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.
