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

Comput Math Methods Med. 2017:2017:7960467. doi: 10.1155/2017/7960467. Epub 2017 Oct 22.


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.

MeSH terms

  • Aged
  • Case-Control Studies
  • Entropy*
  • Exercise Test
  • Female
  • Humans
  • Male
  • Middle Aged
  • Models, Statistical
  • Nonlinear Dynamics
  • Oscillometry
  • Pulmonary Disease, Chronic Obstructive / physiopathology*
  • Pulmonary Disease, Chronic Obstructive / therapy*
  • Respiration
  • Signal Processing, Computer-Assisted*
  • Walking