Last month, Wiley was proud to publish Method of Lines PDE Analysis in Biomedical Science and Engineering which presents the methodology and applications of ODE and PDE models within biomedical science and engineering
With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs.
Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes:
- Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids
- Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithm
- A companion website that provides source code for the R routines
Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.
1. Congratulations on the publication of Method of Lines PDE Analysis in Biomedical Science and Engineering. How did the writing process begin?
The book is a continuation of on-going writing about computer-based mathematical modelling in biomedical science and engineering (BMSE).
2. What were the primary objectives you had in mind during the writing process?
I wanted to report new results (applications) in computer based modelling in BMSE.
3. With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, the book demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Please could you give us an example that is used within the book?
The book is now published and an example is available here.
4. The chapters have a particularly interesting format by the presentation of a model followed by the programming. Please could you explain why you chose to write the chapters this way?
The book is intended as a basic introduction to PDE/MOL analysis. It is not an advanced treatise on PDE analysis. Thus, the chapters are designed to be as self-contained with detailed explanations. The reader can start with computer-based PDE analysis without first studying the many details of numerical methods and programming.
5. If there is one piece of information or advice that you would want your reader to take away and remember after reading your book, what would that be?
Computer-based PDE analysis of BMSE is not difficult (it might seem overwhelming), and can be applied to a broad spectrum of applications in BMSE.
6. Who should read the book and why?
The book should be of interest to biologists, medical researchers and clinicians, biophysicists, biochemists, engineers and applied mathematicians.
7. Why is this book of particular interest now?
Computer-based mathematical modelling in BMSE is a very active and rapidly advancing field.
8. Were there areas of the book that you found more challenging to write, and if so, why?
Explaining mathematical modelling and associated computer coding (programming) to readers who are not expert in these areas.
9. What is it about this area of biomedical science and engineering that fascinates you?
The applications of mathematics to human physiology and pathology as an approach to a better (quantitative) understanding of these problem areas.
10. What will be your next book-length undertaking?
Computer-based mathematical analysis of Alzheimer’s disease, and possibly other neurodegenerative diseases.
11. You are Emeritus McCann Professor of Biomolecular and Chemical Engineering and Professor of Mathematics at Lehigh University. Please could you tell us more about your educational background and what inspired you to pursue your career in this discipline?
I completed my PhD at Princeton University; ScD (honorary) at University of Mons (Belgium) followed by an entire career (44 years teaching) in applied mathematics as implemented on computers. Initially, I viewed this as a new and important area, and after so many years, I still view it this way. In particular, the developments in computers have been extraordinary, so we can analyze problems that we could only imagine at the beginning.