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

Abstract

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.

Energy efficient physiologic coupling of gait and respiration is altered in chronic obstructive pulmonary disease

“…Persons with abnormal airflow demonstrate a less complex and stronger coupling between breathing and walking compared to healthy controls. 29,30 The results of our study are consistent with previous literature. It was found that patients with COPD used less complex frequency ratios of 1:1 and 3:2; whereas, healthy controls did not use these ratios nearly as often.…”

“…Both breathing and walking should mutually adjust to one another, leading to "compromise between stability and independence." 9,43 Although coupling between breathing and walking may be altered across walking speeds in patients with COPD, 29 the association between energy expenditure and coupling was largely unaffected at slower and faster speeds. Demonstrating that although patients with COPD may choose to walk slower, and in return have a slower respiratory rate, energy expenditure is still increased, partially due to abnormal coupling between breathing and walking.…”

“…[53][54][55] This procedure has previously been described in detail. 29 Briefly, both breathing and walking data were reconstructed in appropriate multidimensional space. The Euclidian distance between every set of points was determined.…”

“…28 Previous research demonstrates that patients with COPD display an unvarying locomotor respiratory coupling pattern (ie, one stride to one breath) under various walking speeds. [29][30][31] Furthermore, patients with COPD have increased energy expenditure. [32][33][34][35] Patients with COPD present with abnormal breathing, hypoxaemia, and/ or other metabolic impairments, likely contributing to this increased energy expenditure.…”

“…[32][33][34][35] Patients with COPD present with abnormal breathing, hypoxaemia, and/ or other metabolic impairments, likely contributing to this increased energy expenditure. As has been shown, [29][30][31] patients with COPD have strong and simple coupling, suggesting limited options to exploit more efficient strategies than controls, which could synergize with these other mechanisms, thereby increasing energy cost. Therefore, it is plausible that abnormal coupling between breathing and walking in patients with COPD may contribute to increased energy expenditure.…”