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Computational and Mathematical Methods in Medicine
Volume 2017 (2017), Article ID 7960467, 11 pages
Research Article

Measuring Coupling of Rhythmical Time Series Using Cross Sample Entropy and Cross Recurrence Quantification Analysis

1MORE Foundation, 18444 N. 25th Ave, Suite 110, Phoenix, AZ 85023, USA
2Center for Research in Human Movement Variability, University of Nebraska Omaha, 6160 University Drive, Omaha, NE 68182-0860, USA
3College of Public Health, University of Nebraska Medical Center, 984355 Medical Center, Omaha, NE 68198-4355, USA

Correspondence should be addressed to Jennifer M. Yentes

Received 14 April 2017; Revised 11 July 2017; Accepted 20 August 2017; Published 22 October 2017

Academic Editor: Christopher Rhea

Copyright © 2017 John McCamley et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this investigation was to compare and contrast the use of cross sample entropy (xSE) and cross recurrence quantification analysis (cRQA) measures for the assessment of coupling of rhythmical patterns. Measures were assessed using simulated signals with regular, chaotic, and random fluctuations in frequency, amplitude, and a combination of both. Biological data were studied as models of normal and abnormal locomotor-respiratory coupling. Nine signal types were generated for seven frequency ratios. Fifteen patients with COPD (abnormal coupling) and twenty-one healthy controls (normal coupling) walked on a treadmill at three speeds while breathing and walking were recorded. xSE and the cRQA measures of percent determinism, maximum line, mean line, and entropy were quantified for both the simulated and experimental data. In the simulated data, xSE, percent determinism, and entropy were influenced by the frequency manipulation. The 1 : 1 frequency ratio was different than other frequency ratios for almost all measures and/or manipulations. The patients with COPD used a 2 : 3 ratio more often and xSE, percent determinism, maximum line, mean line, and cRQA entropy were able to discriminate between the groups. Analysis of the effects of walking speed indicated that all measures were able to discriminate between speeds.