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Comparison ofPerron and Floquet Eigenvalues in AgeStructured Cell Division Cycle Models

Published online by Cambridge University Press:  05 June 2009

J. Clairambault ,
S. Gaubert  and
Th. Lepoutre
J. Clairambault
Affiliation:
INRIA, projet BANG, Domaine de Voluceau, BP 105, 78156 Le Chesnay Cedex France INSERM U 776, Hôpital Paul-Brousse, 14, Av. Paul-Vaillant-Couturier F94807 Villejuif cedex
S. Gaubert
Affiliation:
INRIA Saclay – Ile-de-France, projet MAXPLUS CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France
Th. Lepoutre*
Affiliation:
INRIA, projet BANG, Domaine de Voluceau, BP 105, 78156 Le Chesnay Cedex France UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
*
[email protected]
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Abstract

We study the growth rate of a cell population that follows anage-structured PDE with time-periodic coefficients. Our motivationcomes from the comparison between experimental tumor growth curvesin mice endowed with intact or disrupted circadian clocks,known to exert their influence on the cell division cycle.We compare the growth rate of the model controlled by a time-periodiccontrol on its coefficients with the growth rate of stationarymodels of the same nature, but with averaged coefficients. We firstly derive a delay differential equation which allows us to proveseveral inequalities and equalities on the growth rates. We alsodiscuss about the necessity to take into account the structure ofthe cell division cycle for chronotherapy modeling. Numerical simulationsillustrate the results.

Keywords

cell cyclecircadian rhythmschronotherapystructured PDEsdelaydifferential equations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 3: Cancer modelling (Part 2) , 2009 , pp. 183 - 209
Copyright
© EDP Sciences, 2009

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