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 physics 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.
- Presents theoretical (modeling), biological (experimental), and computational (simulation) perspectives
- Features examples, exercises, and MATLAB codes for further reader involvement
- Covers basic and advanced functional and computational techniques throughout the book
Part I. Overview and Preliminaries 1. Elements of mathematical modeling 2. Elements of bioengineering and life sciences 3. Elements of mathematical methods 4. Elements of computational methods 5. Elements of physics 6. Projects and Exercises
Part II. Balance Laws and Constitutive Relations 7. The rational continuum mechanics approach to matter in motion 8. Balance laws in integral form 9. Balance laws in local form 10. Constitutive relations in fluid and solid mechanics 11. Constitutive relations in electromagnetism and ion electrodiffusion 12. Projects and Exercises
Part III. Model Reduction of System Complexity 13. Multiple scales and dimensional analysis 14. Model reduction for current flow in a circuit 15. Model reduction for fluid flow in a tube 16. Electric analogy to fluid flow 17. Projects and Exercises
Part IV. Mathematical Models for Basic Biological Units and Complex Systems 18. From ions, to cells, to systems and back 19. Mathematical models for cellular electrophysiology 20. Mathematical models for cellular functions 21. Mathematical models for physiological fluid flow 22. Mathematical models for biological tissue mechanics 23. Projects and Exercises
Part V. Advanced Mathematical and Computational Methods 24. Functional spaces and functional inequalities 25. Iterative formulations for nonlinear coupled systems 26. Weak formulations for initial-boundary value problems 27. Finite element approximations of initial-boundary value problems 28. Projects and Exercises
Part VI. Simulation Examples and Clinical Applications 29. Ion channel dynamics in cellular membranes 30. Ocular fluid dynamics, biomechanics and oxygenation 31. Systemic features of cardiovascular hemodynamics 32. Projects and Exercises
Dr. Sacco 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 graduated from Politecnico di Milano (Italy) with a BS and MS in electronic engineering (1989), and obtained in 1992 a PhD in applied mathematics from Universita` degli Studi di Milano (Italy). Dr. Sacco was awarded two post-doctoral positions in mathematics from CNR Milano (1992) and Universita` degli Studi di Milano (1994). In 1995 Dr. Sacco joined the faculty at Dipartimento di Matematica Politecnico di Milano (Italy) as assistant professor in Numerical Analysis and later was appointed associate professor in the same institution (2001). Dr. Sacco was included in the "Who's Who in the World 2001" and co-authored with Prof. Alfio Quarteroni and Prof. Fausto Saleri the book "Numerical Mathematics" (1st Ed., Springer New York, 2000). Since 1994 Dr. Sacco has been serving as a referee for more than 20 peer-reviewed international journals ranging from numerical analysis to computational electronics and biology, and since 2006 is serving as reviewer for the American Mathematical Society. More recently, Dr. Sacco has been appointed member of the Editorial Board of the "Journal of Coupled Systems and Multiscale Dynamics" and of "Journal of Modeling for Ophthalmology". In a joint partnership with Prof. Guidoboni and Prof. Harris, Dr. Sacco has promoted over the last years 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 belonging to Applied Sciences and Life Sciences.
Dr. Guidoboni is an applied mathematician with expertise in mathematical and computational modeling of complex fluid flows arising in engineering and biomedical applications. Dr. Guidoboni graduated from the Universita' degli Studi di Ferrara (Italy) with a BS and MS in engineering of materials (2000), and a Ph.D. in mathematics (2004). During her graduate studies, Dr. Guidoboni was a Marie Curie Scholar at the University of Surrey (UK). She began studying mathematical applications involving blood flow in 2004 when she was a Fulbright Scholar at the University of Houston (USA). At the conclusion of her Fulbright Scholarship, Dr. Guidoboni joined the faculty at the University of Houston first as a visiting professor (2004-2007) and later as an assistant professor (2007-2010). In 2010, Dr. Guidoboni joined the Department of Mathematical Sciences at IUPUI (Indiana University Purdue University Indianapolis, USA) as an associate professor and the Department of Ophthalmology at Indiana University School of Medicine as an adjunct professor in 2012. In 2012, she founded the School of Science Institute for Mathematical Modeling and Computational Science (iM2CS), a cross-departmental school-level unit that promotes interdisciplinary research and educational activities, integrating mathematical and computational approaches to address problems arising in various areas of science, engineering and medicine. In 2014, Dr. Guidoboni was awarded the prestigious Chair Gutenberg by the Region Alsace in France, being the first mathematician to receive this award since its inception in 2007, and she was appointed a joint chair between the University of Strasbourg and IUPUI. Since 2010, Dr. Guidoboni's research activities have focused on the modeling of ocular biophysics, pioneering the mathematical description of the fluid-structure interactions involved in ocular blood flow and their clinical applications. Dr. Guidoboni has promoted the development of interdisciplinary approaches in ophthalmology at the international level by co-founding, jointly with Prof. Alon Harris (Glick Eye Institute, Indianapolis, USA), a new peer-reviewed scientific journal entitled "Journal for Modeling in Ophthalmology, for which she currently serves as co-Chief Editor and Managing Editor, and a new series of Interdisciplinary Congresses creating a forum where ophthalmologists, physiologists, mathematicians, engineers, physicists and biologists can discuss new ideas on how to address outstanding challenges in ophthalmology.
Mauri, Aurelio Giancarlo
Aurelio Giancarlo Mauri is currently lecturer at Politecnico di Milano for courses on "Computational Modeling in electronics and Biomathematics and on "Numerical Methods for civil engineering. He is also responsible for the collaboration project with Micron technology named "Computational models for the simulation of piezo-mechanical phenomena. His research interests include different topics: for electronics, modelling the operations of advance non-volatile memories, tunneling in dielectrics media and statistical phenomena (threshold distribution, RTN, traps captures times); for physics, the modelling of impurities diffusion/clustering and extended defect in silicon with KMC approach and the modelling of materials properties with DFT calculations; and for applied mathematics, the numerical approach to the simulations of highly coupled multi-physics system. He is the principal author of FEMOS-MP (Finite Element Method Oriented Simulator for Multiphysics problem) a C++ platform for the simulation of complex multi-physics system including thermo-mechanical effects, chemical reaction and kinetics in PNP framework, semiconductor and ferroelectric materials and atomistic Monte-Carlo approach. He is the author of more than 45 papers on international journals and conferences.