MATHEMATICAL MODELS ON THE GROWTH OF SOLID TUMORS - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 298

The paper is organized as follows. In Section 2, we will discuss dierent
stages of solid tumor. In Section 3, we discuss multistep transformation to
cancer. In Section 4, we discuss experiments on cancer in vitro which are
useful to estimate model parameters. Extracellular scale models, cellular
scale models, and subcellular scales are discussed in Sections 5, 6, and 7
respectively. We discuss models dealing with capsule formation in section
8. The unifying results obtained from models at dierent scales and models
which couple dierent scales are discussed in section 9. In Section 10, we
will make conclusions and outlook.
2. Dierent stages of solid tumor
Cancerous tumors originate from mutation of one or more cells which usu-
ally undergo rapid uncontrolled growth thereby impairing the functioning
of normal tissue. There is a large body of evidence proving that all the cells
within a tumor mass are derived from a single cell. Even though all the cells
within a tumor mass may be derived from a single cell, this does not mean
that all the cells in a tumor are genetically identical. Tumor cells are more
unstable than normal cells, meaning they mutate 1;27 at a much higher rate,
they repair themselves much less eectively and they have ceased to re-
spond to normal growth regulatory mechanism. Therefore, the cells within
a tumor are dierent even from one another.
First, a piece of the DNA strand must be signicantly mutated and the
mutations must slip through the repair mechanisms. These mutations may
take place over generations of cells. For example, one generation may have
one mutation; the next may not have any. A subsequent generation may
have another and so on, until the \cancer mutation" have occurred. The
tumor cells respond both through induced alterations in physiology and
metabolism and through altered gene and protein expression 12;28
Due to these mutations, the cell must gain the ability to proliferate and
thus lose its normal function. In a sense, the major purpose of the cell must
be to divide.
There are probably only a limited number of alterations that will allow
a cell to lose its functions and divide out of control. Some alterations aect
nothing, others may cause a minor change that is not really threatening to
the cell, and others can outrightly kill the cell. So, to become cancerous,
the cell must maintain its ability to divide without causing any damage to
limit its ability to survive.
If a cell becomes bent on dividing, the cell will just continue dividing