MATHEMATICAL MODELS ON THE GROWTH OF SOLID TUMORS - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 297

CHAPTER 14
MATHEMATICAL MODELS ON THE GROWTH
OF SOLID TUMORS
Zachariah Sinkala
Department of Mathematical Sciences, Middle Tennessee State University,
P.O. Box 34, Murfreesboro, Tennessee 37132, USA
E-mail: [e-mail]
This paper discusses mathematical models dealing with the growth of
solid tumors. Tumor growth is a very complex process, involving many
dierent phenomena, which occur at dierent scales: subcellular, cellular,
and extracellular scales. We survey models that address the problem
at: subcellular scale, cellular scale, and extracellular scale. Then after
we discuss multi-scale models and unication of models results from
dierent scales.
1. Introduction
Cancer research has become increasingly important. This is because ma-
lignant neoplasms are the 2nd leading cause of death in the United States
of America, and rank among top killers worldwide. Each year billions of
dollars from government and private funding sources are spent on cancer
research. In order to develop eective treatments, it is important to identify
the mechanisms responsible for cancer growth, how they interact, and how
can most easily be manipulated to eradicate (manage) the disease.
In order to gain such insight, it is usually necessary to perform large
amounts of time consuming and intricating experiments but not always.
Through the development and solutions of mathematical models that de-
scribe dierent aspects of solid tumor growth will provide insight into the
complex mechanisms that control tumor growth and, hence suggest direc-
tions for new therapies. Thus, applied mathematics has potential to prevent
excessive experimentation and also to provide biologists with complemen-
tary and valuable insight into the mechanisms that control the development
of solid tumors.