The biomedical engineering handbook

(BQ) Part 1 The biomedical engineering handbook Medical devices and systems has contents: Digital biomedical signal acquisition and processing, higher order spectral analysis, neural networks in biomedical signal processing, computed tomography,...and other contents.

The Biomedical Engineering Handbook

Third Edition

Medical Devices

and Systems

The Electrical Engineering Handbook Series

Series Editor

Richard C Dorf

University of California, Davis

Titles Included in the Series

The Handbook of Ad Hoc Wireless Networks, Mohammad Ilyas

The Avionics Handbook, Cary R Spitzer

The Biomedical Engineering Handbook, Third Edition, Joseph D Bronzino

The Circuits and Filters Handbook, Second Edition, Wai-Kai Chen

The Communications Handbook, Second Edition, Jerry Gibson

The Computer Engineering Handbook, Vojin G Oklobdzija

The Control Handbook, William S Levine

The CRC Handbook of Engineering Tables, Richard C Dorf

The Digital Signal Processing Handbook, Vijay K Madisetti and Douglas Williams The Electrical Engineering Handbook, Third Edition, Richard C Dorf

The Electric Power Engineering Handbook, Leo L Grigsby

The Electronics Handbook, Second Edition, Jerry C Whitaker

The Engineering Handbook, Third Edition, Richard C Dorf

The Handbook of Formulas and Tables for Signal Processing, Alexander D Poularikas The Handbook of Nanoscience, Engineering, and Technology, William A Goddard, III,

Donald W Brenner, Sergey E Lyshevski, and Gerald J Iafrate

The Handbook of Optical Communication Networks, Mohammad Ilyas and

Hussein T Mouftah

The Industrial Electronics Handbook, J David Irwin

The Measurement, Instrumentation, and Sensors Handbook, John G Webster

The Mechanical Systems Design Handbook, Osita D.I Nwokah and Yidirim Hurmuzlu The Mechatronics Handbook, Robert H Bishop

The Mobile Communications Handbook, Second Edition, Jerry D Gibson

The Ocean Engineering Handbook, Ferial El-Hawary

The RF and Microwave Handbook, Mike Golio

The Technology Management Handbook, Richard C Dorf

The Transforms and Applications Handbook, Second Edition, Alexander D Poularikas The VLSI Handbook, Wai-Kai Chen

Third Edition

Edited by

Joseph D Bronzino

Biomedical Engineering Fundamentals

Medical Devices and Systems Tissue Engineering and Artificial Organs

The Biomedical Engineering Handbook

Third Edition

Medical Devices

and Systems

Edited by Joseph D Bronzino

Trinity College Hartford, Connecticut, U.S.A.

A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.

Boca Raton London New York

Published in 2006 by

CRC Press

Taylor & Francis Group

6000 Broken Sound Parkway NW, Suite 300

Boca Raton, FL 33487-2742

© 2006 by Taylor & Francis Group, LLC

CRC Press is an imprint of Taylor & Francis Group

No claim to original U.S Government works

Printed in the United States of America on acid-free paper

10 9 8 7 6 5 4 3 2 1

International Standard Book Number-10: 0-8493-2122-0 (Hardcover)

International Standard Book Number-13: 978-0-8493-2122-1 (Hardcover)

Library of Congress Card Number 2005056892

This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials

or for the consequences of their use.

No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers

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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.

Library of Congress Cataloging-in-Publication Data

Medical devices and systems / edited by Joseph D Bronzino.

p cm (The electrical engineering handbook series) Includes bibliographical references and index.

ISBN 0-8493-2122-0

1 Medical instruments and apparatus Handbooks, manuals, etc I Bronzino, Joseph D., 1937- II

Title III Series.

R856.15.B76 2006

610.28 dc22 2005056892

Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Taylor & Francis Group

is the Academic Division of Informa plc.

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Introduction and Preface

During the past five years since the publication of the Second Edition — a two-volume set — of the

Biomedical Engineering Handbook, the field of biomedical engineering has continued to evolve and expand.

As a result, this Third Edition consists of a three volume set, which has been significantly modified toreflect the state-of-the-field knowledge and applications in this important discipline More specifically,this Third Edition contains a number of completely new sections, including:

as well as a new section on ethics

In addition, all of the sections that have appeared in the first and second editions have been significantlyrevised Therefore, this Third Edition presents an excellent summary of the status of knowledge andactivities of biomedical engineers in the beginning of the 21st century

As such, it can serve as an excellent reference for individuals interested not only in a review of mental physiology, but also in quickly being brought up to speed in certain areas of biomedical engineeringresearch It can serve as an excellent textbook for students in areas where traditional textbooks have notyet been developed and as an excellent review of the major areas of activity in each biomedical engineeringsubdiscipline, such as biomechanics, biomaterials, bioinstrumentation, medical imaging, etc Finally, itcan serve as the “bible” for practicing biomedical engineering professionals by covering such topics as a his-torical perspective of medical technology, the role of professional societies, the ethical issues associatedwith medical technology, and the FDA process

funda-Biomedical engineering is now an important vital interdisciplinary field funda-Biomedical engineers areinvolved in virtually all aspects of developing new medical technology They are involved in the design,development, and utilization of materials, devices (such as pacemakers, lithotripsy, etc.) and techniques(such as signal processing, artificial intelligence, etc.) for clinical research and use; and serve as members

of the health care delivery team (clinical engineering, medical informatics, rehabilitation engineering,etc.) seeking new solutions for difficult health care problems confronting our society To meet the needs

of this diverse body of biomedical engineers, this handbook provides a central core of knowledge in thosefields encompassed by the discipline However, before presenting this detailed information, it is important

to provide a sense of the evolution of the modern health care system and identify the diverse activitiesbiomedical engineers perform to assist in the diagnosis and treatment of patients

Evolution of the Modern Health Care System

Before 1900, medicine had little to offer the average citizen, since its resources consisted mainly ofthe physician, his education, and his “little black bag.” In general, physicians seemed to be in short

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doctors’ services also was very small, since many of the services provided by the physician also could beobtained from experienced amateurs in the community The home was typically the site for treatmentand recuperation, and relatives and neighbors constituted an able and willing nursing staff Babies weredelivered by midwives, and those illnesses not cured by home remedies were left to run their natural,albeit frequently fatal, course The contrast with contemporary health care practices, in which specializedphysicians and nurses located within the hospital provide critical diagnostic and treatment services, isdramatic

The changes that have occurred within medical science originated in the rapid developments that tookplace in the applied sciences (chemistry, physics, engineering, microbiology, physiology, pharmacology,etc.) at the turn of the century This process of development was characterized by intense interdis-ciplinary cross-fertilization, which provided an environment in which medical research was able totake giant strides in developing techniques for the diagnosis and treatment of disease For example,

in 1903, Willem Einthoven, a Dutch physiologist, devised the first electrocardiograph to measure theelectrical activity of the heart In applying discoveries in the physical sciences to the analysis of thebiologic process, he initiated a new age in both cardiovascular medicine and electrical measurementtechniques

New discoveries in medical sciences followed one another like intermediates in a chain reaction ever, the most significant innovation for clinical medicine was the development of x-rays These “newkinds of rays,” as their discoverer W.K Roentgen described them in 1895, opened the “inner man” tomedical inspection Initially, x-rays were used to diagnose bone fractures and dislocations, and in the pro-cess, x-ray machines became commonplace in most urban hospitals Separate departments of radiologywere established, and their influence spread to other departments throughout the hospital By the 1930s,x-ray visualization of practically all organ systems of the body had been made possible through the use ofbarium salts and a wide variety of radiopaque materials

How-X-ray technology gave physicians a powerful tool that, for the first time, permitted accurate diagnosis

of a wide variety of diseases and injuries Moreover, since x-ray machines were too cumbersome andexpensive for local doctors and clinics, they had to be placed in health care centers or hospitals Oncethere, x-ray technology essentially triggered the transformation of the hospital from a passive receptaclefor the sick to an active curative institution for all members of society

For economic reasons, the centralization of health care services became essential because of many otherimportant technological innovations appearing on the medical scene However, hospitals remained insti-tutions to dread, and it was not until the introduction of sulfanilamide in the mid-1930s and penicillin inthe early 1940s that the main danger of hospitalization, that is, cross-infection among patients, was signi-ficantly reduced With these new drugs in their arsenals, surgeons were able to perform their operationswithout prohibitive morbidity and mortality due to infection Furthermore, even though the differentblood groups and their incompatibility were discovered in 1900 and sodium citrate was used in 1913 toprevent clotting, full development of blood banks was not practical until the 1930s, when technologyprovided adequate refrigeration Until that time, “fresh” donors were bled and the blood transfused while

it was still warm

Once these surgical suites were established, the employment of specifically designed pieces of ical technology assisted in further advancing the development of complex surgical procedures Forexample, the Drinker respirator was introduced in 1927 and the first heart-lung bypass in 1939 Bythe 1940s, medical procedures heavily dependent on medical technology, such as cardiac catheterizationand angiography (the use of a cannula threaded through an arm vein and into the heart with the injection

med-of radiopaque dye) for the x-ray visualization med-of congenital and acquired heart disease (mainly valvedisorders due to rheumatic fever) became possible, and a new era of cardiac and vascular surgery wasestablished

Following World War II, technological advances were spurred on by efforts to develop superior weaponsystems and establish habitats in space and on the ocean floor As a by-product of these efforts, the

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development of medical devices accelerated and the medical profession benefited greatly from this rapidsurge of technological finds Consider the following examples:

1 Advances in solid-state electronics made it possible to map the subtle behavior of the fundamentalunit of the central nervous system — the neuron — as well as to monitor the various physiologicalparameters, such as the electrocardiogram, of patients in intensive care units

2 New prosthetic devices became a goal of engineers involved in providing the disabled with tools toimprove their quality of life

3 Nuclear medicine — an outgrowth of the atomic age — emerged as a powerful and effectiveapproach in detecting and treating specific physiologic abnormalities

4 Diagnostic ultrasound based on sonar technology became so widely accepted that ultrasonic studiesare now part of the routine diagnostic workup in many medical specialties

5 “Spare parts” surgery also became commonplace Technologists were encouraged to providecardiac assist devices, such as artificial heart valves and artificial blood vessels, and the artifi-cial heart program was launched to develop a replacement for a defective or diseased humanheart

6 Advances in materials have made the development of disposable medical devices, such as needlesand thermometers, as well as implantable drug delivery systems, a reality

7 Computers similar to those developed to control the flight plans of the Apollo capsule were used

to store, process, and cross-check medical records, to monitor patient status in intensive care units,and to provide sophisticated statistical diagnoses of potential diseases correlated with specific sets

of patient symptoms

8 Development of the first computer-based medical instrument, the computerized axial tomographyscanner, revolutionized clinical approaches to noninvasive diagnostic imaging procedures, whichnow include magnetic resonance imaging and positron emission tomography as well

9 A wide variety of new cardiovascular technologies including implantable defibrillators andchemically treated stents were developed

10 Neuronal pacing systems were used to detect and prevent epileptic seizures

11 Artificial organs and tissue have been created

12 The completion of the genome project has stimulated the search for new biological markers andpersonalized medicine

The impact of these discoveries and many others has been profound The health care system of todayconsists of technologically sophisticated clinical staff operating primarily in modern hospitals designed

to accommodate the new medical technology This evolutionary process continues, with advances in thephysical sciences such as materials and nanotechnology, and in the life sciences such as molecular biology,the genome project and artificial organs These advances have altered and will continue to alter the verynature of the health care delivery system itself

Biomedical Engineering: A Definition

Bioengineering is usually defined as a basic research-oriented activity closely related to biotechnology and

genetic engineering, that is, the modification of animal or plant cells, or parts of cells, to improve plants

or animals or to develop new microorganisms for beneficial ends In the food industry, for example, thishas meant the improvement of strains of yeast for fermentation In agriculture, bioengineers may beconcerned with the improvement of crop yields by treatment of plants with organisms to reduce frostdamage It is clear that bioengineers of the future will have a tremendous impact on the qualities ofhuman life The potential of this specialty is difficult to imagine Consider the following activities ofbioengineers:

• Development of improved species of plants and animals for food production

• Invention of new medical diagnostic tests for diseases

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Medical &

biological analysis Biosensors

Clinical engineering

Biomedical instrumentation

Neural engineering

Tissue engineering Biotechnology Biomaterials Medical imaging

Prosthetic devices

& artificial organs

FIGURE 1 The World of Biomedical Engineering.

• Production of synthetic vaccines from clone cells

• Bioenvironmental engineering to protect human, animal, and plant life from toxicants andpollutants

• Study of protein–surface interactions

• Modeling of the growth kinetics of yeast and hybridoma cells

• Research in immobilized enzyme technology

• Development of therapeutic proteins and monoclonal antibodies

Biomedical engineers, on the other hand, apply electrical, mechanical, chemical, optical, and otherengineering principles to understand, modify, or control biologic (i.e., human and animal) systems, aswell as design and manufacture products that can monitor physiologic functions and assist in the diagnosisand treatment of patients When biomedical engineers work within a hospital or clinic, they are moreproperly called clinical engineers

Activities of Biomedical Engineers

The breadth of activity of biomedical engineers is now significant The field has moved from beingconcerned primarily with the development of medical instruments in the 1950s and 1960s to include amore wide-ranging set of activities As illustrated below, the field of biomedical engineering now includesmany new career areas (see Figure 1), each of which is presented in this handbook These areas include:

• Application of engineering system analysis (physiologic modeling, simulation, and control) tobiologic problems

• Detection, measurement, and monitoring of physiologic signals (i.e., biosensors and biomedicalinstrumentation)

• Diagnostic interpretation via signal-processing techniques of bioelectric data

• Therapeutic and rehabilitation procedures and devices (rehabilitation engineering)

• Devices for replacement or augmentation of bodily functions (artificial organs)

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• Computer analysis of patient-related data and clinical decision making (i.e., medical informaticsand artificial intelligence)

• Medical imaging, that is, the graphic display of anatomic detail or physiologic function

• The creation of new biologic products (i.e., biotechnology and tissue engineering)

• The development of new materials to be used within the body (biomaterials)

Typical pursuits of biomedical engineers, therefore, include:

• Research in new materials for implanted artificial organs

• Development of new diagnostic instruments for blood analysis

• Computer modeling of the function of the human heart

• Writing software for analysis of medical research data

• Analysis of medical device hazards for safety and efficacy

• Development of new diagnostic imaging systems

• Design of telemetry systems for patient monitoring

• Design of biomedical sensors for measurement of human physiologic systems variables

• Development of expert systems for diagnosis of disease

• Design of closed-loop control systems for drug administration

• Modeling of the physiological systems of the human body

• Design of instrumentation for sports medicine

• Development of new dental materials

• Design of communication aids for the handicapped

• Study of pulmonary fluid dynamics

• Study of the biomechanics of the human body

• Development of material to be used as replacement for human skin

Biomedical engineering, then, is an interdisciplinary branch of engineering that ranges from theoretical,nonexperimental undertakings to state-of-the-art applications It can encompass research, development,implementation, and operation Accordingly, like medical practice itself, it is unlikely that any singleperson can acquire expertise that encompasses the entire field Yet, because of the interdisciplinary nature

of this activity, there is considerable interplay and overlapping of interest and effort between them.For example, biomedical engineers engaged in the development of biosensors may interact with thoseinterested in prosthetic devices to develop a means to detect and use the same bioelectric signal to power

a prosthetic device Those engaged in automating the clinical chemistry laboratory may collaborate withthose developing expert systems to assist clinicians in making decisions based on specific laboratory data.The possibilities are endless

Perhaps a greater potential benefit occurring from the use of biomedical engineering is identification

of the problems and needs of our present health care system that can be solved using existing engineeringtechnology and systems methodology Consequently, the field of biomedical engineering offers hope inthe continuing battle to provide high-quality care at a reasonable cost If properly directed toward solvingproblems related to preventive medical approaches, ambulatory care services, and the like, biomedicalengineers can provide the tools and techniques to make our health care system more effective and efficient;and in the process, improve the quality of life for all

Joseph D Bronzino

Editor-in-Chief

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Editor-in-Chief

Joseph D Bronzino received the B.S.E.E degree from Worcester Polytechnic Institute, Worcester, MA,

in 1959, the M.S.E.E degree from the Naval Postgraduate School, Monterey, CA, in 1961, and the Ph.D.degree in electrical engineering from Worcester Polytechnic Institute in 1968 He is presently the VernonRoosa Professor of Applied Science, an endowed chair at Trinity College, Hartford, CT and President

of the Biomedical Engineering Alliance and Consortium (BEACON) which is a nonprofit organizationconsisting of academic and medical institutions as well as corporations dedicated to the development andcommercialization of new medical technologies (for details visit www.beaconalliance.org)

He is the author of over 200 articles and 11 books including the following: Technology for Patient

Care (C.V Mosby, 1977), Computer Applications for Patient Care (Addison-Wesley, 1982), Biomedical Engineering: Basic Concepts and Instrumentation (PWS Publishing Co., 1986), Expert Systems: Basic Con- cepts (Research Foundation of State University of New York, 1989), Medical Technology and Society: An Interdisciplinary Perspective (MIT Press and McGraw-Hill, 1990), Management of Medical Technology (But-

terworth/Heinemann, 1992), The Biomedical Engineering Handbook (CRC Press, 1st ed., 1995; 2nd ed., 2000; Taylor & Francis, 3rd ed., 2005), Introduction to Biomedical Engineering (Academic Press, 1st ed.,

1999; 2nd ed., 2005)

Dr Bronzino is a fellow of IEEE and the American Institute of Medical and Biological Engineering(AIMBE), an honorary member of the Italian Society of Experimental Biology, past chairman of theBiomedical Engineering Division of the American Society for Engineering Education (ASEE), a chartermember and presently vice president of the Connecticut Academy of Science and Engineering (CASE),

a charter member of the American College of Clinical Engineering (ACCE) and the Association for theAdvancement of Medical Instrumentation (AAMI), past president of the IEEE-Engineering in Medicineand Biology Society (EMBS), past chairman of the IEEE Health Care Engineering Policy Committee(HCEPC), past chairman of the IEEE Technical Policy Council in Washington, DC, and presently Editor-

in-Chief of Elsevier’s BME Book Series and Taylor & Francis’ Biomedical Engineering Handbook.

Dr Bronzino is also the recipient of the Millennium Award from IEEE/EMBS in 2000 and the GoddardAward from Worcester Polytechnic Institute for Professional Achievement in June 2004

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Ville Marie Multidisciplinary

Breast and Oncology Center

Ludwig Boltzmann Research

Institute for Physical

Khosrow Behbehani

The University of Texas atArlington

Arlington, Texasand

The University of TexasSouthwestern Medical CenterDallas, Texas

N Belliveau

Ville Marie MultidisciplinaryBreast and Oncology Center

St Mary’s HospitalMcGill UniversityMontreal, Quebec, Canadaand

London Cancer CentreLondon, Ontario, Canada

Anna M Bianchi

St Raffaele HospitalMilan, Italy

Joseph D Bronzino

Trinity CollegeBiomedical Engineering Allianceand Consortium (BEACON)Harford, Connecticut

Mark E Bruley

ECRIPlymouth Meeting, Pennsylvania

Robert D Butterfield

IVAC CorporationSan Diego, California

Joseph P Cammarota

Naval Air Warfare CenterAircraft DivisionWarminster, Pennsylvania

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National Institute of Child Health

and Human Development

Bethesda, Maryland

David A Chesler

Massachusetts General Hospital

Harvard University Medical

Ian A Cunningham

Victoria HospitalThe John P Roberts ResearchInstitute

andThe University of Western OntarioLondon, Ontario, Canada

Yadin David

Texas Children’s HospitalHouston, Texas

Connie White Delaney

School of Nursing and MedicalSchool

The University of MinnesotaMinneapolis, Minnesota

Mary Diakides

Advanced Concepts Analysis, Inc

Falls Church, Virginia

Nicholas A Diakides

Advanced Concepts Analysis, Inc

Falls Church, Virginia

Night Vision and ElectronicSensors DirectorateFort Belvoir, Virginia

Piscataway, New Jersey

Israel Gannot

Laboratory of Integrative andMedical BiophysicsNational Institute of Child Healthand Human DevelopmentBethesda, Maryland

Leslie A Geddes

Purdue UniversityWest Lafayette, Indiana

Richard L Goldberg

University of North CarolinaChapel Hill, North Carolina

and Electrical Engineering

Henry Samueli School of

Engineering and Applied

National Institute of Child Health

and Human Development

Bethesda, Maryland

David Hattery

Laboratory of Integrative andMedical BiophysicsNational Institute of Child Healthand Human DevelopmentBethesda, Maryland

Jonathan F Head

Elliott-Elliott-Head Breast CancerResearch and Treatment CenterBaton Rouge, Louisiana

Night Vision and ElectronicSensors DirectorateFort Belvoir, Virginia

Xiaoping Hu

Center for Magnetic ResonanceResearch

andThe University of MinnesotaMedical School

Thomas M Judd

Kaiser PermanenteAtlanta, Georgia

Boston, Massachusetts

G.J.L Kaw

Department of DiagnosticRadiology

Tan Tock Seng HospitalSingapore

J.R Keyserlingk

Ville Marie MultidisciplinaryBreast and Oncology Center

St Mary’s HospitalMcGill UniversityMontreal, Quebec, Canadaand

London Cancer CentreLondon, OntarioCanada

C Everett Koop

Department of Plastic SurgeryDartmouth-Hitchcock MedicalCenter

Lebanon, New Hampshire

Hayrettin Köymen

Bilkent UniversityAnkara, Turkey

Luis G Kun

IRMC/National DefenseUniversity

Washington, D.C

Phani Teja Kuruganti

RF and Microwave Systems GroupOak Ridge National LaboratoryOak Ridge, Tennessee

Kenneth K Kwong

Massachusetts General HospitalHarvard University MedicalSchool

Boston, Massachusetts

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Electronics Design Center and

Edison Sensor Technology

Applied Research Associates, Inc

Falls Church, Virginia

Lebanon, New Hampshire

Matthew F McKnight

Department of Plastic SurgeryDartmouth-Hitchcock MedicalCenter

Lebanon, New Hampshire

Foundation “G.d’Annunzio”

andIstituto Nazionale Fisica dellaMateria

Coordinated Group of ChietiChieti-Pescara, Italy

Evangelia Micheli-Tzanakou

Rutgers UnversityPiscataway, New Jersey

UniversityHoughton, Michigan

E.Y.K Ng

College of EngineeringSchool of Mechanical andProduction EngineeringNanyang Technological UniversitySingapore

Paul Norton

U.S Army Communications andElectronics Research,Development and EngineeringCenter (CERDEC)

Night Vision and ElectronicSensors DirectorateFort Belvoir, Virginia

Antoni Nowakowski

Department of BiomedicalEngineering,

Gdansk University of TechnologyNarutowicza

Gdansk, Poland

Banu Onaral

Drexel UniversityPhiladelphia, Pennsylvania

David D Pascoe

Auburn UniversityAuburn, Alabama

Maqbool Patel

Center for Magnetic ResonanceResearch

andThe University of MinnesotaMedical School

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Lebanon, New Hampshire

Gian Luca Romani

Department of Clinical Sciencesand Bioimaging

University “G d’Annunzio”

andInstitute for AdvancedBiomedical TechnologyFoundation “G.d’Annunzio”

andIstituto Nazionale Fisica dellaMateria

Coordinated Group of ChietiChieti-Pescara, Italy

Joseph M Rosen

Department of Plastic SurgeryDartmouth-Hitchcock MedicalCenter

Lebanon, New Hampshire

Eric Rosow

Hartford Hospitaland

Premise DevelopmentCorporationHartford, Connecticut

Subrata Saha

Clemson UniversityClemson, South Carolina

John Schenck

General Electric CorporateResearch and DevelopmentCenter

Schenectady, New York

Edward Schuck

EdenTec CorporationEden Prairie, Minnesota

Joyce Sensmeier

HIMSSChicago, Illinois

Stephen W Smith

Duke UniversityDurham, North Carolina

Nathan J Sniadecki

Department of BioengineeringUniversity of PennsylvaniaPhiladelphia, Pennsylvania

Wesley E Snyder

ECE DepartmentNorth Carolina State UniversityRaleigh, North Carolina

Orhan Soykan

Corporate Science andTechnologyMedtronic, Inc

andDepartment of BiomedicalEngineering

Michigan TechnologicalUniversity

Christopher Swift

Department of Plastic SurgeryDartmouth-Hitchcock MedicalCenter

Lebanon, New Hampshire

Willis A Tacker

Purdue UniversityWest Lafayette, Indiana

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Baltimore, Maryland

Roderick Thomas

Faculty of Applied Design and

Engineering

Swansea Institute of Technology

Swansea, United Kingdom

University of North Carolina

Chapel Hill, North Carolina

National Institute of Child Health

and Human Development

Bethesda, Maryland

Troy, New York

Gregory I Voss

IVAC CorporationSan Diego, California

Alvin Wald

Columbia UniversityNew York, New York

Chen Wang

TTM InternationalHouston, Texas

Lois de Weerd

University Hospital ofNorth NorwayTromsø, Norway

Wang Wei

Radiology DepartmentBeijing You An HospitalBeijing, China

M Yassa

Ville Marie MultidisciplinaryBreast and Oncology Center

St Mary’s HospitalMcGill UniversityMontreal, Quebec, Canadaand

London Cancer CentreLondon, Ontario, Canada

Engineering and AppliedChemistry

Department of BiochemistryInstitute of Biomaterials andBiomedical EngineeringUniversity of TorontoToronto, Ontario, Canada

E Yu

Ville Marie MultidisciplinaryBreast and Oncology Center

St Mary’s HospitalMcGill UniversityMontreal, Quebec, Canadaand

London Cancer CentreLondon, Ontario, Canada

Jason Zeibel

U.S Army Communications andElectronics Research,Development and EngineeringCenter (CERDEC)

Night Vision and ElectronicSensors DirectorateFort Belvoir, Virginia

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Luca T Mainardi, Anna M Bianchi, Sergio Cerutti 2-1

A Enis Çetin, Hayrettin Köymen 3-1

Biomedical Signals

G Faye Boudreaux-Bartels, Robin Murray 4-1

Signal Processing

Nitish V Thakor, Boris Gramatikov, David Sherman 5-1

Athina P Petropulu 6-1

Evangelia Micheli-Tzanakou 7-1

Banu Onaral, Joseph P Cammarota 8-1

Networked Multimedia Communications

Banu Onaral 9-1

Ian A Cunningham , Philip F Judy 11-1

12 Magnetic Resonance Imaging

Steven Conolly, Albert Macovski, John Pauly, John Schenck, Kenneth K Kwong, David A Chesler, Xiaoping Hu,

Wei Chen, Maqbool Patel, Kamil Ugurbil 12-1

15 Magnetic Resonance Microscopy

Xiaohong Zhou, G Allan Johnson 15-1

16 Positron-Emission Tomography (PET)

Thomas F Budinger, Henry F VanBrocklin 16-1

17 Electrical Impedance Tomography

D.C Barber 17-1

18 Medical Applications of Virtual Reality Technology

Walter Greenleaf, Tom Piantanida 18-1

SECTIONIII Infrared Imaging

Nicholas A Diakides

19 Advances in Medical Infrared Imaging

Nicholas Diakides, Mary Diakides, Jasper Lupo,

Jeffrey L Paul, Raymond Balcerak 19-1

20 The Historical Development of Thermometry

and Thermal Imaging in Medicine

E Francis Ring, Bryan F Jones 20-1

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21 Physiology of Thermal Signals

David D Pascoe, James B Mercer, Lois de Weerd 21-1

22 Quantitative Active Dynamic Thermal IR-Imaging and

Thermal Tomography in Medical Diagnostics

Antoni Nowakowski 22-1

23 Thermal Texture Maps (TTM): Concept, Theory, and

Applications

Zhongqi Liu, Chen Wang, Hairong Qi, Yune Yuan, Yi Zeng,

Z.R Li, Yulin Zhou, Wen Yu, Wang Wei 23-1

24 IR Imagers as Fever Monitoring Devices: Physics,

Physiology, and Clinical Accuracy

E.Y.K Ng, G.J.L Kaw 24-1

25 Infrared Imaging of the Breast — An Overview

William C Amalu, William B Hobbins, Jonathan F Head,

Robert L Elliott 25-1

26 Functional Infrared Imaging of the Breast:

Historical Perspectives, Current Application, and

Hairong Qi, Phani Teja Kuruganti, Wesley E Snyder 27-1

28 Advanced Thermal Image Processing

B Wiecek, M Strzelecki, T Jakubowska, M Wysocki,

C Drews-Peszynski 28-1

29 Biometrics: Face Recognition in Thermal Infrared

I Pavlidis, P Tsiamyrtzis, P Buddharaju, C Manohar 29-1

30 Infrared Imaging for Tissue Characterization and Function

Moinuddin Hassan, Victor Chernomordik, Abby Vogel,

David Hattery, Israel Gannot, Richard F Little,

Robert Yarchoan, Amir H Gandjbakhche 30-1

31 Thermal Imaging in Diseases of the Skeletal and

Neuromuscular Systems

E Francis Ring, Kurt Ammer 31-1

32 Functional Infrared Imaging in Clinical Applications

Arcangelo Merla, Gian Luca Romani 32-1

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34 Infrared Imaging Applied to Dentistry

Barton M Gratt 34-1

35 Use of Infrared Imaging in Veterinary Medicine

Ram C Purohit, Tracy A Turner, David D Pascoe 35-1

36 Standard Procedures for Infrared Imaging in Medicine

Kurt Ammer, E Francis Ring 36-1

37 Infrared Detectors and Detector Arrays

Paul Norton, Stuart Horn, Joseph G Pellegrino,

Philip Perconti 37-1

38 Infrared Camera Characterization

Joseph G Pellegrino, Jason Zeibel, Ronald G Driggers,

Philip Perconti 38-1

39 Infrared Camera and Optics for Medical Applications

Michael W Grenn, Jay Vizgaitis, Joseph G Pellegrino,

43 Introduction to Informatics and Nursing

Kathleen A McCormick, Joyce Sensmeier,

Connie White Delaney, Carol J Bickford 43-1

44 Non-AI Decision Making

Ron Summers, Derek G Cramp, Ewart R Carson 44-1

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45 Medical Informatics and Biomedical Emergencies: New

Training and Simulation Technologies for First Responders

Joseph M Rosen, Christopher Swift, Eliot B Grigg,

Matthew F McKnight, Susan McGrath, Dennis McGrath,

Peter Robbie, C Everett Koop 45-1

SECTIONV Biomedical Sensors

SECTIONVI Medical Instruments and Devices

Wolf W von Maltzahn

52 Biopotential Amplifiers

Joachim H Nagel 52-1

53 Bioelectric Impedance Measurements

Robert Patterson 53-1

54 Implantable Cardiac Pacemakers

Michael Forde, Pat Ridgely 54-1

55 Noninvasive Arterial Blood Pressure and Mechanics

Gary Drzewiecki 55-1

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57 External Defibrillators

Willis A Tacker 57-1

58 Implantable Defibrillators

Edwin G Duffin 58-1

59 Implantable Stimulators for Neuromuscular Control

Primoz Strojnik, P Hunter Peckham 59-1

65 Instrumentation for Cell Mechanics

Nathan J Sniadecki, Christopher S Chen 65-1

66 Blood Glucose Monitoring

David D Cunningham 66-1

67 Atomic Force Microscopy: Probing Biomolecular

Interactions

Christopher M Yip 67-1

68 Parenteral Infusion Devices

Gregory I Voss, Robert D Butterfield 68-1

69 Clinical Laboratory: Separation and Spectral Methods

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72 Medical Instruments and Devices Used in the Home

Bruce R Bowman, Edward Schuck 72-1

73 Virtual Instrumentation: Applications in Biomedical

Engineering

Eric Rosow, Joseph Adam 73-1

SECTIONVII Clinical Engineering

Yadin David

74 Clinical Engineering: Evolution of a Discipline

Joseph D Bronzino 74-1

75 Management and Assessment of Medical Technology

Yadin David, Thomas M Judd 75-1

76 Risk Factors, Safety, and Management of Medical Equipment

Michael L Gullikson 76-1

77 Clinical Engineering Program Indicators

Dennis D Autio, Robert L Morris 77-1

78 Quality of Improvement and Team Building

Joseph P McClain 78-1

79 A Standards Primer for Clinical Engineers

Alvin Wald 79-1

80 Regulatory and Assessment Agencies

Mark E Bruley, Vivian H Coates 80-1

81 Applications of Virtual Instruments in Health Care

Eric Rosow, Joseph Adam 81-1

SECTIONVIII Ethical Issues Associated with

the Use of Medical Technology

Subrata Saha and Joseph D Bronzino

82 Beneficence, Nonmaleficence, and Medical Technology

Joseph D Bronzino 82-1

83 Ethical Issues Related to Clinical Research

Joseph D Bronzino 83-1

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I Biomedical Signal

Luca T Mainardi, Sergio Cerutti, Anna M Bianchi 2-1

A Enis Çetin, Hayrettin Köymen 3-1

G Faye Boudreaux-Bartels, Robin Murray 4-1

Nitish V Thakor, Boris Gramatikov, David Sherman 5-1

Athina P Petropulu 6-1

Evangelia Micheli-Tzanakou 7-1

Banu Onaral, Joseph P Cammarota 8-1

I-1

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Multimedia Communications

Banu Onaral 9-1

BIOMEDICAL SIGNAL ANALYSIS CENTERS on the acquisition and processing of

information-bearing signals that emanate from living systems These vital signals permit us to probe the state ofthe underlying biologic and physiologic structures and dynamics Therefore, their interpretationhas significant diagnostic value for clinicians and researchers

The detected signals are commonly corrupted with noise Often, the information cannot be readilyextracted from the raw signal, which must be processed in order to yield useful results Signals and systemsengineering knowledge and, in particular, signal-processing expertise are therefore critical in all phases ofsignal collection and analysis

Biomedical engineers are called on to conceive and implement processing schemes suitable for ical signals They also play a key role in the design and development of biomedical monitoring devicesand systems that match advances in signal processing and instrumentation technologies with biomedicalneeds and requirements

biomed-This section is organized in two main parts In the first part, contributing authors review contemporarymethods in biomedical signal processing The second part is devoted to emerging methods that hold thepromise for major enhancements in our ability to extract information from vital signals

The success of signal-processing applications strongly depends on the knowledge about the origin andthe nature of the signal Biomedical signals possess many special properties and hence require specialtreatment Also, the need for noninvasive measurements presents unique challenges that demand a clearunderstanding of biomedical signal characteristics In the lead chapter, entitled, “Biomedical Signals:Origin and Dynamic Characteristics; Frequency-Domain Analysis,” Arnon Cohen provides a generalclassification of biomedical signals and discusses basics of frequency domain methods

The advent of digital computing coupled with fast progress in discrete-time signal processing has led toefficient and flexible methods to acquire and treat biomedical data in digital form The chapter entitled,

“Digital Biomedical Signal Acquisition and Processing,” by Luca T Mainardi, Anna M Bianchi, and SergioCerutti, presents basic elements of signal acquisition and processing in the special context of biomedicalsignals

Especially in the case of long-term monitoring, digital biomedical signal-processing applications erate vast amounts of data that strain transmission and storage resources The creation of multipatientreference signal bases also places severe demands on storage Data compression methods overcome theseobstacles by eliminating signal redundancies while retaining clinically significant information A EnisCetin and Hayrettin Köymen provide a comparative overview of a range of approaches from conventional

gen-to modern compression techniques suitable for biomedical signals Futuristic applications involving term and ambulatory recording systems, and remote diagnosis opportunities will be made possible bybreakthroughs in biomedical data compression This chapter serves well as a point of departure.Constraints such as stationarity (and time invariance), gaussianity (and minimum phaseness), and theassumption of a characteristic scale in time and space have constituted the basic, and by now implicit,assumptions upon which the conventional signals and systems theories have been founded However,investigators engaged in the study of biomedical processes have long known that they did not hold undermost realistic situations and hence could not sustain the test of practice

long-Rejecting or at least relaxing restrictive assumptions always opens new avenues for research and yieldsfruitful results Liberating forces in signals and systems theories have conspired in recent years to createresearch fronts that target long-standing constraints in the established wisdom (dogma?) of classic signalprocessing and system analysis The emergence of new fields in signals and system theories that addressthese shortcomings and aim to relax these restrictions has been motivated by scientists who, rather

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than mold natural behavior into artificial models, seek methods inherently suited to represent reality.Biomedical scientists and engineers are inspired by insights gained from a deeper appreciation for thedynamic richness displayed by biomedical phenomena; hence, more than their counterparts in otherdisciplines, they more forcefully embrace innovations in signal processing

One of these novel directions is concerned with time–frequency representations tailored for stationary and transient signals Faye Boudreaux-Bartels and Robin Murray address this issue, provide anintroduction to concepts and tools of time–frequency analysis, and point out candidate applications.Many physiologic structures and dynamics defy the concept of a characteristic spatial and temporalscale and must be dealt with employing methods compatible with their multiscale nature Judging fromthe recent success of biomedical signal-processing applications based on time-scale analysis and wavelettransforms, the resolution of many outstanding processing issues may be at hand The chapter entitled,

non-“Time-Scale Analysis and Wavelets in Biomedical Signals,” by Nitish V Thakor, familiarizes the readerwith fundamental concepts and methods of wavelet analysis and suggests fruitful directions in biomedicalsignal processing

The presence of nonlinearities and statistics that do not comply with the gaussianity assumption andthe desire for phase reconstruction have been the moving forces behind investigations of higher-orderstatistics and polyspectra in signal-processing and system-identification fields An introduction to thetopic and potential uses in biomedical signal-processing applications are presented by Athina Petropulu

in the chapter entitled, “Higher-Order Spectra in Biomedical Signal Processing.”

Neural networks derive their cue from biologic systems and, in turn, mimic many of the functions ofthe nervous system Simple networks can filter, recall, switch, amplify, and recognize patterns and henceserve well many signal-processing purposes In the chapter entitled, “Neural Networks in BiomedicalSignal Processing,” Evangelia Tzanakou helps the reader explore the power of the approach while stressinghow biomedical signal-processing applications benefit from incorporating neural-network principles.The dichotomy between order and disorder is now perceived as a ubiquitous property inherent in theunfolding of many natural complex phenomena In the last decade, it has become clear that the commonthreads shared by natural forms and functions are the “physics of disorder” and the “scaling order,” thehallmark of broad classes of fractal entities Biomedical signals are the global observables of underlyingcomplex physical and physiologic processes “Complexity” theories therefore hold the potential to providemathematical tools that describe and possibly shed light on the internal workings of physiologic systems

In the next to last chapter in this section, Banu Onaral and Joseph P Cammarota introduce the reader

to basic tenets of complexity theories and the attendant scaling concepts with hopes to facilitate theirintegration into the biomedical engineering practice

The section concludes with a brief chapter on the visions of the future when biomedical signal cessing will merge with the rising technologies in telecommunication and multimedia computing, andeventually with virtual reality, to enable remote monitoring, diagnosis, and intervention The impact ofthis development on the delivery of health care and the quality of life will no doubt be profound Thepromise of biomedical signal analysis will then be fulfilled

pro-Bronz: “2122_c001” — 2006/2/9 — 21:41 — page 1 — #1

1 Biomedical Signals: Origin and Dynamic

Characteristics; Frequency-Domain

Minimization of Mean Squared Error: The Wiener Filter • Maximization of the Signal-to-Noise Ratio: The Matched Filter

1.11 Adaptive Filtering 1-18 1.12 Segmentation of Nonstationary Signals 1-21 References 1-22

A signal is a phenomenon that conveys information Biomedical signals are signals, used in biomedicalfields, mainly for extracting information on a biologic system under investigation The complete process

of information extraction may be as simple as a physician estimating the patient’s mean heart rate byfeeling, with the fingertips, the blood pressure pulse or as complex as analyzing the structure of internalsoft tissues by means of a complex CT machine

Most often in biomedical applications (as in many other applications), the acquisition of the signal isnot sufficient It is required to process the acquired signal to get the relevant information “buried” in it

1-1

In this chapter, the characteristics of biomedical signals will be discussed [Cohen, 1986] Biomedicalsignals will be divided into characteristic classes, requiring different classes of processing methods Also

in this chapter, the basics of frequency-domain processing methods will be presented

1.1 Origin of Biomedical Signals

From the broad definition of the biomedical signal presented in the preceding section, it is clear thatbiomedical signals differ from other signals only in terms of the application — signals that are used in thebiomedical field As such, biomedical signals originate from a variety of sources The following is a briefdescription of these sources:

1 Bioelectric signals The bioelectric signal is unique to biomedical systems It is generated by nerve cells

and muscle cells Its source is the membrane potential, which under certain conditions may be excited

to generate an action potential In single cell measurements, where specific microelectrodes are used

as sensors, the action potential itself is the biomedical signal In more gross measurements, where, forexample, surface electrodes are used as sensors, the electric field generated by the action of many cells,distributed in the electrode’s vicinity, constitutes the bioelectric signal Bioelectric signals are probablythe most important biosignals The fact that most important biosystems use excitable cells makes itpossible to use biosignals to study and monitor the main functions of the systems The electric fieldpropagates through the biologic medium, and thus the potential may be acquired at relatively convenientlocations on the surface, eliminating the need to invade the system The bioelectric signal requires arelatively simple transducer for its acquisition A transducer is needed because the electric conduction inthe biomedical medium is done by means of ions, while the conduction in the measurement system is byelectrons All these lead to the fact that the bioelectric signal is widely used in most fields of biomedicine

2 Bioimpedance signals The impedance of the tissue contains important information concerning its

composition, blood volume, blood distribution, endocrine activity, automatic nervous system activity,and more The bioimpedance signal is usually generated by injecting into the tissue under test sinusoidalcurrents (frequency range of 50 kHz–1 MHz, with low current densities of the order of 20–20 mA) Thefrequency range is chosen to minimize electrode polarization problems, and the low current densities arechosen to avoid tissue damage mainly due to heating effects Bioimpedance measurements are usuallyperformed with four electrodes Two source electrodes are connected to a current source and are used

to inject the current into the tissue The two measurement electrodes are placed on the tissue underinvestigation and are used to measure the voltage drop generated by the current and the tissue impedance

3 Bioacoustic signals Many biomedical phenomena create acoustic noise The measurement of this

acoustic noise provides information about the underlying phenomenon The flow of blood in the heart,through the heart’s valves, or through blood vessels generates typical acoustic noise The flow of airthrough the upper and lower airways and in the lungs creates acoustic sounds These sounds, known ascoughs, snores, and chest and lung sounds, are used extensively in medicine Sounds are also generated

in the digestive tract and in the joints It also has been observed that the contracting muscle produces

an acoustic noise (muscle noise) Since the acoustic energy propagates through the biologic medium, thebioacoustic signal may be conveniently acquired on the surface, using acoustic transducers (microphones

or accelerometers)

4 Biomagnetic signals Various organs, such as the brain, heart, and lungs, produce extremely weak

magnetic fields The measurements of these fields provides information not included in other biosignals

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(such as bioelectric signals) Due to the low level of the magnetic fields to be measured, biomagnetic signalsare usually of very low signal-to-noise ratio Extreme caution must be taken in designing the acquisitionsystem of these signals

5 Biomechanical signals The term biomechanical signals includes all signals used in the biomedicine

fields that originate from some mechanical function of the biologic system These signals include motionand displacement signals, pressure and tension and flow signals, and others The measurement of bio-mechanical signals requires a variety of transducers, not always simple and inexpensive The mechanicalphenomenon does not propagate, as do the electric, magnetic, and acoustic fields The measurementtherefore usually has to be performed at the exact site This very often complicates the measurement andforces it to be an invasive one

6 Biochemical signals Biochemical signals are the result of chemical measurements from the living

tissue or from samples analyzed in the clinical laboratory Measuring the concentration of various ionsinside and in the vicinity of a cell by means of specific ion electrodes is an example of such a signal.Partial pressures of oxygen (pO2) and carbon dioxide (pCO2) in the blood or respiratory system are otherexamples Biochemical signals are most often very low frequency signals Most biochemical signals areactually dc signals

7 Biooptical signals Biooptical signals are the result of optical functions of the biologic system,

occur-ring naturally or induced by the measurement Blood oxygenation may be estimated by measuoccur-ring the

transmitted and backscattered light from a tissue (in vivo and in vitro) in several wavelengths Important

information about the fetus may be acquired by measuring fluorescence characteristics of the amnioticfluid Estimation of the heart output may be performed by the dye dilution method, which requires themonitoring of the appearance of recirculated dye in the bloodstream The development of fiberoptictechnology has opened vast applications of biooptical signals

Table 1.1 lists some of the more common biomedical signals with some of their characteristics

1.2 Classification of Biosignals

Biosignals may be classified in many ways The following is a brief discussion of some of the mostimportant classifications

1 Classification according to source Biosignals may be classified according to their source or physical

nature This classification was described in the preceding section This classification may be used whenthe basic physical characteristics of the underlying process is of interest, for example, when a model forthe signal is desired

2 Classification according to biomedical application The biomedical signal is acquired and processed

with some diagnostic, monitoring, or other goal in mind Classification may be constructed according tothe field of application, for example, cardiology or neurology Such classification may be of interest whenthe goal is, for example, the study of physiologic systems

3 Classification according to signal characteristics From point of view of signal analysis, this is the most

relevant classification method When the main goal is processing, it is not relevant what is the source ofthe signal or to which biomedical system it belongs; what matters are the signal characteristics

We recognize two broad classes of signals: continuous signals and discrete signals Continuous signals

are described by a continuous function s (t) which provides information about the signal at any given

time Discrete signals are described by a sequence s (m) which provides information at a given discrete

point on the time axis Most of the biomedical signals are continuous Since current technology providespowerful tools for discrete signal processing, we most often transform a continuous signal into a discrete

one by a process known as sampling A given signal s (t) is sampled into the sequence s(m) by

s(m) = s(t)| t =mTs m = , −1, 0, 1, (1.1)

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TABLE 1.1 Biomedical Signals

Bioelectric

Action potential Microelectrodes 100 Hz–2 kHz 10µV–100 mV Invasive measurement of cell

membrane potential Electroneurogram (ENG) Needle electrode 100 Hz–1 kHz 5µV–10 mV Potential of a nerve bundle Electroretinogram (ERG) Microelectrode 0.2–200 Hz 0.5µV–1 mV Evoked flash potential

Electro-oculogram (EOG) Surface electrodes dc–100 Hz 10µV–5 mV Steady-corneal-retinal potential Electroencephalogram (EEG)

potential

pathologies

during alert states

sleep Evoked potentials (EP) Surface electrodes 0.1–20µV Response of brain potential to

stimulus

200-msec duration

Electrocorticogram Needle electrodes 100 Hz–5 kHz Recordings from exposed surface

of brain Electromyography (EMG)

Single-fiber (SFEMG) Needle electrode 500 Hz–10 kHz 1–10µV Action potentials from single

muscle fiber Motor unit action Needle electrode 5 Hz–10 kHz 100µV–2 mV

potential (MUAP)

Surface EMG (SEMG) Surface electrodes

Electrocardiogram (ECG) Surface electrodes 0.05–100 Hz 1–10 mV

High-frequency ECG Surface electrodes 100 Hz–1 kHz 100µV–2 mV Notchs and slus waveforms

superimposed on the ECG

where Ts is the sampling interval and fs = 2π/Ts is the sampling frequency Further characteristicclassification, which applies to continuous as well as discrete signals, is described in Figure 1.1

We divide signals into two main groups: deterministic and stochastic signals Deterministic signals aresignals that can be exactly described mathematically or graphically If a signal is deterministic and itsmathematical description is given, it conveys no information Real-world signals are never deterministic.There is always some unknown and unpredictable noise added, some unpredictable change in the para-meters, and the underlying characteristics of the signal that render it nondeterministic It is, however, veryoften convenient to approximate or model the signal by means of a deterministic function

An important family of deterministic signals is the periodic family A periodic signal is a deterministicsignal that may be expressed by

sient

Non-Special type

FIGURE 1.1 Classification of signals according to characteristics.

where n is an integer and T is the period The periodic signal consists of a basic wave shape with a duration

of T seconds The basic wave shape repeats itself an infinite number of times on the time axis The simplest

periodic signal is the sinusoidal signal Complex periodic signals have more elaborate wave shapes Undersome conditions, the blood pressure signal may be modeled by a complex periodic signal, with the heartrate as its period and the blood pressure wave shape as its basic wave shape This is, of course, a very roughand inaccurate model

Most deterministic functions are nonperiodic It is sometimes worthwhile to consider an “almostperiodic” type of signal The ECG signal can sometimes be considered “almost periodic.” The ECG’s RRinterval is never constant; in addition, the PQRST complex of one heartbeat is never exactly the same

as that of another beat The signal is definitely nonperiodic Under certain conditions, however, the RRinterval is almost constant, and one PQRST is almost the same as the other The ECG may thus sometimes

be modeled as “almost periodic.”

1.3 Stochastic Signals

The most important class of signals is the stochastic class A stochastic signal is a sample function of astochastic process The process produces sample functions, the infinite collection of which is called theensemble Each sample function differs from the other in it fine details; however, they all share the samedistribution probabilities Figure 1.2 depicts three sample functions of an ensemble Note that at any giventime, the values of the sample functions are different

Stochastic signals cannot be expressed exactly; they can be described only in terms of probabilities which

may be calculated over the ensemble Assuming a signal s (t), the N th-order joint probability function

P [s(t1 ) ≤ s1, s(t2) ≤ s2, , s(t N ) ≤ s N ] = P(s1, s2, , s N ) (1.3)

FIGURE 1.2 The ensemble of the stochastic process s (t).

is the joint probability that the signal at time t i will be less than or equal to S i and at time t jwill be less

than or equal to S j, etc This joint probability describes the statistical behavior and intradependence of theprocess It is very often useful to work with the derivative of the joint probability function; this derivative

is known as the joint probability density function (PDF):

p (s1, s2, , s N ) = ∂ N

∂s1∂s2L∂s N [P(s1 , s2, , s N )] (1.4)

Of particular interest are the first- and second-order PDFs

The expectation of the process s (t), denoted by E{s(t)} or by m s, is a statistical operator defined as

E {s(t)} =

∞

The expectation of the function s n (t) is known as the nth-order moment The first-order moment is thus

the expectation of the process The nth-order moment is given by

E {s n (t)} =

∞

−∞s

The second central moment is known as the variance (the square root of which is the standard deviation).

The variance is denoted byσ2:

σ2= µ2 = E{(s − m s )2} =

∞

−∞(s − m s )2p(s) ds (1.8)The second-order joint moment is defined by the joint PDF Of particular interest is the autocorrelation

The cross-correlation function is defined as the second joint moment of the signal s at time t1, s (t1), and

the signal y at time t2, y (t2):

t = t2 − t1 (one-dimensional function) rather than a function of t2 and t1(two-dimensional function).Ergodic stationary processes possess an important characteristic: Their statistical probability distribu-tions (along the ensemble) equal those of their time distributions (along the time axis of any one of itssample functions) For example, the correlation function of an ergodic process may be calculated by itsdefinition (along the ensemble) or along the time axis of any one of its sample functions:

Ergodic processes are nice because one does not need the ensemble for calculating the distributions;

a single sample function is sufficient From the point of view of processing, it is desirable to model thesignal as an ergodic one Unfortunately, almost all signals are nonstationary (and hence nonergodic) Onemust therefore use nonstationary processing methods (such as, for e.g., wavelet transformation) whichare relatively complex or cut the signals into short-duration segments in such a way that each may beconsidered stationary

The sleep EEG signal, for example, is a nonstationary signal We may consider segments of the signal,

in which the subject was at a given sleep state, as stationary In order to describe the signal, we need toestimate its probability distributions However, the ensemble is unavailable If we further assume that theprocess is ergodic, the distributions may be estimated along the time axis of the given sample function.Most of the standard processing techniques assume the signal to be stationary and ergodic

1.4 Frequency-Domain Analysis

Until now we have dealt with signals represented in the time domain, that is to say, we have describedthe signal by means of its value on the time axis It is possible to use another representation for the