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

1st Edition - July 18, 2019

Authors: Riccardo Sacco, Giovanna Guidoboni, Aurelio Giancarlo Mauri

Paperback ISBN:

9 7 8 - 0 - 1 2 - 8 1 2 5 1 8 - 2

eBook ISBN:

9 7 8 - 0 - 1 2 - 8 1 2 5 1 9 - 9

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences provides a systematic methodology to the formulation of problems in biomedical… Read more

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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.

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 Laws
5. 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 Relations
9. 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 Complexity
14. Reduction of the Maxwell Partial Differential System15. Electric Analogy to Fluid Flow

Part V. Mathematical Models of Basic Biological Units and Complex Systems
16. 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 Methods
20. 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 Applications
26. Ion Dynamics in Cellular Membranes27. Interaction Between Hemodynamics and Biomechanics in Ocular Perfusion

Part VIII. Examples, Exercises, and Projects
28. 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

Riccardo Sacco

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.

Affiliations and expertise

Associate Professor, Department of Mathematics, Politecnico di Milano, Italy

Giovanna Guidoboni

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.

Affiliations and expertise

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

Aurelio Giancarlo Mauri

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.”

Affiliations and expertise

Lecturer, Politecnico di Milano, Italy