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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.<\/jats:p>","DOI":"10.3390\/e23080939","type":"journal-article","created":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T10:31:44Z","timestamp":1627036304000},"page":"939","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4301-9399","authenticated-orcid":false,"given":"Andrea","family":"Rozo","sequence":"first","affiliation":[{"name":"STADIUS, Center of Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering (ESAT), KU Leuven, 3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0961-5581","authenticated-orcid":false,"given":"John","family":"Morales","sequence":"additional","affiliation":[{"name":"STADIUS, Center of Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering (ESAT), KU Leuven, 3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Moeyersons","sequence":"additional","affiliation":[{"name":"STADIUS, Center of Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering (ESAT), KU Leuven, 3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6504-9399","authenticated-orcid":false,"given":"Rohan","family":"Joshi","sequence":"additional","affiliation":[{"name":"Department of Patient Care and Monitoring, Philips Research, 5656 AE Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1770-6486","authenticated-orcid":false,"given":"Enrico G.","family":"Caiani","sequence":"additional","affiliation":[{"name":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Borz\u00e9e","sequence":"additional","affiliation":[{"name":"Department of Pneumology, Leuven University Centre for Sleep and Wake Disorders, UZ Leuven, 3000 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bertien","family":"Buyse","sequence":"additional","affiliation":[{"name":"Department of Pneumology, Leuven University Centre for Sleep and Wake Disorders, UZ Leuven, 3000 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7303-9799","authenticated-orcid":false,"given":"Dries","family":"Testelmans","sequence":"additional","affiliation":[{"name":"Department of Pneumology, Leuven University Centre for Sleep and Wake Disorders, UZ Leuven, 3000 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5939-0996","authenticated-orcid":false,"given":"Sabine","family":"Van Huffel","sequence":"additional","affiliation":[{"name":"STADIUS, Center of Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering (ESAT), KU Leuven, 3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9581-0676","authenticated-orcid":false,"given":"Carolina","family":"Varon","sequence":"additional","affiliation":[{"name":"STADIUS, Center of Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering (ESAT), KU Leuven, 3001 Leuven, Belgium"},{"name":"Service de Chimie-Physique E.P., Universit\u00e9 libre de Bruxelles, B-1050 Brussels, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"424","DOI":"10.2307\/1912791","article-title":"Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Published by: The Econometric Society Stable","volume":"37","author":"Granger","year":"1969","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1152\/japplphysiol.00722.2018","article-title":"Cardiorespiratory coupling in preterm infants","volume":"126","author":"Joshi","year":"2019","journal-title":"J. Appl. Physiol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1152\/japplphysiol.01152.2011","article-title":"Breath-by-breath analysis of cardiorespiratory interaction for quantifying developmental maturity in premature infants","volume":"112","author":"Clark","year":"2012","journal-title":"J. Appl. Physiol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1152\/ajpregu.00373.2003","article-title":"Directionality of coupling of physiological subsystems: Age-related changes of cardiorespiratory interaction during different sleep stages in babies","volume":"285","author":"Mrowka","year":"2003","journal-title":"Am. J. Physiol. Regul. Integr. Comp. Physiol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11517-018-1866-4","article-title":"Multi-parametric cardiorespiratory analysis in late-preterm, early-term, and full-term infants at birth","volume":"57","author":"Lucchini","year":"2018","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_6","first-page":"270","article-title":"Coexisting forms of coupling and Phase-Transitions in physiological networks","volume":"438","author":"Bartsch","year":"2014","journal-title":"Commun. Comput. Inf. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1038\/ncomms1705","article-title":"Network physiology reveals relations between network topology and physiological function","volume":"3","author":"Bashan","year":"2012","journal-title":"Nat. Commun."},{"key":"ref_8","first-page":"638","article-title":"Series Clockwork: Time Fluctuations in Population Analysis Animals of","volume":"293","author":"Bjornstad","year":"2001","journal-title":"Adv. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1958","DOI":"10.3390\/e17041958","article-title":"Assessing coupling dynamics from an ensemble of time series","volume":"17","author":"Wu","year":"2015","journal-title":"Entropy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"R46","DOI":"10.1088\/0967-3334\/37\/5\/R46","article-title":"Causality in physiological signals","volume":"37","author":"Kraemer","year":"2016","journal-title":"Physiol. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bossomaier, T., Barnett, L., Harr\u00e9, M., and Lizier, J.T. (2016). An Introduction to Transfer Entropy, Springer International Publishing.","DOI":"10.1007\/978-3-319-43222-9"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Montalto, A., Faes, L., and Marinazzo, D. (2014). MuTE: A MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0109462"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/1475-925X-11-19","article-title":"Transfer Entropy Estimation and Directional Coupling Change Detection in Biomedical Time Series","volume":"11","author":"Lee","year":"2012","journal-title":"BioMed. Eng. Online"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10827-010-0262-3","article-title":"Transfer entropy-a model-free measure of effective connectivity for the neurosciences","volume":"30","author":"Vicente","year":"2011","journal-title":"J. Comput. Neurosci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2006.12.004","article-title":"Causality detection based on information-theoretic approaches in time series analysis","volume":"441","author":"Vejmelka","year":"2007","journal-title":"Phys. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"277","DOI":"10.3390\/e17010277","article-title":"Information decomposition in bivariate systems: Theory and application to cardiorespiratory dynamics","volume":"17","author":"Faes","year":"2015","journal-title":"Entropy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevLett.103.238701","article-title":"Granger causality and transfer entropy Are equivalent for gaussian variables","volume":"103","author":"Barnett","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","first-page":"16","article-title":"Estimating mutual information","volume":"69","author":"Kraskov","year":"2004","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"438","DOI":"10.3390\/e17010438","article-title":"A recipe for the estimation of information flow in a dynamical system","volume":"17","author":"Gencaga","year":"2015","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zuo, K., Bellanger, J.J., Yang, C., Shu, H., and Le Bouquin Jeannes, R. (2013, January 3\u20137). Exploring neural directed interactions with transfer entropy based on an adaptive kernel density estimator. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, Osaka, Japan.","DOI":"10.1109\/EMBC.2013.6610507"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4197","DOI":"10.1142\/S0218127409025298","article-title":"Evaluation of mutual information estimators for time series","volume":"19","author":"Papana","year":"2009","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.jneumeth.2014.04.008","article-title":"Estimation of direct nonlinear effective connectivity using information theory and multilayer perceptron","volume":"229","author":"Khadem","year":"2014","journal-title":"J. Neurosci. Methods"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3736","DOI":"10.1103\/PhysRevLett.85.3736","article-title":"Correlated and uncorrelated regions in heart-rate fluctuations during sleep","volume":"85","author":"Bunde","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","first-page":"6","article-title":"Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments","volume":"65","author":"Kantelhardt","year":"2002","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_25","first-page":"503","article-title":"Complexity and nonlinearities in cardiorespiratory signals in sleep and sleep apnea","volume":"Volume 32","author":"Barbieri","year":"2017","journal-title":"Complexity and Nonlinearity in Cardiovascular Signals"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, J. (2018). Low-dimensional approximation searching strategy for transfer entropy from non-uniform embedding. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0194382"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Darmon, D., and Rapp, P.E. (2017). Specific transfer entropy and other state-dependent transfer entropies for continuous-state input-output systems. Phys. Rev. E, 96.","DOI":"10.1103\/PhysRevE.96.022121"},{"key":"ref_28","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring information transfer","volume":"85","author":"Schreiber","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Murari, A., Lungaroni, M., Peluso, E., Gaudio, P., Lerche, E., Garzotti, L., and Gelfusa, M. (2018). On the use of transfer entropy to investigate the time horizon of causal influences between signals. Entropy, 20.","DOI":"10.3390\/e20090627"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Vlachos, I., and Kugiumtzis, D. (2010). Nonuniform state-space reconstruction and coupling detection. Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 82.","DOI":"10.1103\/PhysRevE.82.016207"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2556","DOI":"10.1109\/TBME.2014.2323131","article-title":"Lag-specific transfer entropy as a tool to assess cardiovascular and cardiorespiratory information transfer","volume":"61","author":"Faes","year":"2014","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wibral, M., Pampu, N., Priesemann, V., Siebenh\u00fchner, F., Seiwert, H., Lindner, M., Lizier, J.T., and Vicente, R. (2013). Measuring Information-Transfer Delays. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0055809"},{"key":"ref_34","first-page":"3","article-title":"Sleep Apnea Detection Using Pulse Photoplethysmography","volume":"2018","author":"Deviaene","year":"2018","journal-title":"Comput. Cardiol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2839","DOI":"10.1109\/TBME.2020.2972126","article-title":"Multilevel Interval Coded Scoring to Assess the Cardiovascular Status of Sleep Apnea Patients Using Oxygen Saturation Markers","volume":"67","author":"Deviaene","year":"2020","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"597","DOI":"10.5664\/jcsm.2172","article-title":"Rules for scoring respiratory events in sleep: Update of the 2007 AASM manual for the scoring of sleep and associated events","volume":"8","author":"Berry","year":"2012","journal-title":"J. Clin. Sleep Med."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Moeyersons, J., Amoni, M., Huffel, S.V., Willems, R., and Varon, C. (2019). R-DECO: An open-source Matlab based graphical user interface for the detection and correction of R-peaks. PeerJ Comput. Sci., 1\u201320.","DOI":"10.1101\/560706"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1109\/TBME.2010.2095011","article-title":"The integral pulse frequency modulation model with time-varying threshold: Application to heart rate variability analysis during exercise stress testing","volume":"58","author":"Laouini","year":"2011","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.1109\/JBHI.2016.2553578","article-title":"Inclusion of Respiratory Frequency Information in Heart Rate Variability Analysis for Stress Assessment","volume":"20","author":"Hernando","year":"2016","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Morales, J., Moeyersons, J., Armanac, P., Orini, M., Faes, L., Overeem, S., Van Gilst, M., Van Dijk, J., Huffel, S.V., and Bailon, R. (2020). Model-Based Evaluation of Methods for Respiratory Sinus Arrhythmia Estimation. IEEE Trans. Biomed. Eng., 1\u201312.","DOI":"10.1109\/TBME.2020.3028204"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Weber, I., Florin, E., Von Papen, M., and Timmermann, L. (2017). The influence of filtering and downsampling on the estimation of transfer entropy. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0188210"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/S0167-2789(00)00043-9","article-title":"Surrogate time series","volume":"142","author":"Schreiber","year":"2000","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevE.83.051112","article-title":"Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique","volume":"83","author":"Faes","year":"2011","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/978-3-030-34461-0_2","article-title":"Nonlinear transfer entropy to assess the neurovascular coupling in premature neonates","volume":"1232","author":"Hendrikx","year":"2020","journal-title":"Adv. Exp. Med. Biol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/939\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:33:49Z","timestamp":1760164429000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/939"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,23]]},"references-count":44,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23080939"],"URL":"https:\/\/doi.org\/10.3390\/e23080939","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,23]]}}}