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Facilitating myocontrol for children with cerebral palsy
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Facilitating myocontrol for children with cerebral palsy
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Content
Facilitating Myocontrol for Children
with Cerebral Palsy
Cassie Borish
A dissertation submitted to the
Faculty of the Graduate School of the
University of Southern California in partial fulllment
of the requirements for the degree
Doctor of Philosophy
Principal Investigator: Terence D. Sanger
Department of Biomedical Engineering
August 2018
Contents
Acknowledgements vi
Abstract vii
1 Introduction 2
1.1 Prosthetic Devices for Children with Cerebral Palsy . . . . . . . . . . . . . . 2
1.2 Myocontrol as a Prosthetic Interface . . . . . . . . . . . . . . . . . . . . . . 2
2 Single Channel Optimization: Using EMG for Filtering 4
2.1 Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Experiment 1: Comparison of Speed-Accuracy Tradeo Between Linear and
Non-linear Filtering Algorithms for Myocontrol . . . . . . . . . . . . . . . . 5
2.2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.5 Discussion: Non-linear Filtering Results in Better Online Performance 12
2.3 Experiment 2: Eect of Target Distance on Controllability for Myocontrol . 17
2.3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.5 Discussion: Small-Distance Targets Can Decrease Online Performance 32
2.4 Chapter Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Interface to Task Space: Using EMG for Biofeedback and Multi-Muscle My-
ocontrol 35
3.1 Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
i
3.2 Experiment 1: Separating Involuntary from Voluntary Components Using
Spatial Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.5 Discussion: Involuntary Components are High Dimensional . . . . . . 48
3.3 Experiment 2: Linear Estimation of Rewarded Force for Children with Cere-
bral Palsy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.4 Discussion: Linear Estimation Improves Performance in Children with
CP and Subjects Respond to Parameter Changes . . . . . . . . . . . 67
3.4 Experiment 3: Non-linear Estimation of Rewarded Force for Children with
Cerebral Palsy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.4.4 Discussion: Non-linear Estimation Does Not Improve Performance but
Subjects Respond to Parameter Changes . . . . . . . . . . . . . . . . 82
3.5 Experiment 4: DOF-wise NMF for 3D myocontrol . . . . . . . . . . . . . . . 86
3.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.5.4 Discussion: Position Control is More Intuitive, but Cartesian Coordi-
nate System Not Ideal for Patients . . . . . . . . . . . . . . . . . . . 92
3.6 Chapter Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 Overall Conclusions and Future Work 95
Bibliography 97
ii
List of Figures
2.1 Average movement times per ID for Bayesian and linear conditions . . . . . 11
2.2 Average success rates per ID for Bayesian and linear conditions . . . . . . . 12
2.3 Average rectied EMG and cursor trajectories . . . . . . . . . . . . . . . . . 13
2.4 Screenshot of user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Example raw and ltered EMG signals . . . . . . . . . . . . . . . . . . . . . 22
2.6 MT of successful trials across IDs and width conditions . . . . . . . . . . . . 25
2.7 Proportion of successful trials across ID and width condition . . . . . . . . . 26
2.8 Overshoot or undershoot across IDs and width conditions . . . . . . . . . . . 27
2.9 Acceleration time across IDs and width conditions . . . . . . . . . . . . . . . 29
2.10 STD of the cursor position during the stabilization phase across IDs and width
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.11 CV of cursor position during the stabilization phase across IDs and width
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Example muscle synergies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Example of muscle and synergy selection . . . . . . . . . . . . . . . . . . . . 45
3.3 Mean and SE of MT of patients using All EMG, Select Synergy, and Select
Muscle control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Mean and SE of TP of patients using All EMG, Select Synergy, and Select
Muscle control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 MT using linear estimation of force from EMG . . . . . . . . . . . . . . . . . 57
3.6 Success rates using linear estimation of force from EMG . . . . . . . . . . . 58
3.7 TP using linear estimation of force from EMG . . . . . . . . . . . . . . . . . 60
3.8 Endpoint error using linear estimation of force from EMG . . . . . . . . . . 61
3.9 Initial angle error using linear estimation of force from EMG . . . . . . . . . 62
3.10 Changes in muscle force for children with CP . . . . . . . . . . . . . . . . . 63
3.11 Changes in EMG onset for TD children . . . . . . . . . . . . . . . . . . . . . 64
3.12 Changes in co-contraction between AD and PD for children with CP . . . . 65
3.13 Changes in co-contraction between AD and PD for TD children . . . . . . . 65
3.14 Changes in co-contraction between biceps and triceps for children with CP . 66
iii
3.15 Changes in co-contraction between biceps and triceps for TD children . . . . 66
3.16 MT using nonlinear estimation of force from EMG . . . . . . . . . . . . . . . 75
3.17 Success rates using nonlinear estimation of force from EMG . . . . . . . . . 76
3.18 TP using using nonlinear estimation of force from EMG . . . . . . . . . . . . 77
3.19 Endpoint error using nonlinear estimation of force from EMG . . . . . . . . 79
3.20 Initial angle error using nonlinear estimation of force from EMG . . . . . . . 80
3.21 Change in muscle force for TD children . . . . . . . . . . . . . . . . . . . . . 81
3.22 Change in EMG onset for CP children . . . . . . . . . . . . . . . . . . . . . 82
3.23 Changes in co-contraction between AD and PD for children with CP . . . . 83
3.24 Changes in co-contraction between AD and PD for TD children . . . . . . . 83
3.25 Changes in co-contraction between biceps and triceps for TD children . . . . 84
3.26 Example of synergies and activation coecients extracted from DOF-wise NMF 89
3.27 MT of force and position control of a robot to perform a discrete tapping task. 91
3.28 Example of Figure 8 trajectories and associated PSDs . . . . . . . . . . . . . 91
3.29 Comparison of the dierence in the ratio of peak x and y frequency components
and the expected ratio of 2 using force and position control. . . . . . . . . . 92
3.30 Example patient synergies extracted from DOF-wise NMF . . . . . . . . . . 93
iv
List of Tables
2.1 Movement Time Likelihood Ratio Results . . . . . . . . . . . . . . . . . . . 24
2.2 Success Likelihood Ratio Results . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Overshoot/Undershoot Likelihood Ratio Results . . . . . . . . . . . . . . . . 27
2.4 Acceleration Time Likelihood Ratio Results . . . . . . . . . . . . . . . . . . 28
2.5 STD Likelihood Ratio Results . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.6 CV Likelihood Ratio Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1 Clinical Characteristics of Subjects with Dyskinetic Cerebral Palsy . . . . . . 40
3.2 Success rate of individual subjects for each condition . . . . . . . . . . . . . 48
3.3 Characteristics of Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 Characteristics of Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
v
Acknowledgements
There are so many people who helped me get through this journey and without whom this
work would not have been completed. First and foremost, I thank my advisor, Terry Sanger,
for his guidance and encouragement, particularly in times when I felt like I was failing. I
have learned so much being part of his lab over the years.
I thank Aprille Tongol for her help in recruiting subjects of all ages for my studies. This
work would have been signicantly harder without her.
I also thank Matteo Bertucco for his mentorship and support.
I thank the rest of my lab, including Diana Ferman, Amber Dunning, Shanie Liyanagam-
age, Adam Feinman, Sirish Nandyala, John Rocamora, Eric Sohn, Enrique Arguelles, Sam
Huynh, Ruta Deshpande, Scott Young, Minos Niu, Nasir Bhanpuri, Maryam Beygi, Shinichi
Amano, Arash Maskooki, Jonny Realmuto, and Diana Ferman for their help, but mostly
their camaraderie.
I thank my committee members for taking the time to hear about my research and pro-
vide me feedback during my qualifying exam and my dissertation: Francisco Valero-Cuevas,
Nicolas Schweighofer, Tishya Wren, and Maryam Shanechi.
I thank my friends for their emotional support, and for being guinea pigs for my experi-
ments.
I thank the patients and their families for being enthusiastic participants in my experi-
ments.
I thank my funding resources for making it possible to do this work: National Institute
of Health grant R01NS052236, the Carter Foundation, the University of Southern California
Body Engineering - Los Angeles GK{12 Fellowship, and the University of Southern California
Biomedical Engineering Department.
I thank my family, who always maintained condence in my ability to complete this
process.
Lastly, I thank my husband, Greg, for his everlasting patience. He stayed with me through
every step of this journey, going through all my ups and downs with me. He helped me stay
positive and kept me grounded along the way.
vi
Abstract
For children with movement disorders due to cerebral palsy (CP), prosthetic devices can pro-
vide mobility, manipulation, and functional communication. However, the goals of prosthetic
control in children with impairments need to be dierent from those in adults. Children need
exible interfaces whose motions are not described in advance, so they can develop their own
movements and explore varying and unpredictable goals. Multi-muscle electromyographic
control (\myocontrol") may accomplish this, however, we must facilitate the controllability
of myocontrol by providing the appropriate interface. This paper details the work done in
eorts to make myocontrol possible for children with CP.
The rst studies focused on establishing initial appropriate design parameters within single
channel EMG. We compared the speed-accuracy tradeo between linear and Bayesian EMG
ltering algorithms in a Fitts' Law task. From this study, we established that Bayesian
ltered EMG has higher throughput, and so this is used for subsequent studies. Next, we
looked at how the speed-accuracy tradeo changes with dierent levels of EMG activation.
This helped us design subsequent experiments with target activations that minimize fatigue
in subjects but also reduce noise at low-level activations.
We then looked at ways to interface multiple channels of EMG to 2D or 3D task spaces. We
rst considered selecting the most controllable muscles and synergies using Fitts' Law. These
most controllable synergies (Select Synergy) and muscles (Select Muscle) were then compared
with All EMG control in a 2-D myocontrol task. Results showed that Select Synergy and
Select Muscle conditions did not improve myocontrol among patients. We then considered
mapping EMG to rewarded force, rather than measured force. We tested two methods to
map EMG to rewarded force in 2-D: using multiple regression (linear estimation) and the
Ghoreyshi-Sanger Algorithm (non-linear estimation). We found that patients were able to
improve performance with linear estimation of EMG, but not with non-linear estimation.
Finally, we considered a DOF-wise semi-supervised approach to implement multi-muscle
myocontrol in 3D. Using DOF-wise NMF, we compared force and position control of a robotic
arm within healthy subjects. Subjects performed a discrete task and continuous task using
force and position control. Results showed that for both tasks, subjects performed better
with position control. However, when implementing 3-D position control with patients,
vii
patients were unable to control the robot, likely due to poor calibration.
In addition to optimizing the myocontrol pipeline for children with CP, we investigated
the use of myocontrol as a tool. In the above, the goal of myocontrol is to interpret the
user's intent and mimic it, requiring minimal learning from the user. However, another use
of myocontrol is mapping muscles onto a dierent set of forces or movements. In this case,
the myocontrol will appear to the user like a tool that must be learned. When learning to
use a tool, users modify their muscle activity, so it's important to look at the interaction
between the human and myocontroller, as this may be useful for rehabilitation. We tested
this interaction by modifying parameters within the linear and non-linear estimations of
rewarded force and observed whether subjects changed EMG patterns. Resulting changes in
EMG suggest that there is a use for myocontrol beyond simply estimating movement intent
from EMG. Indeed, we identify three potential uses for myocontrol: 1) a lter to identify
driving signals for control, 2) as biofeedback, and 3) a tool that can in
uence user behavior.
This work aids in the design of future myocontrol applications not only for children with CP,
but also for other patient populations and healthy subjects.
1
1 Introduction
1.1 Prosthetic Devices for Children with Cerebral Palsy
Children with tetraplegic or dyskinetic CP suer from movement disorders such as muscle
weakness, spasticity, dystonia, and dyspraxia that can prevent meaningful voluntary move-
ment [70]. As a result, these children have a very limited ability to do normal things that
healthy children do, including playing, interacting spontaneously, exploring, and learning
from mistakes. For such children, prosthetic devices may provide mobility, and in more
extreme cases, functional communication.
However, careful consideration must be placed into the interface of such prosthetic devices.
Children may be able to use low-bandwidth interfaces such as a head switch, force-control
joystick, or button interface, however, their output from these devices are often slow and
limited by their own movements. In a previous study, we found that children with CP who
depend on a touch-screen interface to communicate generate an average of only 50 words per
week [68]. In essence, children can no better control such prosthetic devices than they can
their own body. Therefore, if we are to provide prosthetics for this group of children, we must
address the problem of optimal extraction of voluntary controllable signals from involuntary,
unwanted muscle activity. Ultimately, we want to provide prosthetic devices that will allow
these children to explore and manipulate their environment in ways that healthy children do.
Children need
exible real-world interfaces whose motions are not described in advance, so
that they can learn and develop their own movements, and explore varying and unpredictable
goals.
1.2 Myocontrol as a Prosthetic Interface
Myocontrol, the control of prosthetic devices using electromyographic (EMG) signals, may
be a solution for children with CP to control prosthetic devices in a
exible manner. In CP,
there is no disconnect between the brain and the spinal cord as there is in spinal cord injury,
so the EMG signal provides a direct read-out of the movement-related activity in the motor
cortex. Myocontrol is preferable to brain-computer interfaces, which are either invasive
2
(requiring implantation in the brain) or low bandwidth (when using scalp electrodes). It
does not restrict where the child can look, as eye gaze control would. It also allows for
smooth and
exible control, as opposed to button or on/o interfaces. The challenge with
myocontrol for children with CP is separating out the voluntary component of the signal
from the involuntary component in order to drive a prosthetic.
The myocontrol pipeline involves recording EMG from multiple muscles, ltering the sig-
nals of EMG, then interfacing EMG to the task space. Implementing myocontrol in any
given system requires optimization at a couple levels. At the lower level, we must optimize
control for single channel EMG by selecting an appropriate lter and determining reasonable
task demands. At the higher level, we must determine how best to estimate movement intent
from multiple channels of EMG and integrate them to the task space.
This paper overviews the work done to optimize the myocontrol pipeline for children with
CP. The rst experiments detail work to determine how best to lter single channel EMG for
online control and appropriate task demands for single channel EMG that do not compromise
controllability. The subsequent experiments explore dierent ways to interface to the task
space. The goal of this paper is to detail what works and does not work in facilitating
myocontrol for children with CP. The contributions in this report will contribute to the
long-term goal of developing an interface that allows children with CP to control a \virtual
body" that has better function than their own body, allowing them to communicate, play,
and interact as children normally do.
3
2 Single Channel Optimization: Using
EMG for Filtering
2.1 Chapter Introduction
The studies detailed in this chapter were performed to help inform us of single channel EMG
parameters. In Experiment 1, we directly compared the speed-accuracy tradeo in a 1-D
myocontrol task using linear-ltered EMG versus Bayesian-ltered EMG to assess which
ltering algorithm is better for use in myocontrol. In Experiment 2, we investigated how
dierent levels of EMG activation aect myocontrol controllability.
4
2.2 Experiment 1: Comparison of Speed-Accuracy
Tradeo Between Linear and Non-linear Filtering
Algorithms for Myocontrol
A version of the following section was published in Journal of Neurophysiology.
2.2.1 Abstract
Non-linear Bayesian ltering of surface electromyography (EMG) can provide a stable output
signal with little delay and the ability to change rapidly, making it a potential control input
for prosthetic or communication devices. We hypothesized that myocontrol follows Fitts'
Law, and that Bayesian ltered EMG would improve movement times and success rates
when compared with linearly ltered EMG. We tested the two lters using a Fitts' Law
speed-accuracy paradigm in a one-muscle myocontrol task with EMG captured from the
dominant rst dorsal interosseous muscle. Cursor position in one dimension was proportional
to EMG. Six indices of diculty (IDs) were tested, varying the target size and distance. We
examined two performance measures: movement time (MT) and success rate. The lter had
a signicant eect on both MT and success. MT followed Fitts' Law and the speed-accuracy
relationship exhibited a signicantly higher channel capacity when using the Bayesian lter.
Subjects seemed to be less cautious using the Bayesian lter due to its lower error rate and
smoother control. These ndings suggest that Bayesian ltering may be a useful component
for myoelectrically-controlled prosthetics or communication devices.
2.2.2 Introduction
For decades, researchers have been investigating the use of surface electromyography (EMG)
as a noninvasive way to interface with devices, including biofeedback [9, 12] , myoelectric
prosthetic hands [58, 24, 48], hands-free computer interfaces [85], and electrolarynxes [36].
A critical challenge to using EMG in research applications is estimating its magnitude. The
most common methods for interpreting the EMG signal are based on modeling EMG as
amplitude-modulated band-limited noise [39, 38]. This model allows researchers to capture
an amplitude envelope by rectifying the signal followed by low-pass ltering [29].
This EMG processing method has the advantages of simplicity and low computational cost,
but also has a number of known drawbacks. One issue is that causal linear ltering methods
introduce time delays that can be hundreds of milliseconds long. This can be accounted
for in o-line analyses, but can introduce instabilities into on-line myocontrol (i.e., EMG
5
device control) paradigms. A more dicult challenge is removing undesired variability while
retaining intentional rapid changes. Low-pass ltering successfully removes high-frequency
noise from the signal, but also removes much of the high-frequency information from the
signal, impairing the ability to observe rapid changes to the system being controlled [78].
Increasing the cut-o frequency of the lter can mitigate this eect but also allows unwanted
noise back into the signal [56]. There have been recent advances that greatly improve the
quality of the signal [19, 18, 67], but the trade-o between signal smoothness and the ability
to make rapid changes remains.
A non-linear recursive estimator of the EMG signal for online ltering was recently pro-
posed [72] in which the EMG driving signal is modeled as a mixed jump-diusion stochastic
process. The driving signal is recursively estimated by propagating its probability density
using the Fokker-Planck equation, followed by an update of the distribution using Bayes'
Rule to account for the EMG measurement. Where linear lters store previous input and
output values, thereby inserting time delays into the output, the memory of the Bayesian
lter is contained within the probability distribution, which is a re
ection of what we think
we know about the state (e.g., force, neural intent, etc). The lter output is the maximum
a posteriori (MAP) estimate of the probability distribution after each measurement. While
low-pass ltered EMG displays signicant time delays and a slow rise rate, the output sig-
nal from Bayesian ltering shows low variability during periods of steady contraction while
allowing for rapid, step-like changes between dierent levels of contraction. The previous
work provides evidence (in the form of comparing signal-to-noise ratios and graphs of force
and various ltered EMG outputs) that Bayesian ltering improves the estimation of torque.
This algorithm has been used in studies of biofeedback [9] and motor control [90, 88]. While
one might expect the higher signal-to-noise ratio of the Bayesian lter [72] to translate into
better control, it cannot be assumed that subjects will make appropriate use of the ltering
method, nor can we determine a priori whether the magnitude of the improvement will be
sucient to have a signicant eect on performance. We need to have a tool that allows us
to directly compare dierent software applications for on-line EMG ltering.
In this study, we use a Fitts' Law paradigm to characterize isometric myocontrol using
the rst dorsal interosseous (FDI) muscle. The FDI is not used in most device applications,
but it also bears few of the general issues with EMG. It is a supercial, slowly-fatiguing
muscle, so its EMG is easy to capture without concerns about cross-talk or the eect of
fatigue on the EMG-force relationship. It has also been used in studies of motor control
in combination with other intrinsic muscles to measure over
ow [90, 88]. We describe
the relationship between speed and accuracy for myocontrol and the eect of the ltering
algorithm on this relationship. We can calculate the information rate using the Fitts' Law
6
regressions and use these to assess and compare the controllability of the two dierent types
of lter output. Based on the evidence from the study proposing the Bayesian algorithm
[72], we hypothesize that the Bayesian ltering algorithm will permit users to increase speed
for a given diculty and improve success rate by reducing unwanted noise in the EMG signal
without sacricing rapid intentional changes. While the previous study focused on assessing
the Bayesian algorithm as a signal processing algorithm for EMG, this study assesses the use
of the Bayesian algorithm for online EMG control. In other words, in this study, the subjects
see the output of the lter and can adapt their own behavior in order to use the lter as
a tool. We further conjecture that, when appropriately ltered, the speed-accuracy trade-
o using myocontrol from a single muscle should approach the Fitts' Law speed-accuracy
tradeo for isometric force.
2.2.3 Methods
Participants
Ten healthy adult subjects between 21 and 28 years old (2 males, 8 females; mean = 20 years
old; standard deviation = 2 years) were recruited. All signed written informed consent to
participate and US Health Information Portability and Accountability Act (HIPAA) autho-
rization for use of medical and research records, according to the approval of University of
Southern California's Institutional Review Board.
Experimental Setup
The EMG signal was acquired from the dominant hand rst dorsal interosseous (FDI) muscle
by attaching over the belly of the muscle an EMG electrode (DE{2.1 electrodes with a
Bagnoli{8 amplier, Delsys Incorporated, Boston, MA, USA) with a band-pass lter of
20{450 Hz and 1000 times amplication. The EMG signal was sampled at 1 kHz using
an analog-to-digital converter (Power 1401, Cambridge Electronic Design Ltd., Cambridge,
United Kingdom) and custom data collection software. The EMG signal was collected from
the FDI during isometric contraction as the subject pushed against a silicone block, and was
normalized according to the subject's maximum voluntary contraction (MVC), which was
dened as the maximum mean EMG activation measured over a 200 ms window within a 5
s period. EMG was ltered with a 1 Hz, 4th order Butterworth high-pass lter to remove
baseline DC voltage, and subsequently full-wave rectied. At this point, one of the two
output lters was applied.
The subjects were informed that the vertical position of the cursor on the screen was
proportional to the level of contraction of their FDI as they pushed against the block. They
7
were given an opportunity to test how the control of the cursor operated. The height of the
screen was 27 cm and represented 0{30% MVC. (Activity over 30% MVC caused the cursor
to stop at the top of the screen, rather than disappear o the screen.) The subject was then
given an opportunity to practice use of the cursor for the length of one trial (38 seconds).
Four blocks of twelve trials were performed. Trials consisted of 6 targets of various widths
and distances, each presented for 3 seconds with a 3-second rest period in between targets.
In this experiment, \distance" and \width" were expressed in units of %MVC. Target order
was randomized at the beginning of each trial. A trial was considered successful when the
subject was able to stabilize inside the target for 500-ms within the allotted 3-s display time.
The target changed colors upon success to indicate that the subject could relax until the
next target was displayed. Breaks were given between each block of trials to prevent fatigue.
In two of the blocks, the EMG output came from applying a 2 Hz 4th order Butterworth low-
pass lter to the rectied data, and in the other two blocks, the output came from applying
a non-linear Bayesian lter ( = 1e{4, = 1e{18, 128-bin histogram) [72] to the rectied
data. The selected parameters for both lters were considered by pilot subjects to be the
easiest to control. The frequency cutos tested in the original study of the Bayesian lter
(0.1, 1, and 5 Hz) [72] were used as references to determine the appropriate cuto for the
linear lter in this study. We further optimized the linear lter cuto for the task to 2-Hz
with testing on pilot subjects. Block order was randomized for each subject.
Analysis
We examined three outcome measures: movement time, success rate, and channel capacity
(index of performance and throughput). Movement time (MT) was dened as the amount
of time from when the cursor reached 10% of maximum velocity for the movement until the
beginning of the period in which the cursor had successfully stabilized in the target for 500
ms. This outcome measure is analogous to \complete stabilization time" from [32] and the
EMG target mode outcome measure from [66]. Success rate was the fraction of a subject's
trials in which this criterion was satised within the allotted 3 seconds. Only successful trials
were included in Fitts' Law regressions and in statistical analyses of MT.
Fitts' Law states that we should be able to use linear regression to model movement time
as
MT =a +bID (2.1)
where ID refers to Index of Diculty. ID is calculated as
8
ID =log
2
2D
W
(2.2)
where D is the distance to the center of the target from the starting position and W is the
width of the target [33].
Since the design of our experiment had repeated measures, we used linear mixed eects
analysis to express the relationships in our data instead of linear regression analysis, which
requires measurements to be independent. To determine the Fitts' Law relationship, we
entered ID (6 levels) as a xed eect. As random eects, we had intercepts for each lter (2
levels) nested within each subject, as well as random slopes for the eect of ID, resulting in
the following regression model in R:
MTID + (1 +IDjSubject=Filter) (2.3)
The inverse of the random slope given for each lter nested within each subject was the
Index of Performance (IP). Throughput (TP) was calculated as the mean of the ID/MT
ratios over all successful data points within each lter condition for the subject [54]. Both
IP and TP give a quantitative measure of controllability in terms of bit rate. To examine
dierences in channel capacity, paired t-tests were conducted to detect dierences in IP and
TP between the linear and Bayesian lters, with the hypothesis that IP and TP would be
greater for the Bayesian lter.
To determine xed eects signicance on MT and success, the linear mixed eects analysis
comprised ID (6 levels) and Filter (2 levels) as xed eects, and intercepts for each subject
as a random eect. The model was:
DependentvariableID +Filter + (1jSubject) (2.4)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interaction between
the 2 xed eects (ID and Filter), we compared the model that takes into account the
interaction between xed eects (Full) against the model without the interaction (Null).
For all comparisons, P values and Akaike's information criterion values (AIC) were obtained
by likelihood ratio tests of the Full model with the Null model. If the factor in question
signicantly aects the dependent variable, then the comparison will report a signicant P
value (< .05) and an AIC value lower for the Full model. Similarly, a signicant interaction
between factors will result in a signicant dierence between the Full and the Null models
9
(p< 0.05) with a lower AIC for the Full model. Post-hoc two-sample t-tests with Bonferroni
correction were used to identify at which IDs there was a dierence between the two lters
for both MT and success.
To compare the delay of onset between the two lters, we determined the dierence between
cursor onset and unltered EMG onset. Cursor onset was measured as the rst point in which
the cursor signal was greater than a baseline threshold. Similarly, EMG onset was measured
as the rst point in which the rectied EMG was greater than a baseline threshold. To
determine the baseline threshold, we used a one-second period of data collected during rest.
From this period, we calculated the mean and standard deviation (SD) of the EMG and
cursor. The cursor and EMG baseline thresholds were the sum of the mean and three times
the SD of their respective signals during the rest period.
The rectied EMG data for Bayesian and linear conditions were also averaged across
all 24 trials and 10 subjects for each ID to observe changes in behavior for each lter.
From the averaged data, the signal was linearly regressed for the rst 200 ms after EMG
onset to compare the initial rise in EMG (slope) for each condition. Analysis of Covariance
(ANCOVA) was used to statistically compare the slopes for each lter. The covariate was
time (the rst 200 ms of EMG onset), and the independent variable was the lter.
Data analysis was executed with Matlab R2016a (Mathworks, Natick, MA). Statistical
analysis was performed using RStudio, version 0.99.903 (RStudio Inc., Boston, MA), and
the R-package lme4 (version 1.1{12).
2.2.4 Results
Channel Capacity
T-tests showed that subjects had a higher channel capacity using the Bayesian lter by
measure of both IP (p = 0.012) and TP (p< 0.001). IP of the Bayesian lter was 5.50 1.09
bits/s (standard error) and 2.53 0.13 bits/s for the linear lter. TP was 6.01 2.19 bits/s
for the Bayesian lter and 3.32 0.47 for the linear lter.
Movement Time
The likelihood ratio test showed that ID had a signicant eect on MT (AIC
Full
= 2707.2;
AIC
Null
= 3100.0; p < 0.0001), meaning that the task eectively imposed a speed-accuracy
trade-o. On average, MT increased with ID by 0.27 0.013 seconds. The lter also had
a signicant eect on MT (AIC
Full
= 2707.2; AIC
Null
= 2729.8; p < 0.0001). MT with the
Bayesian lter was 0.1092 0.0220 seconds less than MT with the linear lter. A signicant
10
**** **** *** **** ****
0.0
0.5
1.0
1.5
2 3 4
Index of Difficulty (bit)
Movement Time (s)
Filter
Bayesian
Linear
Figure 2.1: Average movement times per ID for Bayesian and linear conditions
(*** = p < 0.001; **** = p < 0.0001).
interaction of the two xed eects was also reported (AIC
Full
= 2650.2; AIC
Null{>= 2707.2;
p< 0.0001), meaning that the eect of ID on MT was dierent for the two lters (Fig. 2.1).
Success Rate
The likelihood ratio test showed that ID had a signicant eect on success (AIC
Full
= {36.006;
AIC
Null
= 48.323; p< 0.0001). On average, success decreased with ID by 22.9 2.02 percent.
The lter also had a signicant eect on success (AIC
Full
= {36.006; AIC
Null
= 13.512;
p<0.0001). Success with the Bayesian lter was 29.2 3.6 percent higher than success with
the linear lter. A signicant interaction of the two xed eects was also reported (AIC
Full
= {130.500; AIC
Null
= {36.006; p < 0.0001) (Fig. 2.2).
Mean EMG Behavior
Figure 2.3 displays average group behavior at each ID in the Bayesian and linear cases. In
the Bayesian paradigm, subjects tended to increase their EMG more quickly and overshoot
on the lower targets to get the cursor moving quickly, then settle their EMG in the target
to stabilize the cursor. In the linear paradigm, subjects selected an EMG level at rst and
only began to adjust their EMG as needed once the cursor responded.
The delay between EMG onset and cursor movement for the linear lter (220 116 ms)
was greater (paired one-tailed t-test, p = 0.046) than the delay for the Bayesian lter (128
84 ms). Furthermore, for each ID, there was a higher initial slope in EMG for the Bayesian
11
**** **** ****
0.0
0.3
0.6
0.9
1.32 1.74 2.32 2.91 3.32 3.91
ID
Success
Filter
Bayesian
Linear
Figure 2.2: Average success rates per ID for Bayesian and linear conditions
(**** = p < 0.0001).
condition (p < 0.0001).
2.2.5 Discussion: Non-linear Filtering Results in Better Online
Performance
In this study, we used Fitts' Law to quantify the speed-accuracy trade-o in a myocontrol
task and identify dierences between interfaces, just as for other human-computer interfaces.
Even though we only performed this analysis in a one-dimensional case, the format of analysis
can be extrapolated to multi-dimensional cases. Also, this method may be used to identify
dierences in a subject's ability to individually control their muscles, which could be useful in
optimizing multi-dimensional interfaces. A benet of using Fitts' Law is that the dierence
in performance is quantied in terms of information-theoretic concepts (bits per second) that
are relevant both for communication and for control of devices.
We used three outcome measures to examine the dierences between the two lters: MT
at each ID , success at each ID, and channel capacity measures (IP and TP). Compared with
the non-linear Bayesian lter, the linear lter had increased movement times and decreased
success, as well as reduced IP and TP. These indicate that subjects had some diculty
accomplishing the task when using the linear lter, particularly for the higher IDs. In
contrast, Bayesian ltering of EMG kept success rates within or near the range of typical
Fitts' Law paradigms for movement or force control, and had a signicantly higher IP and
TP. The Bayesian lter allowed accurate performance even for the most dicult targets.
12
Figure 2.3: Average rectied EMG (gray) and cursor trajectories (black) across 24 trials and
10 subjects for the dierent IDs using the Bayesian ltering paradigm (top) and
linear ltering paradigm (bottom). Vertical lines indicate target start and end,
and horizontal lines indicate the target region.
13
The inclusion of only successful trials for analysis of MT and channel capacity may have
introduced bias by articially decreasing MT, especially for the linear lter at higher IDs.
Had subjects been given innite time to reach all of the targets, we would likely have observed
a more stark dierence between the two lters. There was a large decrease in success for
the last three IDs with the linear lter. These were targets of higher distance, which may
have been more dicult for subjects to reach due to the lter's delayed response. The raw
EMG trajectories showed that subjects generally undershot these targets using the linear
lter. For the Bayesian lter, we observed increased MT for IDs 1 and 3. This may be a
result of some sensitivity of the lter to small-width targets and short distances, as noted
by the large initial overshoot in the average raw EMG trajectories while using the Bayesian
lter for these targets. This sensitivity may be addressed by adjusting the lter parameters.
More study would be needed to conrm this.
In Fitts' original study, he describes the IP of the best conditions as ranging from 10.3{
11.5 bits/sec, but the ranges of IP changed widely both within the stylus task and across the
other tasks in the study. The nature of the task and its relatively complexity does seem to
aect IP calculations. For example, IP is typically lower in serial movements than in discrete
or periodic ones [54]. Nevertheless, the ranges of IP and TP values t into the range one
would expect for a device of this nature.
The values of IP and TP also range greatly across human-computer interface studies. One
of the original studies on the channel capacity of the computer mouse and isometric joysticks
[11] found that the IP for the computer mouse is 10.4 bits/sec and for the isometric joystick
is 4.5 bits/sec. A later study examined use of an isometric joystick to control either the
position (IP = 3.4 bits/sec) or velocity (2.2 bits/sec) of a cursor, with error rates around
25% [43]. More recently, a study of the mouse and joystick found that for the mouse, TP
= 4.9 bits/sec, while for the joystick TP = 1.8 bits/sec, both with error rates in the 9{10%
range [55]. The mean IP and TP values found in this study using Bayesian-ltered EMG
t into the range of IPs and TPs for mice and joysticks described in the literature. This was
achieved by subjects in a novel task with very little practice.
There are few studies that have used Fitts' Law to study myocontrol. One study comparing
myocontrol and force control found that IP ranged from 1.1{2.6 bits/sec for myocontrol using
EMG ltered with a 5th order, 4 Hz low-pass lter [66], which is similar to the IP we found
using our linear lter parameters. Our movement times for both lters are similar to those
reported in another study assessing speed-accuracy tradeo in myocontrol using the hand or
forehead, which reported mean movement times of 932 ms for both locations for IDs ranging
from 1{4 bits [32]. For that study, the EMG signals were converted to root mean square
and smoothed with a moving average of 50 ms. Our results with the linear-ltered EMG
14
are similar to the results presented in both of these studies and with Bayesian-ltered EMG,
the IP is even better. Further advancement is still required for myocontrol to equal motor
control in IP, but transitioning to Bayesian-ltered EMG may help in this endeavor.
We examined the average behavior of the EMG and cursor under each lter to see if
the control strategies of subjects changed between lters. Figure 2.3 shows that use of the
Bayesian lter had a strong impact on the overall strategies of the group. This might be
due to the fact that the delay between EMG onset and cursor movement for the linear lter
was greater than the delay for the Bayesian lter. Since the linear lter was more dicult
to control than the Bayesian lter, the tendency to undershoot before entering the target
may indicate caution. In the linear case, subjects tended to attempt to capture the target
range more cautiously, leading them to contract more slowly and carefully. The predictable
responsiveness of the Bayesian lter allowed subjects to adopt a more aggressive control
strategy: overshoot to increase rate of cursor rise, then settle in the correct range to stop the
cursor in the target. This overshoot has the potential for causing quicker fatigue in muscles,
but it is likely a compensation for the delay between EMG activation and cursor response.
Bayesian ltering of EMG has exciting potential for research and device-design applica-
tions, but is hardly the only attempt to sidestep or compensate for the known issues in using
linear ltering in myocontrol. Other groups have developed methodologies that include using
hidden Markov models [15, 14], wavelet processing [27], Gaussian mixture models [40],
switching regime models [2], cascaded kernel learning [49], and neural network estima-
tors [45]. However, these methodologies are generally focused on classifying patterns from
multiple EMG signals to estimate intended movement. The Bayesian lter estimates the
continuous underlying signal of EMG. Bayesian ltering of EMG provides a clean signal
from a single sensor that is simple to control and has the advantage of simple,
exible im-
plementations. Its use may simplify the use of EMG in future research, clinical diagnostics,
and device design.
Future work is needed to algorithmically determine optimal parameters for the Bayesian
lter. Currently, the jump and drift rate parameters for the lter are chosen empirically,
based on the intended purpose of the ltered data. For example, smooth control of a steering
wheel would use a very low or even zero jump rate whereas rapid response in a reaction-
time or triggering task would use a higher jump rate that would have lower latency. These
parameters are determined more by the task than by the user, and in our experience they
are relatively user-independent since the EMG signal is similar between subjects. The only
parameter that is strongly subject dependent is the amplication, and this depends on the
choice of muscle, thickness of overlying soft tissue, and the muscle size and activation pattern.
The value of the jump parameter is the Poisson rate of jumps, which can be interpreted as
15
the probability of a jump in each sampling time. The value of the drift parameter is the
rate of increase of variance per sample time, if the underlying signal could be considered as a
random walk. The square root of this value can be interpreted as the maximum permissible
rate of change per sample time (in the absence of jumps). In practice, the precise values
of these parameters do not aect the lter behavior, and it is only necessary to optimize to
within one to two orders of magnitude. Further work is also suggested towards examining
use of Bayesian-ltered EMG in multiple degree-of-freedom tasks as well as with tangible
actuators, such as a robotic arm.
16
2.3 Experiment 2: Eect of Target Distance on
Controllability for Myocontrol
A version of the following section was submitted to International Journal of Human-Computer
Studies.
2.3.1 Abstract
Myocontrol holds great promise because it has the potential to provide
exible and accurate
prosthetic control that approaches the quality of normal movement. Speed and accuracy
are important factors to consider when applying myoelectric signals to external devices.
Fitts' Law can be used to assess the speed-accuracy trade-o. We hypothesized that speed
is aected not only by accuracy as prescribed by Fitts' Law, but also by target distances
independent of target size. A total of 12 healthy adult subjects were studied. Subjects
controlled the vertical movement of a computer cursor by contracting their dominant rst
dorsal interosseus to reach targets as quickly as possible. Targets varied in width and distance
from the start position. We compared the movement time to the time predicted by Fitts'
Law. Results showed good agreement for all conditions, with the exception of a signicantly
longer movement time than predicted for targets close to the start point. Movements to these
targets showed signicantly higher relative variance during stabilization, higher overshoot,
and lower success. Therefore, we conclude that small distance movements have a higher
variability, slower velocity, and higher rates of error compared to larger distance movements.
Our results are consistent with the hypothesis that low distances require recruitment of
smaller motor units, resulting in higher variability, and diculty in reaching the target as
required by the task demand. These results have signicance for myocontrol applications,
and we suggest that such applications require control signals with sucient recruitment to
reduce variability at low forces.
2.3.2 Introduction
Myocontrol, the control of external devices using electromyographic (EMG) signals, holds
great promise because it has the potential to provide
exible and accurate control that
approaches the quality of normal movement. Myoelectrically controlled limb prosthetics have
long been in development and have become an established technology [16]. More recently,
the use of myocontrol has extended beyond control of limb prosthetics. Myoelectric signals
can also be used for biofeedback [9, 87, 90, 89, 88] and functional electrical stimulation [75]
for rehabilitation, as well as the control of other external devices such as exoskeletons [1] and
17
speech synthesizers [64]. Due to the increasing prevalence of myocontrol, there is a need to
understand its boundaries of controllability and how to optimize parameters to provide the
best possible control.
There still exist many challenges to using EMG signals for control. The most straightfor-
ward approach to estimate motor intent is by estimating the intensity of the EMG signal.
The clarity of the signal itself can be in
uenced by electrode placement, how the signal is
ltered, and the range of EMG activation. The signal is generally normalized to address
potential dierences in electrode placement [79]. While it is common for the EMG signal
to be linearly ltered to remove noise, it has been shown that a non-linear Bayesian lter
can better estimate rapid changes in the signal [72]. It has also been shown that Bayesian
ltered EMG provides more accurate simultaneous and proportional myocontrol [37].
How EMG activation levels impact the controllability of myocontrol has not been thor-
oughly investigated. While the upper threshold for myocontrol activation is primarily dic-
tated by fatigue, the lower threshold of activation has not been explored.
Speed and accuracy are important factors to consider when applying myoelectric signals
to external devices. Speed is necessary to ensure stability of the system, and better speed
will provide patients a more natural and intuitive interface so that the external device more
closely resembles an extension of their own limb. Accuracy is necessary for users to meet task
demands, but there is a trade-o between speed and accuracy. Fitts' Law is a mathematical
formulation to assess the speed-accuracy trade-o in human-computer interfaces [54]. It is
a model that describes the way that the movement time in targeted ballistic reaching tasks
changes with the distance and width of targets [33]. Every motor control task inherently
has a trade-o between speed and accuracy, but this trade-o does not necessarily have to
follow Fitts' Law. If the model can be t, the Index of Performance (regression of movement
time on index of diculty) from the Fitts' Law model can be interpreted as the bandwidth
of the motor control system for a given task.
Fitts' Law has been used extensively in the eld of human-computer interfaces (HCI) as
a tool to characterize the bandwidth of interfaces, such as mice or trackpads. It may also be
used in myocontrol interfaces. It has been shown that when subjects are asked to stabilize
their myoelectric signals in a target, these signals behave in a manner compatible with the
predictions of Fitts' law [32]. Park et. al. used Fitts' Law to validate the suitability of
EMG compared to force as a control source [65]. Williams and Kirsch used Fitts' Law to
evaluate head orientation and neck muscle EMG signals as control signals for patients with
tetraplegia [87]. Similarly, Choi et. al. quantied the throughput for individuals with spinal
cord injury when using myocontrol to move and click a cursor [17].
These previous studies have not investigated how distance aects performance, indepen-
18
dent of accuracy. Fitts' law predicts that movement time is determined only by the relative
accuracy, the accuracy divided by the distance, and that it does not depend on absolute
distance. Myocontrol is increasingly being used for patient populations that may be aected
by muscle weakness. The aim of this study was to quantitatively assess how the range of
target distances aects controllability in myocontrol. We hypothesized that movement time
is aected not only by Fitts' Law eects due to the size of the target relative to the distance,
but also by the target distance itself.
2.3.3 Methods
Subjects
12 healthy subjects (mean 26 4 years; 7 females) participated in this study. The University
of Southern California Institutional Review Board approved all experimental procedures
(UP{10{00027). Subjects gave written informed consent. The experiment was performed in
accordance with the Declaration of Helsinki and written authorization for use of protected
health information was obtained and stored according to the Health Information Portability
and Accountability Act.
Apparatus
Participants sat on a chair and placed their dominant hand
at on the surface of a table
with the palm down in a comfortable position. The index nger of the dominant hand was
constrained to prevent abduction using a plastic block that adhered to the surface of the
table. A surface EMG electrode (DE-2.3, Delsys Inc., MA, USA) with a band-pass lter of
20-450 Hz and an amplication of 1000 times was placed over the belly of the rst dorsal
interosseous (FDI). The EMG electrode signal was sampled at 1 kHz with an analog to digital
interface (Power 1401, CED Technologies Inc., UK) and custom data acquisition software.
The isometric muscle activation signal for the experimental task was obtained by ltering
the EMG signal from the electrode through three steps used by Young et. al [89]. The signal
was processed with a high-pass Butterworth lter (4th-order, 1Hz cuto), then a Bayesian
lter, and nally a low-pass Butterworth lter (2nd-order, 5 Hz cuto) to reduce jitter in
the output signal. The Bayesian lter produces a smooth output that estimates the drive
underlying the EMG signal, while also allowing fast low-latency changes in the ltered signal
[72]. It is possible that the low-pass lter following the Bayesian ltered signal could add
some delay in myocontrol, however, pilot data on three subjects using the Bayesian lter
alone showed similar results to that presented in this paper.
19
Target
Cursor
Figure 2.4: EMG from the FDI controlled the vertical position of a cursor. Subjects moved
the cursor from rest into a target as fast and accurately as possible using isometric
contractions from the FDI.
Prior to the start of the experiment, the isometric maximal voluntary contraction (MVC)
was measured from the FDI using the following procedure. The EMG signal was displayed
as visual feedback for the participant via a horizontal bar target whose height on the screen
represented the amplitude of the signal. The participant performed three attempts of ve
seconds of maximum contraction for each muscle with encouragement and feedback. MVC
was quantied by the data acquisition software as the maximum mean EMG activation
measured over a 200 ms period. Following this measurement, all muscle activation levels for
the experiment were expressed as normalized EMG, dened as the ratio of the EMG value
of the muscle to its MVC.
Procedure
Each participant attended a single experimental session of approximately 1-hour duration.
The session started with seating at the table, placement of the EMG electrode, and measure-
ment of MVC. The participant then completed a series of trials during which they reached
a target on a computer screen by activating their FDI.
During each trial, the EMG from the FDI controlled the vertical position of a cursor on
a display visible to the subject (Fig. 2.4). Vertical cursor position was proportional to the
EMG such that 0% MVC was the bottom of the screen and 50% MVC was the top of the
screen. The cursor remained at the top of the screen for EMG values greater than 50%
MVC and thus, feedback was eectively capped at 50% MVC. Prior to experimental trials,
subjects were given two practice trials to practice moving the cursor on the screen and to
ensure proper FDI activation.
Subjects were instructed to move the cursor from rest position into targets of dierent
sizes as fast and accurately as possible. Prior to each target, subjects were asked to relax
20
and keep the cursor at the bottom of the screen. As soon as the target appeared, subjects
were instructed to reach the target as quickly as possible and maintain the position for 500
ms. The demand for subjects to stabilize in the target ensured that they maintained some
control over the cursor, rather than inadvertently hitting the target. Attempts where this
500 ms hold time was not accomplished within three seconds were considered unsuccessful.
Three seconds was determined to be ample time for subjects to attempt to reach the targets
quickly and accurately. Subjects had a three second rest period between targets to prevent
fatigue. Subjects completed 10 trials, reaching for 25 targets per trial. Targets had varying
Fitts' indices of diculty (ID), measured in bits and calculated as
ID =log
2
2D
W
(2.5)
where D is the distance of the center of the target from the bottom of the screen, and W
is the width of the target [33]. The 25 targets were divided into 5 width conditions (1.5,
2.5, 3.5, 4.5, 5.5% MVC) with 5 IDs (1.38, 2.18, 2.83, 3.47, 4.06). These IDs were chosen to
provide a large, yet feasible, range of targets. Distances were calculated to keep IDs constant
across width conditions, resulting in target distances ranging from 2.0 to 45.8% MVC. Thus,
each width condition corresponded to a dierent range of distances with the same levels of
diculty. Figure 2.5 shows example raw and ltered EMG signals from one subject for ID
= 1.38 at the smallest and largest width conditions.
Analysis
Data analysis was executed with Matlab R2013a (Mathworks, Natick, MA). Statistical anal-
ysis was performed using RStudio, version 0.98.1056 (RStudio Inc., Boston, MA), and the
R-package lme4, version 1.1{7.
Cursor Analysis With Fitts' Law, only successful trials are used to regress movement time
with ID [33]. In order to correlate other outcome measures with observations from the
movement time regression, only successfCursor ul trials were used for analysis. The start of
the cursor movement was dened as the time when the cursor velocity was at least 5% of
the peak velocity observed during the trial, similar to previous studies [7, 8]. The end of the
movement was at the end of the 500 ms hold inside the target. Movement time (MT) was
dened as the time from the movement start to movement nish.
Cursor velocity and acceleration were derived from the cursor position. From the cursor
velocity, the reaching phase of the movement was determined. Reaching phase was dened
as the time from movement start to when the velocity rst crosses zero. The position at the
21
Figure 2.5: Raw and ltered EMG signals from a subject for ID = 1.38 at width = 1.5 and
5.5. Shaded area represents the target region for each width condition.
22
velocity zero-crossing was used to calculate the overshoot or undershoot of the cursor as
overshoot/undershoot =
x nearest target boundary
A
(2.6)
where x is the cursor position.
Acceleration time was dened as the time from movement start to the time of peak velocity
observed prior to the 500 ms hold.
Standard deviation (STD) and coecient of variation (CV) were also calculated for each
trial. STD of the cursor position was calculated from the end of the reaching phase to the
beginning of the hold, which was dened as the stabilization phase. CV was calculated as
the ratio between STD of the cursor position and the mean of the cursor position during the
stabilization phase.
Statistical Analysis Since the design of our experiment had repeated measures, we used
linear mixed eects analysis to express the relationships in our data instead of linear regres-
sion analysis, which requires measurements to be independent. We examined the following
outcome measures: movement time, success, overshoot/undershoot, acceleration time, STD
and CV.
To determine xed eects signicance on each outcome measure, the linear mixed eects
analysis comprised ID (5 levels) and Width (5 levels) as xed eects, and intercepts for each
subject as a random eect. Regressing on ID showed how outcome measures were aected
by Fitts' Law eects due to the size of the target relative to the distance. Regressing on
Width showed how outcome measures were aected by varying distance when width was
constant. The R model was given by
DependentvariableWidth +ID + (1jSubject) (2.7)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interaction between
the two xed eects (ID and Width), we compared the model that takes into account the
interaction between xed eects (Full) against the model without the interaction (Null).
For all comparisons, p-values and Akaike's information criterion values (AIC) were obtained
by likelihood ratio tests of the Full model with the Null model. If the factor in question
signicantly aects the dependent variable, then the comparison will report a signicant p-
value (< 0.05) and an AIC value lower for the Full model. Similarly, a signicant interaction
between factors will result in a signicant dierence between the Full and the Null models (p
23
Table 2.1: Movement Time Likelihood Ratio Results
Factor AIC
Full
AIC
Null
p-value
ID 4131.3 5289.3 <0.0001
Width 4131.3 4377.3 <0.0001
ID*Width 4087.3 4131.3 <0.0001
< 0.05) with a lower AIC for the Full model. Pairwise t-test with Bonferroni adjustment was
used for post-hoc analysis to identify at which IDs there was a signicant dierence across
width conditions.
2.3.4 Results
Movement Time
Results from the likelihood ratio test on MT are shown in Table 2.1. The likelihood ra-
tio test showed that ID had a signicant eect on MT, meaning that the task eectively
imposed a speed-accuracy trade-o. On average, MT increased with ID by 0.27 0.01
seconds/bit. Target width also had a signicant eect on MT, with MT decreasing with
width by 0.079 0.005 seconds/%MVC. The likelihood ratio test showed that the interac-
tion between target width and ID had a signicant eect on the movement time, meaning
the eect of ID on MT was dierent for the dierent width conditions. Fig. 2.6 showed
at higher width conditions, movement time followed a Fitts' behavior, increasing linearly
with ID with similar slope. However, for W = 1.5, movement time increased at the lower
IDs corresponding to lower target distances. Indeed, the increased movement time at lower
IDs deviates from our predictions based on Fitts' Law. Movement time for W = 1.5 was
signicantly longer than the time for all other targets widths at ID = 1.38 (p < 0.0001) and
ID = 2.18 (p< 0.005). It was longer than the time for the three largest widths at ID = 2.83
(p < 0.01) and ID = 3.47 (p < 0.02). Movement time for W = 2.5 was signicantly longer
than the time for W = 5.5 at ID = 1.38 (p < 0.001) and ID = 3.47 (p = 0.04). At the
highest ID, there was no signicant dierence between width conditions for movement time.
Success
Results from the likelihood ratio test on success are shown in Table 2.2. The likelihood ratio
test showed that ID had a signicant eect on success. On average, success decreased with
ID by 0.087 0.009 per bit. Target width also had a signicant eect on success, with
success increasing with width by 0.064 0.006 per %MVC. The likelihood ratio test showed
24
0.75
1.00
1.25
1.50
1.75
1.38 2.18 2.83 3.47 4.06
Index of Difficulty (bit)
Movement Time (s)
Target Width
1.5
2.5
3.5
4.5
5.5
Figure 2.6: MT of successful trials across IDs and width conditions. There is a signicant
increase in MT at the lower IDs for the smallest target width condition.
25
Table 2.2: Success Likelihood Ratio Results
Factor AIC
Full
AIC
Null
p-value
ID -288.10 -203.16 <0.0001
Width -288.10 -189.75 <0.0001
ID*Width -294.49 -288.10 0.004
0.00
0.25
0.50
0.75
1.00
1.38 2.18 2.83 3.47 4.06
Index of Difficulty (bit)
Success
Target Width
1.5
2.5
3.5
4.5
5.5
Figure 2.7: Proportion of successful trials across ID and width condition. There was lower
success for the smallest width condition.
that the interaction between target width and ID had a signicant eect on success, meaning
the eect of ID on success was dierent for the dierent width conditions. Post-hoc analysis
showed that success for W = 1.5 was signicantly lower than the highest three widths at
ID = 2.18 (p< 0.01) and 2.83 (p< 0.01). Success for W = 1.5 was lower for all other widths
at ID = 3.47 (p < 0.0001) and 4.06 (p < 0.0001) (Fig. 2.7).
Overshoot/Undershoot
Results from the likelihood ratio test on success are shown in Table 2.3. The likelihood
ratio test showed that ID had a signicant eect on overshoot or undershoot. On average,
overshoot or undershoot decreased with ID by -0.039 0.003 per bit. Target width also had
26
Table 2.3: Overshoot/Undershoot Likelihood Ratio Results
Factor AIC
Full
AIC
Null
p-value
ID -3002.5 -2824.0 <0.0001
Width -3002.5 -2984.2 <0.0001
ID*Width -3096.1 -3002.5 <0.0001
-0.1
0.0
0.1
0.2
1.38 2.18 2.83 3.47 4.06
Index of Difficulty (bit)
Overshoot/Undershoot
Target Width
1.5
2.5
3.5
4.5
5.5
Figure 2.8: Overshoot (>0) or undershoot (<0) across IDs and width conditions. At low
IDs, there was more overshoot for the smaller width targets.
a signicant eect on overshoot or undershoot, decreasing with width by 0.0087 0.0019
per %MVC. The likelihood ratio test showed that the interaction between target width and
ID had a signicant eect on the overshoot or undershoot, meaning the eect of ID on
overshoot or undershoot was dierent for the dierent width conditions. At ID = 1.38,
subjects had a signicant overshoot for W = 1.5 compared to W = 4.5 (p < 0.0001) and
W = 5.5 (p < 0.0001). Subjects also had signicant overshoot for W = 2.5 compared to
W = 4.5 (p < 0.001) and W = 5.5 (p < 0.001). There was also a signicant dierence
between W = 3.5 and W = 4.5 (p = 0.003). At ID = 2.18, subjects had more overshoot for
W = 1.5 compared to all other widths (p < 0.01) (Fig. 2.8).
27
Table 2.4: Acceleration Time Likelihood Ratio Results
Factor AIC
Full
AIC
Null
p-value
ID -3135.9 -3003.7 <0.0001
Width -3135.9 -3127.9 0.002
ID*Width -3218.4 -3135.9 <0.0001
Acceleration Time
Results from the likelihood ratio test on success are shown in Table 2.4. The likelihood ratio
test showed that ID had a signicant eect on acceleration time. On average, acceleration
time increased with ID by 0.033 0.003 seconds/bit. Target width also had a signicant
eect on acceleration time, increasing with width by 0.0060 0.0019 seconds/%MVC. The
likelihood ratio test showed that the interaction between target width and ID had a signicant
eect on the acceleration time, meaning the eect of ID on acceleration time was dierent
for the dierent width conditions. At ID = 1.38, the acceleration time for W = 1.5 was
signicantly greater than the time for all other width conditions (p < 0.001). At ID = 4.06,
the acceleration time for W = 1.5 was signicantly shorter than the time for W = 3.5 (p
= 0.004) and W = 5.5 (p < 0.0001). It was also signicantly shorter for W = 2.5 than for
W = 5.5 (Fig. 2.9).
Standard Deviation and Coecient of Variation
Results from the likelihood ratio test on success are shown in Table 2.5. The likelihood ratio
test showed that ID had a signicant eect on STD . On average, STD increased with ID by
0.0025 0.0001 per bit. Target width also had a signicant eect on STD, decreasing with
width by 0.00043 0.00008 per %MVC. There was signicant interaction between target
width and ID on STD (Fig. 2.10).
Results from the likelihood ratio test on success are shown in Table 2.6. The likelihood
ratio test showed that ID had a signicant eect on CV. On average, CV decreased with ID
by 0.018 0.001 per bit. Target width also had a signicant eect on CV, decreasing with
width by 0.026 0.001 per %MVC. There was signicant interaction between target width
and ID on CV (Fig. 2.11).
28
0.10
0.15
0.20
0.25
0.30
1.38 2.18 2.83 3.47 4.06
Index of Difficulty (bit)
Acceleration Time (s)
Target Width
1.5
2.5
3.5
4.5
5.5
Figure 2.9: Acceleration time across IDs and width conditions. At low IDs, the acceleration
time was signicantly longer for W=1.5 than for the rest of the width conditions.
29
0.000
0.005
0.010
0.015
1.38 2.18 2.83 3.47 4.06
Index of Difficulty (bit)
Standard Deviation
Target Width
1.5
2.5
3.5
4.5
5.5
Figure 2.10: STD of the cursor position during the stabilization phase across IDs and width
conditions. There is increasing signal-dependent noise in all width conditions,
but the increase is greater in the larger width targets.
30
0.0
0.1
0.2
0.3
1.38 2.18 2.83 3.47 4.06
Index of Difficulty (bit)
Coefficient of Variation
Target Width
1.5
2.5
3.5
4.5
5.5
Figure 2.11: CV of cursor position during the stabilization phase across IDs and width condi-
tions. There is a larger decrease in coecient of variation for the smaller width
targets.
31
Table 2.5: STD Likelihood Ratio Results
Factor AIC
Full
AIC
Null
p-value
ID -26890 -26501 <0.0001
Width -26890 -26864 <0.0001
ID*Width -26900 -3135.9 <0.001
Table 2.6: CV Likelihood Ratio Results
Factor AIC
Full
AIC
Null
p-value
ID -8494.4 -8334.1 <0.0001
Width -8494.4 -7769.8 <0.0001
ID*Width -8682.2 -8494.4 <0.0001
2.3.5 Discussion: Small-Distance Targets Can Decrease Online
Performance
The purpose of this study was to investigate how target distance aects the controllability in
myocontrol using Bayesian-ltered EMG. To the authors' knowledge, this is the rst study
to observe how the speed-accuracy tradeo in myocontrol changes as a result of varying
ranges of target distances. Subjects had less success reaching targets of the lowest range
of distances. Additionally, low distance targets resulted in longer movement time, more
overshoot, and longer acceleration time at the low ID. These results suggest that movement
time is aected not only by Fitts' Law eects, but also by target distances. Small distances
paired with high accuracy demand actually increased the diculty for subjects to reach the
target. The longer acceleration time may indicate some pre-planning of the movement in
anticipation of the target's perceived diculty. The overshoot suggests that subjects are
unable to initially reach the target at such a small distance.
According to Fitts' Law, movement time should be a linear function of ID. However,
certain width conditions at smaller IDs exhibited a disproportionate increase in movement
time, thus deviating from Fitts' Law. Sheridan noted previously that a reduction in target
width resulted in a higher increase in movement time compared to a similar increase in
distance in Fitts' Law [76]. In an experiment in which subjects tapped between two targets
with a pen, it was shown that distance and accuracy of the targets do not contribute equally
to the increase in movement time [86]. A study in rapid wrist rotations also observed
signicant eects of target width within ID levels [57]. These previous studies suggest that
the observed increase in movement time at small width conditions at lower IDs is a biological
32
property that is not predicted by Fitts' Law, and not unique to myocontrol.
This is not the only study that has observed a deviation from Fitts' Law. Studies involving
whole body or larger limb movements have observed scaling eects for dierent distances
within the same IDs [7, 20, 25, 26, 34]. A reaching study involving postural adjustments
found similar slope regressions for short and long distances, but a shift in intercept for
the long distance targets as a result of the required trunk rotation to reach the farther
targets[8]. When displacing heavy objects, a cubic function better t the data rather than
a linear function, as mass-density are not considered in Fitts' law [13].
With regard to myocontrol, the task demand for subjects to hit low distance, high accuracy
targets as quickly and accurately as possible may actually contradict what they are capable of
accomplishing physiologically. It is possible that at very low distances, subjects are primarily
recruiting smaller motor units. Milner-Brown et. al. found that motor units in the FDI are
recruited in accordance to the size of contraction they produce as subjects maintained a force
at the threshold for steady motor unit recruitment, thus following Henneman's size principle
[61]. In another study, Milner-Brown et. al. had subjects perform a force tracking task with
the FDI. At low force levels, they found that recruitment of additional motor units is the
major mechanism for increasing the force of voluntary contraction [60].
The decreased number of motor unit recruitment also describes the observed increase in
CV at lower IDs, which is consistent with literature that observed increased CV at lower
force levels[35, 28, 46, 63, 83, 42, 23]. Thus, signal-dependent noise is not proportional
to force levels below a certain threshold for the FDI. This has been observed in previous
work on the FDI. In a study looking at eects of age on motor output from the FDI, SD
increased with target force level, while CV decreased with relative target level for both young
and elderly subjects [35, 28]. Laidlaw et. al. found similar results in a study comparing
steadiness of the FDI in young and elderly subjects [46]. Simulations of force produced by
a pool of motor units with characteristics resembling those of the FDI suggest that higher
variability at low forces may result from increased discharge rate variability, as it decreases
exponentially with increasing force in the FDI [63]. It may also be due to synchronization
and low-frequency common oscillation of motor units [83]. Results of another motor-unit
pool model suggest that the orderly recruitment of motor neurons contributes to linearly
increasing signal dependent noise and a higher CV at lower forces [42]. This behavior may
not be limited to the FDI. Simulations of strong and weak muscles suggest that both have
a higher CV in the bottom 5% of the force range as a result of the number of motor units
being recruited [23].
It is also possible that the behavior observed at small distances is a result of the lter.
There are fewer spikes at lower distances, which results in a noisier output in the nonlinear
33
lter, making it dicult to stabilize in the targets with small width. It is possible that the
output could be smoothed with a dierent lter or by changing the lter parameters. More
studies would be required to verify this.
There are some limitations to this study. In order to truly explain what might be happen-
ing at the motoneuron level, intramuscular EMG would be more informative, as EMG may
not be the best indicator to explain what is happening [31, 30]. Force was not measured,
however, literature suggests that isometric EMG is a good estimate of force [59]. The focus
of this study was also on what subjects were able to accomplish with myoelectric signals, so
force measurements were unnecessary to the goal of our study.
Despite the limitations of our study, our results clearly show that there exists a minimal
threshold for fast and accurate myoelectric control. This is important to know when imple-
menting myocontrol clinically. Naturally, myocontrol applications want to use low levels of
muscle activation to avoid fatigue and reduce signal-dependent-noise. However, there exists
a lower threshold that may either be due to physiological limitations or ltering limitations.
Thus, there is a need to pay attention to the levels of muscle activation to optimize control-
lability. For some pathological situations, myocontrol may be used as a rehabilitative tool
[90]. In this case, patients should use their optimal range to receive appropriate feedback on
their muscle activations. For myocontrolled devices, users should be calibrated to operate
the device within an activation range that allows them the highest bandwidth possible for
fast and accurate control. In general, controllability of myocontrolled devices should be facil-
itated as much as possible. Thus, myocontrol applications should require control signals with
sucient recruitment to reduce the variability at low forces, but not such high recruitment
that subjects become fatigued. Future work may focus on modifying other lter properties
such as delay, gain, or frequency components to further improve myocontrol controllability.
2.4 Chapter Conclusions
The studies detailed in this chapter helped inform us on experimental design for the subse-
quent studies laid out in this paper. Based on Experiment 1, we chose to use a Bayesian
lter on the surface EMG signals used for myocontrol. Based on Experiment 2, we selected
targets with at least 5% MVC in amplitude, so as not to make myocontrol tasks unnecessarily
dicult for subjects.
34
3 Interface to Task Space: Using EMG
for Biofeedback and Multi-Muscle
Myocontrol
3.1 Chapter Introduction
In the previous chapter, we looked at how we could facilitate myocontrol on a single-channel
level. In this chapter, we explored dierent ways to interface to a multi-dimensional task
space. For children with CP, we saw two primary ways to map EMG to a task. One option
was to select the best possible muscles or group of muscles for control. Another option
was to try to estimate their intended movements. The rst experiment in this chapter
overviews our work exploring the rst option, in which we used Fitts' Law to identify the
most controllable muscles or synergies to control a cursor in a 2-D task. The subsequent
experiments overview our work exploring estimation of intended movement. Since we cannot
know the true movement intent of a subject, we must infer their true intent. In Experiments
2 and 3, we do this by correlating EMG with a rewarded force that is determined given the
target direction that a subject is trying to reach. There also exists multiple ways to correlate
EMG with rewarded force. In Experiment 2, we detail the use of linear estimation to do
so. In Experiment 3, we detail the use of a non-linear method to estimate rewarded force.
Experiments 2 and 3 can be considered supervised methods, as they also require the use of a
torque sensor to inform us of a subject's intended movement. However, it is also possible to
use a semi-supervised method, in which we infer the direction in which a subject is trying to
move without the use of a torque sensor. Experiment 4 details the use of a semi-supervised
method to control a robotic arm in 3D.
In general, we attempt to estimate user intent in all of these experiments while requiring
minimal learning from the user. In other words, the myocontrol system is as transparent
and congruent as possible with user expectations. Imagery of the cursor movement provides
the user biofeedback so that they have some knowledge of their movements. However, in
Experiments 2 and 3, we also explore the use of myocontrol as a tool for users to learn.
35
By changing myocontrol parameters, we explore how users adjust their EMG behavior in
response to changes made to the system.
36
3.2 Experiment 1: Separating Involuntary from Voluntary
Components Using Spatial Filtering
A version of the following section was prepared for submission to Journal of Child Neurology.
3.2.1 Abstract
The design of myocontrolled devices faces particular challenges in children with dyskinetic
cerebral palsy (CP) because the electromyographic (EMG) signal for control contains both
voluntary and involuntary components. We hypothesized that voluntary and involuntary
components of movements would be uncorrelated and thus detectable as dierent synergistic
patterns of muscle activity, and that removal of the involuntary components would improve
online EMG-based control. Therefore, we performed a synergy-based decomposition of EMG-
guided movements, and evaluated which components were most controllable using a Fitts'
Law task. Similarly, we also tested which muscles were most controllable. We then tested
whether removing the uncontrollable components or muscles improved overall function in
terms of movement time, success rate, and throughput. We found that removal of less
controllable components or muscles did not improve EMG control performance, suggesting
that controllable and involuntary components of movements are correlated in CP and cannot
be spatially separated.
3.2.2 Introduction
Children with tetraplegic or dyskinetic cerebral palsy (CP) suer from movement disorders
such as muscle weakness, spasticity, dystonia, and dyspraxia that can prevent meaningful
voluntary movement [70]. As a result, these children have a very limited ability to do things
that typically developing children do, including playing, interacting spontaneously, explor-
ing, and learning from mistakes. For such children, assistive devices may provide mobility,
and in more extreme cases, functional communication. However, careful consideration must
be placed into the interface of such devices. Children may be able to use low-bandwidth
interfaces such as a head switch, force-control joystick, or button interface, however, their
output from these devices is often slow and limited by their own movements. In a previous
study, we found that children with CP who depend on a touch-screen interface to communi-
cate generate an average of only 50 words per week [68]. In essence, children can no better
control such devices than they can their own body because the interface captures the volun-
tary and involuntary components of their movement. Therefore, if we are to provide assistive
devices for this group of children, we must address the problem of optimal extraction of vol-
37
untary controllable signals from involuntary, unwanted muscle activity. Ultimately, we want
to provide assistive devices that will allow these children to explore and manipulate their
environment in ways that typically developing children do. Children need
exible real-world
interfaces whose motions are not described in advance, so that they can learn and develop
their own movements, and explore varying and unpredictable goals.
The major barrier for children with CP is not the design of the device to be controlled,
but the interface that the child uses to control the device. Myocontrol, the control of devices
using electromyographic (EMG) signals, may be used to allow children with CP to control
assistive devices in a
exible manner. Myoelectric signals have been used for biofeedback [9,
87, 90, 89, 88] and functional electrical stimulation [75] for rehabilitation, as well as the
control of other external devices such as exoskeletons [1] and speech synthesizers [64]. In
CP, there is no disconnect between the brain and the spinal cord as there is in spinal cord
injury, so the EMG signal provides a direct read-out of the movement-related activity in
the motor cortex. Myocontrol is preferable to brain-computer interfaces, which are either
invasive (requiring implantation in the brain) or low bandwidth (when using scalp electrodes).
It does not restrict where the child can look, as eye gaze control would. It also allows for
smooth and
exible control, as opposed to button or on/o interfaces. The challenge with
myocontrol for children with CP is separating out the voluntary component of the signal
from the involuntary component in order to control a device.
A previous study hypothesized that abnormal movements in dyskinetic CP may be due
to an inability to suppress unwanted components of movement [71]. Studies of reaching and
other upper extremity movements in children with CP have found increased variability in
their movements, substantiating this hypothesis [74, 71, 50, 53]. However, the origin of the
variability is still unknown. The noise might re
ect unrelated neural activity. It could also be
the result of a \noise generator" injecting a new source of noise. The ability to characterize
the noise in dyskinetic CP could provide insight into the nature of the movement abnormality
and inform the development of future treatments.
We hypothesized that voluntary and involuntary components of movements would be un-
correlated, and thus detectable as dierent synergistic patterns of muscle activity. Bernstein
proposed that the control of multiple muscles could be simplied by selecting a small set of
patterns, or synergies, to reduce the high dimensionality of the set of possible actions [6].
It has since been shown that kinematics and EMG patterns in humans occupy low dimen-
sional spaces for specic tasks [69, 22, 21, 84]. Synergies likely play a role in aiding typically
developing subjects to learn and accomplish new skills [44]. However, synergies in children
with CP are likely to be distorted by co-contraction [89, 90], signal-dependent noise [74],
and weakness. Thus, selecting the most controllable synergies is particularly important and
38
could provide a method for separating controllable from uncontrollable components of move-
ment for children with CP. Our hypothesis is based on two assumptions: (1) noise in CP is
low-dimensional and (2) the dimension of noise can be identied and isolated by nonnega-
tive matrix factorization (NMF). These assumptions are based on previous work that used
NMF to reduce noise in speech enhancement [62] and imaging mass spectrometry data [77].
By observing how myocontrol performance changes using a reduced EMG representation,
we could potentially learn how noise exhibits itself in CP. If the noise falls primarily on
one component and that component is removed, myocontrol performance should improve.
However, if noise is inherent in all neuronal channels, components would contain a mix of
controllable and noisy signals. Thus, removing a component would not improve myocontrol
performance.
For this study, we performed a synergy-based decomposition on eight muscles of the up-
per limb. We used a one-dimensional Fitts' Law task to determine which components were
most controllable. Similarly, we determined the most controllable muscles. We then com-
pared whether removing the least controllable components or muscles improved myocontrol
performance in a two-dimensional task.
3.2.3 Methods
Inclusion criteria for this study were: (I) CP or dystonia aecting at least one upper extrem-
ity; (II) pediatric age (7{21 years); (III) no cognitive impairment that prevents understanding
of instructions. Five children with cerebral palsy (4 males, 1 female; ages 11 to 18 years,
mean 15 3 years) performed this protocol 3.1. The University of Southern California
Institutional Review Board approved the study protocol. All parents gave informed written
consent for participation and all children gave written assent. Authorization for use of pro-
tected health information was signed in accordance with the Health Information Portability
and Accountability Act. The study was performed in accordance with the Declaration of
Helsinki.
Experimental Setup
Subjects sat in front of a desktop with their more aected forearm inserted in a splint, im-
mobilizing hand, wrist, and forearm. The center of the palm was aligned with the body
midline at the height of the sternum and the elbow was
exed by approximately 90
. A
steel bar at the base of the splint was attached to a 6-axis force transducer (Delta F/T
Sensor, ATI Industrial Automation, Apex, NC, USA) positioned below the table to record
isometric forces and torques. Surface electromyographic (EMG) activity was recorded from
39
Table 3.1: Clinical Characteristics of Subjects with Dyskinetic Cerebral Palsy
BAD Scale Score
ID Sex Age L Arm R Arm Arm Tested Diagnosis Symptoms
1 M 14 1 2 R Cerebral palsy, 7 weeks prema-
ture
Right>leftarmdystoniaandbi-
lateral leg spasticity
2 M 18 1 0 L Cerebral palsy Left arm dystonia
3 F 16 2 3 R Hypoxic ischemic injury Generalized dystonia;
Right > left arm dystonia
4 M 14 3 0 L Hypoxic ischemic injury, sec-
ondary to stroke at birth
Left arm dystonia
5 M 11 3 3 L Hypoxic ischemic injury Generalized dystonia
Abbreviations: BAD Scale, Barry-Albright Dystonia Scale; F, female; L Arm, severity of left arm; M, male; R Arm, severity
of right arm. Scores are based on the BAD Scale[3]; for each segment, the score ranges from 0 - absence of dystonia to 4 -
severe dystonia.
the following eight muscles: pectoralis major, brachioradialis, biceps, triceps, anterior del-
toid, lateral deltoid, posterior deltoid, middle trapezius. EMG activity was recorded with
bipolar electrodes (DE{2.1, Delsys Inc., Boston, MA, USA), band-pass ltered (20{450 Hz)
and amplied (gain 1000, Bagnoli{8, Delsys Inc.). Force and EMG data were sampled at
1 KHz using an analog-to-digital interface (Power 1401, CED Technologies Inc., UK) and
a custom data acquisition software. EMG was ltered with a 1 Hz, 4th order Butterworth
high-pass lter to remove baseline DC voltage, and subsequently full-wave rectied. Then a
non-linear Bayesian lter ( = 1
4
, = 1
18
, 128-bin histogram) [72] was applied to the
rectied signals. Cursor position was proportional to either the actual force recorded by the
transducer (force-control), or the force estimated in real-time from the recorded and rectied
EMGs or synergies [4].
Experimental Protocol
Subjects came in three separate days. On each day, they performed a 2-D, isometric, center-
out speed-accuracy task using myocontrol under one of three conditions: 1) All EMG control,
2) Select Muscle control, and 3) Select Synergy control. All EMG control refers to the
estimation of force from all recorded EMGs. Select Muscle control is the estimation of force
from the most controllable muscles. Select Synergy control is the estimation of force from
the most controllable synergies.
Subjects initially performed two blocks of trials in force-control. In the rst force-control
block, the mean maximum voluntary force (MVF) along eight directions (separated by 45
deg) was estimated as the mean of the maximum force magnitude recorded across 16 trials
(two for each direction) in which subjects were instructed to generate maximum force in each
direction. In the second force-control block, subjects performed 24 trials to targets positioned
at force magnitudes corresponding to 10, 20, and 30% MVF (random order within cycles of
eight directions) with a radius corresponding to 5% MVF, presented in random order. The
40
EMG-to-Force mapping was calculated from the data collected during this block. After this
block, recorded data were processed to construct the myoelectric controller.
For the Select Muscle and Select Synergy conditions, the most controllable muscles and
synergies were selected as detailed inMuscle and Synergy Selection. Subjects then performed
the 2-D task, using myocontrol to reach targets in eight directions (separated by 45
), three
indexes of diculty (ID) per direction for 24 targets total. Targets corresponded to a distance
of 15% MVF from the origin with widths 4.31, 7.24, and 12.18% MVF, resulting in IDs
ranging from 1.16 to 2.16 bits, and were presented in random order. Subjects performed 240
trials for each condition.
EMG-to-Force Mapping
Under isometric conditions, the force generated at the hand is approximately a linear function
of the activation of muscles [4]:
f =Hm +e
f
(3.1)
where f is the generated 2-dimensional force vector, m is the 8-dimensional vector of
muscle activations, andH is a matrix relating muscle activation to force (dimensions 2 x 8),
ande
f
is a 2-dimensional vector of force residuals. Each column ofH is the pulling direction
of one muscle in the 2D plane (Figure 3.2a). The EMG-to-force matrix (H) was estimated
using multiple linear regressions of each applied force component with EMG signals recorded
during the second force-control block. Only data from the dynamic phase of trials were used
for regression, from when the target appeared until the cursor was stabilized in the target
for 0.2 seconds. The force components were low-pass ltered (2nd order Butterworth, 1 Hz
cuto) and normalized to MVF. The EMG signals were normalized to the maximum EMG
activity during the generation of MVF in the rst force-control block.
Synergy Extraction
Muscle synergies were identied by NMF [47] from EMG patterns during the force control
block from target appearance until the cursor was stabilized in the target for 0.2 seconds
(dynamic phase):
m =Wc +e
m
(3.2)
with W a M x N synergy matrix whose columns are vectors specifying relative muscle
activation levels (N number of synergies, and M number of muscles), andc a N -dimensional
41
muscle
activation
0 0.5 1
TRAP
PD
LD
AD
TRIC
BIC
BRACH
PEC
W
1
W
2
W
3
W
4
W
5
Figure 3.1: Muscle synergies (matrix W) identied by non-negative matrix factorization from
the EMG data of subject 5 collected in the force-control block. Each column of
W is a vector specifying a specic pattern of relative level of muscle activation.
Synergies in black represent the ones selected for use in the 2-D myocontrol task
for the Select Synergy condition.
synergy activation vector, and e
m
a M -dimensional vector of muscle activation residuals.
NMF was implemented using the multiplicative update rule and the algorithm stopped when
the reconstruction error (R
2
) was not increased more than 10
4
for 10 consecutive iterations,
or when a maximum number of 10
5
iterations was reached. Synergy extraction was repeated
with the number of synergies (N) ranging from 5 to 8.
For each subject the number of synergies adequately capturing the EMG data (N ) was
selected according to the fraction of data variation explained, dened as
R
2
EMG
= 1
SSE
EMG
SST
EMG
(3.3)
whereSSE
EMG
is the sum of the squared muscle activation residuals and SST
EMG
is the
sum of the squared residuals of the muscle activation from its mean vector. We extracted a
minimum of ve synergies and additionally considered two criteria. The rst criterion was
a threshold of 0.9 onR
2
EMG
. The second criterion was based on the detection of a \knee" in
the slope in the curve of the R
2
value as a function of N. A series of linear regressions were
performed on the portions of the curve included between N and its last point (M ). N was
then selected as the minimum value for which the mean squared error of the linear regression
was less than 10
4
. In case of mismatch between the two criteria, the larger N was chosen.
An example of extracted synergies is shown in Figure 3.1
42
Muscle and Synergy Selection
To select the muscles and synergies used in the 2-D myocontrol task, subjects performed a
1-D isometric speed-accuracy task. For each synergy or muscle, subjects completed 40 trials,
reaching to four targets of dierent widths (3.0, 4.3, 6.1, 8.6 % MVC) and distances (7.5 and
15 % MVC) in each component's natural pulling direction calculated from the EMG-to-Force
mapping (Figures 3.2a and 3.2d ).
The Fitts' Index of Diculty (ID) was calculated with the Shannon formulation:
ID =log
2
2D
W
+ 1
(3.4)
where D is the distance from the the start position to the center of the target and W is
the width of the target [54]. IDs for the 1-D task ranged from 1.16 to 2.16 bits.
Muscles and synergies were then ranked based on average throughput (TP)
TP =
1
x
x
X
i=1
ID
i
MT
i
(3.5)
where x is the number of targets, and MT is the movement time to reach the target
(Figures 3.2b and 3.2e ). TP gives a quantitative measure of controllability in terms of bit
rate.
The dimensionality of the muscle and synergy mappings was then reduced by eliminating
less controllable muscles or synergies. The four muscles and synergies with the highest
throughput were selected for the 2-D task. If the pulling direction of a muscle or synergy
made an angle of 60
or less with that of a previously selected muscle or synergy, we did
not select it in order to ensure that the selected muscles and synergies spanned the 2-D
space (Figures 3.2c and 3.2f ). The angular dierence between two muscles or synergies was
calculated as the inverse cosine of their pulling directions.
EMG- and Synergy-Control
Output forces f during EMG-control were computed using the EMG-to-force mapping (H)
and the recorded muscle activity m by
f =Hm (3.6)
thus allowing for individual muscle control. During synergy-control muscle activity was
substituted by the product of the initially extracted subject-specic synergies (W) and
estimated synergy coecients (^ c), i.e., by f = HW^ c, where HW is the synergy-to-force
43
mapping, and each column is the pulling direction of each synergy. Synergy coecients were
estimated by projecting recorded muscle activity onto the synergy space, i.e., by^ c =W
+
m
, where W
+
is the pseudo-inverse of W, corresponding to estimating ^ c from m as least
squares solution ofm =Wc. Thus, during synergy-control output forces were computed as:
f =HWW
+
m (3.7)
For the Select Muscle and Select Synergy control, the force mappings were reduced to only
use columns corresponding to the select muscles or synergies in the force estimation. For
the Select Muscle mapping, each column vector was normalized (v/kvk) so that EMG values
were projected onto their respective axes. Without normalization, subjects were unable to
reach targets because the controllable space was reduced due to the absence of the excluded
muscles.
Analysis
Data analysis was executed with Matlab R2016a (Mathworks, Natick, MA). Statistical analy-
sis was performed using RStudio, version 0.99.903 (RStudio Inc., Boston, MA), the R-package
lme4, version 1.1{12, and multcomp, version 1.4{8.
Performance Measures We used movement time (MT), success rate, and throughput (TP)
during the speed-accuracy task as outcome measures. MT was calculated as the time from
when the cursor velocity was greater than 5% peak velocity during the trial to the time once
they successfully stabilized in the target for 0.2 seconds. Trials in which subjects successfully
stabilized in the target for 0.2 seconds were considered successful. For unsuccessful trials,
MT was capped at 7.5 seconds, which was the maximum trial length. This provides a
conservative estimate of what MT would have been had subjects been given an indenite
amount of time to reach the target.
TP for each trial was calculated as the ratio between ID and MT, similar to its calculation
in the 1-D case for muscle and synergy selection. However, in the 2-D case, the distance used
to calculate ID was dened as the distance from the cursor position at target presentation to
the target center. This accounts for some trials where subjects were not at the origin during
target presentation.
Since the design of our experiment had multiple measures, we used linear mixed eects
analysis to express the relationships in our data instead of linear regression analysis, which
requires measurements to be independent. Since success was a binomial measure, we used a
generalized linear model with a logistic regression, however, the model was very similar to
44
EMG-to-Force, H
Synergy-to-Force, HW
Select Muscles
Select Synergies
A B C
D E F
7
6
5
4
3
2
1
8
3
4
5
7
1
2
3
4
5
2
3
4
5
TP(bits)
TP(bits)
Pec Brach Bic Tri AD LD PD Trap
Muscle
Synergy
1 2 3 4 5
0.0
0.3
0.6
0.9
0.9
0.6
0.3
0.0
Figure 3.2: (A) EMG-to-force matrix H estimated for subject 5 from EMG and force data
recorded during the force-control block. Each column of H represents the planar
force generated by one muscle (1: pectoralis major, 2: brachioradialis, 3: biceps,
4: triceps, 5: anterior deltoid, 6: lateral deltoid, 7: posterior deltoid, 8: mid-
dle trapezius). (B) TP of each muscle after performing a 1-D speed-accuracy
myocontrol task. Bars in black represent muscles selected for the Select Mus-
cle condition in the 2-D task (C) The reduced mapping for the Select Muscle
condition in the 2-D myocontrol task, using the four muscles with the highest
TP that also spanned the 2-D space. (D) Forces associated with the muscle
synergies [shown in Figure 3.1]. (E) TP of each synergy after performing a 1-D
speed-accuracy myocontrol task. Bars in black represent muscles selected for the
Select Synergy condition in the 2-D task. (F) The reduced mapping for the Select
Synergy condition in the 2-D myocontrol task, using the four synergies with the
highest TP that also spanned the 2-D space.
45
that used for MT and TP. All analyses comprised of ID and myocontrol condition as xed
eects, and intercepts for subjects as a random eect, resulting in the following R regression
model:
DependentvariableID +Condition + (1jSubject) (3.8)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interaction between
the 2 xed eects (ID and Condition), we compared the model that takes into account the
interaction between xed eects (Full) against the model without the interaction (Null).
For all comparisons, p-values and Akaike's information criterion values (AIC) were obtained
by likelihood ratio tests of the Full model with the Null model. If the factor in question
signicantly aects the dependent variable, then the comparison will report a signicant p-
value (< .05) and an AIC value lower for the Full model. Similarly, a signicant interaction
between factors will result in a signicant dierence between the Full and the Null models (p
< 0.05) with a lower AIC for the Full model. Post-hoc multiple comparisons were performed
with Bonferroni correction to determine dierences between specic myocontrol conditions.
Dierences in performance measures within individual subjects were assessed either with
two-sided t-test if the data were distributed normally (according to a Lilliefors test) or by
Wilcoxon ranksum with Bonferroni correction otherwise .
3.2.4 Results
Movement Time
The likelihood ratio test showed that ID had a signicant eect on MT (AIC
Full
= 14694;
AIC
Null
= 14697; p = 0.02), meaning the task eectively imposed a speed-accuracy tradeo.
MT increased with ID by 0.62 0.20 seconds per bit. Condition was also a signicant xed
eect for MT (AIC
Full
= 14694; AIC
Null
= 14713; p< 0.0001). Post-hoc pairwise comparison
showed that MT for the Select Synergy condition was signicantly dierent than MT for the
All EMG condition (p < 0.0001). MT for Select Synergy was 0.47 0.09 seconds higher
than MT for All EMG. Pairwise comparison also showed that MT for Select Muscle was
signicantly dierent than MT for All EMG (p = 0.002). MT for Select Muscle was 0.32
0.10 seconds higher than MT for All EMG. There was no signicant dierence in MT between
Select Synergy and Select Muscle (p = 0.30). On average, the MT for Select Synergy was 0.14
0.09 seconds higher than the MT for Select Muscle. The interaction between Condition
and ID was also a signicant xed eect for MT (AIC
Full
= 14688; AIC
Null
= 14694; p =
46
4
5
6
7
EMG Select Muscle Select Synergy
Condition
Movement Time (s)
Subjects 1 2 3 4 5
Figure 3.3: Mean and SE of MT of patients using All EMG, Select Synergy, and Select
Muscle control.
0.006), suggesting that changes in MT across ID varied for the dierent Conditions.
Analysis of individual subjects showed that MT for Select Synergy was signicantly dier-
ent than MT for All EMG for three out of ve subjects (p< 0.0001, p< 0.001, p = 0.024 for
subjects 1, 2, and 3). MT for Select Synergy was higher than MT for All EMG for subjects
1 and 2, and lower for subject 3. MT for Select Muscle was signicantly dierent than MT
for All EMG for two out of ve subjects (p < 0.0001, p = 0.0035, for subjects 1 and 3).
Subject 1 had higher MT for Select Muscle than for All EMG. Subject 3 had lower MT for
Select Muscle than for All EMG. MT for Select Synergy was signicantly dierent than MT
for Select Muscle for one subject (p = 0.0018 for subject 2), in which it was higher. Results
for MT are shown in Figure 3.3.
Success Rate
The likelihood ratio test showed that ID had a signicant eect on success rate (AIC
Full
=
3536.6; AIC
Null
= 3634.7; p < 0.0001). The odds ratio associated with an increase in ID
was 0.44. Condition also had a signicant eect on success rate (AIC
Full
= 3536.6; AIC
Null
= 3563.5; p < 0.0001). Post-hoc pairwise comparison showed that there was a signicant
dierence between success rate in Select Muscle and All EMG, with Select Muscle having
an odds ratio of 0.44 compared to All EMG (p < 0.0001). There was also a signicant
dierence between success rate in Select Synergy and All EMG, with Select Synergy having
an odds ratio of 0.30 compared to All EMG (p< 0.0001). There was no signicant dierence
47
between Select Synergy and Select Muscle (p = 0.94). The odds ratio of success rate for
Select Synergy to Select Muscle was 1.07. Additionally, interaction between Condition and
ID had a signicant eect on success rate (AIC
Full
= 3523.2; AIC
Null
= 3536.6; p < 0.001),
meaning that change in success rate across ID diered across Conditions. The proportion of
successful trials for each subject is listed in Table 3.2.
Table 3.2: Success rate of individual subjects for each condition
Subject All EMG Select Muscle Select Synergy
1 0.32 0.07 0.11
2 0.78 0.72 0.64
3 0.10 0.20 0.18
4 0.24 0.17 0.21
5 0.50 0.53 0.45
Throughput
The likelihood ratio test showed that Condition was not a signicant eect on TP (p = 0.51).
The estimated dierence in TP between Select Synergy and All EMG was {0.03 0.03. The
estimated dierence in TP between Select Muscle and All EMG was {0.03 0.03. The
estimated dierence in TP between Select Synergy and Select Muscle was 0.002 0.03.
Individual analysis for TP showed that TP for Select Synergy was signicantly dierent
than TP for All EMG for four of ve subjects(p< 0.0001, p = 0.001, p< 0.0001, p< 0.001
for subjects 1, 2, 3, and 4), with all four of the subjects having lower TP for Select Synergy.
TP for Select Muscle was signicantly dierent than TP for All EMG for two out of ve
subjects (p < 0.0001 for subjects 1 and 3), with both subjects having lower TP for Select
Muscle TP for Select Synergy was signicantly dierent than TP for Select Muscle for four
subjects (p = 0.009, p = 0.002, p < 0.001, p = 0.02 for subjects 1, 3, 4, 5).
Subjects 1 and 3 had higher TP with Select Synergy compared to Select Muscle. Subjects 4
and 5 had lower TP with Select Synergy compared to Select Muscle. TP results are shown
in Figure 3.4.
3.2.5 Discussion: Involuntary Components are High Dimensional
We wanted to see if the removal of less controllable synergies or muscles could improve
myocontrol performance compared to All EMG myocontrol. We found that Select Synergy
and Select Muscle myocontrol had higher MT and lower success than All EMG myocontrol.
All conditions had similar TP. Based on these outcome measures, we conclude that Select
Synergy and Select Muscle myocontrol do not adequately improve myocontrol performance.
48
0.3
0.5
0.7
0.9
EMG Select Muscle Select Synergy
Condition
Throughput (bit/s)
Subjects 1 2 3 4 5
Figure 3.4: Mean and SE of TP of patients using All EMG, Select Synergy, and Select Muscle
control.
Based on our results, we can infer that controllable and involuntary components are present
on all EMG channels. Indeed, previous literature suggests that synergies in children with
CP may be similar to those in typically developing children. In a study comparing back and
forth and gure 8 drawing movements, dystonic and typically developing children shared
many similar synergies, however time activations diered [51]. Cappellini et. al. found
that both children with CP and typically developing children had similar structure of motor
output in gait, but children with CP exhibited wider temporal activation patterns [10].
There are some studies showing that children with CP have dierent synergies than typ-
ically developing children. Some have observed that children with CP recruit less synergies
in walking [82, 80]. Tang et. al. also observed CP-specic synergies [82], however, these re-
sults were regarding lower extremities. Discrepancies between these studies and the results
of Cappellini et.al. may be due to dierent numbers of muscles and dierent criteria for
synergy selection [81].
While removing less controllable synergies does not improve myocontrol performance for
children with CP, a dierent approach may involve using synergies to aid learning rather
than execution. A study done on adults showed dierent adaptation rates in a myocontrol
task depending on the span of the synergies [5]. For children with CP, projecting to a
synergy space dierent from their own may lter noise from some dimensions not necessary
for control while allowing subjects to learn to control a lower dimensional space. Future
work would be needed to determine this.
This study sought to determine if spatially ltering EMG from children with CP would
49
improve myocontrol performance. We have learned that selecting the most controllable
muscles or synergies as quantied by Fitts' Law does not improve myocontrol performance
for children with CP, and can make it worse. This appears to result from the spread of
controllability and noise over all available dimensions of control. As a result, the noise is
not conned to a low-dimensional subspace, and cannot be removed by subspace ltering.
Thus, in order to establish myocontrol for children with CP, future work should be focused
on temporally ltering muscle or synergy activations, rather than spatially ltering the less
controllable muscles or synergies. This work provides insight in where the noise lies in the
motor output of children with CP. It suggests that noise or variability is distributed across
the set of controllable synergies and is not conned to a single low-dimensional pattern. As
we develop a better understanding of where the noise is, we may develop a myocontroller
to lter such noise, allowing children with CP to control assistive devices that can perform
movements that the children are unable to perform with their own limbs.
50
3.3 Experiment 2: Linear Estimation of Rewarded Force
for Children with Cerebral Palsy
3.3.1 Introduction
From the previous experiment, we concluded that selecting the most controllable muscles
or synergies was not sucient to facilitate myocontrol for children with CP. Removing less
controllable muscles or synergies also removes signals driving movement intention. Thus,
multi-muscle myocontrol must include all muscles or synergies.
We must also determine how to appropriately map multiple muscles to the task space,
since mapping to measured force as done previously would simply provide an estimate of
their existing movement disorder. Previous research has shown that patients with dyskinetic
CP have increased variability in reaching movements, but their average movement is similar
to that of controls [71]. Thus, we hypothesized that estimating rewarded force instead of
measured force would improve performance compared to direct force control.
In addition to comparing this new method of EMG control to force control, we wanted to
explore how subjects respond to changing lter parameters, if at all. If they do change how
they use their EMG in response to changing parameters, this suggests a new potential use
for myocontrol as a rehabilitative tool to train desired EMG patterns.
3.3.2 Methods
Participants
Inclusion criteria for this study were: (I) CP or dystonia aecting at least one upper extrem-
ity; (II) pediatric age (7{21 years); (III) no cognitive impairment that prevents understanding
of instructions. Six children with cerebral palsy (5 males, 1 female; ages 13 to 20 years, mean
17 3 years) and six typically developing (TD) children (2 males, 4 females; ages 13 to 21
years, mean 17 3 years) performed this protocol. Participant details are shown in Table
3.4. There was no statistical dierence in age between the two groups. The University of
Southern California Institutional Review Board approved the study protocol. All parents
gave informed written consent for participation and all children gave written assent. Autho-
rization for use of protected health information was signed in accordance with the Health
Information Portability and Accountability Act. The study was performed in accordance
with the Declaration of Helsinki.
51
Table 3.3: Characteristics of Subjects
BAD Scale Score
ID Sex Age L Arm R Arm Arm Tested Diagnosis Symptoms
p1 M 18 3 3 R Hypoxic ischemic injury Severe generalized hyperki-
netic dystonia
p2 F 15 0 1 R Traumatic Brain Injury due to MVA Right hemidystonia
p3 M 20 1 0 L Cerebral palsy Left arm dystonia
p4 M 20 3 3 R Hypoxic ischemic injury Severe generalized hyperki-
netic dystonia
p5 M 16 3 0 L Hypoxic ischemic injury Generalized dystonia
p6 M 13 3 3 L Hypoxic ischemic injury Generalized dystonia
c1 F 17 R
c2 F 21 R
c3 F 18 L
c4 F 20 R
c5 M 14 R
c6 M 13 R
Abbreviations: BAD Scale, Barry-Albright Dystonia Scale; F, female; L Arm, severity of left arm; M, male; R Arm, severity
of right arm. Scores are based on the BAD Scale[3]; for each segment, the score ranges from 0 - absence of dystonia to 4 -
severe dystonia.
Experimental setup
Subjects sat in front of a desktop with their dominant (TD) or more aected (CP) forearm
inserted in a splint, immobilizing hand, wrist, and forearm. The center of the palm was
aligned with the body midline at the height of the sternum and the elbow was
exed by
approximately 90
. A steel bar at the base of the splint was attached to a 6-axis force
transducer (Delta F/T Sensor, ATI Industrial Automation, Apex, NC, USA) positioned
below the table to record isometric forces and torques. Surface electromyographic (EMG)
activity was recorded from the following eight muscles: pectoralis major, brachioradialis,
biceps, triceps, anterior deltoid, lateral deltoid, posterior deltoid, middle trapezius. EMG
activity was recorded with bipolar electrodes (DE{2.1, Delsys Inc., Boston, MA, USA),
band-pass ltered (20{450 Hz) and amplied (gain 1000, Bagnoli{8, Delsys Inc.). Force
and EMG data were sampled at 1 KHz using an analog-to-digital interface (Power 1401,
CED Technologies Inc., UK) and a custom data acquisition software. EMG was ltered
with a 1 Hz, 4th order Butterworth high-pass lter to remove baseline DC voltage, and
subsequently full-wave rectied. Then a non-linear Bayesian lter [72] was applied to the
rectied signals. Cursor position was proportional to either the actual force recorded by the
transducer (force-control), or the force estimated in real-time from the recorded and rectied
EMGs
Experimental protocol
Subjects performed a 2-D, isometric, center-out speed-accuracy task using myocontrol.
Subjects initially performed two blocks of trials in force-control. In the rst force-control
block, the mean maximum voluntary force (MVF) along four directions (separated by 90
52
deg) was estimated as the mean of the maximum force magnitude recorded across eight
trials (two for each direction) in which subjects were instructed to generate maximum force
in each direction. In the second force-control block, subjects performed 36 trials to targets
positioned at force magnitudes corresponding to 10, 20, and 30% MVF (random order within
cycles of four directions, three trials per target). After this block, recorded data was processed
to construct the myoelectric controller.
After performing the initial force-control blocks, subjects performed a 2-D isometric center-
out speed-accuracy task rst with force control, then with ve blocks of EMG control in an
ABACA design. In blocks A, or the Baseline EMG block, subjects performed EMG control
with a baseline set of parameters. For block B, or the Noisy EMG block, subjects performed
EMG control with parameters adjusted so that the signal contained more noise. For block
C, or the Delayed EMG block, subjects performed EMG control with parameters adjusted
so that the signal had more delay. They performed 10 trials using each condition, reaching
to targets in two directions, upward and medially, two IDs per direction for four targets
total. Targets corresponded to a distance of 15% MVF from the origin with widths 4.31
and 12.18% MVF, resulting in IDs 1.16 and 2.16 bits, and were presented in random order.
Targets were considered successful if subjects maintained the cursor within the target for 0.2
seconds. Subjects performed 40 trials for each condition.
EMG-to-Force Mapping
Rather than mapping EMG to the measured force, as done in Study 3, EMG was linearly
mapped to the rewarded force:
f
rewarded
=Hm (3.9)
In this case, f
rewarded
is estimated from the measured force during the force-control cali-
bration block as the projection of the measured force to the target force direction:
~
f
rewarded
=
~
f
measured
~
f
target
j
~
f
target
j
~
f
target
(3.10)
Multiple linear regression was then used to calculate the mapping matrixH between EMG
and rewarded force.
To modify the eect of noise and delay in the linear estimation of force from EMG, we
adjusted the non-linear lter parameters of the individual EMG channels. The non-linear
lter uses a Fokker-Planck equation to estimate the value of each EMG channel:
53
@p(emg;t)
@t
=
@
2
p(emg;t)
@x
2
+ [1p(x;t)] (3.11)
Modifying in
uences the level of noise in the channel, while modifying in
uences the
delay of the estimate. and were modied uniformly across all EMG channels prior to
linearly estimating the force. Three dierent pairs of and were compared: 1) = 1
2
and = 1
50
(Baseline), 2) = 1
2
and = 0 (Delayed) and 3) = 1
1
and = 1
50
(Noisy).
Analysis
Data analysis was executed with Matlab R2016a (Mathworks, Natick, MA). Statistical anal-
ysis was performed using RStudio, version 0.99.903 (RStudio Inc., Boston, MA), and the
R-package lme4 (version 1.1{12).
EMG vs Force Control One goal of this study was to determine if EMG control had
improved performance compared to force control. To do so, we compared the force block
(Force) with the rst baseline EMG block (Baseline A) and the last baseline EMG block
(Baseline C). We used movement time (MT), success rate, throughput (TP), endpoint error,
and initial angle error as outcome measures. MT was calculated as the time from when the
cursor velocity was greater than 5% peak velocity during the trial to the time once they
successfully stabilized in the target for 0.2 seconds. Trials in which subjects successfully
stabilized in the target for 0.2 seconds were considered successful. For unsuccessful trials,
MT was capped at 7.5 seconds, which was the maximum trial length. This provides a
conservative estimate of what MT would have been had subjects been given an indenite
amount of time to reach the target. TP for each trial was calculated as the ratio between
ID and MT, similar to its calculation in the 1-D case for muscle and synergy selection.
However, in the 2-D case, the distance used to calculate ID was dened as the distance
from the cursor position at target presentation to the target center. This accounts for some
trials where subjects were not at the origin during target presentation. Endpoint error was
measured as the distance from the target center to the cursor location at movement end.
Initial angle error was measured as the angular dierence between the vector from cursor
position at movement start to the target center position and the vector from the cursor
position at movement start to the cursor position at the rst velocity peak after movement
start.
Since the design of our experiment had multiple measures, we used linear mixed eects
analysis to express the relationships in our data instead of linear regression analysis, which
54
requires measurements to be independent. Since success was a binomial measure, we used
a generalized linear model with a logistic regression, however, the model was very similar
to that used for the other outcome measures. All analyses comprised of Block and Group
as xed eects, and intercepts for subjects as a random eect, resulting in the following R
regression model:
DependentvariableBlock +Group + (1jSubject) (3.12)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interactions between the
xed eects, we compared the model that takes into account the interaction between xed
eects (Full) against the model without the interaction (Null). For all comparisons, P values
and Akaike's information criterion values (AIC) were obtained by likelihood ratio tests of the
Full model with the Null model. If the factor in question signicantly aects the dependent
variable, then the comparison will report a signicant P value (< .05) and an AIC value
lower for the Full model. Similarly, a signicant interaction between factors will result in a
signicant dierence between the Full and the Null models (p < 0.05) with a lower AIC for
the Full model. Post-hoc multiple comparisons were performed with Bonferroni correction
to determine dierences between specic blocks within the two participant groups.
Dierences in performance measures within individual subjects were assessed either with
two-sided t-test if the data were distributed normally (according to a Lilliefors test) or by
Wilcoxon ranksum with Bonferroni correction otherwise .
EMG Comparison The second goal of this study was to determine how EMG behavior
changes as a result of perturbations in lter parameters. We analyzed EMG measures from
the ve EMG blocks (Baseline A, Noise, Baseline B, Delay, and Baseline C). We divided the
blocks into two to separate behavior in the rst half of the block from the second half of
the block. Then, we compared the rst half of each block to the latter half of the preceding
block to note eects that resulted from changing parameters. As EMG measures, we used
muscle force, onset, and co-contraction within the biceps and triceps, and anterior deltoid
(AD) and posterior deltoid (PD). Muscle force was calculated as the the root mean square of
the rectied EMG from movement start to end for each muscle. Onset was measured as the
rst point in which the rectied EMG was greater than a baseline threshold. To determine
the baseliene threshold, we used the data one-second prior to target appearance. From this
period, we calculated the mean and standard deviation (SD) of the EMG. The baseline
threshold was the sum of the mean and three times the SD. For each pair of antagonist
55
muscles, co-contraction was calculated as the minimum value of EMG activation between
the two muscles of each time sample, then averaged over the movement.
Similar to the EMG vs Force Control analysis, we used linear mixed eects analysis to
express the relationships in our data. Analyses comprised of Halfblock and Group as a xed
eects, and intercepts for subjects as a random eect, resulting in the following R regression
model:
DependentvariableHalfblock +Group + (1jSubject) (3.13)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interactions between
the xed eects, we compared the model that takes into account the interaction between
xed eects (Full) against the model without the interaction (Null). For all comparisons,
P values and Akaike's information criterion values (AIC) were obtained by likelihood ratio
tests of the Full model with the Null model. Post-hoc multiple comparisons were performed
with Bonferroni correction to determine dierences between specic half-blocks within the
two participant groups.
3.3.3 Results
EMG vs Force Control
Movement Time The likelihood ratio test showed that Block had a signicant eect on
MT (AIC
Full
= 6032.1; AIC
Null
= 6037.6; p = 0.009). There was a signicant eect for Group
(AIC
Full
= 6032.1; AIC
Null
= 6034.0; p = 0.048). MT for TD children was 1.32 0.61 seconds
lower than MT for CP children. There was a signicant eect for the interaction between
Block and Group (AIC
Full
= 6018.1; AIC
Null
= 6032.1; p< 0.001), suggesting that changes in
MT vary between the two groups. Pairwise comparison showed that there was no signicant
dierence in MT between any of the blocks for TD children. However, for CP children, there
was a signicant dierence in MT between Force and Baseline C, with Baseline C MT being
0.83 0.17 seconds less than the force block MT (p < 0.0001). Also, the MT for Baseline
C was 0.69 0.17 seconds less than MT in Baseline A for CP children (p = 0.0003).
Analysis of individual subjects showed that MT for Baseline A was signicantly dierent
than MT for Force for two out of six CP children (p = 0.04, p = 0.003 for subjects p1 and
p5) and two out of six TD children (p = 0.011, p = 0.01 for subjects c1 and c3). Subjects
p1 and c1 had higher MT for Baseline A compared to Force. Subjects p5 and c3 had lower
MT for Baseline A compared to Force. MT for Baseline C was signicantly dierent than
56
***
****
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0
1
2
3
4
5
Block
Movement Time (s)
Figure 3.5: MT for children with CP (left) and TD children (right) using linear estimation
of force from EMG.
MT for Force for one CP child (p = 0.0007 for subject p2) and two TD children (p = 0.0083,
p = 0.017 for subjects c1 and c3). For p2 and c3, MT was lower in Baseline C compared
to Force. For c1, MT was higher in Baseline C compared to Force. MT for Baseline C was
signicantly lower than MT for Baseline A for three CP children (p < 0.0001, p = 0.025,
p = 0.0018 for subjects p1, p3, and p6) and one TD children (p = 0.031). For all of these
children, MT for Baseline C was lower than MT for Baseline A. Results for MT are shown
in Figure 3.5.
Success Rate The likelihood ratio test did not report a signicant eect of Block on
success rate (p = 0.47). There was not a signicant eect for Group (p = 0.069). There was
a signicant eect for the interaction between Block and Group (AIC
Full
= 857.33; AIC
Null
= 865.91; p = 0.0019). Pairwise comparison showed that there was no signicant dierence
in success rate across blocks for TD children. There was a signicant dierence in success
rate between Baseline A and C for CP children, with Baseline A having an odds ratio of
0.49 compared to Baseline C (p = 0.016) The success rates are shown in Figure 3.6.
57
*
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0.00
0.25
0.50
0.75
1.00
Block
Success
Figure 3.6: Success rates for children with CP (left) and TD children (right) using linear
estimation of force from EMG.
58
Throughput The likelihood ratio test reported a signicant eect for Block on TP (AIC
Full
= 2415.8; AIC
Null
= 2420.3; p = 0.014). There was not a signicant eect for Group (p =
0.20). There was a signicant eect for the interaction between Block and Group (AIC
Full
= 2383.9; AIC
Null
= 2415.8; p < 0.0001). Pairwise comparison showed that there was a
signicant dierence in TP between Force and Baseline C as well as between Baselines A
and C for CP children. For this group, Baseline C had a TP 0.22 0.05 bits/s greater than
Force (p< 0.0001). Similarly, Baseline C had a TP 0.22 0.05 bits/s greater than Baseline
A (p < 0.0001). In contrast, TD children showed a decrease in TP for Baselines A and C
compared to Force. For this group, TP for Baseline A was 0.17 0.05 bits/s less than Force
(p = 0.002). TP for Baseline C was 0.20 0.05 bits/s less than Force (p = 0.0002).
Analysis of individual subjects showed that TP for Baseline A was signicantly dierent
than TP for Force for two CP children (p = 0.032, p = 0.0008 for subjects p5 and p6) and
two TD children (p < 0.0001, p = 0.0006 for subjects c1 and c5). TP for Baseline A was
greater than TP for Force for subject p5, but smaller for p6. For both TD children, TP was
smaller for Baseline A than for Force. TP was signicantly dierent in Baseline C than Force
for two CP children (p = 0.0023, p = 0.011 for subjects p2 and p5) and two TD children (p
< 0.0001, p = 0.02 for subjects c1 and c2). For both CP children, TP was higher for Baseline
C compared to that of Force. For both TD children, TP was lower. TP was signicantly
dierent in Baseline C compared to Baseline A for two CP children (p = 0.0007, p = 0.0002
for subjects p1 and p6) and two TD children (p = 0.025, p = 0.0072 for subjects c2 and c5).
For both CP children, TP was higher in Baseline C compared to Baseline A. Of the two TD
children, TP was lower in Baseline C compared to Baseline A for subject c2 and higher for
subject c5. Results for TP are shown in Figure 3.7.
Endpoint Error The likelihood ratio test did not report a signicant eect for Block on
endpoint error (p = 0.23). There was also not a signicant eect for Group (p = 0.13). There
was a signicant eect for the interaction between Block and Group (AIC
Full
= {4204.9;
AIC
Null
= {4172.7; p < 0.0001). Pairwise comparison showed that there was a signicant
dierence in endpoint error between Force and Baseline C, and Baseline A and Baseline C
for CP children. CP children had 2.68 0.50 %MVC more error in Force than Baseline C
(p < 0.0001). They also had 1.77 0.50 %MVC more error in Baseline A than Baseline
C (p = 0.0013). For TD children, pairwise comparison also showed signicant dierence in
endpoint error between Baseline C versus Baseline A and Force. However, they show an
increase in endpoint error. TD children had 1.46 0.50 %MVC more error in Baseline C
compared to Force (p = 0.012), and 1.32 0.50 %MVC more error in Baseline C compared
to Baseline A (p = 0.025).
59
****
**** **
***
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0.0
0.5
1.0
Block
TP (bit/s)
Figure 3.7: TP for children with CP (left) and TD children (right) using linear estimation
of force from EMG
60
****
** *
*
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0.00
0.03
0.06
0.09
Block
Endpoint Error (%MVC)
Figure 3.8: Endpoint error for children with CP (left) and TD children (right) using linear
estimation of force from EMG.
Analysis of individual subjects showed that endpoint error for Baseline A was signicantly
dierent than error for Force for three of six CP children (p = 0.013, p = 0.0021, p = 0.0035
for subjects p1, p4, and p6). Subjects p1 and p6 had increased endpoint error in Baseline A
compared to Force, while subject d4 had decreased endpoint error. For Baseline C compared
to Force, endpoint error was signicantly dierent for one CP child (p = 0.0002 for subject
p4) and one TD child (p = 0.025 for subject c2). For subject p4, endpoint error decreased
in Baseline C compared to Force, and increased for subject c2. There was also signicant
dierence in endpoint error between Baseline A and C for two CP children (p = 0.0062, p
< 0.0001 for subjects p1 and p6) and one TD child (p = 0.0021 for subject c1). For the
patients, endpoint error decreased in Baseline C compared to Baseline A. For the TD child,
endpoint error increased. Results for endpoint error are shown in Figure 3.8.
Initial Angle Error The likelihood ratio test reported a signicant eect for Block on initial
angle error (AIC
Full
= 15466; AIC
Null
= 15469; p = 0.032). There was not a signicant eect
for Group (p = 0.68). There was a signicant eect for the interaction between Block and
Group (AIC
Full
= 15437; AIC
Null
= 15466; p < 0.0001). Pairwise comparison showed that
there was a signicant dierence in initial angle error between Force and Baseline C for CP
61
*
***
****
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0
25
50
75
Block
Initial Angle Error (deg)
Figure 3.9: Initial angle error for children with CP (left) and TD children (right) using linear
estimation of force from EMG.
children. Baseline C had 11.61 4.64 degrees less initial angle error for CP children (p
= 0.037). Pairwise comparison showed signicant dierences in initial angle error between
Force and Baseline A, and Force and Baseline C for TD children. Baseline A had 16.9
4.64 degrees more initial angle error than Force for TD children (p = 0.0008). Baseline C
had 26.27 4.64 degrees more initial angle error than Force (p < 0.0001).
Analysis of individual subjects showed that initial angle error for Baseline A was signif-
icantly dierent than for Force for two CP children (p = 0.0009, p = 0.11 for subjects p2
and p3) and for two TD children (p < 0.0001, p = 0.0024 for subjects c1 and c4). Initial
angle error for Baseline A was lower than for force for subject p2, but higher for subject p3.
Initial angle error was higher for both TD children. Initial angle error for Baseline C was
signicantly dierent than for Force for three CP children (p = 0.0002, p = 0.033, p = 0.024
for subjects p2, p3, and p5) and four TD children (p < 0.0001, p < 0.0001, p = 0.0062, p
= 0.023 for subjects c1, c2, c4, and c5). It is lower for Baseline C compared to Force for
subjects p2 and p5, and higher for subjects p3 and all four TD children. Initial angle error
was not signicantly dierent between Baselines A and C for any subjects. Results for initial
angle error are shown in Figure 3.9.
62
*
0.00
0.03
0.06
0.09
0.12
Noise-2 Baseline B-1
Block
Muscle Force (mV)
(a)
****
0.00
0.03
0.06
0.09
0.12
Baseline B-2 Delay-1
Block
Muscle Force (mV)
(b)
*
0.00
0.03
0.06
0.09
0.12
Delay-2 Baseline C-1
Block
Muscle Force (mV)
(c)
Figure 3.10: Changes in muscle force for children with CP in (a) Baseline B following Noise,
(b) Delay following Baseline B, and (c) Baseline C following Delay.
Changes in EMG
Muscle Force The likelihood ratio test showed that Halfblock had a signicant eect on
muscle force (AIC
Full
= {21638; AIC
Null
= {21629; p = 0.0011). There was also a signicant
eect for Group (AIC
Full
= {21638; AIC
Null
= {21636; p = 0.041). CP children had 0.050
0.023 mV more muscle force than TD children. There was a signicant eect for the
interaction between Halfblock and Group (AIC
Full
= {21650; AIC
Null
= {21638; p = 0.0004).
Children with CP had 0.017 0.006 mV more muscle force at the start of Baseline B
compared to the end of the Noise block (p = 0.028). They also had 0.028 0.006 mV more
muscle force in the Delay block following Baseline B (p < 0.0001). In Baseline C, they had
less muscle force compared to the end of the Delay block by 0.016 0.006 mV (p = 0.049).
Changes in muscle force for children with CP are shown in Figure 3.10. TD children did not
show any signicant changes in any of the blocks.
Onset Time The likelihood ratio test showed that Halfblock had a signicant eect on onset
time (AIC
Full
= 72349; AIC
Null
= 72357; p = 0.0023). There was not a signicant eect for
Group (p = 0.71). There was a signicant eect for the interaction between Halfblock and
Group (AIC
Full
= 72327; AIC
Null
= 72349; p < 0.0001). Children with CP did not show
signicant changes in onset in any of the blocks. TD children had a somewhat faster onset
in Baseline B following the Noise block (dierence of 0.18 0.07 s, p = 0.055). In contrast,
they had a somewhat slower onset in the Delay block following Baseline B (dierence of 0.17
0.07 s, p = 0.068). Changes in onset for TD children are shown in Figure 3.11.
Co-contraction The likelihood ratio test showed that Halfblock had a signicant eect on
AD/PD co-contraction (AIC
Full
= {5437.6; AIC
Null
= {5412.5; p < 0.0001). There was not
63
†
0.0
0.5
1.0
Noise-2 Baseline B-1
Block
EMG Onset (s)
(a)
†
0.0
0.5
1.0
Baseline B-2 Delay-1
Block
EMG Onset (s)
(b)
Figure 3.11: Changes in EMG onset for TD children in (a) Baseline B following Noise and
(b) Delay following Baseline B.
a signicant eect for Group (p = 0.13). There was a signicant eect for the interaction
between Halfblock and Group on AD/PD co-contraction (AIC
Full
= {5444.1; AIC
Null
= {
5437.6; p = 0.0036). Children with CP had increased AD/PD co-contraction in the Noise
block after Baseline A by 0.037 0.010 (p = 0.0009). They also had increased co-contraction
in Baseline B following the Noise block by 0.045 0.010 (p < 0.0001). Additionally, they
had increased co-contraction in the Delay block following Baseline B by 0.026 0.010 (p =
0.036) (Figure 3.14). TD children only showed increased AD/PD co-contraction in Baseline
C following the Delay block by 0.026 0.010 (p = 0.034) (Figure 3.15.
Results for biceps/triceps co-contraction were similar. The likelihood ratio test showed
that Halfblock had a signicant eect (AIC
Full
= {5376.7; AIC
Null
= {5323.1; p < 0.0001).
There was no signicant eect for Group (p = 0.69). There was a signicant eect for
the interaction between Halfblock and Group (AIC
Full
= {5380.2; AIC
Null
= {5376.7; p =
0.011). Patients show a slight signicant increase in biceps/triceps co-contraction in Baseline
B following the Noise block by 0.023 0.010 (p = 0.085). TD children have increased co-
contraction in Baseline C following the Delay block by 0.054 0.010 (p < 0.0001).
64
***
0.00
0.05
0.10
Baseline A-2 Noise-1
Block
Co-contraction AD/PD
(a)
****
0.00
0.05
0.10
Noise-2 Baseline B-1
Block
Co-contraction AD/PD
(b)
*
0.00
0.05
0.10
Baseline B-2 Delay-1
Block
Co-contraction AD/PD
(c)
Figure 3.12: Changes in co-contraction between AD and PD for children with CP in (a) Noise
following Baseline A, (b) Baseline B following Noise, and (c) Delay following
Baseline B.
*
0.00
0.05
0.10
Delay-2 Baseline C-1
Block
Co-contraction AD/PD
Figure 3.13: Changes in co-contraction between AD and PD for TD children in Baseline C
following the Delay block.
65
†
0.00
0.05
0.10
0.15
0.20
Noise-2 Baseline B-1
Block
Co-contraction Biceps/Triceps
Figure 3.14: Changes in co-contraction between biceps and triceps for children with CP in
Baseline B following Noise.
****
0.00
0.05
0.10
0.15
0.20
Delay-2 Baseline C-1
Block
Co-contraction Biceps/Triceps
Figure 3.15: Changes in co-contraction between biceps and triceps for TD children in Base-
line C following the Delay block.
66
3.3.4 Discussion: Linear Estimation Improves Performance in Children
with CP and Subjects Respond to Parameter Changes
This experiment had two goals. First, we wanted to determine if estimating rewarded force
improved EMG control performance compared to force control. Second, we wanted to explore
how EMG behavior changes in response to altered myocontrol parameters.
To evaluate our rst goal, we compared the force control block with the rst and last
baseline EMG blocks. We found that children with CP had faster MT, higher TP, lower
endpoint error, and lower initial angle error in the nal baseline EMG control block compared
to force control. While success rate was not signicantly dierent between Baseline C and
force control, it was higher. For TD children, there was no signicant dierence across blocks
in terms of MT or success rate. However, TP was lower and initial angle error was higher
in both EMG control blocks. Additionally, endpoint error was higher in Baseline C. These
results suggest that children with CP were able to learn to use the linear mapping and
improve performance over time, even with parameters changing every block. TD children,
on the other hand, had more diculty with EMG control. They were still able to perform
the task with high success, but the quality of their movement decreased. This could be a
result of EMG control feeling less natural. There also exists the possibility that TD children
grew bored during the task, resulting in worse performance in the nal baseline compared
to the initial baseline.
Regarding EMG behavior, we did observe changes in response to dierent lter parameters.
Children with CP had increased muscle force at the starts of Baseline B and the Delay block.
They had decreased muscle force in the nal baseline block. With the exception of the last
EMG block, they also had increased co-contraction between AD and PD at the start of each
new EMG block. Co-contraction between the biceps and triceps only increased following
the Noise block. TD children showed changes in EMG onset, with faster onset following the
Noise block and slower onset in the Delay block. They also showed increased co-contraction
between biceps and triceps in the nal baseline block. More work is required to determine
whether these changes in EMG are adaptations or learned eects. While we see signicant
changes surrounding the time of perturbation, with some measures, such as co-contraction
between AD and PD for children with CP, we see that by the end of the subsequent block,
values appear similar to those of the preceding block. Such temporary changes suggest that
the behavior observed may simply be a strategy that subjects use to initially compensate
for the changes in lter parameters until they adjust to the new parameters. There are,
however, other instances where the change in EMG seems to last throughout the duration of
the block, for example, the increased muscle force in patients in the Delay block (3.10b and
67
3.10c). Such eects that remain may indicate changes that are longer-lasting and perhaps
a learned eect. Finally, in order to use myocontrol as a way to aect desired changes
in EMG, we must investigate further the cause and eect of changing parameters. This
may involve discovering the degree to which we can aect change, or whether there is a
minimum threshold of change in lter parameters required in order to in
uence change in
EMG. In summary, these results suggest that there is a use for myocontrol beyond simply
estimating movement intent from EMG. There also exists the possibility for myocontrol
to train EMG patterns as we better understand how such patterns change in response to
diering myocontrol parameters.
68
3.4 Experiment 3: Non-linear Estimation of Rewarded
Force for Children with Cerebral Palsy
3.4.1 Introduction
We learned from the previous experiment that estimating rewarded force from EMG is a
promising method for interfacing EMG to the task space. Since non-linear ltering results
in improved myocontrol compared to linear ltering at the single channel level, we wanted to
explore the implementation of non-linear estimation at the task level. In this experiment, we
tested an implementation using non-linear estimation of rewarded force with the Ghoreyshi-
Sanger Algorithm [73]. In addition to comparing this method of EMG control to force
control, we again explored how subjects respond to changing lter parameters to further
establish the use of myocontrol as a rehabilitative tool.
3.4.2 Methods
Participants
Inclusion criteria for this study were: (I) CP or dystonia aecting at least one upper extrem-
ity; (II) pediatric age (7{21 years); (III) no cognitive impairment that prevents understanding
of instructions. Six children with cerebral palsy (5 males, 1 female; ages 13 to 20 years, mean
17 3 years) and and six TD children (2 males, 4 females; ages 13 to 21 years, mean 17
3 years)performed this protocol. Participant details are shown in Table 3.4. There was no
statistical dierence in age between the two groups. The University of Southern California
Institutional Review Board approved the study protocol. All parents gave informed written
consent for participation and all children gave written assent. Authorization for use of pro-
tected health information was signed in accordance with the Health Information Portability
and Accountability Act. The study was performed in accordance with the Declaration of
Helsinki.
Experimental setup
Subjects sat in front of a desktop with their dominant (TD) or more aected (CP) forearm
inserted in a splint, immobilizing hand, wrist, and forearm. The center of the palm was
aligned with the body midline at the height of the sternum and the elbow was
exed by
approximately 90
. A steel bar at the base of the splint was attached to a 6-axis force
transducer (Delta F/T Sensor, ATI Industrial Automation, Apex, NC, USA) positioned
below the table to record isometric forces and torques. Surface electromyographic (EMG)
69
Table 3.4: Characteristics of Subjects
BAD Scale Score
ID Sex Age L Arm R Arm Arm Tested Diagnosis Symptoms
p1 M 18 3 3 R Hypoxic ischemic injury Severe generalized hyperki-
netic dystonia
p2 F 15 0 1 R Traumatic Brain Injury due to MVA Right hemidystonia
p3 M 20 1 0 L Cerebral palsy Left arm dystonia
p4 M 20 3 3 R Hypoxic ischemic injury Severe generalized hyperki-
netic dystonia
p5 M 16 3 0 L Hypoxic ischemic injury Generalized dystonia
p6 M 13 3 3 L Hypoxic ischemic injury Generalized dystonia
c1 F 17 R
c2 F 21 R
c4 F 20 R
c5 M 14 R
c7 F 19 R
c8 M 13 R
Abbreviations: BAD Scale, Barry-Albright Dystonia Scale; F, female; L Arm, severity of left arm; M, male; R Arm, severity
of right arm. Scores are based on the BAD Scale[3]; for each segment, the score ranges from 0 - absence of dystonia to 4 -
severe dystonia.
activity was recorded from the following eight muscles: pectoralis major, brachioradialis,
biceps, triceps, anterior deltoid, lateral deltoid, posterior deltoid, middle trapezius. EMG
activity was recorded with bipolar electrodes (DE{2.1, Delsys Inc., Boston, MA, USA),
band-pass ltered (20{450 Hz) and amplied (gain 1000, Bagnoli{8, Delsys Inc.). Force and
EMG data were sampled at 1 KHz using an analog-to-digital interface (Power 1401, CED
Technologies Inc., UK) and a custom data acquisition software. EMG was ltered with a 1
Hz, 4th order Butterworth high-pass lter to remove baseline DC voltage, and subsequently
full-wave rectied. Then a non-linear Bayesian lter ( = 1
4
, = 1
18
, 128-bin histogram)
[72] was applied to the rectied signals. Cursor position was proportional to either the actual
force recorded by the transducer (force-control), or the force estimated in real-time from the
recorded and rectied EMGs
Experimental protocol
Subjects performed a 2-D, isometric, center-out speed-accuracy task using myocontrol.
Subjects initially performed two blocks of trials in force-control. In the rst force-control
block, the mean maximum voluntary force (MVF) along four directions (separated by 90
deg) was estimated as the mean of the maximum force magnitude recorded across eight
trials (two for each direction) in which subjects were instructed to generate maximum force
in each direction. In the second force-control block, subjects performed 36 trials to targets
positioned at force magnitudes corresponding to 10, 20, and 30% MVF (random order within
cycles of four directions, three trials per target). After this block, recorded data was processed
to construct the myoelectric controller.
After performing the initial force-control blocks, subjects performed a 2-D isometric center-
70
out speed-accuracy task rst with force control, then with ve blocks of EMG control in an
ABACA design. In blocks A, or the Baseline EMG block, subjects performed EMG control
with a baseline set of parameters. For block B, or the Noisy EMG block, subjects performed
EMG control with parameters adjusted so that the signal contained more noise. For block
C, or the Delayed EMG block, subjects performed EMG control with parameters adjusted
so that the signal had more delay. They performed 10 trials using each condition, reaching
to targets in two directions, upward and medially, two IDs per direction for four targets
total. Targets corresponded to a distance of 15% MVF from the origin with widths 4.31
and 12.18% MVF, resulting in IDs 1.16 and 2.16 bits, and were presented in random order.
Targets were considered successful if subjects maintained the cursor within the target for 0.2
seconds. Subjects performed 40 trials for each condition.
EMG-to-Force Mapping
For non-linear estimation of rewarded force, we model the force as a stochastic dierential
equation using Ito's notation:
dx =dW + (Ux)dN
(3.14)
where dW is the dierential of standard Brownian motion, dN
is the dierential of a
counting process with rate events per unit time, andU is a random variable uniformly dis-
tributed on [{1, 1] to represent normalized positive and negative force. x is the 1-dimensional
state of each force component (x and y) treated independently. In the absence of new obser-
vations, the probability density of state evolves approximately according to the linear partial
dierential Fokker-Planck equation:
@p(x;t)
@t
=
@
2
p(x;t)
@x
2
+
1
2
p(x;t)
(3.15)
where p(x;t) is the pdf of state. This can be written as _ p = Fp, where F is the linear
Fokker-Planck operator on p, and _ p indicates the partial dierential with respect to t.
At every sampling interval, we receive EMG measurements from the 8 dierent channels.
We use these measurements to update our estimation of the state of the system driving the
observations using the Ghoreyshi-Sanger Algorithm [73]:
@p(x;t)
@t
=Fp(x;t) + [logp(emgjx) logp(emg;t)]p(x;t) (3.16)
We assume that each EMG signal is independent, so
71
p(emgjx) =
n muscles
Y
m
p(emg
m
jx) (3.17)
and
p(emg;t) =
X
i
p(emgjx
i
)p(x
i
) (3.18)
Kernel density estimation was used to estimatep(emg
m
jx) from the force calibration block,
where x is the rewarded force.
To modify the eect of noise and delay in the non-linear estimation of force from EMG, we
adjusted the Fokker-Planck equation coecients in the Ghoreyshi-Sanger Algorithm. This
diers from the linear estimation in that we are modifying coecients to the actual force
estimate, rather than the ltered EMG estimate.
Similar to the linear estimation, modifying in
uences the level of noise in the channel,
while modifying in
uences the delay of the estimate. Three dierent pairs of and were
compared: 1) = 1
1
and = 1
5
(Baseline), 2) = 1
1
and = 0 (Delayed) and 3) = 1
and = 1
5
(Noisy).
Analysis
Data analysis was executed with Matlab R2016a (Mathworks, Natick, MA). Statistical anal-
ysis was performed using RStudio, version 0.99.903 (RStudio Inc., Boston, MA), and the
R-package lme4 (version 1.1{12).
EMG vs Force Control One goal of this study was to determine if EMG control had
improved performance compared to force control. To do so, we compared the force block
(Force) with the rst baseline EMG block (Baseline A) and the last baseline EMG block
(Baseline C). We used movement time (MT), success rate, throughput (TP), endpoint error,
and initial angle error as outcome measures. MT was calculated as the time from when the
cursor velocity was greater than 5% peak velocity during the trial to the time once they
successfully stabilized in the target for 0.2 seconds. Trials in which subjects successfully
stabilized in the target for 0.2 seconds were considered successful. For unsuccessful trials,
MT was capped at 7.5 seconds, which was the maximum trial length. This provides a
conservative estimate of what MT would have been had subjects been given an indenite
amount of time to reach the target. TP for each trial was calculated as the ratio between
ID and MT, similar to its calculation in the 1-D case for muscle and synergy selection.
However, in the 2-D case, the distance used to calculate ID was dened as the distance
72
from the cursor position at target presentation to the target center. This accounts for some
trials where subjects were not at the origin during target presentation. Endpoint error was
measured as the distance from the target center to the cursor location at movement end.
Initial angle error was measured as the angular dierence between the vector from cursor
position at movement start to the target center position and the vector from the cursor
position at movement start to the cursor position at the rst velocity peak after movement
start.
Since the design of our experiment had multiple measures, we used linear mixed eects
analysis to express the relationships in our data instead of linear regression analysis, which
requires measurements to be independent. Since success was a binomial measure, we used
a generalized linear model with a logistic regression, however, the model was very similar
to that used for the other outcome measures. All analyses comprised of Block and Group
as xed eects, and intercepts for subjects as a random eect, resulting in the following R
regression model:
DependentvariableBlock +Group + (1jSubject) (3.19)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interactions between the
xed eects, we compared the model that takes into account the interaction between xed
eects (Full) against the model without the interaction (Null). For all comparisons, P values
and Akaike's information criterion values (AIC) were obtained by likelihood ratio tests of the
Full model with the Null model. If the factor in question signicantly aects the dependent
variable, then the comparison will report a signicant P value (< .05) and an AIC value
lower for the Full model. Similarly, a signicant interaction between factors will result in a
signicant dierence between the Full and the Null models (p < 0.05) with a lower AIC for
the Full model. Post-hoc multiple comparisons were performed with Bonferroni correction
to determine dierences between specic blocks within the two participant groups.
Dierences in performance measures within individual subjects were assessed either with
two-sided t-test if the data were distributed normally (according to a Lilliefors test) or by
Wilcoxon ranksum with Bonferroni correction otherwise .
EMG Comparison The second goal of this study was to determine how EMG behavior
changes as a result of perturbations in lter parameters. We analyzed EMG measures from
the ve EMG blocks (Baseline A, Noise, Baseline B, Delay, and Baseline C). We divided the
blocks into two to separate behavior in the rst half of the block from the second half of
73
the block. Then, we compared the rst half of each block to the latter half of the preceding
block to note eects that resulted from changing parameters. As EMG measures, we used
muscle force, onset, and co-contraction within the biceps and triceps, and anterior deltoid
(AD) and posterior deltoid (PD). Muscle force was calculated as the the root mean square of
the rectied EMG from movement start to end for each muscle. Onset was measured as the
rst point in which the rectied EMG was greater than a baseline threshold. To determine
the baseliene threshold, we used the data one-second prior to target appearance. From this
period, we calculated the mean and standard deviation (SD) of the EMG. The baseline
threshold was the sum of the mean and three times the SD. For each pair of antagonist
muscles, co-contraction was calculated as the minimum value of EMG activation between
the two muscles of each time sample, then averaged over the movement.
Similar to the EMG vs Force Control analysis, we used linear mixed eects analysis to
express the relationships in our data. Analyses comprised of Halfblock and Group as a xed
eects, and intercepts for subjects as a random eect, resulting in the following R regression
model:
DependentvariableHalfblock +Group + (1jSubject) (3.20)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interactions between
the xed eects, we compared the model that takes into account the interaction between
xed eects (Full) against the model without the interaction (Null). For all comparisons,
P values and Akaike's information criterion values (AIC) were obtained by likelihood ratio
tests of the Full model with the Null model. Post-hoc multiple comparisons were performed
with Bonferroni correction to determine dierences between specic half-blocks within the
two participant groups.
3.4.3 Results
EMG vs Force Control
Movement Time The likelihood ratio test showed that Block had a signicant eect on MT
(AIC
Full
= 6547.4; AIC
Null
= 6594.1; p < 0.0001). There was a signicant eect for Group
(AIC
Full
= 6547.4; AIC
Null
= 6550.7; p = 0.022). MT for TD children was 1.72 0.67
seconds lower than MT for CP children. There was a signicant eect for the interaction
between Block and Group (AIC
Full
= 6538.6; AIC
Null
= 6547.4; p< 0.0017), suggesting that
changes in MT vary between the two groups. Pairwise comparison showed that there was
74
****
****
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0
1
2
3
4
5
Block
Movement Time (s)
Figure 3.16: MT for children with CP (left) and TD children (right) using nonlinear estima-
tion of force from EMG.
no signicant dierence in MT between any of the blocks for CP children. However, for TD
children, there was a signicant dierence in MT between Force and Baseline A, and Force
and Baseline C. The MT for TD children in Baseline A was 1.55 0.21 seconds higher than
in Force (p < 0.0001). In Baseline C, it was 1.12 0.21 seconds higher than in Force (p <
0.0001).
Analysis of individual subjects showed that MT for Baseline A was signicantly dierent
than MT for Force for three out of six TD children (p = 0.0005, p < 0.0001, p < 0.0001
for subjects c3, c4, and c5). All three of the TD children had increased MT in Baseline A
compared to Force. MT was signicantly dierent in Baseline C compared to Force for one
of six CP children (p = 0.018 for subject p2) and three of six TD children (p < 0.0001, p<
0.0001, p = 0.0065 for subjects c4, c5, and c6). For the CP child, MT was higher in Baseline
C relative to Force. Also, for subjects c4 and c5, MT was higher in Baseline C. Subject
c6 had lower MT in Baseline C compared to Force. Only one TD child showed signicant
dierence in MT for Baseline C compared to Baseline A (p = 0.0059 for subject c6), in which
MT was lower in Baseline C. Results for MT are shown in Figure 3.16.
75
**
**
****
***
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0.0
0.3
0.6
0.9
Block
meanSuccess
Figure 3.17: Success rates for children with CP (left) and TD children (right) using nonlinear
estimation of force from EMG.
Success Rate The likelihood ratio test reported a signicant eect of Block on success rate
(AIC
Full
= 1281.5; AIC
Null
= 1346.3; p < 0.0001). There was also a signicant eect for
Group (AIC
Full
= 1281.5; AIC
Null
= 1284.0; p = 0.035). Children with CP had an odds ratio
of 0.057 compared to TD children. There was a signicant eect for the interaction between
Block and Group (AIC
Full
= 1234.6; AIC
Null
= 1281.5; p < 0.0001). Pairwise comparison
showed a signicant dierence in success rate of Force compared to Baseline A in CP children,
with Force having an odds ratio of 1.9 compared to Baseline A (p = 0.0072). Children with
CP also had an odds ratio of 1.9 for Force relative to Baseline C (p = 0.0073). TD children
had an odds ratio of 143.23 for Force relative to Baseline A (p < 0.0001) and an odds ratio
of 80.63 for Force relative to Baseline C (p = 0.0001). The success rates are shown in Figure
3.17.
Throughput The likelihood ratio test reported a signicant eect for Block on TP (AIC
Full
= 3014.1; AIC
Null
= 3029.5; p < 0.0001). There was also a signicant eect for Group
(AIC
Full
= 3014.1; AIC
Null
= 3019.7; p< 0.0059). TD children had 0.44 0.13 bits/s higher
TP than CP children. There was not a signicant eect for the interaction between Block
and Group (p = 0.86). Pairwise comparison showed that there was a signicant dierence
76
* **
*
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0.0
0.5
1.0
1.5
Block
TP (bit/s)
Figure 3.18: TP for children with CP (left) and TD children (right) using nonlinear estima-
tion of force from EMG
in TP between Force and Baseline A for both subject groups. CP children had 0.16 0.06
bits/s higher TP in Force than Baseline A (p = 0.030). TD children had 0.21 0.06 bits/s
higher TP in Force than Baseline A (p = 0.0024). TD children also had higher TP in Force
compared to Baseline C, by 0.15 0.6 bits/s (p = 0.037)
Analysis of individual subjects showed that TP for Baseline A was signicantly dierent
than TP for Force for two CP children (p = 0.015, p < 0.001 for subjects p1 and p3) and
two TD children (p = 0.0002, p < 0.0001 for subjects c3 and c5). TP for Baseline A was
less than TP for Force for these four subjects. TP was signicantly dierent in Baseline C
than Force for two CP children (p = 0.0024, p = 0.0096 for subjects p3 and p5) and four
TD children (p = 0.0017, p = 0.029, p< 0.0001, and p = 0.0041 for subjects c3, c4, c5, and
c6). All of these subjects, with the exception of subject c6, had lower TP in Baseline C. TP
was signicantly dierent in Baseline C compared to Baseline A for one CP child (p = 0.031
for subject p6) and two TD children (p = 0.046, p = 0.02 for subjects c5 and c6). For all of
these subjects, TP was higher in Baseline C. Results for TP are shown in Figure 3.18.
Endpoint Error The likelihood ratio test reported a signicant eect for Block on endpoint
error (AIC
Full
= {2950.6; AIC
Null
= {2912.2; p < 0.0001). There was also a signicant
77
eect for Group (AIC
Full
= {2950.6; AIC
Null
= {2948.5; p = 0.041). CP children at 5.18
2.32 %MVC more error than TD children. There was not a signicant eect for the
interaction between Block and Group (p = 0.70). Pairwise comparison showed that there
was a signicant dierent in endpoint error between Force and Baseline A, and Force and
Baseline C for both groups. CP children had 3.09 0.78 %MVC less error in Force than
Baseline A (p = 0.0002). They also had 2.09 0.78 %MVC less error in Force than Baseline
C (p = 0.022). Similarly, TD children had 4.00 0.78 %MVC less error in Force than
Baseline A (p< 0.0001). They also had 2.68 0.78 %MVC less error in Force than Baseline
C (p = 0.0018).
Analysis of individual subjects showed that endpoint error for Baseline A was signicantly
dierent than error for Force for three of six CP children (p = 0.0002, p = 0.031, p = 0.022
for subjects p2, p5, and p6) and two of six TD children (p < 0.0001 for subjects c4 and
c5). For all ve subjects, endpoint error was higher in Baseline A compared to Force. For
Baseline C compared to Force, endpoint error was signicantly dierent for three CP children
(p < 0.0001, p = 0.026, p = 0.0046 for subjects p2, p4, and p5) and two TD children (p <
0.0001 for subjects c4 and c5). For all but subject p4, endpoint error was higher in Baseline
C compared to Force. No children showed signicant dierence in endpoint error between
Baseline A and Baseline C. Results for endpoint error are shown in Figure 3.19.
Initial Angle Error The likelihood ratio test reported a signicant eect for Block on initial
angle error (AIC
Full
= 15548; AIC
Null
= 15561; p = 0.0002). There was also a signicant
eect for Group (AIC
Full
= 15548; AIC
Null
= 15561; p = 0.0002). CP children had 12.7
5.9 degrees more initial angle error than TD children. There was not a signicant eect
for the interaction between Block and Group (p = 0.28). Pairwise comparison showed that
there was a signicant dierence in initial angle error between Force and Baseline A, and
Force and Baseline C for TD children. TD children had 13.52 4.85 degrees less initial
angle error in Force compared to Baseline A (p = 0.016). They had 19.37 4.85 degrees
less initial angle error in Force compared to Baseline C (p = 0.0002). CP children did not
show any signicant dierence in initial angle error across blocks.
Analysis of individual subjects showed that initial angle error was signicantly dierent
for subject p3 in Baseline C compared to Force (p = 0.048), in which the subject had higher
initial angle error. Only one TD subject had signicantly dierent initial angle error across
blocks. Subject c5 had higher initial angle error in Baseline A compared to Force (p =
0.0007). Subject c5 had higher initial angle error in Baseline C compared to Force (p <
0.0001). Also, subject c5 had higher initial angle error in Baseline C compared to Baseline
A (p = 0.027). Results for initial angle error are shown in Figure 3.20.
78
***
*
****
**
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0.00
0.05
0.10
0.15
Block
Endpoint Error (%MVC)
Figure 3.19: Endpoint error for children with CP (left) and TD children (right) using non-
linear estimation of force from EMG.
79
*
***
CP TD
Force Baseline A Baseline C Force Baseline A Baseline C
0
25
50
75
Block
Initial Angle Error (deg)
Figure 3.20: Initial angle error for children with CP (left) and TD children (right) using
nonlinear estimation of force from EMG.
80
**
0.00
0.01
0.02
0.03
0.04
Noise-2 Baseline B-1
Block
Muscle Force (mV)
Figure 3.21: Change in muscle force for TD children in Baseline B following the Noise block.
Changes in EMG
Muscle Force The likelihood ratio test reported a slight signicant eect of Halfblock on
muscle force (AIC
Full
= {44759; AIC
Null
= {44762; p = 0.084). There was not a signicant
eect for Group (p = 0.11). There was a slight signicant eect for the interaction between
Halfblock and Group (AIC
Full
= {44756; AIC
Null
= {44759; p = 0.10). Children with CP had
no signicant changes in muscle force across blocks. However, TD children had 0.011 0.003
mV higher muscle force in Baseline B following the Noise block (p = 0.0048) (Figure 3.21).
Onset Time The likelihood ratio test showed a slight signicant eect of Halfblock on
EMG onset (AIC
Full
= 73699; AIC
Null
= 73697; p = 0.068). There was a signicant eect
for Group on onset (AIC
Full
= 73699; AIC
Null
= 73701; p = 0.032). Onset for children with
CP was 0.43 0.18 s slower than for TD children. There was also a signicant eect for
the interaction between Halfblock and Group on onset (AIC
Full
= 73692; AIC
Null
= 73699;
p = 0.0034). Children with CP had slightly faster onset in the Noise block following Baseline
A by 0.17 0.08 s (p = 0.067) (Figure 3.22). TD children showed no signicant changes in
onset across blocks.
Co-contraction The likelihood ratio test showed that Halfblock had a signicant eect on
AD/PD co-contraction (AIC
Full
= {6700.3; AIC
Null
= {6686.3; p = 0.0002). There was not
a signicant eect for Group (p = 0.45). There was a signicant eect for the interaction
between Halfblock and Group on AD/PD co-contraction (AIC
Full
= {6702.7; AIC
Null
= {
81
†
0.0
0.5
1.0
1.5
Baseline A-2 Noise-1
Block
EMG Onset (s)
Figure 3.22: Change in EMG onset for CP children in the Noise block following Baseline A.
6700.3; p = 0.015). Children with CP had decreased AD/PD co-contraction in the Delay
block after Baseline B by 0.029 0.008 (p = 0.0005) (Figure 3.23). TD children had
increased AD/PD co-contraction in the Noise block after Baseline A by 0.019 0.008 (p =
0.047) (Figure 3.24).
Likelihood ratio tests for co-contraction between biceps and triceps showed similar results.
The likelihood ratio test showed that Halfblock had a signicant eect on biceps/triceps
co-contraction (AIC
Full
= {7376.5; AIC
Null
= {7377.0; p = 0.042). There was no signicant
eect for Group (p = 0.30). There was a signicant eect for the interaction between
Halfblock and Group (AIC
Full
= {7384.2; AIC
Null
= {7376.5; p = 0.0023). TD children
have increased co-contraction in the Noise block following Baseline A by 0.020 pm 0.007
(p = 0.0078) (Figure 3.25. Children with CP show no signicant changes in co-contraction
between biceps and triceps across blocks.
3.4.4 Discussion: Non-linear Estimation Does Not Improve
Performance but Subjects Respond to Parameter Changes
Similar to the previous experiment, in this experiment we wanted to 1) determine if this
method to estimate rewarded force resulted in better performance under EMG control when
compared to force control and 2) explore how EMG behavior changes in response to changed
myocontrol parameters.
As in the previous experiment, we compared the force control block with the rst and
last baseline EMG blocks. Children with CP did not show signicant improvement in MT
82
***
0.000
0.025
0.050
0.075
0.100
Baseline B-2 Delay-1
Block
Co-contraction AD/PD
Figure 3.23: Changes in co-contraction between AD and PD for children with CP in the
Delay block following Baseline B.
*
0.000
0.025
0.050
0.075
0.100
Baseline A-2 Noise-1
Block
Co-contraction AD/PD
Figure 3.24: Changes in co-contraction between AD and PD for TD children in the Noise
block following Baseline A.
83
**
0.000
0.025
0.050
0.075
0.100
Baseline A-2 Noise-1
Block
Co-contraction Biceps/Triceps
Figure 3.25: Changes in co-contraction between biceps and triceps for TD children in the
Noise block following Baseline A.
or initial angle error. They had lower success and TP with EMG control. The only out-
come measure to show improvement in children with CP using EMG control was endpoint
error. TD children performed worse with EMG control, having higher MT, lower success
rate, lower TP, higher endpoint error, and higher initial angle error. These results suggest
that subjects from both groups had a more dicult time using this method compared to the
linear estimation method detailed in the previous experiment. Much of the diculty that
subjects experienced is likely a result of the underlying assumption in this method that each
EMG channel is independent. The linear estimation method considers interactions between
channels when optimizing coecients to estimate force from EMG. For the non-linear es-
timation, we chose to assume EMG parameters were independent in order to simplify the
computation, but our results make it evident that considering interactions between channels
plays a signicant role in facilitating myocontrol.
Although subjects in general struggled more with this method of myocontrol, we still
observed some changes in EMG in response to changing myocontrol parameters. Patients
showed faster EMG onset in the Noise block. They also showed decreased co-contraction
between the AD and PD in the Delay block. TD children showed increased muscle force in
Baseline B following the Noise block. They also showed increased co-contraction between
both the AD and PD, and biceps and triceps in the Noise block. The increased co-contraction
may be an indicator of subjects trying to better stabilize the cursor. Similar to the previous
experiment, more work is necessary to determine which of these observed changes actually
represents learned eects, and whether there exists a trend in EMG changes that follows a
84
trend in changes to the lter.
85
3.5 Experiment 4: DOF-wise NMF for 3D myocontrol
3.5.1 Introduction
In order for children with CP to interact with the environment, we ultimately want to
implement 3D control. Thus far, we have used supervised estimation techniques in order to
calibrate multi-muscle EMG and interface with the task space. We know from our attempt to
select most controllable muscles or synergies that incorporating more muscles and synergies is
actually better for EMG control. Thus, expanding these methods to 3D control would likely
require additional EMG channels for adequate control. An algorithm for 3D myocontrol was
proposed using DOF-wise nonnegative matrix factorization (NMF) [41]. DOF-wise NMF
is an appealing solution because it does not require additional EMG channels, and it does
not require the use of a torque sensor. It was also shown to improve myocontrol compared
to single muscle control in 2D control of a robot for children with dystonia [52]. We tested
DOF-wise NMF in 3D control of a robot in healthy adults and children with CP.
3.5.2 Methods
Participants
Nine healthy adult subjects between 21 and 28 years old (5 males, 4 females; mean = 25 years
old; standard deviation = 4 years) and two children with CP (2 males, ages 13 and 21) were
recruited. Inclusion criteria for the patients in this study were: (I) CP or dystonia aecting at
least one upper extremity; (II) pediatric age (7{21 years); (III) no cognitive impairment that
prevents understanding of instructions. The University of Southern California Institutional
Review Board approved the study protocol. All parents gave informed written consent
for participation and all children gave written assent. Authorization for use of protected
health information was signed in accordance with the Health Information Portability and
Accountability Act. The study was performed in accordance with the Declaration of Helsinki.
Experimental setup
Subjects sat in a chair in front of a robot (Phantom Omni, Sensable Technologies Inc.) with
their dominant (adults) or more aected (patients) arm strapped to the armrest at the wrist
and elbow for isometric conditions. They held a handle secured to the armrest against which
they could push and pull. Surface electromyographic (EMG) activity was recorded from the
following eight muscles: anconeus, brachioradialis, biceps, triceps, anterior deltoid, lateral
deltoid, posterior deltoid,
exor carpi ulnaris. EMG activity was recorded with bipolar
86
electrodes (DE{2.1, Delsys Inc., Boston, MA, USA), band-pass ltered (20{450 Hz) and
amplied (gain 1000, Bagnoli{8, Delsys Inc.). EMG data were sampled at 1 KHz using
an analog-to-digital interface (Power 1401, CED Technologies Inc., UK) and a custom data
acquisition software. EMG was ltered with a 1 Hz, 4th order Butterworth high-pass lter
to remove baseline DC voltage, and subsequently full-wave rectied. Then a non-linear
Bayesian lter ( = 1
4
, = 1
18
, 128-bin histogram) [72] was applied to the rectied
signals.
The task interface was created through two programs that communicated via UDP protocol
(Visual Studio 6.0, Microsoft, Redmond, WA, USA). The rst program was designed to
receive EMG signals from the eight musces and scale those values to corresponding values
in the robot's coordinate space. These values were sent via UDP to a program on a dierent
computer where the robot's current position was read in, and the force needed to move the
robot to the new position was calculated.
Experimental protocol
The healthy adult subjects performed two tasks using two dierent control conditions: 1)
Force control and 2) Position control. With force control, EMG activation dictated the force
applied to the robot endpoint. With position control, EMG activation dictated the desired
position of the robot endpoint from the origin, and the software calculated the necessary
force to get to the desired position. Five subjects performed the experiment beginning with
force control. Four subjects performed the experiment beginning with position control.
Subjects rst performed a trial to obtain maximum voluntary contraction (MVC) values.
Subjects pushed in six directions (right, left, forward, backward, up, and down), three times
in each direction. MVC for each EMG channel was the maximum mean EMG activation
measured over a 200 ms window during this trial. Then, subjects performed a calibration
trial, aimed at recording data to extract oine subject-specic synergies. Next, they were
given a minute to practice controlling the robot with their designated control condition.
Subjects then performed a discrete task followed by a continuous task. The discrete task
used a Fitts' paradigm [33] with four pairs of rectangular targets of varying distances (10.16
cm or 15.24 cm) from one another and widths (2.54 cm or 5.08 cm) . Subjects began with
the robot endpoint at the midpoint of the two targets and were instructed to tap between
the two targets as quickly as possible within a 60s period. Targets were presented in random
order. For the continuous task, subjects attempted to trace a gure 8 as many times as
possible within four minutes. The gure 8 was 15.24 cm by 7.62 cm. Subjects were then
given a minute of practice with the second control condition and repeated the discrete and
continuous task with the opposite condition from which they started.
87
The two patients only attempted to trace a gure 8 using position control of the robot.
Calibration
Subjects were instructed to push the handle in six directions (right, left, forward, backward,
up, and down), ve times in each direction. The goal was to have subjects push in positive
and negative directions of the 3 DOFs of a Cartesian coordinate system. The EMG signals
acquired during this calibration phase were recorded and factorized by applying a DOF-wise
NMF to extract the subject-specic synergy matrix. This modied version of NMF has
been proposed for the application of myocontrol [41]. It models each DOF as driven by two
activation signals, one for each direction of articulation. By applying the NMF algorithm to
the single-DOF EMG signals recorded during the calibration phase, it is possible to extract
two synergies for each DOF separately and associate each synergy to positive or negative
directions of that DOF. The DOF-wise algorithm applied separately to EMG data from each
of the three DOF yields a six-column subject-specic synergy matrix S:
S = [S
+
1
;S
1
;S
+
2
;S
2
;S
+
3
;S
3
] (3.21)
The EMG signals acquired during the calibration phase were also used to compute mul-
tiplicative factors utilized in the online phase to match the relative magnitude of motion
between the user and the robot. For each DOF, two activation coecients were computed
by solving a nonnegative least-squares constraint problem (Matlab function `lsqnonneg').
Then, y
i
was computed as the dierence between the two activation coecients related to
the ith DOF:
y
i
(t) =a
+
i
(t)a
i
(t) (3.22)
The maximum (y
+
) and minimum (y
) values ofy were used to computeG
+
syn
i
andG
syn
i
:
G
+
syn
i
=
MAX
y
+
(3.23)
G
syn
i
=
MAX
y
(3.24)
where
MAX
was known a priori as the position or force to be sent to the robot's single
DOF in order to move the DOF from a neutral zero position to the max force or position.
The multiplicative factor G
syn
i
was then computed as the mean between G
+
syn
i
and G
syn
i
.
88
(a) (b)
Figure 3.26: (a) Example of synergies extracted from DOF-wise NMF as well as (b) example
activation coecients for one pair of DOF synergies. The activation for the
resulting DOF is then calculated as the dierence in activation of the negative
and positive components.
Synergy-based control
For online control, we assumed that a system with three DOF was driven by six activation
signals:
X(t) = [S
+
1
;S
1
;S
+
2
;S
2
;S
+
3
;S
3
][a
+
1
;a
1
;a
+
2
;a
2
;a
+
3
;a
3
]
T
(3.25)
At each time instant, given the online non-linear envelopes of the EMG signals (X(t)) and
the subject-specicS matrix, the algorithm extracted the six activation signals (a
+
1
;a
1
;a
+
2
;a
2
;a
+
3
;a
3
)
used for online simultaneous control of the three DOFs of the robot. In particular, our ap-
proach modeled the ith DOF as driven by the dierence between two activation signals
related to the DOF, scaled by the multiplicative factor G
syn
i
:
i
(t) =G
syn
i
a
+
i
(t)a
i
(t)
(3.26)
Example synergies extracted from DOF-wise NMF are shown in Figure 3.26.
Analysis
For the discrete task, the number of hits per target was counted as an indicator for per-
formance. Also, the movement time (MT) to reach the target for each hit was calculated.
Performance was analyzed by measuring overall movement time aggregated over all targets.
A decrease in overall movement time signied better performance.
89
To determine xed eects signicance on MT, the linear mixed eects analysis comprised
ID, and myocontrol Mode as xed eects, and intercepts for each subject as a random eect.
DependentvariableID +Mode + (1jSubject) (3.27)
Once the models were created, we compared the model including all the factors (Full)
against a reduced model without the eect in question (Null) in order to test if the xed
eects signicantly aected the dependent variable. In order to test interactions between
the xed eects, we compared the model that takes into account the interaction between
xed eects (Full) against the model without the interaction (Null). For all comparisons,
P values and Akaike's information criterion values (AIC) were obtained by likelihood ratio
tests of the Full model with the Null model. If the factor in question signicantly aects
the dependent variable, then the comparison will report a signicant P value (< .05) and
an AIC value lower for the Full model. Similarly, a signicant interaction between factors
will result in a signicant dierence between the Full and the Null models (p < 0.05) with
a lower AIC for the Full model.
To assess performance in the continuous task, we analyzed the kinematics in the frequency
domain. The Fourier transform (FT) of the robot kinematics data was computed. Then the
power spectral density (PSD) was computed based on the FT coecients. In the gure-
eight, the horizontal (f
x
) and vertical (f
y
) frequency components are expected to be in a
ratio of 2:1 ((f
x
= 2f
y
)). As a result, the Y
robot
PSD should present a peak at the frequency
related to the mean duration of the gure-eight movement (f
y
), while theX
robot
PSD should
show a peak at double the gure-eight frequency (f
x
). We determined the peak frequency
associated withX
robot
andY
robot
and calculated the ratio between the two. We assumed that
ratios closer to two indicated better performance for the gure-eight task, so we calculated
the dierence between the resulting ratios and 2.
Data analysis was executed with Matlab R2016a (Mathworks, Natick, MA). Statistical
analysis was performed using RStudio, version 0.99.903 (RStudio Inc., Boston, MA), and
the R-package lme4 (version 1.1{12).
3.5.3 Results
Discrete Task
There was no signicant dierence in performance as a result of the control mode that
subjects used rst (p = 0.40). Though not a signicant dierence, subjects had more target
hits using position control compared to force control (57 22 hits using position control; 50
13 hits using force control). Target ID did not have a signicant eect on MT (p = 0.45),
90
†
2
4
6
8
Force Position
Mode
Movement Time (s)
Figure 3.27: MT of force and position control of a robot to perform a discrete tapping task.
(a) (b)
Figure 3.28: (a) Example of the Figure 8 trajectories and (b) associated PSDs.
indicating this task did not enforce a speed-accuracy tradeo. There was a slight signicant
eect on MT as a result of the Mode of control (AIC
Full
= 5458.8; AIC
Null
= 5460.0; p =
0.075). MT using force control was estimated to be 0.47 0.26 seconds longer than MT
with position control. There was no signicant eect on MT due to the interaction between
ID and Mode (p = 0.94) Results for MT in the discrete task are shown in Figure 3.27.
Continuous Task
In general, subjects struggled with the continuous task using both modes of control. Figure
3.28 illustrates trajectories of the Figure 8 task from one of the more skilled subjects, as well
as the PSDs corresponding to the horizontal and vertical movement components.
91
†
0.0
0.5
1.0
1.5
2.0
Force Position
Mode
Frequency Ratio Difference from 2
Figure 3.29: Comparison of the dierence in the ratio of peak x and y frequency components
and the expected ratio of 2 using force and position control.
The ratio of frequency components was closer to 2 with position control compared to force
control. Additionally, the dierence between the ratio and 2 was signicantly smaller with
position control than with force control (p = 0.05). This suggests that subjects were able to
maintain smoother and more continuous control to draw the Figure 8 using position control.
Results are shown in Figure 3.29.
Patient Performance
Both patients struggled to perform 3D myocontrol of the robot, although they used position
control, which was shown by the healthy adults to be the easier of the two modes to control.
This is most likely a result of poor calibration. Figure 3.30 illustrates the synergies extracted
from a patient using DOF-wise NMF and the corresponding activation coecients from
calibration. The activation coecients should show clear dierences between the positive and
negative components, as was seen in Figure 3.26, however, here we see no clear distinction.
Without the ability to discern between positive and negative components, we are unable to
accurately estimate movement intent.
3.5.4 Discussion: Position Control is More Intuitive, but Cartesian
Coordinate System Not Ideal for Patients
In this experiment, we tested the implementation of DOF-wise NMF for 3D control of a
robot. We also tested whether force or position control is easier for subjects using two
dierent tasks: a discrete tapping task and a continuous drawing task. We found that
healthy adults were able to complete more hits to targets in the discrete task using position
92
(a) (b)
Figure 3.30: (a) Example of synergies extracted from a patient using DOF-wise NMF and
(b) corresponding activation coecients during calibration.
control, and on average they had a faster MT between targets using position control. While
subjects generally struggled to draw the Figure 8 with both control methods, frequency
analysis suggests that it was easier using position control, as they were able to maintain
a frequency ratio closer to the expected ratio when drawing smooth Figure 8s. Results in
healthy subjects overall suggested that position control is more intuitive and results in better
performance compared to force control.
We tested DOF-wise NMF using position control with two patients, however, the patients
struggled to control the robot. This appears to result from the diculty of obtaining a
clean calibration between EMG and movement direction. Our results dier from what was
observed by Lunardini et. al [52], who managed to successfully implement DOF-wise NMF
control for children with dystonia. There are, however, some notable dierences between
their implementation and ours. First, they implemented 2D control, whereas ours was 3D.
Second, they dened DOFs dierently than we did. For their experiment, each DOF was
dened by a joint movement - movement at the elbow was one DOF and movement at the
shoulder was another. In our implementation, we used DOFs as dened by the Cartesian
coordinate system. Our results suggest that DOF-wise NMF would be more successful for
children with CP when implemented in a manner in which negative and positive components
of DOFs can be clearly determined (i.e. joint movements).
93
3.6 Chapter Conclusions
In this chapter, we explored dierent ways to interface multiple EMG channels to 2D and 3D
task spaces. In the rst experiment, we attempted to select the most controllable muscles
or synergies assessed using Fitts' Law. This resulted in no or worse improvement in my-
ocontrol performance compared to using optimal estimation from all muscles. In the second
experiment, rather than estimating force as measured from the torque sensor, we estimated
rewarded force as dened by the given target direction. Here, we observed that patients were
able to improve their performance with practice. TD children did not show improvements
using EMG control, however, that is not unexpected as they are already capable of excellent
force control, and EMG control may actually be more dicult for them because they must
focus their attention on a new medium of control that is less natural for them. Next, we
implemented a non-linear estimation of rewarded force. Neither patients nor TD children
showed clear improvements in performance using EMG control with this method compared
to force control. This is likely due to the assumption in the implementation that EMG
channels behave independently. Finally, we implemented 3D myocontrol using DOF-wise
NMF. From this experiment, we learned that subjects perform better with position control
rather than force control. However, patients struggled to control the robot, likely as a result
of the inability to discern negative and positive components for each DOF. In summary,
multi-muscle myocontrol is better when estimating rewarded force and when interactions
between EMG channels are considered. To expand this work to 3D, more EMG channels
may be required if using the supervised method of estimating rewarded force. Otherwise,
if using DOF-wise NMF, it may be better to estimate DOF movements using joint motions
rather than the Cartesian coordinate system.
In Experiments 2 and 3, we also investigated how subjects change EMG behavior when
myocontrol parameters change. In general, we did observe changes to EMG in response to
parameters changes, however, future work is necessary to gain a better understanding of the
meaning behind these changes. These results suggest that there is a use for myocontrol as a
rehabilitative tool that could potentially be used train desired EMG patterns.
94
4 Overall Conclusions and Future Work
This project highlights the early work in making myocontrol possible for children with CP.
These are the rst steps to optimize the myocontrol pipeline that will make it possible for
children with CP to control a virtual body - a prosthetic device that is capable of performing
the movements that the child struggles to perform with their own limbs.
We began optimizing the myocontrol pipeline at the level of a single EMG channel. We
compared the use of a non-linear Bayesian lter and the standard linear lter for online
EMG control in 1D. Our work validated the use of Bayesian ltering for better performance.
We also established appropriate target parameters to optimize controllability.
Next, we optimized the interface between multiple EMG channels and 2D and 3D spaces.
From this series of experiments, we learned that selecting the most controllable muscles or
synergies is insucient to improve control. Additionally, we cannot assume independence
between EMG channels. We must calibrate using multiple muscles and consider the inter-
action between muscles. Also, if not using a supervised method for calibration, but rather
a semi-supervised method, we must use a coordinate system in which negative and positive
components for each DOF are easily distinguishable. Assessing DOFs at each joint rather
than using a Cartesian coordinate system appears to be a better implementation [52]. Addi-
tional work is needed to optimize myocontrol applications for 3D control, particularly as we
begin to visualize the devices to be myocontrolled. Developing prosthetics for children with
CP such as exoskeletons will not only require 3D control, but will also require non-isometric
control.
In addition to engineering a myocontrol solution for children with CP, these experiments
have provided insight into the movement disorder as well. In testing whether muscle or
synergy selection improves EMG control, we learned that noise in CP is not conned to a
low-dimensional subspace, but rather appears to be high-dimensional. Thus, rather than
focusing on changing spatial structures within children with CP, myocontrol applications
should focus on temporal activations of muscles or synergies. Indeed, our exploration into
EMG changes in response to myocontrol parameter changes suggests that myocontrol itself
may be used to in
uence EMG activation within subjects.
Ultimately, this work highlights multiple uses for myocontrol that may either be used
95
together or separately. One use, which this project began with, is as a lter. In this case, we
identify the driving signal from noisy EMG and the prosthetic device replicates that driving
signal. The goal here is to implement a myocontrol system that feels natural to the user,
to the point that they do not even notice they are using myocontrol [4]. A second use is
biofeedback, providing the user with additional information of their biological signals. Lastly,
myocontrol can be used as a tool. Dierent parameters or mappings within the myocontrol
system may require subjects to learn how to use the system, and can aect how the subject
uses the system. In other words, the design of the myocontrol system can in
uence resulting
EMG patterns from the user. Distinguishing between these dierent uses for myocontrol aids
in the design of future myocontrol applications. In particular, future work may explore the
potential for utilizing the interaction between human and machine, whether the purpose is
to train EMG patterns within human patients or healthy subjects, or make machines more
autonomous in human tasks.
96
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Abstract (if available)
Abstract
For children with movement disorders due to cerebral palsy (CP), prosthetic devices can provide mobility, manipulation, and functional communication. However, the goals of prosthetic control in children with impairments need to be different from those in adults. Children need flexible interfaces whose motions are not described in advance, so they can develop their own movements and explore varying and unpredictable goals. Multi-muscle electromyographic control (“myocontrol”) may accomplish this, however, we must facilitate the controllability of myocontrol by providing the appropriate interface. This paper details the work done in efforts to make myocontrol possible for children with CP. ❧ The first studies focused on establishing initial appropriate design parameters within single channel EMG. We compared the speed-accuracy tradeoff between linear and Bayesian EMG filtering algorithms in a Fitts’ Law task. From this study, we established that Bayesian filtered EMG has higher throughput, and so this is used for subsequent studies. Next, we looked at how the speed-accuracy tradeoff changes with different levels of EMG activation. This helped us design subsequent experiments with target activations that minimize fatigue in subjects but also reduce noise at low-level activations. ❧ We then looked at ways to interface multiple channels of EMG to 2D or 3D task spaces. We first considered selecting the most controllable muscles and synergies using Fitts’ Law. These most controllable synergies (Select Synergy) and muscles (Select Muscle) were then compared with All EMG control in a 2-D myocontrol task. Results showed that Select Synergy and Select Muscle conditions did not improve myocontrol among patients. We then considered mapping EMG to rewarded force, rather than measured force. We tested two methods to map EMG to rewarded force in 2-D: using multiple regression (linear estimation) and the Ghoreyshi-Sanger Algorithm (non-linear estimation). We found that patients were able to improve performance with linear estimation of EMG, but not with non-linear estimation. Finally, we considered a DOF-wise semi-supervised approach to implement multi-muscle myocontrol in 3D. Using DOF-wise NMF, we compared force and position control of a robotic arm within healthy subjects. Subjects performed a discrete task and continuous task using force and position control. Results showed that for both tasks, subjects performed better with position control. However, when implementing 3-D position control with patients, patients were unable to control the robot, likely due to poor calibration. ❧ In addition to optimizing the myocontrol pipeline for children with CP, we investigated the use of myocontrol as a tool. In the above, the goal of myocontrol is to interpret the user’s intent and mimic it, requiring minimal learning from the user. However, another use of myocontrol is mapping muscles onto a different set of forces or movements. In this case, the myocontrol will appear to the user like a tool that must be learned. When learning to use a tool, users modify their muscle activity, so it’s important to look at the interaction between the human and myocontroller, as this may be useful for rehabilitation. We tested this interaction by modifying parameters within the linear and non-linear estimations of rewarded force and observed whether subjects changed EMG patterns. Resulting changes in EMG suggest that there is a use for myocontrol beyond simply estimating movement intent from EMG. Indeed, we identify three potential uses for myocontrol: 1) a filter to identify driving signals for control, 2) as biofeedback, and 3) a tool that can influence user behavior. This work aids in the design of future myocontrol applications not only for children with CP, but also for other patient populations and healthy subjects.
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Creator
Borish, Cassie Nguyen
(author)
Core Title
Facilitating myocontrol for children with cerebral palsy
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
07/27/2018
Defense Date
04/23/2018
Publisher
University of Southern California
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Tag
cerebral palsy,Children,electromyography,Fitts' Law,movement disorders,myocontrol,OAI-PMH Harvest
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Sanger, Terence (
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), Schweighofer, Nicolas (
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), Valero-Cuevas, Francisco (
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cassieborish@gmail.com,cassieng@usc.edu
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Tags
cerebral palsy
electromyography
Fitts' Law
movement disorders
myocontrol