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

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences provides a systematic methodology to the formulation of problems in biomedical engineering and life sciences through the adoption of mathematical models based on fundamental physics principles, such as the conservation of mass, electric charge, momentum, and energy. Readers will then learn to translate the mathematical formulation into a numerical algorithm, implementable on a computer, to determine an approximate problem solution. A Comprehensive Modeling Approach in Bioengineering and Life Sciences employs computational models as synthesized tools for the investigation, quantification, verification and comparison of different conjectures or scenarios of the behavior of a given compartment of the human body under physiological and pathological conditions.

Structured to differentiate between theoretical (modeling), biological (experimental), and computational (simulation) perspectivesEach chapter features examples, exercises, and Matlab codes for further reader involvement Covers basic as well as advanced functional and computational techniques throughout the book

Part I. Mathematical, Computational, and Physical Foundations 1. Elements of Mathematical Modeling 2. Elements of Mathematical Methods 3. Elements of computational methods 4. Elements of Physics

Part II. Balance Laws 5. The Rational Continuum Mechanics Approach to Matter in Motion 6. Balance laws in integral form 7. Balance laws in local form 8. Continuum Approach for Multicomponent Mixtures

Part III. Constitutive Relations 9. Preliminary Considerations on Constitutive Modeling 10. Constitutive Relations for Fluids 11. Constitutive Relations for Solids 12. Constitutive Relations for Multicomponent Mixtures 13. Constitutive Relations in Electromagnetism and Ion Electrodynamics

Part IV. Model Reduction of System Complexity 14. Reduction of the Maxwell Partial Differential System 15. Electric Analogy to Fluid Flow

Part V. Mathematical Models of Basic Biological Units and Complex Systems 16. Cellular Components and Functions: A Brief Overview 17. Mathematical Modeling of Cellular Electric Activity 18. Mathematical Modeling of Electric Propagation Along Nerve Fibers 19. Differential Models in Cellular Functions

Part VI. Advanced Mathematical and Computational Methods 20. Functional Spaces and Functional Inequalities 21. Functional Iterations for Nonlinear Coupled Systems of Partial Differential Equations 22. Time Semidiscretization and Weak Formulations for Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type 23. Finite Element Approximations of Boundary Value Problems of Advection–Diffusion–Reaction Type 24. Finite Element Approximations of Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type 25. Finite Element Approximation of a Unified Model for Linear Elastic Materials

Part VII. Simulation Examples and Clinical Applications 26. Ion Dynamics in Cellular Membranes 27. Interaction Between Hemodynamics and Biomechanics in Ocular Perfusion

Part VIII. Examples, Exercises, and Projects 28. Coding of Examples Using Matlab Scripts 29. Matlab Functions for Algorithm Implementation 30. Homework: Exercises and Projects

Appendix A. Elements of Differential Geometry and Balance Laws in Curvilinear Coordinates