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Modeling and Simulation in Medicine and the Life Sciences / Edition 2

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Overview

The result of lectures given by the authors at New York University, the University of Utah, and Michigan State University, the material is written for students who have had only one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well as solutions to selected exercises, so as to lead readers to discover interesting extensions of that material. Throughout, illustrations depict physiological processes, population biology phenomena, corresponding models, and the results of computer simulations. Topics covered range from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models.

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Editorial Reviews

From the Publisher
"This is an introductory book on mathematical modeling in the bio-sciences. It is written for mathematicians as well as for life scientists. Simple models are presented, and previous knowledge of biology is not required for understanding the book. All the essential biological background is given in the text, while basic mathematical knowledge is sufficient for reading a large part of the book.

In each chapter, the material is organized in increasing order of complexity followed by exercises. Some of the exercises deal with the material of that chapter, while others are projects that extend the preceding material. Many chapters contain sections with suggestions for computing projects. Simulations are done in Matlab and computer code is included in the text...." (Miljenko Marusic, Mathematical Reviews)

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Product Details

  • ISBN-13: 9781441928719
  • Publisher: Springer New York
  • Publication date: 12/1/2010
  • Series: Texts in Applied Mathematics Series , #10
  • Edition description: Softcover reprint of hardcover 2nd ed. 2002
  • Edition number: 2
  • Pages: 355
  • Product dimensions: 0.77 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Series Preface
Preface
Introduction 1
1 The Heart and Circulation 5
1.1 Plan of the Circulation 5
1.2 Volume, Flow, and Pressure 7
1.3 Resistance and Compliance Vessels 8
1.4 The Heart as a Pair of Pumps 10
1.5 Mathematical Model of the Uncontrolled Circulation 14
1.6 Balancing the Two Sides of the Heart and the Two Circulations 18
1.7 The Need for External Circulatory Control Mechanisms 20
1.8 Neural Control: The Baroreceptor Loop 21
1.9 Autoregulation 25
1.10 Changes in the Circulation Occurring at Birth 28
1.11 Dynamics of the Arterial Pulse 33
1.12 Computer Simulation of Pulsatile Blood Flow 39
1.13 Suggestions for Computing Projects Concerning the Circulation 63
2 Gas Exchange in the Lungs 75
2.1 The Ideal Gas Law and the Solubility of Gases 76
2.2 The Equations of Gas Transport in One Alveolus 78
2.3 Gas Transport in the Lung 82
2.4 Optimal Gas Transport 83
2.5 Mean Alveolar and Arterial Partial Pressures 85
2.6 Transport of O[subscript 2] 87
2.7 Computer Solution of the Equations for O[subscript 2] Transport in the Lung 91
2.8 Computing Projects Concerning Oxygen Transport by the Lung 104
3 Control of Cell Volume and Electrical Properties of Cell Membranes 109
3.1 Osmotic Pressure and the Work of Concentration 109
3.2 A Simple Model of Cell Volume Control 113
3.3 The Movement of Ions Across Cell Membranes 115
3.4 The Interaction of Electrical and Osmotic Effects 118
3.5 The Hodgkin-Huxley Equations for the Nerve Action Potential 124
3.6 Computer Simulation of the Nerve Action Potential 132
3.7 Suggestions for Computing Projects Concerning the Nerve Impulse 139
4 The Renal Countercurrent Mechanism 147
4.1 The Nephron 147
4.2 Dynamics of Na[superscript +] and H[subscript 2]O: Transport along the Renal Tubules 150
4.3 The Loop of Henle 152
4.4 The Juxtaglomerular Apparatus and the Renin-Angiotensin System 155
4.5 The Distal Tubule and Collecting Duct: Concentrating and Diluting Modes 157
4.6 Remarks on the Significance of the Juxtaglomerular Apparatus 158
4.7 How Nephrons Do Better Than a Factor of e 159
4.8 Computing Project on the Interacting Nephron Population Model 166
5 Muscle Mechanics 171
5.1 The Force-Velocity Curve 171
5.2 Crossbridge Dynamics 173
5.3 Computer Simulation of Crossbridge Attachment and Detachment 179
5.4 Suggested Computing Projects on Crossbridge Dynamics 188
6 Neural Systems 193
6.1 Guttman's Experiments on Phase Locking 195
6.2 Biological Rhythms 197
6.3 Model Neural Networks 200
7 Population Dynamics 215
7.1 Bacterial Cultures 216
7.2 Age Structures 222
7.3 Microbial Ecology 230
7.4 Nonlinear Reproduction Curves 237
7.5 Controlling Populations 248
8 Genetics 267
8.1 Population Genetics 269
8.2 Biotechnolgoy 277
9 A Theory of Epidemics 295
9.1 Spread of Infection Within a Family 296
9.2 The Threshold of an Epidemic 300
9.3 Predicting the Severity of an Epidemic 303
10 Patterns of Population Growth and Dispersal 311
10.1 Random Walks and the Process of Diffusion 312
10.2 Bacterial Growth on a Petri Plate 321
App. A Getting Started with Matrices and MATLAB 335
App. B Background on Random Processes 343
Index 349
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