Basic principles of the tracer method: Introduction to mathematical tracer kinetics
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Wiley
1962
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 282 S. Ill. |
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| 100 | 1 | |a Sheppard, Charles Wilcox |d 1912- |e Verfasser |0 (DE-588)1028403917 |4 aut | |
| 245 | 1 | 0 | |a Basic principles of the tracer method |b Introduction to mathematical tracer kinetics |c C. W. Sheppard |
| 264 | 1 | |a London |b Wiley |c 1962 | |
| 300 | |a XVIII, 282 S. |b Ill. | ||
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| adam_text | BASIC PRINCIPLES OF THE
TRACER METHOD
Introduction to Mathematical Tracer Kinetics
C W SHEPPARD
Professor of Physiology
University of Tennessee Medical Units
Memphis, Tennessee
t
Supported by aUS Atomic Energy Commission
Research Contract
John Wiley amp; Sons, Inc , New York • London
Contents
CHAPTER 1 Elementary Principles of the Tracer Method I
Introduction 1
Perfect versus imperfect tracers, 2 Tracer statics
• versus kinetics, 3 Tracers and information, 4
The Use of Isotopes as Tracers 5
Isotope mixing, diffusion, and interfusion, 5 Tracers
and the exponential function, 6
Closed versus Open Systems 8
Two-compartment systems; initiiil rates, 8 Kinetic
equations for two compartments 10 One-compart
ment open systems, 12 Solving for rates, 13 Physical
analogs, 14
C HAPTER 2 ^Tracer Experiments in Compartmental Systems 15
Components of the Tracer Method 15
Compartments and systems, 15 Compartmental
indices, 18 Specific activities and abundance ratios, 19
Transport rates, 19 Communication between com
partments, 21
Practical Considerations in Two-Compartment Systems 24
Three-Compartment Systems 25
Incomplete Mixing 26
C HAPTER 3 Theory of Tracer Experiments in Multi-
Compartment Systems 30
General Principles 30
Solution of the Equations 36
Experiments Late in Time 40
Initial Rates of Change 41
Inferences in Compartments Which Cannot be Entered 42
Constrained Systems 43
ix
x Contents
CHAPTER 4 Kinetic Equations for Compartmental Systems:
The Mammillary System 47
Model Systems 47
Use of the Laplace Transform 49
Application to the two-compartment system, 51
General Kinetic Equations for a Closed Multi-Compart
ment System 53
Constant coefficients, 54
Kinetics of Mammillary Systems 55
Solution for a Three-Compartment Mammillary System
with Central Compartment Initially Labeled 57
The central compartment, 57 7 he peripheral compart
ment, 59 Lumping of peripheral compartments, 59
General conclusions in a mammillarv system with
central compartment initially labeled: Inversion by
partial fractions, 60 The principle of lumping, 63
Further Analysis of a Mammillary System: One
Peripheral Compartment Initially Labeled 64
Practical Illustration of the Use of General Solutions 66
The Superposition Principle 68
CHAPTER 5 Other Steady-State and Quasi-Steady Systems,
Approximation Methods 71
Catenary Systems 71
The quasi-steady catenary system, 71 Pure exchange in
a closed three-compartment catenary system, 73
t Simple turnover in catenary systems, 75
Cyclic Systems 76
Approximation Methods 79
Systems with widely differing rates, 79 Numerical
reduction of expressions to particular cases, 81
Perturbation methods, 83 The convolution theorem,
driving and driven compartments, 85 Practical pro
cedures for solving multicompartment systems, 87
CHAPT ER 6 Analog Simulation of Compartmental Tracer
Experiments
Non-Electrical Types of Analogs
Resistance-Capacitance Networks as Electrical Analogs
Verification of the Analog Equations
Quantitation in Simulation; The Analog Computer
Operational units and essential components of electronic
analog computers, 98 Initial conditions, 100 Other
operational units, 101
Contents xi
Practical Considerations in Analog Computation 103
Scale factors and time constants, 103 Connection of
operational units, 104 Summary of rules for connection
of operational units, 105
Engineering Considerations in Electric Analogs 106
Some Typical Analog Setups 108
Analog Solution of a Typical Problem 113
CHAPTER 7 Non-Steady-State Compartmental Systems 124
The Two-Compartment System 125
The Three-Compartment System 126
Successive Approximations and Numerical Solutions 127
Practical numerical solutions, 128 Programming the
numerical solution method for machine computation
with the IBM 650 computer, 128 FORTRAN state
ments for three-compartment solution, 131 Input and
output format, 136 Card layout, 137 Preparation
of input data—use of 602A calculating punch, 139
Final assembly of input data, 146 Typical results,
General Remarks Concerning the Use of Digital
Computation 150
CHAPTE R 8 Non-Compartmental Systems—Basic Tracer
Equations 152
*The Tracing of Substances in Continuous Systems 152
Diffusion versus Interfusion 153
Generalization of the Interfusion Equation 155
Heat-Flow Analogy 157
Lumping in the Solution of Heat-Flow Problems:
Application to Tracer Systems 158
Integral Equation Description of Tracer Theory: The
Age Concept 160
Sources and Sinks in Tracer Equations 163
Membrane Processes 164
CHAPTER 9 Tracers and the Study of the Circulation:
Stochastic Processes 166
Laminar Flow in Long Uniform Tubes 166
Non-Deterministic Processes 172
The unit spike and the delta function, 172 Bolus
response versus infusion response, 175
xii Contents
The Stewart-Hamilton Principle 176
Bloodflow, 176 The determination of labyrinth volume,
178 Basic postulates in circulation studies, 180 The
age concept in circulation studies, 181
The Shape of First-Circulation Curves: Stochastic
Models 184
Random walks versus compartments, 186 Random-
walk models, 187 Compartmental models, 190
The Use of Dimensionless Variables—the T Variable 193
The random walk and the r variable, 195
More General Random Walks 198
Shifted walks and double-peaked curves, 198 Walks
in two and three dimensions, 199 Parallel systems of
walks, 200 Asymptotic expressions, 201
Lumping and Simulation of First-Passage Curves by
Analogs 202
The convolution integral, 204 The recirculation
problem, 206 Use of approximate dispersion functions
in recirculation problems, 208 Simulation of recircula
tion by analogs, 211
Mathematical Tools for the Physiologist 213
CHAPTER 10 The Movement of Tracer Substances from the
Circulation 214
}
Disappearance of Injected Substances—General Con
sideration and Isolated Systems 214
Disappearance from a uniform pool, 215 First-order
disappearance processes, 216 Local first-order pro
cesses; tubes of flow, 217 First-order processes for
constant v and p, 218 General first-order processes,
218 Exchange between a vessel and its surroundings,
219 Arterio-venous differences and non-uniform
mixing, 221 Diffusible versus indiffusible
tracers, 224 Outflow versus inflow in a perfused
organ, 225
The Circulation as a Whole 226
IntegraI equation formulation 226 Partition of
cardiac output, 227 Analog simulation of tracer
disappearance, 229
Disappearance of Labeled Formed Elements from the
Blood 231
Contents xiii
CHAPTER 11 Matrix Methods and Fitting Models to Data 234
Matrix Formulation of Tracer Kinetics 234
Numbers, vectors, and matrices, •34 Matric equation
for a multicompartment system, 236 Matric defer
ential equations, 238
Constant Linear Systems 240
Matric models for compartmental systems, 240 Per
missible models for underdetermined systems, 241
Statistics and Curve Fitting 242
Estimation of best values, 242 Regression and curve
fitting, 244 Fitting of multiple exponentials to data:
general considerations, 245 Non-linear least squares,
247 Uniform spacing of abscissa! values, 249 A
semi-objective peeling technique, 249 Concluding
remarks concerning curve fitting, 250
Appendix 251
First Traversals of the Random Walk 251
Some Properties of the Random Walk Function 252
Principal landmarks, 253
Moments of F(j) for the Compartmental System 263
References 265
/
Index 271
|
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| discipline | Energietechnik, Energiewirtschaft Biologie Chemie |
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| spelling | Sheppard, Charles Wilcox 1912- Verfasser (DE-588)1028403917 aut Basic principles of the tracer method Introduction to mathematical tracer kinetics C. W. Sheppard London Wiley 1962 XVIII, 282 S. Ill. txt rdacontent n rdamedia nc rdacarrier Indikatormethode (DE-588)4072770-1 gnd rswk-swf Indikatormethode (DE-588)4072770-1 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001257362&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sheppard, Charles Wilcox 1912- Basic principles of the tracer method Introduction to mathematical tracer kinetics Indikatormethode (DE-588)4072770-1 gnd |
| subject_GND | (DE-588)4072770-1 |
| title | Basic principles of the tracer method Introduction to mathematical tracer kinetics |
| title_auth | Basic principles of the tracer method Introduction to mathematical tracer kinetics |
| title_exact_search | Basic principles of the tracer method Introduction to mathematical tracer kinetics |
| title_full | Basic principles of the tracer method Introduction to mathematical tracer kinetics C. W. Sheppard |
| title_fullStr | Basic principles of the tracer method Introduction to mathematical tracer kinetics C. W. Sheppard |
| title_full_unstemmed | Basic principles of the tracer method Introduction to mathematical tracer kinetics C. W. Sheppard |
| title_short | Basic principles of the tracer method |
| title_sort | basic principles of the tracer method introduction to mathematical tracer kinetics |
| title_sub | Introduction to mathematical tracer kinetics |
| topic | Indikatormethode (DE-588)4072770-1 gnd |
| topic_facet | Indikatormethode |
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