Modeling and Simulation in Medicine and the Life Sciences

Transcription

1 Frank C. Hoppensteadt Charles S. Peskin Modeling and Simulation in Medicine and the Life Sciences Second Edition With 93 Illustrations fyj Springer

2 Contents Series Preface Preface vii ix Introduction 1 1 The Heart and Circulation Plan of the Circulation Volume, Flow, and Pressure Resistance and Compliance Vessels The Heart as a Pair of Pumps Mathematical Model of the Uncontrolled Circulation Balancing the Two Sides of the Heart and the Two Circulations The Need for External Circulatory Control Mechanisms Neural Control: The Baroreceptor Loop Autoregulation Changes in the Circulation Occurring at Birth Dynamics of the Arterial Pulse Computer Simulation of Pulsatile Blood Flow Suggestions for Computing Projects Concerning the Circulation Annotated References 68 Exercises 69

3 xii Contents 2 Gas Exchange in the Lungs The Ideal Gas Law and the Solubility of Gases The Equations of Gas Transport in One Alveolus Gas Transport in the Lung Optimal Gas Transport Mean Alveolar and Arterial Partial Pressures Transport of O Computer Solution of the Equations for O2 Transport in the'lung Computing Projects Concerning Oxygen Transport by the Lung Annotated References 107 Exercises Control of Cell Volume and Electrical Properties of Cell Membranes Osmotic Pressure and the Work of Concentration A Simple Model of Cell Volume Control The Movement of Ions Across Cell Membranes The Interaction of Electrical and Osmotic Effects The Hodgkin-Huxley Equations for the Nerve Action Potential Computer Simulation of the Nerve Action Potential Suggestions for Computing Projects Concerning the Nerve Impulse Annotated References 143 Exercises The Renal Countercurrent Mechanism The Nephron Dynamics of Na + and H 2 O: Transport along the Renal Tubules The Loop of Henle The Juxtaglomerular Apparatus and the Renin-Angiotensin System The Distal Tubule and Collecting Duct: Concentrating and Diluting Modes Remarks on the Significance of the Juxtaglomerular Apparatus How Nephrons Do Better Than a Factor of e Computing Project on the Interacting Nephron Population Model Annotated References 168 Exercises 169

4 Contents xiii 5 Muscle Mechanics The Force-Velocity Curve Crossbridge Dynamics Computer Simulation of Crossbridge Attachment and Detachment Suggested Computing Projects on Crossbridge Dynamics Annotated References 190 Exercises Neural Systems Guttman's Experiments on Phase Locking Biological Rhythms Modulating the Clock on the Wall Biological Clocks Electronic Clocks: Voltage-Controlled Oscillators Model Neural Networks A Thalamocortical Circuit Hippocampus Annotated References 207 Exercises Population Dynamics Bacterial Cultures Batch Culture Growth Least-Squares Estimation of the Growth Rate Age Structures Cohort Analysis Birth Rates Age Distributions Microbial Ecology Uptake of Nutrients Growth and Quiescence Biofilms and Growth in a Continuous Flow A Solutivory Food Chain Nonlinear Reproduction Curves Compensatory Growth: Verhulst's Model Chaos Controlling Populations Cell Synchronization Cohort Dynamics near the Limits of Growth Harvesting: Economics of Populations Annotated References 256 Exercises 257

5 xiv Contents 8 Genetics Population Genetics Natural Selection Slow Selection Genotype Frequencies Random Genetic Drift Biotechnology Plasmids ' Control of Plasmid Replication Regulation of Gene Expression Stoichiometry of Metabolic Pathways Annotated References 291 Exercises A Theory of Epidemics Spread of Infection Within a Family The Threshold of an Epidemic Predicting the Severity of an Epidemic Annotated References 306 Exercises Patterns of Population Growth and Dispersal Random Walks and the Process of Diffusion Random Walks Boundary Conditions Sample Paths Diffusion Approximation Two-Dimensional Diffusion Sample Paths in Two-Dimensions Numerical Solutions: The Method of Lines Bacterial Growth on a Petri Plate Diffusion of a Drop of Substrate Bacterial Growth Due to Diffusing Nutrition Growth Patterns Due to Two Nutrients Concluding Remarks Annotated References 326 Exercises 326 Appendix A Getting Started with Matrices and MATLAB 335 Appendix B Background on Random Processes 343 Index 349