MC 5417

## Candidate

Seyed Ali Madani Tonekaboni, Applied Math, University of Waterloo

## Title

Quantitative Approaches to the Cancer Stem Cell Hypothesis

## Abstract

In
this
thesis,
phenotype
switching
in
cancer
cell
populations
is
modeled.
We
focus
on
the
behavior
of
cells
at
the
phenotypic
level
and
present
mathematical
models
to
capture
the
results
of
available
experiments.
The
models,
based
on
the
cancer
stem
cell
hypothesis
(in
addition
to
the
new
concept
of
plasticity
in
tumor
populations),
are
also
employed
to
predict
cancer
cell
growth
*
in
vitro*
and
*
in
vivo*.

The models are analyzed in the two limits of large and small cell numbers. We use stochastic analysis to capture the random behavior of cells in the limit of low number as observed in mammosphere formation assays (MFAs). The deterministic solution of the models is also obtained to simulate the average behavior of cells. The importance of stochastic analysis and deterministic simulations is discussed in detail.

The primary purpose of the thesis is to highlight the importance of stochastic analysis in cancer stem cell experiments. The models are developed or modified based on the idea that both stochastic and deterministic behavior of cells should be considered simultaneously. In order to describe the behavior of the cells in cancer stem cell assays, the developed models are then used to investigate the possible experimental errors in the area and suggest possible filtration methods for corresponding experiments. In addition, the models are used to investigate the behavior of tumors under radiotherapy; and the effects of phenotype switching on the efficiency of therapies are investigated in the final part of the thesis.