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

Erscheinungsjahr 2019
ISBN: 978-0-12-812518-2
Verlag: Elsevier Science Publishing Co Inc

Buch, Englisch, 854 Seiten, Format (B × H): 189 mm x 236 mm, Gewicht: 1687 g

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.

Zielgruppe

Biomedical engineers, life sciences researchers, as well as undergraduate and graduate students in Biomedical Engineering, Electrical Engineering, Mathematics, Biology and Medicine.

Fachgebiete

• Naturwissenschaften Biowissenschaften Biowissenschaften
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Medizintechnik, Biomedizintechnik
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizintechnik, Biomedizintechnik, Medizinische Werkstoffe

Inhaltsverzeichnis

Part I. Mathematical, Computational, and Physical Foundations1. Elements of Mathematical Modeling2. Elements of Mathematical Methods3. Elements of computational methods4. Elements of Physics

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

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

Part IV. Model Reduction of System Complexity14. Reduction of the Maxwell Partial Differential System15. Electric Analogy to Fluid Flow

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

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

Part VII. Simulation Examples and Clinical Applications26. Ion Dynamics in Cellular Membranes27. Interaction Between Hemodynamics and Biomechanics in Ocular Perfusion

Part VIII. Examples, Exercises, and Projects28. Coding of Examples Using Matlab Scripts29. Matlab Functions for Algorithm Implementation30. Homework: Exercises and Projects

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