Combination of R-R Interval and Crest Time in Assessing Complexity Using Multiscale Cross-Approximate Entropy in Normal and Diabetic Subjects

Abstract

The present study aimed at testing the hypothesis that application of multiscale cross-approximate entropy (MCAE) analysis in the study of nonlinear coupling behavior of two synchronized time series of different natures [i.e., R-R interval (RRI) and crest time (CT, the time interval from foot to peakof a pulse wave)] could yield information on complexity related to diabetes-associated vascular changes. Signals of a single waveform parameter (i.e., CT) from photoplethysmography and RRI from electrocardiogram were simultaneously acquired within a period of one thousand cardiac cycles for the computation of different multiscale entropy indices from healthy young adults (n = 22) (Group 1), upper-middle aged non-diabetic subjects (n = 34) (Group 2) and diabetic patients (n = 34) (Group 3). The demographic (i.e., age), anthropometric (i.e., body height, body weight, waist circumference, body-mass index), hemodynamic (i.e., systolic and diastolic blood pressures), and serum biochemical (i.e., high- and low-density lipoprotein cholesterol, total cholesterol, and triglyceride) parameters were compared with different multiscale entropy indices including small- and large-scale multiscale entropy indices for CT and RRI [MEI_SS(CT), MEI_LS(CT), MEI_SS(RRI), MEI_LS(RRI), respectively] as well as small- and large-scale multiscale cross-approximate entropy indices [MCEI_SS, MCEI_LS, respectively]. The results demonstrated that both MEI_LS(RRI) and MCEI_LS significantly differentiated between Group 2 and Group 3 (all p < 0.017). Multivariate linear regression analysis showed significant associations of MEI_LS(RRI) and MCEI_LS(RRI,CT) with age and glycated hemoglobin level (all p < 0.017). The findings highlight the successful application of a novel multiscale cross-approximate entropy index in non-invasively identifying diabetes-associated subtle changes in vascular functional integrity, which is of clinical importance in preventive medicine.

Keywords: R-R interval; crest time; cross-approximate entropy; diabetes; multiscale entropy (MSE).

Figure 1

Recording of 1000 consecutive cardiac cycles from electrocardiogram (ECG) and simultaneous arterial waveform signals from photoplethysmography (PPG). RRI: R-R interval; CT: Crest time (i.e., time from foot point to peak of a waveform); RRI(n): RRI during the nth cardiac cycle; CT(n): CT during the nth cardiac cycle.

Figure 2

(a) Sample entropy of crest time (CT) series of the three groups of testing subjects; (b) Sample entropy of R-R interval (RRI) series of the three groups of testing subjects. Values expressed as mean ± standard deviation (SD); Group 1: Healthy young subjects; Group 2: Non-diabetic upper middle-aged subjects; Group 3: Diabetic upper middle-aged subjects; † p < 0.017 (p corrected): Group 3 vs. Group 1 and Group 2; †† p < 0.001: Group 3 vs. Group 1 and Group 2; * p < 0.05: Group 1 vs. Group 2 and Group 3.

Figure 3

Multiscale cross-approximate entropy analysis of synchronized R-R interval (RRI) and crest time (CT) time series showing changes in cross-approximate entropyof the three groups of testing subjects with time scale 1 to 6. Group 1: Healthy young subjects; Group 2: Non-diabetic upper middle-aged subjects; Group 3: Diabetic upper middle-aged subjects; * p < 0.017 (p corrected): Group 1 vs. Group 2; † p < 0.017: Group 2 vs. Group 3.