Mathematical Models in the Health Sciences was first published in 1979. This book, designed especially for use in graduate courses in the health sciences, will be useful also as a reference work for scientists in various disciplines. It provides an introduction to mathematical modeling through the use of selected examples from the health sciences. Where appropriate, computer techniques are discussed and illustrated with examples drawn from studies by the authors and their colleagues. An introductory chapter discusses mathematical models and their roles in biomedical research. The rest of the material is divided in three sections of four chapters each: Deterministic Models, Time Series Analysis, and Information and Simulation. A bibliography accompanies each chapter. In their conclusion the authors place mathematical biology and its techniques in perspective.
Author(s): Eugene Ackerman, Lael Cranmer Gatewood
Publisher: Univ of Minnesota Pr
Year: 1979
Language: English
Pages: 372
Contents......Page 10
Preface......Page 6
INTRODUCTION......Page 16
A. Origins and Definitions......Page 18
B. Automated Computational Aids......Page 20
C. Deterministic and Stochastic Models......Page 21
D. Inverse Solutions......Page 22
E. Model Conformation and Parameter Estimation......Page 23
F. Health-Related Goals......Page 26
G. Notation Used in Text......Page 28
H. Summary......Page 29
DETERMINISTIC MODELS......Page 32
A. Illustrative Examples......Page 34
B. Compartmental Analysis......Page 39
C. Single Compartment Models......Page 42
D. Parameter Estimation......Page 47
E. Multicompartment Models......Page 49
F. Computer Simulation......Page 53
G. Non-Linear Parameter Estimation......Page 56
H. Model Selection and Validation......Page 60
I. Summary......Page 64
A. Extensions of Compartmental Analysis......Page 68
B. Blood Glucose Regulation......Page 69
C. Ceruloplasmin Synthesis......Page 79
D. Dye Dilution Curves......Page 83
E. Lung Models......Page 84
F. Summary......Page 87
A. Enzymes and Biology......Page 91
B. Proteins and Amino Acids......Page 92
C. Prosthetic Groups, Cofactors, and Coenzymes......Page 95
D. Molecular Conformation and Chemical Reactions......Page 97
E. Michaelis-Menten Kinetics......Page 100
F. Estimation of Michaelis-Menten Parameters......Page 103
G. Catalase and Peroxidase Reactions......Page 107
H. Enzyme Kinetics and Mathematical Biology......Page 111
A. Transient Kinetics......Page 114
B. Perturbation Kinetics......Page 115
C. King-Altman Patterns......Page 119
D. Metabolic Pathways......Page 122
E. Oxidative Phosphorylation......Page 124
F. Simulation of Multienzyme Systems......Page 128
G. Summary......Page 136
TIME SERIES......Page 138
A. Introduction......Page 140
B. Analog to Digital Signal Conversion......Page 141
C. Fourier Transforms......Page 143
D. Discrete Fourier Transforms......Page 153
E. Fast Fourier Transforms......Page 157
F. Laplace Transforms......Page 163
G. Sampling Theorems......Page 165
H. Summary......Page 170
A. Transfer Functions......Page 172
B. Convolution Integrals......Page 174
C. Compartmental Analysis......Page 179
D. Dye Dilution Curves......Page 184
E. Fast Walsh Transforms......Page 187
F. Applications......Page 190
A. Physiological Basis......Page 193
B. EKG Characteristics......Page 197
C. VKG Patterns......Page 200
D. Abnormalities......Page 204
E. Simulation and the Inverse Problem......Page 206
F. Automated Interpretation of the EKG......Page 212
G. Automated Aids to Clinical Diagnosis......Page 215
H. Summary......Page 217
A. Central Nervous System......Page 221
B. EEG Characteristics......Page 224
C. Applications of EEG Patterns......Page 228
D. Sleep Stages......Page 229
E. Spectral Analyses......Page 231
F. Compressed Spectral and Other Analyses......Page 235
G. Spatial Analyses......Page 239
H. Evoked Response Averages......Page 242
I. Automation and the EEG......Page 244
INFORMATION AND SIMULATION......Page 248
A. Basic Concepts......Page 250
B. Messages and Entropy......Page 253
C. Redundancy......Page 254
D. Continuous Signals......Page 255
E. Analog Digitization......Page 258
F. Discrete Systems......Page 259
G. Health Sciences Applications......Page 263
A. Genes and Chromosomes......Page 265
B. Cell Replication and Division......Page 267
C. Molecular Basis of Genetics......Page 268
D. Information Content of DNA......Page 270
E. Types of Genes......Page 274
F. RNA and Protein Synthesis......Page 277
G. Information Theory and Evolution......Page 280
H. Genetic Models and Evolution......Page 282
A. Epidemics and Epidemic Theory......Page 286
B. Simulation of Stochastic Models......Page 289
C. Simplest Stochastic Models......Page 291
D. Competition and Vaccination......Page 297
E. Structured Populations......Page 304
F. Influenza Epidemic Model......Page 308
G. Overview......Page 315
A. Introduction: Population Models......Page 319
B. Exponential Growth......Page 321
C. Logistic Growth......Page 324
D. Competition and Predator-Prey Interactions......Page 327
E. Other Ecology Models......Page 332
F. World Systems Models......Page 335
G. Simulation and Prediction......Page 340
H. Summary......Page 345
OVERVIEW......Page 348
A. Summary of Text......Page 350
B. Other Areas of Mathematical Biology......Page 352
C. Other Health Science Applications......Page 354
D. Health Computer Sciences......Page 356
E. Future Implications......Page 357
Index......Page 360
B......Page 362
C......Page 363
E......Page 364
F......Page 365
H......Page 366
L......Page 367
O......Page 368
Q......Page 369
S......Page 370
W......Page 371
Z......Page 372
