Time With Rapid Change of Glucose

Abstract

Background:

A variety of metrics are used to describe glycemic variation, some of which may be difficult to comprehend or require complex strategies for smoothing of the glucose curve. We aimed to describe a new metric named time with rapid change of glucose (TRC), which is presented as percentage of time, similar to time above range (TAR), time in range (TIR), and time below range (TBR).

Method:

We downloaded glucose data for 90 days from 159 persons with type 1 diabetes using the Abbott Freestyle Libre version 1. We defined TRC as the proportion of time (%) with an absolute rate of change of glucose > 1.5 mmol/L/15 minutes (1.8mg/dL/min) corresponding to a minimum rate of change for glucose in the 3.9-10.0 mmol/L (70-180 mg/dL) range within 1 hour. TRC is related to the other glucose variability metrics: CV within day (CVw) and mean amplitude of glycemic excursion (MAGE).

Results:

The more than 1.27 million glucose rates were t-location scale distributed with SD 0.91 mmol/L/15 min (1.1 mg/dL/15 min). The median TRC was 6.9% (IQR 4.5%-9.5%). The proportion of TRC with positive slope was 3.9% (2.6%-5.3%) and significantly higher than the proportion with negative slope 2.8% (1.5%-4.4%) P < .001. TRC correlated with CVw and MAGE (Spearman’s correlation coefficient .56 and .65, respectively, P < .001).

Conclusion:

TRC is proposed as an easily perceived metric to compare the performance of hybrid or fully automated closed-loop insulin delivery systems to obtain glucose homeostasis.

Introduction

Numerous metrics have been used to describe glycemic variation^1-5 but none cover all aspects. In clinical practice, only the glucose coefficient of variation (CV) is a standard part of the information provided in the ambulatory glucose profile (AGP) report from continuous glucose monitoring (CGM). The advantage of CV is its independence of mean glucose, the association with hypoglycemia,^4,6 and the presence of a commonly accepted cut-off value < 36%. ⁷ The original definition of CV and the related cut-off value were based on calculation of the mean CV within days (CVw). ⁸ In contrast, the CV presented in AGP reports describes the combined glucose variation within and between days (CV total). As CV is calculated as SD/mean glucose this metric does not reflect the magnitude of absolute glucose changes. Coefficient of variation often remains unchanged if both SD and mean glucose are reduced as seen after the initiation of pumps with automated insulin delivery (AID).^9-11 Clearly, CV is less useful for describing the effect of AID pumps on glucose excursion. The visual presentation of glucose interquartile range (IQR) on the 24-hour mean glucose curve in the AGP report can be helpful, but the information cannot be condensed to a single metric.

Glucose rate of change (ROC) is a glycemic variability metric which has derived metrics such as the continuous overall net glycemic action (CONGAn) and the standard deviation of ROC (SDROC) as originally described in detail by McDonnell et al ¹² and Kovatchev et al.^13,14

The aim of this study was to present a new metric to describe glycemic variation termed time with rapid change (TRC) also derived from the distribution of ROC data. Unlike the previously mentioned metrics, TRC conceptually fits into the presentation of glucose ranges as percentage of the period with CGM much like the metrics time above range (TAR), time in range (TIR), and time below range (TBR). We also relate TRC to other glycemic metrics: CV within day (CVw) and mean amplitude of glycemic excursion (MAGE) commonly applied for describing glycemic variability.

Methods

Glucose data from 159 persons with type 1 diabetes using intermittently scanned CGM with Abbott Freestyle Libre (version 1) (Abbott Diabetes Care, Alameda, CA) as previously described ¹⁵ were downloaded from Diasend (Glooko, Palo Alto, CA) for a 90-day period with no imputation of missing data. Information about instant interstitial glucose values was obtained by swiping a receiver unit in close proximity to a sensor on the upper arm. In addition, glucose data recorded every 15 minutes for the preceding 8 hours were imported, and a trend arrow indicated if glucose was stable, increasing, or decreasing. We calculated the average of imported and scanned glucose values (if any) for each 15-minute period.

Glucose ROC was calculated as glucose (t min) − glucose (t-15min). We define TRC as the time in percent with glucose changing by more than 1.5 mmol/L per 15-minute (1.8 mg/dL/min). The period with glucose increasing > 1.5 mmol/L was coined TRC+ and the period with glucose decreasing > 1.5 mmol/L was termed TRC−. It follows that for the individual patient: TRC(%) = TRC+(%) + TRC−(%). The concept of TRC is illustrated in Figure 1.

Figure 1.

An illustration of the calculation of TRC in a 24-hour period with a glucose value every 15 minute, except for 1 missing period. The number of 15-minute periods marked with red (n = 1 + 3 + 1 = 5) indicates a glucose rate of change > 1.5 mmol/L/15 min (27 mg/dL/15 min) and contributes to TRC+. The number of 15 minute periods marked with blue (n = 4 + 3 = 7) contributes to TRC− and indicates periods with a glucose rate of change < −1.5 mmol/L/15min. Of the 96 periods in 24 hours, only 93 periods in this example are available for rate of glucose calculation. TRC+ is (5/93) × 100 = 5.4%, TRC− is (7/93) × 100 = 7.5% and TRC is (12/93) × 100 = 12.9%.

Statistical Analysis

Normal distribution was assessed by visual inspection of QQ plots and data presented as mean ± SD or median (IQR) as appropriate. CV and CVw are compared with Student’s paired t test and presented as mean difference and 95% confidence interval. TRC+ and TRC− are compared with Wilcoxon signed-rank test. Correlations are given as Spearman’s correlation coefficient. The glucose ROC was calculated from the downloaded glucose data based on our development of a program in the statistical package R ver. 4.2. For a time period comprising n intervals of 15 minutes TRC (%) was calculated by determining the number of 15-minute intervals with changes > 1.5 mmol/L divided by (n − 1) multiplied by 100. The 1/(n − 1) factor is explained by the fact that only n − 1 time interval pairs are available for TRC calculation within a sequence of n 15-minute intervals.

Mean CVw were calculated as the (mean of daily SD/mean glucose for 90 days) × 100 as described by Julla et al. ⁸ MAGE was calculated from the “mage” function of the open source “iglu” statistical package in R.^16,17 For this purpose, glucose data were smoothened by application of short (4 observations, corresponding to 1 hour) and long (24 observations, corresponding to 6 hours) moving averages to identify true turning points. Periods with fewer than 10 glucose data were merged with the nearest time period. MAGE is presented as mean value weighted for the duration of each uninterrupted period. Statistical analysis was performed with SPSS ver. 20.0

Results

The total number of 15-minute CGM datapoints was 1 290 889 from which we could only calculate 1 278 629 ROC values (8041 ± 507 per person), because there were 12 260 interruptions.

The cumulative distribution function of pooled ROC values is shown in Figure 2. A t-location scale function described the distribution of ROC values better than a normal distribution. The SD for the t-location scale distribution of ROC was 0.91 mmol/L/15min (1.1 mg/dL/min), with location parameter −0.038 mmol/L/15min (−0.05 mg/dL/min) and shape parameter (degrees of freedom) 3.12. The SD for a normal distribution was 0.82 mmol/L (1.0 mg/dL/min) (Figure 3).

Figure 2.

The cumulative distribution function (CDF) of pooled values of glucose rate of change (1 278 629 values) during 90 days from 159 persons with type 1 diabetes (black stepwise curve). The vertical dotted lines indicate a glucose rate of change of –1.5 mmol/L/15min and +1.5 mmol/L/15min (27 mg/dL/15min). The red curve is a t-location scale distribution and the blue curve is a normal distribution.

Figure 3.

A density histogram of rate glucose changes in intervals of 0.25 mmol/L/15min (4.5 mg/dL/15min). The blue curve is a normal distribution, SD 0.82 mmol/L/15min (15 mg/dL/15min) and the red curve is t-location scale distribution, SD 0.546 mmol/L/15min, (10 mg/dL/15min).

The median TRC for the total population was 6.9% (IQR 4.5%-9.5%) TRC+ was 3.9% (2.6%-5.3%) and TRC− was 2.8% (1.5%-4.4%). TRC+ was statistically significantly higher than TRC− (P < .001), Figure 4.

Figure 4.

Time with rapid glucose decrease with negative sign (TRC−) plotted against time with rapid glucose increase (TRC+). The line of identity is shown.

Out of the total TRC, 83% originated from a single transition or from 2 consecutive transitions between 15 minutes time intervals (Figure 5).

Figure 5.

Histogram of 15-minute intervals in a row with glucose rate of change > 1.5 mmol/L/15min (27 mg/dL/15 min).

Mean glucose was 9.7 ± 1.7 mmol/L (175 ± 31 mg/dL) and the mean of individual glucose SD was 3.8 ± 0.8 mmol/L (68 ±14 mg/dL). CVtotal was 39.2% ± 6.1% and CVw 33.8% ± 5.5% (difference 5.3%, 95% CI: 5.0%–5.6%, P < .001). TRC correlated statistically significantly with CVw and MAGE (Spearman’s correlation coefficient .56 and .65, respectively, P < .01) (Figure 6).

Figure 6.

Time with rapid glucose rate of change (TRC) plotted against within day glucose coefficient of variation (CVw) and mean amplitude of glucose excursions (MAGE).

Discussion

Time with rapid change of glucose, a simplified metric derived from glucose ROC analysis represents the percentage of glucose ROC for the total glucose sampling period, similar to TAR, TIR, and TBR. Like these metrics TRC is straight forward to comprehend. Kovatchev has suggested the principle that glycemic variability metrics should describe both glucose amplitude and timing. ⁴ However, this is difficult to achieve by a single metric.

The TRC metric does not describes the amplitude of glucose excursion, even though the total duration of each interval with rapid change of glucose may to some extent reflect glucose amplitude. Of note, the vast majority of episodes lasted 30 minutes or less. Despite this limitation, we suggest that TRC may be a valuable instrument for describing glucose homeostasis, including the performance of different AID pump algorithms. We are unaware of any studies reporting TRC from AID pumps.

We chose TRC as the time period during which glucose change more than 1.5 mmol/L (27 mg/dL) per 15-minute because the TRC corresponds to the rate for changing glucose from 3.9 to 10.0 mmol/L (70-180 mg/dL) (ie, TIR) in 1 hour. In an experimental inpatient protocol with hypoglycemic- and hyperglycemic challenges in type 1 diabetes (30 persons) blood glucose levels were obtained every 15 minutes (12 025 observations) for 3 days. The study reported that 95.2% of all ROCs were between −1.67 and +1.67 mmol/L/15min (−2 and +2 mg/dL/min). ¹³ For these reasons our suggestion of a TRC definition based on the period in which ROC exceeds 1.5 mmol/L/15min seems reasonable. Various sensors display glucose trend arrows to indicate rapidly changing glucose values. The Libre system indicates a rapid glucose change at 0.1 mmol/L/min (2 mg/dL/min), the Dexcom and Guardian at 0.17 mmol/L/min (3 mg/dL/min). ¹⁸

So far, there is no strong evidence indicating that glucose variability or TRC is casually linked to endothelial damage or inflammation. From a physiological point of view TRC should be as low and possible, just like TBR and cut off values are only suggestive. The suggested cut off value for TBR < 4% is somewhat arbitrary, there is consensus that the duration with glucose < 3.9 mmol/L should be less than 1 hour per day. ¹⁹ Likewise, an obvious objective optimal standard for TRC is lacking and we expect that TRC may primarily be used for benchmarking. From a pragmatic point of view, a TRC+ or TRC− value above 4% is unwarranted.

In this study, TRC+ was systematically higher than TRC− indicating the difference between the effects of carbohydrate intake and the pharmacodynamics of fast acting insulin. In accordance with this finding we previously reported that the frequency of episodes with rebound hyperglycemia, glucose > 10 mmol/L (180 mg/dL) within 120 minutes after hypoglycaemia < 3.9 mmol/L (70 mg/dL,) is higher than the frequency of rebound hypoglycaemia (glucose > 10 mmol/L within 120 minutes before hypoglycaemia < 3.9 mmol/L). ¹⁵

Time with rapid change of glucose calculation depends on the definition of rapid change while CONGAn and SDROC are independent of such a definition. Interestingly, SDROC calculated from 15 minutes time intervals is identical to the CONGA15 minute.^4,12 Time with rapid change of glucose, as a glucose variability metric, is not a simple reflection of CVw or MAGE since it is only weakly correlated with these metrics. In contrast, MAGE is strongly correlated with glucose SD. ²⁰ Although TRC is statistically significantly correlated with CVw and MAGE, the relationship is not impressive as judged from Figure 6 and TRC is clearly not a simple derivative of CVw, MAGE or SD.

The sensor used in this study provide a glucose value per 15 minutes compared with a value every 5 minutes for other sensors. For sampling with shorter intervals than 15 minutes, it has been recommended to calculate ROC as the slope of a least-squares linear regression analysis based on 4 CGM readings over the previous 15 minutes. ¹⁸ We emphasize the robustness of our results derived from a very large data set comprising more than 1.27 million observations of glucose rate values from 159 persons.

We suggest that algorithms for AID pumps may be assessed by their ability to maintain glucose in range (represented by TIR), avoid hypoglycaemia (TBR), reduce rapid glucose change (TRC), and avoid large glucose amplitudes (SD).

In conclusion, TRC is a simple novel metric to describe glucose excursions. It may serve as a benchmark for the performance of AID pumps.