Mathematical Sciences: Mathematical Models of Cell Population Dynamics

数学科学：细胞群动力学的数学模型

• 批准号: 9001790
• 负责人: Glenn Webb
• 金额: $ 6.86万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001790&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Models; Cell; Population

This project will make theoretical and numerical investigations of the nonlinear partial differential equations that describe structured models of cell population dynamics. Individual cells are distinguished by structure variables corresponding to size, age, or other physical characteristics. The populations are divided into population subclasses that interact through nonlinear transition rates. The main objective will be to understand the qualitative behavior of the populations, the on- set of oscillatory phenomena, and the response to external periodic loss functions. The main methods will apply the theory of semigroups of positive linear and nonlinear operators in Banach lattices. The main applications will be to tumor cell populations with proliferating and quiescent classes and to multi-level blood cell production systems. The goal in the tumor cell population studies will be to understand the role of quiescence in tumor growth and tumor therapy. The goal in the blood cell population studies will be to understand the regulation processes in normal and abnormal systems.

本计画将进行理论与数值研究 非线性偏微分方程描述了 细胞群体动力学的结构化模型。 单个细胞 通过对应于尺寸的结构变量来区分， 年龄或其他身体特征。 述群体的 分为不同的种群亚类， 非线性跃迁速率 主要目标是 了解人口的定性行为， 一系列振荡现象，以及对外部 周期损失函数 主要方法将应用该理论 正线性和非线性算子半群的 Banach格 主要应用于肿瘤细胞 人口与增殖和静止类， 多层次血细胞生产系统。 过门 肿瘤细胞群的研究将是了解的作用， 在肿瘤生长和肿瘤治疗中的静止。 过门 血细胞数量的研究将是为了了解 正常和异常系统中的调节过程。