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Abstract

Background:

Automated insulin delivery (AID) algorithms can benefit from tuning of their aggressiveness to meet individual needs, as insulin requirements vary among and within users. We introduce the Performance-Based Adaptation Index (PAI), a tool designed to enable automatic adjustment of an AID system aggressiveness based on continuous glucose monitoring (CGM) metrics.

Methods:

PAI integrates two CGM-based metrics—one for hypoglycemia and another for hyperglycemia exposure—over a previous time window into a single index ( $α_{θ}$ ). We propose two methods to compute $α_{θ}$ : one based on time in range (TIR, 70-180 mg/dL), and the other on glycemic risk indices. Using $α_{θ}$ , we developed a multiplicative strategy to adjust the AID system’s aggressiveness, accounting for situations where $α_{θ}$ cannot be reliably calculated. The feasibility of this method was assessed in-silico using the UVA/Padova Type 1 Diabetes Simulator and our full closed-loop algorithm (UVA-model predictive control (MPC)) across five scenarios: optimal tuning (baseline), conservative and aggressive tunings, and temporary and permanent changes in insulin needs. Glycemic outcomes were evaluated from the simulated glucose traces.

Results:

Negligible performance variations were observed in the baseline scenario. For the conservative scenario, adjusting $α_{θ}$ improved TIR (35.1% vs 71.8%) and increased total daily insulin (32.1 U vs 41.2 U). Conversely, for the aggressive scenario, it reduced hypoglycemia exposure (TBR: 2.6% vs 1.4%) and overall insulin usage (45.6 U vs 43.0 U).

Conclusion:

In-silico results demonstrated the safety and efficacy of using PAI to automatically tune the UVA-MPC controller, achieving TIR values above 70% under fully closed-loop conditions and across various physiological states. Clinical validation of these results is warranted.

Keywords

automated insulin delivery glucose control artificial pancreas insulin therapy adaptation type 1 diabetes fully automated closed loop

Introduction

Automated insulin delivery (AID) systems have significantly simplified glucose management for individuals with type 1 and type 2 diabetes (T1D and T2D).^1-4 However, achieving safe and effective glucose control can still pose challenges for some individuals due to the considerable variability in metabolic and psycho-behavioral factors, including circadian rhythms, physical activity, menstrual cycle, diet, and stress. Since customizing an AID system for each user is impractical, there is a clear need to develop AID algorithms that can adapt to individual insulin requirements and their temporal variations.^5,6

Adaptive AID systems are those capable of modifying themselves in response to physiological and/or behavioral changes.⁵ While there are specific definitions for adaptive problems, for our purposes, we can categorize AID adaptation as either indirect or direct. In the case of indirect adaptation, the parameters of the underlying design model or plant are updated, resulting in a readjustment of the control response. For example, this could involve re-identifying the glucose metabolic model in response to increased insulin sensitivity due to physical activity, ultimately leading to a more conservative control law. Typically, this adaptation requires solving an optimization problem to re-identify a set of model parameters periodically using historical observations.^7-10

On the other hand, direct approaches involve adjusting the controller parameters based on specific criteria or measurements, such as hypoglycemia risk. In the literature, various approaches such as run-to-run strategies and iterative learning control have been suggested to update these parameters. These methods involve adjusting penalty weights in optimization-based control algorithms or incorporating time-varying constraints based on predefined rules for glucose regulation performance.^6,11-13

In this paper, we introduce a novel Performance-Based Adaptation Index (PAI) that could be seamlessly integrated into any AID system. Performance-Based Adaptation Index consolidates glucose performance metrics into a single index, which can be then communicated across the internal logic of the AID system. While various retuning strategies can be followed, we propose a simple Performance-based Adaptation System (PAS). In this system, PAI modulates a predefined set of controller parameters multiplicatively. We test this strategy with our fully automated UVA-model predictive control (MPC) system, demonstrating how continuous adaptation with PAS can safely and effectively overcome performance plateaus.

Materials and Methods

Performance-Based Index Computation

The goal of PAI is to consolidate CGM-based metrics that represent exposure to hypoglycemia ( $P_{h y p o}$ ) and hyperglycemia ( $P_{h y p e r}$ ) over a previous time window into a single daily performance index ( $α_{θ}$ ). Metrics for $P_{h y p o}$ could include the percentage of time spent below 70 mg/dL (time below range, $T B R$ ) or the Low Blood Glucose Index (LBGI). For $P_{h y p e r}$ , metrics could be the percentage of time spent above 180 mg/dL (time above range, $T A R$ ) or the High Blood Glucose Index¹⁴ (HBGI).

If the AID was active for at least 80% of the time, and at least 80% of the CGM data was available, the following procedure is followed for calculating $α_{θ}$ daily at a specified time $t = t_{A d a p t}$ :

1. Retrieve the previous day’s CGM and insulin records, and compute $P_{h y p o}$ and $P_{h y p e r}$ .

2. Construct an array of all daily metrics estimate $P_{h y p o}^{V}$ and $P_{h y p e r}^{V}$ over the chosen time window of N days for $P_{h y p o}$ and $P_{h y p e r}$ , respectively. At day 1, $P_{h y p o}^{V}$ and $P_{h y p e r}^{V}$ are initialized, backpropagating the first available metric to each array’s position. From day 2 onwards, when a new metric becomes available, it is appended to the corresponding array, while the oldest metric (first element) is dropped.

3. Compute average metrics over the time window as follows:

\bar{P_{h y p o}} = \sum_{i = 1}^{N} ϑ_{i} P_{h y p o_{i}}^{V}

(1)

\bar{P_{h y p e r}} = \sum_{i = 1}^{N} ϑ_{i} P_{h y p e r_{i}}^{V}

(2)

with $P_{h y p o_{i}}^{V}$ and $P_{h y p e r_{i}}^{V}$ being the elements of $P_{h y p o}^{V}$ and $P_{h y p e r}^{V}$ , respectively, and $ϑ_{i} = e^{- τ D_{j}}$ representing an exponential decay where $τ$ is the time constant and $D_{j}$ is the day index in reverse order (from N to 1). In this way, more weight is given to newer data points and less to older ones.

4. Compute the dimensionless index as follows:

α_{θ} = α_{h y p o} + α_{h y p e r}

(3)

with $α_{h y p o}$ and $α_{h y p e r}$ being individual indices that suggest the direction of changes in the controller’s aggressiveness based solely on $\bar{P_{h y p o}}$ and $\bar{P_{h y p e r}}$ , and given by:

α_{h y p o} = \max (\min (f_{1} (\bar{P_{h y p o}}), 1), l_{α})

(4)

α_{h y p e r} = \min (\max (f_{2} (\bar{P_{h y p e r}}), 0), 1)

(5)

where $f_{1}$ and $f_{2}$ are design functions to regulate how sensitive $α_{h y p o}$ and $α_{h y p e r}$ are to performance changes, and $l_{α}$ is a lower bound for $α_{h y p o}$ to avoid zero values. Note that all parameters in equations (3) to (6) are dimensionless and, given the feasible domain for $α_{h y p o}$ and $α_{h y p e r}$ , $α_{θ} \in [l_{α}, 2]$ (see Appendix A-1). In addition, if lower ( $u_{θ}$ ) and upper ( $l_{θ}$ ) bounds are added to constraint $α_{θ}$ , equation (3) could be modified as:

α_{θ} = \max (\min (α_{h y p o} + α_{h y p e r}, u_{θ}), l_{θ})

(6)

The 80% data availability requirement is a design choice intended to ensure that sufficient data is available to evaluate the AID system’s performance. The index $α_{θ}$ will not be updated until this requirement is met.

Functions $f_{1}$ and $f_{2}$ were obtained by fitting a set of design points to relate CGM-based metrics and their directional changes to the $α_{h y p o}$ and $α_{h y p e r}$ indices. The continuous functions for f1 and f2 were added into the controller formulation to compute $α_{θ}$ each day. Two alternatives for calculating $f_{1}$ and $f_{2}$ are proposed here (details are presented in Appendix A-1):

1. If $T B R$ and $T A R$ are used to estimate $P_{h y p o}$ and $P_{h y p e r}$ , respectively, $f_{1}$ and $f_{2}$ can be computed as follows:

f_{1} (\bar{P_{h y p o}}) = 0.8756 e^{(- 0.08348 \bar{P_{h y p o}})} + 0.1537 e^{(- 0.001772 \bar{P_{h y p o}})}

(7)

f_{2} (\bar{P_{h y p e r}}) = 9.85 x 10^{- 5} {\bar{P_{h y p e r}}}^{2} + 3.1 x 10^{- 4} \bar{P_{h y p e r}}

(8)

From equations (4) and (7), $α_{h y p o}$ will rapidly drop when $\bar{P_{h y p o}} > 1 %$ , decelerate the fall when $\bar{P_{h y p o}} > 25 %$ and reach a plateau at $l_{α}$ when $\bar{P_{h y p o}} = 100 %$ . On the other hand, from (5) and (8), $α_{h y p e r}$ will be close to zero when $\bar{P_{h y p e r}} < 20 %$ , and then gradually increase for higher $\bar{P_{h y p e r}}$ values until it reaches a plateau at 1 when $\bar{P_{h y p e r}} = 100 %$ .

2. If $L B G I$ and $H B G I$ are used to estimate $P_{h y p o}$ and $P_{h y p e r}$ , respectively, $f_{1}$ and $f_{2}$ can be computed as follows:

f_{1} (\bar{P_{h y p o}}) = 1.0347 e^{(- 0.3807 \bar{P_{h y p o}})} + 0.1542 e^{(- 0.00808 \bar{P_{h y p o}})}

(9)

f_{2} (\bar{P_{h y p e r}}) = 0.00135 {\bar{P_{h y p e r}}}^{2} + 0.0084 \bar{P_{h y p e r}} - 0.0009

(10)

Equations (9) and (10) have the same form as equations (7) and (8), respectively. So $α_{h y p o}$ will rapidly drop when LBGI increases, and $α_{h y p e r}$ will be close to zero for lower values of HBGI before gradually increasing. These coefficients were tuned to achieve similar performance to the TBR and TAR equations. Low Blood Glucose Index and HBGI scale non-linearly with glucose, allowing the system to penalize more extreme variations in glucose.

PAS: Performance-Based Adaptation System

We propose a simple PAS to adjust automatically the AID system using $α_{θ}$ in a multiplicative manner. Thus, given a controller’s aggressiveness index $θ$ , its value at iteration $j - 1$ can be updated at iteration $j$ as follows:

θ^{j} = θ^{j - 1} \cdot α_{θ}^{j}

(11)

The AID system can then propagate $θ^{j}$ internally to adjust each module’s aggressiveness based on achieved performance. Finally, to avoid the risk of $θ$ potentially decreasing $(α_{θ} < 1)$ or increasing $(α_{θ} > 1)$ indefinitely due to performance plateaus, lower and upper bounds for $θ$ should also be considered to enforce $θ \in [θ_{l}, θ_{u}]$ . Note that the units of $θ$ may vary from one AID system to another depending on the parameter chosen to be modulated, but it holds since $α_{θ}$ is unitless.

Modulating the Aggressiveness of the UVA AID System

The UVA AID system has been extensively described in previous works.^15-18 It integrates four main components: a core MPC for background insulin regulation (see Appendix A-2), a Bolus Priming System (BPS)¹⁷ to safely administer insulin when glucose levels rise rapidly, and a Hyperglycemia Mitigation System (HMS) and Safety Supervision Module (SSM) to correct sustained hyperglycemia and protect against hypoglycemia,¹⁹ respectively. Figure 1 shows a block diagram of the UVA AID system in which $θ$ serves as a unitless proxy for insulin needs and is used by the controller’s modules to adjust their level of aggressiveness. Since total daily insulin (TDI) shares a similar conceptual meaning, $θ$ is initialized using the participant’s initial TDI.

Figure 1.

Component diagram of UVA AID system with PAS. The data cleaning block refers to the process of verifying that at least 80% of the CGM data is available and that the system was in closed-loop mode for at least 80% of the day. The green blocks show the controller modules that use $θ^{j}$ as input. The solid lines indicate controller calculations and the dashed lines refer to the historical data flow.

At each step $k$ , the MPC solves a cost function that minimizes the deviation between (i) the glucose output and an asymmetric, time-varying reference signal, (ii) the insulin input deviation from the basal insulin infusion rate, which is computed as a function of $θ$ , and (iii) the hypoglycemia incidence along the prediction horizon. As shown in Figure 1, the index $θ$ is provided to the MPC block and used together with the Insulin on Board to redefine the weight that penalizes (i)²⁰ (see Appendix A-2). Other controller modules, like BPS, HMS, and SSM (see),^17-19 are also influenced by parameter $θ$ . For the cases of HMS and BPS, $θ$ modules how much insulin is infused as correction doses to treat sustained hyperglycemia and the priming doses infused when a positive glycemia disturbance is detected, respectively. Such modulation allows the controller to be more aggressive by increasing the upper bounds for boluses when TAR is higher than the target value. Finally, the SSM is also affected as it saturates insulin based on fractions of the prevailing basal rate, which is defined as $θ / 48$ .

In Silico Study Designs

The 100-adult cohort of the UVA/Padova T1D Simulator was considered to evaluate the performance of the UVA AID system with and without PAS in five different scenarios:

Baseline: Defining $θ^{0}$ as the subject’s TDI.

Conservative: Defining $θ^{0}$ as 50% of the subject’s TDI.

Aggressive: Defining $θ^{0}$ as 150% of the subject’s TDI.

Disturbance in insulin sensitivity (IS): Defining $θ^{0}$ as the subject’s TDI and increasing IS parameters by 40% for three days starting on day 8 to simulate a period of increased insulin sensitivity.

Change in insulin needs: Defining $θ^{0}$ as the subject’s TDI and reducing IS parameters by 40% on day 5 until the end of the simulation to simulate a long period of decreased insulin sensitivity.

For each scenario, simulations were performed over 21 days, considering intra/inter-day variability in insulin sensitivity parameters. The eating patterns included three meals (breakfast, lunch, and dinner) and up to three snacks per day based on the body weight (BW) of each subject. Meals and snack sizes were randomly selected from uniform distributions between [0.7, 1] g/kg and [0.15, 0.4] g/kg, respectively, with the possibility to skip snacks. Mealtimes were randomly selected from uniform distributions within [7, 13, 19] ± 1.5 hours for main meals and [9, 16, 22] ± 1 hours for snacks. Hypoglycemia rescues were administered every 20 minutes when simulated blood glucose dropped below 70 mg/dL. Note that scenarios 4 and 5 were designed to evaluate the system’s performance during changes in insulin requirements due to, for instance, menses, exercise, illness, or periods of stress.

Simulation conditions for each scenario were maintained across all controller settings and the entire resulting glucose traces were used to compute the outcomes for each in-silico individual. Due to space limitations, only the results of the in-silico analysis using TBR and TAR for computing $α_{θ}$ will be presented here, while the results using LBGI and HBGI will be discussed in the “Discussion” section. The computation of $α_{θ}$ was performed over a rolling two-week window, resulting in vectors $P_{h y p o}^{V}$ and $P_{h y p e r}^{V}$ of dimension 14 × 1. In addition, $l_{α} = 0.014$ , $u_{θ} = 2$ , $l_{θ} = 0.014$ were defined in this analysis to explore the whole range for $α_{h y p o}$ and $α_{h y p e r}$ .

Outcomes and Statistical Analysis

Simulations, data formatting, preparation, and analysis, and statistical analyses were performed in MATLAB R2022a and Simulink (MathWorks, Natick, MA, USA). Performance glycemic metrics were computed from the simulated BG traces and include average glucose concentration (mg/dL), standard deviation (mg/dL), coefficient of variation (%), percentages of time spent below 54 mg/dL, below 70 mg/dL (TBR), between 70 and 140 mg/dL (TTR), between 70 and 180 mg/dL (TIR), above 180 mg/dL (TAR) and above 250 mg/dL, TDI, total daily basal insulin (TDBa), total daily bolus insulin (TDBo), and number of hypo-treatments per day. All results are presented as across-subject mean value and standard deviation, unless otherwise stated. Comparison between different therapy adjustments was performed using the paired-sample t-test and a paired two-sided Wilcoxon signed rank, with significance level at a P-value <.05 if the distribution of the differences was normally or non-normally distributed, respectively. Normality was addressed using Lilliefors Test.

Results

Glycemic metrics for the baseline scenario under both controller settings (i.e., AID and AID+PAS) are reported in Table 1 for days 1, 5, 21, and overall. As shown, overall glycemic metrics show slight changes between both controller settings. Average BG was slightly reduced, while TIR increased by 1.4% and TBR by 0.1% when using PAS. In addition, insulin infusion, both basal and boluses, increased following elevated TAR, which remained higher than the desired target. Notably, after day 7 (not shown in the table), the θ values remained virtually unchanged, with the population’s mean fluctuating between 44.6 and 45.3.

Table 1.

Glycemic Outcomes During the “Baseline” Scenario for AID and AID With PAS.

	Day 1		Day 5		Day 21		Overall
Glycemic metric	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS
Average of BG levels [mg/dL]^a	153.5 (45.4)	153.5 (45.4)	152.7 (46.9)	150.9 (46.9)	153.3 (47.0)	151.4 (48.2)	152.2 (46.3)	150.2 (46.5)
Standard deviation of BG [mg/dL] ^a	41.7 (14.1)	41.7 (14.1)	44.0 (13.1)	43.9 (12.9)	44.3 (12.6)	44.4 (13.7)	43.4 (12.9)	43.2 (13.3)
Coeff. of variation of BG levels [%]^a	26.8 (7.4)	26.8 (7.4)	28.5 (7.1)	28.8 (7.0)	28.5 (6.5)	28.9 (6.8)	28.2 (6.9)	28.4 (7.0)
Time spent <54 mg/dL [%]	0.1 (0.4)	0.1 (0.4)	0.1 (0.3)	0.1 (0.3)	0.2 (0.7)	0.1 (0.4)	0.1 (0.5)	0.1 (0.3)
Time spent <70 mg/dL [%]^a	0.8 (1.4)	0.8 (1.4)	1.1 (1.8)	1.1 (1.5)	1.3 (1.9)	1.3 (1.6)	1.1 (1.7)	1.2 (1.4)
Time spent in 70-140 mg/dL [%]^a	43.5 (9.7)	43.5 (9.7)	45.1 (10.2)	46.9 (10.7)	43.6 (8.8)	46.6 (10.2)	44.8 (9.6)	46.8 (10.3)
Time spent in 70-180 mg/dL [%]^a	74.7 (12.0)	74.7 (12.0)	74.1 (11.4)	74.8 (12.2)	72.8 (12.5)	73.9 (13.3)	74.0 (12.0)	75.4 (12.4)
Time spent >180 mg/dL [%]^a	24.5 (11.4)	24.5 (11.4)	24.8 (10.4)	24.1 (11.2)	25.9 (11.5)	24.8 (12.3)	24.8 (11.1)	23.4 (11.5)
Time spent >250 mg/dL [%]	3.7 (6.1)	3.7 (6.1)	3.6 (5.7)	3.5 (5.9)	3.3 (5.3)	3.6 (6.5)	3.4 (5.3)	3.4 (5.9)
Num HT/Day^a	0.8 (1.1)	0.8 (1.1)	0.9 (1.3)	0.9 (1.1)	1.0 (1.3)	1.0 (1.1)	0.9 (1.2)	1.0 (1.1)
GRI ^a	27.4 (23.4)	27.4 (23.4)	25.5 (22.6)	27.8 (22.9)	29.7 (24.3)	29 (25.3)	28.9 (22.9)	27.3 (22.9)
TDI [U] ^a	43.2 (14.1)^b	43.2 (14.1)	41.4 (13.5)	42.0 (14.3)	42.0 (13.5)	42.7 (14.4)	41.5 (13.6)	42.3 (14.5)
TDBa [U] ^a	39.3 (12.1)	39.3 (12.1)	37.4 (11.8)	37.6 (11.8)	38.2 (12.1)	38.4 (12.1)	37.7 (11.9)	38.0 (12.0)
TDBo [U] ^a	3.9 (3.8)	3.9 (3.8)	4.0 (3.7)	4.5 (4.4)	3.7 (3.5)	4.3 (4.4)	3.8 (3.5)	4.3 (4.3)
$θ$ [-]^a	40.4 (13.0)^b	40.4 (13.0)	40.4 (13.0)	43.5 (17.9)	40.4 (13.0)	44.8 (21.3)	40.4 (13.0)	44.1 (19.0)

Results presented as mean (standard deviation).

Abbreviation: BG, simulated blood glucose.

Statistically significant differences in glycemic metrics between two controller settings for the overall period (P > .05).

Note that for day 1, TDI and $θ$ are different since here TDI refers to the total insulin delivered by the controller instead of the initialization value.

Simulation results for the conservative and aggressive scenarios under both controller settings are presented in Figures 2 and 3, respectively. In addition, all glycemic metrics for day 21 and overall are reported in Tables 2 and 3 for the conservative and aggressive scenarios, respectively.

Figure 2.

Glycemic metrics (TBR, TIR, and TAR) per day when using AID (top panel) and AID+PAS (bottom panel) in the conservative scenario.

Figure 3.

Glycemic metrics (TBR, TIR, and TAR) per day when using AID (top panel) and AID+PAS (bottom panel) in the aggressive scenario.

Table 2.

Glycemic Outcomes During The “Conservative” Scenario for AID and AID With PAS.

	Day 21		Overall
Glycemic metric	AID	AID+PAS	AID	AID+PAS
Average of BG levels [mg/dL]^a	218.3 (69.4)	151.8 (48.3)	216.2 (68.1)	156.0 (48.4)
Standard deviation of BG [mg/dL] ^a	63.0 (21.0)	44.5 (13.7)	61.7 (20.3)	45.1 (13.7)
Coeff. of variation of BG levels [%]	28.6 (8.0)	29.0 (6.9)	28.3 (7.9)	28.5 (7.0)
Time spent <54 mg/dL [%]^a	0.0 (0.0)	0.1 (0.5)	0.0 (0.0)	0.1 (0.3)
Time spent <70 mg/dL [%]^a	0.1 (0.4)	1.3 (1.7)	0.0 (0.2)	1.1 (1.4)
Time spent in 70-140 mg/dL [%]^a	11.8 (8.7)	46.1 (10.0)	12.1 (9.1)	43.0 (9.4)
Time spent in 70-180 mg/dL [%]^a	34.2 (13.1)	73.7 (13.2)	35.1 (13.0)	71.8 (11.8)
Time spent >180 mg/dL [%]^a	65.7 (13.1)	25.0 (12.1)	64.9 (13.0)	27.1 (10.9)
Time spent >250 mg/dL [%]^a	30.3 (14.5)	3.7 (6.6)	29.0 (14.9)	5.2 (6.5)
Num HT/day^a	0.1 (0.4)	1.1 (1.1)	0.0 (0.2)	0.9 (1.0)
GRI ^a	100 (34.6)	29.3 (25.8)	98.3 (34.7)	32.9 (23.4)
TDI [U] ^a	32.4 (11.2)	42.5 (14.4)	32.1 (11.1)	41.2 (14.3)
TDBa [U] ^a	30.2 (10.3)	38.3 (12.3)	29.9 (10.1)	37.2 (11.9)
TDBo [U] ^a	2.3 (1.8)	4.2 (4.4)	2.2 (1.8)	4.0 (4.1)
$θ$ [-]^a	20.2 (6.5)	44.5 (21.3)	20.2 (6.5)	41.1 (18.2)

Results are presented as mean (standard deviation).

Abbreviation: BG, simulated blood glucose.

Statistically significant differences in glycemic metrics between two controller settings for the overall period (P > .05).

Table 3.

Glycemic Outcomes During The “Aggressive” Scenario for AID and AID With PAS.

	Day 21		Overall
Glycemic metric	AID	AID+PAS	AID	AID+PAS
Average of BG levels [mg/dL]^a	138.0 (41.9)	150.7 (48.4)	137.3 (41.8)	147.3 (46.3)
Standard deviation of BG [mg/dL] ^a	40.0 (10.1)	44.3 (14.1)	39.6 (10.9)	42.6 (13.3)
Coeff. of variation of BG levels [%]	28.7 (6.0)	28.9 (6.9)	28.6 (6.6)	28.5 (6.8)
Time spent <54 mg/dL [%]^a	0.5 (1.2)	0.1 (0.5)	0.3 (0.9)	0.1 (0.4)
Time spent <70 mg/dL [%]^a	2.9 (2.7)	1.4 (1.6)	2.6 (2.4)	1.4 (1.5)
Time spent in 70-140 mg/dL [%]^a	55.0 (11.2)	47.3 (11.4)	55.9 (10.7)	49.5 (11.8)
Time spent in 70-180 mg/dL [%]^a	81.2 (10.1)	74.4 (13.8)	82.3 (9.9)	77.0 (12.8)
Time spent >180 mg/dL [%]^a	15.9 (8.9)	24.2 (12.8)	15.1 (8.7)	21.5 (11.9)
Time spent >250 mg/dL [%]^a	1.2 (2.6)	3.7 (6.8)	1.3 (3.1)	3.1 (5.7)
Num HT/day^a	2.2 (1.8)	1.1 (1.1)	2.0 (1.7)	1.2 (1.1)
GRI ^a	23.1 (21.4)	28.9 (26.4)	21.3 (10.4)	25.8 (23.4)
TDI [U] ^a	46.3 (14.6)	42.8 (14.3)	45.6 (14.8)	43.0 (14.7)
TDBa [U] ^a	40.6 (12.4)	38.5 (12.2)	39.9 (12.1)	38.4 (12.0)
TDBo [U] ^a	5.7 (5.3)	4.3 (4.2)	5.7 (5.4)	4.6 (4.7)
$θ$ [-]^a	60.6 (19.5)	45.8 (21.4)	60.6 (19.5)	48.2 (20.9)

Results are presented as mean (standard deviation).

Abbreviation: BG, simulated blood glucose.

Statistically significant differences in glycemic metrics between two controller settings for the overall period (P > .05).

For the conservative scenario, it can be observed how the performance of the AID system is affected when the initialization of $θ$ is underestimated (top panel of Figure 2). This could occur when an AID system intended for a diverse population is evaluated in a population with significant insulin resistance. Consequently, since the controller tuning parameters remain unchanged and are inadequate to meet insulin requirements, the AID performance is characterized by a high TAR (mean: 64.9%) and a poor TIR (mean: 35.1%) over the days.

However, when the AID is integrated with PAS, after 5 days, the glycemic control is improved, reaching TIR values (mean: 73.7% at day 21) similar to those of the nominal controller performance (i.e., observed in the baseline scenario), and is maintained throughout the days. As shown in Figure 2, TIR increased by about 10% from day 1 to 2, 15% from day 2 to 3, and 5% from day 3 to 4, with a slight increase in TBR but remaining around 1%. The increase in TIR can be attributed to reductions in TAR across days.

The effect of retuning the controller’s aggressiveness using PAS can also be seen in the differences in TDI and $θ$ between both controller settings, as shown in Table 2. When using PAS, TDI increased by about 9 U overall and 10 U for day 21 due to the changes in $α_{θ}$ driven by TBR and TAR. Thus, by design, increasing $α_{θ}$ also increases $θ$ , and as this propagates throughout the controller modules, it allows the controller to infuse more insulin, either basal or bolus, to mitigate hyperglycemia events in the postprandial and fasting conditions.

In the aggressive scenario, TBR is around 2% on day 1 due to an overestimation of $θ_{0}$ , which could correspond to the case where the controller, as designed, is used in a very insulin-sensitive population. Similar to what happened in the conservative case, the AID alone is not able to readjust the insulin infusion to reduce the TBR (around 3% on day 21) even when the TIR is higher than the one expected by design. However, as shown in Figure 3, when PAS is used in this scenario, average TBR decreases from 2% on day 1 to 1.4% on day 21, resulting in a reduction of about 1.5% in TBR compared to not using PAS. Furthermore, at the end of the simulation on day 21, the glycemic metrics and controller settings were similar to those of the baseline scenario (scenario 1), demonstrating the convergence of the proposed methodology. Finally, when PAS was used, both TDI and the number of hypoglycemia rescues per day were reduced in comparison to the AID alone case, see Table 3.

Finally, simulation results for scenarios 4 (Disturbance in insulin sensitivity) and 5 (Change in insulin needs) are presented in Tables 4 and 5, respectively, for the representative days of the modifications in the IS parameters. Table 4 shows that during the disturbance period (day 8 to 10) of increased IS parameters, PAS compensates for the rise in TBR (2.1% at day 8 and 1.6% at day 10) by reducing TDI (35.9 U at day 8 and 34.2 U at day 10) through adjustments in $θ$ . For the AID alone case, TBR increased slightly during the disturbance days. However, 3 days later, the difference between AID and AID+PAS became negligible, with both controllers recovering nominal performance. Similarly, Table 5 illustrates the performance after the modification in the insulin needs (at day 5) for scenario 5. AID+PAS recovered baseline performance after 5 days, whereas AID alone did not. For AID alone, TIR decreased by about 17% from day 5 to 21, despite an increase in insulin infusion of about 12 U. In contrast, AID+PAS led to an increase in $θ,$ and therefore in insulin infusion of about 18 U after 5 days and 20 U by the end of the simulation, allowing it to recover the baseline TIR by day 11. It should be noted that all simulations considered different meal sizes and times between days, resulting in slightly different glycemic metrics before and after changes in IS.

Table 4.

Glycemic Outcomes During The “Disturbance in IS” Scenario for AID and AID With PAS.

	Nominal SI		Increased SI—day 1		Increased SI—last day		Nominal SI
	Day 7		Day 8		Day 10		Day 13		Day 21
Glycemic metric	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS
Average of BG levels [mg/dL]^a	153.2 (47.6)	150.6 (47.5)	140.8 (41.7)	138.8 (42.1)	139.7 (42.4)	143.0 (44.6)	151.6 (45.2)	151.5 (45.1)	153.3 (47.0)	151.8 (48.0)
Standard deviation of BG [mg/dL] ^a	44.6 (13.4)	44.0 (13.8)	39.8 (10.5)	39.9 (10.7)	40.2 (11.2)	41.4 (12.6)	42.5 (12.4)	42.3 (12.2)	44.2 (12.7)	44.3 (13.7)
Coeff. of variation of BG levels [%]^a	28.8 (7.1)	28.9 (7.3)	28.1 (6.3)	28.5 (6.3)	28.5 (6.7)	28.6 (6.9)	27.7 (6.7)	27.6 (6.7)	28.5 (6.6)	28.8 (6.9)
Time spent <54 mg/dL [%]	0.2 (0.6)	0.1 (0.3)	0.2 (0.5)	0.2 (0.5)	0.3 (0.7)	0.2 (0.6)	0.2 (0.7)	0.1 (0.4)	0.2 (0.7)	0.1 (0.5)
Time spent <70 mg/dL [%]^a	1.2 (1.7)	1.3 (1.5)	1.9 (1.8)	2.1 (1.8)	2.0 (1.9)	1.6 (1.6)	1.2 (1.7)	1.1 (1.4)	1.3 (1.9)	1.3 (1.7)
Time spent in 70-140 mg/dL [%]^a	45.2 (10.4)	47.2 (10.4)	54.1 (10.2)	55.3 (11.0)	54.9 (10.7)	52.9 (12.0)	44.4 (9.4)	44.8 (9.4)	43.7 (8.8)	46.2 (10.1)
Time spent in 70-180 mg/dL [%]^a	73.4 (11.6)	75.0 (12.0)	80.9 (9.2)	81.9 (9.6)	81.4 (10.8)	79.3 (12.0)	74.8 (12.0)	75.1 (11.9)	72.9 (12.6)	73.7 (13.3)
Time spent >180 mg/dL [%]^a	25.4 (10.8)	23.7 (11.0)	17.2 (8.5)	16.0 (8.6)	16.6 (9.9)	19.0 (11.2)	24.0 (11.1)	23.8 (11.1)	25.8 (11.5)	25.0 (12.2)
Time spent >250 mg/dL [%]	4.1 (6.1)	3.8 (6.6)	1.5 (3.1)	1.5 (3.5)	1.6 (3.1)	2.4 (5.0)	2.4 (4.4)	3.0 (5.4)	3.3 (5.3)	3.7 (6.4)
Num HT/day ^a	0.9 (1.2)	1.1 (1.1)	1.5 (1.3)	1.7 (1.3)	1.6 (1.4)	1.3 (1.2)	0.9 (1.2)	0.9 (1.1)	1.0 (1.3)	1.0 (1.2)
GRI ^a	30.4 (24.8)	28.4 (23.8)	21.3 (17.6)	20.8 (18.3)	21.5 (19.5)	23.4 (22.6)	26.5 (22.1)	26.8 (22.1)	29.6 (24.3)	29.3 (25.6)
TDI [U] ^a	41.6 (13.3)	42.5 (14.4)	35.3 (11.6)	35.9 (12.3)	34.7 (11.4)	34.2 (11.7)	41.2 (13.2)	41.6 (13.9)	42.0 (13.4)	42.6 (14.4)
TDBa [U] ^a	37.9 (12.0)	38.0 (11.9)	31.5 (10.2)	31.5 (10.2)	30.7 (9.7)	30.2 (9.6)	37.4 (11.2)	37.6 (11.4)	38.2 (11.8)	38.3 (12.0)
TDBo [U] ^a	3.8 (3.4)	4.5 (4.4)	3.9 (3.4)	4.5 (4.1)	4.1 (3.5)	4.0 (3.7)	3.8 (3.6)	4.1 (4.2)	3.8 (3.5)	4.3 (4.4)
$θ$ [-]^a	40.4 (13.0)	44.6 (19.2)	40.4 (13.0)	44.5 (19.1)	40.4 (13.0)	39.0 (16.4)	40.4 (13.0)	42.3 (17.9)	40.4 (13.0)	44.3 (20.4)

Results are presented as mean (standard deviation).

Abbreviation: BG, simulated blood glucose.

Statistically significant differences in glycemic metrics between two controller settings for the overall period (P > .05).

Table 5.

Glycemic Outcomes During the “Change in Insulin Needs” Scenario for Both AID and AID With PAS.

	Day 4		Day 5		Day 11		Day 21
Glycemic Metric	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS	AID	AID+PAS
Average of BG levels [mg/dL]^a	152.8 (46.1)	151.2 (46.1)	178.0 (59.5)	175.1 (59.1)	179.4 (57.4)	154.2 (48.7)	180.6 (57.6)	154.2 (49.8)
Standard deviation of BG [mg/dL] ^a	43.3 (12.5)	43.0 (12.6)	54.6 (17.4)	53.8 (17.4)	51.4 (18.5)	45.1 (14.7)	52.3 (17.4)	46.1 (13.9)
Coeff. of variation of BG levels [%]^a	28.1 (6.6)	28.1 (6.6)	30.2 (7.5)	30.2 (7.5)	28.1 (7.8)	28.8 (7.3)	28.5 (7.2)	29.5 (6.9)
Time spent <54 mg/dL [%]	0.1 (0.5)	0.1 (0.3)	0.0 (0.1)	0.0 (0.0)	0.0 (0.1)	0.1 (0.3)	0.0 (0.2)	0.1 (0.4)
Time spent <70 mg/dL [%]^a	1.2 (2.0)	1.3 (1.7)	0.2 (0.7)	0.2 (0.5)	0.4 (0.9)	1.4 (1.7)	0.4 (1.2)	1.5 (1.7)
Time spent in 70-140 mg/dL [%]^a	44.8 (9.6)	46.4 (9.9)	30.7 (8.5)	32.5 (9.1)	28.0 (9.1)	42.8 (8.8)	26.9 (9.1)	43.4 (10.0)
Time spent in 70-180 mg/dL [%]^a	73.0 (11.9)	74.5 (11.9)	58.1 (12.4)	60.5 (12.7)	56.9 (15.7)	73.0 (13.3)	55.3 (13.7)	71.5 (13.7)
Time spent >180 mg/dL [%]^a	25.7 (10.9)	24.2 (10.6)	41.6 (12.2)	39.3 (12.5)	42.7 (15.4)	25.6 (12.2)	44.3 (13.3)	26.9 (12.5)
Time spent >250 mg/dL [%]	3.4 (5.2)	3.3 (5.8)	13.2 (11.9)	12.0 (11.9)	12.5 (12.7)	4.8 (7.7)	12.7 (12.1)	4.7 (7.4)
Num HT/ Day^a	1.0 (1.4)	1.1 (1.2)	0.2 (0.6)	0.2 (0.5)	0.3 (0.7)	1.1 (1.2)	0.3 (0.8)	1.3 (1.3)
GRI ^a	29.2 (23.3)	28 (22.7)	54.8 (30.8)	51.1 (30.2)	55.1 (35.1)	31.8 (27.1)	56.7 (33.5)	31.9 (27.1)
TDI [U] ^a	42.0 (14.2)	42.8 (15.3)	52.7 (17.7)	54.0 (19.3)	53.6 (18.0)	61.6 (22.2)	54.3 (18.3)	62.9 (22.3)
TDBa [U] ^a	38.0 (12.3)	38.4 (12.7)	48.7 (15.8)	49.6 (16.6)	49.6 (16.1)	55.0 (17.2)	50.3 (16.8)	55.9 (18.0)
TDBo [U] ^a	4.1 (3.5)	4.3 (4.2)	4.0 (3.7)	4.4 (4.5)	4.0 (3.6)	6.6 (7.4)	4.0 (3.4)	7.0 (7.4)
$θ$ [-]^a	40.4 (13.0)	43.3 (17.7)	40.4 (13.0)	43.5 (17.9)	40.4 (13.0)	65.6 (31.9)	40.4 (13.0)	68.9 (34.1)

Results are presented as mean (standard deviation).

Abbreviation: BG, simulated blood glucose.

Statistically significant differences in glycemic metrics between two controller settings for the overall period (P > .05).

Discussion

Designing individualized or personalized control strategies for glycemic control remains a challenge in diabetes technology. Automated insulin delivery systems are typically designed at a population level, which could prove impractical for each patient due to individual fluctuations in insulin needs over time. While AID systems are primarily tuned considering in-silico populations that represent the variability of the real T1D population, edge cases can still result in high hyperglycemia or hypoglycemia exposure, regardless of whether more aggressive or more conservative control algorithms are used.

To overcome the challenges of designing a control system for each individual, various adaptation and personalization strategies have been proposed in the literature. However, most of these strategies require highly demanding computational implementations for real-time optimizations to adjust the controller.

In this work, we presented a strategy to automatically adapt or retune the controller’s aggressiveness on a daily basis using CGM-based hypo- and hyperglycemic metrics (PAI). In our proposal, two different options to compute PAI were considered, one based on time in ranges and another based on risks (LBGI and HBGI) over the previous two weeks. Both the glycemic metrics and the length of the time window can be modified as needed. Modifications to account for other relevant factors to insulin therapy, such as hypoglycemia treatments, could also be included. For instance, combining hypoglycemia rescues with TBR or LBGI as a new metric of hypoglycemia could help account for unreliable TBR resulting from consecutive hypoglycemia rescues, which may mainly affect in-silico testing where hypoglycemia treatments are automated.

Simulation results showed that the proposed PAS is safe in all the scenarios, as it keeps the controller settings consistent with the baseline scenario and recovers to approximately the desired glycemic outcomes (TBR and TAR) in the conservative and aggressive scenarios. For the baseline scenario, no differences between AID and AID+PAS were expected as the controller was tuned for the same in-silico population and with the correct TDI to initialize $θ$ . This simulation scenario showed that PAI will not modify the controller’s settings once the desired performance is achieved and will presumably reach a stationary state while insulin requirements remain constant over time. In addition, simulation results for the conservative and aggressive scenarios showed how PAS adjusts the controller safely and progressively to meet the individual insulin needs and performance goals. These scenarios aim to address one of the most common causes of poor AID performance in T1D, in which control algorithms may be either too aggressive or too conservative due to variable insulin needs, resulting in suboptimal glucose control.

Although it is not presented here, a similar analysis was performed using LBGI and HBGI to compute PAI. Simulation results show similar results to those computed using TBR and TAR. There was a slight improvement in TAR and a larger improvement on the time above 250 mg/dL, while maintaining similar levels of TBR. However, the $θ$ values for individual subjects tended to be more oscillatory, and sensitive to outlying glucose excursion events.

Scenarios 4 and 5 demonstrated the performance of the proposed PAS using PAI when insulin requirements change temporarily or permanently. In the first case, PAS safely attempted to mitigate the increase in TBR by reducing insulin infusion. This showed how the proposed strategy can handle such disturbances without compromising overall glycemic control. In addition, when a permanent change in insulin requirements was tested, the results showed that using AID+PAS the baseline performance of the controller could recover progressively and without oscillations that would put the patient at risk of hyperglycemia or hypoglycemia. A limitation of these simulations is the absence of a CGM error model, which may slightly affect the results.

Although the proposed index and strategy were evaluated only with our UVA AID, PAI, and PAS can be used in any AID system, as PAI is designed based exclusively on controller-agnostic metrics. In this regard, simulations with other control systems could be performed straightforwardly. Finally, the use of PAS is currently undergoing a clinical trial with humans and results are expected to be presented in 2025 (NCT06041971).

Conclusions

Individual variations in insulin needs present obstacles to optimal control in T1D, even to AID systems. Our work introduces a novel strategy for adapting the controller’s aggressiveness by using CGM-based metrics (PAI), offering a promising solution to this challenge. Simulations demonstrated that the proposed strategy effectively maintained safe control across various scenarios, adjusting insulin delivery accordingly. Furthermore, PAS showed resilience in addressing temporary and permanent changes in insulin requirements. Importantly, our approach is not limited to specific control algorithms, offering potential applicability across various AID systems. Clinical trials with the UVA AID + PAS are underway, promising further insights into its efficacy in real-world settings.

Supplemental Material

sj-docx-1-dst-10.1177_19322968251315499 – Supplemental material for A Performance-Based Adaptation Index for Automated Insulin Delivery Systems

Supplemental material, sj-docx-1-dst-10.1177_19322968251315499 for A Performance-Based Adaptation Index for Automated Insulin Delivery Systems by Jenny L. Diaz C., Patricio Colmegna, Elliot Pryor and Marc D. Breton in Journal of Diabetes Science and Technology

Footnotes

Abbreviations

AID, automated insulin delivery; T1D, type 1 diabetes; TIR, time in range; TBR, time below range; TDI, total daily insulin, therapy adaptation; FCL, fully automated closed loop; MPC, model predictive control.

Declaration of Conflicting Interests

The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: JD is at present an employee of Insulet Co. and this work was performed during her postdoctoral program at UVA during which she received research support and royalties from Dexcom handled by the University of Virginia’s Licensing and Ventures Group. P.C. is at present an employee of Dexcom, Inc. The work presented in this article was performed as part of his UVA appointment and is independent of his employment with Dexcom, Inc. MDB has received research support from Tandem Diabetes Care, Dexcom, and Novo Nordisk through his institution. MDB has received honoraria, travel expenses, and consulting fees from Roche Diagnostics, Dexcom, Vertex, Tandem, Sanofi, BoydSense, and Portal Insulin.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Jenny L. Diaz C.

Patricio Colmegna

Elliot Pryor

Marc D. Breton

Supplemental Material

Supplemental material for this article is available online.

References

Sherr

Heinemann

Fleming

, et al. Automated insulin delivery: benefits, challenges, and recommendations. A consensus report of the joint diabetes technology working group of the European Association for the Study of Diabetes and the American Diabetes Association. Diabetes Care. 2022;45(12):3058-3074. doi:10.2337/DCI22-0018.

Almurashi

Rodriguez

Garg

. A multidisciplinary reviews journal emerging diabetes technologies: continuous glucose monitors/artificial pancreases. J Indian Inst Sci. 2023;103:205-230. doi:10.1007/s41745-022-00348-3.

Brown

Forlenza

Bode

, et al. Multicenter trial of a tubeless, on-body automated insulin delivery system with customizable glycemic targets in pediatric and adult participants with type 1 diabetes. Diabetes Care. 2021;44(7):1630-1640. doi:10.2337/DC21-0172.

Karol

O’Malley

Fallurin

Levy

. Automated insulin delivery systems as a treatment for type 2 diabetes mellitus: a review. Endocr Pract. 2023;29(3):214-220. doi:10.1016/j.eprac.2022.10.001.

Turksoy

Cinar

. Adaptive control of artificial pancreas systems—a review. J Healthc Eng. 2014;5(1):1-22.

Toffanin

Visentin

Messori

Palma

Magni

Cobelli

. Toward a run-to-run adaptive artificial pancreas: in silico results. IEEE Trans Biomed Eng. 2018;65(3):479-488. doi:10.1109/TBME.2017.2652062.

Resalat

Hilts

Youssef

Tyler

Castle

Jacobs

. Adaptive control of an artificial pancreas using model identification, adaptive postprandial insulin delivery, and heart rate and accelerometry as control inputs. J Diabetes Sci Technol. 2019;13(6):1044-1053. doi:10.1177/1932296819881467.

Eren-Oruklu

Cinar

Quinn

Smith

. Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes. J Process Control. 2009;19(8):1333-1346. doi:10.1016/j.jprocont.2009.04.004.

Hajizadeh

Rashid

Samadi

, et al. Adaptive personalized multivariable artificial pancreas using plasma insulin estimates. J Process Control. 2019;80:26-40. doi:10.1016/j.jprocont.2019.05.003.

10.

Hajizadeh

Rashid

Sevil

, et al. Adaptive model predictive control for nonlinearity in biomedical applications. IFAC-PapersOnLine. 2018;51(20):368-373. doi:10.1016/j.ifacol.2018.11.061.

11.

Villa-Tamayo

Rivadeneira

. Adaptive impulsive offset-free MPC to handle parameter variations for type 1 diabetes treatment. Ind Eng Chem Res. 2020;59(13):5865-5876. doi:10.1021/acs.iecr.9b05979.

12.

Shi

Dassau

Doyle

. Adaptive zone model predictive control of artificial pancreas based on glucose- and velocity-dependent control penalties. IEEE Trans Biomed Eng. 2019;66(4):1045-1054. doi:10.1109/TBME.2018.2866392.

13.

Berget

Sherr

DeSalvo

, et al. Clinical implementation of the Omnipod 5 automated insulin delivery system: key considerations for training and onboarding people with diabetes. Clin Diabetes. 2022;40(2):168-184. doi:10.2337/CD21-0083.

14.

Kovatchev

. Glycemic variability: risk factors, assessment, and control. J Diabetes Sci Technol. 2019;13(4):627-635. doi:10.1177/1932296819826111.

15.

Garcia-Tirado

Corbett

Colmegna

Breton

. Advanced hybrid artificial pancreas system improves on unannounced meal response—In silico comparison to currently available system. Comput Methods Programs Biomed. 2021;211:106401. doi:10.1016/J.CMPB.2021.106401.

16.

Garcia-Tirado

Diaz

Esquivel-Zuniga

, et al. Advanced closed-loop control system improves postprandial glycemic control compared with a hybrid closed-loop system following unannounced meal. Diabetes Care. 2021;44(10):2379-2387. doi:10.2337/DC21-0932.

17.

Corbett

Garcia-Tirado

Colmegna

Diaz Castaneda

Breton

. Using an online disturbance rejection and anticipation system to reduce hyperglycemia in a fully closed-loop artificial pancreas system. J Diabetes Sci Technol. 2022;16(1):52-60. doi:10.1177/19322968211059159.

18.

Colmegna

Diaz

Garcia-Tirado

Breton

. Enabling anticipatory response in multi-stage MPC formulation for fully automated artificial pancreas system. Paper presented at the Proceedings of the 2022 IEEE 61st Conference on Decision and Control; December 2022; Cancun, Mexico. doi:10.1109/CDC51059.2022.9993157.

19.

Breton

Keith-Hynes

, et al. Overnight glucose control with an automated, unified safety system in children and adolescents with type 1 diabetes at diabetes camp. Diabetes Care. 2014;37(8):2310-2316. doi:10.2337/dc14-0147.

20.

Moscoso-Vásquez

Garcia-Tirado

Colmegna

Breton

. Reshaping model predictive control penalties for an automated insulin delivery system in type 1 diabetes. IFAC-PapersOnLine. 2023;56(2):9660-9665. doi:10.1016/J.IFACOL.2023.10.274.

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