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

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## Abstract

**:**

_{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.

## 1. Introduction

## 2. Methods

#### 2.1. Study Population

#### 2.2. Study Protocol

_{SS}(CT), MEI

_{LS}(CT), MEI

_{SS}(RRI), MEI

_{LS}(RRI), MCEI

_{SS}, MCEI

_{LS}] with 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 of the three groups of testing subjects were analyzed and compared.

#### 2.3. Data Acquisitionand Analysis

#### 2.3.1. Definition of Two Synchronized Physiological Signals: R-R Interval (RRI) and Crest Time (CT)

#### 2.3.2. MSE and MCAE Analyses

_{RRI(i)}and SD

_{CT(j)}represent the standard deviations of series {RRI(i)}and {CT(j)}, respectively. $\overline{\mathrm{RRI}\left(i\right)}$ denotes the mean of the {RRI(i)} series, while $\overline{\mathrm{CT}\left(j\right)}$ represents the mean of the {CT(j)} series:

_{SS}(RRI) vs. MEI

_{SS}(CT), while the mean of sample entropy in large scales of $\left\{{\mathrm{RRI}}^{\prime}\left(i\right)\right\}$ and $\left\{{\mathrm{CT}}^{\prime}\left(j\right)\right\}$ series was defined as MEI

_{LS}(RRI) vs. MEI

_{LS}(CT).To ensure efficiency and accuracy of calculation, the parameters of this study were set at N = 1000, m = 2, and r = 0.15 multiplied by the standard deviation of the time series of $\left\{{\mathrm{RRI}}^{\prime}\left(i\right)\right\}$ and $\left\{{\mathrm{CT}}^{\prime}\left(j\right)\right\}$.

#### 2.4. Statistical Analysis

_{SS}(RRI), MEI

_{LS}(RRI), MEI

_{SS}(CT), MEI

_{LS}(CT), MCEI

_{SS}, and MCEI

_{LS}) among different groups was determined using independent sample t-test with Bonferroni correction. The correlation between parameters and risk factors for different groups was compared using Pearson correlation test with Bonferroni correction. For significant parameters acquired through univariate analysis, multivariate regression analysis was used for further verification of the statistical significance. Statistical Package for the Social Science (SPSS, version 14.0 for Windows, SPSS Inc., Chicago, IL, USA) was used for all statistical analyses. Statistical significance was determined using p value corrected as shown at the end of each figure and table in the Results section.

## 3. Results

#### 3.1. MSE Analysis on Single Waveform Contour Cardiovascular System-Related Parameters (RRI and CT)

#### 3.2. MultiscaleCross-Approximate Entropy Analysis of Synchronized RRI and CT Time Series

_{SS}(RRI)] successfully differentiated Group 2 from Group 1 at time scale 2 (Figure 2a). As a whole, MEI

_{SS}(RRI) was significantly lower in Group 2 than that in Group 1 (Table 2). By contrast, MEI for RRI of Group 3 was significantly lower than that in Group 2 at scale 3, 4, 5, and 6. Consistently, large-scale MEI for RRI [i.e., MEI

_{LS}(RRI)] was significantly lower in Group 3 than that in Group 2 (p < 0.001). As for cross-approximate entropy index for synchronized RRI and CT time series [i.e., MCEI(RRI,CT)], it is interesting to find that there were significant differences among the three groups at scale 4. On the other hand, large-scale MCEI [i.e., MCEI

_{LS}(RRI,CT)] was significantly lower in Group 3 than that in Groups 1 and 2 (Table 2).

#### 3.3. Correlations of Different Multiscale Entropy Indices with Demographic, Anthropometric, Hemodynamic, and Serum Biochemical Parameters in the Testing Subjects

_{SS}(CT), MEI

_{LS}(CT), MEI

_{SS}(RRI), MEI

_{LS}(RRI), MCEI

_{LS}(RRI,CT), MCEI

_{SS}(RRI,CT)]with demographic, anthropometric, hemodynamic, and serum biochemical parameters in non-diabetic subjects, healthy young individuals (Group 1) and upper middle-aged non-diabetic subjects (Group 2) were investigated (Table 3). Total cholesterol levelwas found to be negatively associated with MEI

_{LS}(RRI) (p = 0.003).

_{LS}(RRI,CT) (p < 0.017). Besides, waist circumference was negatively related to MEI

_{LS}(CT), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) (all p < 0.017). By contrast, pulse pressure was positively correlated with MCEI

_{SS}(RRI,CT) (p < 0.017). On the other hand, MEI

_{LS}(RRI) was negatively associated with glycated hemoglobin (HbA1c) level and fasting blood sugar concentration (both p < 0.017) (Table 4).

_{SS}(RRI), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) were found to be negatively associated with age in a highly significant way (all p < 0.005). Moreover, negative correlations were also noted between body weight and MEI

_{SS}(CT) (p < 0.017). While waist circumference was negatively correlated with all multiscale entropy parameters except MCEI

_{SS}(RRI,CT), body-mass index was negatively associated with MEI

_{SS}(RRI), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) (all p < 0.017). On the other hand, glycated hemoglobin levelwas negatively associated with MEI

_{LS}(CT), MEI

_{SS}(RRI),MEI

_{LS}(RRI), andMCEI

_{LS}(RRI,CT), while fasting blood sugar levels were negatively associated with MEI

_{SS}(RRI), MEI

_{LS}(RRI),and MCEI

_{LS}(RRI,CT) (all p < 0.017).Both sugar control parameters were highly significantly correlated withMEI

_{LS}(RRI) and MCEI

_{LS}(RRI,CT) in a negative fashion (all p < 0.005).

#### 3.4. Multivariate Analysis for MEI_{LS}(CT), MEI_{LS}(RRI), and MCEI_{LS}(RRI,CT)

_{LS}(CT), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) for which multivariate analysis was performed. The results showed significant associations of MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) with age and glycated hemoglobin level in all subjects as a whole without focusing on the effects of age and diabetes (all p < 0.05) (Table 6).

## 4. Discussion

_{SS}(RRI) identified age-related vascular changes by significantly differentiating between young (Group 1) and healthy upper middle-aged (Group 2) subjects (p = 0.015) (Table 2). Since small scales (i.e., scale 1 to 3) reflects autonomic nervous control of the cardiovascular system in the present setting, the finding of reduced MEI

_{SS}(RRI) in Group 2 suggests significantly elevated resting sympathetic tone in Group 2 compared to that in Group 1. The results is supported by a previous study showing an increase in resting sympathetic outflow with age [32]. In addition, our results demonstrated consistent and significant reductions of MEI

_{LS}(RRI) in upper middle-aged individuals with diabetes (Group 3) compared to those without (Group 2) (Table 2), highlighting its ability to identify diabetes-associated vascular changes. The finding is consistent with the fact that diabetes impairs vascular structural integrity [33]. On the other hand, MEI

_{LS}(RRI) failed to detect age-related vascular changes (i.e., between Group 1 and Group 2), underscoring its limitation in this aspect.

_{LS}(RRI) with serum cholesterol level (Table 3). As large-scale entropy represents vascular regulatory function, the finding is consistent with that of a previous study demonstrating that the cellular and molecular mechanisms underlying hypercholesterolemia could contribute to an imbalance between phosphorylation and dephosphorylation of lipid and protein kinase, thereby modulating vascular endothelial L-arginine/nitric oxide synthetase (eNOS) and produce vascular endothelium dysfunction [36]. The significant negative correlations ofbody weightwith MCEI

_{LS}(RRI,CT) as well as wrist circumference with MEI

_{LS}(CT), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) in upper middle-aged subjects with and without diabetes (Group 3 and Group 2) (Table 4) imply an association of increased anthropometric parameters with impaired vascular function in the aged subjects. The significant negative associations of MEI

_{LS}(RRI) with fasting blood sugar andglycated hemoglobin levels (Table 4) further highlight the adverse impact of diabetes on vascular endothelial function in both acute [37] and chronic [38] hyperglycemia, respectively.

_{SS}(RRI), MEI

_{LS}(RRI), MCEI

_{LS}were all negatively associated with age in a highly significant manner (p < 0.005). The results underscore the sensitivity of MEI(RRI) in discerning age-related changes in both autonomic nervous control and function of the cardiovascular system, while MCEI seems sensitive to age-related alterations in cardiovascular function. On the other hand, negative associations of different multiscale entropy indices with anthropometric parameters (i.e., waist circumference, and body-mass index) in general reflect the sensitivity of these indices in identifying anthropometric anomalies contributing to adverse changes in cardiovascular function. In addition, the significant negative associations of MEI

_{SS}(RRI), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) with the parameters of acute (i.e., fasting blood sugar level) and chronic (i.e., glycated hemoglobin concentration) blood sugar control indicate the sensitivity of MEI(RRI) in reflecting blood sugar-related changes in both autonomic nervous control and function of the cardiovascular system, whereas MEI(CT) and MCEI appear to be indicators of hyperglycemia-related vascular changes. To further elucidate the significance of these parameters, multivariate linear regression analysis demonstrated significant associations of MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) with age and glycated hemoglobin level (all p < 0.05) (Table 6).

_{LS}(RRI), the successful differentiation between upper-middle aged subjects with (Group 3) and without (Group 2) diabetes using MCEI

_{LS}(RRI,CT) (Table 2) highlights the ability of this index to discern diabetes-related changes in vascular regulatory function. In addition, MCEI(RRI,CT) was the only multiscale entropy index that successfully differentiated among the three groups at scale 4 in the present study (Figure 3). This index was also found to be negatively related to anthropometric parameters (i.e., wrist circumference, body-mass index) and fasting blood sugar (Table 5), underlining its association with metabolic syndrome.

## 5. Conclusions

_{LS}could serve as a novel non-invasive biomarker for discerning diabetes-related changes in the cardiovascular system, which is of clinical importance in preventive medicine. The results of the current study successfully identified the risk factors for cardiovascular diseases by comparing the nonlinear coupling behavior of two cardiovascular system-related synchronized time series of different natures. It is anticipated that the risk factors of diseases of other organ systems could be identified with this approach through the analysis ofnonlinear coupling of different synchronized physiological signals pertinent to different organ systems.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**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.

**Table 1.**Demographic, anthropometric, hemodynamic, and serum biochemical parameters of the testing subjects.

Parameters | Group 1 (n = 22) | Group 2 (n = 34) | Group 3 (n = 34) |
---|---|---|---|

Male/Female | 13/9 | 10/24 | 22/12 |

Age (years) | 28.68 ± 6.34 | 56.21 ± 10.72 ** | 60.71 ± 8.46 |

Body weight (kg) | 68.27 ± 15.89 | 61.73 ± 10.55 | 73.88 ± 14.86 †† |

WC(cm) | 82.30 ± 13.53 | 80.79 ± 9.43 | 95.00 ± 11.56 †† |

BMI (kg/m^{2}) | 23.60 ± 4.48 | 23.72 ± 3.54 | 27.92 ± 4.70 †† |

SBP (mmHg) | 117.46 ± 10.94 | 118.97 ± 16.60 | 127.38 ± 17.14 †† |

DBP (mmHg) | 73.91 ± 7.02 | 72.97 ± 9.03 | 76.06 ± 10.16 |

PP (mmHg) | 43.55 ± 7.65 | 46.00 ± 11.12 | 51.32 ± 13.84 |

HDL (mg/dL) | 46.46 ± 15.34 | 55.27 ± 19.34 | 40.21 ± 13.13 †† |

LDL (mg/dL) | 124.86 ± 41.11 | 157.88 ± 43.48 * | 148.62 ± 47.39 |

Cholesterol (mg/dL) | 174.64 ± 56.33 | 165.44 ± 94.19 | 154.94 ± 53.51 |

Triglyceride (mg/dL) | 79.64 ± 36.31 | 102.03 ± 30.99 * | 117.59 ± 45.06 † |

HbA1c(%) | 5.51 ± 0.34 | 5.87 ± 0.40 ** | 8.14 ± 1.27 †† |

PWV_{finger}(m/sec) | 4.48 ± 0.87 | 4.88 ± 0.49 | 5.93 ± 0.58 † |

_{finger}: Left index finger pulse wave velocity [19]; * p < 0.017 (p corrected): Group 1 vs. Group2; ** p < 0.001: Group 1 vs. Group 2; † p < 0.017: Group 2 vs. Group 3; †† p < 0.001: Group 2 vs. Group 3.

**Table 2.**Multiscale entropy indices for crest time and R-R interval at different time scales in three groups of testing subjects.

Parameters | Group 1 (n = 22) | Group 2 (n = 34) | Group 3 (n = 34) |
---|---|---|---|

MEI_{SS}(CT) | 0.65 ± 0.13 | 0.65 ± 0.12 | 0.65 ± 0.13 |

MEI_{LS}(CT) | 0.49 ± 0.07 | 0.47 ± 0.06 | 0.44 ± 0.08 |

MEI_{SS}(RRI) | 0.64 ± 0.08 | 0.58 ± 0.11 * | 0.51 ± 0.17 |

MEI_{LS}(RRI) | 0.54 ± 0.06 | 0.52 ± 0.07 | 0.44 ± 0.11 †† |

MCEI_{SS}(RRI,CT) | 0.70 ± 0.11 | 0.64 ± 0.10 | 0.63 ± 0.12 |

MCEI_{LS}(RRI,CT) | 0.55 ± 0.06 | 0.51 ± 0.06 | 0.46 ± 0.08 † |

_{SS}(CT): Small-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 1, 2, and 3); MEI

_{LS}(CT): Large-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 4, 5, and 6); MEI

_{SS}(RRI): Small-scale multiscale entropy index for R-R interval (i.e., average MEI forRRI series at time scale 1, 2, and 3); MEI

_{LS}(RRI): Large-scale multiscale entropy index for R-R interval (i.e., average MEI for RRI series at time scale 4, 5, and 6); MCEI

_{SS}(RRI,CT): Small-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 1, 2, and 3); MCEI

_{LS}(RRI,CT): Large-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 4, 5, and 6); * p < 0.017 (p corrected): Group 1 vs. Group 2; † p < 0.017: Group 2 vs. Group 3; †† p < 0.001: Group 2 vs. Group 3.

**Table 3.**Correlations of different multiscale entropy indices with demographic, anthropometric, hemodynamic, and serum biochemical parameters in young healthy individuals (Group 1) and non-diabetic upper middle-aged subjects (Group 2) (n = 56).

MEI_{SS}(CT) | MEI_{LS}(CT) | MEI_{SS}(RRI) | MEI_{LS}(RRI) | MCEI_{SS} | MCEI_{LS} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

p | r | p | r | p | r | p | r | p | r | p | r | |

Age (years) | 0.736 | 0.046 | 0.649 | −0.062 | 0.102 | −0.221 | 0.385 | −0.118 | 0.408 | −0.113 | 0.125 | −0.207 |

BH (cm) | 0.254 | −0.155 | 0.265 | −0.151 | 0.819 | −0.031 | 0.227 | −0.164 | 0.537 | 0.084 | 0.491 | −0.094 |

BW (kg) | 0.081 | −0.236 | 0.996 | 0.001 | 0.152 | −0.194 | 0.327 | −0.134 | 0.921 | −0.014 | 0.771 | −0.040 |

WC (cm) | 0.064 | −0.250 | 0.974 | −0.005 | 0.180 | −0.182 | 0.301 | −0.141 | 0.584 | −0.075 | 0.506 | −0.091 |

BMI (kg/m^{2}) | 0.161 | −0.190 | 0.362 | 0.124 | 0.074 | −0.241 | 0.705 | −0.052 | 0.449 | −0.103 | 0.874 | 0.022 |

SBP (mmHg) | 0.209 | 0.171 | 0.259 | 0.153 | 0.398 | 0.115 | 0.332 | 0.132 | 0.113 | 0.214 | 0.107 | 0.218 |

DBP (mmHg) | 0.742 | 0.045 | 0.183 | 0.181 | 0.740 | 0.045 | 0.877 | −0.021 | 0.533 | 0.085 | 0.525 | 0.087 |

PP (mmHg) | 0.115 | 0.213 | 0.584 | 0.075 | 0.334 | 0.131 | 0.117 | 0.212 | 0.070 | 0.244 | 0.065 | 0.248 |

HDL (mg/dL) | 0.802 | 0.034 | 0.254 | −0.153 | 0.819 | −0.031 | 0.915 | −0.015 | 0.418 | −0.110 | 0.254 | −0.155 |

LDL (mg/dL) | 0.515 | 0.089 | 0.590 | −0.074 | 0.051 | −0.263 | 0.239 | −0.160 | 0.927 | −0.012 | 0.259 | −0.153 |

Cholesterol (mg/dL) | 0.403 | −0.114 | 0.740 | −0.045 | 0.067 | −0.247 | 0.003* | −0.394 | 0.058 | −0.255 | 0.020 | −0.311 |

Triglyceride (mg/dL) | 0.958 | −0.007 | 0.857 | 0.025 | 0.681 | −0.056 | 0.365 | −0.123 | 0.910 | 0.016 | 0.451 | −0.103 |

HbA1c (%) | 0.332 | 0.132 | 0.947 | 0.009 | 0.226 | −0.164 | 0.911 | 0.015 | 0.958 | 0.007 | 0.641 | 0.064 |

FBS (mg/dL) | 0.626 | 0.066 | 0.606 | 0.070 | 0.683 | 0.056 | 0.315 | −0.137 | 0.759 | −0.042 | 0.451 | −0.103 |

_{τ=n}(CT): Multiscale entropy index for crest time series at time scale n; MEI

_{SS}(CT): Small-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 1, 2, and 3); MEI

_{LS}(CT): Large-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 4, 5, and 6); MEI

_{τ=n}(RRI): Multiscale entropy index for R-R interval series at time scale n; MEI

_{SS}(RRI): Small-scale multiscale entropy index for R-R interval (i.e., average MEI forRRI series at time scale 1, 2, and 3); MEI

_{LS}(RRI): Large-scale multiscale entropy index for R-R interval (i.e., average MEI for RRI series at time scale 4, 5, and 6); MCEI

_{τ=n}(RRI,CT): Multiscale cross-approximate entropy index for synchronized R-R interval and crest time series at time scale n;MCEI

_{SS}(RRI,CT): Small-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 1, 2, and 3); MCEI

_{LS}(RRI,CT): Large-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 4, 5, and 6); * p < 0.017 (p corrected).

**Table 4.**Correlations of different multiscale entropy indices with demographic, anthropometric, hemodynamic, and serum biochemical parameters in upper middle-aged non-diabetic subjects (Group 2) and diabetic patients (Group 3) (n = 68).

MEI_{SS}(CT) | MEI_{LS}(CT) | MEI_{SS}(RRI) | MEI_{LS}(RRI) | MCEI_{SS} | MCEI_{LS} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

p | r | p | r | p | r | p | r | p | r | p | r | |

Age (years) | 0.409 | 0.102 | 0.778 | −0.035 | 0.395 | −0.105 | 0.029 | −0.264 | 0.725 | 0.043 | 0.272 | −0.135 |

BH (cm) | 0.079 | −0.214 | 0.248 | −0.142 | 0.656 | −0.055 | 0.793 | −0.032 | 0.070 | −0.221 | 0.222 | −0.150 |

BW (kg) | 0.044 | −0.245 | 0.040 | −0.250 | 0.086 | −0.210 | 0.057 | −0.232 | 0.032 | −0.260 | 0.017 * | −0.288 |

WC (cm) | 0.031 | −0.262 | 0.009 * | −0.314 | 0.063 | −0.227 | 0.014 * | −0.298 | 0.042 | −0.248 | 0.004 * | −0.343 |

BMI (kg/m^{2}) | 0.190 | −0.161 | 0.105 | −0.198 | 0.067 | −0.223 | 0.043 | −0.246 | 0.139 | −0.181 | 0.047 | −0.242 |

SBP (mmHg) | 0.136 | 0.183 | 0.580 | 0.068 | 0.729 | 0.043 | 0.416 | −0.100 | 0.165 | 0.170 | 0.875 | 0.019 |

DBP (mmHg) | 0.757 | −0.038 | 0.924 | 0.012 | 0.213 | −0.153 | 0.116 | −0.192 | 0.540 | −0.076 | 0.697 | −0.048 |

PP (mmHg) | 0.022 | 0.276 | 0.498 | 0.084 | 0.156 | 0.174 | 0.936 | 0.010 | 0.017 * | 0.288 | 0.611 | 0.063 |

HDL (mg/dL) | 0.923 | 0.012 | 0.267 | 0.136 | 0.400 | 0.104 | 0.067 | 0.224 | 0.636 | 0.058 | 0.077 | 0.216 |

LDL (mg/dL) | 0.555 | 0.073 | 0.833 | 0.026 | 0.187 | −0.162 | 0.829 | −0.027 | 0.869 | 0.020 | 0.482 | 0.087 |

Cholesterol (mg/dL) | 0.464 | −0.090 | 0.905 | 0.015 | 0.179 | −0.165 | 0.087 | −0.209 | 0.263 | −0.138 | 0.259 | −0.142 |

Triglyceride (mg/dL) | 0.671 | 0.052 | 0.434 | 0.096 | 0.762 | 0.037 | 0.760 | 0.038 | 0.531 | 0.077 | 0.383 | 0.107 |

HbA1c (%) | 0.808 | 0.030 | 0.102 | −0.200 | 0.225 | −0.149 | 0.015 * | -0.294 | 0.875 | 0.020 | 0.077 | −0.216 |

FBS (mg/dL) | 0.778 | 0.035 | 0.092 | −0.206 | 0.148 | −0.177 | 0.005 * | -0.335 | 0.955 | 0.007 | 0.043 | −0.246 |

_{τ=n}(CT): Multiscale entropy index for crest time series at time scale n; MEI

_{SS}(CT): Small-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 1, 2, and 3); MEI

_{LS}(CT): Large-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 4, 5, and 6); MEI

_{τ=n}(RRI): Multiscale entropy index for R-R interval series at time scale n; MEI

_{SS}(RRI): Small-scale multiscale entropy index for R-R interval (i.e., average MEI forRRI series at time scale 1, 2, and 3); MEI

_{LS}(RRI): Large-scale multiscale entropy index for R-R interval (i.e., average MEI for RRI series at time scale 4, 5, and 6); MCEI

_{τ=n}(RRI,CT): Multiscale cross-approximate entropy index for synchronized R-R interval and crest time series at time scale n;MCEI

_{SS}(RRI,CT): Small-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 1, 2, and 3); MCEI

_{LS}(RRI,CT): Large-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 4, 5, and 6); * p < 0.017 (p corrected).

**Table 5.**Correlations of different multiscale entropy indices with demographic, anthropometric, hemodynamic, and serum biochemical parameters in healthy young adults (Group 1), upper middle-aged non-diabetic subjects (Group 2) and diabetic patients (Group 3) (n = 90).

MEI_{SS}(CT) | MEI_{LS}(CT) | MEI_{SS}(RRI) | MEI_{LS}(RRI) | MCEI_{SS} | MCEI_{LS} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

p | r | p | r | p | r | p | r | p | r | r | |

Age (years) | 0.779 | 0.030 | 0.097 | −0.176 | 0.003 * | −0.310 | 0.001 * | −0.332 | 0.135 | −0.159 | −0.334 |

BH (cm) | 0.037 | −0.221 | 0.272 | −0.117 | 0.838 | 0.022 | 0.743 | 0.035 | 0.696 | −0.042 | −0.013 |

BW (kg) | 0.006* | −0.286 | 0.053 | −0.204 | 0.040 | −0.217 | 0.046 | −0.211 | 0.089 | −0.180 | −0.237 |

WC (cm) | 0.008 * | −0.280 | 0.012 * | −0.263 | 0.007 * | −0.284 | 0.004 * | −0.300 | 0.038 | −0.219 | −0.327 |

BMI (kg/m^{2}) | 0.065 | −0.195 | 0.137 | −0.158 | 0.008 * | −0.276 | 0.010 * | −0.269 | 0.073 | −0.190 | −0.261 |

SBP (mmHg) | 0.343 | 0.101 | 0.894 | 0.014 | 0.744 | −0.035 | 0.309 | −0.108 | 0.368 | 0.096 | −0.016 |

DBP (mmHg) | 0.728 | −0.037 | 0.907 | 0.013 | 0.143 | −0.156 | 0.078 | −0.187 | 0.538 | −0.066 | −0.073 |

PP (mmHg) | 0.119 | 0.165 | 0.927 | 0.010 | 0.504 | 0.071 | 0.966 | −0.005 | 0.089 | 0.180 | 0.034 |

HDL (mg/dL) | 0.653 | 0.048 | 0.247 | 0.123 | 0.340 | 0.102 | 0.044 | 0.213 | 0.963 | 0.005 | 0.172 |

LDL (mg/dL) | 0.555 | 0.063 | 0.449 | −0.081 | 0.043 | −0.213 | 0.229 | −0.128 | 0.895 | −0.014 | −0.074 |

Cholesterol (mg/dL) | 0.495 | −0.073 | 0.897 | −0.014 | 0.316 | −0.107 | 0.114 | −0.168 | 0.241 | −0.125 | −0.139 |

Triglyceride (mg/dL) | 0.815 | 0.025 | 0.983 | −0.002 | 0.467 | −0.078 | 0.333 | −0.103 | 0.885 | 0.015 | −0.053 |

HbA1c (%) | 0.842 | 0.021 | 0.013 * | −0.261 | 0.013 * | −0.261 | 0.001 ** | −0.354 | 0.430 | −0.084 | −0.306 |

FBS (mg/dL) | 0.846 | 0.021 | 0.023 | −0.239 | 0.012 * | −0.263 | <0.001 ** | −0.384 | 0.391 | −0.091 | −0.322 |

_{τ=n}(CT): Multiscale entropy index for crest time series at time scale n; MEI

_{SS}(CT): Small-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 1, 2, and 3); MEI

_{LS}(CT): Large-scale multiscale entropy index for crest time (i.e., average MEI for CT series of time scale 4, 5, and 6); MEI

_{τ=n}(RRI): Multiscale entropy index for R-R interval series at time scale n; MEI

_{SS}(RRI): Small-scale multiscale entropy index for R-R interval (i.e., average MEI forRRI series at time scale 1, 2, and 3); MEI

_{LS}(RRI): Large-scale multiscale entropy index for R-R interval (i.e., average MEI for RRI series at time scale 4, 5, and 6); MCEI

_{τ=n}(RRI,CT): Multiscale cross-approximate entropy index for synchronized R-R interval and crest time series at time scale n;MCEI

_{SS}(RRI,CT): Small-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 1, 2, and 3); MCEI

_{LS}(RRI,CT): Large-scale multiscale cross-approximate entropy index (i.e., average MCEI for synchronized RRI and CT series at time scale 4, 5, and 6); * p < 0.017 (p corrected), ** p < 0.001.

**Table 6.**Multivariate linear regression analysis for MEI

_{LS}(CT), MEI

_{LS}(RRI), and MCEI

_{LS}(RRI,CT) for all subjects (n = 90).

MEI_{LS}(CT) | MEI_{LS}(RRI) | MCEI_{LS}(RRI,CT) | |||||||
---|---|---|---|---|---|---|---|---|---|

B-Coef | SE | p | B-Coef | SE | p | B-Coef | SE | p | |

Variable | |||||||||

Age (year) | 0.000 | 0.001 | 0.569 | −0.001 | 0.001 | 0.040 | −0.001 | 0.001 | 0.022 |

HbA1c(%) | −0.012 | 0.006 | 0.041 | −0.018 | 0.007 | 0.012 | −0.012 | 0.006 | 0.041 |

B0 | 0.563 | 0.039 | <0.001 | 0.686 | 0.046 | <0.001 | 0.644 | 0.036 | <0.001 |

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## Share and Cite

**MDPI and ACS Style**

Xiao, M.-X.; Wei, H.-C.; Xu, Y.-J.; Wu, H.-T.; Sun, C.-K.
Combination of R-R Interval and Crest Time in Assessing Complexity Using Multiscale Cross-Approximate Entropy in Normal and Diabetic Subjects. *Entropy* **2018**, *20*, 497.
https://doi.org/10.3390/e20070497

**AMA Style**

Xiao M-X, Wei H-C, Xu Y-J, Wu H-T, Sun C-K.
Combination of R-R Interval and Crest Time in Assessing Complexity Using Multiscale Cross-Approximate Entropy in Normal and Diabetic Subjects. *Entropy*. 2018; 20(7):497.
https://doi.org/10.3390/e20070497

**Chicago/Turabian Style**

Xiao, Ming-Xia, Hai-Cheng Wei, Ya-Jie Xu, Hsien-Tsai Wu, and Cheuk-Kwan Sun.
2018. "Combination of R-R Interval and Crest Time in Assessing Complexity Using Multiscale Cross-Approximate Entropy in Normal and Diabetic Subjects" *Entropy* 20, no. 7: 497.
https://doi.org/10.3390/e20070497