Modeling and Simulation in Medicine and the Life Sciences

1 The Heart and Circulation.- 1.1 Plan of the Circulation.- 1.2 Volume, Flow, and Pressure.- 1.3 Resistance and Compliance Vessels.- 1.4 The Heart as a Pair of Pumps.- 1.5 Mathematical Model of the Uncontrolled Circulation.- 1.6 Balancing the Two Sides of the Heart and the Two Circulations.- 1.7 The Need for External Circulatory Control Mechanisms.- 1.8 Neural Control: The Baroreceptor Loop.- 1.9 Autoregulation.- 2 Gas Exchange in the Lungs.- 2.1 The Ideal Gas Law and the Solubility of Gases.- 2.2 The Equations of Gas Transport in One Alveolus.- 2.3 Gas Transport in the Lung.- 2.4 Optimal Gas Transport.- 2.5 Mean Alveolar and Arterial Partial Pressures.- 2.6 Transport of O2.- 2.7 Computer Solution of the Equations for O2 Transport in the Lung.- 2.8 Computing Projects Concerning Oxygen Transport by the Lung.- 2.9 Annotated References.- Exercises.- 3 Control of Cell Volume and Electrical Properties of Cell Membranes.- 3.1 Osmotic Pressure and the Work of Concentration.- 3.2 A Simple Model of Cell Volume Control.- 3.3 The Movement of Ions Across Cell Membranes.- 3.4 The Interaction of Electrical and Osmotic Effects.- 3.5 The Hodgkin-Huxley Equations for the Nerve Action Potential.- 3.6 Computer Simulation of the Nerve Action Potential.- 3.7 Suggestions for Computing Projects Concerning the Nerve Impulse.- 3.8 Annotated References.- Exercises.- 4 The Renal Countercurrent Mechanism.- 4.1 The Nephron.- 4.2 Dynamics of Na+ and H2O: Transport along the Renal Tubules.- 4.3 The Loop of Henle.- 4.4 The Juxtaglomerular Apparatus and the Renin-Angiotensin System.- 4.5 The Distal Tubule and Collecting Duct: Concentrating and Diluting Modes.- 4.6 Remarks on the Significance of the Juxtaglomerular Apparatus.- 4.7 How Nephrons Do Better Than a Factor of e.- 4.8 Computing Project on theInteracting Nephron Population Model.- 4.9 Annotated References.- Exercises.- 5 Muscle Mechanics.- 5.1 The Force-Velocity Curve.- 5.2 Crossbridge Dynamics.- 5.3 Computer Simulation of Crossbridge Attachment and Detachment.- 5.4 Suggested Computing Projects on Crossbridge Dynamics.- 5.5 Annotated References.- Exercises.- 6 Neural Systems.- 6.1 Guttman’s Experiments on Phase Locking.- 6.2 Biological Rhythms.- 6.3 Model Neural Networks.- 6.4 Annotated References.- Exercises.- 7 Population Dynamics.- 7.1 Bacterial Cultures.- 7.2 Age Structures.- 7.3 Microbial Ecology.- 7.4 Nonlinear Reproduction Curves.- 7.5 Controlling Populations.- 7.6 Annotated References.- Exercises.- 8 Genetics.- 8.1 Population Genetics.- 8.2 Biotechnology.- 8.3 Annotated References.- Exercises.- 9 A Theory of Epidemics.- 9.1 Spread of Infection Within a Family.- 9.2 The Threshold of an Epidemic.- 9.3 Predicting the Severity of an Epidemic.- 9.4 Annotated References.- Exercises.- 10 Patterns of Population Growth and Dispersal.- 10.1 Random Walks and the Process of Diffusion.- 10.2 Bacterial Growth on a Petri Plate.- 10.3 Concluding Remarks.- 10.4 Annotated References.- Exercises.- Appendix A Getting Started with Matrices and Matlab.- Appendix B Background on Random Processes.