Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals
Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals
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DOI：
10.1007/s00422-001-0292-z
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发表时间：
2002-03-01
影响因子：
1.9
通讯作者：
van de Borne, P
中科院分区：
文献类型：
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作者：
Porta, A;Furlan, R;van de Borne, P
相干函数测量两个信号x和y之间的相关性，作为频率的函数，独立于它们的因果关系。因此，相干函数在确定x和y之间是否存在开环关系（x作用于y，但阻止反向关系）或x和y在闭环中相互作用（x影响y，反之亦然）时是没有用的。本研究提出了一种基于二元自回归模型的方法来推导闭环双臂上的因果耦合强度。该方法利用了因果一致性的定义。在对模型系数进行闭环辨识后，分别关闭反馈或前馈路径，计算因果相干性，从而打开闭环，确定因果关系。该方法在模拟中进行了测试，并应用于评估两个已知在闭环中主要在低频（LF，约0.1 Hz）和高频（HF，以呼吸频率）相互作用的变量之间的因果耦合程度：心脏周期（RR间隔）和收缩压（SAP）。在对照组中，RR间隔和SAP在HF时高度相关。这种耦合发生在从RR区间到SAP的因果方向（机械路径）上，而反向因果方向（气压反射路径）上的耦合不显著，从而指出呼吸对RR区间的直接影响的重要性。通过在SAP对RR间隔的影响水平上打开闭环，完全的压力感受性断神经并没有改变这些结果。在老年健康男性休息时，RR间期和SAP在LF和HF高度相关。在高频，发现两个因果方向上的显著耦合，即使在少数情况下检测到闭环相互作用。在LF，压力反射通路上的连接相对于反向机械通路上的连接可以忽略不计。在心脏移植受者中，SAP的变化不会由于心脏去神经支配而引起RR间期的变化，该方法仅在RR间期到SAP的通路上正确地检测到显著的耦合。
The coherence function measures the amount of correlation between two signals x and y as a function of the frequency, independently of their causal relationships. Therefore, the coherence function is not useful in deciding whether an open-loop relationship between x and y is set (x acts on y, but the reverse relationship is prevented) or x and y interact in a closed loop (x affects y, and vice versa). This study proposes a method based on a bivariate autoregressive model to derive the strength of the causal coupling on both arms of a closed loop. The method exploits the definition of causal coherence. After the closed-loop identification of the model coefficients, the causal coherence is calculated by switching off separately the feedback or the feedforward path, thus opening the closed loop and fixing causality. The method was tested in simulations and applied to evaluate the degree of the causal coupling between two variables known to interact in a closed loop mainly at a low frequency (LF, around 0.1 Hz) and at a high frequency (HF, at the respiratory rate): the heart period (RR interval) and systolic arterial pressure (SAP). In dogs at control, the RR interval and the SAP are highly correlated at HF. This coupling occurs in the causal direction from the RR interval to the SAP (the mechanical path), while the coupling on the reverse causal direction (the baroreflex path) is not significant, thus pointing out the importance of the direct effects of respiration on the RR interval. Total baroreceptive denervation, by opening the closed loop at the level of the influences of SAP on RR interval, does not change these results. In elderly healthy men at rest, the RR interval and SAP are highly correlated at the LF and the HF. At the HF, a significant coupling in both causal directions is found, even though closed-loop interactions are detected in few cases. At the LF, the link on the baroreflex pathway is negligible with respect to that on the reverse mechanical one. In heart transplant recipients, in which SAP variations do not cause RR interval changes as a result of the cardiac denervation, the method correctly detects a significant coupling only on the pathway from the RR interval to the SAP.