Biomedical Engineering Reference
In-Depth Information
The coupling of angiogenesis models to tumour growth models is usually done
via the concentration in oxygen (or nutrients), the time and space evolution of which
is given by a reaction-diffusion PDE based on the fact that oxygen is delivered by
the vasculature and mostly consumed by tumour cells. This coupling enables to
describe in a more realistic way the effects of anti-angiogenic therapies on tumour
vasculature and thus on tumour growth.
Thus, Sinek et al. [
128
] based on the model of vascular tumour growth developed
by Zheng et al. [
141
] and on experimental data to develop a model of tumour
growth and vascular network coupled to a multi-compartment pharmacokinetic-
pharmacodynamic (PK-PD) model. Their purpose was to analyse the effect on
tumour growth of two anti-cancer drugs, doxorubicin and cisplatin (compartments
of the PK-PD model were drug-specific). They concluded that drug and oxygen
heterogeneities, possibly due to irregularities of the vasculature, can impact drug
efficacy on tumour cells. Kohandel et al. [
79
] proposed a model that also takes into
account tumour cells, the tumour vascular network and oxygen to investigate the
effect on tumour growth of different schedules of single and combined radiotherapy
and anti-angiogenic therapy.
3.3
Phase-Structured Cellular Automata for the Cell Division
Cycle and Drug Effects
Drug effects on tumour growth can also be investigated by means of phase-
structured cellular automata to represent the cell division cycle. Cellular automata
enable to describe individual cancer cell evolution within a population of cells.
Thus Altinok et al. developed a cellular automaton for the cell cycle [
3
-
6
]. This
automaton does not take into account molecular events but phenomenologically
describes cell cycle progression. The states of this automaton correspond to the
phases of the cell cycle. Transition between two states of the automaton correspond
to cell progression through the cell cycle, or exit from the cell cycle, and are
supposed to respect some prescribed rules. For instance each phase of the cell cycle
is supposed to be characterised by a mean duration and a variability in order to take
into account inter-cell variability that can appear within a population. This model
enables to study, on a whole population of cells, the impact of the variability in the
duration of the cell cycle phases on cell desynchronisation through the cell cycle.
Such modelling is motivated by the fact that one way to optimise pharmacolog-
ical treatments in cancer, taking into account of the cell division cycle on which
tissue proliferation relies, is to take advantage of the control that circadian clocks
are known to exert on it. Such treatments are termed chronotherapies of cancer
[
87
-
92
]. In order to investigate the effects of chronotherapy on the growth of a
tumour cell population, Altinok et al. coupled this cellular automaton with a model
of the circadian clock through kinases known to induce or inhibit the transition
from
G
2
to
M
. For instance, in [
3
,
4
], the authors were interested in the action of
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