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

Table of Contents

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

Authors

Riccardo Sacco Associate Professor, Department of Mathematics, Politecnico di Milano, Italy. Riccardo Sacco, PhD, is an applied mathematician whose research and teaching activities span a wide variety of topics, including computational biology, semiconductor device modeling and simulation, computational fluid mechanics, and finite element analysis. Dr. Sacco has been appointed as a member of the Editorial Board of the "Journal of Coupled Systems and Multiscale Dynamics� and of the "Journal of Modeling for Ophthalmology.� In a joint partnership with Prof. Guidoboni and Prof. Harris, Dr. Sacco has promoted a series of international workshops, congresses, and doctoral courses with the twofold purpose of disseminating the use of mathematical and numerical methods in the study and clinical treatment of ophthalmological diseases and of fostering and favoring the interaction among students, scientists, and researchers in the fields of applied sciences and life sciences. Giovanna Guidoboni Professor of Electrical Engineering and Computer Science, University of Missouri, Professor of Mathematics, University of Missouri, Adjunct Professor of Mathematical Sciences, Indiana University Purdue University Indianapolis, Adjunct Professor of Ophthalmology, Indiana University School of Medicine. Giovanna Guidoboni, PhD, is an applied mathematician with expertise in mathematical and computational modeling of complex fluid flows arising in engineering and biomedical applications. Dr. Guidoboni has promoted the development of interdisciplinary approaches in physiology and ophthalmology at the international level. She co-founded a new peer-reviewed scientific journal titled "Journal for Modeling in Ophthalmology,� for which she currently serves as co-Chief Editor and Managing Editor, and a new series of interdisciplinary congresses and doctoral courses creating a forum where ophthalmologists, physiologists, mathematicians, engineers, physicists, and biologists can discuss new ideas on how to address outstanding challenges in ophthalmology. Aurelio Giancarlo Mauri Lecturer, Politecnico di Milano, Italy. Aurelio Giancarlo Mauri, MSc, is a Senior Member of the Technical Staff of Micron Technology, where he currently works in the numerical simulation group appointed for the physical modeling of electronic devices. He is the main author of FEMOS-MP (Finite Element Method Oriented Simulator for Multiphysics Problems), a C++ platform for the simulation of complex multiphysics systems including thermomechanical effects, chemical reactions and kinetics, semiconductors, and nonconventional materials in the continuum framework and using atomistic kinetic Monte Carlo methods. Currently, he also holds a lecturer fellowship at Politecnico di Milano for the courses "Numerical Analysis� and "Computational Modeling for Electronics and Biomathematics.�