Biomedical Engineering Reference
In-Depth Information
of the stochastic birth-death process, proliferation is equivalent to birth
and dierentiation to death in general terms in the stochastic birth-death
process. Notice that cell dierentiation is not death but simply a process
to remove cells from the cell population.
Remark 2: In the multi-stage stochastic models, as illustrated in
many publications 36;38;39;55;58 , to apply the classical method to derive an-
alytical results, one need to make several assumptions. These assumptions
include: (a) The last stage initiated cell (ie. I k cells in the k-stage model)
grow instantaneously into malignant tumors, (b) the mutation rates, birth
rates, death rates are independent of time (i.e., time homogeneous), (c)
all mutation rates before the (k-1)-stage in the k-stage model are equal 39 .
(d) the number of normal stem cells is a deterministic function of time
and hence grows deterministically with no random disturbances. Obviously,
many of these assumptions do not hold in many practical situations 68 . For
example, assumptions (b) and (c) may not hold in many cases and if as-
sumption (a) is violated, the process involving cancer tumors is no longer
Markov (see [58]). Hanin and Yakovlev 24 have also shown that even for
the simplest 2-stage homogeneous model, using the classical approach the
model is not identiable in the sense that one can only estimate 3 paramet-
ric functions; in particular, one can not estimate the birth rate and death
rate of the initiated cell, only the dierence of birth rate and death rate.
2. Some Recent Cancer Biology for Modeling
Carcinogenesis
Using tissue culture method, biologists have shown that all organs consist
of two types of cells: The dierentiated cells which are major components
of the organ proper and the stem cells from which cancer tumors develop
(see [1, 4]). Only stem cells can divide giving rise to new stem cells and new
dierentiated cells to replace old dierentiated cells; the dierentiated cells
do not divide and are end cells to serve as components of the tissue and to
perform specic functions of the tissue. That is, stem cells are subject to
stochastic proliferation and dierentiation with dierentiated cells replacing
old cells of the organ.
To understand cancer, notice that in normal individuals, there is a bal-
ance between proliferation and dierentiation in stem cells and there are
devices such as the DNA repair system and apoptosis in the body to protect
against possible errors in the metabolism process. Thus, in normal individ-
uals, the proliferation rate of stem cells equals to the dierentiation rate
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