Schulz S, Bauernschmitt R, Schwarzhaupt A, Vahl C F, Kiencke U
Dept. of Cardiac Surgery, University of Heidelberg, Germany.
Biomed Sci Instrum. 1997;34:269-74.
The classical description of ventriculoarterial coupling by calculating the ratio between the effective arterial elastance Ea to the end-systolic elastance Ees does not give insight into the underlying dynamics of the interaction between left-ventricular pressure (LVP) and aortic pressure (AOP) and flow (AOF). The aim of this study was to introduce a state space representation for the ventriculoarterial coupling and to quantify changes of the coupling state.
A ventriculoarterial state space orbit VAO was defined to be dependent on three variables: VAO = [LVP(t), AOP(t + delta t), AOF(t + delta t)]. Changes in the coupling effect directly or indirectly on the time series of these parameters. They reflect the actual state of the cardiovascular system. The time delay delta t between the LVP and the aortic signals takes respect to the short delay between the heart action and the resulting waves in the arterial tree. The recurrence map of the VAO(i) (i = 1 .. N, N = number of points) is constructed by plotting the index i of every single point on the orbit (x-axis) against the indices of his 10 nearest neighbors (y-axis) in distance. The data were recorded in 9 anaesthetized pigs with a sample frequency of 512 Hz over a period of 6 seconds using piezoelectric pressure sensors and a Doppler flowmeter. A control condition was compared to a total occlusion of the descending aorta as a strong artificial disturbance of ventriculoarterial interaction. The nonlinear parameters percent recurrence, percent determinism and the entropy were calculated from the plot.
Periodic crossing points and forbidden zones in all plots identify the nonlinear character of the chosen variables. The recurrent patterns are less rigid for control conditions than for total occlusion. Entropy (2.3% rise) and determinism (24% rise) are significantly (p < 0.003) increased. Total aortic occlusion leads to more complex time correlation patterns.
These results may reflect the loss of an ideal coupling state leading to a more complex deterministic behavior of the overall regulatory system. Because recurrence plots do not impose rigid constraints on data set size, stationarity, or statistical distribution, we hypothesize that this technique might be useful to describe the nonlinear dynamics between left ventricle and arterial system.
通过计算有效动脉弹性Ea与收缩末期弹性Ees之间的比值来对心室动脉耦合进行经典描述，并不能深入了解左心室压力（LVP）、主动脉压力（AOP）和流量（AOF）之间相互作用的潜在动力学。本研究的目的是引入一种用于心室动脉耦合的状态空间表示法，并量化耦合状态的变化。
定义一个心室动脉状态空间轨道VAO，使其依赖于三个变量：VAO = [LVP(t), AOP(t + Δt), AOF(t + Δt)]。耦合效应的变化直接或间接地作用于这些参数的时间序列。它们反映了心血管系统的实际状态。LVP与主动脉信号之间的时间延迟Δt考虑了心脏活动与动脉树中产生的波动之间的短延迟。通过将轨道上每个单点的索引i（x轴）与其距离最近的10个邻居的索引（y轴）进行绘图，构建VAO(i)（i = 1 .. N，N =点数）的递归图。使用压电压力传感器和多普勒流量计，以512 Hz的采样频率在6秒内记录9只麻醉猪的数据。将对照条件与降主动脉完全闭塞进行比较，降主动脉完全闭塞是对心室动脉相互作用的强烈人为干扰。从图中计算非线性参数重现百分比、确定性百分比和熵。
所有图中的周期性交叉点和禁区确定了所选变量的非线性特征。对照条件下的递归模式不如完全闭塞时那么严格。熵（增加2.3%）和确定性（增加24%）显著增加（p < 0.003）。主动脉完全闭塞导致更复杂的时间相关模式。
这些结果可能反映了理想耦合状态的丧失，导致整个调节系统出现更复杂的确定性行为。由于递归图对数据集大小、平稳性或统计分布没有严格限制，我们推测该技术可能有助于描述左心室与动脉系统之间的非线性动力学。
