Optimisation of Cancer Drug Treatments Using Cell Population Dynamics - Mathematical Methods and Models in Biomedicine - page 255

Optimisation of Cancer Drug Treatments Using
Cell Population Dynamics

Frederique Billy, Jean Clairambault, and Olivier Fercoq

1 Introduction

Cancer is primarily a disease of the physiological control on cell population
proliferation. Tissue proliferation relies on the cell division cycle: one cell becomes
two after a sequence of molecular events that are physiologically controlled at each
step of the cycle at so-called checkpoints, in particular at transitions between phases
of the cycle [ 105 ]. Tissue proliferation is the main physiological process occurring
in development and later in maintaining the permanence of the organism in adults,
at that late stage mainly in fast renewing tissues such as bone marrow, gut and skin.
Proliferation is normally controlled in such a way that tissue homeostasis is
preserved. By tissue homeostasis we mean permanence in the mean of tissue in
volume, mass and function to ensure satisfaction of the needs of the whole organism.
In cancer tissues, this physiological control, which also relies on the so-called
checkpoints in the division cycle of individual replicating cells, is disrupted, leading
to an overproduction of cells that eventually results in the development of tumours.
Anticancer drugs all attack the cell division cycle, either by slowing it down
(possibly until quiescence, i.e., non-proliferation, cells remaining alive), or by
blocking it at checkpoints, which in the absence of cell material repair eventually
leads to cell death.
Various mathematical models have been proposed to describe the action of
anticancer drugs in order to optimise it, that is to minimise the number of cancer
cells or a related quantity, as the growth rate of the cancer cell population.

F. Billy ( ) ￿ J. Clairambault
INRIA BANG team, BP 105, F78153 Rocquencourt, and LJLL,
UPMC, 4 Place Jussieu, F75005 Paris, France
e-mail: [e-mail] ; [e-mail]
O. Fercoq
INRIA MAXPLUS team, CMAP, Ecole Polytechnique, F91128 Palaiseau, France
e-mail: [e-mail]