Bioelectricity: A Quantitative Approach / Edition 1

Bioelectricity: A Quantitative Approach / Edition 1

by Roger C. Barr, Robert Plonsey
     
 

ISBN-10: 0306428946

ISBN-13: 9780306428944

Pub. Date: 08/31/1988

Publisher: Springer US

The study of electrophysiology has progressed rapidly because of the precise, delicate, and ingenious experimental studies of many investigators. The field has also made great strides by unifying these experimental observations through mathematical descriptions based on electromagnetic field theory, electrochemistry, etc., which underlies these experiments. In turn

Overview

The study of electrophysiology has progressed rapidly because of the precise, delicate, and ingenious experimental studies of many investigators. The field has also made great strides by unifying these experimental observations through mathematical descriptions based on electromagnetic field theory, electrochemistry, etc., which underlies these experiments. In turn, these quantitative materials provide an understanding of many electrophysiological applications through a relatively small number of fundamental ideas.

Bioelectricity: A Quantitative Approach, is the new edition of the classic introductory text to electrophysiology. It covers many topics that are central to the field including:

- electrical properties of the cell membrane
- action potentials
- cable theory
- electrical stimulation
- extracellular waveforms
- cardiac electrophysiology
- function stimulation (FES)

Organized as a textbook for the student needing to acquire the core competencies, Bioelectricity: A Quantitative Approach will meet the demands of advanced undergraduate or graduate coursework in biomedical engineering and biophysics.

Key Features:

  • New Detailed Illustrations
  • Example Problems
  • Exercises with many solutions (CD-ROM) Enclosed
  • Useful Appendixes and Study Guides

Authors:

Robert Plonsey is a Pfizer-Pratt Professor Emeritus of Biomedical Engineering at Duke University. He received the PhD in Electrical Engineering from University of California in 1955.He received the Dr. of Technical Science from the Slovak Academy of Science in 1995 and was Chair, Department of Biomedical Engineering, Case Western Reserve, University, 1976-1980, Professor 1968-1983. Awards: Fellow of AAAS, William Morlock Award 1979, Centennial Medal 1984, Millennium Medal 2000, from IEEE Engineering in Medicine and Biology Society, Ragnar Granit Prize 2004, (First) Merit Award, 1997, International Union for Physiological & Engineering Science in Medicine, the Theo Pilkington Outstanding Educator Award, 2005, Distinguished Service award, Biomedical Engineering Science, 2004, ALZA distinguished lecturer, 1988. He was elected Member, National Academy of Engineering, 1986 ("For the application of electromagnetic field theory to biology, and for distinguished leadership in the emerging profession of biomedical engineering").

Roger C. Barr is Professor of Biomedical Engineering and Associate Professor of Pediatrics at Duke University. In past years he served as the Chair of the Department of Biomedical Engineering at Duke, and then as Vice President and President of the IEEE Engineering in Medicine and Biology Society. He received the Duke University Scholar-Teacher Award in 1991. He is the author of more than 100 research papers about topics in bioelectricity and is a Fellow of the IEEE and American College of Cardiology. This text is a product of interactions with students, and in this regard he has taught the bioelectricity course sequence numerous times.

Praise for Previous Editions:

"This fine text, by two well-known bioengineering professors at Duke University, is an introduction to electrophysiology aimed at engineering students. Most of its chapters cover basic topics in electrophysiology: the electrical properties of the cell membrane, action potentials, cable theory, the neuromuscular junction, extracellular fields, and cardiac electrophysiology. The authors discuss many topics that are central to biophysics and bioengineering [and] the quantitative methods [they] teach will surely be productive in the future." (IEEE Engineering in Medicine and Biology)

"The authors' goal in producing this book was to provide an introductory text to electrophysiology, based on a quantitative approach. In attempting to achieve this goal, therefore, the authors have opened the book with a useful, and digestible, introduction to various aspects of the mathematics relevant to this field, including vectors, introduction to Laplace, Gauss's theorem, and Green's theorem. This book will be useful for students in medical physics and biomedical engineering wishing to enter the field of electrophysiological investigation. It will also be helpful for biologists and physiologists who wish to understand the mathematical treatment of the processes and signals at the center of the interesting interdisciplinary field." (Medical and Biomedical Engineering and Computing)

Product Details

ISBN-13:
9780306428944
Publisher:
Springer US
Publication date:
08/31/1988
Edition description:
1988
Pages:
306
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Vector Analysis
1(20)
Introduction
1(1)
Vectors and Scalars
1(1)
Vector Algebra
2(3)
Sum
2(1)
Vector Times Scalar
2(1)
Unit Vector
2(1)
Dot Product
2(1)
Resolution of Vectors
3(1)
Cross Product
4(1)
Gradient
5(3)
Potential Change Written as Dot Product
6(1)
Properties of G
7(1)
Gradient δ
7(1)
Comments about the Gradient
8(1)
Divergence
8(4)
Outflow through Surfaces 1 and 2
9(1)
Outflow through All Six Surfaces
10(1)
Divergence
10(1)
Comments about the Divergence
11(1)
Laplacian
12(1)
Comments about the Laplacian
12(1)
Vector Identities
13(1)
Useful Vector Identities
13(1)
Verification of Eq. (1.38)
13(1)
The Gradient of Source and Field Points
14(2)
Gradient of (1/r)
15(1)
Gradient of (1/r)
15(1)
Gauss's Theorem
16(1)
Green's Theorem
16(2)
Green's First Identity
16(1)
Green's Second Identity
17(1)
Comment on Green's Theorem
17(1)
Summary of Operations
18(1)
Exercises
18(3)
Electrical Sources and Fields
21(12)
Fundamental Relationships
21(2)
Potentials, Fields, Currents
21(1)
Poisson's Equation
22(1)
Duality
23(1)
Monopole Field
24(2)
Dipole Field
26(3)
Expressing r1 in Terms of r
27(1)
Evaluation of the 1/r Derivative
27(1)
Taking the Gradient
28(1)
Units for Some Electrical Quantities
29(1)
Exercises
30(3)
Introduction to Membrane Biophysics
33(32)
Introduction
33(1)
Membrane Structure
33(2)
Ionic Composition
35(1)
Nernst--Planck Equation
36(2)
Diffusion
36(1)
Electric Field
37(1)
Einstein's Equation
37(1)
Total Flow
38(1)
Equivalent Conductance
38(2)
Transference Numbers
40(1)
Nernst Potential
41(3)
Concentration Cell
41(1)
Nernst Equilibrium
42(1)
Biological Membrane
43(1)
Relative Charge Depletion
43(1)
Resting Potential
44(1)
Donnan Equilibrium
44(4)
Two Ion Species
44(2)
More Than Two Ion Species
46(1)
Distribution of Ions
46(1)
Biological Systems
47(1)
Goldman Equations
48(4)
Analysis for One Ion
49(1)
Combined Flow of Several Ions
50(1)
Goldman's Equation for the Membrane Voltage
51(1)
Slope and Chord Conductance
52(1)
Role of Chloride Ion at Rest
52(4)
Chloride Tracks Potassium
52(1)
Experimental Study of the Resting Potential
52(2)
Experimental Effects of Chloride Ion
54(2)
Exercises
56(9)
Design Project: AC Biogenerator
60(1)
Other Information
61(4)
Action Potentials
65(40)
Observed Action Potentials
65(3)
Earthworm Action Potentials
65(2)
Earthworm Extracellular Potentials
67(1)
Nonlinear Membrane Behavior
68(3)
Action Potentials in Crab Axon
69(1)
Stimulus and Response in Crab Axon
70(1)
Nonlinear Membrane Measurements
71(1)
Origin of Action Potential, Resting and Peak Voltages
71(3)
Changing Permeabilities
71(1)
Resting and Peak Voltages of Aplysia
72(1)
Gross Explanation of Action Potential Origin
73(1)
Movements of Ionic Tracers
73(1)
Voltage Clamp
74(1)
A More Detailed Action Potential Explanation
74(1)
More Detailed Model
74(1)
Notation for Transmembrane Potential
75(1)
Notation for Intra- and Extracellular Potentials
75(1)
Parallel-Conductance Model
75(3)
Ionic Currents
75(2)
Capacitative Current
77(1)
Vm as Related to Total Current
77(1)
Example for Squid Axon
77(1)
Voltage Clamp
78(7)
Origin of Voltage Clamp
78(1)
Basic Voltage Clamp Design
79(1)
Voltage Clamp Records
80(2)
Current--Voltage Curves
82(1)
Independence Principle
83(1)
Separation of Ionic Current into Components
84(1)
Hodgkin--Huxley Equations
85(6)
Model for Potassium
86(2)
Model for Sodium
88(3)
HH Method for Evaluating h∞
91(1)
Simulation of Membrane Action Potential
91(4)
Analytical Evaluation
92(1)
Numerical Procedure
93(1)
Calculation Results
94(1)
Action Potential Characteristics
95(2)
Refractory Periods
95(1)
Anode Break Excitation
96(1)
Active Transport
97(4)
Pump's Characteristics
97(1)
Formal Stoichiometric Approach
98(1)
Pump Included in Steady-State Model
99(2)
Exercises
101(4)
Propagation
105(20)
Introduction
105(1)
Core-Conductor Model
105(3)
Resistance and Capacitance in a Cylindrical Fiber
105(1)
Electrical Model
106(2)
Core-Conductor Model Assumptions
108(1)
Cable Equations
108(4)
Relationship of Potential to Longitudinal Current
109(1)
Relationship of Longitudinal Intracellular Current to Transmembrane Current
109(1)
Expression Relating Longitudinal Extracellular Current to the Total Transmembrane Current (Including Applied Currents)
109(1)
Spatial Derivatives of Φ and Φ
110(1)
vm Related to Φe and Φi
111(1)
Membrane Current Related to 2Vδm/δx2
112(1)
Local Circuit Currents during Propagation
112(2)
Mathematics of Propagating Action Potentials
114(1)
Numerical Solutions for Propagating Action Potentials
115(1)
Propagation Velocity Related to Radius
116(2)
Propagation in Myelinated Nerve Fibers
118(2)
Myelin Sheath
118(1)
Propagation
119(1)
Exercises
120(5)
Subthreshold Stimuli
125(24)
Linear Subthreshold Conditions
125(2)
Space and Time Constants
127(1)
Stimulus Current at Origin (Steady-State Solution)
128(3)
The Problem
128(1)
Equations Governing vm
128(1)
Region of the Stimulus
129(1)
The Homogeneous Solution
129(1)
Imposing Boundary Conditions at Origin
130(1)
The Steady-State Solution
131(1)
Step Current at Origin. General Time-Varying Solution
131(4)
Laplace Transformation
132(1)
Boundary Condition
132(2)
Solution
134(1)
Interpretation of Spatial and Temporal Response
135(1)
Cable Input Impedance
135(3)
Cables of Finite Length
138(3)
Finding Zin in General
138(1)
Reflection Coefficient
139(1)
Zin for a Terminated Cable
140(1)
Cable of Finite Length
140(1)
Single Spherical Cell
141(4)
Response to Current Step
141(2)
Rheobase
143(1)
Chronaxie
143(1)
Comparison to Experimental Findings
144(1)
Exercises
145(4)
Extracellular Fields
149(16)
Introduction
149(1)
Basic Formulation
149(5)
Fiber Source Model
150(1)
Potentials from Source Elements
150(1)
Potentials in Terms of vm
151(1)
Monopole Source Density
152(1)
Dipole Source Density
153(1)
Modification for Thick Fiber
154(1)
Fiber Source Models: Dipoles
154(3)
Depolarization and Repolarization Dipoles
155(1)
Quadrupolar Source
156(1)
Rectangular Action Potential
156(1)
Fiber Source Models: Monopoles
157(3)
Triangular Action Potentials
159(1)
Quadrupole Approximation
159(1)
Exercises
160(3)
Extracellular Detection Design
163(1)
References
163(2)
Membrane Biophysics
165(40)
Introduction
165(1)
Voltage Clamp
166(1)
Space-Clamp Uniformity
166(1)
Error in Sensing Vm
167(2)
Newer Voltage Clamp Methods
169(2)
Sucrose Gap
169(2)
Two- and Three-Microelectrode Voltage Clamp
171(4)
Spherical Cell
171(1)
Cylindrical Cell
172(3)
Single-Microelectrode Voltage Clamp
175(1)
Patch Clamp
176(4)
Single-Channel Morphology
180(1)
Single-Channel Currents
181(1)
Single-Channel Kinetics
182(2)
Fluctuation--Dissipation Theorem
184(1)
Channel Statistics
185(2)
Membrane Current
187(4)
Hodgkin--Huxley Potassium Channel---General Comments
191(1)
Hodgkin--Huxley Potassium Channel Fluctuation Noise
192(3)
Sources of Membrane Noise
195(1)
Thermal Noise
195(1)
Shot Noise
196(1)
1/f Noise
196(1)
Appendix: Random Variables, Autocorrelation Function, and Power Density Spectra
196(6)
Random Variables
197(1)
Random Processes
197(1)
Correlation Functions
198(1)
Spectral Analysis
199(3)
Exercises
202(3)
The Electrophysiology of the Heart
205(40)
Overview
205(2)
Electrical Nature of Intercellular Communication
207(1)
Evidence for Functional Continuity in Cardiac Muscle
208(2)
Free Wall Activation of the Heart
210(3)
Double-Layer Sources
213(3)
Heart Vector (Dipole)
216(1)
Lead Vector
217(1)
Standard Leads
218(4)
Lead Field
222(4)
The Source-Field Description
222(1)
Reciprocity
223(1)
Lead Field
224(1)
Multiple Dipoles
225(1)
Lead System Design
225(3)
Application of Lead Field Theory to Standard Electrocardiographic Lead I
228
Recording
226(8)
Intracellular versus Extracellular
227(1)
Extracellular Recordings
227(1)
Reference Electrodes
228(1)
Intramural Electrodes for Cardiac Activity
229(1)
Wave Thickness
230(4)
Human Cross-Sectional Anatomy
234(1)
Body Surface Potentials from Distributed Cardiac Potentials
234(5)
Green's Theorem Applied to Body Volume
235(1)
Simplification of Integral
236(1)
Introduction of Solid Angle
237(1)
Body Potential from Epicardial Potentials and Gradients
237(1)
Simplifications
238(1)
Transfer Coefficients
238(1)
Exercises
239(4)
References
243(2)
The Neuromuscular Junction
245(14)
Introduction
245(1)
Neuromuscular Junction
246(2)
Evidence for Quantal Nature of Transmitter Release
248(1)
Poisson Statistics for Transmitter Release---Single Trial
249(2)
Expressions for Effect of Ca2+ and Mg2+ on Transmitter Release
251(3)
Postjunctional Response to Transmitter
254(2)
Exercises
256(1)
References
257(2)
Skeletal Muscle
259(12)
Muscle Structure
259(1)
Muscle Contraction
260(2)
Structure of the Myofibril
262(3)
Sliding Filament Theory
265(4)
Excitation--Contraction
269(1)
Exercises
270(1)
References
270(1)
Functional Neuromuscular Stimulation
271(30)
Introduction
271(1)
Electrodes
271(1)
Electrode --Tissue Behavior
272(2)
Electrode Operating Characteristics
274(4)
Electrode Materials
278(1)
Types of Electrode (for Specific Application)
278(2)
Nerve Excitation
280(3)
Secondary Pulse Considerations
283(1)
Excitation of Myelinated Nerve
284(2)
Cuff Electrodes
286(5)
Recruitment
291(1)
Nerve Cuff Electrode
292(1)
Surface Electrode
293(1)
Intramuscular Electrode
293(1)
Muscle Alterations Induced by Electrical Activation
293(2)
Recruitment Regimen
295(1)
Clinical Applications
296(1)
Exercises
296(3)
References
299(2)
Index 301

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