Abbiw-Jackson R M, Langford W F
Department of Mathematics, University of Maryland, College Park 20742, USA.
J Math Biol. 1998 Sep;37(3):203-34. doi: 10.1007/s002850050126.
"Mayer waves" are long-period (6 to 12 seconds) oscillations in arterial blood pressure, which have been observed and studied for more than 100 years in the cardiovascular system of humans and other mammals. A mathematical model of the human cardiovascular system is presented, incorporating parameters relevant to the onset of Mayer waves. The model is analyzed using methods of Liapunov stability and Hopf bifurcation theory. The analysis shows that increase in the gain of the baroreflex feedback loop controlling venous volume may lead to the onset of oscillations, while changes in the other parameters considered do not affect stability of the equilibrium state. The results agree with clinical observations of Mayer waves in human subjects, both in the period of the oscillations and in the observed age-dependence of Mayer waves. This leads to a proposed explanation of their occurrence, namely that Mayer waves are a gain-induced oscillation.
“迈尔波”是动脉血压中的长周期（6至12秒）振荡，在人类和其他哺乳动物的心血管系统中已被观察和研究了100多年。提出了一个人类心血管系统的数学模型，纳入了与迈尔波发作相关的参数。使用李雅普诺夫稳定性和霍普夫分岔理论方法对该模型进行了分析。分析表明，控制静脉容量的压力反射反馈回路增益增加可能导致振荡的发作，而所考虑的其他参数的变化不会影响平衡状态的稳定性。这些结果在振荡周期和观察到的迈尔波年龄依赖性方面均与人类受试者迈尔波的临床观察结果一致。这导致了对其发生的一种解释，即迈尔波是增益诱导的振荡。
