Mathematical Models of Cell Population Dynamics

首席研究员研究细胞种群动态的数学模型。模型由线性和非线性常微分方程和偏微分方程组成。本研究将应用于以下项目：(1)造血系统的群体模型和前体干细胞的持续成熟增殖；(2)艾滋病进展阶段人体免疫系统HIV感染发病机制和CD4 T淋巴细胞耗竭的群体模型；(3)通过染色体末端端粒片段长度的缩短来揭示细胞系繁殖史的种群模型；(4)细胞周期中位置为1、S、G2、M或G0的细胞损失过程的群体模型。在这些模型中，主要研究者在群体水平上研究细胞的行为，以及细胞分裂、细胞成熟、细胞死亡、原始细胞来源和细胞从静止状态过渡到静止状态的动态过程。主要研究者运用微分方程理论，算子理论，泛函分析，数值分析和计算模拟。这项研究的意义在于发展了分析描述细胞群体过程的微分方程解的定性行为的数学方法。首席研究员将这些方法应用于细胞群问题的定性和定量理解。在本研究中，群体过程的数学理论被应用于分析正常和异常的血细胞生产系统，CD4 T细胞在HIV感染的免疫系统中在HIV进展到艾滋病期间的耗竭，以及肿瘤的生长。首席研究员研究这些生物现象作为动态过程描述的数学模型的群体行为。本研究将理论数学分析与模型数值模拟相结合。这项研究的目的是促进对正常和异常细胞增殖过程的理解。

Webb9805515 The principal investigator studies mathematical models ofcell population dynamics. The models consist of linear andnonlinear ordinary and partial differential equations.Applications of the research are made to the following projects:(1) population models of the blood production system and thecontinuous maturation-proliferation of precursor stem cells; (2)population models of the pathogenesis of HIV infection of thehuman immune system and the depletion of CD4 T lymphocytes duringthe stages of AIDS progression; (3) population models ofreplicative histories of cell lines as indicated by shortening oftelomere fragment lengths on the ends of chromosomes; and (4)population models of cell loss processes specific to the positionG1, S, G2, M, or G0 in the cell cycle. In these models theprincipal investigator studies the behavior of cells at thepopulation level and the dynamic processes of cell division, cellmaturation, cell mortality, naive cell sources, and celltransition to and from quiescence. The principal investigatorutilizes differential equations theory, operator theory,functional analysis, numerical analysis, and computationalsimulation. The significance of the research is in the development ofmathematical methods to analyze the qualitative behavior ofsolutions to the differential equations that describe cellpopulation processes. The principal investigator applies thesemethods to the qualitative and quantitative understanding of cellpopulation problems. In this research the mathematical theory ofpopulation processes is applied to analyze normal and abnormalblood cell production systems, the depletion of CD4 T cells inthe HIV infected immune system during HIV progression to AIDS,and the growth of tumors. The principal investigator studiesthese biological phenomena as dynamic processes described bymathematical models of population behavior. The research combinestheoretical mathematical analysis and numerical computersimulations of the models. The goal of the research is to advanceunderstanding of normal and abnormal cell proliferationprocesses.