Dynamical glucometry: use of multiscale entropy analysis in diabetes

The complexity of glucose time series is associated with short- and long-term mortality in critically ill adults: a multi-center, prospective, observational study

BACKGROUND

The wealth of data taken from continuous glucose monitoring (CGM) remains to be fully used. We aimed to evaluate the relationship between a promising new CGM metric, complexity of glucose time series index (CGI), and mortality in critically ill patients.

METHODS

A total of 293 patients admitted to mixed medical/surgical intensive care units from 5 medical centers in Shanghai were prospectively included between May 2020 and November 2021. CGI was assessed using intermittently scanned CGM, with a median monitoring period of 12.0 days. Outcome measures included short- and long-term mortality.

RESULTS

During a median follow-up period of 1.7 years, a total of 139 (47.4%) deaths were identified, of which 73 (24.9%) occurred within the first 30 days after ICU admission, and 103 (35.2%) within 90 days. The multivariable-adjusted HRs for 30-day mortality across ascending tertiles of CGI were 1.00 (reference), 0.68 (95% CI 0.38-1.22) and 0.36 (95% CI 0.19-0.70), respectively. For per 1-SD increase in CGI, the risk of 30-day mortality was decreased by 51% (HR 0.49, 95% CI 0.35-0.69). Further adjustment for HbA1c, mean glucose during hospitalization and glucose variability partially attenuated these associations, although the link between CGI and 30-day mortality remained significant (per 1-SD increase: HR 0.57, 95% CI 0.40-0.83). Similar results were observed when 90-day mortality was considered as the outcome. Furthermore, CGI was also significantly and independently associated with long-term mortality (per 1-SD increase: HR 0.77, 95% CI 0.61-0.97).

CONCLUSIONS

In critically ill patients, CGI is significantly associated with short- and long-term mortality.

Associations between complexity of glucose time series and cognitive function in adults with type 2 diabetes

AIMS

To characterize the comparative contributions of different glycaemic indicators to cognitive dysfunction, and further investigate the associations between the most significant indicator and cognitive function, along with related cerebral alterations.

MATERIALS AND METHODS

We performed a cross-sectional study in 449 subjects with type 2 diabetes who completed continuous glucose monitoring and cognitive assessments. Of these, 139 underwent functional magnetic resonance imaging to evaluate cerebral structure and olfactory neural circuit alterations. Relative weight and Sobol's sensitivity analyses were employed to characterize the comparative contributions of different glycaemic indicators to cognitive dysfunction.

RESULTS

Complexity of glucose time series index (CGI) was found to have a more pronounced association with mild cognitive impairment (MCI) compared to glycated haemoglobin, time in range, and standard deviation. The proportion and multivariable-adjusted odds ratios (ORs) for MCI increased with descending CGI tertile (Tertile 1: reference group [≥4.0]; Tertile 2 [3.6-4.0] OR 1.23, 95% confidence interval [CI] 0.68-2.24; Tertile 3 [<3.6] OR 2.27, 95% CI 1.29-4.00). Decreased CGI was associated with cognitive decline in executive function and attention. Furthermore, individuals with decreased CGI displayed reduced olfactory activation in the left orbitofrontal cortex (OFC) and disrupted functional connectivity between the left OFC and right posterior cingulate gyrus. Mediation analysis demonstrated that the left OFC activation partially mediated the associations between CGI and executive function.

CONCLUSION

Decreased glucose complexity closely relates to cognitive dysfunction and olfactory brain activation abnormalities in diabetes.

Software Packages and Tools for the Analysis of Continuous Glucose Monitoring Data

The advancement of technology in the field of glycemic control has led to the widespread use of continuous glucose monitoring (CGM), which can be nowadays obtained from wearable devices equipped with a minimally invasive sensor, that is, transcutaneous needle type or implantable, and a transmitter that sends information to a receiver or smart device for data storage and display. This work aims to review the currently available software packages and tools for the analysis of CGM data. Based on the purposes of this work, 12 software packages have been identified from the literature, published until December 2021, namely: GlyCulator, EasyGV (Easy Glycemic Variability), CGM-GUIDE^© (Continuous Glucose Monitoring Graphical User Interface for Diabetes Evaluation), GVAP (Glycemic Variability Analyzer Program), Tidepool, CGManalyzer, cgmanalysis, GLU, CGMStatsAnalyser, iglu, rGV, and cgmquantify. Comparison of available software packages and tools has been done in terms of main characteristics (i.e., publication year, presence of a graphical user interface, availability, open-source code, number of citations, programming language, supported devices, supported data format and organization of the data structure, documentation, presence of a toy example, video tutorial, data upload and download, measurement-units conversion), preprocessing procedures, data display options, and computed metrics; also, each of the computed metrics has been analyzed in terms of its adherence to the American Diabetes Association (ADA) 2017 international consensus on CGM data analysis and the ADA 2019 international consensus on time in range. Eventually, the agreement between metrics computed by different software and tools has been investigated. Based on such comparison, usability and complexity of data management, as well as the possibility to perform customized or patients-group analyses, have been discussed by highlighting limitations and strengths, also in relation to possible different user categories (i.e., patients, clinicians, researchers). The information provided could be useful to researchers interested in working in the diabetic research field as to clinicians and endocrinologists who need tools capable of handling CGM data effectively.

Decreasing complexity of glucose time series derived from continuous glucose monitoring is correlated with deteriorating glucose regulation

Most information used to evaluate diabetic statuses is collected at a special time-point, such as taking fasting plasma glucose test and providing a limited view of individual's health and disease risk. As a new parameter for continuously evaluating personal clinical statuses, the newly developed technique "continuous glucose monitoring" (CGM) can characterize glucose dynamics. By calculating the complexity of glucose time series index (CGI) with refined composite multi-scale entropy analysis of the CGM data, the study showed for the first time that the complexity of glucose time series in subjects decreased gradually from normal glucose tolerance to impaired glucose regulation and then to type 2 diabetes (P for trend < 0.01). Furthermore, CGI was significantly associated with various parameters such as insulin sensitivity/secretion (all P < 0.01), and multiple linear stepwise regression showed that the disposition index, which reflects β-cell function after adjusting for insulin sensitivity, was the only independent factor correlated with CGI (P < 0.01). Our findings indicate that the CGI derived from the CGM data may serve as a novel marker to evaluate glucose homeostasis.

Impact of the complexity of glucose time series on all-cause mortality in patients with type 2 diabetes

CONTEXT

Previous studies suggest that the complexity of glucose time series may serve as a novel marker of glucose homeostasis.

OBJECTIVE

We aimed to investigate the relationship between the complexity of glucose time series and all-cause mortality in patients with type 2 diabetes.

METHODS

Prospective data of 6000 adult inpatients with type 2 diabetes from a single center was analyzed. The complexity of glucose time series index (CGI) based on continuous glucose monitoring (CGM) was measured at baseline with refined composite multi-scale entropy. Participants were stratified by the tertiles of CGI: < 2.15, 2.15-2.99, and ≥ 3.00. Cox proportional hazards regression models were used to assess the relationship between CGI and all-cause mortality.

RESULTS

During a median follow-up of 9.4 years, 1217 deaths were identified. A significant interaction between glycated hemoglobin A1c (HbA1c) and CGI in relation to all-cause mortality was noted (P for interaction = 0.016). The multivariable-adjusted hazard ratios for all-cause mortality at different CGI levels [≥ 3.00 (reference group), 2.15-2.99, and < 2.15] were 1.00, 0.76 (95% CI 0.52-1.12), and 1.47 (95% CI 1.03-2.09) in patients with HbA1c < 7.0%, while the association was nonsignificant in those with HbA1c ≥ 7.0%. The restricted cubic spline regression revealed a non-linear (P for non-linearity = 0.041) relationship between CGI and all-cause mortality in subjects with HbA1c < 7.0% only.

CONCLUSIONS

Lower CGI is associated with an increased risk of all-cause mortality among patients with type 2 diabetes achieving the HbA1c target. CGI may be a new indicator for the identification of residual risk of death in well-controlled type 2 diabetes.

Next-Generation Personalized Medicine: Implementation of Variability Patterns for Overcoming Drug Resistance in Chronic Diseases

Chronic diseases are a significant healthcare problem. Partial or complete non-responsiveness to chronic therapies is a significant obstacle to maintaining the long-term effect of drugs in these patients. A high degree of intra- and inter-patient variability defines pharmacodynamics, drug metabolism, and medication response. This variability is associated with partial or complete loss of drug effectiveness. Regular drug dosing schedules do not comply with physiological variability and contribute to resistance to chronic therapies. In this review, we describe a three-phase platform for overcoming drug resistance: introducing irregularity for improving drug response; establishing a deep learning, closed-loop algorithm for generating a personalized pattern of irregularity for overcoming drug resistance; and upscaling the algorithm by implementing quantified personal variability patterns along with other individualized genetic and proteomic-based ways. The closed-loop, dynamic, subject-tailored variability-based machinery can improve the efficacy of existing therapies in patients with chronic diseases.

Glycaemia dynamics in gestational diabetes mellitus

Pregnant women may develop gestational diabetes mellitus (GDM), a disease of pregnancy characterised by maternal and fetal hyperglycaemia with hazardous consequences to the mother, the fetus, and the newborn. Maternal hyperglycaemia in GDM results in fetoplacental endothelial dysfunction. GDM-harmful effects result from chronic and short periods of hyperglycaemia. Thus, it is determinant to keep glycaemia within physiological ranges avoiding short but repetitive periods of hyper or hypoglycaemia. The variation of glycaemia over time is defined as 'glycaemia dynamics'. The latter concept regards with a variety of mechanisms and environmental conditions leading to blood glucose handling. In this review we summarized the different metrics for glycaemia dynamics derived from quantitative, plane distribution, amplitude, score values, variability estimation, and time series analysis. The potential application of the derived metrics from self-monitoring of blood glucose (SMBG) and continuous glucose monitoring (CGM) in the potential alterations of pregnancy outcome in GDM are discussed.

A Subject-Tailored Variability-Based Platform for Overcoming the Plateau Effect in Sports Training: A Narrative Review

The plateau effect in training is a significant obstacle for professional athletes and average subjects. It evolves from both the muscle-nerve-axis-associated performance and various cardiorespiratory parameters. Compensatory adaptation mechanisms contribute to a lack of continuous improvement with most exercise regimens. Attempts to overcome this plateau in exercise have been only partially successful, and it remains a significant unmet need in both healthy subjects and those suffering from chronic neuromuscular, cardiopulmonary, and metabolic diseases. Variability patterns characterize many biological processes, from cellular to organ levels. The present review discusses the significant obstacles in overcoming the plateau in training and establishes a platform to implement subject-tailored variability patterns to prevent and overcome this plateau in muscle and cardiorespiratory performance.

A Review of the Serrated-Flow Phenomenon and Its Role in the Deformation Behavior of High-Entropy Alloys

High-entropy alloys (HEAs) are a novel class of alloys that have many desirable properties. The serrated flow that occurs in high-entropy alloys during mechanical deformation is an important phenomenon since it can lead to significant changes in the microstructure of the alloy. In this article, we review the recent findings on the serration behavior in a variety of high-entropy alloys. Relationships among the serrated flow behavior, composition, microstructure, and testing condition are explored. Importantly, the mechanical-testing type (compression/tension), testing temperature, applied strain rate, and serration type for certain high-entropy alloys are summarized. The literature reveals that the serrated flow can be affected by experimental conditions such as the strain rate and test temperature. Furthermore, this type of phenomenon has been successfully modeled and analyzed, using several different types of analytical methods, including the mean-field theory formalism and the complexity-analysis technique. Importantly, the results of the analyses show that the serrated flow in HEAs consists of complex dynamical behavior. It is anticipated that this review will provide some useful and clarifying information regarding the serrated-flow mechanisms in this material system. Finally, suggestions for future research directions in this field are proposed, such as the effects of irradiation, additives (such as C and Al), the presence of nanoparticles, and twinning on the serrated flow behavior in HEAs.

Suppressing the Influence of Ectopic Beats by Applying a Physical Threshold-Based Sample Entropy

Sample entropy (SampEn) is widely used for electrocardiogram (ECG) signal analysis to quantify the inherent complexity or regularity of RR interval time series (i.e., heart rate variability (HRV)), with the hypothesis that RR interval time series in pathological conditions output lower SampEn values. However, ectopic beats can significantly influence the entropy values, resulting in difficulty in distinguishing the pathological situation from normal situations. Although a theoretical operation is to exclude the ectopic intervals during HRV analysis, it is not easy to identify all of them in practice, especially for the dynamic ECG signal. Thus, it is important to suppress the influence of ectopic beats on entropy results, i.e., to improve the robustness and stability of entropy measurement for ectopic beats-inserted RR interval time series. In this study, we introduced a physical threshold-based SampEn method, and tested its ability to suppress the influence of ectopic beats for HRV analysis. An experiment on the PhysioNet/MIT RR Interval Databases showed that the SampEn use physical meaning threshold has better performance not only for different data types (normal sinus rhythm (NSR) or congestive heart failure (CHF) recordings), but also for different types of ectopic beat (atrial beats, ventricular beats or both), indicating that using a physical meaning threshold makes SampEn become more consistent and stable.

Dynamic properties of glucose complexity during the course of critical illness: a pilot study

Methods to control the blood glucose (BG) levels of patients in intensive care units (ICU) improve the outcomes. The development of continuous BG levels monitoring devices has also permitted to optimize these processes. Recently it was shown that a complexity loss of the BG signal is linked to poor clinical outcomes. Thus, it becomes essential to decipher this relation to design efficient BG level control methods. In previous studies the BG signal complexity was calculated as a single index for the whole ICU stay. Although, these approaches did not grasp the potential variability of the BG signal complexity. Therefore, we setup this pilot study using a continuous monitoring of central venous BG levels in ten critically ill patients (EIRUS platform, Maquet Critical CARE AB, Solna, Sweden). Data were processed and the complexity was assessed by the detrended fluctuation analysis and multiscale entropy (MSE) methods. Finally, recordings were split into 24 h overlapping intervals and a MSE analysis was applied to each of them. The MSE analysis on time intervals revealed an entropy variation and allowed periodic BG signal complexity assessments. To highlight differences of MSE between each time interval we calculated the MSE complexity index defined as the area under the curve. This new approach could pave the way to future studies exploring new strategies aimed at restoring blood glucose complexity during the ICU stay.

Detrended Fluctuation Analysis in the prediction of type 2 diabetes mellitus in patients at risk: Model optimization and comparison with other metrics

Complexity analysis of glucose time series with Detrended Fluctuation Analysis (DFA) has been proved to be useful for the prediction of type 2 diabetes mellitus (T2DM) development. We propose a modified DFA algorithm, review some of its characteristics and compare it with other metrics derived from continuous glucose monitorization in this setting. Several issues of the DFA algorithm were evaluated: (1) Time windowing: the best predictive value was obtained including all time-windows from 15 minutes to 24 hours. (2) Influence of circadian rhythms: for 48-hour glucometries, DFA alpha scaling exponent was calculated on 24-hour sliding segments (1-hour gap, 23-hour overlap), with a median coefficient of variation of 3.2%, which suggests that analysing time series of at least 24-hour length avoids the influence of circadian rhythms. (3) Influence of pretreatment of the time series through integration: DFA without integration was more sensitive to the introduction of white noise and it showed significant predictive power to forecast the development of T2DM, while the pretreated time series did not. (4) Robustness of an interpolation algorithm for missing values: The modified DFA algorithm evaluates the percentage of missing values in a time series. Establishing a 2% error threshold, we estimated the number and length of missing segments that could be admitted to consider a time series as suitable for DFA analysis. For comparison with other metrics, a Principal Component Analysis was performed and the results neatly tease out four different components. The first vector carries information concerned with variability, the second represents mainly DFA alpha exponent, while the third and fourth vectors carry essentially information related to the two “pre-diabetic behaviours” (impaired fasting glucose and impaired glucose tolerance). The scaling exponent obtained with the modified DFA algorithm proposed has significant predictive power for the development of T2DM in a high-risk population compared with other variability metrics or with the standard DFA algorithm.

A Personalized Signature and Chronotherapy-Based Platform for Improving the Efficacy of Sepsis Treatment

Sepsis remains a major therapeutic challenge and is associated with a high rate of morbidity and mortality. It is a dynamic condition in which multiple parameters change over time, rendering it difficult to overcome the various injurious responses, which worsen the prognosis in these patients. The prognosis of sepsis is associated with a disbalance of compensatory responses to infectious triggers, part of which can be deleterious. Marked inter- and intra-patient variability characterizes the mechanisms that underlie sepsis progression and determine the response to therapy. In this paper, we review some of the data on the use of chronopharmacological approaches for the treatment of patients with sepsis and discuss the role of the autonomic nervous system in the mechanisms associated with immune response and chronotherapy in these patients. We describe the implementation of an individualized platform that is based on the personalized autonomic nervous system, immune, and chronobiology-derived parameters for generating a patient-tailored therapeutic regimen. The notion of overcoming the deleterious compensatory response in a highly dynamic system in sepsis is presented to ensure an improved response to current therapies.

Performance, complexity and dynamics of force maintenance and modulation in young and older adults

The present study addresses how task constraints and aging influence isometric force control. We used two tasks requiring either force maintenance (straight line target force) or force modulation (sine-wave target force) around different force levels and at different modulation frequencies. Force levels were defined relative the individual maximum voluntary contraction. A group of young adults (mean age ± SD = 25 ± 3.6 years) and a group of elderly (mean age = 77 ± 6.4 years) took part in the study. Age- and task-related effects were assessed through differences in: (i) force control accuracy, (ii) time-structure of force fluctuations, and (iii) the contribution of deterministic (predictable) and stochastic (noise-like) dynamic components to the expressed behavior. Performance-wise, the elderly showed a pervasive lower accuracy and higher variability than the young participants. The analysis of fluctuations showed that the elderly produced force signals that were less complex than those of the young adults during the maintenance task, but the reverse was observed in the modulation task. Behavioral complexity results suggest a reduced adaptability to task-constraints with advanced age. Regarding the dynamics, we found comparable generating mechanisms in both age groups for both tasks and in all conditions, namely a fixed-point for force maintenance and a limit-cycle for force modulation. However, aging increased the stochasticity (noise-driven fluctuations) of force fluctuations in the cyclic force modulation, which could be related to the increased complexity found in elderly for this same task. To our knowledge this is the first time that these different perspectives to motor control are used simultaneously to characterize force control capacities. Our findings show their complementarity in revealing distinct aspects of sensorimotor adaptation to task constraints and age-related declines. Although further research is still needed to identify the physiological underpinnings, the used task and methodology are shown to have both fundamental and clinical applications.

Analyzing Complexity and Fractality of Glucose Dynamics in a Pregnant Woman with Type 2 Diabetes under Treatment

Currently, the rapid development of continuous glucose monitoring (CGM) device brings new insights into the treatment of diabetic patients including those during pregnancy. Complexity and fractality have recently under fast development for extracting information embodied in glucose dynamics measured using CGM. Although scientists have investigated the difference of complexity in glucose dynamics between diabetes and non-diabetes in order to discover better approaches for diabetes care, no one has analyzed the complexity and fractality of glucose dynamics during the process of adopting CGM to successfully treat pregnant women with type 2 diabetes. Thus, we analyzed the complexity and fractality using power spectral density (PSD), multi-scale sample entropy (MSE) and multifractal detrended fluctuation analysis (MF-DFA) in a clinical case. Our results show that (i) there exists multifractal behavior in blood glucose dynamics; (ii) the alpha stable distribution fits to the glucose increment data better than the Gaussian distribution; and (iii) the "global" complexity indicated by multiscale entropy, spectrum exponent and Hurst exponent increase and the "local" complexity indicated by multifractal spectrum decrease after the successful therapy. Our results offer findings that may bring value to health care providers for managing glucose levels of pregnant women with type 2 diabetes as well as provide scientists a reference on applying complexity and fractality in the clinical practice of treating diabetes.

Heart rate fragmentation: using cardiac pacemaker dynamics to probe the pace of biological aging

This perspectives article discusses the use of a novel set of dynamical biomarkers in the assessment of biological versus chronological age. The basis for this development is a recently delineated property of altered sinoatrial pacemaker-neuroautonomic function, termed heart rate fragmentation (HRF). Fragmented rhythms manifest as an increase in the density of changes in heart rate acceleration sign, not mechanistically explicable by physiological cardiac vagal tone modulation. We reported that HRF increased monotonically with cross-sectional age and that HRF measures, but not conventional heart rate variability metrics, were significantly associated with major incident cardiovascular events in the Multi-Ethnic Study of Atherosclerosis (MESA). Furthermore, HRF measures added value to both Framingham and MESA cardiovascular risk indices. Here, we propose that interventions that fundamentally slow or reverse the pace of biological aging, via system-wide effects, should be associated with a decrease in the degree of HRF and possibly with a reemergence of the nonfragmented ("fluent") patterns associated with more youthful heart rate dynamics.

Decreased complexity of glucose dynamics in diabetes in rhesus monkeys

Until recently, preclinical and clinical work on diabetes has focused on the understanding of blood glucose elevation and its detrimental metabolic sequelae. The advent of continuous glucose monitoring (CGM) technology now allows real time monitoring of blood glucose levels as a time series, and thus the exploration of glucose dynamics at short time scales. Previous work has shown decreases in the complexity of glucose dynamics, as measured by multiscale entropy (MSE) analysis, in diabetes in humans, mice, and rats. Analyses for non-human primates (NHP) have not been reported, nor is it known if anti-diabetes compounds affect complexity of glucose dynamics. We instrumented four healthy and six diabetic rhesus monkeys with CGM probes in the carotid artery and collected glucose values at a frequency of one data point per second for the duration of the sensors' life span. Sensors lasted between 45 and 78 days. Five of the diabetic rhesus monkeys were also administered the anti-diabetic drug liraglutide daily beginning at day 39 of the CGM monitoring period. Glucose levels fluctuated during the day in both healthy and diabetic rhesus monkeys, peaking between 12 noon - 6 pm. MSE analysis showed reduced complexity of glucose dynamics in diabetic monkeys compared to healthy animals. Although liraglutide decreased glucose levels, it did not restore complexity in diabetic monkeys consistently. Complexity varied by time of day, more strongly for healthy animals than for diabetic animals. And by dividing the monitoring period into 3-day or 1-week subperiods, we were able to estimate within-animal variability of MSE curves. Our data reveal that decreased complexity of glucose dynamics is a conserved feature of diabetes from rodents to NHPs to man.

Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm

BACKGROUND AND OBJECTIVES

The adoption in clinical practice of electronic portable blood or interstitial glucose monitors has enabled the collection, storage, and sharing of massive amounts of glucose level readings. This availability of data opened the door to the application of a multitude of mathematical methods to extract clinical information not discernible with conventional visual inspection. The objective of this study is to assess the capability of Permutation Entropy (PE) to find differences between glucose records of healthy and potentially diabetic subjects.

METHODS

PE is a mathematical method based on the relative frequency analysis of ordinal patterns in time series that has gained a lot of attention in the last years due to its simplicity, robustness, and performance. We study in this paper the applicability of this method to glucose records of subjects at risk of diabetes in order to assess the predictability value of this metric in this context.

RESULTS

PE, along with some of its derivatives, was able to find significant differences between diabetic and non-diabetic patients from records acquired up to 3 years before the diagnosis. The quantitative results for PE were 3.5878 ± 0.3916 for the nondiabetic class, and 3.1564 ± 0.4166 for the diabetic class. With a classification accuracy higher than 70%, and by means of a Cox regression model, PE demonstrated that it is a very promising candidate as a risk stratification tool for continuous glucose monitoring.

CONCLUSION

PE can be considered as a prospective tool for the early diagnosis of the glucoregulatory system.

Applications of Variability Analysis Techniques for Continuous Glucose Monitoring Derived Time Series in Diabetic Patients

Methods from non-linear dynamics have enhanced understanding of functional dysregulation in various diseases but received less attention in diabetes. This retrospective cross-sectional study evaluates and compares relationships between indices of non-linear dynamics and traditional glycemic variability, and their potential application in diabetes control. Continuous glucose monitoring provided data for 177 subjects with type 1 (n = 22), type 2 diabetes (n = 143), and 12 non-diabetic subjects. Each time series comprised 576 glucose values. We calculated Poincaré plot measures (SD1, SD2), shape (SFE) and area of the fitting ellipse (AFE), multiscale entropy (MSE) index, and detrended fluctuation exponents (α1, α2). The glycemic variability metrics were the coefficient of variation (%CV) and standard deviation. Time of glucose readings in the target range (TIR) defined the quality of glycemic control. The Poincaré plot indices and α exponents were higher (p < 0.05) in type 1 than in the type 2 diabetes; SD1 (mmol/l): 1.64 ± 0.39 vs. 0.94 ± 0.35, SD2 (mmol/l): 4.06 ± 0.99 vs. 2.12 ± 1.04, AFE (mmol²/l²): 21.71 ± 9.82 vs. 7.25 ± 5.92, and α1: 1.94 ± 0.12 vs. 1.75 ± 0.12, α2: 1.38 ± 0.11 vs. 1.30 ± 0.15. The MSE index decreased consistently from the non-diabetic to the type 1 diabetic group (5.31 ± 1.10 vs. 3.29 ± 0.83, p < 0.001); higher indices correlated with lower %CV values (r = -0.313, p < 0.001). In a subgroup of type 1 diabetes patients, insulin pump therapy significantly decreased SD1 (-0.85 mmol/l), SD2 (-1.90 mmol/l), and AFE (-16.59 mmol²/l²), concomitantly with %CV (-15.60). The MSE index declined from 3.09 ± 0.94 to 1.93 ± 0.40 (p = 0.001), whereas the exponents α1 and α2 did not. On multivariate regression analyses, SD1, SD2, SFE, and AFE emerged as dominant predictors of TIR (β = -0.78, -1.00, -0.29, and -0.58) but %CV as a minor one, though α1 and MSE failed. In the regression models, including SFE, AFE, and α2 (β = -0.32), %CV was not a significant predictor. Poincaré plot descriptors provide additional information to conventional variability metrics and may complement assessment of glycemia, but complexity measures produce mixed results.

Heart Rate Fragmentation as a Novel Biomarker of Adverse Cardiovascular Events: The Multi-Ethnic Study of Atherosclerosis

Background: A major objective of precision medicine is the elucidation of non-invasive biomarkers of cardiovascular (CV) risk. Recently, we introduced a new dynamical marker of sino-atrial instability, termed heart rate fragmentation (HRF), which outperformed traditional and nonlinear heart rate variability metrics in separating ostensibly healthy subjects from patients with coronary artery disease. Accordingly, we hypothesized that HRF may be a dynamical biomarker of adverse cardiovascular events (CVEs). Methods: This study employed data from a cohort of participants in the Multi-Ethnic Study of Atherosclerosis (MESA), a prospective study of sub-clinical heart disease. Interbeat interval time series (n = 1963), derived from the electrocardiographic channel of the polysomnogram study, were analyzed using the newly introduced metrics of fragmentation, as well as traditional heart rate variability (HRV) indices and the short-term detrended fluctuation analysis exponent. Cox regression analysis was used to assess the association between HR dynamic indices and CV outcomes in unadjusted and adjusted models. Results: The mean (± SD) follow-up time was 2.97 ± 0.63 years. In adjusted models, higher fragmentation was significantly associated with incident CVEs (number of events; hazard ratio [95% confidence interval]: n = 72, 1.43 [1.16-1.76]) and CV death (n = 21; 1.65 [1.15-2.36]). The traditional HRV and the fractal indices were not associated with CVEs or CV death. The most discriminatory fragmentation indices added significant value to Framingham and MESA CV risk indices in all analyses. Conclusion: Our findings show that HRF has promise as a non-invasive, automatable biomarker of CV risk. The basic mechanisms underlying fragmentation remain to be delineated. Its association with incident outcomes raises the possibility of connections to degenerative changes in the multisystem network controlling SAN function.

Glucose Variability: A Review of Clinical Applications and Research Developments

Glycemic variability (GV) is a major consideration when evaluating quality of glycemic control. GV increases progressively from prediabetes through advanced T2D and is still higher in T1D. GV is correlated with risk of hypoglycemia. The most popular metrics for GV are the %Coefficient of Variation (%CV) and standard deviation (SD). The %CV is correlated with risk of hypoglycemia. Graphical display of glucose by date, time of day, and day of the week, and display of simplified glucose distributions showing % of time in several ranges, provide clinically useful indicators of GV. SD is highly correlated with most other measures of GV, including interquartile range, mean amplitude of glycemic excursion, mean of daily differences, and average daily risk range. Some metrics are sensitive to the frequency, periodicity, and complexity of glycemic fluctuations, including Fourier analysis, periodograms, frequency spectrum, multiscale entropy (MSE), and Glucose Variability Percentage (GVP). Fourier analysis indicates progressive changes from normal subjects to children and adults with T1D, and from prediabetes to T2D. The GVP identifies novel characteristics for children, adolescents, and adults with type 1 diabetes and for adults with type 2. GVP also demonstrated small rapid glycemic fluctuations in people with T1D when using a dual-hormone closed-loop control. MSE demonstrated systematic changes from normal subjects to people with T2D at various stages of duration, intensity of therapy, and quality of glycemic control. We describe new metrics to characterize postprandial excursions, day-to-day stability of glucose patterns, and systematic changes of patterns by day of the week. Metrics for GV should be interpreted in terms of percentiles and z-scores relative to identified reference populations. There is a need for large accessible databases for reference populations to provide a basis for automated interpretation of GV and other features of continuous glucose monitoring records.

Associations of blood glucose dynamics with antihyperglycemic treatment and glycemic variability in type 1 and type 2 diabetes

AIMS

The dynamical structure of glucose fluctuation has largely been disregarded in the contemporary management of diabetes.

METHODS

In a retrospective study of patients with diabetes, we evaluated the relationship between glucose dynamics, antihyperglycemic therapy, glucose variability, and glucose exposure, while taking into account potential determinants of the complexity index. We used multiscale entropy (MSE) analysis of continuous glucose monitoring data from 131 subjects with type 1 (n = 18), type 2 diabetes (n = 102), and 11 nondiabetic control subjects. We compared the MSE complexity index derived from the glucose time series among the treatment groups, after adjusting for sex, age, diabetes duration, body mass index, and carbohydrate intake.

RESULTS

In type 2 diabetic patients who were on a diet or insulin regimen with/without oral agents, the MSE index was significantly lower than in nondiabetic subjects but was lowest in the type 1 diabetes group (p < 0.001). The decline in the MSE complexity across the treatment groups correlated with increasing glucose variability and glucose exposure. Statistically, significant correlations existed between higher MSE complexity indices and better glycemic control. In multivariate regression analysis, the antidiabetic therapy was the most powerful predictor of the MSE (β = -0.940 ± 0.242, R ² = 0.306, p < 0.001), whereas the potential confounders failed to contribute.

CONCLUSIONS

The loss of dynamical complexity in glucose homeostasis correlates more closely with therapy modalities and glucose variability than with clinical measures of glycemia. Thus, targeting the glucoregulatory system by adequate therapeutic interventions may protect against progressive worsening of diabetes control.

Temporal Analysis of Cardiovascular and Respiratory Complexity by Multiscale Entropy Based on Symbolic Dynamics

The effect of an orthostatic stress on cardiovascular and respiratory complexity was investigated to detect impaired autonomic regulation in patients with vasovagal syncope (VVS). A total of 16 female patients and 12 age-matched healthy female subjects were enrolled in a passive 70° head-up tilt test. Also, 12 age-matched healthy male subjects were enrolled to study gender differences. Analysis was performed dynamically using various short-term (5 min) windows shifted by 1 min as well as by 20 min of orthostatic phase (OP) to evaluate local and global complexity. Complexity was determined over multiple time scales by the established method of refined composite multiscale entropy (RCMSE) and by a new proposed method of multiscale entropy based on symbolic dynamics (MSE-SD). Concerning heart rate variability (HRV) during OP, both methods revealed the highest complexity for female controls followed by lower complexity in male controls (p < 0.01) and by the lowest complexity in female patients (p < 0.01). For blood pressure variability (BPV), no gender differences in controls were shown by any method. However, MSE-SD demonstrated highly significantly increased BPV complexity in patients during OP (p < 0.01 on 4 time-scales after 7 min, p < 0.001 on 5 time-scales after 11 min) while RCMSE did not reveal considerable differences (p < 0.05 on 2 time scales after 7 min). Respiratory complexity was further increased in patients primary shown by MSE-SD. Findings indicated impaired autonomic regulation in VVS patients characterized by predominantly increased BPV complexity accompanied with decreased HRV complexity. In addition, results suggested extending the concept of complexity loss with disease.

Decreased complexity of glucose dynamics preceding the onset of diabetes in mice and rats

Continuous glucose monitoring (CGM) is a platform to measure blood glucose (BG) levels continuously in real time with high enough resolution to document their underlying fluctuations. Multiscale entropy (MSE) analysis has been proposed as a measure of time-series complexity, and when applied to clinical CGM data, MSE analysis revealed that diabetic patients have lower MSE complexity in their BG time series than healthy subjects. To determine if the clinical observations on complexity of glucose dynamics can be back-translated to relevant preclinical species used routinely in diabetes drug discovery, we performed CGM in both mouse (ob/ob) and rat (Zucker Diabetic Fatty, ZDF) models of diabetes. We demonstrate that similar to human data, the complexity of glucose dynamics is also decreased in diabetic mice and rats. We show that low complexity of glucose dynamics is not simply a reflection of high glucose values, but rather reflective of the underlying disease state (i.e. diabetes). Finally, we demonstrate for the first time that the complexity of glucose fluctuations in ZDF rats, as probed by MSE analysis, is decreased prior to the onset of overt diabetes, although complexity undergoes further decline during the transition to frank diabetes. Our study suggests that MSE could serve as a novel biomarker for the progression to diabetes and that complexity studies in preclinical models could offer a new paradigm for early differentiation, and thereby, selection of appropriate clinical candidate molecules to be tested in human clinical trials.

Investigation of glucose fluctuations by approaches of multi-scale analysis

Glucose variability provides detailed information on glucose control and fluctuation. The aim of this study is to investigate the glucose variability by multi-scale analysis approach on 72-h glucose series captured by continuous glucose monitoring system (CGMS), gaining insights into the variability and complexity of the glucose time series data. Ninety-eight type 2 DM patients participated in this study, and 72-h glucose series from each subject were recorded by CGMS. Subjects were divided into two subgroups according to the mean amplitude of glycemic excursions (MAGE) value threshold at 3.9 based on Chinese standard. In this study, we applied two types of multiple scales analysis methods on glucose time series: ensemble empirical mode decomposition (EEMD) and refined composite multi-scale entropy (RCMSE). With EEMD, glucose series was decomposed into several intrinsic mode function (IMF), and glucose variability was examined on multiple time scales with periods ranging from 0.5 to 12 h. With RCMSE, complexity of the structure of glucose series was quantified at each time scale ranging from 5 to 30 min. Subgroup with higher MAGE value (>3.9) presented higher glycemic baseline and variability. There were significant differences in glycemic variability on IMFs3-5 between subgroups with MAGE>3.9 and MAGE < = 3.9 (p<0.001), but no significant differences in variability on IMFs1-2. The complexity of glucose series quantified by RCMSE showed statistically difference on each time scale from 5 to 30 min between subgroups (p<0.05). Glucose series from subjects with higher MAGE value represented higher variability but lower complexity on multiple time scales. Compared with traditional matrices measuring the glucose variability, approaches of EEMD and RCMSE can quantify the dynamic glycemic fluctuation in multiple time scales and provide us more detailed information on glycemic variability and complexity.

Metrics for glycaemic control - from HbA1c to continuous glucose monitoring

As intensive treatment to lower levels of HbA_1c characteristically results in an increased risk of hypoglycaemia, patients with diabetes mellitus face a life-long optimization problem to reduce average levels of glycaemia and postprandial hyperglycaemia while simultaneously avoiding hypoglycaemia. This optimization can only be achieved in the context of lowering glucose variability. In this Review, I discuss topics that are related to the assessment, quantification and optimal control of glucose fluctuations in diabetes mellitus. I focus on markers of average glycaemia and the utility and/or shortcomings of HbA_1c as a 'gold-standard' metric of glycaemic control; the notion that glucose variability is characterized by two principal dimensions, amplitude and time; measures of glucose variability that are based on either self-monitoring of blood glucose data or continuous glucose monitoring (CGM); and the control of average glycaemia and glucose variability through the use of pharmacological agents or closed-loop control systems commonly referred to as the 'artificial pancreas'. I conclude that HbA_1c and the various available metrics of glucose variability reflect the management of diabetes mellitus on different timescales, ranging from months (for HbA_1c) to minutes (for CGM). Comprehensive assessment of the dynamics of glycaemic fluctuations is therefore crucial for providing accurate and complete information to the patient, physician, automated decision-support or artificial-pancreas system.

Glucose time series complexity as a predictor of type 2 diabetes

BACKGROUND

Complexity analysis of glucose profile may provide valuable information about the gluco-regulatory system. We hypothesized that a complexity metric (detrended fluctuation analysis, DFA) may have a prognostic value for the development of type 2 diabetes in patients at risk.

METHODS

A total of 206 patients with any of the following risk factors (1) essential hypertension, (2) obesity or (3) a first-degree relative with a diagnosis of diabetes were included in a survival analysis study for a diagnosis of new onset type 2 diabetes. At inclusion, a glucometry by means of a Continuous Glucose Monitoring System was performed, and DFA was calculated for a 24-h glucose time series. Patients were then followed up every 6 months, controlling for the development of diabetes.

RESULTS

In a median follow-up of 18 months, there were 18 new cases of diabetes (58.5 cases/1000 patient-years). DFA was a significant predictor for the development of diabetes, with ten events in the highest quartile versus one in the lowest (log-rank test chi2 = 9, df = 1, p = 0.003), even after adjusting for other relevant clinical and biochemical variables. In a Cox model, the risk of diabetes development increased 2.8 times for every 0.1 DFA units. In a multivariate analysis, only fasting glucose, HbA_1c and DFA emerged as significant factors.

CONCLUSIONS

Detrended fluctuation analysis significantly performed as a harbinger of type 2 diabetes development in a high-risk population. Complexity analysis may help in targeting patients who could be candidates for intensified treatment. Copyright © 2016 The Authors. Diabetes/Metabolism Research and Reviews Published by John Wiley & Sons Ltd.

Sublimation-like Behavior of Cardiac Dynamics in Heart Failure: A Malignant Phase Transition?

An abrupt transition from sinus cardiac rhythm to atrial fibrillation (AF) is common in patients with chronic heart failure (CHF). We propose a conceptual framework for viewing this malignant transition in terms of a type of sublimation marked by the switch from highly periodic sinus interbeat interval dynamics characteristic of CHF to a state of random disorganization with AF. Sublimation of physical substances involves an increase in entropy via heat transfer. In contrast, the disease-related sublimation-like behavior involves a loss of information content, associated decreases in cardiac bioenergetic capacity and in multiscale entropy.

Delay in the Detrended Fluctuation Analysis Crossover Point as a Risk Factor for Type 2 Diabetes Mellitus

Detrended Fluctuation Analysis (DFA) measures the complexity of a glucose time series obtained by means of a Continuous Glucose Monitoring System (CGMS) and has proven to be a sensitive marker of glucoregulatory dysfunction. Furthermore, some authors have observed a crossover point in the DFA, signalling a change of dynamics, arguably dependent on the beta-insular function. We investigate whether the characteristics of this crossover point have any influence on the risk of developing type 2 diabetes mellitus (T2DM). To this end we recruited 206 patients at increased risk of T2DM (because of obesity, essential hypertension, or a first-degree relative with T2DM). A CGMS time series was obtained, from which the DFA and the crossover point were calculated. Patients were then followed up every 6 months for a mean of 17.5 months, controlling for the appearance of T2DM diagnostic criteria. The time to crossover point was a significant predictor risk of developing T2DM, even after adjusting for other variables. The angle of the crossover was not predictive by itself but became significantly protective when the model also considered the crossover point. In summary, both a delay and a blunting of the crossover point predict the development of T2DM.

Dynamical disease: Challenges for nonlinear dynamics and medicine

Dynamical disease refers to illnesses that are associated with striking changes in the dynamics of some bodily function. There is a large literature in mathematics and physics which proposes mathematical models for the physiological systems and carries out analyses of the properties of these models using nonlinear dynamics concepts involving analyses of the stability and bifurcations of attractors. This paper discusses how these concepts can be applied to medicine.

Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series

We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSE_n, where the subscript denotes the moment used to coarse-grain a time series. MSE_μ, described previously, uses the mean value (first moment). Here, we focus on MSEσ2, which uses the second moment, i.e., the variance. MSEσ2 quantifies the dynamics of the volatility (variance) of a signal over multiple time scales. We use the method to analyze the structure of heartbeat time series. We find that the dynamics of the volatility of heartbeat time series obtained from healthy young subjects is highly complex. Furthermore, we find that the multiscale complexity of the volatility, not only the multiscale complexity of the mean heart rate, degrades with aging and pathology. The “bursty” behavior of the dynamics may be related to intermittency in energy and information flows, as part of multiscale cycles of activation and recovery. Generalized MSE may also be useful in quantifying the dynamical properties of other physiologic and of non-physiologic time series.

Asymmetric asynchrony of financial time series based on asymmetric multiscale cross-sample entropy

The paper proposes the asymmetric multiscale cross-sample entropy (AMCSE) method and applies it to analyze the financial time series of US, Chinese, and European stock markets. The asynchronies of these time series in USA, China, and Europe all decrease (the correlations increase) with the increase in scale which declares that taking into account bigger time scale to study these financial time series is capable of revealing the intrinsic relations between these stock markets. Meanwhile, we find that there is a crossover between the upwards and the downwards in these AMCSE results, which indicates that when the scale reach a certain value, the asynchronies of the upwards and the downwards for these stock markets are equal and symmetric. But for the other scales, the asynchronies of the upwards and the downwards are different from each other indicating the necessity and importance of multiscale analysis for revealing the most comprehensive information of stock markets. The series with a positive trend have a higher decreasing pace on asynchrony than those with a negative trend, while the asynchrony between the series with a positive or negative trend is lower than that between the original series. Moreover, it is noticeable that there are some small abnormal rises at some abnormal scales. We find that the asynchronies are the highest at scales smaller than 2 when investigating the time series of stock markets with a negative trend. The existences of asymmetries declare the inaccuracy and weakness of multiscale cross-sample entropy, while by comparing the asymmetries of US, Chinese, and European markets, similar conclusions can be drawn and we acquire that the asymmetries of Chinese markets are the smallest and the asymmetries of European markets are the biggest. Thus, it is of great value and benefit to investigate the series with different trends using AMCSE method.

Rethinking energy in parkinsonian motor symptoms: a potential role for neural metabolic deficits

Parkinson’s disease (PD) is characterized as a chronic and progressive neurodegenerative disorder that results in a variety of debilitating symptoms, including bradykinesia, resting tremor, rigidity, and postural instability. Research spanning several decades has emphasized basal ganglia dysfunction, predominantly resulting from dopaminergic (DA) cell loss, as the primarily cause of the aforementioned parkinsonian features. But, why those particular features manifest themselves remains an enigma. The goal of this paper is to develop a theoretical framework that parkinsonian motor features are behavioral consequence of a long-term adaptation to their inability (inflexibility or lack of capacity) to meet energetic demands, due to neural metabolic deficits arising from mitochondrial dysfunction associated with PD. Here, we discuss neurophysiological changes that are generally associated with PD, such as selective degeneration of DA neurons in the substantia nigra pars compacta (SNc), in conjunction with metabolic and mitochondrial dysfunction. We then characterize the cardinal motor symptoms of PD, bradykinesia, resting tremor, rigidity and gait disturbance, reviewing literature to demonstrate how these motor patterns are actually energy efficient from a metabolic perspective. We will also develop three testable hypotheses: (1) neural metabolic deficits precede the increased rate of neurodegeneration and onset of behavioral symptoms in PD; (2) motor behavior of persons with PD are more sensitive to changes in metabolic/bioenergetic state; and (3) improvement of metabolic function could lead to better motor performance in persons with PD. These hypotheses are designed to introduce a novel viewpoint that can elucidate the connections between metabolic, neural and motor function in PD.