Yambe T, Nitta S, Naganuma T, Saijoh Y, Naganuma S, Kobayashi S, Tanaka M, Yoshizawa M
Department of Medical Engineering and Cardiology, Tohoku University, Sendai.
J Cardiol. 1994 Nov-Dec;24(6):469-74.
To analyze the entire left ventricular wall motion, not the decomposed motion, nonlinear mathematical techniques were used to describe graphically time series data for the left ventricular contraction. Time series data of the left ventricular wall motion were recorded by M-mode echocardiography, and embedded into three-dimensional phase space. The largest Lyapunov exponents, a measure of the rate of divergence in phase space, were calculated to detect the sensitive dependence on initial conditions. The reconstructed attractor of the left ventricular contraction showed a lower dimensional strange attractor, and calculation of the Lyapunov exponents indicated sensitivity to initial conditions. These results suggest that time series data of the left ventricular contraction show the characteristics of deterministic chaos. The chaotic system can provide an intelligent and flexible control system. Our results suggest that the circulatory control system, which mediates the cardiac contractility, may be a flexible dynamic compatible with deterministic chaos.
为了分析整个左心室壁运动，而非分解后的运动，采用非线性数学技术以图形方式描述左心室收缩的时间序列数据。左心室壁运动的时间序列数据通过M型超声心动图记录，并嵌入三维相空间。计算最大Lyapunov指数（一种相空间中发散率的度量）以检测对初始条件的敏感依赖性。左心室收缩的重构吸引子显示为低维奇怪吸引子，Lyapunov指数的计算表明对初始条件敏感。这些结果表明左心室收缩的时间序列数据呈现出确定性混沌的特征。混沌系统可以提供一个智能且灵活的控制系统。我们的结果表明，介导心脏收缩力的循环控制系统可能是一个与确定性混沌兼容的灵活动态系统。
