Biomedical Engineering Reference
In-Depth Information
The constraints at stake, met everyday in the clinic of cancers, are related mainly
to resistance to treatment in cancer cell populations and to unwanted toxicity in
healthy tissues.
We briefly review some of these models, namely ordinary differential equation
(ODE) models, partial differential equation (PDE) models with spatial structure,
phase structured cellular automata and physiologically structured PDE models. We
do not claim to be exhaustive in a field where so much has been published in the
last 50 years. However, we present the main models used in cancer treatment in the
last decades, together with the biological phenomena that can be described by each
of them.
We then present some techniques used for the identification of the parameters
of population dynamic models used in chemotherapy. We also briefly review
theoretical therapeutic optimisation methods that can be used in the context of
different models of cell population growth, according to the clinical problem at
stake, to the available data and to the chosen model, with their advantages and
pitfalls.
We then focus on a novel method of optimisation under unwanted toxicity
constraints, presented here in the context of cancer chronotherapeutics. This method
is based on optimisation of eigenvalues in an age-structured model of cell population
dynamics, the parameters of which can be identified in cell cultures by using recent
intracellular imagery techniques relying on fluorescence quantification. Thanks to
these fine level quantitative cell observations, the structured cell population model,
which takes the cell division cycle into account, gives interesting results for the
optimisation of the pharmacological treatments of cancer.
Finally, bases for cell population dynamic models, with external control targets,
that ought to be used to physiologically represent the effects of different anticancer
drugs in use in the clinic, are sketched, as are possible schemes for multitarget
multidrug delivery optimisation, designed to meet present clinical challenges in
everyday oncology.
2
Drugs Used in Cancer Treatments and Their Targets
Although these are important co-occurring phenomena in cancer and make all
its malignancy, tissue invasion and the development of distant metastases will
not be mentioned here, for the simple reason that no efficient treatments exist
against them specifically so far. For instance, matrix metalloprotease inhibitors
(anti-invasive agents) were tested in the past, even until phase II clinical trials, but
their development has been arrested in particular due to high toxicity. We will thus
stick to drugs that impact on local cancer growth, a process which itself is initiated
by growing impairment of the normal physiological control on the cell division cycle
in cell populations.
From this point of view, drugs used in cancer treatments may be roughly divided
into those that drive cells to their death, which we define here as cytotoxic, and
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