STOCHASTIC AND STATE SPACE MODELS OF CARCINOGENESIS: SOME NEW MODELING APPROACHES - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 64

of stem cells so that the size of organ is normally not changed. If some
genetic changes have occurred in a stem cell to increase the proliferation
rate of the cell; then the proliferation rate is greater than the dierentiation
rate in this genetically altered cell so that this type of genetically altered
cells will accumulate; however, with high probability these genetically al-
tered cells will be eliminated by apoptosis or other protection devices unless
more genetic changes have occurred in these cells to abrogate apoptosis and
to overcome other existing protection devices. Furthermore, it requires at
least one round of cell proliferation for a genetic change to be xed (see [15,
33]). Also, since genetic changes are rare events, further genetic changes
will occur in at least one of the genetically altered cells only if the number
of these cells is very large. These steps have clearly been demonstrated by
cell culture experiments by Barrett and coworkers 42 using rat tracheal ep-
ithelial cells and on Syrian hamster embryo broblasts; for more detail and
some more specic examples, see Chapter 1 in Tan 55 .
These results as well as cancer biology studies 41 indicate that carcino-
genesis in humans and animals is a multi-step random process and that
these steps reect genetic changes and/or epigenetic changes that drive the
progressive transformation of normal stem cells into highly malignant ones.
The age-dependent cancer incidence data for many human cancers imply
four to seven rate-limiting stages from normal stem cells to malignant can-
cer tumors 48 .
The above discussion and studies in cancer biology 41 illustrate that can-
cer is initiated by some genetic changes or epigenetic changes to increase
cell proliferation while decreasing dierentiation and death. Further genetic
changes or epigenetic changes are required to overcome existing protection
devises in the body resulting in abrogation of apoptosis, telomere protec-
tion (immortalization) and uncontrolled growth as well as angiogenesis and
metastasis. Because somatic cell division occurs through cell division cycle
whereas gene mutation and genetic changes occur only during cell division,
most of the genetic changes aect carcinogenesis through the control of
cell division cycle. By articulating these ndings, Hanahan and Weinberg 23
have proposed six basic acquired capabilities which each normal stem cell
must require to become a malignant cancer tumor. These six capabilities
are: (1) Self-suciency of growth factor signals via genetic changes and/or
epigenetic changes. This follows from the observation that cells can be in-
duced to enter cell division cycle to start cell division only by growth factor
signals 23 . (2) Insensitivity to anti-growth signals via silencing or inactiva-
tion of some tumor suppressor genes to abrogate cell dierentiation. (3)