Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models
Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models
复制标题
DOI：
10.1051/mmnp/20094308
复制
发表时间：
2009-01-01
影响因子：
2.2
通讯作者：
Lepoutre, Th.
中科院分区：
文献类型：
--
作者：
Clairambault, J.;Gaubert, S.;Lepoutre, Th.
我们研究了一个细胞群体的生长速率，遵循一个年龄结构的PDE与时间周期系数。我们的动机来自于实验性肿瘤生长曲线之间的比较，小鼠具有完整或破坏的生物钟，已知对细胞分裂周期产生影响。我们比较的增长率的模型控制的时间周期控制其系数与增长率的平稳模型的相同性质，但平均系数。我们首先推导出一个时滞微分方程，它允许我们证明几个不等式和等式的增长率。我们还讨论了考虑时间疗法建模的细胞分裂周期结构的必要性。数值模拟说明了结果。
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.