Multiscale cross-approximate entropy analysis as a measure of complexity among the aged and diabetic

The futility of long-term predictions in bipolar disorder: mood fluctuations are the result of deterministic chaotic processes

BACKGROUND

Understanding the underlying architecture of mood regulation in bipolar disorder (BD) is important, as we are starting to conceptualize BD as a more complex disorder than one of recurring manic or depressive episodes. Nonlinear techniques are employed to understand and model the behavior of complex systems. Our aim was to assess the underlying nonlinear properties that account for mood and energy fluctuations in patients with BD; and to compare whether these processes were different in healthy controls (HC) and unaffected first-degree relatives (FDR). We used three different nonlinear techniques: Lyapunov exponent, detrended fluctuation analysis and fractal dimension to assess the underlying behavior of mood and energy fluctuations in all groups; and subsequently to assess whether these arise from different processes in each of these groups.

RESULTS

There was a positive, short-term autocorrelation for both mood and energy series in all three groups. In the mood series, the largest Lyapunov exponent was found in HC (1.84), compared to BD (1.63) and FDR (1.71) groups [F (2, 87) = 8.42, p < 0.005]. A post-hoc Tukey test showed that Lyapunov exponent in HC was significantly higher than both the BD (p = 0.003) and FDR groups (p = 0.03). Similarly, in the energy series, the largest Lyapunov exponent was found in HC (1.85), compared to BD (1.76) and FDR (1.67) [F (2, 87) = 11.02; p < 0.005]. There were no significant differences between groups for the detrended fluctuation analysis or fractal dimension.

CONCLUSIONS

The underlying nature of mood variability is in keeping with that of a chaotic system, which means that fluctuations are generated by deterministic nonlinear process(es) in HC, BD, and FDR. The value of this complex modeling lies in analyzing the nature of the processes involved in mood regulation. It also suggests that the window for episode prediction in BD will be inevitably short.

Sulprostone-Induced Gastric Dysrhythmia in the Ferret: Conventional and Advanced Analytical Approaches

Nausea and emesis resulting from disease or drug treatment may be associated with disrupted gastric myoelectric activity (GMA). Conventional analytical techniques can determine the relative degrees of brady-, normo-, and tachygastric power, but lose information relative to the basic slow wave shape. The aim of the present study was to investigate the application of advanced analytical techniques in the analysis of disrupted GMA recorded after administration of sulprostone, a prostaglandin E_3/1 agonist, in ferrets. Ferrets were implanted with radiotelemetry devices to record GMA, blood pressure, heart rate (HR) and core body temperature 1 week before the administration of sulprostone (30 μg/kg) or vehicle (saline, 0.5 mL/kg). GMA was initially analyzed using fast Fourier transformations (FFTs) and a conventional power partitioning. Detrended fluctuation analysis (DFA) was also applied to the GMA recordings to reveal information relative to the fluctuation of signals around local trends. Sample entropy (SampEn) analysis was used for examining the regularity of signals. Conventional signal processing techniques revealed that sulprostone increased the dominant frequency (DF) of slow waves, with an increase in the percentage power of the tachygastric range and a decrease in the percentage power of the normogastric range. DFA revealed that sulprostone decreased the fluctuation function, indicative of a loss of the variability of GMA fluctuations around local trends. Sulprostone increased SampEn values, indicating a loss of regularity in the GMA data. Behaviorally, sulprostone induced emesis and caused defecation. It also increased blood pressure and elevated HR, with an associated decrease in HR variability (HRV). Further analysis of HRV revealed a decrease in both low-frequency (LF) and high-frequency (HF) components, with an overall increase in the LF/HF ratio. Sulprostone did not affect core body temperature. In conclusion, DFA and SampEn permit a detailed analysis of GMA, which is necessary to understand the action of sulprostone to modulate gastric function. The action to decrease HRV and increase the LF/HF ratio may be consistent with a shift toward sympathetic nervous system dominance, commonly seen during nausea.

Compatibility of pulse-pulse intervals with R-R intervals in assessing cardiac autonomic function and its relation to risks of atherosclerosis

OBJECTIVE

Heart rate variability (HRV) analysis using electrocardiographic R-R intervals (RRIs) in either a time or a frequency domain is a useful tool for assessing cardiac autonomic dysfunction in clinical research. For convenience, pulse-pulse intervals (PPIs) acquired by photoplethysmography have been used to assess HRV. However, the compatibility of PPI with RRI is controversial.

MATERIALS AND METHODS

In this study, we investigated the compatibility of PPI with RRI in five groups of participants, including nonoverweight young individuals with a body mass index (BMI) <24 kg/m2 (Group 1, n = 20, aged 18-40 years), overweight young individuals with a BMI ≥24 kg/m2 (Group 2, n = 13, aged 21-38 years), nonoverweight upper middle-aged individuals with a BMI <24 kg/m2 (Group 3, n = 21, aged 45-89 years), overweight upper middle-aged individuals with a BMI ≥24 kg/m2 (Group 4, n = 14, aged 43-74 years), and diabetic patients with a BMI ≥24 kg/m2 (Group 5, n = 19, aged 35-74 years). We then used cross-approximate entropy (CAE) to assess the compatibility between RRI and PPI and analyzed HRV in the time and frequency domains derived from PPR and RRI with traditional methods.

RESULTS

The CAE values in Group 1 were significantly lower than those in Group 2 (1.68 ± 0.16 vs. 1.78 ± 0.15, P = 0.041), Group 3 (1.68 ± 0.16 vs. 2.05 ± 0.27, P < 0.001), Group 4 (1.68 ± 0.16 vs. 1.87 ± 0.23, P = 0.023), and Group 5 (1.68 ± 0.16 vs. 2.09 ± 0.23, P < 0.001). There were no significant differences in HRV acquired by PPI and RRI, except for proportion of pairs of adjacent NN intervals differing by more than 50 ms in the entire recording in Group 1. All HRVs derived from PPI were different from those acquired from RRI in the other groups.

CONCLUSION

PPI may be an alternative parameter for effectively assessing cardiac autonomic function in nonoverweight healthy individuals. It should be used carefully in overweight, elderly, or diabetic individuals.

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

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.

Complexity Change in Cardiovascular Disease

With the fast development of wearable medical device in recent years, it becomes critical to conduct research on continuously measured physiological signals. Entropy is a key metric for quantifying the irregularity and/or complexity contained in human physiological signals. In this review, we focus on exploring how entropy changes in various physiological signals in cardiovascular diseases. Our review concludes that the direction of entropy change relies on the physiological signals under investigation. For heart rate variability and pulse index, the entropy of a healthy person is higher than that of a patient with cardiovascular diseases. For diastolic period variability and diastolic heart sound, the direction of entropy change is reversed. Our conclusion should not only give valuable guidance for further research on the application of entropy in cardiovascular diseases but also provide a foundation for using entropy to analyze the irregularity and/or complexity of physiological signals measured by wearable medical device.

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

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-ApEnSS) and of scale factors 6–10 (MC-ApEnLS) were defined as the small- and large-scales MC-ApEn, respectively. The MC-ApEnLS 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-ApEnSS index did not differ between groups. Our findings suggested that the bilateral fingertips large-scale MC-ApEnLS index of PPG pulse amplitudes might be able to evaluate the glycemic status and detect subtle vascular disease in type 2 diabetes.

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

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 sMSE500 in 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.

Aging effect on microcirculation: A multiscale entropy approach on laser speckle contrast images

PURPOSE

It has long been known that age plays a crucial role in the deterioration of microvessels. The assessment of such deteriorations can be achieved by monitoring microvascular blood flow. Laser speckle contrast imaging (LSCI) is a powerful optical imaging tool that provides two-dimensional information on microvascular blood flow. The technique has recently been commercialized, and hence, few works discuss the postacquisition processing of laser speckle contrast images recorded in vivo. By applying entropy-based complexity measures to LSCI time series, we present herein the first attempt to study the effect of aging on microcirculation by measuring the complexity of microvascular signals over multiple time scales.

METHODS

Forearm skin microvascular blood flow was studied with LSCI in 18 healthy subjects. The subjects were subdivided into two age groups: younger (20-30 years old, n = 9) and older (50-68 years old, n = 9). To estimate age-dependent changes in microvascular blood flow, we applied three entropy-based complexity algorithms to LSCI time series.

RESULTS

The application of entropy-based complexity algorithms to LSCI time series can differentiate younger from older groups: the data fluctuations in the younger group have a significantly higher complexity than those obtained from the older group.

CONCLUSIONS

The effect of aging on microcirculation can be estimated by using entropy-based complexity algorithms to LSCI time series.

Glycemic Control, Hand Activity, and Complexity of Biological Signals in Diabetes Mellitus

Both glycemic control and handgrip strength affect microvascular function. Multiscale entropy (MSE) of photoplethysmographic (PPG) pulse amplitudes may differ by diabetes status and hand activity. Of a middle-to-old aged and right-handed cohort without clinical cardiovascular disease, we controlled age, sex, and weight to select the unaffected (no type 2 diabetes,n=36),the well-controlled diabetes (HbA1c < 8%,n=22), and the poorly controlled diabetes (HbA1c ≥ 8%,n=22) groups. MSEs were calculated from consecutive 1,500 PPG pulse amplitudes of bilateral index fingertips. Thesmall-,  medium-,and large-scale MSEs were defined as the average of scale 1 (MSE1), scales 2–4 (MSE2–4), and scales 5–10 (MSE5–10), respectively. Intra- and intergroups were compared by one- and two-samplet-tests, respectively. The dominant handMSE5–10was lower in the poorly controlled diabetes group than the well-controlled diabetes and the unaffected (1.28 versus 1.52 and 1.56,p=0.019and 0.001, resp.) groups, whereas the nondominant handMSE5–10was lower in the well- and poorly controlled diabetes groups than the unaffected group (1.35 and 1.29 versus 1.58,p=0.008and 0.005, resp.). TheMSE1of dominant hand was higher than that of nondominant hand in the well-controlled diabetes (1.35 versus 1.10,p=0.048). In conclusion, diabetes status and hand dominance may affect the MSE of PPG pulse amplitudes.

Symmetry Analysis of Gait between Left and Right Limb Using Cross-Fuzzy Entropy

The purpose of this paper is the investigation of gait symmetry problem by using cross-fuzzy entropy (C-FuzzyEn), which is a recently proposed cross entropy that has many merits as compared to the frequently used cross sample entropy (C-SampleEn). First, we used several simulation signals to test its performance regarding the relative consistency and dependence on data length. Second, the gait time series of the left and right stride interval were used to calculate the C-FuzzyEn values for gait symmetry analysis. Besides the statistical analysis, we also realized a support vector machine (SVM) classifier to perform the classification of normal and abnormal gaits. The gait dataset consists of 15 patients with Parkinson's disease (PD) and 16 control (CO) subjects. The results show that the C-FuzzyEn values of the PD patients' gait are significantly higher than that of the CO subjects with a p value of less than 10⁻⁵, and the best classification performance evaluated by a leave-one-out (LOO) cross-validation method is an accuracy of 96.77%. Such encouraging results imply that the C-FuzzyEn-based gait symmetry measure appears as a suitable tool for analyzing abnormal gaits.

Traumatic brain injury detection using electrophysiological methods

Measuring neuronal activity with electrophysiological methods may be useful in detecting neurological dysfunctions, such as mild traumatic brain injury (mTBI). This approach may be particularly valuable for rapid detection in at-risk populations including military service members and athletes. Electrophysiological methods, such as quantitative electroencephalography (qEEG) and recording event-related potentials (ERPs) may be promising; however, the field is nascent and significant controversy exists on the efficacy and accuracy of the approaches as diagnostic tools. For example, the specific measures derived from an electroencephalogram (EEG) that are most suitable as markers of dysfunction have not been clearly established. A study was conducted to summarize and evaluate the statistical rigor of evidence on the overall utility of qEEG as an mTBI detection tool. The analysis evaluated qEEG measures/parameters that may be most suitable as fieldable diagnostic tools, identified other types of EEG measures and analysis methods of promise, recommended specific measures and analysis methods for further development as mTBI detection tools, identified research gaps in the field, and recommended future research and development thrust areas. The qEEG study group formed the following conclusions: (1) Individual qEEG measures provide limited diagnostic utility for mTBI. However, many measures can be important features of qEEG discriminant functions, which do show significant promise as mTBI detection tools. (2) ERPs offer utility in mTBI detection. In fact, evidence indicates that ERPs can identify abnormalities in cases where EEGs alone are non-disclosing. (3) The standard mathematical procedures used in the characterization of mTBI EEGs should be expanded to incorporate newer methods of analysis including non-linear dynamical analysis, complexity measures, analysis of causal interactions, graph theory, and information dynamics. (4) Reports of high specificity in qEEG evaluations of TBI must be interpreted with care. High specificities have been reported in carefully constructed clinical studies in which healthy controls were compared against a carefully selected TBI population. The published literature indicates, however, that similar abnormalities in qEEG measures are observed in other neuropsychiatric disorders. While it may be possible to distinguish a clinical patient from a healthy control participant with this technology, these measures are unlikely to discriminate between, for example, major depressive disorder, bipolar disorder, or TBI. The specificities observed in these clinical studies may well be lost in real world clinical practice. (5) The absence of specificity does not preclude clinical utility. The possibility of use as a longitudinal measure of treatment response remains. However, efficacy as a longitudinal clinical measure does require acceptable test-retest reliability. To date, very few test-retest reliability studies have been published with qEEG data obtained from TBI patients or from healthy controls. This is a particular concern because high variability is a known characteristic of the injured central nervous system.

Fronto-parietal connectivity changes following noxious stimulation during anesthesia

RATIONALE

The aim of our study was to assess the changes in the fronto-parietal connectivity estimated by the cross approximate entropy (XAppEn) during noxious stimulation while under chloral hydrate anaesthesia, in rats.

METHOD

A group of 11 Wistar rats chronically implanted with Ni-Cr electrodes, which were placed on the dura mater of the right hemisphere (over the olfactory cortex, the frontal and the parietal lobes), were used in the present study. Noxious stimuli of a mechanical and thermal nature were applied on the left hindpaw during chloral hydrate anesthesia. The anesthetic depth was estimated through median frequency computation, which in that instance was of 2-3 Hz. Fronto-parietal functional cortical connectivity was assessed by using XAppEn.

RESULTS

After data processing and analysis we observed an increase of fronto-parietal functional connectivity during mechanical and thermal noxious stimulation. In addition, MEF increased both in frontal and parietal areas during the mechanical and thermal stimulation compared to baseline.

CONCLUSION

Mechanical and thermal stimulation induces an increase in the fronto-parietal connectivity during chloral hydrate anesthesia in rats.

Multiscale cross-approximate entropy analysis as a measurement of complexity between ECG R-R interval and PPG pulse amplitude series among the normal and diabetic subjects

Physiological signals often show complex fluctuation (CF) under the dual influence of temporal and spatial scales, and CF can be used to assess the health of physiologic systems in the human body. This study applied multiscale cross-approximate entropy (MC-ApEn) to quantify the complex fluctuation between R-R intervals series and photoplethysmography amplitude series. All subjects were then divided into the following two groups: healthy upper middle-aged subjects (Group 1, age range: 41-80 years, n = 27) and upper middle-aged subjects with type 2 diabetes (Group 2, age range: 41-80 years, n = 24). There are significant differences of heart rate variability, LHR, between Groups 1 and 2 (1.94 ± 1.21 versus 1.32 ± 1.00, P = 0.031). Results demonstrated differences in sum of large scale MC-ApEn (MC-ApEn(LS)) (5.32 ± 0.50 versus 4.74 ± 0.78, P = 0.003). This parameter has a good agreement with pulse-pulse interval and pulse amplitude ratio (PAR), a simplified assessment for baroreflex activity. In conclusion, this study employed the MC-ApEn method, integrating multiple temporal and spatial scales, to quantify the complex interaction between the two physical signals. The MC-ApEn(LS) parameter could accurately reflect disease process in diabetics and might be another way for assessing the autonomic nerve function.