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Author Notes:

Joon Lee: joonlee@mit.edu; Shamim Nemati: shamim.nemati@emory.edu; Ikaro Silva: ikaro@mit.edu; Bradley A Edwards: baedwards@partners.org; James P Butler: jbutler@hsph.harvard.edu; Atul Malhotra: amalhotra1@partners.org

JL and SN conceived of the study, developed and implemented the D-V partitioning transfer entropy estimation algorithm, conducted the experiments, and wrote the entire manuscript.

IS conceived of the study, contributed to the algorithm development, and wrote parts of the manuscript.

BE supplied the lamb data and rigorously revised the manuscript.

JB and AM thoroughly revised the manuscript.

The content of this document is solely the responsibility of the authors and does not necessarily represent the official views of the NIH, AHA, or NSERC.

The authors would also like to thank Professor George Verghese for his helpful comments.

The authors declare that they have no competing interests.


Research Funding:

This research work was funded by the National Institutes of Health (NIH) (through grant numbers R01-EB001659, R01-HL73146, HL085188-01A2, HL090897-01A2, K24 HL093218-01A1, cooperative agreement U01-EB-008577, and training grant T32-HL07901) and American Heart Association (AHA) (grant 0840159N).

Dr. Lee holds a Postdoctoral Fellowship funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Dr. Edwards is the recipient of the Thoracic Society of Australia and New Zealand/Allen and Hanburys Respiratory Research Fellowship.


  • Science & Technology
  • Technology
  • Engineering, Biomedical
  • Engineering
  • FLOW
  • CO2

Transfer Entropy Estimation and Directional Coupling Change Detection in Biomedical Time Series


Journal Title:

BioMedical Engineering OnLine


Volume 11


, Pages 19-19

Type of Work:

Article | Final Publisher PDF


BACKGROUND: The detection of change in magnitude of directional coupling between two non-linear time series is a common subject of interest in the biomedical domain, including studies involving the respiratory chemoreflex system. Although transfer entropy is a useful tool in this avenue, no study to date has investigated how different transfer entropy estimation methods perform in typical biomedical applications featuring small sample size and presence of outliers. METHODS: With respect to detection of increased coupling strength, we compared three transfer entropy estimation techniques using both simulated time series and respiratory recordings from lambs. The following estimation methods were analyzed: fixed-binning with ranking, kernel density estimation (KDE), and the Darbellay-Vajda (D-V) adaptive partitioning algorithm extended to three dimensions. In the simulated experiment, sample size was varied from 50 to 200, while coupling strength was increased. In order to introduce outliers, the heavy-tailed Laplace distribution was utilized. In the lamb experiment, the objective was to detect increased respiratory-related chemosensitivity to O2 and CO2 induced by a drug, domperidone. Specifically, the separate influence of end-tidal PO2 and PCO2 on minute ventilation (V˙E) before and after administration of domperidone was analyzed. RESULTS: In the simulation, KDE detected increased coupling strength at the lowest SNR among the three methods. In the lamb experiment, D-V partitioning resulted in the statistically strongest increase in transfer entropy post-domperidone for PO2 → VE. In addition, D-V partitioning was the only method that could detect an increase in transfer entropy for PCO2 → VE, in agreement with experimental findings. CONCLUSIONS: Transfer entropy is capable of detecting directional coupling changes in non-linear biomedical time series analysis featuring a small number of observations and presence of outliers. The results of this study suggest that fixed-binning, even with ranking, is too primitive, and although there is no clear winner between KDE and D-V partitioning, the reader should note that KDE requires more computational time and extensive parameter selection than D-V partitioning. We hope this study provides a guideline for selection of an appropriate transfer entropy estimation method.

Copyright information:

©2012 Lee et al; licensee BioMed Central Ltd.

This is an Open Access work distributed under the terms of the Creative Commons Attribution 2.0 Generic License (http://creativecommons.org/licenses/by/2.0/).

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