Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

A Minimal Model Approach for the Description of Postprandial Glucose Responses from Glucose Sensor Data in Diabetes Mellitus

Modelling of the gluco-regulatory system in response to an oral glucose tolerance test (OGTT) has been the subject of research for decades. This paper presents an adaptation to the well-established oral minimal model that is identifiable from glucose data only and is able to capture the dynamics of glucose following both OGTT and mixed meal consumption. The model is in the form of low-dimensional differential equations with a recently introduced input function consisting of Gaussian shaped components. It was identified from glucose data recorded from six subjects without diabetes, prediabetes and type 2 diabetes under controlled conditions. The inferred parameters of the model are shown to have physiological meaning and produce realistic steady state behavior. This model may be useful in the development of clinical advisory tools for the treatment and prevention of non-insulin dependent type 2 diabetes mellitus.

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.

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.

A data driven nonlinear stochastic model for blood glucose dynamics

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.

Utility of different glycemic control metrics for optimizing management of diabetes

The benchmark for assessing quality of long-term glycemic control and adjustment of therapy is currently glycated hemoglobin (HbA1c). Despite its importance as an indicator for the development of diabetic complications, recent studies have revealed that this metric has some limitations; it conveys a rather complex message, which has to be taken into consideration for diabetes screening and treatment. On the basis of recent clinical trials, the relationship between HbA1c and cardiovascular outcomes in long-standing diabetes has been called into question. It becomes obvious that other surrogate and biomarkers are needed to better predict cardiovascular diabetes complications and assess efficiency of therapy. Glycated albumin, fructosamin, and 1,5-anhydroglucitol have received growing interest as alternative markers of glycemic control. In addition to measures of hyperglycemia, advanced glucose monitoring methods became available. An indispensible adjunct to HbA1c in routine diabetes care is self-monitoring of blood glucose. This monitoring method is now widely used, as it provides immediate feedback to patients on short-term changes, involving fasting, preprandial, and postprandial glucose levels. Beyond the traditional metrics, glycemic variability has been identified as a predictor of hypoglycemia, and it might also be implicated in the pathogenesis of vascular diabetes complications. Assessment of glycemic variability is thus important, but exact quantification requires frequently sampled glucose measurements. In order to optimize diabetes treatment, there is a need for both key metrics of glycemic control on a day-to-day basis and for more advanced, user-friendly monitoring methods. In addition to traditional discontinuous glucose testing, continuous glucose sensing has become a useful tool to reveal insufficient glycemic management. This new technology is particularly effective in patients with complicated diabetes and provides the opportunity to characterize glucose dynamics. Several continuous glucose monitoring (CGM) systems, which have shown usefulness in clinical practice, are presently on the market. They can broadly be divided into systems providing retrospective or real-time information on glucose patterns. The widespread clinical application of CGM is still hampered by the lack of generally accepted measures for assessment of glucose profiles and standardized reporting of glucose data. In this article, we will discuss advantages and limitations of various metrics for glycemic control as well as possibilities for evaluation of glucose data with the special focus on glycemic variability and application of CGM to improve individual diabetes management.

Empirical mode decomposition analysis of near-infrared spectroscopy muscular signals to assess the effect of physical activity in type 2 diabetic patients

Type 2 diabetes is a metabolic disorder that may cause major problems to several physiological systems. Exercise has proven to be very effective in the prevention, management and improvement of this pathology in patients. Muscle metabolism is often studied with near-infrared spectroscopy (NIRS), a noninvasive technique that can measure changes in the concentration of oxygenated (O2Hb) and reduced hemoglobin (HHb) of tissues. These NIRS signals are highly non-stationary, non-Gaussian and nonlinear in nature. The empirical mode decomposition (EMD) is used as a nonlinear adaptive model to extract information present in the NIRS signals. NIRS signals acquired from the tibialis anterior muscle of controls and type 2 diabetic patients are processed by EMD to yield three intrinsic mode functions (IMF). The sample entropy (SE), fractal dimension (FD), and Hurst exponent (HE) are computed from these IMFs. Subjects are monitored at the beginning of the study and after one year of a physical training programme. Following the exercise programme, we observed an increase in the SE and FD and a decrease in the HE in all diabetic subjects. Our results show the influence of physical exercise program in improving muscle performance and muscle drive by the central nervous system in the patients. A multivariate analysis of variance performed at the end of the training programme also indicated that the NIRS metabolic patterns of controls and diabetic subjects are more similar than at the beginning of the study. Hence, the proposed EMD technique applied to NIRS signals may be very useful to gain a non-invasive understanding of the neuromuscular and vascular impairment in diabetic subjects.

Declining ß-cell function is associated with the lack of long-range negative correlation in glucose dynamics and increased glycemic variability: A retrospective analysis in patients with type 2 diabetes

Objective

To determine whether characteristics of glucose dynamics are reflections of β-cell function or rather of inadequate diabetes control.

Materials/methods

We analyzed historical liquid meal tolerance test (LMTT) and continuous glucose monitoring (CGM) data, which had been obtained from 56 non-insulin treated type 2 diabetic outpatients during withdrawal of antidiabetic drugs. Computed CGM parameters included detrended fluctuation analysis (DFA)-based indices, autocorrelation function exponent, mean amplitude of glycemic excursions (MAGE), glucose SD, and measures of glycemic exposure. The LMTT-based disposition index (LMTT-DI) calculated from the ratio of the area-under-the-insulin-curve to the area-under-the-glucose-curve and Matsuda index was used to assess relationships among β-cell function, glucose profile complexity, autocorrelation function, and glycemic variability.

Results

The LMTT-DI was inverse linearly correlated with the short-range α1 and long-range scaling exponent α2 (r = −0.275 and −0.441, respectively, p < 0.01) such that lower glucose complexity was associated with better preserved insulin reserve, but it did not correlate with the autocorrelation decay exponent γ. By contrast, the LMTT-DI was strongly correlated with MAGE and SD (r = 0.625 and 0.646, both p < 0.001), demonstrating a curvilinear relationship between β-cell function and glycemic variability. On stepwise regression analyses, the LMTT-DI emerged as an independent contributor, explaining 20, 38, and 47% (all p < 0.001) of the variance in the long-range DFA scaling exponent, MAGE, and hemoglobin A1C, respectively, whereas insulin sensitivity failed to contribute independently.

Conclusions

Loss of complexity and increased variability in glucose profiles are associated with declining β-cell reserve and worsening glycemic control.

Using hemoglobin A1C as a predicting model for time interval from pre-diabetes progressing to diabetes

OBJECTIVE

The early identification of subjects at high risk for diabetes is essential, thus, random rather than fasting plasma glucose is more useful. We aim to evaluate the time interval between pre-diabetes to diabetes with anti-diabetic drugs by using HbA1C as a diagnostic tool, and predicting it using a mathematic model.

METHODS

We used the Taipei Medical University Affiliated Hospital Patient Profile Database (AHPPD) from January-2007 to June-2011. The patients who progressed and were prescribed anti-diabetic drugs were selected from AHPPD. The mathematical model used to predict the time interval of HbA1C value ranged from 5.7% to 6.5% for diabetes progression.

RESULTS

We predicted an average overall time interval for all participants in between 5.7% to 6.5% during a total of 907 days (standard error, 103 days). For each group found among 5.7% to 6.5% we determined 1169.3 days for the low risk group (i.e. 3.2 years), 1080.5 days (i.e. 2.96 years) for the increased risk group and 729.4 days (i.e. 1.99 years) for the diabetes group. This indicates the patients will take an average of 2.49 years to reach 6.5%.

CONCLUSION

This prediction model is very useful to help prioritize the diagnosis at an early stage for targeting individuals with risk of diabetes. Using patients' HbA1C before anti-diabetes drugs are used we predicted the time interval from pre-diabetes progression to diabetes is 2.49 years without any influence of age and gender. Additional studies are needed to support this model for a long term prediction.

Entropy analysis of muscular near-infrared spectroscopy (NIRS) signals during exercise programme of type 2 diabetic patients: quantitative assessment of muscle metabolic pattern

Diabetes mellitus (DM) is a metabolic disorder that is widely rampant throughout the world population these days. The uncontrolled DM may lead to complications of eye, heart, kidney and nerves. The most common type of diabetes is the type 2 diabetes or insulin-resistant DM. Near-infrared spectroscopy (NIRS) technology is widely used in non-invasive monitoring of physiological signals. Three types of NIRS signals are used in this work: (i) variation in the oxygenated haemoglobin (O2Hb) concentration, (ii) deoxygenated haemoglobin (HHb), and (iii) ratio of oxygenated over the sum of the oxygenated and deoxygenated haemoglobin which is defined as: tissue oxygenation index (TOI) to analyze the effect of exercise on diabetes subjects. The NIRS signal has the characteristics of non-linearity and non-stationarity. Hence, the very small changes in this time series can be efficiently extracted using higher order statistics (HOS) method. Hence, in this work, we have used sample and HOS entropies to analyze these NIRS signals. These computer aided techniques will assist the clinicians to diagnose and monitor the health accurately and easily without any inter or intra observer variability. Results showed that after a one-year of physical exercise programme, all diabetic subjects increased the sample entropy of the NIRS signals, thus revealing a better muscle performance and an improved recruitment by the central nervous system. Moreover, after one year of physical therapy, diabetic subjects showed a NIRS muscular metabolic pattern that was not distinguished from that of controls. We believe that sample and bispectral entropy analysis is need when the aim is to compare the inner structure of the NIRS signals during muscle contraction, particularly when dealing with neuromuscular impairments.