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 the life sciences through the adoption of mathematical models based on physical principles, such as the conservation of mass, electric charge, momentum, and energy. It then teaches how to translate the mathematical formulation into a numerical algorithm that is implementable on a computer. The book 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.
1. Introduction - p. 1 2. Chapter 1: Elements of Mathematical Modeling - p. 2 3. Chapter 2: Elements of Mathematical Methods - p. 17 4. Chapter 3: Elements of Computational Methods - p. 62 5. Chapter 4: Elements of Physics - p. 111 6. Part 2: Balance Laws - p. 171 7. Introduction - p. 173 8. Chapter 5: The Rational Continuum Mechanics Approach to Matter in Motion - p. 174 9. Chapter 6: Balance Laws in Integral Form - p. 201 10. Chapter 7: Balance Laws in Local Form - p. 211 11. Chapter 8: Continuum Approach for Multicomponent Mixtures - p. 231 12. Part 3: Constitutive Relations - p. 253 13. Introduction - p. 255 14. Chapter 9: Preliminary Considerations on Constitutive Modeling - p. 256 15. Chapter 10: Constitutive Relations for Fluids - p. 262 16. Chapter 11: Constitutive Relations for Solids - p. 294 17. Chapter 12: Constitutive Relations for Multicomponent Mixtures - p. 325 18. Chapter 13: Constitutive Relations in Electromagnetism and Ion Electrodynamics - p. 335 19. Part 4: Model Reduction of System Complexity - p. 373 20. Introduction - p. 375 21. Chapter 14: Reduction of the Maxwell partial differential system - p. 375 22. Chapter 15: Electric Analogy to Fluid Flow - p. 389 23. Part 5: Mathematical Models of Basic Biological Units and Complex Systems - p. 415 24. Introduction - p. 417 25. Chapter 16: Cellular Components and Functions: A Brief Overview - p. 418 26. Chapter 17: Mathematical Modeling of Cellular Electric Activity - p. 424 27. Chapter 18: Mathematical Modeling of Electric Propagation Along Nerve Fibers - p. 460 28. Chapter 19: Differential Models in Cellular Functions - p. 465 29. Part 6: Advanced Mathematical and Computational Methods - p. 491 30. Introduction - p. 493 31. Chapter 20: Functional Spaces and Functional Inequalities - p. 495 32. Chapter 21: Functional Iterations for Nonlinear Coupled Systems of Partial Differential Equations - p. 516 33. Chapter 22: Time Semidiscretization and Weak Formulations for Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type - p. 531 34. Chapter 23: Finite Element Approximations of Boundary Value Problems of Advection–Diffusion–Reaction Type - p. 545 35. Chapter 24: Finite Element Approximations of Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type - p. 577 36. Chapter 25: Finite Element Approximation of a Unified Model for Linear Elastic Materials - p. 595 37. Part 7: Simulation Examples and Clinical Applications - p. 630 38. Introduction - p. 631 39. Chapter 26: Ion Dynamics in Cellular Membranes - p. 632 40. Chapter 27: Interaction Between Hemodynamics and Biomechanics in Ocular Perfusion - p. 651 41. Part 8: Examples, Exercises, and Projects - p. 670 42. Introduction - p. 671 43. Chapter 28: Coding of Examples Using Matlab Scripts - p. 671 44. Chapter 29: Matlab Functions for Algorithm Implementation - p. 736 45. Chapter 30: Homework: Exercises and Projects - p. 770 46. Appendix A: Elements of Differential Geometry and Balance Laws in Curvilinear Coordinates - p. 785 47. Bibliography - p. 805 48. Index - p. 819
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 the life sciences through the adoption of mathematical models based on physical principles, such as the conservation of mass, electric charge, momentum, and energy. It then teaches how to translate the mathematical formulation into a numerical algorithm that is implementable on a computer. The book 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.
1. Introduction - p. 1 2. Chapter 1: Elements of Mathematical Modeling - p. 2 3. Chapter 2: Elements of Mathematical Methods - p. 17 4. Chapter 3: Elements of Computational Methods - p. 62 5. Chapter 4: Elements of Physics - p. 111 6. Part 2: Balance Laws - p. 171 7. Introduction - p. 173 8. Chapter 5: The Rational Continuum Mechanics Approach to Matter in Motion - p. 174 9. Chapter 6: Balance Laws in Integral Form - p. 201 10. Chapter 7: Balance Laws in Local Form - p. 211 11. Chapter 8: Continuum Approach for Multicomponent Mixtures - p. 231 12. Part 3: Constitutive Relations - p. 253 13. Introduction - p. 255 14. Chapter 9: Preliminary Considerations on Constitutive Modeling - p. 256 15. Chapter 10: Constitutive Relations for Fluids - p. 262 16. Chapter 11: Constitutive Relations for Solids - p. 294 17. Chapter 12: Constitutive Relations for Multicomponent Mixtures - p. 325 18. Chapter 13: Constitutive Relations in Electromagnetism and Ion Electrodynamics - p. 335 19. Part 4: Model Reduction of System Complexity - p. 373 20. Introduction - p. 375 21. Chapter 14: Reduction of the Maxwell partial differential system - p. 375 22. Chapter 15: Electric Analogy to Fluid Flow - p. 389 23. Part 5: Mathematical Models of Basic Biological Units and Complex Systems - p. 415 24. Introduction - p. 417 25. Chapter 16: Cellular Components and Functions: A Brief Overview - p. 418 26. Chapter 17: Mathematical Modeling of Cellular Electric Activity - p. 424 27. Chapter 18: Mathematical Modeling of Electric Propagation Along Nerve Fibers - p. 460 28. Chapter 19: Differential Models in Cellular Functions - p. 465 29. Part 6: Advanced Mathematical and Computational Methods - p. 491 30. Introduction - p. 493 31. Chapter 20: Functional Spaces and Functional Inequalities - p. 495 32. Chapter 21: Functional Iterations for Nonlinear Coupled Systems of Partial Differential Equations - p. 516 33. Chapter 22: Time Semidiscretization and Weak Formulations for Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type - p. 531 34. Chapter 23: Finite Element Approximations of Boundary Value Problems of Advection–Diffusion–Reaction Type - p. 545 35. Chapter 24: Finite Element Approximations of Initial Value/Boundary Value Problems of Advection–Diffusion–Reaction Type - p. 577 36. Chapter 25: Finite Element Approximation of a Unified Model for Linear Elastic Materials - p. 595 37. Part 7: Simulation Examples and Clinical Applications - p. 630 38. Introduction - p. 631 39. Chapter 26: Ion Dynamics in Cellular Membranes - p. 632 40. Chapter 27: Interaction Between Hemodynamics and Biomechanics in Ocular Perfusion - p. 651 41. Part 8: Examples, Exercises, and Projects - p. 670 42. Introduction - p. 671 43. Chapter 28: Coding of Examples Using Matlab Scripts - p. 671 44. Chapter 29: Matlab Functions for Algorithm Implementation - p. 736 45. Chapter 30: Homework: Exercises and Projects - p. 770 46. Appendix A: Elements of Differential Geometry and Balance Laws in Curvilinear Coordinates - p. 785 47. Bibliography - p. 805 48. Index - p. 819
