Comparison of Perron and Floquet eigenvalues in age structured cell division cycle models

TL;DR

This paper compares growth rates of age-structured cell division models with periodic and averaged coefficients, highlighting the importance of cell cycle structure in tumor growth and chronotherapy.

Contribution

It introduces a delay differential equation framework to compare Perron and Floquet eigenvalues in periodic versus stationary models, emphasizing the role of cell cycle structure.

Findings

Periodic models can differ significantly from averaged models in growth rate.

Delay differential equations help establish inequalities and equalities for growth rates.

Numerical simulations support theoretical results.

Abstract

We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in 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-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged coefficients. We firstly derive a delay differential equation which allows us to prove several inequalities and equalities on the growth rates. We also discuss about the necessity to take into account the structure of the cell division cycle for chronotherapy modeling. Numerical simulations illustrate the results.