1st Edition
by William E. Schiesser (Author)
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
algorithms
- 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.
