Cleave J P, Levine M R, Fleming P J
J Theor Biol. 1984 May 21;108(2):261-83. doi: 10.1016/s0022-5193(84)80070-3.
Serial measurements of respiration in infants from birth to 7 months have revealed a changing pattern of response with age to spontaneous transient disturbances (e.g. deep sighs). These responses may be interpreted in terms of changing stability of the respiratory control system. The simplest possible model of respiratory control is analysed here. The control system is described by a feedback loop comprising a lung compartment, central and peripheral CO2 detectors and a circulatory delay. The differential equations representing this model are analysed in terms of the phase portrait. First we define the bounds of the solutions in the phase space and the equilibrium points. Next we discuss the local stability and damping of the system under small displacements from these equilibrium points. This local stability can be described in terms of the solution of a linear approximation about the equilibrium points. The trajectories of the solution vector under larger displacements from the equilibrium points are discussed in terms of Taylor expansions. It is shown by this analyses that this simple model can account qualitatively for the observed patterns of respiration following a deep sigh and the changes in that response from birth to 7 months.
对从出生到7个月大的婴儿进行的连续呼吸测量显示，随着年龄增长，对自发短暂干扰（如深呼吸）的反应模式在发生变化。这些反应可以根据呼吸控制系统稳定性的变化来解释。本文分析了最简单的呼吸控制模型。该控制系统由一个反馈回路描述，该反馈回路包括一个肺腔、中枢和外周二氧化碳探测器以及一个循环延迟。根据相图分析表示该模型的微分方程。首先，我们定义相空间中解的边界和平衡点。接下来，我们讨论系统在偏离这些平衡点的小位移下的局部稳定性和阻尼。这种局部稳定性可以根据关于平衡点的线性近似解来描述。根据泰勒展开式讨论解向量在偏离平衡点较大位移下的轨迹。通过这种分析表明，这个简单模型可以定性地解释深呼吸后观察到的呼吸模式以及从出生到7个月该反应的变化。
