drCORRECT: An Algorithm for the Preventive Administration of Postprandial Corrective Insulin Boluses in Type 1 Diabetes Management

Abstract

Background:

In type 1 diabetes therapy, precise tuning of postprandial corrective insulin boluses (CIBs) is crucial to mitigate hyperglycemia without inducing dangerous hypoglycemic events. Several heuristic formulas accounting for continuous glucose monitoring (CGM) trend have been proposed in the literature. However, these formulas suggest a lot of quantized CIB adjustments, and they lack personalization.

Method:

drCORRECT algorithm proposed in this work employs a patient-specific time parameter and the “dynamic risk” (DR) measure to determine postprandial CIB suggestion. The expected benefits include the reduction of time in hyperglycemia, thanks to the preventive action exploited through DR. drCORRECT has been assessed retrospectively vs the literature methods proposed by Aleppo et al (AL), Bruttomesso et al (BR), and Ziegler et al (ZI) using a data set of 49 CGM daily traces recorded in free-living conditions. Retrospective evaluation of the algorithms is made possible by the use of ReplayBG, a digital twin-based tool that allows assessing alternative insulin therapies on already collected glucose data. Efficacy in terms of glucose control was measured by temporal, risk indicators, and dedicated hyperglycemic/hypoglycemic events metrics.

Results:

drCORRECT significantly reduces time spent in hyperglycemia when compared with AL and BR (33.52 [24.16, 39.89]% vs 39.76 [22.54, 48.15]% and 36.32 [26.91, 45.93]%, respectively); significantly reduces daily injected insulin (5.97 [3.80, 8.06] U vs 7.5 [5.21, 10.34] U), glycemia risk index (38.78 [26.58, 55.39] vs 40.78 [27.95, 70.30]), and time spent in hypoglycemia (0.00 [0.00, 1.74]% vs 0.00 [0.00, 10.23]%) when compared with ZI, resulting overall in a safer strategy.

Conclusions:

The proposed drCORRECT algorithm allows preventive actions thanks to the personalized timing configuration and the introduction of the innovative DR-based CIB threshold, proving to be a valid alternative to the available heuristic literature methods.

Introduction

In type 1 diabetes (T1D) insulin therapy, one of the major problems is the fear of overdosing. ¹ As reported in the study of Driscoll et al. ² T1D patients feel safer maintaining elevated blood glucose (BG) levels by intentionally withholding insulin to avoid risk of hypoglycemic events and symptoms. Therefore, meal insulin boluses (MIBs) and corrective insulin boluses (CIBs) have to be scheduled and thoroughly tuned in their dosing and timing. In recent years, various algorithms for bolus calculation have been published both for MIB and CIB.^{3 -9} In particular, the literature guidelines^{3 -8} suggest adjusting CIB dosing obtained by the standard formula: ¹⁰

$$\mathrm{CIB}=\frac{\mathrm{BG}-\mathrm{GT}}{\mathrm{CF}}-\mathrm{IOB}$$

(1)

accounting for the glucose rate of change (ROC) provided by continuous glucose monitoring (CGM) sensors, where BG (mg/dL) is the actual BG value, GT (mg/dL) is the patient target glucose value, CF (mg/dL/U) is the patient correction factor, and IOB (U) is the so-called insulin-on-board, that is, an estimate of the amount of insulin that is still acting on the body from previous administrations. In particular, in Noaro et al. ¹¹ an in-silico evaluation shows that the methods^{3 -8} outperform the standard formula given by equation (1) in terms of prandial glucose control, especially when ROC is negative. This highlights how the proposed guidelines are valuable strategies to improve CIB delivery. However, three main limitations can be identified:

1. Literature guidelines do not consider the large differences in the glucose-insulin dynamics among individuals with T1D.

2. Insulin adjustments are defined for a quantized combination of the parameters (eg, 180 < BG < 250 mg/dL and BG > 250 mg/dL; 1 < ROC < 2 mg/dL/min, 2 < ROC < 3 mg/dL/min, and ROC > 3 mg/dL/min). This means that, given an ROC = 2 mg/dL/min, a BG value of 250 mg/dL, or a BG value of 350 mg/dL leads to the same insulin correction, even if these two values are clearly characterized by a different level of risk.

3. For each published guideline, there are several combinations to modify equation (1) (up to 80 different combinations of the actual glycemic values and glucose ROC associated with a specific insulin adjustment). From a practical perspective, memorizing them could add further burden to individuals with diabetes, who would have to always keep a summary table with them and consult it to inject the proper amount of insulin at the right time.

This paper aims to overcome the above-mentioned literature limitations by proposing a new algorithm, drCORRECT, which determines postprandial CIB suggestions using:

1. The dynamic risk (DR) associated with the current CGM value and its ROC, ¹² which will be mainly used to trigger the CIB.

2. A patient-specific time parameter (estimated from the individual insulin absorption kinetics) to suggest CIB after a meal or in situations in which one or more insulin boluses have already been administered.

Thanks to the inherently predictive nature of DR, drCORRECT is expected to avoid, or at least mitigate, the duration of hyperglycemic events, and to maximize glucose control, without increasing the risk of hypoglycemic events.

The efficacy of drCORRECT is retrospectively evaluated and compared vs three approaches for CIB suggestion available in the literature, respectively, proposed by Aleppo et al (AL), ⁶ Bruttomesso et al (BR), ⁷ and Ziegler et al (ZI). ⁸ Real data of 30 subjects acquired in daily-life condition have been considered for the assessment, which was made possible by the use of ReplayBG, ¹³ a digital twin-based tool that allows assessing alternative insulin therapies on already collected CGM data.

The paper is organized as follows. The “Methods” section reports the data set, the description of the proposed algorithm, and the assessment strategy with the chosen evaluation metrics. The “Results” section documents the quantitative performance of drCORRECT and the comparison vs AL, BR, and ZI. The “Discussion and Conclusion” section contains a discussion of the results and the main findings of the comparison (ie, a reduction of the time spent above range and of the hyperglycemia duration without any increase in the risk for the patient), which demonstrates that the combined used of preventive suggestions and patient-specific CIB timing may be an effective solution to reduce the risk of hyperglycemia in open-loop T1D insulin therapy.

Methods

Data Set

Data collected during the Control-To-Range 3 study (CTR3) ¹⁴ were considered. Following an initial one-month phase 1 involving 30 subjects, 14 individuals with T1D continued with a five-month phase 2, which included 24/7 closed-loop control using the wireless portable Diabetes Assistants (DiAs) developed at the University of Virginia Center for Diabetes Technology. The data set contains information about CGM and self-monitoring BG readings, ingested carbohydrates (CHO), injected boluses, and basal insulin. It also contains some personal patient’s information, as age, gender, body weight, and therapy’s parameters as CF and CHO-to-insulin ratio.

For the aim of this work, we portioned the data set in daily traces, and we selected only those days that (1) contain data about the three main meals (breakfast, lunch, and dinner) and (2) present at least a hyperglycemic event lasting for three hours. The first selection criterion aimed to avoid the data set to be biased by missing meal information, which is often present when working with real-world and self-reported data. The second criterion aimed to identify prolonged hyperglycemia where CIB algorithms can be triggered, thus enabling a comprehensive and fair comparison among all of them. After this procedure, we selected and identified 49 daily traces.

The New drCORRECT Algorithm

Figure 1 shows through a flowchart the logical functioning of the proposed algorithm. In details, drCORRECT starts after the main meals and works as follow:

Wait a patient-specific t_pers time;

Look at the last measured CGM value;

Compute the DR associated to the CGM value;

IF DR is greater than a threshold corresponding to the static risk (SR) computed at BG_th=190 mg/dL, ie, 9.62:

IF no previous CIB have been suggested after the specific meal:

Trigger a CIB according to Equation (1);

Wait a patient-specific t_pers time;

Return to DR computation (line 3) with the next measured CGM value in order to suggest another CIB if needed.

ELSE:

IF the first-order derivative of DR is positive:

Suggest a CIB according to Equation (1);

Wait a patient-specific t_pers time;

Return to DR computation (line 3) with the next measured CGM value in order to suggest another CIB if needed.

ELSE:

Return to DR computation (line 3) with the next measured CGM value.

ELSE:

Return to DR computation (line 3) with the next measured CGM value.

Figure 1.

Proposed strategy’s flowchart. Abbreviations: personalized time between boluses (t_pers) dynamic risk (DR), static risk (SR), and corrective insulin boluses (CIBs).

“Dynamic risk” for CIB suggestion

The first novelty with respect to literature contributions is the use of the glucose risk indexes, that is, the static risk (SR) ¹⁵ and the DR. ¹² These risk measures have been widely applied in risk analysis and to assess glucose variability.^{16 -18} Moreover, SR and DR have already been used for developing a decision support system (DSS) algorithm targeting hypoglycemia. ¹⁹ This proved to be successful in suggesting preventive hypotreatments (HTs) based on DR measures leading to a significant reduction of hypoglycemia without increasing hyperglycemia. For this reason, following a similar approach, we decided to explore the potential of SR and DR measure to trigger preventive CIBs.

Static risk can be interpreted as a measure of the risk for the patient associated with a static BG level. It is defined by a non-linear transformation of BG concentration:

$$U\left(BG,\alpha ,\beta ,\gamma \right)=\gamma \cdot {\left(\log \left(BG\right)\right)}^{\alpha }-\beta$$

(2a)

$$SR\left(BG\right)=10\cdot U{\left(BG\right)}^2$$

(2b)

which appropriately weights glucose variations in both hypoglycemia and hyperglycemia to obtain a symmetric distribution of glycemic values, where α = 1.084, β = 5.381, γ = 1.509 when BG is measured in mg/dL. In this way, SR converts every BG measurement in a “risk” value, which ranges from a minimum of 0 to a maximum of 100 and increases much faster in hypoglycemia than in hyperglycemia when moving below or above the hypoglycemic/hyperglycemic threshold, respectively.

Similarly, DR can be viewed as a modified version of SR. In addition to BG level, DR considers the ROC provided by CGM sensor to modulate the risk level according to glucose trend magnitude and direction.

Personalized time for CIB suggestion

Based on the published guidelines, it is suggested to wait at least two hours after a meal before administering any other insulin bolus. This time-window aims to avoid insulin stacking and it is fixed for all individuals with T1D, following a one-size-fit-all approach. However, it is well known that insulin dynamics may vary among individuals, highlighting the need for a personalized therapy. For this reason, in our strategy, we replaced the literature fixed two-hour time-window with a patient-specific “waiting time” derived from patients’ physiological glucose-insulin dynamic. This personalized waiting period, hereafter labeled as t_pers, is retrieved, for each patient, from a simplified version of the subcutaneous insulin absorption subsystem described in the work of Schiavon et al. ²⁰ which represents the dynamics of exogenous insulin absorption into plasma as a three-compartment model schematized in Figure 2.

Figure 2.

Subcutaneous insulin absorption system schematics.

Particularly, exogenous insulin is infused to the first compartment, which represents insulin in a non-monomeric state. From the first compartment, insulin diffuses to the second one, which represents insulin in a monomeric state, and eventually reaches plasma.

Model equations for the insulin absorption subsystem used for the calculation of the personalized timing are:

$$\{\begin{array}{c}{\stackrel{.}{I}}_{sc1}\left(t\right)=-k_d·I_{sc1}\left(t\right)+I(t-\beta )/V_I\\ {\stackrel{.}{I}}_{sc2}\left(t\right)=k_d·I_{sc1}\left(t\right)-k_{a2}·I_{sc2}(t)\\ {\stackrel{.}{I}}_p\left(t\right)=k_{a2}·I_{sc2}\left(t\right)-k_e·I_p(t)\end{array}$$

(3)

where I_sc1 (mU/kg) and I_sc2 (mU/kg) represent insulin in non-monomeric and monomeric states, respectively; I_p (mU/L) represents insulin plasmatic concentration; k_d (min⁻¹) is the rate constant of diffusion form the first to the second compartment; k_a2 (min⁻¹) is the rate constant of diffusion from the second compartment to plasma; k_e (min⁻¹) is the fractional clearance rate; V_I (L/kg) is the volume of insulin distribution; β (min) is the delay in the appearance of insulin in the first compartment. The model parameters k_d, k_a2, k_e are estimated by exploiting a Markov Chain Monte Carlo-based Bayesian approach, while V_I and β are fixed to population values reported in the works of Schiavon et al ²⁰ and Dalla Man et al ²¹ Some information on the identification procedure is reported within the description of the assessment tool in “Retrospective Assessment of the Algorithms” section, but we refer the interested reader to Cappon et al ¹³ for further details.

For t_pers calculation, we first solved the insulin absorption subsystem with initial conditions:

$$\{\begin{array}{c}{I}_{sc1}\left(0\right)=I_{ss}/k_d\\ I_{sc2}\left(0\right)=I_{ss}/k_{a2}\\ I_p\left(0\right)=I_{ss}/k_e\end{array}$$

(4)

through ode45 MATLAB function, where I_ss (U) is the total insulin at the steady state.

By doing so, we calculated the delay of insulin action, that is, the time in which the rate of appearance in plasma reaches its maximum value. To avoid possible insulin stacking, we decided to use the 150% of that value, that is:

$$t_{\mathrm{pers}}=150\%\cdot \underset{t}{\max }{I}_p(t)$$

(5)

Retrospective Assessment of the Algorithms

As previously stated, drCORRECT is compared with AL, BR, and ZI. All approaches suggest modifying the amount of CIB given by equation (1) by adding or subtracting a fixed amount of insulin depending on ROC, CF, and actual BG concentration. Aleppo et al strategy also includes specific postprandial recommendations retrieved from REPLACE-BG clinical trial ⁹ to mitigate postprandial hyperglycemia. We refer the reader to Supplementary Tables for more details on AL, BR, and ZI.

To compare the effectiveness of the corrective actions suggested by the considered algorithms, a digital twin-based approach ²² is adopted. Specifically, we resorted to ReplayBG, a recently proposed open-source simulation tool ¹³ that allows to retrospectively assess the outcome of alternative therapy regimes on already collected real-world T1D data. The core of this approach is the minimal model described by Bergman, ²³ which describes the action of plasma insulin on plasma glucose. Such a model has been expanded by adding a model of subcutaneous insulin infusion (describing how exogenous insulin diffuses through plasma) ²⁰ and a model of oral glucose assumption (describing how CHO influence BG). ²¹

As depicted in Figure 3, the methodology consists of two sequential steps. In the first step, using easily accessible patient data, that is, CHO intakes, insulin infusions, and CGM values, ReplayBG create a digital twin of the patient identifying a (non-linear) model of glucose-insulin dynamics through a robust and powerful Bayesian technique. Then, the identified model (the digital patient twin) is used to simulate the subject’s (interstitial) glucose profile that would have been obtained by adopting alternative treatments, that in our case consists of adding CIBs suggested by a specific algorithm.

Figure 3.

Overview of the two steps of ReplayBG. Abbreviations: CHO, carbohydrates; CGM, continuous glucose monitoring; T1D, type 1 diabetes.

Other specific details about such in-silico framework or about the identification procedure can be found in the work of Cappon et al. ¹³

Evaluation Metrics

Glucose control is evaluated on the simulated glucose trace, for each individual and algorithm, using a subset of the control metrics presented in the work of Battelino et al ²⁴ calculated with the AGATA ²⁵ software. In particular, the selected metrics are time in range (TIR, that is, 70 ≤ BG ≤ 180 mg/dL), time above range (TAR, ie, BG > 180 mg/dL), time below range (TBR, ie, BG < 70 mg/dL), number of hyperglycemic events per day (#Hyper) and their duration (HyperD), and glycemia risk index (GRI). ²⁶ The number of suggested CIB (#CIB) and the total daily insulin injected (INS) through them have also been calculated to evaluate the potential burden on patients’ daily routine. Finally, the low-blood glucose index (LBGI), ¹⁸ the number of hypoglycemic events per day (#Hypo), and the cumulative number of hypoglycemic events in the whole data set (cumulativeHypo) have been calculated to quantify the impact on hypoglycemia due to a possible CIB overdosing.

Statistically significant differences between metric distributions obtained for all considered methodologies were evaluated through Student’s t test, if normality distribution assumption has not been rejected according to the Lilliefors test, and through the Wilcoxon signed-rank test otherwise. Particularly, a significance level of 5%, corrected through the Bonferroni method in case of multiple comparison, is used.

Results

Comparison With Literature Methods

As baseline comparator strategy, we considered the scenario in which no CIBs are delivered. This is possible by simulating BG profiles via ReplayBG and removing all CIBs originally injected by the patients. In this way, we wanted to avoid any bias due to patient actions. Note that for the calculation of CIB amount through equation (1), GT value was set as 120 mg/dL, for all the considered algorithms.

Figure 4 shows the comparison, in a representative subject, between drCORRECT, which is characterized by a glucose trigger threshold equals to BG_th= 190 mg/dL and by a t_pers from meal and between boluses, as previously described by the flowchart in Figure 1, and AL’s algorithm as representative of the literature. The subject’s original data (not shown in Figure 4 for sake of readability) have been fitted with ReplayBG tool to create a digital twin from which we built the baseline profile, in which no CIBs are delivered (black dotted line). Then, ReplayBG model has been used to evaluate the impact of adding CIBs as suggested by the considered strategies. In particular, the green line represents the glucose trace with CIBs (green diamonds) given following the strategy drCORRECT; the red line represents the glucose profile with CIBs (red dots) suggested by AL’s guidelines; and the blue arrows represent the ingested meals. Figure 4 presents a practical example in which both the impact of personalized timing for bolus generation and the impact of the risk-based threshold above which administer CIBs are highlighted. Indeed, drCORRECT injects CIBs before glycemia crosses the hyperglycemic threshold: one of 2.42 U at time 13:00, followed by another CIB of 4.77 U after a t_pers= 65 minutes, and one of 2.57 U at time 19:40, thanks to the personalized timing after the meal and after previous boluses. Of note, the last bolus is being suggested when glycemia is still growing. Aleppo et al, on the other hand, waits for four hours after the meal, generating a CIB of 4.68 U at time 15:40 and of 4.07 U at time 21:30, when glycemia is already lowering. Acting proactively, drCORRECT reduces TAR by 11.36% compared with baseline and by 6.55% compared with AL, which lowers TAR only by 4.81% compared with baseline. Moreover, GRI lowers from 36.33 for baseline, to 32.49 for AL and 27.25 drCORRECT, improving safety for the patient.

Figure 4.

Comparison of drCORRECT (with a t_pers= 65 minutes) and Aleppo algorithms via ReplayBG on a representative subject. In the upper panel, the dotted line represents the baseline glucose trace; the green line represents the glucose track with CIB (green diamonds) given following the strategy drCORRECT; the red line represents the glucose track with CIB (red dots) given following AL’s guidelines; and the blue arrows represent the ingested meals. Abbreviations: CIB, corrective insulin bolus; AL, Aleppo.

Table 1 reports the median and (25th-75th) percentile results obtained comparing the baseline, in which no CIBs are delivered, our proposed algorithm drCORRECT, and the latest published strategies for CIB suggestions (AL, BR, and ZI).

Table 1.

Comparison Between Baseline, drCORRECT, and Literature Approaches (AL, BR, and ZI), in Terms of Median and (25th-75th] Percentile of the Evaluation Metrics.

	Baseline	AL	BR	ZI	drCORRECT
TIR (%) 70 mg/dL ≤BG ≤ 180 mg/dL	52.25 (39.55, 62.61)	57.65 (47.81, 69.94)	60.63 (49.10, 70.48)	60.61 (50.00, 69.49)	63.72* (51.83, 72.90)
TAR (%) BG > 180 mg/dL	46.89 (37.39, 60.45)	39.76 (22.54, 48.15)	36.32 (26.91, 45.93)	33.86 (22.24, 39.74)	33.52* + ^ (24.16, 39.89)
TBR (%) BG < 70 mg/dL	0.00 (0.00, 0.00)	0.00 (0.00, 0.00)	0.00 (0.00, 0.10)	0.00 (0.00, 10.23)	0.00* (0.00, 1.74)
GRI (unitless)	52.64 (35.46, 67.99)	42.03 (28.79, 57.87)	43.63 (28.02, 61.14)	40.78 (27.95, 70.30)	38.78* + ^ (26.58, 55.39)
LBGI (unitless)	0.01 (0.00, 0.16)	0.07 (0.00, 0.36)	0.16 (0.00, 0.62)	0.26 (0.01, 2.48)	0.16* (0.01, 0.66)
#Hypo (unitless)	0 (0, 0)	0 (0, 0)	0 (0, 0)	0 (0, 1)	0* (0, 1)
cumulativeHypo (unitless)	5	13	15	22	15
#Hyper (unitless)	2 (1, 2)	2 (1, 2)	2 (2, 2)	2 (1, 2)	2 (1.75, 2)
HyperD (minutes)	258.8 (217.5, 325.0)	222.50 (117.5, 252.5)	200.00 (161.9, 230.6)	195.00 (155.0, 223.1)	192.5* + ^ (142.5, 222.5)
#CIB (unitless)	—	2 (2, 2)	2 (1.75, 2)	3 (2, 4)	2 ^ (2, 3.25)
INS (U)	—	5.16 (3.58, 8.44)	5.00 (3.42, 6.37)	7.50 (5.21, 10.34)	5.97 ^ ~ (3.80, 8.06)

Abbreviations: AL, Aleppo et al; BR, Bruttomesso et al; ZI, Ziegler et al; TIR, time in range; TAR, time above range; BG, blood glucose; TBR, time below range; GRI, glucose risk index; LBGI, low-blood glucose index; CIB, corrective insulin bolus; INS = insulin injected.

*

Statistically significant variation between baseline and drCORRECT, ⁺statistically significant variation between AL and drCORRECT, ^ statistically significant variation between BR and drCORRECT, ~statistically significant variation between ZI and drCORRECT; Bonferroni correction has been used for dealing with multiple comparison.

With respect to baseline, drCORRECT improves the glucose control during and after the meal. In fact, by administrating a median value of two boluses/day, both TIR and TAR are significantly improved (from 52.28% to 63.72% and from 46.89% to 33.52%, respectively), as well as the overall risk index (GRI lowers from 52.64 to 38.78), achieving also a significant reduction in hyperglycemia duration (from 258.8 to 192.5 minutes).

Compared with ZI, drCORRECT reduces TBR (75th percentile from 10.23% to 1.74%, no statistically different), median GRI (from 40.78% to 38.78%, no statistically different) and, injecting a median value of 1/day bolus less, provides a significant decrease of INS (from 7.50 to 5.97 U), which improves safety for patients. Despite the same median number of hypoglycemic events per day (null for both), drCORRECT reduces cumulativeHypo from 22 to 15 and median LBGI (from 0.26 to 0.16, not statistically different). Also, drCORRECT reduces median TAR (33.86% to 33.52%, not statistically different) and hyperglycemia duration (from 195.0 to 192.5 minutes, not statistically different) while enhancing median TIR (from 60.61% to 63.72%, not statistically different). Besides that, our approach is proved to be more effective than AL and BR: with the same median number of generated CIBs (two boluses/day) and almost the same amount of daily injected insulin (5.16, 5.00, and 5.97 U for AL, BR, and drCORRECT, respectively), HyperD is significantly reduced (from 222.8 min and 200.0 min to 192.5 min, respectively). More importantly, drCORRECT also reduces TAR (from 39.76 to 33.52% for AL and from 36.32 to 33.52% for BR, with statistical differences) and GRI (from 42.03 to 38.78 for AL and from 43.76 to 38.78 for BR, with statistical differences) with a very limited increase to the 75th percentile of TBR (no statistically significant variation). Indeed, drCORRECT performances are in line with the ones of AL and BR in terms of hypoglycemic metrics. Moreover, median TIR is also improved (57.65%, 60.63%, and 63.72%, for AL, BR, and drCORRECT, respectively, without statistical difference).

Assessment of the Main Features in drCORRECT

To better distinguish and quantify separately the impact of DR and t_pers on the performance of drCORRECT, we present specific analyses in which we consider only one feature at a time.

Personalized timing between boluses: t_pers

To highlight the importance of CIB personalization, in this subsection, we investigate three different timing configurations of: (1) the amount of time that is required to be waited to inject the first CIB after meal ingestion and (2) the consecutive CIBs after the injection of the first one. These two waiting periods can be fixed at two hours, as suggested by the literature, or personalized with the t_pers previously proposed. In particular, we show the results for: (1) fixed timing after meal and fixed timing between boluses (named fixed-fixed [FF] in Table 2, and set at two hours according to the literature studies), (2) fixed timing after meal and t_pers between boluses (named fixed-personalized [FP] in Table 2), and (3) t_pers for both the waiting period after meal and between boluses (named personalized-personalized [PP] in Table 2).

Table 2.

Quantitative Assessment of the Impact of Personalized Timing for CIB Generation.

	FF	FP	PP—drCORRECT
TIR (%) 70 mg/dL ≤ BG ≤ 180 mg/dL	60.68 (50.74, 72.70)	61.67* (50.62, 72.70)	63.72 (51.83, 72.90)
TAR (%) BG > 180 mg/dL	35.18 (26.80, 43.96)	35.18* (26.13, 41.96)	33.52* (24.16, 39.89)
TBR (%) BG < 70 mg/dL	0.00 (0.00, 0.10)	0.00 (0.00, 1.70)	0.00 (0.00, 1.74)
GRI (unitless)	40.00 (27.60, 61.03)	40.44 (27.00, 61.03)	38.78 (26.58, 55.39)
LBGI (unitless)	0.16 (0.00, 0.62)	0.19 (0.00, 0.73)	0.16 (0.01, 0.66)
#Hypo (unitless)	0 (0, 0)	0 (0, 1)	0 (0, 1)
cumulativeHypo (unitless)	14	15	15
#Hyper (unitless)	2 (1.75, 2)	2 (1.75, 2)	2 (1.75, 2)
HyperD (minutes)	203.8 (158.8, 233.8)	193.8 (151.3, 227.5)	192.5* (142.5, 222.5)
#CIB (unitless)	2 (1.75, 2.25)	2 (2, 3)	2 (2, 3.25)
INS (U)	5.13 (3.65, 6.83)	6.06* (3.99, 8.40)	5.97* (3.80, 8.06)

FF has fixed time (two hours as in the literature) for both after meal and after previous CIBs; FP has fixed time after meal and personalized time after CIB; PP has personalized timing both after meal and after CIB (drCORRECT algorithm).

Abbreviations: FF, fixed-fixed timing configuration; FP, fixed-personalized timing configuration; PP, personalized-personalized timing configuration; TIR, time in range; TAR, time above range; BG, blood glucose; TBR, time below range; GRI, glucose risk index; LBGI, low-blood glucose index; CIB, corrective insulin bolus; INS, insulin injected.

*

Statistically significant variation compared with FF; FP and PP are not statistically different; Bonferroni correction has been used for dealing with multiple comparison.

Figure 5 displays a practical example of how the personalized timing of drCORRECT operates in a representative subject. In particular, in the upper panel, the green line represents the glucose profile obtained using ReplayBG model and adding CIBs by following drCORRECT algorithm (green diamonds), which is characterized by t_pers after meal and between boluses (PP configuration, as described by the flowchart in Figure 1); the orange line represents the glucose profile obtained by simulating the addition of CIBs (orange square) delivered by drCORRECT with FP timing configuration; the red line represents the replayed glucose profile with the addition of CIBs (red dots) delivered by drCORRECT with FF timing configuration; and the blue arrows represent the ingested meals. The three bottom panels show the inactivation slots for FF configuration (red, two hours after meals and between boluses), FP configuration (orange, two hours after meals and t_pers= 60 minutes between boluses), and PP configuration (green, t_pers = 60 minutes after meals and between boluses), respectively. Thanks to the personalized timing, PP algorithm acts ahead in time compared with the FP and FF configurations: after breakfast, both FP and FF suggest the first CIB of 4.36 U at time 11:10, while PP generates a CIB of 3.09 U at time 10:10, allowing to proactively manage hyperglycemic events, that is, to be effective in reducing glycemia. The same situation occurs also after dinner, where both FP and FF suggest a bolus at time 21:05 (entity 5.79 and 4.95 U, respectively) and PP suggests a bolus of 4.12 U at time 20:05. After lunch instead, the three timing configurations FF, FP, and PP suggest a first bolus at time 15:15 (entity 2.40 U), when the risk of hyperglycemia is above the pre-determined threshold and the hyperglycemic events is going to occur, but then the behavior differs from FF, and FP, PP: a second bolus of 4.51 U is suggested at time 17:15 in the first case (FF); a second bolus of 4.05 U at time 16:15 is suggested in the second case (FP and PP), driving more rapidly the BG concentration within the safe range.

Figure 5.

Application of drCORRECT algorithms via ReplayBG on a representative subject, with a t_pers = 60 minutes. In the upper panel, the red line represents the glucose track with CIB (red dots) given following the strategy drCORRECT with FF configuration; the orange line represents the glucose track with CIB (orange squares) given following the strategy drCORRECT with FP configuration; the green line represents the glucose track with CIB (green diamonds) given following the strategy drCORRECT with PP configuration; and the blue arrows represent the ingested meals. The middle-up, middle-bottom, and bottom panels show the difference in FF, FP, and PP timing configuration inactivation slots. Abbreviations: CIB, corrective insulin bolus; FF, fixed-fixed; FP, fixed-personalized; PP, personalized-personalized.

Table 2 reports the overall results in terms of median and (25th-75th] percentile with different timing configurations. Comparing the three configurations, it was generally found that the gradual introduction of a patient-specific timing improves the general performances. Indeed, with the same median number of injected CIBs, the introduction of personalized timing allows a significant reduction of HyperD by 5.52% from FF to PP, as well as a concomitant reduction of TAR from 35.18% for FF to 33.52% for PP, achieving the goal of reducing hyperglycemia. At the same time, median TIR grows consistently from 60.68% for FF to 61.67% for FP and 63.75% for PP. Although the overall GRI gradually lowers toward the personalized timing introduction from 40.00 for FF to 38.78 for PP, the significant increase of injected insulin slightly affects TBR, whose median value stay equal to zero but whose 75th percentile grows up to 1.74% for PP.

Furthermore, we conducted a sensitivity analysis to evaluate the impact of a sub-optimal estimate of t_pers on the results. As detailed in Supplementary Table 4, the use of a sub-optimal t_pers provides performances comparable with the original version of drCORRECT, underscoring the robustness of our algorithm to this parameter. For detailed information, please refer to Supplementary Table 4.

Dynamic risk CIB trigger threshold: BG_th

This section shows the impact of the use of DR in CIB triggering: changing BG_th, that is, the SR-dependent threshold above which drCORRECT suggests a CIB, also the DR level necessary to trigger a CIB changes.

Qualitatively, a low BG_th, value increases the number of CIBs and, consequently, it increases the amount of injected insulin, making the algorithm more aggressive to prolonged hyperglycemic levels. Therefore, we expect to increase TIR and to reduce TAR, and also to increase TBR as well as the risk for patients in terms of GRI. On the contrary, a high BG_th value makes the algorithm less aggressive since less CIBs are suggested. This entails a lower hyperglycemic control: TAR slightly increases, as well as HyperD and GRI. We choose BG_th = 190 mg/dL as the most suitable value to be effective in triggering preventive CIBs and to limit possible risk of hypoglycemia. We refer to Supplementary Table 5 for more details on the comparison of different BG_th with t_pers after meal and between boluses configuration (PP).

Discussion and Conclusion

In this work, we proposed drCORRECT, a novel algorithm for postprandial CIB administration characterized by two new features: (1) the DR value associated with the current BG reading and (2) a patient-specific waiting time, retrieved from patient’s personal glucose-insulin dynamic, which is used to schedule CIB release from the last meal and between consecutive boluses. The proposed algorithm is computationally cheap and simple to implement: the DR is computed in real-time with a negligible effort, and the physiological model needed to extract the personalized timing can be identified offline from a small portion of glucose, insulin, and meal data.

Considering the results in Tables 1 and 2, the introduction of DR for CIB triggering and of a personalized timing for CIB generation led to promising results. While DR allowed the injection of preventive CIB when the risk of hyperglycemia was elevated, compared with the usage of a fixed waiting time from previous boluses of two hours, the patient-specific timing led to a median improve of TIR, a median reduction of GRI, and a significant reduction of TAR and hyperglycemia duration. This was due to the additional amount of injected insulin, which, however, did not affect patient safety: the overall risk value was lower than the baseline’s one in all the cases and median TBR remained equals to zero. To reach the goal of reducing hyperglycemia without increasing risk for patients, we chose the most suitable DR threshold beyond which trigger a bolus by computing a trade-off between improvements of glucose control and number of needed actions. Compared with the literature, drCORRECT granted improvements with respect to AL and BR: HyperD, TAR, and GRI have all been reduced. Median improvements of the metrics were also achieved when compared with ZI: in this case, our strategy also enhanced patient safety (GRI, LBGI, and TBR has been reduced) maintaining the overall performances.

In processing the data set for this study, we carefully selected traces featuring prolonged hyperglycemic events (lasting more than three hours). In addition, we designed the baseline data by excluding all correction boluses (CIBs) administered by the patients. This process resulted in a data set suitable for evaluating the effectiveness of CIBs, albeit with limited occurrences of hypoglycemia. Despite this limitation, the data set proved to be sufficient (even if not ideal) to preliminary assess the possible impact of CIB overdosing. As shown by the hypoglycemic metrics in Tables 1 and 2, drCORRECT proved to be effective in reducing hyperglycemia without increasing the risk of hypoglycemia. It should also be noted that, unlike real-life practice, we did not simulate any intake of HT to address hypoglycemic occurrence, to avoid the introduction of biases in assessing the performances of the algorithms for CIB administrating.

The retrospective assessment of the CIB strategies was possible thanks to the simulation tool ReplayBG, which allows to replay already collected CGM portions of data (creating a digital twin of individuals with T1D) and evaluate how interstitial glucose would have been modified by applying CIBs suggested by the algorithms. We acknowledge that adding CIBs modifies the glucose trace and, thus, can have an impact on the calculation of the amount of insulin of following MIBs, which should be modified consequently. This calls for the development of a more complex and dynamic simulation tool where patients’ meals and their corresponding insulin boluses can vary based on the current glycemic level and on previous corrective actions. While a dynamic simulation can modify the numerical values of the performance, this does not affect the relative difference between the proposed approach and the other methods employed as comparators. Indeed, although the promising results obtained by identifying and then replaying real patient data should be interpreted as preliminary, they pave the way for a further validation on real clinical data.

Future work will deal with a more robust assessment of drCORRECT on much larger data sets and with a validation of drCORRECT suggestions in a more realistic scenario, that is, when coupled with other DSS algorithms targeting hypoglycemia. Thus, allowing the investigation of a dynamic simulation mode, modifying MIBs according to the new glycemic level. Finally, from the algorithmic point of view, we plan to personalize insulin dosing by adjusting the CIB amount based on DR and BG information to further improve the effectiveness and safety the proposed approach.

In conclusion, results show that drCORRECT allowed reducing the time spent in hyperglycemia and the hyperglycemic events duration, without increasing the time below hypoglycemic threshold. drCORRECT algorithm can be a valuable solution for CIB suggestion to be used in DSSs, with the aim of enhancing the overall glucose control.

Supplemental Material

sj-docx-1-dst-10.1177_19322968231221768 – Supplemental material for drCORRECT: An Algorithm for the Preventive Administration of Postprandial Corrective Insulin Boluses in Type 1 Diabetes Management

Supplemental material, sj-docx-1-dst-10.1177_19322968231221768 for drCORRECT: An Algorithm for the Preventive Administration of Postprandial Corrective Insulin Boluses in Type 1 Diabetes Management by Elisa Pellizzari, Francesco Prendin, Giacomo Cappon, Giovanni Sparacino and Andrea Facchinetti in Journal of Diabetes Science and Technology