010, Santello and Soechting, 2000,
Latash and Zatsiorsky, 2009], a solution consists of finding a configuration ofn fingertip
force vectors, whose summation will create a net force and moment vector that leads to
successful task performance. For instance, in static three-finger grasping of rigid objects
studied here, one can squeeze an object harder, without translating or rotating it, or the
pressing of a key can be performed as long as the normal force is sufficiently large and
the tangential force components are inside the friction cone.
Mathematically, the redundant space of all applicable forces can be separated into
the mutually orthogonal subspaces of force variability that has no effect on the task
(e.g. squeezing the object in static grasp) and force variability that violates the task
64
constraints. We refer to the former subspace as the task-irrelevant space, or ”null
space”. Faced with the above mentioned ”problem” of selecting particular solutions,
researchers have suggested that the nervous system only needs to identify and control
the latter, task-relevant subspace, and can disregard the former subspace, thereby sim-
plifying the control task. This idea of control is known as the ”Uncontrolled Man-
ifold” hypothesis [Scholz and Schner, 1999, Scholz et al., 2002, Latash et al., 2010]
or ”Principle of minimal intervention” [Jordan, 2003, Valero-Cuevas et al., 2009b].
Studies have considered as evidence for this strategy the observation that task-
irrelevant dimensions exhibit relatively larger variability than task-relevant dimen-
sions [Scholz and Schner, 1999]. Such stratified variability has been demonstrated in
analyses of kinematic [Tseng and Scholz, 2005], kinetic [Santello and Soechting, 2000]
and EMG variability [Valero-Cuevas et al., 2009b]. In this sense, large variability in
a task dimension reflects the absence of control of this dimension during successful
task performance. On the other hand, even a task-relevant dimension will exhibit some
amount of variability. Therefore, the magnitude of variability is not necessarily a good
predictor of task-relevance and in fact, proponents of the UCM hypothesis admit the
possibility of preferential as opposed to a separation into strictly controlled and uncon-
trolled variables [Latash et al., 2010]. Despite this admission, a specific quantification
that would allow us to predict task-relevance based on variability is currently missing.
However, little attention has so far been directed at the temporal structure of vari-
ability in the task null space. Being considered uncontrolled, the implicit assump-
tion is that task-irrelevant variability exhibits the properties of either a white noise
process, consisting of uncorrelated samples, or Brownian motion, formed by the
integration of uncorrelated samples [Kantz and Schreiber, 2004]. Conversely, a con-
trolled process, continuously or intermittently controlled [Collins and De Luca, 1994,
Milton et al., 2009], will exhibit correlations between time samples. Both linear
65
and nonlinear time series analysis have been commonly employed to reveal tempo-
ral correlation structure indicative of control strategies, primarily in postural control
research [Jeka et al., 2004, Collins and De Luca, 1994]. For instance, in a seminal paper
by Collins and de Luca [Collins and De Luca, 1994] the authors demonstrated a com-
plex correlation structure in the center-of-pressure time series recorded during quiet
stance, a highly redundant task.
Here, we test the hypothesis that a time-series, or temporal, analysis of forces in
the ”task-irrelevant” subspace of static tripod grasp reveals more than just an uncor-
related process with relatively large variance. We selected the task of static tri-
pod grasp, because it is one of the most common but simple motor tasks. Yet
at the same time, it allows for multiple solutions in terms of fingertip force vec-
tor configurations, since the object can be squeezed harder or the intersection point
of the three force vectors can move, without imparting a moment or acceleration
on the object [Yoshikawa and Nagai, 1991, Flanagan et al., 1999]. Thus, static tri-
pod grasp has an intuitive associated task null space. To reveal temporal correla-
tion and thus structure indicative of control, we apply Detrended Fluctuation Analysis
(DFA) [Kantelhardt et al., 2001] to the time series of mechanically task-irrelevant vari-
ables to reveal long-range correlations indicative of corrective feedback control of these
variables. Such temporal structure of task-irrelevant variability challenges the thinking
that task-irrelevant variables are not controlled. Instead, these results suggest that task-
relevance needs to be understood more broadly than just mechanically and is incommen-
surate with a simple separation into task-relevant and task-irrelevant variables. Rather,
task variables need to be ranked according to this extended understanding of relevance.
We speculate that the control of mechanically irrelevant variables can help to improve
task performance.
66
4.3 Methods
4.3.1 Data collection
We asked 12 young subjects (ages 20-36, 6 male, 9 right-handed) to perform a static
tripod grasp of an instrumented object designed and built in our lab (Figure 4.1). While
performing the grasp, the thumb, index and middle finger were in contact with three ATI
Nano17 6-axis force transducers (Apex, NC, USA) locked in a configuration comfort-
able for each subject. The angle between index and middle finger was approximately
30

, while the angles formed with the thumb by each finger were approximately 165

.
Each force transducer was coated with a teflon surface to reduce reliance on friction by
the subjects to achieve a stable grasp. The force transducers were connected to a 16-bit
National Instruments 6225 M-series data acquisition card (National Instruments, Austin,
TX, USA). Attached to the object were three markers for motion capture, forming an
equilateral triangle, whose plane was parallel to the grasp plane of the three fingertips.
7 motion capture cameras (Vicon, Oxford, UK) allowed us to measure the object’s posi-
tion and orientation to quantify how well the subject met the task goal of maintaining a
simple static grasp.
Subjects performed all trials with their dominant hand [Oldfield, 1971]. Subjects
were seated in a chair, with the grasping hand resting on the chair’s armrest (Figure 4.1).
Moreover, we asked subjects to immobilize the wrist of their grasping hand by gripping
the wrist with their non-dominant hand to minimize wrist rotation and hand translation,
since we were interested in the coordination of fingertip forces for steady-state static
grasp.
Subjects performed steady-state static grasps under three weight and two visual con-
ditions, for a total of 6 conditions. Three different weights, 50 g, 100 g and 200 g, were
screwed to the object from below (Figure 4.1) to add to the 50 g weight of the object
67
itself. The torques induced by the lowered center of mass helped to minimize rotations
of the object, except those about the vertical axis. In the visual feedback trials, we pre-
sented a crosshair on the screen, whose height represented total grasp force as the sum
of the three normal forces (Figure 4.1). We updated the position of the crosshairs at a
rate of 50 Hz. Subjects had to control normal forces such that the crosshairs would align
with a horizontal target line, in addition to minimizing object translations and rotations.
The visual feedback screen was placed approximately 1.5 m away from the subject,
ensuring that the subject would be able to track the horizontal line.
Subjects performed static grasp trials of 68 s duration three times for each weight,
and for each visual condition, for a total of 18 trials per subject (3x3x2). Between trials,
subjects had one minute of rest to avoid fatigue. The different weights were attached
in random order, while the nine trials involving visual feedback were always performed
after the ones without, because the target line height was based on the self-selected
average sum of normal forces subjects applied to the force sensors for a given weight in
the non-visual condition.
4.3.2 Data preprocessing
The three-dimensional force data recorded by each transducer were sampled at 400 Hz,
while the marker positions were sampled at 200 Hz (both force and motion data col-
lection were triggered synchronously). We removed the first seven and last 1 second(s)
from each trial’s time series to avoid transients. Next, we downsampled both the force
and motion capture time series to 100 Hz. Due to the type of data analysis we per-
formed, we did not filter the data to avoid creating artifactual correlations (see below
and Results section).
68
Load Cell
Arm
Hinge
a b
F
N
F
T
c d
Figure 4.1: a.-b. The apparatus designed and built in our lab. It consists of three arms
rotating about a common hinge. Each arm is instrumented with a 6-axis force transducer,
which form the contact surfaces for tripod grasp. c. The static grasp posture during
trials. In addition, subjects were asked to hold their wrist with their non-dominant hand.
d. The visual feedback on the sum of normal forces. Subjects had to align the crosshair
with the target line.
69
4.3.3 Data analysis
To analyze the spatial coordinated action among the three fingertip forces, we first per-
formed principal component analysis (PCA) on the time series of each sensors normal
forces, for each trial. PCA is a common linear method for the estimation of spatial
correlation structures in data [Clewley et al., 2008]. Specifically, we computed the three
principal components of the 3x3 normal force covariance matrix (q-PCA). PCA has been
commonly used to estimate effective degrees of freedom in motor systems; and in the
context of the Uncontrolled Manifold (UCM) hypothesis to compute task-relevant and
-irrelevant latent variables, which are represented by the orthogonal PC vectors. As is
commonly done [Kutch and Valero-Cuevas, 2012], we then projected the 3-dimensional
normal forces (one normal force per force sensor) time series data onto the three princi-
pal components. We also tested doing this same analysis on the full 9-dimensional data
sets (3 force components per force sensor) but the results are unchanged from when
using only the normal force component from each sensor). As described in the Results,
the first, second, and third principal components can be called the grasp, compensation
and hinge modes of this task (Figure 4.3).
Next, we applied Detrended Fluctuation Analysis (DFA) to each projected time
series [Kantelhardt et al., 2001]. DFA is a tool for the detection of long-range temporal
correlations in non-stationary time series, and has the advantage (in particular, over the
classical time-lagged autocorrelation function) that it can distinguish unwanted trends
of arbitrary order, which can give rise to spurious non-zero correlations, from actual
long-range correlations in non-stationary data. DFA has been used extensively for the
analysis of behavioral and physiological data [Hausdorff et al., 1996a, Peng et al., 1998,
70
Penzel et al., 2003]. Mathematically, DFA quantifies the power-law increase of the root-
mean square deviations from a trend in the time series fluctuations, once segments of
increasing lengthn have been subtracted from it to remove trends of that length:
F (n) =
"
1
L
L
X
j=1
(X
j
a
j
b)
2
#
1
2
WhereX
j
a
j
b represents the residuals of the linear fita
j
b to the time series segmentX
j
of length n. For a given segment length n, there are L overlapping segments in the
process. The complete expression forF (n) represents the average root mean squared
deviation at segment length, or time scale,n. In a non-stationary process, this time scale
is related toF (n) by the relationship
F (n)/n

This power-law increase in root-mean square deviation is mathematically linked to long-
range temporal correlations in the data: negative correlations will, over time, lead to a
smaller rate of increase than positive correlations. In particular, scaling exponents can
be fit to the logarithmic plots of the time scales n vs. the F (n): on the one hand, a
scaling exponent> 0:5 indicates persistence, meaning that the time series increments
at a particular time scale n are positively correlated with the time series increment at
time scale = 0. In other words, a positive (negative) increment at time scale = t
is associated with a positive (negative) increment at time scale = 0. On the other
hand, a scaling exponent < 0:5 indicates anti-persistence, i.e. positive (negative)
increments are followed by negative (positive) increments. If = 0:5, there is a lack of
correlation between the increments at that particular time scale and the time series is
equivalent to a purely diffusive and random (i.e., Brownian) walk. Because long-range
71
negative correlations reflect corrective actions that prevent dissipation, they are inter-
preted as evidence for the workings of corrective and stabilizing (i.e., negative feed-
back) control, while positive correlations can be interpreted as evidence of feedforward
control [Collins and De Luca, 1994].
DFA reveals empirically the inherent time scales for which different temporal cor-
relations exist in the data. We found that the steady-state static grasp data naturally
contained three inherent time scales: 1-50 ms, 200-500 ms, and 3500-7000 ms (Fig-
ure ??). These time scales are found based on regions of linearity in the logarithmic
plots ofn vs.F (n), and thus regions of actual power-law scaling.
We noticed that some trials exhibited a relaxation of the total grasp force, likely an
adaptation to reduce fingertip forces when no perturbations are expected and to mitigate
fatigue. Therefore, to test for reliability of our results, we repeated the DFA on the
first and second half of each trial to test if normal force coordination patterns are time-
varying and sensitive to the location in the trial, and in the level of total grasp force.
Note that here we do not employ DFA to determine self-similarity or fractional
dimensionality in the data, as has been done in some studies [Hausdorff et al., 1996b,
Hausdorff et al., 1996a]. In those studies, the linearity in the logarithmic plots needs
to extend over at least one order of magnitude to count as strong evidence of fraction-
ality [Kantz and Schreiber, 2004]. In our case the requirements for the linearity of the
logarithmic plots are not as rigid because the quantification of long-range correlations
applies to data where the linearity extends over shorter ranges of time scales.
4.3.4 Identification and modeling of the mechanical requirements
of the task and its nullspace
Each fingertip applies a three-dimensional force
~
f to the object. Computing the cross
product of the moment arm, i.e. the vector between the point of force application and
72
the object’s center of mass, with the fingertip force vector yields the moment applied
to the object. The total 6-dimensional force and moment applied to the object can be
computed with the following mappingW:
2
4
P
f
P
m
3
5
6x1
=
2
4
I
3x3
I
3x3
I
3x3
M
th
M
ind
M
mid
3
5
6x9
2
6
6
6
6
4
~
f
th
~
f
ind
~
f
mid
3
7
7
7
7
5
9x1
= W
~
f
whereI
3x3
is the unit matrix andM
fth, ind, midg
is the skew-symmetric matrix representing
the cross-product between the moment arm of the finger and its force vectorf
fth, ind, midg
.
SinceW is a mapping from 9-dimensional to 6-dimensional space, the associated null
space, i.e. the space of vectors for which
~
0 = W~ x has 3 dimensions. Any vector~ x in
this space represents a solution to the static grasp requirement
2
4
P
f
P
m
3
5
=
2
4
~
0
~
0
3
5
, i.e.
that both the sum of forces and the sum of moments should be zero.
However, this is a necessary requirement only. Additionally, we require that at the
finger tip contact points the tangential forces are upper-bounded through the relationship
f
tangential
f
normal
, i.e. the tangential force cannot exceed the normal force, multiplied
with the friction coefficient, which we have set to 0.04, the friction coefficient of teflon.
This represents a lower bound on the coefficient of friction, since this coefficient is
certainly greater when fingertip and teflon surface interact - the grasp under experimental
conditions is actually far less constrained. The sum of tangential forces applied needs to
oppose the force applied to the object by gravity. The simulated object had a weight of
100 g, hence the sum of tangential forces had to equal 0.981 N, which in turn determined
the sign (positive, i.e. into the object) and the minimum magnitude of the normal forces.
We sampled vectors
~
f
t
null
from the null space of the above linear matrix by multi-
plying the three null space basis vectors ~ n
i
with random values a;b;c, drawn from a
73
standard Brownian random walk:
~
f
t
null
= a~ n
1
+b~ n
2
+c~ n
3
. We then added the
null space vector
~
f
null
to the minimum sum-of-squared-forces solution
~
f
min sq
of force
vectors that met all the above described static grasp constraints:
~
f
t
=
~
f
min sq
+
~
f
t
null
, using
MATLAB’s (Natick, MA)quadprog() function to determine the actual solution with
minimum Euclidean distance to
~
f
min sq
+
~
f
t
null
.
Constraint Magnitude Interpretation
P
F [0; 0;mg]
T
Sum of forces equal and opposite to gravity force, i.e. no net force
P
M 0 Sum of moments equals zero, i.e. no net moment
F
i
T
F
i
N
Tangential force at thei-th finger cannot exceed normal force
Table 4.1: List of relevant constraints in static grasp
4.4 Results
4.4.1 Principal component analysis of simulated normal forces
The three individual simulated normal forces are shown on the right in Figure 4.4. Note
that despite their apparent variability, each sample represents a valid solution to the con-
strained problem of steady-state static grasp. Furthermore, on the left in Figure 4.4 we
show the simulated normal forces plotted against each other, and it becomes obvious that
the valid solutions populate a plane. Applying Principal Component Analysis (PCA) to
the simulated data to determine the two basis vectors of that plane, we find that it is
spanned by the vectors [0:8; 0:4; 0:4]
T
and [0:0;0:7; 0:7]
T
, explaining together 100%
of data variance. Hence, if the variability of normal fingertip forces exhibits this struc-
ture in steady-state static tripod grasp, such variability will not give rise to accelerations
or rotations of the grasped object and exists entirely in the null space of the task, while
actual acceleration or rotation of the object is associated with normal force variability
perpendicular to this plane, along the vector [0:6;0:5;0:5].
74
7.5
8.5
9.5
4
5
6
4
4.5
5
Thumb Force [N]
Index Force [N]
Middle Force [N]
7
8
9
10
Middle Force [N]
4
5
6
Index Force [N]
10 20 30 40 50 60
4
5
6
Time [s]
Thumb Force [N]
Figure 4.2: Representative plot of the simulated thumb, index and middle finger normal
forces. Top: The three simulated normal forces plotted against each other. Note that
the force fluctuations come to lie on a plane, whose orientation we compute using PCA.
Bottom: The three simulated normal forces during a trial plotted individually. Note that
the floor effect results from the minimum normal force constraint.
We refer to these three principal components found in the simulations as: (i) the
grasp mode, along [0:8; 0:4; 0:4]
T
, as it reflects synchronous increases and decreases in
75
the three normal forces, which are also known as grasp forces, (ii) the compensation
mode, along [0:0;0:71; 0:71]
T
, reflecting the out-of-phase opposition, or compensa-
tion, of thumb normal force by either the index or middle finger normal force, and (iii)
the hinge mode, along [0:6;0:5;0:5], reflecting an increase (decrease) in thumb nor-
mal force accompanied by a simultaneous decrease (increase) in the index and middle
finger normal forces, which would typically occur if the object was accelerated by the
thumb or rotated, thus violating the mechanical task requirements of static grasp. These
three normal force modes are illustrated in Figure 4.3.
Mechanically, the dynamics associated with the compensation mode reflect
movement of the intersection point of the three force vectors, as shown
in [Yoshikawa and Nagai, 1991, Flanagan et al., 1999]. As long as the force vectors,
extended from their respective application points intersect in one common point inside
the object, there will be no moment exerted on the object. This intersection point can
move inside an area spanned by the friction cones without violating the task require-
ments. Its motion indicates that the tangential force components parallel to the grasp
plane are changing, as the normal forces, in turn, need to be compensated in synchrony,
to avoid both slippage of fingers and accelerations of the object.
4.4.2 Principal component analysis of experimental forces
As expected, subjects met the task requirements well but not perfectly: movements
of the object markers were well within 5 mm in all directions. Object motion was
significantly affected by the presence of visual feedback, but not weight. Importantly,
the small but measurable object accelerations are not caused by force dynamics inside
the two-dimensional manifold spanned by the grasp and compensation modes found in
the simulations (above), but are due to dynamics along the hinge mode and the tangential
force components.
76
Behavioral
mode
PC loadings
[thumb index middle]
Mechanical
coupling of
force variability
Time series
example
Graphical
Interpretation
Variability plotted in
Force-Force-Force
space
5
3
1
4
2
5
3
1
F-Middle
F-Index
F-Thumb
Grasp force Compensation force Hinge force
5
3
1
4
2
[0.8 0.4 0.4]
T
[0 -0.71 0.71]
T
[0.6 -0.5 0.5]
T
thumb
middle
index
hinge
all in phase
index and middle out of
phase with each other
index and middle in phase
with each other but out of
phase with thumb
time
force
thumb
middle
index
5
3
1
4
2
5
3
1
towards/away from origin on surface sideways on surface perpendicular to surface
(approximate)
I II III
Figure 4.3: Illustration of the three normal force modes associated with the principal
components computed from the data and the simulations, across all subjects and condi-
tions.
We applied PCA to the time series of experimental normal forces (Figure 4.4 for
a representative figure), and found that across all trials and subjects, and therefore
regardless of task condition, normal force variability consistently exhibited a structure
described by the three principal components found in the simulation: [0:8; 0:4; 0:4]
T
,
[0:0;0:7; 0:7]
T
and [0:6;0:5;0:5] (Figure 4.6). Note that the slight deviations from
these directions are unlikely to reflect violations of the task requirements, since subjects
performed the task well (above), but could be due to one of the following: (i) The grasp
77
plane formed by the three fingertips is not perfectly parallel to ground. If you consider
Figure 4.1, this seems plausible. Subjects performed this task in a posture that was com-
fortable for them. (ii) The individual grasp mode vector components reflect the degree
of opposition between thumb normal force and the other two normal forces and are
therefore influenced by the apparatus arm angles and the finger tip contact points. In the
experiments, we adjusted the arm angles for subjects’ individual comfort and subjects
decided where to place their fingertips.
As expected from a spatial variability standpoint, the grasp mode explains approxi-
mately 90% of the normal force variance, while the compensation mode approximately
5-10% and the hinge mode 1-3% (Figure 4.7). In the trials with visual feedback, grasp
and compensation modes contribute equally to the normal force variance, slightly less
than 50% each (Figure 4.7) and again 1-3% by the hinge mode, which means that the
null space manifold is evenly populated by the normal force dynamics in these trials.
The low percentage of variance explained by the hinge mode in both cases shows that
subjects satisfied the task requirements of not accelerating or rotating the object.
Projecting the fingertip force time series data without visual feedback onto the grasp
mode shows a very slow monotonic downward trend (Figure 4.8 for a representative
trial). This slow trend is interpreted by PCA as a contributor to large spatial variability
explained by this mode and is caused by the three fingers reducing their normal forces
simultaneously. In trials with visual feedback, the grasp force mode does not exhibit
such a trend (Figure 4.5 for a representative trial), which is not surprising, since keep-
ing the sum of normal forces constant becomes a task requirement, which the subjects
did meet. Thus, visual feedback has the effect of reducing the grasp mode’s contri-
bution to the overall force variability due to the absence of the above mentioned slow
trend. In turn, the compensation mode now contributes a larger proportion of the overall
variability (Figure 4.7). The compensation mode also exhibits a slow non-monotonic
78
4.5
5.5
6.5
2.5
3
3.5
3.5
5
Thumb Force [N]
Index Force [N]
Middle Force [N]
4.5
5.5
6.5
Thumb Force [N]
2.5
3
3.5
Index Force [N]
10 20 30 40 50 60
3.5
5
Time [s]
Middle Force [N]
Figure 4.4: Representative plot of experimental thumb, index and middle finger normal
forces recorded during one trial with a 200 g weight. Top: The three normal forces
plotted against each other. Note that the force fluctuations come to lie on a plane, whose
orientation we computed using PCA. Bottom: The three normal forces during a trial
plotted individually. Note the common downward trend across the three fingers.
79
4
5
2.4
3
3.4
4
Thumb Force [N]
Index Force [N]
Middle Force [N]
3.5
5
Middle Force [N]
2
3.5
Index Force [N]
10 20 30 40 50 60
3
4.5
Time [s]
Thumb Force [N]
Figure 4.5: Representative plot of experimental thumb, index and middle finger nor-
mal forces recorded during one trial with a 200 g weight, when visual feedback was
presented. Top: The three normal forces plotted against each other. Note that the force
fluctuations come to lie on a plane, as in tasks without visual feedback, but the dynamics
populate the plane differently. Bottom: The three normal forces during a trial plotted
individually. Note the absence of a downward trend across the three fingers, due to the
enforcement of the sum of normal forces constraint.
80
modulation both increasing and decreasing over time (Figure 4.8). This indicates that
index and middle finger normal forces are slowly and continuously modulated, out of
phase, during static grasp, unlike a white noise process. Lastly and not surprisingly, the
hinge mode shows almost no variation over time.
0
1−1
0
1
−1
0
1
0.74
0.39
0.44
Index F
N
0.58
−0.56
−0.52
Thumb F
N
−0.04
−0.66
0.65
Middle F
N
Grasp mode
Compensation mode
Hinge mode
Figure 4.6: Distribution of data principal components (dots). The colored lines show
the mean grasp, compensation and hinge mode directions.
81
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Proportion of variance
Grasp Compensation Hinge Grasp Compensation Hinge
Figure 4.7: Mean proportions of variance explained by the grasp, compensation and
hinge mode, respectively, in the simple trials with (right) and without (left) visual feed-
back. In trials without visual feedback, most variance occurs along the grasp mode,
capturing the downward trend across all finger normal forces.
4.4.3 Detrended Fluctuation Analysis of time series projected onto
principal components
DFA of the normal force time series projected onto the three principal components
reveals long-range correlations indicative of both the presence and absence of time-
delayed corrective control in all three modes. In the following, all reported changes
in Hurst exponents (i.e., slopes of the log-log plots) are statistically significant at the
p < .01 level, based on Kruskal-Wallis (across the three weight conditions) or Mann-
Whitney tests (across the two visual feedback conditions).
Consider Figure 4.9, which shows the scaling exponents in the first and second
halves of the trials, respectively. At short time scales (1-50 ms), the slopes associ-
ated with both the compensation and hinge mode time series are close to 0.5, indicating
82
−1 0 1
−0.5
0
0.5
Grasp Mode [N]
Compensation Mode [N]
−2
0
2
Grasp Mode [N]
−2
0
2
Comp. Mode [N]
10 20 30 40 50 60
−2
0
2
Time [s]
Hinge Model [N]
Figure 4.8: Representative plot of the above experimental normal forces projected onto
the three principal components. Top: The force fluctuations on the plane spanned by
the grasp and compensation modes. Bottom: The three principal component time series
during a trial plotted individually. Note how the grasp mode captures the common down-
ward trend, while the hinge mode has comparatively minimal variability.
lack of negative correlation between increments and thus absence of a corrective control
83
effort, while the grasp mode has a slope of 0.7, reflective of positive correlations in the
time series.
At medium time scales (200-500 ms), the slope of the grasp mode decreases to 0.5,
indicating lack of corrective control effort along this dimension, while the compensation
mode now indicates the activity of a stabilizing or correcting effort, having decreased
to a value 0.3, and the hinge mode shows a very distinct slowing down of RMS devi-
ation scaling with exponent 0.1, indicating strong concentration around a mean level.
Importantly, the 200-500 ms time delays include the shortest voluntary time scales of
the sensorimotor system [Kawato, 1999].
The long time scale (3500-7000 ms) is not particularly different from the 200-500 ms
time scale in terms of DFA slopes, except that the grasp mode now becomes corrective
as well, with a slope having decreased to 0.3 from 0.5.
Its slope at this time scale is further reduced to 0.1 in trials with visual feedback,
thus reflecting the lack of slow trends in the grasp mode, since the sum of normal forces
has to be kept constant. The hinge mode is also affected by vision at long time scales,
becoming slightly but significantly more corrective as it is changing from 0.13 to 0.1.
Increasing the weight has the effect that it increases the slope of the grasp mode at
small time scales (1-50 ms) to 1.0, perhaps reflecting the increase in signal-dependent
noise, which scales linearly with force and is observed in the 8-12 Hz frequency band
of force measurements ([Jones et al., 2002], i.e. time scales of< 125 ms) and induces
positive mechanical correlations across fingers due to reaction forces. Another effect
of weight increase is a slight increase of the hinge mode slope with weight, possibly
reflecting the increased difficulty of maintaining stable the more inert object and the
increased need for corrective efforts.
Adding visual feedback also increases the slope of the grasp mode at short time
scales (1-50 ms), which again might reflect the increased amount of signal-dependent
84
noise, since the grasp force level had to be kept constant and could not decrease, as in
the trials without visual feedback.
Finally, the fact that the results are so similar between the first and the second halves
of the trials indicates that the observed dynamics and the associated correlation structure
depend neither on time nor the total grasp force (which can be interpreted as location in
the force space; or in control terms the ”state space” of the system). This in turn indicates
a control strategy that is state-independent except potentially at the boundaries. While
the increase in weight and the addition of visual feedback does seem to modulate the
dynamics on the individual dimensions, it does not lead to a crossing of the 0.5 line and
therefore not to a fundamental change in the control strategy.
Importantly, we see that each mode, both mechanically task-relevant and -irrelevant,
exhibits features of control as well as the absence of control, at some time scale.
4.5 Discussion
While we cannot claim at this point that the neural controller actively controls the spe-
cific dimensions of normal force coordination determined through PCA, our simulation
results nevertheless clearly indicate that the first two principal components, the grasp
and compensation modes, span the null space of force dynamics associated with static
grasp: variation of force inside this planar manifold does not violate the constraints of
static grasp (i.e. zero net force and moment). Given however that noise is an inevitable
reality in neuromuscular systems, successful task completion therefore naturally leads
to the population of the null space manifold, while variability orthogonal to it will be
minimal, but not necessarily zero.
85
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1−50 ms 200−500 ms 3500−7500 ms 1−50 ms 200−500 ms 3500−7500 ms 1−50 ms 200−500 ms 3500−7500 ms
Time scale
Grasp Mode
Scaling exponent
Compensation Mode Hinge Mode
Figure 4.9: The distribution of DFA scaling exponents of the normal forces projected
onto the three force modes - during the first (left box plots) and the second half (right
box plots) of the trials. Note the large exponent of the grasp mode at short time scales,
while the other two modes exhibit a lack of correlation at this time scale. At larger
time scales, the hinge mode exponent is very close to 0, reflecting the fact that subjects
hardly accelerated the object. The grasp mode, on the other hand, exhibits no correlation
at the medium time scale. Importantly, there is no significant difference between scaling
exponent between the first and the second half of the trials.
These results regarding the distribution of variability in space seem to agree with
the Uncontrolled Manifold (UCM) Hypothesis and the Minimal Intervention Princi-
ple [Scholz and Schner, 1999, Jordan, 2003]: that the nervous system chooses to control
only the task-relevant dimensions of a task and keeping their variance small, since they
interfere with the task, while allowing larger variability in directions or variables that
do not affect task performance. This control strategy is reflected in the distribution of
variability along different dimensions of the task. Since static tripod grasp has an asso-
ciated multi-dimensional task-irrelevant manifold, on which fluctuations do not require
corrective intervention, i.e. the grasp and compensation modes found here through PCA,
86
task-irrelevant variables not affecting the mechanical requirements of the task certainly
exist.
However, the temporal DFA applied to task-irrelevant variables and the task-relevant
hinge mode gives a much more complex picture, in which variables of both types appear
to be controlled at uncontrolled, depending on the time scale considered. It is impor-
tant to note that the UCM hypothesis would predict a lack of any correlation in task-
irrelevant variables. On the one hand, grasp mode variability exhibits a lack of long-
range correlation at medium time scales (300-1000 ms) and an absence of corrective
dynamics at short time scales (1-50 ms), while the compensation mode is entirely ran-
dom at short time scales (1-50 ms): being mechanically task-irrelevant, these results
seems to support lack of intervention by the neural controller. Qualitatively, the grasp
mode exhibits a slow downward trend in trials without visual feedback, which might
be a consequence of not controlling forces at medium time scales, while the positive
correlations at short time scales can be shown to be a result of the interplay between
signal-dependent noise [Jones et al., 2002] and reaction forces, i.e. of purely mechani-
cal origin.
On the other hand, the grasp mode exhibits negative correlations indicative of cor-
rective control at large time scales and contrary to the prediction of the UCM hypothe-
sis. These negative correlations cannot solely be attributed to control intervention when
there is a risk of dropping the object due to a reduction in grasp mode force. Instead,
the non-zero scaling below 0.5 observed in our experimental data, both in the first and
second half of the trials (Figure 4.9), suggests control intervention independent of state-
space location. Next, the task-irrelevant compensation mode exhibits negative correla-
tions at medium and large time scales, again contrary to the UCM hypothesis predic-
tion. Lastly, DFA exposes an absence of correlation at very short time scales in the
task-relevant hinge mode, indicating an absence of control. Given the existence of loop
87
delays in neuromuscular systems, the absence of correlations along the hinge mode at
short time scales is not surprising.
These results expose a fundamental limitation of the UCM hypothesis and the Min-
imum Intervention Principle: their focus on spatial aspects of motor variability and dis-
regard for temporal aspects. ”Spatial aspects” refers to latent variables, or instantaneous
correlation modes of elemental variables in motor tasks, which can be revealed through
the use of PCA, among other methods. ”Temporal aspects” refers to the correlations
over time along such latent correlation modes. In other words, due to physiological
limitations, even highly task-relevant variables can be uncontrolled temporarily.
We conclude that controlled and uncontrolled dynamics vary as functions not only
of spatial, but also temporal constraints of the task due to physiological and other lim-
itations, and argue that the UCM hypothesis and the Minimum Intervention Principle
need to be extended by considerations of temporal aspects of motor control, as revealed
through our DFA applied to all task variables. In their current form, these theories
of motor control are incommensurate with our results in that these theories assume a
simple separation of task variables into relevant and irrelevant ones, entirely based on
mechanical considerations. The results presented here instead suggest a continuum of
task-relevance based on aspects beyond those of pure mechanics.
What aspects are potentially relevant to motor tasks, other than mechanics? One
possible explanation for the observed negative correlations along the grasp and com-
pensation modes could be that traversing this manifold is an active process, through
which the CNS actually takes advantage of redundancy. Specifically, controlled dynam-
ics along the compensation mode correspond to the regulation of the index and middle
finger contributions to the opposition of thumb normal force. We speculate that the
CNS is actively trying to shift the demands between the two fingers over time, which
88
in turn might mitigate effects of fatigue at the muscle level. By gradually varying end-
point forces, the CNS achieves a change in the underlying muscle coordination pattern,
which in turn will change the rates of fatiguing of individual muscles, thus allowing for
improved use of available resources. Furthermore, the slow downward trend along the
grasp mode direction of normal forces would fall in line with this hypothesis: a general
reduction of forces generated by the muscles leads to a reduction in the fatigue rate.
This intriguing hypothesis deserves further investigation.
89
Chapter 5
An Involuntary Stereotypical Grasp
Strategy Pervades Voluntary Dynamic
Multifinger Manipulation
5.1 Abstract
We used a novel apparatus with three hinged finger pads to characterize collaborative
multifinger interactions during dynamic manipulation requiring individuated control of
fingertip motions and forces. Subjects placed the thumb, index and middle fingertips
on each hinged finger pad, and held it with constant total grasp force while voluntarily
oscillating the thumbs pad. This task combines the need to (i) hold the object against
gravity while (ii) dynamically reconfiguring the grasp. Fingertip force variability in this
combined motion and force task exhibited strong synchrony among normal (i.e., grasp)
forces. Mechanical analysis and simulation show that such synchronous variability is
unnecessary and cannot be explained solely by signal dependent noise. Surprisingly,
such variability also pervaded Control Tasks requiring different individuated fingertip
motions and forces - but not tasks without finger individuation such as static grasp.
These results critically extend notions of finger force variability by exposing and quan-
tifying a pervasive challenge to dynamic multifinger manipulation: the need for the
neural controller to carefully and continuously overlay individuated finger actions over
mechanically unnecessary synchronous interactions. This is compatible with - and may
90
explain - the phenomenology of strong coupling of hand muscles when this delicate bal-
ance is not yet developed, as in early childhood, or when disrupted, as in brain injury.
We conclude that the control of healthy multifinger dynamic manipulation has barely
enough neuromechanical degrees-of-freedom to meet the multiple demands of ecolog-
ical tasks, and critically depends on the continuous inhibition of synchronous grasp
tendencies, which we speculate may be of vestigial evolutionary origin.
5.2 Introduction
Successful dexterous manipulation requires dynamic collaborative use of our fin-
gers. Clearly, the neural control must actuate the system properly to satisfy the
mechanical constraints of the task. Numerous studies have investigated how we
adapt grasp to different friction contact [Johansson and Westling, 1984], object cur-
vature [Jenmalm et al., 2003], fingertip positions [Baud-Bovy and Soechting, 2001],
perturbations [Eliasson et al., 1995, Kim et al., 2006, van de Kamp and Zaal, 2007],
object manipulations [Flanagan et al., 1999, Shim et al., 2005, Winges et al., 2008]
and dexterity requirements [Johanson et al., 2001, Valero-Cuevas et al., 2003,
Venkadesan et al., 2007]. These prior studies have identified voluntary and invol-
untary collaborative force interactions among fingertips to reduce task variability
when pressing or grasping rigid objects (e.g., [Baud-Bovy and Soechting, 2001,
Scholz et al., 2002, Shim et al., 2005, Latash and Zatsiorsky, 2009]; and for a
review [Schieber and Santello, 2004]). This study, however, examines the behavior of
collaborative, multifinger interactions during more ecological dynamic manipulation of
a deformable object requiring the simultaneous control of fingertip motion and force.
It is motivated by prior work aiming to clarify an apparent and long-standing paradox
between the scientific concepts of muscle redundancy and robustness, vs. the clinical
91
reality of motor development and dysfunction [Venkadesan and Valero-Cuevas, 2008,
Keenan et al., 2009, Kutch and Valero-Cuevas, 2011]. If, say, hand musculature
is so redundant, why then is dynamic manipulation so vulnerable to devel-
opmental problems [Forssberg et al., 1991], mild neurological pathologies, and
aging [Schreuders et al., 2006]? This paradox may arise simply because exper-
iments and models often use simplified tasks for which the musculature is
indeed redundant [Loeb, 2000]. In contrast, everyday ecological behavior often
involves tasks that require meeting multiple mechanical constraints and transi-
tioning between constraints. Our prior work on single fingers indicates that even
ordinary manipulation tasks can push the neuromuscular system to its limit of
performance when they require combinations of, or transitions between, motion
and force constraints [Venkadesan and Valero-Cuevas, 2008, Keenan et al., 2009,
Kutch and Valero-Cuevas, 2011]. Here we extend that prior work to multifinger
function by investigating ordinary, yet critical, multifinger tasks: dynamic manipulation
of deformable objects requiring continuous and simultaneous regulation of fingertip
motions and forces.
5.3 Methods
5.3.1 Experimental procedure
We designed a novel instrumented apparatus with three hinged finger pads to be held
using a tripod grasp with the thumb, index and middle fingers (Figure 5.1). Each finger
pad consisted of a six-axis load cell (Nano 17, ATI/Industrial Automation, Apex, NC,
USA) at one end of a rigid link to measure forces used to grasp and manipulate the
object, with the other end connected by a common planar hinge instrumented to measure
angles between the finger pads [Valero-Cuevas and Brown, 2006]. The grip surface of
92
the load cell was 30 mm from the hinge axis and covered with fine (360 grit) sandpaper.
The objects mass is approximately 60 g to mitigate fatigue. Lastly, to ensure rotation of
the thumb pad at the appropriate frequency, we used a software metronome (Metronome
1.1, Keaka Jackson, The World, 2008).
Mechanics dictates that the direction of fingertip force vectors for a static grasp must
intersect at a point or the forces would create a net moment about the center of mass and
cause a rotation (e.g., Yoshikawa and Nagai, 1991, Flanagan et al., 1999). The loca-
tion of this point is arbitrary as long as the conditions imposed by the friction cones
at the fingertips are satisfied, and the zero net force constraint is met. In this study, in
contrast, the fingertip forces are constrained to intersect at a specified point (a central
hinge) or else the finger pads will rotate. Holding the apparatus with a given total grasp
force while reconfiguring the angles between the hinged finger pads requires collabo-
rative multifinger interactions to control fingertip motions and force vectors. Thus, this
apparatus explicitly distinguishes the multifinger interactions needed to hold the object
against gravity (i.e., total grasp force) from those needed to dynamically reconfigure the
grasp (i.e., compensating for thumb oscillations). Total grasp force is an independent
task constraint from compensations in fingertip force vectors when reconfiguring the
grasp: one can squeeze tighter without moving the pads, or reconfigure the grasp while
producing the same total grasp force.
We tested six consenting subjects (1 female, 5 male; 21-31 years; 5 right-handed,
1 left-handed) using a protocol approved by the USC Institutional Review Board.
Subjects held the test object with the thumb, middle and index fingers of the domi-
nant [Oldfield, 1971] hand in a tripod grasp (Figure 5.1a, the subject flexed the ring and
little fingers out of the way).
In the original task, subjects were instructed to maintain 10 N of total grasp force,
defined as the sum of the normal forces at each fingertip, while oscillating the thumb
93
Load Cell
Arm
Hinge & Potentiometer
Sandpaper
a
b
F
N
F
T
c
x
y
Θ
1
Θ
2
Θ
3
Figure 5.1: Experimental setup. a. Subjects held the object in a precision tripod grasp.
b. The test object connected three load cells with a central hinge that allowed movement
of the fingers. Normal force in this work is defined as the force directed at the hinge. c.
The coordinates used in deriving the equations of motion
94
position in time to an audible metronome. The visual feedback consisted of a line and
a crosshair presented on a computer screen at a distance approximately 1 m from the
subject. The line represented the 10 N target sum of the three normal forces, which
is consistent with the sum of normal forces used to lift a 400 g object with three fin-
gers [Flanagan et al., 1999], while the crosshair represented the sum of normal forces
actually applied by the subjects. Simultaneously, subjects were asked to oscillate the
thumb pad of the grasping device in time with the audible metronome at 1 Hz, such that
the leftmost and rightmost angular displacements of the thumb pad were reached on the
metronome beat at a frequency of 0.5 Hz. The angular displacement of the thumb was
left to the subjects preference. In the following, we will refer to this task as the original
task.
Subjects had several practice trials, repeated with 60 s rest between trials until they
reported to be comfortable with the task (from two to six repetitions, three typical).
We did not do additional training because subjects reported to be very satisfied with
their performance, likely because humans perform such tasks regularly and our task was
designed to be similar to many ecological tasks as mentioned above. We then recorded
95 s of force and angle data at 400 samples/s (PCI 6025, National Instruments, Austin,
TX) for each subject to obtain up to 47 full task cycles per subject. Data acquisition and
visual feedback was provided with a program written in Matlab using the Data Acquisi-
tion Toolbox (Natick, MA, USA). Subject visual feedback on the force magnitude was
updated at a rate of 50 Hz. The needed forces were so low that subjects did not report
fatigue, but 60 s of mandatory rest were always enforced before each trial.
To rule out potential confounds or alternative interpretations of our results, we also
studied six different Control Tasks (Table 5.1) were performed in addition to the Original
Task - all of which were done in block-randomized order and repeated three times each
for 95 s, and for which subjects had practice trials as in the Original Task. These Control
95
Tasks establish baseline performance for a variety of combinations of fingertip motion
and force constraint, and were added after the initial pilot work to better understand the
performance of the Original Task.
Control 1: Perform the above-described Original Task, but with the instrumented
object attached to ground. Doing this enabled us to distinguish force fluctuation
correlations across fingers due to neuromuscular from purely mechanical causes
associated with motion or reaction forces. Furthermore, this task removes the need
for force dynamics that could be attributed to behavioral responses to dropping the
object or vertical slip-grip responses.
Control 2: The instrumented object was handheld, but we locked the pads in
a configuration comfortable for the subject (making it a rigid object) and asked
them to oscillate the normal force between index and middle finger at a frequency
of 0.5 Hz, while holding the thumb still, thus mimicking the oscillations in nor-
mal forces the subjects needed to apply to compensate for thumb pad motion.
The visual feedback in this condition consisted of two 0.5 Hz sinusoidal curves,
phase shifted by 180 degrees and two crosshairs, representing the individual nor-
mal forces applied by index and middle finger. There was no explicit feedback on
the total grasp force in this condition, but the amplitude of the sinusoidal curves
corresponded to the amplitude of the oscillations in the Original Task. This Con-
trol Task helps to elucidate the coupling of two dimensions of force, which are at
least mathematically independent [Gao et al., 2005]: the grasp force that counter-
acts gravity and the force compensating for thumb motion. It removes an explicit
enforcement of a target total grasp force, as long as it is sufficient to hold the
object.
96
Control 3: The instrumented object was handheld but with unlocked pads and we
asked subjects to oscillate the total grasp force, that is, oscillate in-phase the nor-
mal forces of thumb, index and middle finger at 1 Hz, thus voluntarily reproducing
the synchronous grasp variability (i.e., Grasp Mode, see Results) observed experi-
mentally in the Original Task. Here, the visual feedback consisted of a sinusoidal,
whose amplitude we determined for each subject from his or her actual perfor-
mance of the Original Task trials. While Control Task 2 above removed the tar-
get total grasp force enforcement, this task removes the requirement to modulate
force variability compensating for thumb motion. It complements Control Task
2, in that it quantifies the coupling of the two force components, i.e. synchronous
and compensatory normal force variability.
Control 4: Control Task 3 was repeated, but this time with the pads locked as a
rigid object to investigate the effect of removing the instability of the hinged pads
on the Grasp Mode.
Control 5 and 6: The final two tasks consisted of simple static grasps (handheld
object with no oscillation of the thumb), with the target sum of normal forces to be
maintained at 10 N, with pads either free (Control Task 5) or locked (Control Task
6) to separate force variability caused by visual processing from other contribu-
tors. These tasks allow us to quantify the contribution to the total force variability
by corrective action vis--vis the visual feedback.
5.3.2 Mechanical Analysis
We found the closed-form analytical solution to the necessary fingertip forces and
motions to perform the task. Comparing experimental forces to the analytical solution
disambiguates mechanically necessary from neurally driven interactions. We modeled
97
Task
Hinge
state
Thumb
motion
Object
displace-
ment
Target force Goal
Original Free 0.5 Hz Free 10 N grasp
Characterize multifinger interactions during
dynamic manipulation requiring simultaneous
control of fingertip motions and forces.
Control 1 Free 0.5 Hz Fixed 10 N grasp
Same as original task, but with object fixed
to ground to remove slip-grip response and
behavioral fear of dropping object.
Control 2 Fixed None Free
0.5 Hz
oscillating
compensa-
tion
V oluntarily produce the compensation mode
(alternating index and middle finger forces) as
seen in original task, but with a locked object
to remove hinge instability and voluntary fin-
ger motions.
Control 3 Free None Free
1 Hz oscillat-
ing grasp
V oluntarily produce the oscillations in the
grasp mode (synchronous normal force mod-
ulation across fingers) as seen in original task,
but without voluntary finger motions.
Control 4 Fixed None Free
1 Hz oscillat-
ing grasp
Same as in Control 3, but with a locked object
to remove hinge instability.
Control 5 Free None Free 10 N grasp
Simple static grasp with visual feedback to
assess effect of visuomotor feedback loop on
grasp force variability.
Control 6 Fixed None Free 10 N grasp
Same as in Control 5, but with a locked object
to remove hinge instability.
Simulation 1 Free Oscillating
Free but
stationary
10 N
Mechanical constraints of successful task per-
formance dictate variability.
Simulation 2 Free Oscillating Fixed 10 N + noise
Signal-dependent noise informs force variabil-
ity patterns more than the task mechanics.
Simulation 3 Free Oscillating
Free but
stationary
10 N + noise
Task mechanics govern force variability pat-
terns.
Simulation 4
Free but
stationary
None
Free but
stationary
10 N + noise
Task mechanics govern force variability pat-
terns.
Table 5.1: Explanation of tests and simulations used to support hypothesis
the system as a planar, rigid-body mechanism with five degrees of freedom: x and y
location of the hinge axis on the plane, and the absolute angle of each pad. All three fin-
ger pads (which are each reduced to a point collocated with the center of pressure of the
finger pad) and their links are in the horizontal plane, and gravity acts perpendicular to
the plane in a downward direction, eliminating the vertical force from the analysis. The
six control inputs in the plane of the finger pads are the normal (toward the hinge) and
tangential components of fingertip forces for each of the three fingers. The normal and
tangential forces of both the model and the experimental data are measured with respect
to the hinge rather than the grip surface to reflect the task goals and to more easily
separate the grasp force and compensation to thumb oscillation modes (Figure 5.1b).
98
5.3.3 Equations of motion for a 2-D system of three links connected
via a common hinge
We derived the dynamic equations of motion for a simplified planar model of the
grasper set-up using the Lagrange method (see, e.g. [Williams and Willima, 1996]). The
Lagrange method requires generalized coordinates (q
i
) that describe the configuration of
the object. The kinetic and potential energy (T andV ) are expressed as functions of the
qi and generalized forces (F
i
) that act on each generalized coordinate. The Lagrangian is
the kinetic minus potential energy:L =TV , and is inserted into Lagranges equation:
d
dt

_ q
i
L

q
i
=F
i
The grasp-device system has two translational degrees of freedom (DOF) relative to
an inertially fixed coordinate reference frame and three rotational DOF - one for each
pad. Since we observed very limited motion in the vertical direction and rotation of
the device itself, we disregarded these 4 dimensions (1 translational, 3 rotational) in
our modeling analysis. For the generalized coordinates, we selected x and y position
of the hinge and the absolute angle of each pad relative to the fixed coordinate system

i
;i = 1; 2; 3 (Figure 5.1c). Using these coordinates, the 2-D vector for the position of
each pad is:
r
i
=
2
4
x
y
3
5
+d
i
2
4
cos
i
sin
i
3
5
whered
i
is the distance from the hinge to the center of mass of thei-th pad. Differ-
entiating this expression yields the velocity
99
v
i
=
2
4
_ x
_ y
3
5
+d
i
_

i
2
4
sin
i
cos
i
3
5
where the over dot represents the derivative with respect to time. The velocity deter-
mines the kinetic energy of each body. Letm
i
be the mass of thei-th pad and Ii be the
scalar moment of inertia of thei-th pad about a vertical (out of the page) axis through
the center of mass of link I. The kinetic energy of the system is given as the sum of
the energy of the individual parts. The partial derivatives in the Lagrangian eliminate
potential energy terms from the equation because gravity acts perpendicular to the sys-
tem. Thus the Lagrangian is given by the kinetic energy:
L =T =
X
1
2
m
i
(v
i
v
i
) +
1
2
I
i
_

2
i
The generalized forces for this simple system are the resultant forces or torques when
all generalized coordinates are fixed except one. Fixing all coordinates and allowingx
to vary gives us the generalized force forx:
F
x
=
X
F
N
i
cos
i
F
T
i
sin
i
which is all the forces in thex-direction. The forcesF
N
i
andF
T
i
are the normal and
tangent forces at the grip surface on each pad (Figure 5.1b). Likewise for they direction,
the generalized force is:
F
y
=
X
F
N
i
sin
i
F
T
i
cos
i
The generalized forces corresponding to the angles are physically torques. The resul-
tant torque when allowing only one angle to vary is given by:
100
T

i
=lzF
T
i
The component parts are arranged according to Lagranges equation to arrive at the
following equations of motion, written in matrix form for computational ease:
2
6
6
6
6
6
6
6
6
6
4
M m
1
d
1
s
1
m
2
d
2
s
2
m
3
d
3
s
3
M m
1
d
1
c
1
m
2
d
2
c
2
m
3
d
3
c
3
m
1
d
1
s
1
m
1
d
1
c
1
m
1
d
2
1
+I
1
m
2
d
2
s
2
m
2
d
2
c
2
m
2
d
2
2
+I
2
m
3
d
3
s
3
m
3
d
3
c
3
m
3
d
2
3
+I
3
3
7
7
7
7
7
7
7
7
7
5

2
6
6
6
6
6
6
6
6
6
4
x
y

1

2

3
3
7
7
7
7
7
7
7
7
7
5
+
2
4
d
1
c
1
d
2
c
2
d
3
c
3
d
1
s
1
d
2
s
2
d
3
s
3
3
5

2
6
6
6
4
_

2
1
_

2
2
_

2
3
3
7
7
7
5
=
2
6
6
6
6
6
6
6
6
6
4
c
1
c
2
c
3
s
1
s
2
s
3
s
1
s
2
s
3
c
1
c
2
c
3
lz
0 lz
lz
3
7
7
7
7
7
7
7
7
7
5

2
6
6
6
6
6
6
6
6
6
6
6
6
4
F
N
1
F
N
2
F
N
3
F
T
1
F
T
2
F
T
3
3
7
7
7
7
7
7
7
7
7
7
7
7
5
This can be written compactly using matrix and vector notations with obvious mean-
ing as
M x +C _ x
2
=DF
The model takes the dynamics of the position and angles as inputs and outputs the
normal and tangential forces. This gives us a one-parameter subspace of the possible
forces. The grasp force is added to the equations to completely determine the forces
necessary for successful completion of the experimental task. In simulation, we fix x and
y at the origin, maintain the middle and index angles at 130 and 230 deg, respectively,
and prescribe the grasp force as ether constant or noisy. The reduced model with these
assumptions is:
101
2
6
6
6
6
6
6
6
6
6
6
6
6
6
4
d
1
c
1

_

2
1
d
1
s
1

_

2
1
(m
1
d
2
1
+I
1
)

1
0
0
F
grasp
3
7
7
7
7
7
7
7
7
7
7
7
7
7
5
=
2
6
6
6
6
6
6
6
6
6
6
6
6
6
4
c
1
c
2
c
3
s
1
s
2
s
3
s
1
s
2
s
3
c
1
c
2
c
3
lz
0 lz
lz
1 1 1 0 0 0
3
7
7
7
7
7
7
7
7
7
7
7
7
7
5

2
6
6
6
6
6
6
6
6
6
6
6
6
6
4
F
N
1
F
N
2
F
N
3
F
T
1
F
T
2
F
T
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
5
The last row of this equation comes from the definition of grasp force as the sum of
the normal forces.
5.3.4 Simulations
In the closed-form inverse dynamics solution we calculate fingertip forces necessary to
produce the desired motion and total grasp force. The desired motion maintains the
index- and middle-finger angles fixed at 130 and 230 deg while the thumb angle oscil-
lates through an arc with amplitude of 30 degrees following a sine function with a period
of 2 s (0.5 Hz). In this way we defined a comfortable configuration that would reveal
clear changes in forces, shown in Figure 5.3. For comparison, a plot of the measured
angles from one representative subject is shown in Figure 5.3. Note that in the subjects
data, the angle between the middle and index finger pads also changed slightly during
the trial, but the motion of the thumb is much greater and the mechanical solutions retain
their same form in the plot of the normal forces (Figure 5.2). The experimental appara-
tus was built to have very low friction at the hinge, thus the modeled and experimentally
measured tangential forces are very small relative to the normal forces (3000x smaller in
the frictionless model and 20x smaller in the experimental data) and were excluded from
the analysis. Instead, the adaptation of the normal forces to the changing configuration
102
captures the relevant behavior due to the thumb oscillations. We further justify using
only the three normal forces to characterize the task because they fully account for the
two active degrees of freedom of the system: grasp force and compensation to thumb
oscillation. A system or study designed to consider additional degrees of freedom would
need to include the tangential forces for the very low frictions.
10 N
grasp
a
5
3
1
4
2
5
3
1
Middle
Index
Thumb
b
5
3
1
4
2
5
3
1
Middle
Index
Thumb
5
3
1
4
2
5
3
1
Middle
Index
Thumb
c
Figure 5.2: Force space. a. A perfectly executed task traverses the thick line shown here.
Connecting the lines created by a variety of grasp forces (from 5 to 12 N) illustrates the
manifold of allowable forces. b. The subject data lies on the manifold described by the
model, but with varying grasp force magnitude. c. The subject data and the manifold
have slight curvature when viewed from the [1; 1; 1] direction.
We simulated four conditions for the grasp force 5.1:
Simulation 1: Idealized Original Task; where the grasp force was ideally constant,
while the index and middle finger generated the exact normal forces necessary to
compensate for the reconfiguration of the grasp as the thumb pad oscillated.
Simulation 2: Same as Simulation 2, but with the object fixed to ground and each
finger generating a zero mean Gaussian distributed noisy normal force, whose
variance was adjusted such that either the grasp force magnitude or the grasp force
error was reproduced. The noise was not bandlimited to the 8-12 Hz frequency
band, however, with which signal-dependent noise is commonly associated. This
103
condition simulates the effects of signal-dependent noise [Jones et al., 2002] at
each fingertip but since it does not consider reaction forces at the other fingertips,
this condition in effect simulates the first Control Task in which the device was
attached to ground.
Simulation 3: the noisy normal forces acting on the object and inducing reaction
forces in the other fingers, thus simulating correlations between fingers that would
arise purely due to mechanics. This condition simulates the Original Task with
noise.
Simulation 4: a simple static grasp without thumb oscillations, but including the
requirement to generate a 10 N sum of normal forces and correlations due to
mechanics (simulating the fifth and sixth Control Tasks for simple static grasp).
This condition helps to separate contributions to visual feedback error by correc-
tive actions and by signal-dependent noise.
In Simulations 3 and 4 there is no unique mechanical solution so we computed the
reaction forces by solving a underconstrained system of linear equations, solving for
zero force and moment using the pseudoinverse matrix (i.e., the least-squares energy
solution). In Simulation 1 we modeled constant total grasp forces ranging from 5 N to
12 N to find the full solution manifold (i.e., the set of all mechanically feasible fingertip
forces to accomplish the task). This set of mechanically feasible forces is the slightly
curved manifold shown as a curved surface in (Figure 5.2).
5.3.5 Data analysis
Plotting the normal component of the fingertip forces (i.e., the component of finger-
tip force acting on the finger pad and directed toward the hinge) against each other
in the three-dimensional space of normal forces is an effective way to visualize the
104
0 2 4 6 8 10
90
120
150
Time [s]
Angle [deg]
Middle-Index
Index-Thumb
Thumb-Middle
0 2 4 6 8 10
90
120
150
Subject 3, filtered 0-5 Hz
Time [s]
a
b
0 2 4 6 8 10
!
c
Time [s]
Force [N]
12
9
6 !
0 2 4 6 8 10
!
d
Time [s]
12
9
6 !
Figure 5.3: Sample time histories. a. The ideal inter-finger angles used in the model.
The equations reference all angles to a fixed ground, but are shown relative to one
another here to be consistent with the experimental data. b. Measured angles from a
representative subjects data. c. The grasp force target used by the model is either con-
stant (dashed line) or variable. d. Measured grasp force from the same data as b. Note
the quasi-periodicity in the measured data.
experimental and simulation results. Each coordinate axis in this three-dimensional
space represents the normal force of a given finger (thumb, index, and middle finger),
and a combination of three forces is represented as a point in this space. The analyti-
cal solution to the task shows that the feasible set of fingertip forces lies on a slightly
curved, nearly planar surface in force space (Figure 5.2). This is because the mechan-
ical constraints of the task, such as the equilibrium equations for different finger pad
configurations, represent lines or nearly planar surfaces in the force space. That is, only
105
combinations of forces that lie on the constraint lines or surfaces are valid solutions to
the grasp problem, and linear analysis tools may be used, such as principal components
analysis (PCA, [Clewley et al., 2008]).
We used the 3D force vector and torques on each finger pad (Figure 5.1b) to extract
the center of pressure location and force components in the normal, tangent and vertical
(F
N
;F
T
;F
V
) directions relative to the hinge (Figure 5.1b). The normal force covariance
patterns completely determine the grasp force and manipulation force components; the
others are not included in the analysis as discussed above. The first 5 s and last 1 s of
data were removed to eliminate transient behavior in the data.
The data, represented by a 3-by-N matrix, where N is the number of samples, were
filtered with a sliding band pass Butterworth filter of width 1 Hz and 99% overlap
between filter windows, starting from 0.1 Hz up to 10 Hz, to extract the normal force
dynamics in each of these frequency bins. We performed PCA on the 3-by-3 normal
force covariance matrix computed from each set of filtered data associated with a partic-
ular filter window, and computed the loadings of the three resulting principal component
(PC) vectors (r-mode PCA, computed from covariances between variables) as well as the
percentage of variance explained by each PC. Next, we compared the loadings of each
PC to the theoretical grasp force mode and compensation-to-thumb-oscillation mode for
each frequency range, by computing the angle between the experimentally observed PC
and the PC associated with the mechanical simulation of the task. Lastly, to determine
whether variability along a PC in the Original Task changed in a state-dependent manner,
e.g. variability at the extreme points of thumb motion vs. at the middle point, we com-
puted the variance over a window, whose length was one third of the thumb oscillation
period, i.e., 0.6 s, and slid the window over the trial data. This tests the hypothesis that
increased grasp force variability reflects the action of a purposeful mechanism, such as
guarding against drop of the object by squeezing it at critical locations in the state space.
106
5.4 Results
5.4.1 Analytical Solution and Simulations
The analytical solution to the manipulation task shows that the feasible set of fingertip
forces lies in a tilted and slightly curved plane in the force space (Figure 5.4). It is to
be expected, therefore, that the PCA of the subjects data will naturally approximate this
manifold well (Figure 5.2c) and that subjects PCs will align with the manifolds PCs, for
the following reasons.
First, grasp force is the sum of the fingertip normal forces, and is equal to the pro-
jection of the current force vector [F
middle
;F
index
;F
thumb
]
T
onto the [1; 1; 1]
T
direction
1
(Column I in Figure 5.4). Changes in grasp force magnitude cause movement towards
or away from the origin in force space, while not moving the object. Therefore a PC
of the subjects data with loadings of the same sign and similar magnitude indicates a
changing grasp force. We say this PC aligns with the grasp mode.
Second, as the thumb oscillates from side to side, the relative magnitude of the mid-
dle and index fingers forces alternates to compensate for the change in direction of the
thumbs force vector during the task. Thus the manipulation force is the projection of the
current force vector onto the [-1, 1, 0] T direction (Column II in Figure 5.4). The chang-
ing force magnitudes of the index and middle fingers for a given thumb force magnitude
causes lateral movement in force space as described by the compensations to thumb
oscillation mode. The mechanics of the task result in grasp force and compensations
to thumb oscillation being orthogonal modes in force space. This is the mathematical
way of saying that one can produce the same magnitude of grasp force while moving
1
For the sake of clarity in the text and figures, we indicate PCs as vectors with 1s and 0s. The math-
ematical convention would be to present them as unit vectors. In particular, [0:5;0:5;0:7]
T
is a better
approximation of the grasp mode, since index and middle finger form a smaller angle.
107
Behavioral
mode
PC loadings
[index middle thumb]
Mechanical
coupling of
force variability
Time series
example
Graphical
Interpretation
Variability plotted in
Force-Force-Force
space
5
3
1
4
2
5
3
1
F-Middle
F-Index
F-Thumb
Grasp force
Compensation force
(Compensations to
thumb oscillation)
Hinge constraint
5
3
1
4
2
[1 1 1]
T
[-1 1 0]
T
[-1 -1 1]
T
thumb
middle
index
hinge
all in phase
index and middle out of
phase with each other
index and middle in phase
with each other but out of
phase with thumb
time
force
thumb
middle
index
5
3
1
4
2
5
3
1
towards/away from origin on surface sideways on surface perpendicular to surface
(approximate)
I II III
Figure 5.4: Overview over the 3 force variability modes. The Grasp force mode (column
I) is the dimension of force variability that is associated with simultaneous, or in-phase,
increases and decreases by all three finger normal forces. Graphically (bottom row), this
can be expressed as motion along a line in 3D normal force space, which has components
in every dimension. The Compensation force mode (column II), explains out-of-phase
variation of index and middle finger force, with no contribution by the thumb. In 3D
normal force space, this corresponds to motion at a constant thumb force level, between
index and middle finger axes, along a slightly curved line. Lastly, the Hinge force mode
explains that force variability whereby middle and index finger vary their normal force
in-phase, while varying out-of-phase with the thumb normal force. This will lead to
accelerations of the object.
the thumb or conversely, vary the grasp force without affecting the thumbs positional
control. We say this PC aligns with the compensation mode.
108
The third mode of force interactions is variability perpendicular to the constraint
plane and represents errors in maintaining the hinge constraint. Namely, the task
requires that the force vectors intersect at or near the hinge, and this constraint is vio-
lated if the point of intersection of forces moves in towards or away from the thumb the
[1;1; 1]
T
direction (Column III in Figure 5.4). Variability along this dimension is
associated with translations and rotations of the grasped object. We say this PC aligns
with the hinge mode.
5.4.2 Principal component associated with the modeled ideal per-
formance of the task.
The fingertip forces necessary to produce motion of the thumb while maintaining a per-
fectly constant grasp force create a horizontal line that is slightly curved in force space
(Column II in Figure 5.4), and the family of lines for a variety of grasp force magnitudes
creates a slightly curved surface defining all feasible solutions to the task. For this ideal
case (Simulation 1, Figure 5.7) the variability in normal forces is associated purely with
compensations for movement of the thumb (i.e., column II in Figure 5.4, which is seen
as traveling back and forth along the thick line as the thumb moves from side-to-side).
The loadings of each PC for this ideal case are shown in the first row of column II of
Figure 5.4 and, as expected, the compensation mode is the PC that explains> 99% of
the variance (i.e., [1; 1; 0]
T
). The small contribution of the hinge constraint mode PC
(i.e., [1;1; 1]
T
direction) reflects the slight curvature of the force trajectory in force
space. The grasp force mode PC (i.e., [1; 1; 1]
T
direction) shows zero variance in the
grasp force by construction (i.e., the ideal task has no variability in grasp force). This
result applies equally to all frequency bands.
109
5.4.3 Summary of experimental PCA result and comparison with
the modeled ideal performance of the task
Figure 5.5 summarizes our findings. As expected by the mechanical requirements of
the task shown in Simulation 1 and Figures 5.7 & 5.2, the Compensation Mode domi-
nates in the Original Task. But whereas Simulation 1 only shows residual levels of the
Grasp and Compensation Modes (due to the linear approximation to the slightly curved
solution manifold), the performance of the Original Task by the subjects was accompa-
nied by mechanically unnecessary variability in the form of substantial amounts of the
Grasp Mode; and small amounts of Hinge Mode. The Control Tasks (Table 5.1) go on to
demonstrate that the Grasp Mode strongly pervaded manipulation tasks requiring differ-
ent fingertip motion and force constraints (Figure 5.5 shows only Control Tasks 1 & 2 for
clarity, others are presented below in detail). Only simple static grasp (Control Tasks 5
& 6) exhibits much small levels of force variability in general. Importantly, these results
cannot be explained by signal dependent noise (Simulations 2-4), whether the objects is
deformable vs. rigid (hinge state), or hand held vs. attached to ground (object displace-
ment). Taken together, these results demonstrate that stereotypical grasp-and-release
synchronous interactions (i.e., Grasp Mode) pervade multifinger manipulation when the
manipulation task requires orchestrating individuated fingertip motions and forces, as
explained in the Discussion.
5.4.4 Experimental PCA result and comparison with the modeled
ideal performance of the task
We can see from Figure 5.6 (bottom plot) that on average, subjects were able to
meet the 10 N sum of normal forces requirement, with a standard deviation of 0.5
110
N. Across the physiologically plausible frequency range for control of force produc-
tion [Johansson and Birznieks, 2004], the modes observed in the experimental data
match the theoretical ones quite well: the median angle difference between the experi-
mental and theoretical modes never exceeds 30 degrees, indicating that the simulations
predict the structure of variability faithfully (Figure 5.6, middle plot). Beyond 12 Hz
(not shown), and thus at time scales shorter than those of the shortest sensorimotor
loops for sensory mediated force production [Johansson and Birznieks, 2004], the pre-
dicted structure breaks down, i.e. it converges to a purely white noise process in a 3-
dimensional space, which suggests that the structure of variability is plausibly imposed
by cortically and spinally mediated drive to alpha motoneuron pools (as opposed to neu-
ral or measurement white or Gaussian noise with broad bandwidth). Figure 5.6 (top plot)
shows that the magnitude of the compensation mode PC is in agreement with that found
in the simulated task (Figure 5.7). The compensation mode dominates the variability
below and at the oscillation frequency, then falls off sharply above. While this is not
surprising, since the task determines this magnitude of variability, the magnitudes of the
grasp mode show a very different picture, compared to the simulation, the modeled ideal
performance of the task. The simulations suggest that there should be no grasp mode and
very little hinge mode variability across the entire physiologically plausible frequency
range. However, near the oscillation frequency, the grasp mode in the experimental data
explains approximately 30 % of the overall normal force variance, or alternatively, has
a standard deviation of almost 0.2 N. Beyond the task-relevant frequency of 0.5 Hz, the
grasp mode explains most of the force variance and thus dominates its variability, even
though the compensation mode magnitude does not fall off as sharply with frequency
as in the simulation. The milder roll-off can be explained by imperfect matching of the
task frequency by subjects over the course of an entire 95 s trial. The strong contribution
of the grasp mode at all frequencies, on the other hand, is plausibly a consequence of
111
neural and biomechanical coupling between the control of forces which compensate for
object manipulation and that of forces required to hold it.
There are two objections which can be made against the interpretation that the con-
trol of force modes is coupled: firstly, the strong contribution of the Grasp Mode to the
overall normal force variability could be attributed to the interplay between mechanics
of the task and signal-dependent noise at the fingertips [Jones et al., 2002], whose mag-
nitude scales with the mean force. According to this objection, noise generated by each
of the fingertips will show up as reaction force at the other two fingertips, thus giving
rise to positive correlations (theoretically instantaneous but perhaps with small delay due
to tissue deformation and compression) across fingertips and thereby causing the Grasp
Mode variability observed in the experiments. Secondly, the large variability along the
Grasp Mode direction could be attributed to the visuomotor loop involving the visual
feedback, which instructed subjects to generate a constant 10 N sum of normal forces,
and subjects efforts to maintain this force after seeing the visual feedback. The simplest
strategy to correct for displayed deviations from the target force is to increase or decrease
forces across all fingertips simultaneously, hence in alignment with the observed Grasp
Mode. It should be noted, however, that i) subjects were encouraged to make their best
possible effort at maintaining this force and ii) that the visuomotor loop has a defined
latency and operates at time scales considerably shorter than that of the thumb oscil-
lation frequency, and in particular, cannot be expected to be present across the entire
range of frequencies. We investigate both of the above objections in the following two
paragraphs.
112
0
0.2
0.4
0.6
N
0 1 2 3
Frequency [Hz]
Grasp Mode
Hinge Mode
Compensation Mode
thumb
middle
index
hinge
Simulation 1: Meeting mechanical requirements of original task
Original task as performed by subjects
Control 1: Original task with object fixed to ground
Control 2: Voluntary alternation of index and middle finger forces
Control 5 & 6: Simple static grasp
Grasp Mode pervades
manipulation tasks
Figure 5.5: Summary figure showing the normal force variability magnitudes of the
three force modes (Compensation, Grasp and Hinge Modes) across the low frequency
range, found through PCA in the Original and the Control Tasks as well as Simulation 1.
The results are grouped by mode and in each group, the first graph shows the magnitudes
found in Simulation 1 (noiseless, ideal performance). Note that due to the curvature
of the solution manifold (Figure 3), the Hinge mode is not exactly zero even in the
simulation. Most importantly, the Original Task and Control Task 1 both reproduce the
expected magnitude of the Compensation Mode, while they exhibit much larger Grasp
Mode magnitude.
5.4.5 Comparison with the modeled imperfect performance and the
experimentally grounded task
To address the first objection, we added signal-dependent noise to the simulated forces
generated by each fingertip, whose magnitude was proportional to that force (simulation
2). The noise proportionality constant was chosen so that the resulting grasp force mode
113
0
0.2
0.4
0.6
0.8
1
N
Grasp mode
Compensation mode
Hinge mode
0 1 2 3 4 5
0
10
20
30
40
50
60
70
80
90
Frequency [Hz]
Angle [deg]
0 10 20 30 40 50 60 70 80 90
5
6
7
8
9
10
11
12
13
14
15
Time [s]
Sum of normal forces [N]
a
b
c
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
N
d
PC magnitudes (unfiltered data)
Figure 5.6: a. The measured magnitudes of the three principal components vs. fre-
quency in the original object manipulation task. Not surprisingly, near the task-relevant
frequency of 0.5 Hz (vertical red dashed line), the Compensation Mode dominates the
overall force variability, as suggested by Simulation 1. However, at those frequencies,
subjects exhibit considerable contributions to force variability from the Grasp Mode.
Box plots indicate the distribution of these variability contributions across the 7 sub-
jects. b. The difference in angle between the directions of the measured and the ana-
lytical principal components. The box plots reflect the fact that the three normal force
correlation modes did not vary much across subjects and were closely aligned with the
theoretical correlation modes. Differences across subjects and between observed and
theoretical modes mostly indicate the variability of object orientation during task per-
formance c. Average sum of normal forces across the 7 subjects in the original object
manipulation task, Subjects were well able to meet the 10 N target. d. The three force
mode magnitudes computed from the unfiltered data (square root of the eigenvalues),
showing that overall, the Compensation Mode contributes most of the force variability
and the Hinge Mode contributes the least, reflecting successful task performance. (Note
that the values are in Newtons, and do not represent proportions of variance. No statis-
tical tests are done on these data because they simply show the total variance across all
frequencies.)
114
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
Frequency [Hz]
N
Grasp mode
Compensation mode
Hinge mode
Figure 5.7: The three mode magnitudes vs. frequency in the noiseless simulation of the
Original Task (Simulation 1). The Compensation Mode explains almost all the force
variability and only near the task frequency of 0.5 Hz (vertical red dashed line). The
remaining variability is explained by the Hinge Mode, near the task frequency, which
can be attributed to the curvature of the solution manifold (Figure 5.2). The Grasp Mode
does not contribute to force variability at any frequency.
variability would match experimental observations near the frequency of thumb oscil-
lation. Since there is no connection between fingertips, neural or mechanic, principal
components analysis does not reveal any correlation structure and the sum of normal
forces varies wildly about the 10 N mean (results not shown). This is what we would
expect in an experiment in which the device is attached to ground, and all the variabil-
ity observed was due to signal-dependent noise at the fingertips. As a refinement, we
introduced mechanical connection between fingertips and computed and added the reac-
tion forces at the other fingertips (simulation 3). Figure 5.8 shows that the magnitudes
of compensation and hinge modes are unaffected, while the grasp mode magnitude is
increased and matches the experimental observations. However, its magnitude does not
115
roll off across the entire frequency range, thus differing significantly from the exper-
imental observations. This is not surprising, since we did not band-limit the noise.
However, band-limiting the noise in our simulations to the frequency range observed
by [Jones et al., 2002], i.e. 8-12 Hz, does not reproduce the results either, as the track-
ing error is still vastly larger than in the original experimental task. More importantly,
however, comparing the results of the original task with the first control task in which
the device was attached to ground, we find that the experimental grasp mode magnitude
is equally large (Figures 5.5 and 5.9). This is surprising because the device is attached
to ground and correlations across fingertips cannot be explained by mechanical coupling
(i.e., force variability and errors are shunted to ground and do not affect the other fin-
gers), and mismatches in forces do not accelerate the object. Moreover, simulation 2
above predicted a complete absence of correlation modes. In summary, these results
challenge the alternative interpretation that signal-dependent noise in conjunction with
mechanics explains the experimentally observed, yet mechanically unnecessary, Grasp
mode variability.
5.4.6 Comparison with the simple static hold control tasks
To investigate the second objection, that grasp mode variability is attributable solely to
corrections to drifts in the visual feedback, we analyzed the normal force data of the
fifth and sixth control tasks, in which subjects simply held the object statically (did not
oscillate the thumb) and only tracked the 10 N sum of normal force visual feedback.
As in the other experiments, the three modes of force variability match those predicted
by Simulation 1, the modeled ideal performance, across the low frequency range (Fig-
ure 5.10b). Furthermore, while the compensation mode is now contributing 20 % and
less to the force variability near the frequency of thumb oscillation, the variability mag-
nitude along the grasp mode is also reduced by approximately 50 %. This can be seen in
116
0
0.2
0.4
0.6
0.8
1
N
Frequency [Hz]
a
c
0 10 20 30 40 50 60 70 80 90
0
2
4
6
8
10
12
14
16
18
20
Sum of normal forces [N]
d
Time [s]
0 1 2 3 4 5

0
0.2
0.4
0.6
0.8
1
N
0
2
4
6
8
10
12
14
16
18
20
Sum of normal forces [N]
b
Grasp mode
Compensation mode
Hinge mode
Figure 5.8: a. The simulated magnitudes of the three principal components vs. fre-
quency in the original object manipulation task, including signal-dependent noise,
whose standard deviation is proportional to the mean force. The proportionality factor
was chosen such that the grasp force magnitude at the task-frequency of 0.5 Hz (ver-
tical red dashed line) matches that measured in the Original Task. However, the noise
is not band-limited to the low frequencies, since signal-dependent noise is associated
with higher frequency bands, and thus the grasp force mode magnitude is considerably
larger than the measured one at all other frequencies. b. The simulation also exhibits
much greater variability in terms of the sum of normal forces, making signal-dependent
noise an unlikely source of the grasp force variability. c and d. If, on the other hand, the
signal-dependent noise magnitude is scaled to the error observed in the sum of normal
forces (right plot), the resultant grasp force magnitude does not match the experimen-
tally observed one (left plot).
(Figure 5.10a). Similarly, the standard deviation of the sum of normal forces is reduced
by half (Figure 5.10c). These results suggest that voluntary (i.e., visuomotor) corrective
action does explain some of the variability in the grasp mode, since this control exper-
iment failed to abolish grasp mode variability altogether - but a large proportion (as
117
0
0.2
0.4
0.6
0.8
1
N
0 1 2 3 4 5
0
10
20
30
40
50
60
70
80
90
Frequency [Hz]
Angle [deg]
0 10 20 30 40 50 60 70 80 90
5
6
7
8
9
10
11
12
13
14
15
Sum of normal forces [N]
a
b
c
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
N
d
PC magnitudes (unfiltered data)
Grasp mode
Compensation mode
Hinge mode
Figure 5.9: a. The measured force modes magnitudes vs. frequency in the original
task, in which however, the device was attached to ground (Control task 1). Although
the load cells are now mechanically decoupled and thus, noise originating at one finger
does not get transmitted to the other fingers, the grasp mode contribution in this case is
just as strong as in the original task. b. The measured principal component directions
agree with the theoretical across the frequency range, although to a lesser extent than
in the original task. Note, however, that the measured grasp mode shows the greatest
agreement (vertical red dashed line indicates 0.5 Hz frequency of thumb oscillation).
c. Average subject performance at maintaining the 10 N target force. d. The force
variability analysis reveals that even though the object is attached to ground, and safety
or signal-dependent noise is not an issue, the grasp force variability is as present as in
the Original Task. Note however, that the Hinge Mode contributes stronger, too.
much as 50 %) of that variability needs to be attributed to causes other than voluntary
modulation of force and the limitations of the visuomotor loop associated with it.
118
0
0.2
0.4
0.6
0.8
1
N
0 1 2 3 4 5
0
10
20
30
40
50
60
70
80
90
Frequency [Hz]
Angle [deg]
0 10 20 30 40 50 60 70 80 90
5
6
7
8
9
10
11
12
13
14
15
Time [s]
Sum of normal forces [N]
a
b
c
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PC magnitudes (unfiltered data)
N
Grasp mode
Compensation mode
Hinge mode
d
Figure 5.10: a. Force mode magnitudes vs. frequency in the simple hold task (control
tasks 5 and 6). Although for this task, grasp force variability is also unnecessary, we
see some contribution to force variability by it. However, it is much smaller than in the
original task, suggesting that force corrections to the visual feedback are not the sole
cause of grasp mode contribution. b. The measured modes agree with the hypothesized
modes across all frequencies (vertical red dashed line indicates 0.5 Hz frequency of
thumb oscillation). c. Subject performance at maintaining the 10 N target force in the
simple hold task. d. Analyzing the unfiltered simple grasp data, we find that the order
of force modes in the Original Task is preserved, but there is much less force variability.
The amount of grasp force variability in this task indicates the variability arising from
tracking the constant visual feedback.
5.4.7 Comparison with the alternating index/middle finger normal
force task
One can argue that cognitive load may explain the higher corrective activity (i.e., dom-
inant Grasp mode) seen when the thumb is being oscillated, since moving the thumb
could consume resources that could otherwise be fully devoted to the maintenance of
the task requirements. Using the range of compensation force magnitudes observed in
119
each subject, we asked them to voluntarily generate alternating index and middle fin-
ger forces of the same frequency and magnitude, but without oscillating the thumb and
while the pads were locked into a rigid object (second Control task). Once again, the
experimental force variability structure matches the predictions (Figure 5.11b). Further-
more, we see that despite the absence of any finger motion in this task, the contribution
of the grasp mode is just as strong as in the original task (Figure 5.11a and 5.5). Lastly,
the feedback in this control task was based on the alternation of index and middle finger
normal forces and no explicit feedback about the force error was presented for the sum
of normal forces. Hence, despite the absence of an explicitly enforced requirement on
the grasp force, variability along this mode is just as present and thus likely to be linked
to the explicitly enforced Compensation mode requirements.
5.4.8 Comparison with voluntarily oscillated grasp force
So far, we have shown that the grasp mode is present when performing a voluntary
compensatory task. We then used the third and fourth control cases to test the inverse,
i.e., whether voluntary grasp mode produces a corresponding involuntary compensation
mode. While, for the sake of brevity, we do not show the results here, we find that
such coupling is not present. In other words, generating voluntary grasp force does not
increase the magnitude of compensation force variability beyond what is seen in static
grasp in control cases 5 and 6 (Figure 5.10 and 5.5). This is in contrast to the voluntary
production of the compensation mode, which even in the absence of thumb motion gives
rise to even larger magnitudes of grasp force variability than observed in the original task
(Figure 5.11 and 5.5).
120
0
0.2
0.4
0.6
0.8
1
N
0 1 2 3 4 5
0
10
20
30
40
50
60
70
80
90
Frequency [Hz]
Angle [deg]
0 10 20 30 40 50 60 70 80 90
5
6
7
8
9
10
11
12
13
14
15
Time [s]
Sum of normal forces [N]
a
b
c
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PC magnitudes (unfiltered data)
N
Grasp mode
Compensation mode
Hinge mode
d
Figure 5.11: a. Force mode magnitudes vs. frequency in the index-middle finger alter-
nating normal force task (control task 2). Since in this task production of alternating
index and middle fingers was encouraged, not surprisingly, we see a large contribution
from the compensation mode. There was no motion component in this task and yet, the
grasp force contribution near the task frequency of 0.5 Hz (vertical red dashed line) is
quite considerable, too. b. Measured force mode directions are in agreement with the
simulation directions. c. The visual feedback was not explicitly given on the 10 N tar-
get force, but the sinusoids that mimicked the thumb force compensation mode. Hence,
greater error on the target force is to be expected, but also a reduced need to correct via
the grasp mode. d. While the magnitudes of force mode variability computed from the
unfiltered data is approximately twice of that observed in the Original Task, the order of
force modes in terms of magnitude and their relative magnitudes are preserved.
5.5 Discussion
While it is clear that the human nervous system has distinct adaptations that enable
dexterous manipulation - a functional hallmark of our species-, we demonstrate that
multifinger manipulation exposes strong limitations even for ordinary and ecological
tasks requiring the simultaneous control of individuated finger motion and force, such
121
as unscrewing a bottle cap. We systematically explored the potential confounds that
could explain our results of unnecessary grasp-and-release force variability pervading
the Original Task of holding the object while reconfiguring the grasp. Now we discuss
why we can now confidently argue that the underlying cause of such pervasive Grasp
Mode variability is likely a context-sensitive coupling in the actual drive to the alpha
motoneuron pools across fingers. Moreover, our control experiments and numerical
simulations, when put in the context of seminal work by human neuroanatomists, help
interpret those limitations as consequences of evolutionarily vestigial properties of corti-
cal projections to hand muscles. We speculate that the results reveal strong competition
between descending commands to grasp vs. manipulate, likely driven by competition
between the phylogenic older reticulospinal vs. the newer corticospinal tracts. This
suggests that, for all its neuro-musculo-skeletal uniqueness and versatility, the healthy
human hand critically depends on maintaining a delicate balance between competing
descending commands. This may explain the disproportionately severe disruption of
manipulation after neurological injury such as stroke, or even with healthy aging.
We begin by emphasizing that holding and reconfiguring our novel hinged
apparatus defines an unstable mechanical system that requires the nervous system
to generate fingertip force vectors that intersect at or close to the hinge at all
times [Flanagan et al., 1999]. For a variety of magnitudes of total grasp force, the set of
valid combinations of fingertip forces defines a slightly curved manifold (Figure 5.2).
We provided subjects with visual feedback to produce a constant sum of 10 N of total
grasp force while oscillating the thumb.
The fact that our analytical model of the task revealed the solutions to be well
approximated by a linear manifold (see discussion in [Clewley et al., 2008]) both justify
and motivate the use of PCA, which in turn allows us to disambiguate mechanically nec-
essary from neurally driven variability in the experimental data [Tresch and Jarc, 2009].
122
Variability in the compensation mode (PC [1; 1; 0]
T
in Figure 5.4) represents the
instructions given to the subjects to oscillate the thumb, which results in compensatory
alternating force magnitudes of the index and middle fingers as they maintain equilib-
rium. It is not surprising, therefore, that this PC explains the greatest variance in the
data near the thumb oscillation frequency of 0.5 Hz because it is driven by the mechan-
ical requirements of the task. On the other hand, given that the subjects succeeded at
the task and did not greatly translate or rotate the object, the data exhibited the lowest
variability along the hinge mode (PC [1;1; 1]
T
). In fact, the mechanical require-
ments of the task explain both the low variability in the hinge constraint and the high
variability in the compensation mode near 0.5 Hz. Had we not modeled the analytical
dynamical solution to the task, we may have been tempted to interpret the Compensation
mode variability as indicative of properties of the neural controller, such as coherence
modes in the control of motoneuron pools across fingers, for which there is some evi-
dence [Schieber and Santello, 2004, Tresch and Jarc, 2009]. Contrast this to the Grasp
Mode PC [1; 1; 1]
T
, which represents unnecessary grasp-and-release force variability
that is not part of the mechanical requirements of the task, which in turn leads to the
population of a manifold of mechanically feasible solutions (Figure 5.4b). Its lack of
mechanical relevance renders the Grasp Mode critically informative of the neural con-
troller’s performance and limitations.
5.5.1 Ruling out potential confounds
The additional six systematic control tasks, plus four simulations of mechanically driven
correlations between clean and noisy fingertip forces (Table 5.1), strongly indicate that
the variability along the grasp force mode cannot be attributed to signal-dependent noise
and only to a limited extent - if at all - to visuomotor corrective actions along the grasp
force direction at low frequencies. That is, (i) signal-dependent noise is associated with a
123
higher frequency band (8-12 Hz, [Jones et al., 2002]) than the one in which we observed
large and unnecessary grasp force fluctuations; and (ii) the first Control Task, with the
apparatus fixed to ground to abolish - by shunting to ground - any fingertip force cor-
relations arising from reaction forces driven by signal dependent noise, exhibited the
same unnecessary contribution by the Grasp Mode (Figures 5.5 and 5.9). Therefore, we
conclude that signal-dependent noise in conjunction with instantaneous action-reaction
mechanics cannot explain this unnecessary variability.
Secondly, simple static grasp in the fifth and sixth Control Tasks, in which a 10 N
sum of normal force was to be maintained, exhibits greatly diminished variability along
the Grasp Mode direction (Figures 5.5 and 5.10). This variability reflects, among other
things, the corrective activity in response to visual feedback error. Its small magnitude
here suggests that the much stronger presence of Grasp Mode in the Original Task is not
primarily driven by the interaction with visual feedback. Importantly, Control Tasks 2, 3
and 4, involving voluntary generation of grasp and compensation forces, show that vol-
untary production of Compensation Mode variability leads to involuntary Grasp Mode
variability, but not vice versa. We therefore conclude that the mechanically unnecessary
(and potentially counterproductive?) Grasp Mode variability is of involuntary neural
origin, and that such stereotypical grasp-and-release synchronous interactions pervade
multifinger manipulation when the manipulation task requires individuated fingertip
motions and forces.
What could be the causes of this neurally driven, context sensitive involuntary vari-
ability in the Grasp Mode? A behavioral explanation is that subjects may have simply
chosen not to track the constant visual feedback in spite of our encouragement to do
so. However, all subjects reported to perform the task in all conditions to the best of
their ability and satisfaction with using visual feedback to explicitly help them maintain
a given grasp force level (recall that we have ruled out by visuomotor corrective actions
124
as the main source of the Gasp Mode). Moreover, subjects are familiar with and adept at
common motor tasks requiring the reconfiguration of grasp during their daily activities,
such as rotating an object in the hand or unscrewing a bottle cap.
Alternatively, one can be tempted to attribute such variability to the principle of min-
imal intervention, giving rise to an uncontrolled manifold [Scholz and Schner, 1999,
Todorov and Jordan, 2002]. Having dedicated most of its control efforts to meet-
ing the critical constraint of not accelerating or rotating the object (hinge constraint
mode PC [1;1; 1]
T
) while also visibly moving the thumb (compensation mode PC
[1;1; 1]
T
), the nervous system may have chosen to assign the regulation of the grasp
force PC [1; 1; 1]
T
the lowest priority. After all, varying total grasp force does not imme-
diately lead to mechanical failure of the task and is a task variable (i.e., constraint) that
might be given lower priority (i.e., an uncontrolled manifold). However, constant total
grasp force is an explicit task constraint that is part of our instructions and visual feed-
back. In fact, Control Task 2 shows that Grasp Mode variability does not increase even
when it is not an explicitly part of the instructions (i.e., demoting the relevance of the
Grasp Mode does not increase it). Conversely, Control Task 1 shows that Grasp Mode
variability is not decreased when the object is attached to ground either, even though
there is no concern of dropping the object or involuntary slip-grip response. Therefore,
the observed Grasp Mode variability arguably does not reflect controller prioritization
la minimal intervention or uncontrolled manifold.
125
5.5.2 Grasp Mode variability reveals fundamental challenges to
controlling dynamic multifinger manipulation
This leads to the intriguing third explanation that manipulating an object while dynam-
ically reconfiguring the grasp is challenging enough to expose limitations in the neuro-
muscular control of multifinger manipulation. That is, when performing certain mul-
tifinger tasks requiring individuated finger actions to meet multiple requirements (i.e.,
maintaining hold of an object while also reconfiguring the grasp), the nervous system is
physiologically bound to violate some task constraints. We see this here as a pervasive
Grasp Force variability. This is quite different from choosing to prioritize some task
constraints as in the first two explanations above. In fact, this agrees well with other
work with single fingers, where even ordinary manipulation tasks can push the neuro-
muscular system to its limit of performance when they require combinations of, or tran-
sitions between, motion and force constraints [Venkadesan and Valero-Cuevas, 2008,
Keenan et al., 2009]. Thus we are compelled to conclude that, when manipulating an
object with individuated finger actions such as dynamically reconfiguring the grasp, the
neural controller must carefully and continuously overlay individuated finger actions
over unavoidable and mechanically unnecessary, yet strongly structured, synchronous
interactions.
This superposition of the Grasp Mode should not be confused with the notion of
functional coupling as in the context of the principle of superposition [Gao et al., 2005].
In that functional superposition, necessary internal forces (such as the grasp forces)
are coupled to manipulation forces (required to accelerate an object) in a simultane-
ous, appropriate, and intentional fashion. Such coupling is determined by the goals of
the task, such as the simultaneous increase of grip and load force to prevent slip, or
deceleration forces at the extreme points of an oscillating motion. Here, in contrast,
126
we showed that our multifinger manipulation task is unavoidably accompanied by func-
tionally unnecessary (and even inappropriate) synchrony across fingertip forces. This
pervasive synchrony is neither an epiphenomenon of the task nor a desired feature of
the task.
In fact, in agreement with [Schieber and Santello, 2004] who review the literature
on peripheral and central limitations of multifinger manipulation, we argue that the ner-
vous system has to superimpose finger individuation over a propensity to modulate fin-
gertip forces in synchrony. A potential explanation for this is the emerging picture
from seminal and recent work [Donald and Kuypers, 1968, Lang and Schieber, 2004,
Lemon, 2008]; for a review, [Baker, 2011]) on different neural pathways that project
on hand motoneuronal pools and segmental interneurons. The divergent projections
to flexor muscle motoneuronal pools by the reticulospinal tract seem to be in com-
petition with inhibitory corticospinal projections [Riddle et al., 2009]. Thus, the con-
stant presence of the Grasp Mode perhaps reflects the inability of the (evolutionar-
ily younger?) corticospinal tract from the neocortex to completely override projec-
tions from the reticular formation (one of the phylogenetically oldest portions of the
human brain [Ranson, 1953]). Thus the strongly structured stereotypical interactions
that pervade voluntary dynamic multifinger manipulation may be the modern echoes of
an evolutionarily vestigial tendency for grasp so critical to brachiation or early tool
use [Donald and Kuypers, 1968, Baker, 2011]. As a consequence, the human hand
might not have enough neuromechanical, as opposed to strictly mechanical, degrees
of freedom to meet both the constraints of grasp (i.e., holding the object steadily against
gravity) and manipulation (i.e., reconfiguring the grasp).
This interpretation that, in spite of its complexity and redundancy, a
neuromuscular system can run out of neuromechanical degrees of free-
dom if the task is sufficiently demanding has been proposed elsewhere (see,
127
e.g., [Loeb, 2000, Venkadesan and Valero-Cuevas, 2008, Keenan et al., 2009,
Kutch and Valero-Cuevas, 2011]). That is, in spite of the evolutionary adapta-
tions and apparent versatility and redundancy of the human hand, our results strongly
suggest that the human hand has barely enough neuromechanical degrees of freedom
to meet the multiple simultaneous mechanical demands of ecological tasks. This helps
explain the apparent paradox [Keenan et al., 2009] that, for all the neuromechanical
redundancy of the human hand, multifinger manipulation is susceptible to even mild
neurological conditions, takes years to develop in childhood, and degrades in healthy
with aging.
128
Chapter 6
Prenatal Motor Development Under
Different Incubation Periods Affects
Postural Control in Domestic Chick
6.1 Abstract
Domestic chicks walk within 3-4 hr after hatching following 21 days of incubation.
However, differences in light exposure can significantly extend the incubation range (20
to 22 days). Based on observations that differences in incubation duration do not affect
morphological measurements such as weight, height and tibial bone length, we hypoth-
esized that chicks hatch when they are sufficiently mature to cope with the environ-
ment. However, we recently found differences in some gait measures suggesting postu-
ral control at hatching may be more advanced by light exposure during embryogenesis,
so in this study we further test for potential differences and reconsider our hypothesis.
Employing 3 light exposure conditions established in our earlier study and robot-assisted
posturography methods, we report significant differences in several indicators of postu-
ral control as evidence that light exposure during embryogenesis advances maturation
of control. Hatchlings experiencing the greatest light exposure during embryogenesis
exhibited the least sway area, mean speed and distance from the center-of-pressure cen-
troid during quiet stance. Further, when posture was randomly perturbed during quiet
stance, they also recovered postural stability significantly more rapidly than hatchlings
129
exposed to less or no light during embryogenesis, as indicated by the fastest attenuation
of perturbation-induced sway oscillations. Although all groups exhibited general postu-
ral competence, consistent with our original hypothesis, we conclude that environmental
light during development not only accelerates morphogenesis but that it can also impart
a developmental advantage. These findings offer new important considerations relevant
to debate regarding the impact of prenatal and postnatal conditions on the development
of the human fetus and infant.
6.2 Introduction
The ongoing debate on the influence of light on neonatal development and maturation
during intensive care [Miller et al., 1995, Brandon et al., 2002] necessitates the testing
of relevant hypotheses in a suitable animal model: in particular, the domestic chick
has proved useful addressing questions of motor control development. Within a few
hours after hatching, domestic chicks (Gallus gallus) are capable of walking, stand-
ing and resisting perturbations to quiet stance. Furthermore, chicks typically hatch
at 21 days of incubation [Romijn and Roos, 1938, Hamburger and Hamilton, 1992,
Noy and Sklan, 1997] but the duration of incubation can be modulated through dif-
ferential light exposure. In particular, continuous light exposure will accelerate
hatching, while the continuous absence of light will decelerate it, each by up to
one day [Shutze et al., 1962, Siegel et al., 1969, Lauber, 1975, Ghatpande et al., 1995,
Fairchild and Christensen, 2000]. Importantly, the differences in light condition and
thus in incubation duration do not affect the viability of hatchlings, compared to natural
conditions [Lauber and Shutze, 1964]. More specifically, morphological measures such
as body weight and height and tibia bone lengths show no significant differences across
conditions [Sindhurakar and Bradley, 2010]. Together, these features make chicks a
130
valuable model for examining the impact of light on locomotor development, since
observed differences can clearly be attributed to the interplay between the nervous sys-
tem, muscles and mechanics, rather than mechanics in itself.
While it is known that light exposure accelerates morphological development,
among other things, by increasing the number of nuclei in the chick blasto-
derm [Ghatpande et al., 1995] or increasing early body weight [Lauber, 1975], and
modify posthatching behavior, such as increasing the rate of feather picking
between hatchlings [Riedstra and Groothuis, 2004] and attack and copulation behav-
iors [Zappia and Rogers, 1983], it is currently unknown if light exposure has an effect
on the development of locomotor competence. On the other hand, it is known that criti-
cal neurodevelopmental events occur very shortly prior to hatching. For instance, elec-
tromyographic (EMG) and kinematic studies of leg movements during embryonic motil-
ity have provided evidence that circuits involved in locomotor control are established 1-
3 days pre-hatching [Bradley et al., 2005, Bradley et al., 2008, Ryu and Bradley, 2009].
However, light seems to have little or no influence on these components of develop-
ment, since intralimb EMG patterns for stepping have been shown to be expressed
even in the absence of sensory or descending inputs [Jacobson and Hollyday, 1982,
Bekoff et al., 1987, Bekoff et al., 1989]. Our study extends and complements previ-
ous kinematic and EMG studies of locomotor development in chicks by providing the
first analyses of postural control and postural stability parameters, commonly used in
human posture analysis, on the day of hatching. Our primary goal in this study was
to determine if the maturation of postural control is affected by different light expo-
sure conditions during incubation. Based on our previous kinematic study of the influ-
ence of incubation light on chick gait parameters, which found no differences between
conditions as well as other studies, indicating that intra- and interlimb coordination
are well established within the first day after hatching [Jacobson and Hollyday, 1982,
131
Johnston and Bekoff, 1992, Johnston and Bekoff, 1996], we predicted that there would
be no differences in our current study. Surprisingly, the kinetic and more sensitive analy-
sis of quiet stance and stance perturbation response showed significant differences across
the three conditions, with chicks spending the shortest time inside the egg exhibiting the
best stabilization performance. These results indicate an influence of incubation light
condition on the development of motor skills and cast doubt on the assumption that by
the time of hatching, all chicks are equally competent.
6.3 Methods
6.3.1 Subjects
We obtained fertile Leghorn chicken (Gallus gallus) eggs from a local hatchery and
incubated them in force draft, humidified incubators at standard temperature (37.5

) and
humidity (62%). Prior to the onset of incubation, we weighed the eggs and randomly
assigned them to 1 of 3 incubators modified as described below. Onset of incubation
was considered embryonic day E0. We moved all eggs to nonrotating shelves within
the same incubator 3 days before anticipated hatching. We examined the eggs at 2 hr
intervals thereafter to determine the approximate time of pipping, a crack in the shell
indicating the onset of hatching, and when hatching was completed. After hatching, we
weighed the chicks and moved them to a brooder (47 cm x 47 cm x 20 cm). Hatchings
were trained for and tested in only 1 of the 2 experiments of this study. All training
and testing procedures were completed within 24 hours of hatching. At the end of data
collection, we euthanized the animals. All procedures were approved by the University
Institutional Animal Care and Use Committee.
132
6.3.2 Incubation Conditions
Standard industrial incubators were modified to house fluorescent lighting and/or to
eliminate external sources of light without disrupting internal temperature and humidity.
Fertile eggs were maintained throughout embryogenesis in a single incubator adapted
to provide continuous light exposure 24 hr daily (24 L) at 4,000 - 7,000 lx; 12hr light
exposure daily (12L) at 650 - 3,000 lx; or continuous dark exposure 24hr daily (24D) at
1lx. The range in light intensities indicate the variation in luminance at the egg shell
as the incubator shelf automatically rotated in 2 hr intervals, alternately placing the egg
closer to or further from the light source (Figure 6.1).
6.3.3 Acceleration of embryogenesis through light exposure
The average duration of embryogenesis in domestic chicks (Gallus gallus) is 21 days.
In a recent study we established 3 light exposure conditions that significantly varied the
length of incubation [Sindhurakar and Bradley, 2010]. Bright light exposure throughout
embryogenesis (24L conditions) reduced incubation to 20 days, where as12L conditions
resulted in hatching at 21 days, and absence of light exposure lengthened incubation to
22 days. An array of light conditions similar to 24L exposure was also employed in ear-
lier studies and was shown to significantly accelerate embryogenesis [Siegel et al., 1969,
Lauber, 1975, Coleman and McDaniel, 1976, Ghatpande et al., 1995]. We selected 12L
condition to approximate periodic indoor/outdoor light exposure during normal embryo-
genesis and 24D conditions as a control for light exposure.
6.3.4 Quiet Stance Training
Within 2-4 hours of hatching chicks were trained to stand upright on a platform similar
to the force platform. Chicks were encouraged to stand upright without taking steps
133
or sitting down for at least 30 seconds at a time. If they made an attempt to escape or
sit, the experimenter intervened to discourage the behavior. After each trial of training
they were allowed to rest for few minutes. This procedure was repeated until the chicks
stood upright without any interruptions. It typically took 3-5 trials per chick to complete
the training regardless of the incubation condition. Young hatchlings are frequently dis-
tracted by the environment so the training procedure was conducted in a quiet room with
dim lights. Further, hatchlings are susceptible to shivers at room temperature, which is
not only uncomfortable for the chicks but also an undesirable behavior with regards to
acquisition of postural control data as it might introduce noise. Thus, the training area
was warmed up with a space heater. Animals were tested within 2-4 hours of training
and data from the animals that were uncooperative after 2-3 trials were excluded from
analysis.
6.3.5 Data collection
Quiet stance experiments
In our first experiments we sought to quantify static postural stability by recording forces
during quiet stance. To collect forces applied during quiet stance, we designed and built
a force platform (Figure 6.2): two square-shaped boards made from ASB material (10
cm x 10 cm x 0.9 cm) were screwed together from above and below to a 6-axis ATI
Nano17 force transducer (ATI, Apex, NC). The platform surface was covered with sand-
paper to minimize slippage of the feet, as the animals movements were unconstrained
and to protect the load cell from dirt. We also sought to minimize postural noise due to
distractions during recordings by designing a wall, consisting of four sheets made from
ASB material (9 cm x 5 cm) that surrounded the chick and was mounted on the force
platform. For the static postural control experiments, we collected 1 to 6 trials per chick,
134
with each trial of 30 s in duration. We recorded fewer than 6 trials if the chick stopped
behaving or fell asleep repeatedly. Because chicks occasionally fell asleep or ceased
to cooperate, care was taken ensure that we only collected data from awake chicks that
maintained upright stance. We collected quiet stance trials for 10 chicks per incubation
condition, for a total of 30 chicks.
Figure 6.1: The incubator. Note that the surface holding the eggs was rotated at 2-hour
intervals to ensure equal light exposure.
Stance perturbation experiments
In our second experiments we sought to quantify dynamic postural stability by recording
forces during random perturbations of quiet stance. For these experiments, we mounted
the same force plate as in the quiet stance experiments onto the end-effector of an Adept6
300 6-degrees-of-freedom robot arm (Adept, Pleasanton, CA), where the robot can be
seen in its ”home” configuration, that is, its configuration prior to applying a perturba-
tion to the force platform. The robot control software was implemented in the Adept V+
language. We used a tcp/ip client-server connection between the robot controller and a
135
Figure 6.2: Chick on force platform. The stance platform, made from ASB material,
was mounted on a ATI Nano17 force sensor. The chick was standing on a sheet of sand
paper, to increase stance stability.
desktop computer to trigger perturbations from within MATLAB (Natick, MA) software
we designed for data acquisition. Every 10 s, we applied a perturbation along 1 of 8 ran-
domly selected directions in the horizontal plane at random amplitudes ranging from 0
to 25 mm. The randomized directions were drawn from a discrete uniform distribution,
while the randomized amplitudes were drawn from a discretized normal distribution
with standard deviation 15 mm (based on our quiet stance results). Using a mean-zero
normal distribution for amplitudes effectively interspersed sham perturbations to prevent
chicks from anticipating the next perturbation trial. While the maximum force platform
velocity was kept constant at 2500 mm/s, the acceleration profile consisted of a step
input, followed by a very slow deceleration until the final position was reached. The
final position was maintained for 2 seconds, before returning the robot to its ”home”
configuration. Robot movement did not exhibit extraneous oscillations. We performed
a total of 29 perturbations within a 5 min test session and conducted 3-4 test sessions to
136
−5 0 5 10
−10
0
10
Anterior−Posterior [mm]
Medio−Lateral [mm]
5
-5
Figure 6.3: Sample 30 s center-of-pressure dynamics of one 24L chick. Coordinates are
rotated so as to align with the major (anterior-posterior) and minor (medio-lateral) axes
of sway.
obtain a potential sample of 87-116 perturbations. We videotaped all perturbation trials,
to estimate post-trial the direction of each perturbation relative to postural orientation,
because chicks typically moved about the platform during the test session. We selected
perturbations for data analysis, those trials when chicks did not take a step or sit down
for 1 s immediately before and after the perturbation. We successfully tested 12 chicks
from 24L conditions, 11 chicks from 24D and 12 chicks from 12L conditions.
137
6.3.6 Data processing
We sampled force data at 1000 Hz and then down-sampled to 100 Hz for subsequent
analyses. For classical posture analysis methods and analyses of stance perturbation
responses the data were low-pass filtered using a 4th order bidirectional Butterworth
filter with the cut-off frequency at 20 Hz and 5 Hz, respectively. However, data were
left unfiltered for the drift-diffusion approach discussed below.
The x and y coordinates for center of pressure (COP) data were computed from the
forces applied to the force platform as follows, for the n-th sample:
x[n] =
M
y
[n] +cF
x
[n]
F
z
[n]
y[n] =
M
x
[n]cF
y
[n]
F
z
[n]
Where M
y
[n] is the y moment applied to the force sensor, while F
x
[n];F
y
[n] and
F
z
[n] are the three force components as measured by the force transducer, andc is the
thickness of the force platform that was attached to the force transducer (here, c = 9
mm).
It was not possible to guarantee that chicks assumed identical stance orientation
across trials. Therefore, we performed the subsequent data analysis not with respect to
the force sensor coordinate system but instead, rotated the coordinate system so as to
align with the chicks major and minor axes of sway (denoted MA and MI below). To
this end, we performed Principal Components Analysis (PCA) to identify the two axes
of sway directly from the COP patterns. For improved robustness, we computed the
PCA on the time series of COP increments x =x[n + 1]x[n], which is stationary,
rather than directly on the COP data, where estimation can be affected by data clustering.
For an example of the rotated COP time series, see Figure 6.3. Since PCA requires
138
subtraction of the mean from the data, the major and minor axis components represent
the distances from the data mean along their respective associated directions.
6.3.7 Center of pressure dynamics analysis: classical approach
In [Prieto et al., 1993], a variety of metrics applicable to center of pressure measure-
ments in humans are described. We applied the following three metrics to the chick
COP measurements:
Mean distance:
d =
1
N
X
n

MA[n]
2
+MI[n]
2
1
2
Mean speed:
v =
1
T
X
n
[(MA[n + 1]MA[n])
2
+ (MI[n + 1]MI[n])
2
]
1
2
Sway area:
s =
1
2T
X
n
jMA[n + 1]MI[n]
MA[n]MI[n + 1]j
Where n refers to the current data sample,N to the total number of samples recorded
in the trial, while T is the total duration of the trial, hence T = 30 s. We restrict
ourselves to reporting the results for the three most meaningful metrics, although most
of them showed significant differences.
139
Center of pressure dynamics analysis: drift-diffusion approach
Assuming that the dynamics of a given system can be described by a Langevin equa-
tion [Kantz and Schreiber, 2004]:
x
t
=f(x(t)) +g(x(t))(t)
wherex represents the state of a system,x2R
N
, whilef(x) describes the determin-
istic dynamics of the system. g(x) scales, in a state-dependent way, the normally dis-
tributed noise, whereN(0; 1) and correlation functionE[x(t)x(t
0
)] =K(tt
0
).
Due to the stochastic forcingg(x(t))(t), the statex(t) follows a probability distribution
p(x;t), whose (deterministic) time evolution can be shown [Kantz and Schreiber, 2004]
to be described by the Fokker-Planck equation, assuming the Markov property:
p(x;t)
t
=

x
[D
1
(x;t)p(x;t)] +

2
x
2
[D
2
(x;t)p(x;t)]
Where we refer toD
1
as the drift coefficient and toD
2
as the diffusion coefficient.
D
1
(x;t) describes the state-dependent change in the mean of the probability distribu-
tion p(x;t) at time t, while the diffusion term D
2
(x;t) describes the state-dependent
change in the variance ofp(x;t) at timet. Since the stochastic forcingg(x(t))(t) in the
Langevin equation is normally distributed, the Fokker-Planck equation fully captures the
dynamics of this stochastic system with Markov property. If there were no stochastic
forcing, the drift termD
1
(x;t) would be equivalent to the description of a deterministic
system.
140
A novel approach for determining driftD
1
and diffusionD
2
from time series data,
in particular, posture-related data, was proposed in[Gottschall et al., 2009]. The drift
coefficient can be computed as follows:
D
1
i
(x) =hx
i
(t + t)x
i
(t)ij
x(t)=x
ref
In other words, by finding the average change in statex during a time interval t,
and across all data samples in a suitably chosen neighborhood of a reference statex
ref
.
Next, the diffusion coefficient is computed as follows:
D
2
ii
(x) =h(x
i
(t + t)x
i
(t))
2
ij
x(t)=x
ref
I.e. by taking the average of the square of the change in state during a time inter-
val t near the state x
ref
. States can then be mapped to both the computed drift and
diffusion coefficients, and polynomials fitted to this mapping. Finally, we can compute
comparative statistics on the coefficients of these polynomials to quantify differences
between conditions and to infer control strategies.
6.3.8 Center of pressure dynamics analysis: perturbation response
For every successful perturbation, as described above, we computed the mean m in
terms of the x and y coordinates of the pre-perturbation COP time series. This mean
served as the reference point for the computation of Euclidean distance (D([n] =
p
(x[n]m
x
)
2
+ (y[n]m
y
)
2
), which we used for the subsequent data analysis. We
chose to analyze the dynamics of the Euclidean distance rather than those of the x and y
coordinates, since it was not possible to estimate major and minor axes of sway for such
short duration events. In successful perturbations, the response generally followed a
141
profile that consisted of two successively smaller peaks, reflecting the oscillatory nature
of the perturbation response (Figure 6.4). We extracted the following metrics:
Time of first peak:n = arg max
k
(D[k])
wherek is the data point time index relative to the time of perturbation application.
This metric is based on the assumption that neuromuscular activity can modulate the
oscillations that are purely due to mechanics; a relatively smaller n would reflect a
faster response.
Magnitude of first and second peaks:m
1
= max
k
(D[k]);m
2
= max
k
(D[k]);k>n
Together with the previous metric, this represents the degree of preparedness of the
chick and its ability to counteract perturbations.
Ratio of second and first peak:
m
2
m
1
This metric quantifies how effectively the chick can attenuate the perturbation-
induced oscillations.
Time difference between first and second peak:d =t
2
t
2
Where a smaller difference corresponds to a higher oscillation frequency, which in
turn can indicate a faster response.
Ratios of first peak or second peak and perturbation amplitude:r =m
1;2
=p
This metric’s value corresponds to the chick’s ability to absorb a perturbation.
6.3.9 Statistical Analysis
Since the resulting distributions of these all metrics, for both the quiet stance and the
stance perturbation experiments were found to be non-normally distributed by inspec-
tion of P-P and Q-Q plots, we applied Kruskal-Wallis tests to determine differences
across all three incubation conditions and Mann-Whitney U tests for pairwise differ-
ences as these statistical tests are suitable for non-normal distributions. The statistical
significance level was set top<:05. We tested for the effects of light condition on the
142
0.2 0.4 0.6 0.8 1
0
5
10
15
Time [s]
Distance [mm]
Pre−perturbation
0.2 0.4 0.6 0.8
0
5
10
15
Time [s]
Post−perturbation
First peak time: 80 ms
Peaks time difference: 340 ms
Max. excursion: 12.35 mm
Attenuation: 0.89
Damping: 0.77
Figure 6.4: Representative example of center of pressure excursion (i.e., COP vector
squared) dynamics during the second before (left plot) and after the perturbation (right
plot). The right plot exhibits the typical 2-peak response profile, with the second peak
smaller than the first. Also shown are the metrics we computed for each perturbation.
The example shown is from a 12L condition chick, experiencing a perturbation of ampli-
tude 16 mm.
three quiet stance metrics and the seven stance perturbation response metrics, comparing
between the three groups. Furthermore, to assess the influence of perturbation direction
on each of the three light conditions, we repeated the statistical comparisons (two-way
design) for lateral perturbation directions (45, 90 and 135

), anterior-posterior directions
(0 or 180

), assuming sagittal and frontal symmetry. To assess the influence of perturba-
tion amplitude, we compared the metrics across the three light conditions for small ( 7
mm) and large perturbations (> 7 mm). We chose 7 mm as cutoff was to for equal num-
bers of perturbations in each subsample. Individual perturbations were removed from
the analysis, if the value of one of the seven metrics exceeded its distribution by more
143
than two standard deviations. In total, we removed 31 perturbations from analyses, 14
perturbations from 24L condition, 13 from 24D and 11 from 12L conditions.
6.4 Results
6.4.1 Quiet stance experiment
Analyses of static postural control compared forces during quiet stance under all 3 light
conditions 24D (51 trials), 12L (76 trials) and 24L (50 trials). Results indicated that all
3 classic measures of sway [Prieto et al., 1993], mean distance, mean speed and sway
area (Figures 6.5-6.7), were significantly different, both across conditions as well as in
pairwise comparisons. In particular, hatchlings incubated in 24L conditions swayed the
smallest mean distance, at the lowest speed and over the smallest sway area, whereas
hatchlings incubated in 24D conditions swayed the greatest mean distance, at the highest
speed and over the largest sway area. Thus there was a consistent continuum in that all
parameters for the 3 hatchling groups were negatively correlated with the extent of light
exposure. Similarly, the linear coefficients of the drift function and the intercept coeffi-
cients of the diffusion function are were significant across all light conditions as well as
in pairwise comparisons. 24L animals had the smallest drift linear coefficient and dif-
fusion intercept, whereas 24D animals had the largest, once again showing a consistent
continuum. While the classical metrics simply suggested a difference in the sway pattern
across the three incubation conditions, the drift/diffusion analysis indicated, for reasons
discussed below, that the 3 groups of hatchlings employed different control strategies.
Since the results nevertheless do not provide an insight into the maturity of motor com-
petence, we performed postural perturbations to test for differences in dynamic postural
control.
144
0 5 10 15 20 25 30 35 40 45 50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mean distance [mm]
Proportion

24L
12L
24D
Figure 6.5: Mean distance from COP centroid distribution across the three incubation
conditions. Note that while there is considerable overlap between conditions, we also
observe a positive correlation between incubation duration and the magnitude of this
metric, with 24D chicks exhibiting the largest mean distance.
6.4.2 Stance perturbation experiment
We recorded 586 successful perturbations in total, representing a 61% success rate for
hatchlings in 24L condition; 462 successful perturbations (43% success rate) for hatch-
lings in 24D conditions, and 605 successful perturbations (53% success rate) for hatch-
lings in 12L conditions. We found significant differences across conditions in the fol-
lowing metrics: the amplitude of the second peak, the ratio of second and first peak
amplitude, the ratio of second peak to perturbation amplitude and the area covered by
the post-perturbation center of pressure (Figures 6.9-6.12). In particular, hatchlings
incubated in 24L attenuated the oscillations by the largest degree, as indicated by the rel-
atively small ratio of second to first peak magnitude. Furthermore, these chicks resisted
the initial perturbation to a greater extent as evidenced by the smallest ratio of center
145
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mean speed [mm/s]
Proportion

24L
12L
24D
Figure 6.6: Mean speed distribution across the three incubation conditions. Unlike mean
distance, the distributions for each condition are more separated, indicating the positive
correlation between incubation duration and the magnitude of this metric, with 24D
chicks having the largest mean speed.
of pressure maximum excursion to perturbation amplitude. As in earlier trends, hatch-
lings incubated in 24D conditions exhibited the greatest excursion in the second peak
and the ratio of second peak to first peak amplitude. Regarding the metrics that did not
exhibit significant differences: the maximum excursion value was reached at approxi-
mately the same time and the perturbation oscillations occurred at similar frequencies
across hatchlings in all groups.
We then investigated the effect of perturbation direction by restricting the compari-
son across incubation conditions to lateral perturbations (45, 90 and 135

) and found the
same significant differences as above. However, comparing anterior-posterior perturba-
tions (0 or 180

) across light conditions, we found that the second peak excursion was
146
0 10 20 30 40 50 60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sway area [mm ]
Proportion

24L
12L
24D
Figure 6.7: Sway area distribution across the three incubation conditions. As before, a
positive correlation between incubation duration and this metric can be seen, with 24D
chicks covering the largest COP area during quiet stance.
no longer significantly different across conditions. Besides perturbation direction, we
also investigated the effect of perturbation amplitude, separating the data into responses
to perturbations of amplitudes smaller and larger than 7 mm, and find that the above
reported differences between light conditions do not change when controlling for per-
turbation amplitude.
6.5 Discussion
The results of this study are contrary to our null hypothesis that by the time of their
hatching, domestic chicks (Gallus gallus) have reached a specific level of maturation
that makes them equally competent at motor skills, regardless of light exposure and
147
−60 −40 −20
−20
0
20
mm
mm
0.2 0.4 0.6 0.8
−40
−20
0
Time [s]
mm
−60 −40 −20
−20
0
20
mm
mm
0
Figure 6.8: Representative example of center of pressure dynamics during the second
before (top plot) and the second after the perturbation (middle plot), as well as the indi-
vidual COP coordinates plotted against time (bottom plot, upper graph: y-coordinate,
lower graph: x-coordinate). In the middle plot, the red arrow shows the direction of
the perturbation, while the green plot shows the orientation of the chick. The example
shown is from a 12L condition chick, experiencing a perturbation of amplitude 16 mm.
incubation duration. While an earlier study [Sindhurakar and Bradley, 2010] found no
148
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
0.25
2nd peak excursion [mm]
Proportion

12L
24D
24L
Figure 6.9: 2nd peak magnitude distribution. The values from 24L condition are most
concentrated on the left.
significant differences in common gait parameters across 12L, 24D and 24L incuba-
tion light conditions, we show here that during quiet stance, light does have a signif-
icant impact on motor behavior, as measured by several common and novel metrics
computed from posturographic data [Prieto et al., 1993, Gottschall et al., 2009]. Fur-
thermore, since the quiet stance results by themselves do not allow an interpretation
with regards to maturational progress, we applied force platform perturbations, using
a robot. While the analysis of the perturbation response data again showed significant
differences across the three conditions, they indicate, in addition, that 24L chicks return
to stable stance most rapidly. This in turn suggests that under increased light exposure,
the in-ovo-maturation process is improved and possibly accelerated. In the following,
we will discuss and interpret the results from the two parts of the study in greater detail.
In the quiet stance experiments, chicks from the 24D condition exhibited the
largest mean speed and distance from COP centroid and covered the largest sway
149
0 0.5 1 1.5 2 2.5 3
0
0.05
0.1
0.15
0.2
0.25
0.3
2nd peak / 1st peak amplitude
Proportion

12L
24D
24L
Figure 6.10: 2nd peak to 1st peak ratio distribution. The values from 24L condition are
most concentrated on the left, indicating the most rapid attenuation by these chicks.
area. Traditionally, a large sway area is associated with the COP profile seen in
patients suffering from neurological disorders such as paresis or Parkinson’s dis-
ease [Baszczyk et al., 2007]. This would at first glance suggest that 24D chicks are
the least progressed in their maturation, despite having had the longest incubation and
thus having had the most time to develop. However, the association of large sway
area and maturational deficit needs to be supported by more direct evidence. On
the one hand, aging and neurological disorders lead to a greater lack of stability, as
indicated by an increased fall-rate in the relevant populations [Overstall et al., 1977,
Baszczyk et al., 2007]. Conversely, a larger sway area can also be indicative of supe-
rior control [Cabrera and Milton, 2004], if the objective is to minimize expenditure of
computational resources - the controller would intervene only when stance reaches a
critical point.
150
0 0.5 1 1.5 2 2.5 3
0
0.05
0.1
0.15
0.2
0.25
2nd peak excursion/Perturbation amplitude
Proportion

12L
24D
24L
Figure 6.11: 2nd peak magnitude to perturbation magnitude ratio distribution. The
values from 24L condition are most concentrated on the left, indicating that these chicks
respond most effectively.
Therefore, based on the assumption that rapid attenuation of impulse-like perturba-
tions to quiet stance reflect stabilization competence and thus the progress in maturation
of motor competence, we analyzed the response to perturbations.
The lack of significant differences with regard to first peak time, peak time differ-
ence, maximum excursion and the ratio of maximum excursion to perturbation ampli-
tude, suggests that the immediate dynamics observed afer a perturbation is dominated by
the purely mechanical interplay between the perturbation and the anatomy of the chick.
Being morphologically equal [Sindhurakar and Bradley, 2010], chicks seem equally
(un)prepared for the perturbation and reach the first peak in a similar manner. How-
ever, the later response, reflected by the properties of the second peak, is affected by the
incubation condition, with 24L chicks apparently returning to a stable quiet stance most
rapidly, as evidenced by the smaller magnitude of the second peak, the smaller ratio of
151
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
0.25
0.3
Post−perturbation sway area [mm
2
]
Proportion

12L
24D
24L
Figure 6.12: Post-perturbation sway area distribution. Chicks from 24L condition
occupy the smallest area after a perturbation.
second peak to first peak and the smaller ratio of second peak to perturbation amplitude
in this condition.
We conclude that by the time of hatching, chicks are not equally competent at motor
skills, Instead, we assume that other developmental milestones override neurodevelop-
ment in determining the time of hatching, thus causing chicks incubated under different
light conditions to hatch at different stages of acquiring kinetic skills. Surprisingly,
chicks that have spent the longest amount of time in ovo, 24D, appear to be the least
progressed maturationally, suggesting that neuromuscular development in 24L chicks
is accelerated by at least 2 days (or 10 %). We speculate that neuromuscular devel-
opment is affected directly by light, which probably stimulates neurotrophic factors or
encourages early in-ovo motor practice.
152
0
5
10
2nd peak magnitude [mm]
12L 24D 24L
0
1
2
Second peak/first peak
0
1
2
0
5
10
123456789 10 11 12
Chick number
12345678 91011
Chick number
12345678 9101112
Chick number
2nd peak excursion/Perturbation amplitude
Post−perturbation sway area [mm
2
]
Figure 6.13: Boxplots of the metrics that were found to exhibit significant differences
across incubation conditions for each chick individually. We find that chick 11 in 24D,
and chicks 3 and 12 in 24L seem to exhibit behavior uncommon for their respective
conditions. Removing these outliers actually enhances the difference between 24D and
24L.
153
0
5
10
12L
0
5
10
24D
0
5
10
24L
0
1
2
2nd peak / 1st peak
0
1
2
0
1
2
0
1
2
2nd peak excursion/Perturbation amplitude
0
1
2
0
1
2
0
5
10
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Perturbation number
Post−perturbation sway area [mm
2
]
0
5
10
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Perturbation number
0
5
10
123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Perturbation number
2nd peak magnitude
Figure 6.14: Boxplots of the metrics that were found to exhibit significant differences
across incubation conditions versus the perturbation number. The lack of trends for any
of the metrics indicates the absence of a learning effect.
154
Chapter 7
Summary and Conclusions
Having read this dissertation, I hope that the reader now understands the need for a hier-
archical and successively more general view of motor redundancy, going from one level
of redundancy to the next. Espousing this view aids both in the design of experiments
and the interpretation of observed dynamics: for instance, it makes obvious the need to
constrain the endpoint force vectors in isometric tasks to study redundancy solely at the
muscle level. While this will not prevent dynamics at all more special levels of redun-
dancy, such as motor unit redundancy, it does prevent the ”leveraging” of more general
redundancy levels. It can be argued that for instance, in [Danna-Dos Santos et al., 2010]
not sufficient care was taken to minimize wrench dynamics in a fatiguing submaximal
isometric tripod grasp. Specifically, no feedback on the tangential components of force
was provided to subjects and tangential force dynamics were not analyzed, other than
quantifying their mean. The authors concluded, based on fine-wire EMG measurements
in 12 muscles that the nervous system employs a constant activation proportions strat-
egy (see Chapter 2) of multi-muscle control. However, we found in Chapter 2 that fol-
lowing such a strategy leads to violations of the minimum tangential force constraint -
in [Danna-Dos Santos et al., 2010], only a verbal encouragement was given to minimize
that component. Thus, in order to enforce a synergy on the muscle level, constraints at
the wrench level are by necessity violated. In conclusion, a proper design of this exper-
iment would include feedback on the tangential component of force while a correct
interpretation of the observed EMG dynamics needs to include a precise quantification
of changes in tangential force.
155
The aforementioned term ”leveraging of redundancy” implies that the nervous sys-
tem takes advantage of redundancy at all levels, for instance, to mitigate effects of mus-
cle fatigue (studied in Chapter 2 and 3) or the adaptation of tactile sensors in the skin
(see below). We found here that for submaximal tasks, the nervous system not only
improves its performance - in terms of endurance time - by allowing dynamics in both
muscle activation and force spaces (not proportional to each other), but it is actually
required to produce such dynamics for it to succeed at the motor task. Suppressing these
dynamics, on the other hand, when muscle synergies are enforced, leads to immediate
task failure.
We need to distinguish between necessary and optional motor redundancy
dynamics. The results from the studies by Kouzaki et al. [Kouzaki et al., 2002,
Kouzaki et al., 2004, Kouzaki and Shinohara, 2006] - entirely at the muscle activation
level, because we cannot measure individual muscle forces - indicate that in sumax-
imal tasks, the nervous system goes further than just the necessary dynamics, which
can be masked by the limited surface EMG resolution, in that it completely deacti-
vates rectus femoris and the vasti in alternation, to allow for their recovery of force
production ability. These optional muscle activation dynamics are very encouraging
with respect to the development of medical devices that either compensate for muscle
weakness or dysfunction or enhance force production in healthy humans. In a recent
paper [Decker et al., 2010], it was shown that taking over the CNS’ job and actively
stimulating electrically, in an alternating fashion, rectus femoris and two of the vasti, in
subjects with debilitating spinal cord injury significantly improved their endurance in a
cycling task, compared to a protocol, where the same muscles were stimulated simulta-
neously. This result indicates that even the very short periods of 100 ms of deactivation
allowed for muscle recovery, sufficient for task performance improvement.
156
Opportunities for fatigue mitigation exist at the level of wrench redundancy as
well, although experimental results are currently lacking. For the task of static tripod
grasp, some initial simulations suggest a benefit of varying fingertip vectors, as com-
pared to a strategy whereby these vectors are kept constant. However, the experimen-
tally observed dynamics (Chapter 4) of applied forces are very different: they exhibit
a drift and jump behavior, whereby longer periods of slow changes (drifts) alternate
with shorter periods of large changes (jumps) within the two-dimensional manifold of
mechanically task-irrelevant normal force dynamics. These drift and jump dynamics are
reminiscent of microsaccade dynamics, observed in another highly redundant system:
vision. One suggested purpose of microsaccades is that they represent a mechanism
to prevent perceptual fading, a consequence of the depletion of chemicals in photore-
ceptors [Skavenski et al., 1979, Rolfs, 2009]: during a ”jump” event, i.e. the actual
microsaccade, the sensory system switches from using one subset of photoreceptors,
possibly depleted during the ”drift” phase, to another subset, which is undepleted, thus
allowing the previous subset to recover. Two hypotheses that emerge from this interpre-
tation for motor systems that exhibits redundancy at the wrench level are: 1.) the drift
and jump dynamics of fingertip forces serve to mitigate or prevent adaptation of tactile
receptors in the fingertips by increasing and decreasing the force at each fingertip and
2.) these dynamics reflect the targeted dynamic activation of the 21 muscles actuating
thumb, index and middle fingers, to mitigate fatigue and even allow recovery of some
muscles. These fascinating hypotheses deserve further experimental work.
Lastly, potential benefits of redundancy have been investigated at the posture and
kinematic levels as well. Most experimental studies have indeed reported kinematic
changes in repeated performances of the task, such as increased coupling between
arm segments or increased kinematic variability, due to repetitive movement-induced
fatigue [Cote et al., 2002, Gates and Dingwell, 2008, Fuller et al., 2009]. Such fatigue
157
was found to be non-detrimental to task performance. Since these changes occurred long
before exhaustion, it can be argued that the changes reflect a fatigue-mitigating strategy.
Mathematically, the increased coupling reflects a fatigue-induced collapse of the pos-
ture solution space. Furthermore, there exist a number of modeling studies, mostly from
the ergonomics research community [Ma et al., 2011], which deal with the prediction of
optimal posture in a static motor task, minimizing muscle fatigue dynamically. Using a
biomechanical model of the arm, with very simple dynamics of fatigue and recovery, the
authors can predict fatigue and discomfort for all admissible postures and muscle activa-
tion patterns in a one-handed drilling task, and compute an optimal posture or work-rest
schedule, respectively.
I conclude that there remain great opportunities for the study of beneficial dynam-
ics at each level of motor redundancy, both in terms of modeling and experimentation.
Besides, a reinterpretation of motor variability observed in previously conducted exper-
iments, in the light of the motor redundancy hierarchy promoted here, might lead to new
insights into the benefits of redundancy and the true reasons for observed failures.
158
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Asset Metadata

Creator Rácz, Kornelius (author), Raths, Cornelius (author)

Core Title Neuromuscular dynamics in the context of motor redundancy

Contributor Electronically uploaded by the author (provenance)

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Neuroscience

Publication Date 05/24/2012

Defense Date 04/30/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag dynamics,knee extension,motor control,motor development,motor variability,muscle fatigue,neural control,neural pathways,neuromuscular,OAI-PMH Harvest,optimization,posture,redundancy,static grasp

Language English

Advisor Bradley, Nina S. (committee chair), Kutch, Jason J. (committee member), Udwadia, Firdaus E. (committee member), Valero-Cuevas, Francisco J. (committee member)

Creator Email raths@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-42874

Unique identifier UC11289345

Identifier usctheses-c3-42874 (legacy record id)

Legacy Identifier etd-RathsCorne-858.pdf

Dmrecord 42874

Document Type Dissertation

Rights Raths, Cornelius; Rácz, Kornelius

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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Abstract (if available)

Abstract Motor redundancy in neuromuscular systems exists on multiple levels. The term ”motor redundancy” represents the availability of infinitely many different solutions to perform a motor task. This dissertation is concerned with three particular of those levels: muscle redundancy, wrench redundancy and posture redundancy, which are successively more general forms of redundancy, each of which will be explained in detail. ❧ The first level corresponds to the phenomenon that for a given constant vector of submaximal limb endpoint force in isometric tasks, an infinite multitude of muscle coordination patterns exists. The motor control research community refers to this kind of redundancy as muscle redundancy, and traditionally, the selection of a particular mus- cle coordination pattern has been considered a computational problem for the nervous system. Mathematically, the possible muscle activations span an n-dimensional space - n being the number of independently controlled muscles - and the mapping between this space and that of isometrically generated endpoint forces is projective, therefore giving rise to a null space. The null space comprises those muscle activation vectors that do not have an effect on the endpoint forces, due to the mutual cancellations of generated forces. Specifically, the space of endpoint force vectors is 6-dimensional, consisting of three linear and three rotational components, leaving n-6 degrees of freedom. In the present work, I am studying a potential benefit of muscle redundancy, namely the mitigation of muscle fatigue through the dynamic switching between muscle activation patterns. Based on my results, I am proposing to abandon the view of muscle redundancy as a computational problem for the nervous system, since in the presence of muscle fatigue even the alleged simplification of this problem, that is, dimension reduction through muscle synergies requires awareness of the full dimensionality of the motor task. Instead, future research should focus on how the nervous system responds flexibly to the challenge of time-variance due to fatiguing and actually leverages muscle redundancy. ❧ The second level of motor redundancy is concerned with the phenomenon that in addition to the redundancy of muscles, infinitely many different combinations of endpoint forces and moments all achieve successful task performance. Again, this redundancy has been considered a computational problem for the nervous system and various ways of how it simplifies the selection of a particular wrench have been proposed. Note that the selected solution in terms of endpoint forces constrains the muscle coordina- tion solution space, in which a particular solution has to be found. Hence, wrench redundancy is a generalization of muscle redundancy. In the case of three-finger grasp, for instance, different fingertip force vector combinations result in an absence of net forces and moments applied to a grasped object, due to mutual cancellation of forces and moments applied by the fingertips. For example, one way to vary the applied forces is to squeeze the object harder and still succeed at the motor task of static grasp. I refer to this kind of redundancy as wrench redundancy: the same 6-dimensional wrench vector applied to an object can be produced by a multitude of force vectors individually acting on the object. Wrench redundancy can possibly help to mitigate effects of fatigue, namely through the dynamic shifting between endpoint force vector com- binations, just like shifting between coordination patterns achieves this at the muscle level. In the present work, however, I am pursuing a different path of research: In the first study, looking at the normal force dynamics in static tripod grasp, I will show how mathematically independent wrench space dimensions are actually controlled in quite different ways, reflecting their specific roles in achieving dexterous manipulation. This work shows that a purely spatial analysis of endpoint force variability is not sufficient and that temporal correlations can reveal important aspects of motor control. In particular, the dynamics of forces indicate a hierarchy of task dimensions in terms of task-relevance and contradict the view held by some that task variables can be separated into task-relevant and -irrelevant (i.e. the Uncontrolled Manifold Hypothesis). According to this view, large variability in a mechanically task-irrelevant dimension reflects the lack of control of this dimension by the nervous system. Based on these results, I am proposing to abandon the view of wrench redundancy as a purely spatial problem and to espouse the use of time series analysis to determine neural control strategies. In the second study of wrench dynamics, I will show how in a non-redundant dexterous manipulation task, where all wrench dimensions are task-relevant due to simultaneous force and motion requirements, the control of different task dimensions is likely coupled through neurophysiological pathways, whose separation during evolution has been incomplete. Specifically, I will show how different wrench space dimensions of the motor task, though mathematically independent, are nevertheless coupled in the performance of the task, thus limiting the ability to match the perfect mechanical solution of the task. We see here an important interaction between the wrench and the muscle level: when the wrench level becomes non-redundant, the muscle level also seems to hit a boundary and reveals limitations in the independence of control of muscles across fingers. ❧ Finally, the third level is concerned with postural redundancy, meaning that during the performance of a motor task the task goal can be achieved with different limb configurations, described in terms of joint angles. Once again, this level of redundancy is a generalization of the previous level and potentially extends the potential benefits of the former: a selected posture that enables motor task performance will constrain the admissible endpoint force space, which in turn will constrain the muscle coordination space. One common task taking advantage of postural redundancy is quiet stance. During quiet bipedal stance, two-legged animals are usually swaying or shifting from one posture to another, the former of which can be attributed to motor noise and the latter of which is likely a fatigue mitigation strategy. In this dissertation, I will present results of an analysis of postural control in one-day old domestic chicks (Gallus gallus) that reveal differences in prenatal motor development, which were induced by different amounts of light exposure during incubation. ❧ In summary, it can be said that the nervous system is remarkable in that it is capable of monitoring and reconciling continuously multiple levels of redundancy during performance of common motor tasks, in particular, since the kinematic degrees of freedom of limbs are not controlled directly by the brain. Instead, their actuation is achieved through a complex mapping starting with the degrees of freedom found at the brain level, where the task is likely represented very differently from joint angles. Importantly however, not even the three levels studied and discussed here are exhaustive: at one end, muscle redundancy specializes to the little studied motor unit redundancy, whereby different subsets of motor units in a single muscle generate the same muscle force. Motor units represent the control subunits that make up and provide graded control of muscle activity. At the other end of the redundancy spectrum, postural redundancy generalizes to behavioral redundancy, that is, using different strategies to achieve a task, for instance, walking vs. running, etc. Personally, I found that the separation of motor control into different levels of redundancy espoused here to be uncommon in the literature and the field, although it has helped me tremendously in forming hypotheses, designing experiments and attributing causes of failure in motor tasks to specific neuromuscular factors, and would certainly help the field of motor control research as well. I hope that the following work induces the reader to consider adopting this hierarchical view of motor redundancy, which is different from, and can potentially exist alongside other, hierarchical views of the neuromuscular system.