Entropy

Research

24 pages, 5726 KiB

Open AccessFeature PaperArticle

Dynamical Pattern Representation of Cardiovascular Couplings Evoked by Head-up Tilt Test

by Danuta Makowiec, Dorota Wejer, Beata Graff and Zbigniew R. Struzik

Entropy 2018, 20(4), 235; https://doi.org/10.3390/e20040235 - 28 Mar 2018

Cited by 4 | Viewed by 3846

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human [...] Read more.

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human underwent a provocation test using the head-up tilt (HUT) protocol. The information provided by ShE and TE is evaluated from two aspects: that of the algorithmic stability and that of the recognised physiology of the cardiovascular response to the HUT test. To address both of these aspects, two types of symbolization of three-element subsequent values of a signal are considered: one, well established in heart rate research, referring to the variability in a signal, and a novel one, revealing primarily the dynamical trends. The interpretation of ShE shows a strong dependence on the method that was used in signal pre-processing. In particular, results obtained from normalized signals turn out to be less conclusive than results obtained from non-normalized signals. Systematic investigations based on surrogate data tests are employed to discriminate between genuine properties—in particular inter-system coupling—and random, incidental fluctuations. These properties appear to determine the occurrence of a high percentage of zero values of TE, which strongly limits the reliability of the couplings measured. Nevertheless, supported by statistical corroboration, we identify distinct timings when: (i) evoking cardiac impact on the vascular system, and (ii) evoking vascular impact on the cardiac system, within both the principal sub-systems of the baroreflex loop. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

680 KiB

Open AccessArticle

Information Theory to Probe Intrapartum Fetal Heart Rate Dynamics

by Carlos Granero-Belinchon, Stéphane G. Roux, Patrice Abry, Muriel Doret and Nicolas B. Garnier

Entropy 2017, 19(12), 640; https://doi.org/10.3390/e19120640 - 25 Nov 2017

Cited by 15 | Viewed by 5127

Abstract

Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in clinical practice to assess the baby’s health status and to detect fetal acidosis. It is usually analyzed by visual inspection grounded on FIGO criteria. Characterization of intrapartum fetal heart rate temporal dynamics [...] Read more.

Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in clinical practice to assess the baby’s health status and to detect fetal acidosis. It is usually analyzed by visual inspection grounded on FIGO criteria. Characterization of intrapartum fetal heart rate temporal dynamics remains a challenging task and continuously receives academic research efforts. Complexity measures, often implemented with tools referred to as approximate entropy (ApEn) or sample entropy (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. We explore how information theory, and especially auto-mutual information (AMI), is connected to ApEn and SampEn and can be used to probe FHR dynamics. Applied to a large (1404 subjects) and documented database of FHR data, collected in a French academic hospital, it is shown that (i) auto-mutual information outperforms ApEn and SampEn for acidosis detection in the first stage of labor and continues to yield the best performance in the second stage; (ii) Shannon entropy increases as labor progresses and is always much larger in the second stage; (iii) babies suffering from fetal acidosis additionally show more structured temporal dynamics than healthy ones and that this progressive structuration can be used for early acidosis detection. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

1137 KiB

Open AccessArticle

Informative Nature and Nonlinearity of Lagged Poincaré Plots Indices in Analysis of Heart Rate Variability

by Berik Koichubekov, Viktor Riklefs, Marina Sorokina, Ilya Korshukov, Lyudmila Turgunova, Yelena Laryushina, Riszhan Bakirova, Gulmira Muldaeva, Ernur Bekov and Makhabbat Kultenova

Entropy 2017, 19(10), 523; https://doi.org/10.3390/e19100523 - 10 Oct 2017

Cited by 10 | Viewed by 6006

Abstract

Lagged Poincaré plots have been successful in characterizing abnormal cardiac function. However, the current research practices do not favour any specific lag of Poincaré plots, thus complicating the comparison of results of different researchers in their analysis of heart rate of healthy subjects [...] Read more.

Lagged Poincaré plots have been successful in characterizing abnormal cardiac function. However, the current research practices do not favour any specific lag of Poincaré plots, thus complicating the comparison of results of different researchers in their analysis of heart rate of healthy subjects and patients. We researched the informative nature of lagged Poincaré plots in different states of the autonomic nervous system. It was tested in three models: different age groups, groups with different balance of autonomous regulation, and in hypertensive patients. Correlation analysis shows that for lag l = 6, SD1/SD2 has weak (r = 0.33) correlation with linear parameters of heart rate variability (HRV). For l more than 6 it displays even less correlation with linear parameters, but the changes in SD1/SD2 become statistically insignificant. Secondly, surrogate data tests show that the real SD1/SD2 is statistically different from its surrogate value and the conclusion could be made that the heart rhythm has nonlinear properties. Thirdly, the three models showed that for different functional states of the autonomic nervous system (ANS), SD1/SD2 ratio varied only for lags l = 5 and 6. All of this allow to us to give cautious recommendation to use SD1/SD2 with lags 5 and 6 as a nonlinear characteristic of HRV. The received data could be used as the basis for continuing the research in standardisation of nonlinear analytic methods. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

811 KiB

Open AccessArticle

Novel Early EEG Measures Predicting Brain Recovery after Cardiac Arrest

by Kab-Mun Cha, Nitish V. Thakor and Hyun-Chool Shin

Entropy 2017, 19(9), 466; https://doi.org/10.3390/e19090466 - 2 Sep 2017

Cited by 2 | Viewed by 5736

Abstract

In this paper, we propose novel quantitative electroencephalogram (qEEG) measures by exploiting three critical and distinct phases (isoelectric, fast progression, and slow progression) of qEEG time evolution. Critical time points where the phase transition occurs are calculated. Most conventional measures have two major [...] Read more.

In this paper, we propose novel quantitative electroencephalogram (qEEG) measures by exploiting three critical and distinct phases (isoelectric, fast progression, and slow progression) of qEEG time evolution. Critical time points where the phase transition occurs are calculated. Most conventional measures have two major disadvantages. Firstly, to obtain meaningful time-evolution over raw electroencephalogram (EEG), these measures require baseline EEG activities before the subject’s injury. Secondly, conventional qEEG measures need at least 2∼3 h recording of EEG signals to predict meaningful long-term neurological outcomes. Unlike the conventional qEEG measures, the two measures do not require the baseline EEG information before injury and furthermore can be calculated only with the EEG data of 20∼30 min after cardiopulmonary resuscitation (CPR). Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Graphical abstract

2451 KiB

Open AccessArticle

Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure

by Chengyu Liu and Rui Gao

Entropy 2017, 19(6), 251; https://doi.org/10.3390/e19060251 - 31 May 2017

Cited by 40 | Viewed by 6769

Abstract

Cardiovascular systems essentially have multiscale control mechanisms. Multiscale entropy (MSE) analysis permits the dynamic characterization of the cardiovascular time series for both short-term and long-term processes, and thus can be more illuminating. The traditional MSE analysis for heart rate variability (HRV) is performed [...] Read more.

Cardiovascular systems essentially have multiscale control mechanisms. Multiscale entropy (MSE) analysis permits the dynamic characterization of the cardiovascular time series for both short-term and long-term processes, and thus can be more illuminating. The traditional MSE analysis for heart rate variability (HRV) is performed on the original RR interval time series (named as MSE_RR). In this study, we proposed an MSE analysis for the differential RR interval time series signal, named as MSE_dRR. The motivation of using the differential RR interval time series signal is that this signal has a direct link with the inherent non-linear property of electrical rhythm of the heart. The effectiveness of the MSE_RR and MSE_dRR were tested and compared on the long-term MIT-Boston’s Beth Israel Hospital (MIT-BIH) 54 normal sinus rhythm (NSR) and 29 congestive heart failure (CHF) RR interval recordings, aiming to explore which one is better for distinguishing the CHF patients from the NSR subjects. Four RR interval length for analysis were used (

N = 500, N = 1000

,

N = 2000

and

N = 5000

). The results showed that MSE_RR did not report significant differences between the NSR and CHF groups at several scales for each RR segment length type (Scales 7, 8 and 10 for

N = 500

, Scales 3 and 10 for

N = 1000

, Scales 2 and 3 for both

N = 2000

and

N = 5000

). However, the new MSE_dRR gave significant separation for the two groups for all RR segment length types except

N = 500

at Scales 9 and 10. The area under curve (AUC) values from the receiver operating characteristic (ROC) curve were used to further quantify the performances. The mean AUC of the new MSE_dRR from Scales 1–10 are 79.5%, 83.1%, 83.5% and 83.1% for

N = 500

,

N = 1000

,

N = 2000

and

N = 5000

, respectively, whereas the mean AUC of MSE_RR are only 68.6%, 69.8%, 69.6% and 67.1%, respectively. The five-fold cross validation support vector machine (SVM) classifier reports the classification Accuracy (

A c c

) of MSE_RR as 73.5%, 75.9% and 74.6% for

N = 1000

,

N = 2000

and

N = 5000

, respectively, while for the new MSE_dRR analysis accuracy was 85.5%, 85.6% and 85.6%. Different biosignal editing methods (direct deletion and interpolation) did not change the analytical results. In summary, this study demonstrated that compared with MSE_RR, MSE_dRR reports better statistical stability and better discrimination ability for the NSR and CHF groups. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

1984 KiB

Open AccessArticle

Entropy in Investigation of Vasovagal Syndrome in Passive Head Up Tilt Test

by Katarzyna Buszko, Agnieszka Piątkowska, Edward Koźluk and Grzegorz Opolski

Entropy 2017, 19(5), 236; https://doi.org/10.3390/e19050236 - 20 May 2017

Cited by 8 | Viewed by 5142

Abstract

This paper presents an application of Approximate Entropy (ApEn) and Sample Entropy (SampEn) in the analysis of heart rhythm, blood pressure and stroke volume for the diagnosis of vasovagal syndrome. The analyzed biosignals were recorded during positive passive tilt tests—HUTT(+). Signal changes and [...] Read more.

This paper presents an application of Approximate Entropy (ApEn) and Sample Entropy (SampEn) in the analysis of heart rhythm, blood pressure and stroke volume for the diagnosis of vasovagal syndrome. The analyzed biosignals were recorded during positive passive tilt tests—HUTT(+). Signal changes and their entropy were compared in three main phases of the test: supine position, tilt, and pre-syncope, with special focus on the latter, which was analyzed in a sliding window of each signal. In some cases, ApEn and SampEn were equally useful for the assessment of signal complexity (p < 0.05 in corresponding calculations). The complexity of the signals was found to decrease in the pre-syncope phase (SampEn (RRI): 1.20–0.34, SampEn (sBP): 1.29–0.57, SampEn (dBP): 1.19–0.48, SampEn (SV): 1.62–0.91). The pattern of the SampEn (SV) decrease differs from the pattern of the SampEn (sBP), SampEn (dBP) and SampEn (RRI) decrease. For all signals, the lowest entropy values in the pre-syncope phase were observed at the moment when loss of consciousness occurred. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

897 KiB

Open AccessArticle

Multiscale Cross-Approximate Entropy Analysis of Bilateral Fingertips Photoplethysmographic Pulse Amplitudes among Middle-to-Old Aged Individuals with or without Type 2 Diabetes

by Hsien-Tsai Wu, Cheng-Chan Yang, Gen-Min Lin, Bagus Haryadi, Shiao-Chiang Chu, Chieh-Ming Yang and Cheuk-Kwan Sun

Entropy 2017, 19(4), 145; https://doi.org/10.3390/e19040145 - 30 Mar 2017

Cited by 10 | Viewed by 4691

Abstract

Multiscale cross-approximate entropy (MC-ApEn) between two different physiological signals could evaluate cardiovascular health in diabetes. Whether MC-ApEn analysis between two similar signals such as photoplethysmographic (PPG) pulse amplitudes of bilateral fingertips can reflect diabetes status is unknown. From a middle-to-old-aged population free of [...] Read more.

Multiscale cross-approximate entropy (MC-ApEn) between two different physiological signals could evaluate cardiovascular health in diabetes. Whether MC-ApEn analysis between two similar signals such as photoplethysmographic (PPG) pulse amplitudes of bilateral fingertips can reflect diabetes status is unknown. From a middle-to-old-aged population free of prior cardiovascular disease, we selected the unaffected (no type 2 diabetes, n = 36), the well-controlled diabetes (glycated hemoglobin (HbA1c) < 8%, n = 30), and the poorly- controlled diabetes (HbA1c ≥ 8%, n = 26) groups. MC-ApEn indexes were calculated from simultaneous consecutive 1500 PPG pulse amplitudes signals of bilateral index fingertips. The average of scale factors 1–5 (MC-ApEn_SS) and of scale factors 6–10 (MC-ApEn_LS) were defined as the small- and large-scales MC-ApEn, respectively. The MC-ApEn_LS index was highest in the unaffected, followed by the well-controlled diabetes, and then the poorly-controlled diabetes (0.70, 0.62, and 0.53; all paired p-values were <0.05); in contrast, the MC-ApEn_SS index did not differ between groups. Our findings suggested that the bilateral fingertips large-scale MC-ApEn_LS index of PPG pulse amplitudes might be able to evaluate the glycemic status and detect subtle vascular disease in type 2 diabetes. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

1498 KiB

Open AccessArticle

Discrepancies between Conventional Multiscale Entropy and Modified Short-Time Multiscale Entropy of Photoplethysmographic Pulse Signals in Middle- and Old- Aged Individuals with or without Diabetes

by Gen-Min Lin, Bagus Haryadi, Chieh-Ming Yang, Shiao-Chiang Chu, Cheng-Chan Yang and Hsien-Tsai Wu

Entropy 2017, 19(3), 132; https://doi.org/10.3390/e19030132 - 18 Mar 2017

Cited by 12 | Viewed by 4716

Abstract

Multiscale entropy (MSE) of physiological signals may reflect cardiovascular health in diabetes. The classic MSE (cMSE) algorithm requires more than 750 signals for the calculations. The modified short-time MSE (sMSE) may have inconsistent outcomes compared with the cMSE at large time scales and [...] Read more.

Multiscale entropy (MSE) of physiological signals may reflect cardiovascular health in diabetes. The classic MSE (cMSE) algorithm requires more than 750 signals for the calculations. The modified short-time MSE (sMSE) may have inconsistent outcomes compared with the cMSE at large time scales and in a disease status. Therefore, we compared the cMSE of 1500 (cMSE₁₅₀₀) consecutive and 1000 photoplethysmographic (PPG) pulse amplitudes with the sMSE of 500 PPG (sMSE₅₀₀) pulse amplitudes of bilateral fingertips among middle- to old-aged individuals with or without type 2 diabetes. We discovered that cMSE₁₅₀₀ had the smallest value across scale factors 1–10, followed by cMSE₁₀₀₀, and then sMSE₅₀₀in both hands. The cMSE₁₅₀₀, cMSE₁₀₀₀ and sMSE₅₀₀ did not differ at each scale factor in both hands of persons without diabetes and in the dominant hand of those with diabetes. In contrast, the sMSE₅₀₀ differed at all scales 1–10 in the non-dominant hand with diabetes. In conclusion, autonomic dysfunction, prevalent in the non-dominant hand which had a low local physical activity in the person with diabetes, might be imprecisely evaluated by the sMSE; therefore, using more PPG signal numbers for the cMSE is preferred in such a situation. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

428 KiB

Open AccessArticle

Use of Accumulated Entropies for Automated Detection of Congestive Heart Failure in Flexible Analytic Wavelet Transform Framework Based on Short-Term HRV Signals

by Mohit Kumar, Ram Bilas Pachori and U. Rajendra Acharya

Entropy 2017, 19(3), 92; https://doi.org/10.3390/e19030092 - 27 Feb 2017

Cited by 59 | Viewed by 6360

Abstract

In the present work, an automated method to diagnose Congestive Heart Failure (CHF) using Heart Rate Variability (HRV) signals is proposed. This method is based on Flexible Analytic Wavelet Transform (FAWT), which decomposes the HRV signals into different sub-band signals. Further, Accumulated Fuzzy [...] Read more.

In the present work, an automated method to diagnose Congestive Heart Failure (CHF) using Heart Rate Variability (HRV) signals is proposed. This method is based on Flexible Analytic Wavelet Transform (FAWT), which decomposes the HRV signals into different sub-band signals. Further, Accumulated Fuzzy Entropy (AFEnt) and Accumulated Permutation Entropy (APEnt) are computed over cumulative sums of these sub-band signals. This provides complexity analysis using fuzzy and permutation entropies at different frequency scales. We have extracted 20 features from these signals obtained at different frequency scales of HRV signals. The Bhattacharyya ranking method is used to rank the extracted features from the HRV signals of three different lengths (500, 1000 and 2000 samples). These ranked features are fed to the Least Squares Support Vector Machine (LS-SVM) classifier. Our proposed system has obtained a sensitivity of 98.07%, specificity of 98.33% and accuracy of 98.21% for the 500-sample length of HRV signals. Our system yielded a sensitivity of 97.95%, specificity of 98.07% and accuracy of 98.01% for HRV signals of a length of 1000 samples and a sensitivity of 97.76%, specificity of 97.67% and accuracy of 97.71% for signals corresponding to the 2000-sample length of HRV signals. Our automated system can aid clinicians in the accurate detection of CHF using HRV signals. It can be installed in hospitals, polyclinics and remote villages where there is no access to cardiologists. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics II)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Entropy and Cardiac Physics II

Share This Special Issue

Special Issue Editor

Special Issue Information

Benefits of Publishing in a Special Issue

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI