Getto Philipp, Marciniak-Czochra Anna
TU Dresden, Fachrichtung Mathematik, Institut für Analysis, 01062, Dresden, Germany,
Methods Mol Biol. 2015;1293:247-66. doi: 10.1007/978-1-4939-2519-3_15.
Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.
数学建模是解决各种复杂生物系统中关键问题和范式的强大技术，能够为细胞动力学、命运决定以及细胞群体发育提供定量见解。本章致力于回顾使用常微分方程的数学方法对干细胞起始系统动力学进行建模的情况。总结并介绍了一些细胞群体动力学的基本概念和工具，作为对非数学专业人士的初步介绍。这些模型考虑了调节稳态的不同合理机制。提出了两个数学框架，分别反映了分化阶段之间转变的离散特征（由分裂事件间断）和连续特征。通过血液系统模型实例阐述了这些数学方法的优缺点，并与健康造血的患者数据进行了比较。
