# Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant; Jean Clairambault; Francis Lévi

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 6, page 1069-1086
- ISSN: 0764-583X

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topBasdevant, Claude, Clairambault, Jean, and Lévi, Francis. "Optimisation of time-scheduled regimen for anti-cancer drug infusion." ESAIM: Mathematical Modelling and Numerical Analysis 39.6 (2010): 1069-1086. <http://eudml.org/doc/194297>.

@article{Basdevant2010,

abstract = {
The chronotherapy concept takes advantage of the circadian rhythm of
cells physiology in maximising a treatment efficacy on its target
while minimising its toxicity on healthy organs. The
object of the present paper is to investigate mathematically and
numerically optimal strategies in cancer chronotherapy. To this
end a mathematical model describing the time evolution of efficiency
and toxicity of an oxaliplatin anti-tumour treatment has been derived.
We then applied an optimal control technique to search for the best
drug infusion laws.
The mathematical model is a set of six coupled differential
equations governing the time evolution of both the tumour cell population
(cells of Glasgow osteosarcoma, a mouse tumour) and the mature jejunal
enterocyte population, to be shielded from unwanted side effects
during a treatment by oxaliplatin.
Starting from known tumour and villi populations, and a time dependent free
platinum Pt (the active drug) infusion law being given,
the mathematical model allows to compute the time evolution of both tumour and
villi populations. The tumour population growth is based on Gompertz law
and the Pt anti-tumour efficacy takes into account the circadian
rhythm. Similarly the enterocyte population is subject to a circadian toxicity
rhythm. The model has been derived using, as far as possible, experimental data.
We examine two different optimisation problems. The eradication
problem consists in finding the drug infusion law able to minimise
the number of tumour cells while preserving a minimal level for the
villi population. On the other hand, the containment problem searches
for a quasi periodic treatment able to maintain the tumour population
at the lowest possible level, while preserving the villi cells. The
originality of these approaches is that the objective and constraint
functions we use are L∞ criteria. We are able to derive
their gradients with respect to the infusion rate and then to
implement efficient optimisation algorithms.
},

author = {Basdevant, Claude, Clairambault, Jean, Lévi, Francis},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = { Dynamical systems; optimisation; circadian rhythms; drugs;
therapeutics; cancer.; therapeutics; cancer},

language = {eng},

month = {3},

number = {6},

pages = {1069-1086},

publisher = {EDP Sciences},

title = {Optimisation of time-scheduled regimen for anti-cancer drug infusion},

url = {http://eudml.org/doc/194297},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Basdevant, Claude

AU - Clairambault, Jean

AU - Lévi, Francis

TI - Optimisation of time-scheduled regimen for anti-cancer drug infusion

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 6

SP - 1069

EP - 1086

AB -
The chronotherapy concept takes advantage of the circadian rhythm of
cells physiology in maximising a treatment efficacy on its target
while minimising its toxicity on healthy organs. The
object of the present paper is to investigate mathematically and
numerically optimal strategies in cancer chronotherapy. To this
end a mathematical model describing the time evolution of efficiency
and toxicity of an oxaliplatin anti-tumour treatment has been derived.
We then applied an optimal control technique to search for the best
drug infusion laws.
The mathematical model is a set of six coupled differential
equations governing the time evolution of both the tumour cell population
(cells of Glasgow osteosarcoma, a mouse tumour) and the mature jejunal
enterocyte population, to be shielded from unwanted side effects
during a treatment by oxaliplatin.
Starting from known tumour and villi populations, and a time dependent free
platinum Pt (the active drug) infusion law being given,
the mathematical model allows to compute the time evolution of both tumour and
villi populations. The tumour population growth is based on Gompertz law
and the Pt anti-tumour efficacy takes into account the circadian
rhythm. Similarly the enterocyte population is subject to a circadian toxicity
rhythm. The model has been derived using, as far as possible, experimental data.
We examine two different optimisation problems. The eradication
problem consists in finding the drug infusion law able to minimise
the number of tumour cells while preserving a minimal level for the
villi population. On the other hand, the containment problem searches
for a quasi periodic treatment able to maintain the tumour population
at the lowest possible level, while preserving the villi cells. The
originality of these approaches is that the objective and constraint
functions we use are L∞ criteria. We are able to derive
their gradients with respect to the infusion rate and then to
implement efficient optimisation algorithms.

LA - eng

KW - Dynamical systems; optimisation; circadian rhythms; drugs;
therapeutics; cancer.; therapeutics; cancer

UR - http://eudml.org/doc/194297

ER -

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