Transfer entropy ($TE$) has been used to identify and quantify interactions between physiological systems. Different methods exist to estimate $TE$, but there is no consensus about which one performs best in specific applications. In this study, five methods (linear, k-nearest neighbors, fixed-binning with ranking, kernel density estimation and adaptive partitioning) were compared. The comparison was made on three simulation models (linear, nonlinear and linear + nonlinear dynamics). From the simulations, it was found that the best method to quantify the different interactions was adaptive partitioning. This method was then applied on data from a polysomnography study, specifically on the ECG and the respiratory signals (nasal airflow and respiratory effort around the thorax). The hypothesis that the linear and nonlinear components of cardio-respiratory interactions during light and deep sleep change with the sleep stage, was tested. Significant differences, after performing surrogate analysis, indicate an increased $TE$ during deep sleep. However, these differences were found to be dependent on the type of respiratory signal and sampling frequency. These results highlight the importance of selecting the appropriate signals, estimation method and surrogate analysis for the study of linear and nonlinear cardio-respiratory interactions.

中文翻译：

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用于研究线性和非线性心肺相互作用的基准传递熵方法

转移熵 ($吨乙$) 已被用于识别和量化生理系统之间的相互作用。存在不同的估计方法$吨乙$，但对于哪一种在特定应用中表现最好并没有达成共识。在这项研究中，比较了五种方法（线性、k-最近邻、固定分箱与排序、核密度估计和自适应分区）。对三种仿真模型（线性、非线性和线性 + 非线性动力学）进行了比较。从模拟中发现，量化不同相互作用的最佳方法是自适应分区。然后将该方法应用于多导睡眠图研究的数据，特别是 ECG 和呼吸信号（鼻腔气流和胸部周围的呼吸努力）。测试了浅睡眠和深睡眠期间心肺相互作用的线性和非线性分量随睡眠阶段而变化的假设。显着差异，$吨乙$在深度睡眠期间。然而，发现这些差异取决于呼吸信号的类型和采样频率。这些结果强调了为研究线性和非线性心肺相互作用选择合适的信号、估计方法和替代分析的重要性。