A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences

<p>Part I. Mathematical, Computational, and Physical Foundations1. Elements of Mathematical Modeling2. Elements of Mathematical Methods3. Elements of computational methods4. Elements of Physics</p> <p>Part II. Balance Laws5. The Rational Continuum Mechanics Approach to Matter in Motion6. Balance laws in integral form7. Balance laws in local form8. Continuum Approach for Multicomponent Mixtures</p> <p>Part III. Constitutive Relations9. Preliminary Considerations on Constitutive Modeling10. Constitutive Relations for Fluids11. Constitutive Relations for Solids12. Constitutive Relations for Multicomponent Mixtures13. Constitutive Relations in Electromagnetism and Ion Electrodynamics</p> <p>Part IV. Model Reduction of System Complexity14. Reduction of the Maxwell Partial Differential System15. Electric Analogy to Fluid Flow</p> <p>Part V. Mathematical Models of Basic Biological Units and Complex Systems16. Cellular Components and Functions: A Brief Overview17. Mathematical Modeling of Cellular Electric Activity18. Mathematical Modeling of Electric Propagation Along Nerve Fibers19. Differential Models in Cellular Functions</p> <p>Part VI. Advanced Mathematical and Computational Methods20. Functional Spaces and Functional Inequalities21. Functional Iterations for Nonlinear Coupled Systems of Partial Differential Equations22. Time Semidiscretization and Weak Formulations for Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type23. Finite Element Approximations of Boundary Value Problems of Advection–Diffusion–Reaction Type24. Finite Element Approximations of Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type25. Finite Element Approximation of a Unified Model for Linear Elastic Materials</p> <p>Part VII. Simulation Examples and Clinical Applications26. Ion Dynamics in Cellular Membranes27. Interaction Between Hemodynamics and Biomechanics in Ocular Perfusion</p> <p>Part VIII. Examples, Exercises, and Projects28. Coding of Examples Using Matlab Scripts29. Matlab Functions for Algorithm Implementation30. Homework: Exercises and Projects</p> <p>Appendix A. Elements of Differential Geometry and Balance Laws in Curvilinear Coordinates</p>