Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions

Abstract

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.

Exploring the use of Granger causality for the identification of chemical exposure based on physiological data

“…As a result, only the linear interactions could be captured, thereby ignoring possible nonlinearities that could be strongly affected by the exposure. Therefore, future work should focus on the quantification of these possibly nonlinear interactions ( Rozo et al, 2021 ). Secondly, the interactions between the features were assumed to be constant throughout the 15 or 45 min after the exposure.…”

“…A study by Faes et al (2015) applied GC to map directional interactions in brain-brain and brain-heart networks in different sleep states, exemplifying the added value of GC in neuroscience ( Porta & Faes, 2015 ; Seth et al, 2015 ). A study by Rozo et al (2021) demonstrated that different methods to quantify RSA, based on GC principles, captured the cardiorespiratory changes expected during different non-REM sleep stages. Interactions between respiration, blood pressure and heart rate have been found to be influenced by factors such as body position ( Mary et al, 2019 ) and deep versus normal breathing ( Mary et al, 2018 ).…”

Kendall transfer entropy: a novel measure for estimating information transfer in complex systems

“…The Laplace distribution provides a better representation of physiological signal noise than Gaussian noise [15]. Following Rozo et al [16], b was set to four. Thus, a nonlinear interaction was generated from X to Y at time lag 2.…”

“…Lee et al proposed the D-V partitioning method (DVP) by combining fixed-binning quantization and an adaptive partitioning algorithm [15]. Rozo et al demonstrated that DVP was the best method for identifying the different interactions among the five most commonly used methods for TE computation [16]. Based on the idea of symbolic processing in permutation entropy [17], the symbolization is also a commonly used method for quantization in nonlinear measurement [18].…”

Volatility Dynamics of Non-Linear Volatile Time Series and Analysis of Information Flow: Evidence from Cryptocurrency Data

“…Therefore, the choice of the best method to estimate TE for each specific application is still an open problem. For instance, Rozo et al studied five different estimation methods, and the results suggest the adaptive partitioning method outperformed [ 31 ]. However, the literature emphasizes that for highly nonlinear and non-Gaussian data, for example, in our case of cryptocurrency data, it is better to approach causality using the TE information method instead of the traditional Granger causality test [ 32 ].…”