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

Abstract

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.

Keywords

complexity of glucose time series / continuous glucose monitoring / impaired glucose regulation / insulin secretion and sensitivity / refined composite multi-scale entropy

1 Introduction

Continuous glucose monitoring (CGM), a newly developed glucose-monitoring technology, has been widely applied in clinical practice. This constantly updating technology has expanded blood glucose monitoring from “point” (time-point blood glucose) to an intuitive “line”, leading to the dynamic evaluation of individual glucose status [1]. Recent studies have confirmed the close relationship between common indices assessed by CGM and diabetes complications, such as the reverse association between time in range (TIR) and vascular complications [2–4]. Thus, the indices have been recognized in several international consensuses for assessing glycemic control [5,6].

CGM data, a continuous and nonlinear time series, could provide abundant information on blood glucose, which promotes the use of data mining to further characterize glucose dynamics. In recent years, time-series analyses have been applied to explore the dynamic structure of glycemic fluctuations, such as Fourier analysis, periodograms, and multiscale entropy (MSE) analysis [7]. Among these methods, MSE analysis was introduced by Costa et al. [8] to analyze the complexity of physiologic time series. Previous studies proved that the complexity of glucose time series in individuals with type 2 diabetes (T2D) has been decreased, compared with that in healthy individuals [9,10]. In addition, previous studies focused on the relationship between the complexity of glucose time series calculated by MSE and indices of glycemic variability (GV), but they did not further investigate the clinical significance [9,10].

Individuals with impaired glucose regulation (IGR) are at high risk of developing diabetes [11]. Discovering the characteristics of blood glucose of individuals is conducive to the early detection and follow-up management of diabetes. Thus, the features of blood glucose in IGR have received considerable attention [12,13]. In our previous studies, we have conducted a series of analyses across the glycemic continuum, attempting to paint a holistic picture of the changes in glucose homeostasis. Previous results showed that GV has already increased in individuals with IGR [14], and we also revealed that the dawn phenomenon occurred in one third of individuals with IGR, which was associated with worsened glucose metabolism [15]. However, there remains a paucity across the glycemic continuum concerning the complexity of glucose time series.

Therefore, utilizing CGM data and refined composite multi-scale entropy (RCMSE) algorithm, which is improved on the basis of MSE to analyze shorter time series [16], this exploratory study aimed to investigate the complexity of glucose time series in subjects with normal glucose tolerance (NGT), IGR, and newly diagnosed T2D and its underlying pathophysiological characteristics, including the relationship between the complexity of glucose time series and insulin secretion/sensitivity.

2 Material and methods

2.1 Study population

This study was a post-hoc analysis of a multi-center CGM study in China from 2007 to 2009 [17,18]. Subjects included volunteers recruited from an outpatient department of 11 hospitals in China (specific hospitals are listed in the Appendix). Recruitment criteria have been published previously [17,18]. A total of 756 subjects with complete CGM data were included in this study. All the subjects did not receive any hypoglycemic treatment before or during the study period.

This study was approved by the ethics committees of each hospital in accordance with the 1964 Declaration of Helsinki. All subjects were provided with informed consent prior to enrollment.

2.2 Anthropometric and biochemical assessments

All subjects received a physical examination, including height, bodyweight, and blood pressure tests, after enrollment. Body mass index (BMI) was measured as weight (kg)/height (m)². Fasting plasma glucose (FPG) and fasting serum insulin (FINS) were measured after at least 8 h fasting, and each subject underwent a 75 g oral glucose tolerance test (OGTT) to assay the 30 min and 2 h plasma glucose (30 min PG and 2 h PG), along with 30 min and 2 h serum insulin (30 min INS and 2 h INS). Venous blood was collected for blood glucose and insulin measurement. HbA_1c levels were measured as previously described [17,18]. A fully automatic biochemistry analyzer (Hitachi 7600-020; Hitachi, Tokyo, Japan; enzymatic methods) was used to determine triglyceride (TG), total cholesterol (TC), high-density lipoprotein cholesterol (HDL-c), and low-density lipoprotein cholesterol (LDL-c) levels.

The diagnosis of glucose regulation status was evaluated in accordance with the 2007 American Diabetes Association diabetes diagnostic criteria [19]: NGT was defined as FPG < 5.6 mmol/L and 2 h PG < 7.8 mmol/L; IGR was defined as FPG ≥ 5.6 mmol/L and ≤ 6.9 mmol/L and/or 2 h PG ≥ 7.8 mmol/L and ≤ 11.0 mmol/L; T2D was defined as FPG ≥ 7.0 mmol/L and/or 2 h PG ≥ 11.1 mmol/L.

2.3 CGM parameters

All subjects received a retrospective CGM evaluation (CGMS GOLD; Medtronic Inc., Northridge, CA, USA), and CGM systems were inserted by the same trained nurses in each hospital. The first CGM calibration by finger stick capillary blood glucose was performed in a hospital after 1 h of initialization, and then subjects wore the CGM for 3 consecutive days. Subjects were all instructed, and at least four capillary blood glucose readings per day were measured at home by using a SureStep blood glucose meter (LifeScan, Milpitas, CA, USA) for CGM calibration. We selected a complete 24 h CGM data to calculate the following parameters: mean sensor glucose (MSG), standard deviations of sensor glucose (SDSG), coefficient of variation (CV), and TIR. TIR was defined as the percent of time in the glucose range of 3.9–10.0 mmol/L.

Participants were required to follow the dietary instruction when wearing the CGM system. Total calorie intake from three daily meals was 30 kcal/kg/day, with 50% from carbohydrates, 15% from proteins, and 35% from fats. The calorie distribution between breakfast, lunch, and dinner was 20%, 40%, and 40%, respectively. The time for meals were as follows: 6:30–7:30 AM for breakfast, 11:30 AM to 12:30 PM for lunch, and 6:00–7:00 PM for dinner. Each meal had to be consumed within 30 min. The participants were also asked to maintain their original lifestyle and not to exercise intensively.

2.4 Insulin secretion and insulin sensitivity evaluation

Homeostasis model assessment of β-cell function (HOMA-β) was calculated as basal insulin release: HOMA-β = FINS \times 20/(FPG − 3.5) [20]. Post-load insulin secretion was calculated by the total insulin area under the curve divided by the total glucose area under the curve during the 2 h OGTT (AUC_INS120/AUC_GLU120). Early-phase insulin release was calculated as the total insulin area under the curve divided by the total glucose area under the curve during the first 30 min of the OGTT (△INS30/△GLU30).

Homeostasis model assessment of insulin resistance (HOMA-IR) was calculated as FINS × FPG/22.5 [20]. Insulin sensitivity index (ISI) was evaluated by using the Cederholm formula [21]: ISI = M/[MGLU × lg(MINS)]. M = 75 000/120 + (FPG − 2 h PG) × 180 × 0.19 × body weight/120, M_GLU = (FPG + 2 h PG)/2, lg(MINS) = [lg(FINS) + lg(2 h INS)]/2. Disposition index (DI) was defined as follows: DI = (AUC_INS120/AUC_GLU120) × ISI [22].

2.5 Complexity of glucose time series

The RCMSE algorithm was used as previously described [16], and the irregularity of a time series shorter than 750 points was quantified. Time scale was a value defined to determine the number of points taken when the time series was coarse-grained (a process to simplify time series for subsequent analysis). Based on the defined time scale, the original time series was divided into several non-overlapping windows, and the data points contained in each window were averaged, on which subsequent analysis were proceeded [16]. Using different time scales could make full use of the data to investigate the complex structure of time series. In the present study, the complexity of glucose time series was computed as sample entropy at time scales of 1 to 6. Given that the CGM system recorded a glucose value every 5 min, time scales of 1 to 6 correspond to the period of 5 to 30 min. The complexity of glucose time series index (CGI) was defined as the sum of sample entropy at each time scale, and lower CGI represented lower complexity of glucose time series. The sample entropy on each time scale and CGI were calculated as the average of two complete days of CGM data.

2.6 Statistical analysis

CGMS 3.0 (Medtronic MiniMed, Northridge, CA, USA) was applied to process CGM data. RCMSE analysis was performed by MATLAB R2019b (MathWorks, Inc., Natick, MA, USA). Other data were performed using SPSS version 24.0 (SPSS, Inc., Chicago, IL, USA) and R version 3.2.5 (RStudio, Inc., Boston, MA, USA). Non-normally distributed variables were presented as median with interquartile ranges. Mann–Whitney test or Kruskal–Wallis test was used for intergroup comparisons of non-normally distributed data. Trends of continuous variables across various groups were assessed using the Jonckheere–Terpstra test for non-normally distributed data. A chi-square test was used to determine the differences in categorical variables between two groups. Propensity score matching was used to match three groups by age, sex, and BMI in a 1:1:1 ratio. Covariates for matching the three groups included age, gender, and BMI, and nearest-neighbor matching was used as the matching algorithm. Propensity scores were generated using a logistic regression model. Spearman correlation coefficients and multiple linear stepwise regression analysis were used to analyze the relationship between the complexity of glucose time series and insulin secretion and sensitivity. P values < 0.05 (two-tailed) were considered statistically significant.

3 Results

3.1 Clinical characteristics, CGM profile, and complexity of glucose time series of study subjects

A total of 756 participants, including subjects with NGT (n = 343), IGR (n = 164), and newly diagnosed T2D (n = 249), were enrolled in this study. The basic clinical characteristics and CGM profile of the three groups are summarized in Table S1. Figure S1 shows the sample entropy at each time scale in three groups.

As sex composition, age, and BMI differed significantly in the three groups (Table S1), these factors were matched across individuals with NGT, IGR, and newly diagnosed T2D using propensity score matching, resulting in 111 paired sets (n = 333). The basic clinical characteristics and CGM profiles of the three matched groups are shown in Tab.1. MSG and GV gradually increased (both P < 0.001), whereas TIR decreased (P < 0.001) gradually in the three groups (Tab.1).

For each time scale, RCMSE analysis showed that the sample entropy decreased from NGT to IGR and T2D group (all P for trend < 0.001, Fig.1). Similarly, CGI progressively decreased across the glycemic continuum (NGT vs. IGR vs. T2D, 3.43 (2.83–4.18) vs. 3.09 (2.26–3.69) vs. 2.56 (1.91–3.28), P for trend < 0.001).

3.2 Relationship of the complexity of glucose time series and clinical parameters (CGM parameters)

In the matched sample (n = 333), correlation analysis showed that CGI was negatively related to FPG, 2 h PG, MSG, SGSD, and CV (all P < 0.001) but positively correlated with TIR (P < 0.001, Tab.2).

3.3 Relationship of the complexity of glucose time series and insulin secretion/sensitivity

We selected 427 subjects with complete insulin data (Table S2) and matched the three groups with different glucose regulation categories by age, sex, and BMI to explore the association between the complexity of glucose time series and insulin secretion and sensitivity. The resulting sample consisted of 61 paired sets of subjects (n = 183), the clinical information of whom is depicted in Table S3. Fig.2 illustrates all indices of insulin secretion and sensitivity, which significantly decreased with the deterioration of glucose metabolism (all P for trend < 0.01, Fig.2–2E). In addition, similar trends were observed for DI and CGI across the three groups (both P for trend < 0.01).

In this subgroup (n = 183), Spearman correlation analysis showed that CGI was positively correlated with insulin secretion and insulin sensitivity (all P < 0.001, Tab.3), and CGI was also positively associated with DI (P < 0.001, Tab.3). Multiple linear stepwise regression analysis demonstrated that DI was the only independent factor of CGI, after adjustment for systolic blood pressure, TG, HDL-c, and HOMA-IR (P < 0.001, Table S4). For each SD increase in DI, CGI increased by 0.61 (P < 0.001).

4 Discussion

The present study was the first to investigate the complexity of glucose time series calculated by RCMSE analysis across the glycemic continuum (healthy–prediabetes–diabetes) and revealed that decreasing the complexity of glucose time series derived from CGM was closely correlated with deteriorating glucose regulation. The results initially showed that the complexity of glucose time series has been decreased in individuals with IGR, and DI, which reflects β-cell function after adjusting for insulin sensitivity, was the only independent factor correlated with CGI. These findings indicate that the CGI may serve as a novel marker to evaluate glucose homeostasis.

With the development of CGM, researchers have explored new indicators to analyze the characteristics of glucose dynamics across the glycemic continuum. Acciaroli et al. [12] attempted to classify healthy subjects, prediabetes, and diabetes using CGM-based GV indices, whereas the indices showed good accuracy in classifying healthy and subjects with impaired glucose tolerance (IGT) or T2D. The results of classification in IGT and T2D were critical. Chakarova et al. [13] considered GV as an additional parameter to evaluate blood glucose homeostasis at the early stage of IGR. Compared with common indices of CGM such as GV, time series analyses have allowed researchers to explore the characteristics of blood glucose, including the perspective of time. However, previous studies were restricted to investigating the complexity of glucose time series by MSE analysis in patients with diabetes and healthy controls [9,10,23–25]. Consistent with these reports, the decreased complexity of glucose time series in T2D was confirmed in our study. Although a previous animal study showed that the complexity of glucose time series of Zucker diabetic fatty rats decreased before evident diabetic manifestation [26], the present study first revealed that the complexity of glucose time series calculated by RCMSE analysis has already been decreased in subjects with IGR, when compared with healthy controls. Therefore, our study filled the gap between healthy subjects and patients with diabetes and proved early dysglycemia in individuals with IGR from a new parameter using CGM and RCMSE analysis, providing new insights into the characteristics of blood glucose.

The relationships between the complexity of glucose time series measured by RCMSE analysis and insulin secretion/sensitivity have not been examined. Our study was the first to discover that DI was the independent factor correlated with CGI. Bergman et al. [27] defined DI as the product of β-cell function and insulin sensitivity, as β-cell function and insulin sensitivity are complementary and interactive when it comes to maintaining glucose homeostasis. Thus, the findings indicate that the complexity of glucose time series might reflect the glucose homeostasis in vivo. The more components the body could utilize, when coping with external stimuli, such as meals or exercise, the more difficult it is to predict the change in blood glucose time series, which indicates a more complex structure of the glucose time series. However, we did not measure other hormones, such as glucagon and glucagon-like peptide-1. Thus, we could not investigate the relationship between the complexity of glucose time series and other glucose-regulating hormones. Collectively, given the progressive impairment of the complexity of glucose time series across the glycemic continuum (i.e., healthy–prediabetes–diabetes) and the correlation of this indicator with insulin secretion/sensitivity observed in our study, the complexity of glucose time series calculated by RCMSE analysis could be a new marker for the status of glucose metabolism. The identification of abnormal glucose regulation may provide timely intervention strategies to reduce the burden of diabetes. Whether this indicator could predict the development of diabetes at an early stage, even before the elevation in fasting and/or postprandial glucose levels, needs further prospective studies.

As for additional clinical practice, the complexity of glucose time series may become a part of big data analysis in the future to provide more information on the glucose characteristics of individuals, as CGM data and artificial intelligence have already been widely used to improve diabetes management. For example, Li et al. [28] used a time-series clustering method to predict treatment outcomes in patients with T2D. They reported that the trend components observed by this method were significantly associated with the improvements in glycemic markers, including HbA_1c, after 6 months of glucose-lowering treatment. Therefore, the development of new methods of analysis using CGM data may provide additional information beyond traditional metrics of glycemic control and lead to better diabetes management.

The current study also has some limitations. First, this was a cross-sectional study; thus, we could not examine the temporal relationship between the complexity of glucose time series and glucose status. Second, CGM was conducted for 3 days for each participant, which may be relatively short for the confident evaluation of the glucose profile. Third, although instructions on diet and physical activities were given to each participant, relevant patient behavior was not strictly followed and documented, which might influence the glucose levels observed in study. Therefore, our findings must be interpreted with caution. Moreover, the present study did not consider the changes in weight and diet before enrollment. Finally, the study did not include patients with type 1 diabetes; thus, any conclusion is limited to those with NGT, IGR, and newly diagnosed T2D.

The complexity of glucose time series calculated by RCMSE analysis decreased progressively with deteriorating glucose regulation, which is accompanied by alterations in insulin sensitivity/secretion. Our findings indicate that the CGI derived from CGM data may serve as a novel marker of glucose homeostasis, the clinical utility of which warrants further investigation.

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