Mathematical Sciences: Mathematical Models of Cell Population Dynamics

研究人员将研究线性和非线性部分 细胞群体结构模型的微分方程 动力学 方程模型的生长和治疗正常和 肿瘤细胞群。 模型使用年龄和大小作为结构 变量来跟踪细胞周期中的单个细胞。 的 模型涉及方程组来解释相互作用 在增殖和静止或耐药细胞之间 亚群 研究的目的是获得 解的行为的定性信息 方程式 这种行为包括异步指数 生长的早期生长阶段肿瘤，静止作为一种机制， 晚期肿瘤的Gompertzian型生长， 连续和周期性的治疗，以及同相共振- 具体的定期治疗。 研究方法采用 线性算子的谱理论，线性算子的半群理论 Banach格中的非线性算子， 微扰技术 该项目使用数学建模和数值 模拟理解细胞基本生物学特征 人口增长。 人口的内在质量特征 生长过程可以通过这些数学模型来揭示。 人口增长过程的复杂性要求 结合单个细胞行为的数学模型。 的 本研究的意义在于， 分析结构化人口模型的数学方法， 在确定这些模型的定性特征时， 具有潜在的生物适用性。 结果 该项目可能揭示肿瘤的行为。

The investigator will study the linear and nonlinear partial differential equations of structured models of cell population dynamics. The equations model growth and treatment of normal and tumor cell populations. The models use age and size as structure variables to track individual cells through the cell cycle. The models involve systems of equations to account for interaction between proliferating and quiescent or drug-resistant cell subpopulations. The objective of the research is to obtain qualitative information about the behavior of the solutions of the equations. Such behavior includes asynchronous exponential growth of early growth stage tumors, quiescence as a mechanism in Gompertzian type growth in late stage tumors, comparison of continuous and periodic treatment, and resonances in phase- specific periodic treatment. The methods of the research use spectral theory of linear operators, semigroup theory of linear and nonlinear operators in Banach lattices, and nonlinear perturbation techniques. The project uses mathematical modelling and numerical simulation to understand essential biological features of cell population growth. Inherent qualitative features of population growth processes can be revealed by these mathematical models. The complexity of the population processes requires sophisticated mathematical models incorporating individual cell behavior. The significance of this research lies both in the development of mathematical methods to analyze structured population models and in the identification of the qualitative features of these models that have potential biological applicability. Results of the project may shed light on the behavior of tumors.