生长因子介导的造血模型及其在周期性血液病中的应用
Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases
摘要：
造血是一个复杂的生物过程，导致血细胞的产生和调节。它基于干细胞在生长因子作用下的分化。本文提出了一种对这一过程进行数学处理的方法，用以解释某些以循环血细胞振荡为特征的血液疾病。分析了一个含有时滞的三个微分方程系统，时滞对应于细胞周期的持续时间。通过研究一个系数依赖于时滞的指数多项式特征方程，得到了正平衡态的Hopf分支的存在性。数值模拟表明，在该模型中可以获得长周期振荡，对应于血细胞和生长因子之间的反馈调节的不稳定。这强调了反馈回路中周期性血液病的定位。
英文摘要：
Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop.
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