MYOELECTRIC PROSTHESES : NOVEL METHODOLOGIES FOR ENHANCING

USABILITY AND CONTROL

A Dissertation Submitted

to the Graduate School

University of Arkansas at Little Rock

in partial fulfillment of requirements

for the degree of

DOCTOR OF PHILOSOPHY

in Engineering Science and Systems

in the Department of Systems Engineering

of the Donaghey College of Engineering and Information Technology

May 2014

Ghulam Rasool

B.E., National University of Sciences and Technology, Pakistan, 1999

M.Sc., Center for Advanced Studies in Engineering, Pakistan, 2010

Copyright by

Ghulam Rasool

2014

This dissertation, ``Myoelectric Prostheses : Novel Methodologies for Enhancing Usability and

Control,'' by Ghulam Rasool, is approved by:

Dissertation Advisor: Kamran Iqbal

Professor of Systems Engineering

Dissertation Committee: Andrew Wright

Associate Professor of Systems Engineering

Cang Ye

Associate Professor of Systems Engineering

Keith Bush

Assistant Professor of Computer Science

Gannon White

Assistant Professor of Health, Human Performance, and SportManagement

Nidhal Bouaynaya

Assistant Professor of Electrical Engineering, Rowan University

Program Coordinator: Yupo Chan

Professor of Systems Engineering

Interim Graduate Dean: Paula J. Casey

Professor of Law

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revised in 1976). Consistent with fair use as defined in the Copyright Laws, brief quotations from

this material are allowed with proper acknowledgement. Use of this material for financial gain

without the author's express written permission is not allowed.

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the University of Arkansas at Little Rock to arrange for duplication of this dissertation for

educational or scholarly purposes when so requested by a library user. The duplication will be at

the user's expense.

MYOELECTRIC PROSTHESES : NOVEL METHODOLOGIES FOR ENHANCING

USABILITY AND CONTROL by Ghulam Rasool, May 2014

ABSTRACT

Control of powered prostheses using the information from leftover muscles in amputees is a

challenging problem. I investigated the problem with a view to find clinically reliable and robust

schemes that can interpret human intent and control a powered prosthesis in real-time. Recently,

pattern classification systems have been suggested to map muscle activation patterns to the

human intent (or the movement). However, due to the underlying generic structure,

system-specific information cannot be exclusively incorporated into pattern classification

algorithms. I have proposed two new methodologies in my research. The first one extended the

pattern classification with a new feature set comprised of autoregressive-autoregressive

generalized conditional heteroscedastic (AR-GARCH) coefficients, that outperformed the

conventional feature set (p < .01). The second methodology addressed the problem by suggesting

a novel physiologically-relevant mathematical model. The hypothesis of muscle synergies was

employed to formulate a state-space representation of the neural signals. The proposed model is

based on the assumption that the neural drive originating from the central nervous system (CNS)

and terminating at the peripheral muscles contains task-specific information. Therefore, the

neural drive was estimated accurately using a recursive Bayesian technique. Later, the estimated

neural drive and task-specific muscle synergies were used to identify the intended/performed task.

Detailed performance analysis was performed in off-line as well as real-time using a virtual

prosthesis. The proposed scheme outperformed the pattern classification systems in off-line

accuracy (p < .001) and real-time controllability (p < .01).

ACKNOWLEDGEMENTS

I would never have been able to finish my dissertation without the guidance of my committee

members, help from friends, and support from my family and wife.

I would like to express my deepest gratitude to my advisor, Dr. Kamran Iqbal, for his excellent

guidance, caring, patience, and providing me with an excellent atmosphere for doing research.

It is with immense gratitude that I acknowledge the support and help of Dr. Nidhal Bouaynaya

in all matters related to research and beyond, especially correcting my writings patiently and

financially supporting my research. I would like thank Dr. Gannon White and the Chair of

department of Health, Human Performance, and Sport Management, Dr. Donna Quimby, for

letting me use the Human Performance lab for my research and data collections. Special thanks

goes to Dr. Andrew Wright, who was willing to participate in my final defense committee at the

last moment.

I would like to thank the Dean of College of Engineering and Information Technology, Dr.

Eric Sandgren for providing a handsome amount to purchase equipment for my research. I would

also like to thank the Associate Dean College of Engineering and Information Technology, Dr.

Abhijit Bhattacharyya for valuable advices and financial support.

I am indebted to my parents and family for assisting me in my all endeavors. Special thank

goes to my father, mother, brothers, sisters and especially my wife for patience, help and support.

PROTOCOL APPROVAL STATEMENT

Name of project : Human Movement Analysis for Myoelectric Controlled Prostheses.

Committee Name : Ghulam Rasool and Kamran Iqbal

Approval date : 12 February, 2013

Protocol number : 13-144

Approved By : Dr. Elisabeth Sherwin, IRB Chair, UALR

Name of project : Human Movement Analysis for Myoelectric Controlled Prostheses.

Committee Name : Ghulam Rasool and Gannon White

Approval date : 14 January, 2014

Protocol number : 13-144 C1

Approved By : Dr. Elisabeth Sherwin, IRB Chair, UALR

MEMORANDUM TO: Ghulam Rasool, Dr. Kamran Iqbal (EIT) CC: Rhiannon Morgan, Research Compliance Officer FROM: Dr. Elisabeth Sherwin, IRB Chair UALR Institutional Review Board DATE: February 12, 2013

RE: IRB Request for Exemption

Thank you for your recent Institutional Review Board Request for Exemption (Protocol # 13-144) titled Human Movement Analysis for Myoelectric Controlled Prostheses. We have reviewed this request and find that it meets the IRBs criteria for protection of human participants. Your project has IRB approval from today until 2/11/14 and you are free to proceed with data collection. After this date, all interaction with human subjects and data collection for this project must cease. Continuations If you would like this study to continue unchanged for more than one year, you will need to submit a Request for Continuing Review 4 weeks prior to the above expiration date. Expired protocols will not be granted a continuation or extension by the IRB. Please note that if your original protocol was approved by review at a convened meeting, then your request for continuation or annual review must follow the same process. Modifications to Approved Research It is the responsibility of the PI (Principal Investigator) to notify the IRB if substantive changes to the research are desired. This would include, but is not limited to: modifications to recruitment strategies, the addition of new personnel

to the study, changes in target population, or data collection methods. Any and all changes to the study must be reviewed and approved by the IRB prior to implementation. Please submit a Request for Modification/Amendment form if you wish to modify your research. Changes implemented without IRB approval are in violation of 45 CFR 46 and UALR institutional policy. Adverse Event Reporting Principle Investigators are required to report unanticipated problems or adverse events involving human subjects to the IRB promptly. If you have an event to report, please document the incident and call the UALR Research Compliance Officer, Rhiannon Morgan, at (501) 569-8657. For regulatory guidance and definitions on adverse events and reporting timelines, please see the link below. http://www.hhs.gov/ohrp/policy/advevntguid.html

MEMORANDUM TO: Ghulam Rasool/Dr. Gannon White CC: Rhiannon Gschwend, Research Compliance Officer FROM: Dr. Elisabeth Sherwin, IRB Chair UALR Institutional Review Board DATE: January 14, 2014

RE: IRB Request for Continuation

Thank you for your recent Institutional Review Board Request for Continuation (Protocol # 13-144 C1) titled Human Movement Analysis for Myoelectric Controlled Prostheses. We have reviewed this request and find that it meets the IRBs criteria for protection of human participants. Your project has IRB approval from today until 1/13/15 and you are free to proceed with data collection. After this date, all interaction with human subjects and data collection for this project must cease. Continuations If you would like this study to continue unchanged for more than one year, you will need to submit a Request for Continuing Review 4 weeks prior to the above expiration date. Expired protocols will not be granted a continuation or extension by the IRB. Please note that if your original protocol was approved by review at a convened meeting, then your request for continuation or annual review must follow the same process. Modifications to Approved Research It is the responsibility of the PI (Principal Investigator) to notify the IRB if substantive changes to the research are desired. This would include, but is not limited to: modifications to recruitment strategies, the addition of new personnel

to the study, changes in target population, or data collection methods. Any and all changes to the study must be reviewed and approved by the IRB prior to implementation. Please submit a Request for Modification/Amendment form if you wish to modify your research. Changes implemented without IRB approval are in violation of 45 CFR 46 and UALR institutional policy. Data Storage and Retention Federal regulations require researchers to store data from human subject research in a secure manner for a period of three years after completion. All data, whether in electronic or paper format, must be maintained on the UALR campus and made accessible to the IRB, Compliance Office or other auditors as needed. The requirement applies to all consent and assent forms, receipts of incentives paid to subjects, and related documents. You are also required to maintain documentation of your IRB approval and all applicable ethics training. For questions about data storage and retention, please contact the Research Compliance Office. Adverse Event Reporting Principle Investigators are required to report unanticipated problems or adverse events involving human subjects to the IRB promptly. If you have an event to report, please document the incident and call the UALR Research Compliance Officer, Rhiannon Morgan, at (501) 569-8657. For regulatory guidance and definitions on adverse events and reporting timelines, please see the link below. http://www.hhs.gov/ohrp/policy/advevntguid.html

Table of Contents

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Myoelectric Signal Classification Using the AR-GARCH Model . 5

1.4.2 Task Discrimination Using the Hypothesis of Muscle Synergies . 6

2 Background and Literature Review 8

2.1 Human Motor Control and Myoelectric Prostheses . . . . . . . . . . . . . 8

2.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Muscle Synergies . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.3 Extraction of Muscle Synergies . . . . . . . . . . . . . . . . . . . 14

2.1.4 Muscle Synergies for Myoelectric Prosthesis . . . . . . . . . . . 15

2.2 Control Paradigms for Myoelectric Prostheses . . . . . . . . . . . . . . . 16

2.3 Pattern Classification in Myoelectric Prostheses . . . . . . . . . . . . . . 17

2.3.1 Performance Parameters for Pattern Classification Systems . . . . 17

xii

2.3.2 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.3 Analysis Windows . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.4 Feature Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.5 Classification Algorithms . . . . . . . . . . . . . . . . . . . . . . 22

2.3.6 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.7 Sensor Orientation and Site Configurations . . . . . . . . . . . . 24

2.3.8 EMG Signal Sources : Surface vs. Intramuscular EMG . . . . . . 25

2.3.9 Training Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.10 Weight and Inertia of the Prosthesis . . . . . . . . . . . . . . . . 29

2.4 Challenges in Surface EMG Processing . . . . . . . . . . . . . . . . . . 29

2.4.1 Muscle Crosstalk . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.2 Amplitude Cancellation . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.3 Absence of Physiologically Relevant Musculature . . . . . . . . . 30

2.4.4 Limited Access to Deep Muscles . . . . . . . . . . . . . . . . . . 31

2.5 Classification Accuracy vs. Usability of Myoelectric Prostheses . . . . . 31

2.5.1 Performance Evaluation Metrics . . . . . . . . . . . . . . . . . . 32

2.5.2 Virtual Environments for Prosthesis Performance Evaluation . . . 33

3 Myoelectric Signal Classification Using the AR-GARCHModel 34

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Heteroscedastic Processes and Myoelectric Signal Modeling . . . . . . . 37

xiii

3.2.1 The GARCH Process . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.2 The AR-GARCH Process . . . . . . . . . . . . . . . . . . . . . . 42

3.2.3 Modeling Heteroscedastic Processes . . . . . . . . . . . . . . . . 43

3.3 Material and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3.2 Movements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3.3 Myoelectric Data Recording . . . . . . . . . . . . . . . . . . . . 47

3.3.4 Data Collection Protocol . . . . . . . . . . . . . . . . . . . . . . 48

3.3.5 Myoelectric Signal Processing . . . . . . . . . . . . . . . . . . . 49

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.4.1 Myoelectric Signal Modeling and Analysis . . . . . . . . . . . . 50

3.4.2 Myoelectric Feature Extraction and Classification . . . . . . . . . 55

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4 Task Discrimination Using the Hypothesis of Muscle Synergies 62

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2 Mathematical Modeling of the Neural Drive . . . . . . . . . . . . . . . . 65

4.2.1 The Neural Drive Model . . . . . . . . . . . . . . . . . . . . . . 65

4.2.2 The Muscle Synergy Model . . . . . . . . . . . . . . . . . . . . 68

4.3 Estimation of the Neural Drive and Task Discrimination . . . . . . . . . . 70

xiv

4.3.1 BSS Algorithm Selection . . . . . . . . . . . . . . . . . . . . . . 70

4.3.2 The Neural Drive Estimation . . . . . . . . . . . . . . . . . . . . 70

4.3.3 Task Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.3.4 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.3.5 Task Discrimination Algorithm . . . . . . . . . . . . . . . . . . . 75

4.4 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.4.1 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . 78

4.4.2 EMG Data Recording . . . . . . . . . . . . . . . . . . . . . . . . 79

4.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.5.1 Off-line Performance Analysis . . . . . . . . . . . . . . . . . . . 80

4.5.2 Real-time Performance Evaluation . . . . . . . . . . . . . . . . . 89

4.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.6 Nonlinear System Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 95

4.6.1 The Particle Filters . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.6.2 Neural Drive Estimation . . . . . . . . . . . . . . . . . . . . . . 100

4.6.3 Constrained Particle Filter . . . . . . . . . . . . . . . . . . . . . 101

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5 Summary and Future Work 104

5.1 Research Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.2 Future Extensions for Research . . . . . . . . . . . . . . . . . . . . . . . 106

xv

5.2.1 Clinical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.2.2 Algorithmic Extensions . . . . . . . . . . . . . . . . . . . . . . . 108

5.2.3 Theoretical Work . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Bibliography 110

xvi

List of Figures

2.1 Description of the muscle synergies. . . . . . . . . . . . . . . . . . . . . 13

2.2 Control paradigms for myoelectric prostheses. . . . . . . . . . . . . . . . 16

2.3 Schematic layout of the pattern classification system. . . . . . . . . . . . 17

2.4 Non-overlapping and overlapping analysis windows. . . . . . . . . . . . 19

2.5 Transient and steady-state phases of the myoelectric signal. . . . . . . . . 27

3.1 Proposed approach to the AR-GARCH modeling. . . . . . . . . . . . . . 38

3.2 Comparison of the GARCH process with the Gaussian noise . . . . . . . 41

3.3 Experimental setup for data collection. . . . . . . . . . . . . . . . . . . . 47

3.4 Ljung-Box Q-test results for the myoelectric signal. . . . . . . . . . . . . 51

3.5 K-S testing results for the myoelectric signal. . . . . . . . . . . . . . . . 53

3.6 Goodness of fit testing for the myoelectric signal. . . . . . . . . . . . . . 54

3.7 Schematic layout for the AR-GARCH coefficient extraction . . . . . . . 56

3.8 Average classification errors for all participants. . . . . . . . . . . . . . . 58

3.9 Average classification errors using three feature sets. . . . . . . . . . . . 59

4.1 The proposed mathematical model of the neural drive. . . . . . . . . . . . 67

4.2 Relation of the neural drive to muscle synergies. . . . . . . . . . . . . . . 68

4.3 Schematic layout of MSD algorithm . . . . . . . . . . . . . . . . . . . . 72

xvii

4.4 System model and neural drive estimation . . . . . . . . . . . . . . . . . 73

4.5 Sequence of execution of the MSD scheme . . . . . . . . . . . . . . . . . 76

4.6 Synergy extraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.7 Task discrimination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.8 Post-processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.9 The hardware setup for the data collection. . . . . . . . . . . . . . . . . . 79

4.10 Neural drive estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.11 Performance analysis of theMSDalgorithm : synergies and analysis windows 83

4.12 Performance analysis of theMSDalgorithm : processing time and comparison

with the LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.13 Discrimination errors for all participants. . . . . . . . . . . . . . . . . . . 87

4.14 Robustness analysis of the proposed MSD algorithm . . . . . . . . . . . 88

4.15 TAC test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.1 Proposed research extensions. . . . . . . . . . . . . . . . . . . . . . . . . 107

xviii

List of Tables

2.1 Mathematical definitions of TDAR features. . . . . . . . . . . . . . . . . 21

3.1 Heteroscedasticity in the myoelectric signal. . . . . . . . . . . . . . . . . 52

3.2 A summary of statistical tests to model the myoelectric signal as an AR-

GARCH process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3 Feature sets selected for the pattern classification algorithms. . . . . . . . 57

3.4 Sensitivity and specificity of the LDA algorithm. . . . . . . . . . . . . . 59

4.1 TAC test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

xix

1

Chapter 1

Introduction

1.1 Motivation

The ease and accuracy of volitional activities, like reaching and grasping that we perform

routinely without much effort, hide the complexity of underlying neuromusculoskeletal processes

that take place to perform these. In addition, changes in the environmental conditions, sensitivity

of the task to be performed in terms of accurate vs. coarse movements and changes in actuation

mechanisms, i.e., the musculature, are readily incorporated in the movement plan or learned as a

routine. The complexity of the movement generation system may be revealed in some cases, e.g.,

when a part of body (e.g. a limb) is impaired or missing as a result of a traumatic incident or

congenital deficit. In upper-extremity limb impairment, functional deficiencies are more

pronounced as compared to lower-extremity. The situation may be even worst for bilateral and

proximal amputations. In any case, the loss of a limb has multiple distressing facets. These may

include a reduced functionality, social and psychosocial problems, and the worst may be the

acceptance of own amputation condition. Prostheses are a suitable alternate and may mitigate the

2

distressing conditions. Cosmetic prostheses help in public appearance, while body-powered

prostheses increase functionality in activities of daily living (ADLs). In contrast, the externally

powered prostheses controlled by the neural signals, such as surface myoelectric signal, provide

enhanced dexterity, low cognitive burden and improved functionality. Myoelectric prostheses

(prostheses driven by the control information extracted from the myoelectric signals) fall under

the umbrella of a larger area known as the body-machine interface (BMI) [1].

1.2 Background

The idea of controlling externally powered prostheses for upper-extremity using myoelectric or

electromyogram (EMG) signals is not a new one [2], [3], [4], [5], [6], [7]. The first effort to use

myoelectric signals as a control source for externally powered prosthetic device was done as early

as 1945 by Reinhold Reiter, a physics student at Munich University [7]. The prosthetic arm was

designed for an amputee factory worker. Since that time, different research groups from all over

the world have been involved in advancing the field of myoelectric prostheses [2], [7].

In myoelectric control, the electrical activity in the muscles representing their activation is

recorded using surface electrodes. The recorded signal is processed through statistical and signal

processing techniques to identify the movement intent of the user. A naive approach to estimate

the movement intent is to measure the intensity of the myoelectric signal [8]. Based on the

measured intensity, pre-defined control commands are issued. An artificial limb consisting of

mechanical links and motors is driven through external power using the control commands. Such

a control paradigm enables basic functionality in the form of an on/off control. Even in a

rudimentary form, myoelectric prostheses have found an important place in clinical setups. In

3

upper-limb amputees, myoelectric prostheses have much less rejection rate than passive and body

powered prostheses (39%, 53% and 50% respectively) [9]. However, despite a lower rejection

rate, the lack of dexterity and the absence of sensory feedback have been reported as the design

issues requiring the most attention [9], [10], [11], [12].

The primary challenge in the myoelectric prosthesis design is the myoelectric signal itself. The

signal represents a complex biological process, i.e., the electrical activity in a muscle and can be

considered an indirect representative of the force [13]. The signal can be detected with sensors

placed on the surface of the skin or with the needle/wire sensors introduced into the muscle

tissue [14], [15]. The surface EMG being the least invasive is commonly employed in prostheses

applications, albeit intramuscular and intra-neural signal acquisition and processing are also

active research areas [16].

1.3 Research Objectives

The literature review for the research included a vast array of topics including but not limited to

body/brain-machine interfaces (BMIs), myoelectric signal processing, myoelectric prostheses,

pattern classification for myoelectric prostheses, human motor control, hypothesis of muscle

synergies and related topics in neuroscience, physiology and anatomy. Based on an extensive

literature review, following research objectives were identified.

1. Develop a basic understanding of the BMIs with a focus on prosthetic devices for

upper-extremity disabilities. With enhanced breadth of knowledge in BMIs, develop

in-depth understanding of neural signals especially the myoelectric signal. Understand

4

generation mechanism of the signal in the spinal cord and its manifestation as muscle

activations.

2. Develop in depth understanding of the state-of-the-art in the field of myoelectric prostheses,

i.e., the pattern classification systems. Critically analyze the functional principles of pattern

classification systems, especially the process of information extraction from the

myoelectric signals in the form of representative feature sets.

3. Analyze a commonly employed feature set, i.e., the autoregressive (AR) model coefficients

in myoelectric prosthesis. Special emphasis is to be laid on the heteroscedasticity of the

myoelectric signal, i.e., the time-varying variance of the AR modeling residuals. In the light

of new findings, suggest an improved feature set focusing on the heteroscedastic modeling

of the myoelectric signal.

4. Investigate myoelectric prostheses problem to understand the dynamics of the CNS in

planning, execution and coordination of voluntary movements. Emphasis is to be laid on

the role of spinal cord in all three phases. The focus of the research will be the hypothesis

of muscle synergies.

5. By employing hypothesis of muscle synergies, develop a mathematical model for the neural

drive estimation. Further, explore novel methods to discriminate between different tasks /

movements based on the estimated neural drive.

6. Propose a comprehensive experimental protocol for myoelectric data collection to validate

the theoretical results. Experimental protocols should be designed in a way that the derived

5

results can be generalize to all upper-extremity movements. However, the designed

protocols should be specific enough to verify proposed methodologies also.

7. Explore various methodologies for virtual testing and performance evaluation of

myoelectric prostheses. Newly proposed algorithm should be evaluated in the virtual

environment with respect to the controllability of the system as a whole.

1.4 Research Contributions

Keeping the research objectives in view, a multi-pronged investigation was undertaken. Based on

preliminary findings, two specific research paths were identified. The first approach consisted of

surface myoelectric signal classification using the Autoregressive-Generalized Autoregressive

Conditional Heteroscedastic (AR-GARCH) model and is discussed in detail in Chapter 3. The

other approach explored muscle synergies for task discrimination and is presented in Chapter 4.

Original research contributions for both adopted approaches are enumerated below.

1.4.1 Myoelectric Signal Classification Using the AR-GARCHModel

1. AR modeling of the myoelectric signal was analyzed using the Ljung-Box Q-test. Later, the

modeling residuals were tested for heteroscedasticity, i.e., the time-varying variance, using

the Engle's test. The myoelectric signal was, in general, found to exhibit heteroscedasticity.

2. The AR-GARCH process was used to model the myoelectric signal, where the GARCH

process was used to capture the heteroscedasticity in the AR modeling residuals. Various

6

statistical tests including the goodness of fit confirmed the validity of the proposed

AR-GARCH model.

3. A new feature set based on the proposed modeling scheme, i.e., the AR-GARCH process,

was used in the pattern classification system. The newly proposed feature set significantly

outperformed (p < .01) the conventional AR feature set in the classification accuracy.

4. Experimental data was collected from human forearm muscles (six participants) to verified

the increased classification accuracy.

1.4.2 Task Discrimination Using the Hypothesis of Muscle Synergies

1. The problem of myoelectric prostheses was investigated in its true domain, i.e., the human

motor control domain. The hypothesis of muscle synergies was explored in detail to

understand the fixed spatial inter-muscle coordination. The focus of the investigation was

to find a physiologically-relevant mathematical model for task discrimination.

2. Based on the hypothesis of muscle synergies, a physiologically-relevant mathematical

model of the neural drive was proposed. The proposed model captures the time evolution of

the task-specific neural drive.

3. A modified form of the Kalman filter, i.e., the state-constrained Kalman filter was

employed to solve the state-space model and estimate the neural drive, i.e., the latent state

in the proposed state-space model.

4. The estimated neural drive was used to discriminate between a set of selected tasks using

different similarity measures.

7

5. The discrimination decision by the proposed model was further processed to increase

classification accuracy using a novel post-processing routine.

6. Experimental data was collected from twelve participants to ascertain the efficacy of the

proposed discrimination scheme. In addition to off-line performance analysis, a virtual

prosthesis was used to quantitatively measure the controllability of the algorithm. The

proposed scheme outperformed the conventional classification algorithms in off-line

accuracy (p < .001) and as well as real-time controllability (p < .01).

8

Chapter 2

Background and Literature Review

The chapter provides a detailed description of the related work in the field of myoelectric

prostheses. We start with the hypothesis of muscle synergies and later provide a detailed review

of state-of-the-art in the field of myoelectric prosthesis.

2.1 Human Motor Control and Myoelectric Prostheses

How the central nervous system (CNS) masters the many degrees-of-freedom (DOFs) of the

musculoskeletal system to control and coordinate a goal-directed movement is a long standing

question. Myriad of hypotheses exist to explain the control strategies adopted by the CNS [17].

While planning and executing a voluntary movement, the CNS is confronted with the problem (or

bliss [18]) of redundancy (or abundance [18]) at both the neuromuscular and the biomechanical

levels. For example, to perform a reaching movement, an infinite number of trajectories can be

9

planned; and for every trajectory there are more DOFs available than actually required. Once a

trajectory is selected, an inverse dynamics model has to be solved to find joint torques (and

ultimately neural commands) for moving the limb on the desired trajectory to complete the

intended movement. However, skeletal muscles can only contract and generate force in one

direction. Therefore, muscles across a joint function as an agonist/antagonist pair to generate

torque by their collective action. Due to such a pairing, an infinite levels of individual muscle

forces can be combined to produce the required torque at each joint. Furthermore, bi-articular

muscles (muscle crossing multiple joints), if present around the joint of interest, complicate the

task of calculating a desired torque at that joint. Finally, many different combinations of motor

units within a muscle can fire to achieve the same force level [19], [20], [21]. Therefore, the

above mentioned inverse dynamics problem, i.e., calculation of neural activation signals required

to perform a planned movement is termed as an ill-posed one [19].

Similarly, due to the tight coupling between force, position, and velocity of the end effector

(hand / end of the limb), a forward model of the actuator has to be incorporated by the

CNS [22], [23]. Also, the CNS has to incorporate afferent (feedback) information into the

movement planning and execution. Similarly, during the execution of the movement, any changes

in the forward model and/or environmental conditions have to be taken into account by the

CNS [17], [19]. In the following section we will briefly describe different theories that have been

proposed to answer the above mentioned questions.

10

2.1.1 Background

Earlier in the twentieth century, some researches proposed that the feedback of stretch reflex from

muscle spindles (MS) may cause initiation of the movement [24]. Similarly, later in 1970s it was

hypothesized by Merton that the central commands initiate movement via the gamma () system

(muscle spindles), rather than activating muscles directly through the alpha () motor

neurons [25]. However, due to some obvious limitations in this feedback-only approach,

feed-forward control solution was proposed. The feed-forward scheme states that the CNS may

be carrying out inverse kinematic and dynamic computations while moving a limb in a purposeful

way [26]. However, for a multi-joint system the inverse dynamic computations can be enormous.

A few research efforts were undertaken to expound the underlying mechanics and it was proposed

that a fixed set of solutions in the form of a lookup table may already be stored by the CNS,

whereby a value of toque has been pre-calculated and stored for each possible value of position,

velocity and acceleration [27], [28]. However, an apparent limitation was that for a complete arm

model with seven joint coordinates, the entries in the table exponentially grow to 104. Some

efforts were done to reduce the number of entries in the look-up table but there were other

problems also, e.g., interaction with the environment which is not accounted for by the

feed-forward only solution.

2.1.1.1 Equilibrium Point Hypothesis

Another effort by the name of equilibrium point hypothesis was proposed as an alternative to the

problem of inverse dynamic computations; the hypothesis specifies physiological variables

controlled by the CNS [29], [30]. The hypothesis states that centrally generated motor commands

11

modulate the stiffness and rest length of the muscles that act as flexors and extensors about the

joint; and as a result, the elastic behavior of the muscles, like that of an opposing spring, defines a

single equilibrium position of the forearm [17]. A sequence of equilibrium positions produced

during movement by all the muscular activations has been called the virtual trajectory [31].

Generalizations of the equilibrium point hypothesis have also been proposed and further work is

still underway [32], [33], [34], [35], [36].

2.1.1.2 Uncontrolled Manifold (UCM)

The idea of uncontrolled manifold (UCM) was proposed with an emphasis on the variability of a

movement in multiple trials [37], [38], [39]. The roots of the UCM hypothesis can be traced back

to the experiments of Bernstein [40], where the end effector paths were less variable than the joint

level trajectories. Under the UCM hypothesis, to make a comparison of both variances, i.e.,

overall trajectory variance and the joint space variance, a joint space as an embedding space is

used, in which all variance is measured and the structure of the variance is interpreted relative to

spatial task variables. This is done by defining a subset, the UCM that contains all those

combinations of joint angles that are consistent with one particular end-effector position. There is

such an UCM for any position of the end effector. According to the UCM hypothesis, at any

given point during the movement, joint configurations vary primarily within that subset rather

than outside of it [34], [35], [36]. Recently, Neilson and Neilson extended the UCM to a

computational theory, named as the adaptive model theory (AMT) [41].

12

2.1.2 Muscle Synergies

It is hypothesized that the activity of motor system may result from combination of discrete

elements or primitive building blocks, called the muscle

synergies [42], [17], [43], [44], [45], [46], [47] or muscle modes (M-modes) [48], [49], [38]. By

definition, muscle synergies are fixed relative levels of activation of different muscles [50], and the

recruitment of a large number of muscles may be performed by a reduced number of independent

control signals (i.e., the synergy activation coefficients). The activation signals are translated into

individual muscular activation patterns by a transformation matrix, called the synergy matrix [51].

This definition of muscle synergies is different from the one by Mark L. Latash, i.e., ``synergy is

a neural organization of a multi-element system that, 1) organizes sharing of task among a set of

elemental variables; and 2) ensures co-activation among elemental variables with the purpose to

stabilize performance variables" [38]. A closer look at both definitions reveal that the former

definition of muscle synergies is a subset of the later. However, we will use the former definition

of muscle synergies in our research, being mathematically and computationally more tractable.

The fundamental movement primitives or muscle synergies are assumed to serve two

purposes. First, they constrain the neuromusculoskeletal system, thus making the problem of

controlling and coordinating movement a well-posed one (which was previously an ill-posed).

Second, they increase the efficiency of the CNS, i.e., using fewer commands to control a large

space. Experimental evidence for the hypothesis of muscle synergies in the spinal motor system

comes from a number of experiments on spinalized frogs [52], [53], [54], freely moving

frogs [55], [56], rats [57], primates [58], human arm and hand

movements [50], [51], [59], [60], [61], [62], human postural task [63], [45], and locomotion [64].

13

A B C D

A B C D

Act

ivat

ion

Stre

ngth

s Observed muscle activations

A B C D

=

=1

2

1

Muscles

0.5

0.5

(a)

Muscle Synergies

EMG Data

M1

M2

M3

Coefficients

Time

Time

(b)

Figure 2.1: Two simple cases of muscle synergies, where activation levels of muscles are relatively

fixed within a muscle synergy. a) Each of the two muscle synergy consists of four muscles. A

discrete coefficient set is being specified by the CNS to combine the muscle synergies [65]. b) A

simple muscle synergy scheme for three muscles and two muscle synergies. A continuous stream

of parameters is being provided by the CNS to activate three muscles [66].

Muscle synergies come in two different flavors, i.e., synchronous muscle synergies and

asynchronous or time-varying muscle synergies [56]. In the former case, no temporal delay is

allowed in the activation of different muscles. In contrast, a time-varying synergy is a time

sequence of vectors representing a collection of muscle activation waveforms [56]. For activating

each synergy, the number of variables to be specified by the CNS in the case of asynchronous

muscle synergies are two as compared to one for the synchronous case [55]. Fig. 2.1 presents two

simple cases of synchronous muscle synergies. In Fig. 2.1(a), we present two muscle synergies

each consisting of four muscles. The CNS specifies two discrete parameters to combine the two

muscle synergies for activating four muscles. In Fig. 2.1(b), we present two muscle synergies

each consisting of three muscles. In this case, the CNS specifies two continuous streams of

parameters to activate three muscles continuously.

While the muscle synergies focus on relatively fixed activation levels of muscles, some

researchers favor the idea of individual motions and emphasize the uncoupled control of

14

individual joints and muscles to generate necessary kinetics and kinematics of the movement [67].

Whether the muscle synergies have a neural origin or not is still an open question [65], [68], [69].

However, various aspects of muscle synergies are being vigorously

investigated [70], [71], [72], [73], [74], [75], [76], [77], [78], [79].

2.1.3 Extraction of Muscle Synergies

Various matrix factorization algorithms have been suggested for the decomposition of muscle

activity patterns, recorded through the myoelectric signal, into muscle synergies [80]. These

algorithms include the PCA [81], ICA [82], [83], [84], probabilistic ICA (pICA) [85],

NMF [50], [51], [46], [58], [52], [86] and factor analysis (FA) [87].

Considering the case of synchronous muscle synergies, we have

yi(k) =nj=1

wijxj(k), {yi, wij, xj} 0, i = 1, . . . ,m; j = 1, . . . , n, (2.1)

where n is the number of muscle synergies,m is the number of muscles, yi represents activation

level of the ith muscle, wij is the gain of jth neural command for ith muscle, and xj is the applied

neural command. We can write (2.1) in the vector form

y(k) = Wx(k), (2.2)

where y(k) = [y1(k), . . . , ym(k)]T specifies activation levels ofm muscles,W is am n matrix

whose columns are the muscle synergies and x(k) = [x1(k), . . . , xn(k)]T is the neural command

vector (i.e., muscle synergy activation coefficients or the neural drive) at time k. The relations

15

[(2.1) and (2.2)] can be extended for multiple trials, i.e., k = 1, . . . , K.

YmK = WmnXnK . (2.3)

The subscripts in (2.3) indicate the dimensions of the matrices with Y a known quantity andW

and X being unknowns. This problem is known as a blind source separation (BSS) problem in

estimation theory. Various unsupervised learning algorithms can be employed to estimate the

parameters of the mixing systemW and true physical sourcesX . Such algorithms exploit a priori

knowledge about the true nature or structure of the hidden variables such as non-negativity,

statistical independence, sparseness, spatio-temporal de-correlation, smoothness or lowest

possible complexity [88]. Due to the physiological constraints, all elements inW and X matrices

must be non-negative, i.e., the muscle activations cannot be a negative quantity [47].

2.1.4 Muscle Synergies for Myoelectric Prosthesis

There has been no explicit effort on using the hypothesis of muscle synergies to discriminate

between various tasks for the myoelectric prosthesis application. Recently, Ajiboye and Weir used

a subset of static hand postures of the American Sign Language (ASL) to estimate the muscle

synergies and then predicted other remaining ASL postures [59]. The authors reported that as few

as 11 basic postures were sufficient to predict all 33 postures of the ASL with an accuracy of

90%. However, the authors did not extend their work to tackle myoelectric prosthesis problem.

16Feature Extraction Data Segmentation Pattern Classification Control Scheme

Data Segmentation Change Point Detection Control Scheme

Data Segmentation Finite State Machine Feature Extraction

(a) Signal amplitude based control scheme.

Feature Extraction Data Segmentation Pattern Classification Control Scheme

Data Segmentation Change Point Detection Control Scheme

Data Segmentation Finite State Machine Feature Extraction

(b) Event driven finite state based control scheme.

Feature Extraction Data Segmentation Pattern Classification Control Scheme

Data Segmentation Change Point Detection Control Scheme

Data Segmentation Finite State Machine Feature Extraction

(c) Pattern classification based control scheme.

Figure 2.2: Three most common control paradigms for myoelectric prostheses [16].

2.2 Control Paradigms for Myoelectric Prostheses

Various paradigms have been proposed for controlling the hand prosthesis using the myoelectric

signals [16]. Fig. 2.2 presents three most common control schemes found in the myoelectric

prostheses literature. Fig. 2.2(a) presents a simple on/off control scheme. After myoelectric data

segmentation, a change point is detected using statistical techniques and the control algorithm

performs already established movements. As evident, the applicability of such a framework is

limited to one, or at the most two degrees-of-freedom (DOFs) devices. Fig. 2.2(b) presents an

event driven finite state (EDFS) control scheme. Dalley et al. proposed the EDFS approach for a

multi-grasp prosthetic hand with an average grasp completion rate of 99.2% [89]. Fig. 2.2(c)

presents the state-of-the-art control paradigm, i.e., the pattern classification system. In such an

arrangement, a representative feature set from the myoelectric signal is extracted and a

classification algorithm is trained. Later, the classifier is used to perform classification [90], [16].

A detailed description of pattern classification systems is presented in Section 2.3.

17

Feature Extraction

Data Segmentation

Pattern Classification

Data Preprocessing

Post-processing

Movement Class Labels

Myoelectric Signal

Figure 2.3: Schematic layout of the pattern classification system for extraction of control

information from the EMG signal [90].

2.3 Pattern Classification in Myoelectric Prostheses

The pattern classification for myoelectric control is based on the assumption that there exist

distinguishable and repeatable signal patterns among different types of muscular activations [91].

A schematic layout of pattern classification schemes used in myoelectric prostheses is given in

Fig. 2.3 [92]. Myoelectric signals are recorded from multiple muscle sites, followed by the data

segmentation process to form analysis windows. In some cases, data preprocessing may precede

the data segmentation. A representative set of features is extracted from the analysis windows and

a classification algorithm is trained. Depending upon the type of the classification algorithm, it

may require supervised or semi-unsupervised learning before going into the operational mode.

The output of the classification algorithm is a single class label. The post-processing routines may

also be included in the overall scheme to further improve the classification results. Most of the

classification schemes reported in the literature are capable of performing classification of four or

more distinct movements. Pattern classification systems have produced promising results, i.e.,

classification accuracy in the range of 90% or above [90], [93], [16], [94], [95].

2.3.1 Performance Parameters for Pattern Classification Systems

A general layout of the pattern classification systems is shown in Fig. 2.3. However, exact

configuration may vary considerably due to the type of selected features, pre-/post-processing

18

algorithms, classification algorithms, experimental protocols used for the EMG data collection,

and number and type of movements. A brief discussion on all related issues is presented in the

following.

2.3.2 Preprocessing

A few preprocessing techniques have been investigated in the literature to improve classification

accuracy. One recently proposed scheme consists of pre-whitening the myoelectric signal. The

pre-whitening process de-correlates the myoelectric signal and may improved classification

accuracy by approximately 5% for small analysis windows (< 100 ms) [96]. The principal

component analysis (PCA) algorithm has also been proposed for dimensionality reduction of the

myoelectric signal before the feature extraction, which results in an improved classification

accuracy as well as reduced computational time for the feature extraction and classification [97].

2.3.3 Analysis Windows

The stochasticity and the variability inherent in the myoelectric signal limits its direct use in the

classification, although such efforts were attempted with limited success [98]. Therefore, a

segmentation operation on the EMG signal is performed to form analysis windows. Owing to the

real-time operational requirement, the size of analysis window is critical [99], [100]. A large

analysis window results in a better classification accuracy but may introduce delay in intent

interpretation (decision of the movement class by the classifier). On the other hand, a small

analysis window presents reduced amount of information to the feature extraction routine, and

resultantly increases the variance of the classifier, thereby increasing the classification errors.

19

D1

D2

: Processing time : Window increment time : Analysis window size

Decision Di = +

(a) Non-overlapping analysis windows.

D1

D2

: Processing time : Window increment time

: Analysis window size

First decision D1 = + Subsequent decisions Dk =

(b) Overlapping analysis windows.

Figure 2.4: Two different types of segmentation operations for the myoelectric signal are shown,

non-overlapping and overlapping analysis windows. Symbols D1 and D2 represent decisions from

the classification algorithm, Ta represents the analysis windows size, Td the processing time andTinc the increment time for the overlapping analysis windows. Modified from [92].

Additionally, in most cases, a sliding (overlapping) analysis window is introduced to provide a

rich stream of input data to the classifier. Effect of the size of analysis window on the

classification accuracy has been investigated in detail and optimal values have been found for

different feature sets and classification algorithms [92], [100], [99]. An analysis window of 150

ms to 250 ms may be a reasonable choice based on the feature set and the classification

algorithm [100]. In Fig. 2.4, we present non-overlapping and overlapping analysis windows.

2.3.4 Feature Sets

After data segmentation, representative features are extracted from analysis windows. A large

variety of features, individually and in groups, can be extracted to increase information density.

Broadly, four categories of features have been identified [16].

1. Time Domain (TD) features include mean absolute value (MAV), integrated absolute

value (IAV), variance (VAR), mean absolute value slope (MAVS), Willison amplitude

(WA), zero crossing (ZC), slope sign change (SSC), mean square value (MSV), and

20

waveform length

(WL) [101], [102], [103], [104], [105], [94, 106], [107], [108], [109], [110].

2. Time serial features include the AR model

coefficients [111], [106], [112], [94], [109], [113], [114], [115], [116], [117], and cepstral

coefficients [118], [112], [94].

3. Spectral domain and time-scale features include power spectrum, mean and median

frequency, frequency ratio, wavelet transform (WT), wavelet packet transform (WPT) and

short-time Fourier transform (STFT) [119], [120], [121], [94], [122], [117], [114].

4. Advanced spectral features, such as multifractal singularity spectrum [123].

It has been shown that for a slowly varying myoelectric signal, a combination of the AR model

coefficients and the TD features (MAV, MAVS, ZC, SSC, WL) gives good performance with

respect to computational time and classification accuracy [124], [90], [116]. Mathematical

definitions of the TD and AR features (usually referred to as TDAR in the literature) are given in

Table 2.1.

2.3.4.1 Feature set dimensionality reduction

In case, a large number of features are extracted from the analysis windows, the final feature set

consisting of multiple myoelectric channels may become large. Such practice may result in an

increased computational time for classifier training and/or degraded classification accuracy. To

circumvent, dimensionality reduction methodologies are often used [125], [90], [16]. Some

adopted techniques include the PCA [97], [126], independent component analysis (ICA) [127],

nonlinear projection [128], [129] or the fuzzy discriminant analysis [125].

21

Table 2.1: Mathematical definitions of TDAR features. xi(k) is the kth signal sample of the ith

segment, N is the number of samples in the segment i, xth is a predefined threshold [16], [92].

Feature Mathematical Definition

Mean absolute value MAVi =1N

Nk=1

|xi(k)|

Integrated absolute value IAVi =Nk=1

|xi(k)|

Variance V ARi =1N

Nk=1

(xi xi)2, where xi = 1NNi=1

xi

Mean absolute value slope MAV Si = MAVi+1 MAVi

Willison amplitude WAMPiNk=1

f(|xi(k) xi(k + 1)|)

with f(x) =

{1 if x > xth0 otherwise

Zero crossing ZCi =Nk=1

f(k)

with f(k) = 1 if xi(k) xi(k + 1) < 0 and|xi(k) xi(k + 1)| > xth

Slope sign change SSCi =N1k=1

f [{xi(k) xi(k + 1)}{xi(k) + xi(k + 1)}]

with f(x) =

{1 if x > xth0 otherwise

Meas square value MSVi =1N

Nk=1

[xi(k)]2

Waveform length WLi =Nk=1

(|xi(k) xi(k + 1|)

Autoregressive coefficients xi(k) =nj=1

ajxi(k j), an nth order AR model with aj features

2.3.4.2 Feature set stability

Under dynamic contractions and noisy signal acquisition conditions, the performance of the

selected feature set may degrade. Tkach et al. investigated this phenomenon for different feature

sets under common conditions, such as, the electrode location shift, variation in the muscle

contraction effort, and muscle fatigue [130]. The authors reported that the muscle fatigue had the

smallest effect on the selected feature set, while electrode location shift and varying effort level

significantly reduced the classification accuracy for most of the feature sets.

22

2.3.5 Classification Algorithms

Considerable efforts have been invested in exploring various classification algorithms for

myoelectric prostheses [131]. A classification algorithm has to take into account the stochastic

nature of the myoelectric signal as well as the noise added during the recording process. On the

other hand, the constraint of real-time decision making limits the computational time for the

classification algorithm. The classification algorithms reported in the literature include but are not

limited to the list presented here. Please refer to recent reviews and references therein for detailed

description of the classification algorithms [16], [90], [93], [132], [95]

1. Linear discriminant analysis (LDA) [101], [111], [119], [122].

2. Gaussian mixture model (GMM) [116], [133], [134] and log-linear GMM (LLGMM) [135].

3. Support vector machine (SVM) [120], [113], [110], [136].

4. Parallel multiple binary classification (MBC) and uncorrelated linear discriminant analysis

(ULDA) [137].

5. K-nearest neighbor (K-NN) with lazy learning [138] and genetic algorithms [139].

6. Parzen classifier, Fisher discriminant analysis and Quadratic discriminant analysis

(QDA) [131].

7. Hidden Markov models (HMM) [115].

8. Various types of artificial neural networks (ANN) in different configurations, i.e.,

multilayer perceptron (MLP), Radial Basis Functions (RBF), time-delayed ANN

23

(TDANN), Elman neural network

(ENN) [102], [109], [140], [128], [106], [141], [121], [142], [143], [144], [98], [145].

9. Fuzzy and neuro-fuzzy based classifiers [114], [146], [112], [147], [107], [105], [148].

It is evident that a myriad of classification algorithms have been used in the myoelectric control

literature. However, it is known that once sufficient EMG channels are available (in the case of

forearm, a symmetrical arrangement of 4 to 6 EMG channels [124], [149]) and appropriate

features are selected, most of the modern classification algorithms perform well [90], [124], [131].

The analyses performed in various studies using the same set of EMG data revealed no statistical

differences between various classification algorithms [124], [131]. It is also known that with an

appropriate feature representation the myoelectric classification reduces to a linear problem [90].

2.3.6 Post-processing

The post-processing of the classification decision may improve overall pattern classification

system accuracy [92], [150], [151]. However, the post-processing may have additional

computational cost. Generally, the decision to include a post-processing routine may depend on

the type of classifier, number and type of features, analysis window size and available

computational power.

Majority voting (MV) is a common post-processing technique [92]. For a given decision point,

the MV decision includes previousm samples (of the decision stream) and nextm samples. The

final decision by the post-processing algorithm will be the class with the greatest number of

occurrences in the 2m+ 1 decision stream. The number of samples used in the MV (the

parameterm) is determined by the available processing time and the acceptable delay. However,

24

it has been reported that despite the fact that MV improves classification accuracy, it does not

improve system usability and controllability [151].

Recently Simon et al. proposed a velocity ramp based post-processing scheme [151]. The

authors propose to keep the initial velocity of the movement low and increase it once an error-free

decision steam is received to the post-processing algorithm.

2.3.7 Sensor Orientation and Site Configurations

In the daily usage of a prosthesis, certain assumptions of the controlled laboratory experiments

may not hold. One such assumption is related to myoelectric sensors. In controlled laboratory

environment, the EMG electrodes are placed over precisely selected muscle sites parallel to

muscle fibers for optimal signal acquisition. On the other hand in actual prosthesis, EMG sensors

are permanently attached inside the socket of the prosthesis. Such an arrangement of the EMG

sensors makes it impossible for a user to adjust sensors exactly at the same spot each time he/she

dons the device. The resulting phenomenon is referred to as the socket misalignment. To quantify

the effects of socket misalignment, Young et al. investigated the pattern classification system

under various conditions of socket misalignment [152], [111]. Specifically the authors

investigated effects of socket misalignment on electrode orientation (parallel or perpendicular to

muscle fibers), inter-electrode distance (IED; which is fixed at the time of installation of the EMG

electrodes inside the socket), the size of electrode detection-surface (fixed once the electrode is

manufactured), and number of electrodes (EMG channels). The authors used two common feature

sets, i.e., the TD and AR. Some relevant conclusions by the authors are presented:

25

1. Maximum classification accuracy was achieved while electrodes were oriented parallel to

the muscle fibers (p < .01) under both shift and no-shift conditions.

2. Electrode shifts perpendicular to muscle fibers increased classification error more than the

electrode shifts parallel to muscle fibers (p < .01).

3. An increase in IED from 2 cm (which is a considered a standard in myoelectric literature) to

4 cm improved system performance (p < .01).

4. An increase in electrode detection surface increased the classifier accuracy but not the

prosthesis usability.

5. Four to six channels performed well under shift/no-shift conditions.

6. The LDA classifier with an AR feature set outperform the TD feature set under electrode

shift condition (p < .01).

7. A combination of longitudinal and transverse electrodes yielded highest system usability

under electrode shift condition.

2.3.8 EMG Signal Sources : Surface vs. Intramuscular EMG

Given the fact that surface myoelectric signal exhibits some undesirable characteristics (e.g., the

muscle crosstalk, amplitude cancellation and limited access to deep musculature), feasibility of

using intramuscular EMG in myoelectric prosthesis has been investigated. Farrell and Weir

explored the effect of surface vs. intramuscular myoelectric signals on classification

accuracy [149]. The authors studied targeted and un-targeted conditions for both surface and

intramuscular EMG. In summary, the authors investigated four distinct cases, i.e., targeted

26

surface, targeted intramuscular, un-targeted surface and un-targeted intramuscular. After a

detailed statistical analysis authors concluded that there were no statistical differences in the

classification accuracy of any of the four conditions. Similar results were earlier reported by

Hargrove et al. [124]. Both studies concluded that 4 to 6 equally spaced EMG electrodes around

the forearm provided more than 90% classification accuracy with TDAR feature set and the LDA

classifier.

2.3.9 Training Regimes

In myoelectric prostheses, the classification accuracy of the system also depends on the training

dataset as well as training conditions. In the following we discuss some related issues.

2.3.9.1 Transient vs. steady-state part of the myoelectric signal

In experimental studies, any voluntary movement (e.g., the wrist flexion) can be roughly divided

into three phases: the initial transient phase, middle steady-state phase, and the final transient

phase. The same three phases are also reflected in the myoelectric signal. The steady-state phase

is also called the isometric contraction as the muscle length do not change in this phase. The

other two phases are referred to as dynamic contraction phases. Fig. 2.5 presents all three phases

of a myoelectric signal recorded from the forearm. For extraction of features from the myoelectric

signal, few initial studies used only the transient phase [119], or the steady-state phase of the

signal [121]. However, later investigations revealed that both the steady-state and transient phases

of the signal provided better usability of the prosthesis, although the accuracy of the classifier

may be reduced [153], [154]. Another way to handle the transient information is by specifying the

27

Initial transient

phase

Terminal transient

phase

Steady-state phase

cTp = 50%

cTp = 100%

Figure 2.5: Transient and steady-state phases in the myoelectric signal recorded from the forearm

muscle during a reaching movement.

contraction time percentage (cTp) [155]. A cTp value of 50% will remove all transient

information (from both sides of the signal) while a value of 100% will retain all information.

2.3.9.2 Variations in initial limb position

Variations in the limb position associated with normal use of the prosthesis and the position at

which the classifier was trained could have a substantial impact on the accuracy of the pattern

classification system [156], [157]. An increase in average classification error from 3.8% to 18%

has been reported in the literature when classifier was trained at one initial limb position and used

for classification with different initial position. Fougner et al. proposed to use accelerometers to

measure position of the arm and train the classifier in different limb positions. The authors

reported a reduction in the classification error from 18% to 5% using the proposed solution [156].

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2.3.9.3 Training using the kinematic and kinetic Data

Jiang et al. proposed to use the kinetic data (force and torques) in the training phase of the

classification algorithms [158]. The authors proposed a nonnegative matrix factorization (NMF)

algorithm based semi-unsupervised training regime. The same approach was used by Nielsen et

al., however, the kinetic data was recorded from the contra-lateral limb and an ANN based

classifier was trained to estimate force [159]. Later, Muceli et al., and Jiang et al. extended the

same concept to kinematic data where joint angles were mapped to muscle activations using a

MLP classifier [160], [109].

Instead of training the classifier on some preselected movements, user-selected training

regimes have also been explored where a user is at liberty to specify and make any movements for

the classifier training [107]. Momen et al. allowed users to select movements and induce muscle

activations for classifier training. The authors reported a classification accuracy of 92.7% 3.2%

for four different movements with a training time of 2 minutes [107].

Bunderson and Kuiken studied the effect of already acquired experience on the training

regime [161]. In the reported study, the participants included novice and experienced users of the

pattern classification system. The authors concluded that after a brief exposure to the training

scheme, the classification errors in novice users were reduced, although not to the level of

experienced ones. While the level of intraclass variability in novice users was similar to that of

the experienced users, they did not achieve the same level of interclass distance.

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2.3.10 Weight and Inertia of the Prosthesis

Unlike native human limb, a prosthesis is an alien object which an amputee has to lift and carry

by using force from his remaining muscles. Therefore, while wearing a prosthesis, some relevant

muscles of the forearm remain in a pre-activated state. In such a condition, any classifier trained

in relaxed muscle states will exhibit increased error rate [162].

2.4 Challenges in Surface EMG Processing

The extraction of a desired information from the surface myoelectric signal has its own

challenges. The contributing factors may include biological stochasticity, intrinsic

non-stationarity, and the heteroscedasticity of the signal. Additionally, the recording procedures,

instrument noise and skin condition also affect the quality of the acquired signal. Some relevant

challenges in the myoelectric signal processing with regards to the extraction of control

information are discussed here.

2.4.1 Muscle Crosstalk

A common problem typical to the surface myoelectric signal is the muscle crosstalk. Formally

defined as ``a signal detected over a muscle, however, generated by another muscle close to the

first one'' [163]. The phenomenon of crosstalk is referred as one of the most important sources of

error in the surface myoelectric signal interpretation [163], [164]. The effect of crosstalk worsens

in surface myoelectric recordings where muscles are relatively smaller in size and located inside a

compact area. For example, muscles responsible for hand postures (extrinsic muscle of the hand)

and wrist movements are densely packed in layers in the human forearm [165]. While the

30

myoelectric signal is being recorded using multiple surface electrodes, the crosstalk adds a

correlation between independent sources of information, thus making some of the information

redundant.

2.4.2 Amplitude Cancellation

As the myoelectric signal represents a temporal and spacial sum of electrical spikes in multiple,

may be thousand or more, muscle fibers, some relevant information may be lost in the summation

process. The phenomenon is referred to as ``amplitude cancellation'' [166], [167], [168], [169].

The phenomenon of amplitude cancellation may cause loss of important control information in

the myoelectric signal.

2.4.3 Absence of Physiologically Relevant Musculature

A challenging difficulty in myoelectric signal recording (and in turn processing) may be the

absence of the physiologically relevant musculature [170]. Congenitally or after acquired

amputation, there may not exist relevant muscles for an access to myoelectric information. The

problem is intensified for individuals with proximal amputations, e.g., intrinsic and extrinsic hand

muscles found in the forearm are altogether absent in a shoulder dis-articulation amputee.

Recently proposed novel surgical procedure, called the targeted muscle reinnervation (TMR),

circumvents the problem by remapping the leftover nerves to different and biomechanically less

active sites [171]. After the TMR procedure, surface myoelectric signals can be recorded from

new sites using conventional procedures.

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2.4.4 Limited Access to Deep Muscles

The surface EMG recording procedure has inherently limited access to the deep musculature. The

phenomenon is more evident for surface myoelectric recordings from the forearm, where intrinsic

hand muscles are deep inside under a layer of superficial muscles.

2.5 Classification Accuracy vs. Usability of Myoelectric

Prostheses

The issue of accuracy of the pattern classification system vs. the usability of the myoelectric

prosthesis was raised by Lock [172]. The author designed a virtual environment where a

prosthetic arm was used to perform a clothespin test [173], [174]. Specifically, in an experimental

setup after classifier training, participants were asked to remove a clothespin from a horizontal

bar and attach it to the vertical bar. The time to complete a clothespin task, i.e., removing the

clothespin from a horizontal bar and placing it over the vertical bar, was the only metric used. The

author used three feature sets, i.e., the AR, TD, and a combination of both (TDAR) with three

classifiers, i.e., the LDA, ANN and GMM. The author reported that the correlation between the

classification accuracy of the selected pattern classification system and the usability of the

myoelectric prosthesis (time for clothespin test) was altogether absent or weak at best

(R2 = 0.238) [172].

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2.5.1 Performance Evaluation Metrics

Given the fact that the accuracy of the classification system does not translate into prostheses

usability, it was imperative to define new performance measures. These measures/metrics must

focus on the clinical usability of the device in addition to classification accuracy. Some relevant

measures/metrics proposed in the literature are discussed here.

2.5.1.1 The Motion Test

The Motion test is used to evaluate the real-time classification accuracy of the pattern

classification system [171]. The performance is evaluated using three metrics, i.e., the motion

selection time, motion completion time, and motion completion rate. The motion selection time is

the time taken to correctly select a target motion and is defined as the time from movement onset

to the first correct classification. The metric quantity measures how quickly motor commands can

be translated into correct motion predictions. The motion completion time is defined as the time

from movement onset to a preset number of correct classifications. The motion completion rate is

the percentage of successfully completed motions out of the total attempted.

2.5.1.2 Target Achievement Control (TAC) Test

The target achievement control (TAC) test is used to evaluate the resulting controllability of the

prosthetic systems as a whole [175]. The TAC test is relatively a challenging test for prosthesis

performance evaluation. The users are required to activate specific DOFs to achieve a target

posture. The TAC test performance metrics include the completion time, completion rate, and the

path efficiency. The completion time is the time from trial start to the successful achievement of

the target posture, not including the dwell time at the target posture. The completion rate is the

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percentage of successfully completed postures in a set of trials. Finally, the path efficiency is the

shortest path to the target divided by the total distance traveled.

2.5.2 Virtual Environments for Prosthesis Performance Evaluation

A virtual environment with a prosthetic limb (arm and hand) can be used for performance

evaluation of the myoelectric prosthesis [171], [155], [176], [177], [178]. The virtual prosthetic

arm mimics the hand/arm movements of the user in real-time. First, the EMG data is collected

from the participant and a classification algorithm is trained. Later, the trained algorithm

classifies the EMG signal is real-time and the virtual prosthetic limb performs the selected

movement in the virtual environment. A virtual environment provides a reasonable alternative to

actual prosthetic device.

34

Chapter 3

Myoelectric Signal Classification Using the

AR-GARCHModel

In the pattern classification paradigm for controlling myoelectric prosthesis, the autoregressive

(AR) model coefficients are generally considered an efficient and robust feature set. However, no

formal statistical methodologies or tests are reported in the literature to analyze and model the

myoelectric signal as an AR process. We analyzed the myoelectric signal as a stochastic

time-series and found that the signal is heteroscedastic, i.e., the AR modeling residuals exhibit a

time-varying variance. Heteroscedasticity is a major concern in statistical modeling because it

can invalidate statistical tests of significance which may assume that the modeling errors are

uncorrelated and that the error variances do not vary with the effects being modeled. We

subsequently proposed to model the myoelectric signal as an Autoregressive-Generalized

Autoregressive Conditional Heteroscedastic (AR-GARCH) process and used the model

35

parameters as a feature set for signal classification. Multiple statistical tests including the

Ljung-Box Q-test, Engle's test for heteroscedasticity, Kolmogorov-Smirnov (K-S) test and the

goodness of fit test were performed to show the validity of the proposed model. Our experimental

results show that the proposed AR-GARCH model coefficients, when used as a feature set in two

different classification schemes, significantly outperformed (p < .01) the conventional AR model

coefficients.

3.1 Background

In the myoelectric control, the choice of an appropriate feature set is crucial for the pattern

classification. Parker et al. have shown that the classification accuracy in a pattern pattern

classification scheme is more affected by the choice of the feature set than by the classification

algorithm [179]. A common and promising feature set considered in the myoelectric control

literature consists of AR coefficients [16], [95], [90]. Tkach et al. investigated different features

under conditions of change in muscle effort level, muscle fatigue and electrode shift, and found

the AR coefficients to be one of the most robust features [130]. Similarly, Young et al. found that,

under conditions of socket misalignment, the AR features performed better than the time-domain

features [111]. However, in the myoelectric control literature, there has not been an exclusive

effort to model the myoelectric signal as an AR process using formal statistical tools. A generally

adopted procedure in the literature is to adjust (increase or decrease) the AR model order based on

the required classification accuracy and available computational resources. Such practice usually

results in an AR model order in the range of 4 to 6 [16], [95]. We believe that a detailed statistical

study is essential to, 1) identify the parsimonious AR model order for the myoelectric signal, 2)

36

measure the the goodness of fit of the identified model, and 3) evaluate various characteristics of

the modeling residuals, such as the sample autocorrelation and/or the heteroscedasticity.

In this chapter, we show that modeling the myoelectric signal as an AR process results into the

residual errors that exhibit heteroscedasticity, i.e., ``variability" in the variance. [180]. In order to

illustrate the concept of heteroscedasticity, let us consider a simple linear regression model

between two variables x and y,

y = + x+ , (3.1)

where represents the regression error. We call homoscedasticity the assumption that the

expected size of the error is constant. We call heteroscedasticity the assumption that the expected

size of the error term is not constant [181]. The assumption of homoscedasticity is standard in

regression theory because of its mathematical convenience. However, in many applications, this

assumption may be unreasonable. A classic example of heteroscedasticity is that of income

versus expenditure. Those with higher income will display a greater variability in consumption

than lower-income individuals who tend to spend a rather constant amount. The concept of

heteroscedasticity generalizes to many other linear and non-linear models including the AR

model. The presence of heteroscedasticity in a time-series can invalidate statistical tests that

assume that the model residual variances are uncorrelated. It is possible to specify a stochastic

process for the residual errors and predict the average size of the error terms [181] using the

Autoregressive Conditional Heteroscedasticity (ARCH) [182] or the Generalized ARCH

(GARCH) models [183]. The GARCH process is a generalization of the ARCH process, and can

model the heteroscedasticity more parsimoniously.

37

In engineering applications, the GARCH models have been employed to extract features from

the electroencephalogram (EEG) signals within the framework of wavelet transforms [184]. The

GARCH models have also been used within a state-space framework and the Kalman filter for

modeling non-stationary variance in the EEG signal [185], or modeling covariance for generation

of the EEG signal [186]. On the other hand, GARCH models have been successfully used to

model and enhance speech signals in the time-frequency domain [187]. Furthermore, voice

activity detection (VAD) is another area where GARCH models have been successfully used to

distinguish between the voice and the noise in a speech signal [188], [189]. In the case of

myoelectric signals, the GARCH process has been used for noise suppression with wavelet

coefficients [190]. However, to the best of our knowledge, no exclusive effort is reported in the

literature to model the myoelectric signal as an AR-GARCH process and use its parameters as a

basis for statistical inference and biophysical interpretation. In Fig 3.1, we contrast the proposed

approach with the conventional AR feature approach. The proposed AR-GARCH model extracts

more information from the myoelectric signal as compared to the convectional scheme as the AR

residuals further modeled as a GARCH process.

3.2 Heteroscedastic Processes and Myoelectric Signal

Modeling

Heteroscedastic processes are characterized by a volatile nature, and are often encountered in

econometrics and finance, as for instance in stock prices, which exhibit periods of large inter-day

price variability followed by periods of relative stability. The ARCH and GARCH processes are

38

AR Modeling

Classification

AR coefficients

GARCH Modeling

AR Residuals

Classification

AR-GARCH coefficients

GARCH coefficients

Segmented myoelectric signal

Conventional scheme

Proposed scheme

Figure 3.1: Proposed and conventional approaches to AR modeling of the myoelectric signal. The

proposed approach captures more information from the myoelectric signals as the AR residuals are

further modeled as the GARCH process.

used to model heteroscedastic time-series [182], [183]. There are numerous generalizations of

these processes, e.g., nonlinear asymmetric GARCH, integrated GARCH, exponential GARCH,

quadratic GARCH, Glosten-Jagannathan-Runkle GARCH and threshold GARCH [191]. In this

paper, we focus on the GARCH process to model heteroscedasticity exhibited by the myoelectric

signal.

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3.2.1 The GARCH Process

Let Zt be a sequence of i.i.d. random variables with zero mean and unit variance from some

specified probability density function. The process Yt is called GARCH(p, q) if

Yt = tZt, t Z, (3.2a)

2t = 0 +

qi=1

iY2ti +

pj=1

j2tj, (3.2b)

where 0 > 0, i 0 and j 0, i, j; t 0 and Zt N (0, 1). If the parameter p = 0 in the

second summation in (3.2b), the GARCH(p, q) process reduces to an ARCH(q) process [182]. In

an ARCH(q) process, the conditional variance is a linear function of past sample variances only,

whereas the GARCH(p, q) process takes into account lagged conditional variances as well [183].

If both p = q = 0, the process Yt is a pure white noise with variance specified by the parameter

0. Some relevant properties of the GARCH process are discussed below. The expected value

(E[ . ]) of the GARCH (p, q) process is given by

E[Yt] = E[tZt] = E[t]E[Zt] = 0. (3.3)

Similarly, the variance (V [ . ]) of the GARCH (p, q) process is given by

V [Yt] = E[Y2t ] [E(Yt)]2 = E[Y 2t ] = E[2t ],

= 0 +

qi=1

iE[Y2t ] +

pj=1

jE[2t ],

=0

1qi=1

i p

j=1

j

. (3.4)

40

From Eqs. (3.3) and (3.4), it is clear that the GARCH(p, q) is a zero mean process with a

constant variance, which is specified by the parameters {i}qi=0 and {j}pj=1. The GARCH

process is also statistically uncorrelated, i.e.,

E[YtYs] = E[tZtsZs] = E[tZts]E[Zs] = 0. (3.5)

We show next that the conditional variance of the GARCH process is time-varying, reflecting the

volatility of the stochastic signal. Let Ft = {Ys : s t} represent the history of the process up to

time t. We have

E[Yt|Ft1] = E[tZt|Ft1]

= tE[Zt|Ft1] = tE[Zt] = 0 (3.6)

V [Yt|Ft1] = E[2tZ2t |Ft1]

= 2t V [Zt] = 2t (3.7)

From (3.6) and (3.7), we see that the conditional expected value of the GARCH process is also

zero but the conditional variance is equal to 2t , which is a time-varying quantity. In summary, we

have shown that the GARCH(p, q) process is a white noise process with time-varying conditional

variance.

To understand the difference between a white noise process and the GARCH process, in Fig.

3.2, we generated a Gaussian white noise, wt with zero-mean and unit variance, and a GARCH

process, Yt, using Gaussian innovations. A total of 10,000 realizations for each process were

generated. The sample autocorrelations of the two precesses, wt, Yt, and the squared processes,

41

0 5000 10000-5

0

5

Samples

Am

plitu

de

Gaussian White Noise

0 5000 10000

-100

-50

0

50

100

Samples

Am

plitu

de

GARCH(1,1) Process

0 5 10 15 20-0.5

0

0.5

1

Lag

Sam

ple

Aut

ocor

rela

tion

White Noise

0 5 10 15 20-0.5

0

0.5

1

Lag

Sam

ple

Aut

ocor

rela

tion

White Noise (Squared Samples)

0 5 10 15 20-0.5

0

0.5

1

Lag

Sam

ple

Aut

ocor

rela

tion

GARCH(1,1) Process

0 5 10 15 20-0.5

0

0.5

1

Lag

Sam

ple

Aut

ocor

rela

tion

GARCH(1,1) Process (Squared Samples)

Figure 3.2: A comparison of the Gaussian white noise and the GARCH(1,1) process. The first

column presents Gaussian white noise and the second column presents GARCH(1,1) process. Top

row shows both processes, mid row shows the samples autocorrelation values for 20 lags, and the

last row presents the sample autocorrelations of the squared processes. We can see that the GARCH

process is a white noise just like the Gaussian white noise, but with a unique characteristic, i.e.,

there is a significant autocorrelation in its squared sample values as is evident in the lower right

figure. The Gaussian noise was generated using standard normal distribution, and the GARCH

process was generated using Zt N (0, 1), 0 = 2, 1 = 0.09 and 1 = 0.9.

42

w2t , Y2t , were computed for 20 lag values. It is evident from Fig. 3.2 that the squared sample

a