Performance Effect of Adjusting Insulin Sensitivity for Model-Based Automated Insulin Delivery Systems

Abstract

Background:

Model predictive control (MPC) has become one of the most popular control strategies for automated insulin delivery (AID) in type 1 diabetes (T1D). These algorithms rely on a prediction model to determine the best insulin dosing every sampling time. Although these algorithms have been shown to be safe and effective for glucose management through clinical trials, managing the ever-fluctuating relationship between insulin delivery and resulting glucose uptake (aka insulin sensitivity, IS) remains a challenge. We aim to evaluate the effect of informing an AID system with IS on the performance of the system.

Method:

The University of Virginia (UVA) MPC control-based hybrid closed-loop (HCL) and fully closed-loop (FCL) system was used. One-day simulations at varying levels of IS were run with the UVA/Padova T1D Simulator. The AID system was informed with an estimated value of IS obtained through a mixed meal glucose tolerance test. Relevant controller parameters are updated to inform insulin dosing of IS. Performance of the HCL/FCL system with and without information of the changing IS was assessed using a novel performance metric penalizing the time outside the target glucose range.

Results:

Feedback in AID systems provides a certain degree tolerance to changes in IS. However, IS-informed bolus and basal dosing improve glycemic outcomes, providing increased protection against hyperglycemia and hypoglycemia according to the individual’s physiological state.

Conclusions:

The proof-of-concept analysis presented here shows the potentially beneficial effects on system performance of informing the AID system with accurate estimates of IS. In particular, when considering reduced IS, the informed controller provides increased protection against hyperglycemia compared with the naïve controller. Similarly, reduced hypoglycemia is obtained for situations with increased IS. Further tailoring of the adaptation schemes proposed in this work is needed to overcome the increased hypoglycemia observed in the more resistant cases and to optimize the performance of the adaptation method.

Keywords

type 1 diabetes automated insulin delivery model predictive control insulin sensitivity glucose management

Introduction

Automated insulin delivery (AID) systems have been shown to be safe and effective in improving glycemic outcomes in individuals with type 1 diabetes (T1D). However, insulin dosing in T1D is complicated by several physiological and psychobehavioral aspects influencing insulin demand. Fluctuating insulin needs due to metabolic variability are mostly linked to changes of an individual’s insulin sensitivity (IS), driven by factors such as circadian rhythms, physical activity, psychological stress, and menstrual cycle.^1,2 These time-varying insulin requirements represent an important challenge for fully closed-loop (FCL) systems. In this context, model predictive control (MPC) has become one of the most popular regulatory strategies for AIDs due to its flexibility and predictive ability.^3-6 These algorithms rely on a model of insulin-glucose dynamics to compute an optimal control policy satisfying a set of constraints within a predefined time horizon at each sampling. Although the effectiveness of MPC-based AID systems has been evaluated in various clinical studies, there are still challenges related to parametric uncertainty and unmodeled phenomena that could affect the performance of MPC.³,^7-9 These challenges are mainly due to the setting of biased parameters that negatively affect the accuracy of the model,^6,10,11 and the use of compact (oversimplified) models that only capture the basic dynamics and neglect complex interactions within the process.^3,12 To overcome these aspects, several approaches include a disturbance input to account for unmodeled phenomena. These approaches use low-order population models.^9,13 This provides a lumped measure of the overall model mismatch at each time instant, which increases the robustness of the controller. Alternatively, personalization strategies have been explored by modifying either the controller’s internal model^6,9,^14-20 and/or controller hyperparameters^3,13,16,^21-24 based on subject-specific clinical variables such as total daily insulin (TDI), correction factor (CR), or body weight (BW), or on the estimation of the transient dynamics and glucose variability, or model-individual mismatch. Furthermore, there is evidence that increasing model complexity in an MPC framework has no significant effect on controller performance, while adapting model parameters to a virtual patient population increases time in the normoglycemic range and decreases time in hypoglycemia.²⁵ In particular, online model identification to estimate IS and update the prediction model within the MPC has shown to reduce model-plant mismatch and improve glycemic control in situations where insulin action changes due to variations of insulin clearance or acute IS fluctuations due to exercise or during pregnancy.^17-19,²⁶ It is worth noting that in the latter approaches, the MPC does not include a disturbance input. In this regard, there is evidence indicating that personalized models and disturbance inputs can be used to improve performance within a zone MPC framework.^13,20 In addition, considering hybrid closed-loop (HCL) systems, different techniques were proposed to continuously track postprandial glucose dynamics and IS within an adaptive basal-bolus calculator,¹⁸ showing an increase in time in target range, and the ability of this scheme to handle different parametric variations by solely adjusting IS. Similarly, in Hovorka et al²⁷ a technique was proposed for tracking IS in real time from CGM and insulin pump data for its use in a smart bolus calculator; this algorithm was clinically validated, showing a reduced postprandial hypoglycemia following an exercise-induced IS increase.

Given the advantages that model personalization and IS tracking have shown in closed-loop systems, and in particular for MPC-based systems, in this work we evaluate whether these benefits are observed within our AID system both in its HCL and in its FCL configurations.²⁸ Considering that this AID system uses a disturbance input to account for the differences between the model and the individual, we aim to evaluate whether tracking the current metabolic state of the individual and tailoring the controller to adapt to it achieves protection against hypoglycemia and hyperglycemia when the person is experiencing increased or decreased IS. To evaluate how this adaptation can affect closed-loop performance in terms of clinically relevant metrics, we leverage the Food and Drug Administration–accepted University of Virginia (UVA)/Padova T1D simulator²⁹ to (1) obtain estimates of IS for the adult in silico population under different conditions and (2) evaluate the impact of IS-based controller adaptation using a novel performance index.

Methods

Evaluation of the effect on performance of an IS-informed HCL/FCL was performed in silico using the 100-adult UVA/Padova simulator^30,31 cohort in three steps: (1) modification of IS parameters in the simulator, (2) estimation of IS, and (3) performance analysis.

IS Variations in the Simulator

Modification of IS parameters related to insulin-dependent glucose utilization was made by multiplying each parameter by a factor $α \in [0.3, 2.5] .$ Specifically, insulin-dependent glucose utilization $(U_{i d} (t))$ in the simulator is modeled as follows:

U_{i d} (t) = \frac{(V_{m 0} + V_{m x} X (t)) G (t)}{K_{m 0} + G (t)},

(1)

where $X (t)$ is insulin action above the basal state, $G (t)$ is glucose concentration, and $V_{m 0}, V_{m x}, K_{m 0}$ are parameters regulating the behavior of glucose utilization as a function of glucose and insulin. To simulate changes of IS, parameters $V_{m 0}$ and $V_{m x}$ were multiplied by the factor α, allowing us to modify glucose utilization both in steady state (ie, when $I (t) = I_{b}$ and $X (t) = 0$ ) and in dynamic conditions. Then, for each value of $α,$ basal insulin infusion $(J_{b})$ to maintain a target glucose level of 120 mg/dL was obtained and kept constant during the whole experiments for the estimation of IS. Correction factors were not modified for these experiments.

Estimation of IS

Estimates of IS were obtained by means of a simulated mixed meal glucose tolerance test.³² For this, one-day simulations with a single meal with 80 g of carbohydrates (CHO) were performed, providing an insulin bolus determined based only on each subject’s CR. The estimation was performed based on a variation of the Subcutaneous Oral Glucose Minimal Model,³³ with a triangular submodel for the subcutaneous insulin transport infusion. The model equations are as follows:

\overset{\cdot}{G} = - S_{g} (G - G_{b}) - S_{I} X \cdot G + \frac{f R_{a} (t)}{V_{g}},

(2)

\overset{\cdot}{X} = - p_{2} X + p_{2} (I_{p} - I_{b}),

{\overset{\cdot}{I}}_{s c 1} = - (k_{a 1} + k_{d}) I_{s c 1} + J (t),

{\overset{\cdot}{I}}_{s c 2} = - k_{a 2} I_{s c 2} + k_{d} I_{s c 1},

I R_{a} = k_{a 1} I_{s c 1} + k_{a 2} I_{s c 2},

\dot{I_{p}} = - k_{c l} I_{p} + \frac{I R_{a}}{V_{I} \cdot B W} .

State variables and parameters for the model are described in Table 1.

Table 1.

State Variables, Input Variables, and Parameters With Their Respective Units and Population Values.

State	Description		Units
State variables
$G$	Blood glucose concentration		mg/dL
$X$	Insulin concentration in the remote compartment		mU/L
$I_{s c 1}$	Amount of insulin, first compartment		mU
$I_{s c 2}$	Amount of insulin, second compartment		mU
$I R_{a}$	Insulin rate of appearance in plasma		mU/kg/min
$I_{p}$	Insulin concentration in plasma		mU/L
Input variables
$R_{a} (t)$	Glucose rate of appearance in plasma		mU/kg/min
$J (t)$	Exogenous insulin infusion rate		mU/min
Parameter	Description	Nominal value	Units
$S_{g}$	Fractional glucose effectiveness	0.0046	$m i n^{- 1}$
$S_{I}$	Insulin sensitivity	$e x p (- 6.4417 - 0.063546 T D I^{a} + 0.05794 T D B^{b})$	$1 / m i n$ per m $U / L$
	Rate constant	0.01	$m i n^{- 1}$
$k_{a 1}$	Subcutaneous insulin model rate constant	0.001	$m i n^{- 1}$
$k_{d}$	Subcutaneous insulin model rate constant	0.018	$m i n^{- 1}$
$k_{a 2}$	Subcutaneous insulin model rate constant	0.0132	$m i n^{- 1}$
$k_{c l}$	Insulin clearance rate constant	0.127	$m i n^{- 1}$
$V_{g}$	Distribution volume of glucose	1.8	dL/kg
$f$	Fraction of intestinal absorption in plasma	0.9	[-]
$V_{I}$	Insulin distribution volume	9.31	L/kg
$G_{b}$	Basal glucose concentration	120	$m g / d L$
$I_{b}$	Basal insulin concentration	Subject-specific	mU/L
$B W$		Subject-specific	Kg

Abbreviation: BW, body weight.

Total daily insulin.

Total daily basal insulin.

Parameter $S_{I},$ representing IS, was estimated through model identification for all considered values for factor $α$ , maintaining all the other parameters at their population value. For this procedure, the prior for IS was obtained by means of the equation indicated in Table 1 for IS nominal value. In addition, bearing in mind that the AID system uses a linearized version of the model,¹ we set $G_{b}$ as 120 mg/dL and find $J_{b}$ as the insulin infusion required to maintain this target. This allows to obtain total daily basal and TDI under the assumption that basal needs correspond to 50% of the daily insulin requirements of the person. Estimates of IS were obtained by minimizing the squared difference between model predictions and the glucose trace obtained in the simulated oral glucose tolerance test, using Mathworks Matlab R2022b. The minimization was made using nonlinear least squares optimization (lsqnonlin) using a tolerance of $1 \times 10^{- 10},$ relative tolerance of $1 \times 10^{- 4},$ and a maximum number of function evaluations of 100.000. Model predictions were obtained solving the differential equations (ode45) using a maximum time step of five minutes.

Strategy for informing IS to the AID system

This individualization is carried out by modifying the MPC prediction model and key parameters in the controller according to the estimated IS. A schematic representation of the AID system and the key parameters modified is presented in Figure 1.

Figure 1.

Schematic representation of the AID system, displaying the key systems components and the integration of the estimated IS values.

AID system

The UVA AID system is a system that integrates the following modules: (1) a safety system (SSM) to compensate for imminent hypoglycemia by attenuating the control action; (2) a Hyperglycemia Mitigation System (HMS) to compensate for prevailing hyperglycemia by delivering correction doses; (3) a Bolus Priming System (BPS) to mitigate abrupt positive disturbances; (4) a Kalman Filter (KF) to estimate both states and disturbance input; (5) a linear MPC algorithm that regulates the basal insulin based on the KF estimates; and (6) a Bolus Calculator (BC) to generate prandial insulin boluses. The HCL uses all the modules, while in the FCL configuration, the BC module is turned off to not require any meal announcements. The reader is referred to³ a full description of each module.

Controller individualization

The proposed adaptation of the system considers modifications of the HMS, BPS, BC, and MPC modules. Overall, we modify key parameters within each module by a factor depending on the physiological state of the subject, defined as

S I_{r a t i o} = \frac{S I_{n o m}}{S I_{e s t}},

(3)

where $S I_{n o m}$ is the nominal or basal IS and $S I_{e s t}$ is the estimated IS of the subject. In this way, $S I_{r a t i o}$ is greater than one when an increased resistance (reduced IS) state is detected, and lower than one when an increased sensitivity (increased IS) state is detected.

KF and MPC

In order to embed the metabolic model¹ into the AID linear MPC formulation, the meal subsystem in the model is disregarded (for both HCL and FCL configurations) and a disturbance input $d (t)$ is added to account for unmodeled dynamics. The model is linearized and discretized with a five-minute sampling time, at $(u_{o p}, G_{o p}) = (J_{b}, 120),$ with $J_{b}$ being the subject-specific basal insulin rate determined in the “Estimation of IS” section. Input $d (t)$ is then estimated in the KF using CGM and insulin records from the last six hours. Tuning parameters for the filter are considered on a population basis and were optimized using clinical data. State and measurement noises were assumed to be white noise processes with covariance matrices selected to reflect the magnitude of disturbances and sensor noise.³⁴ In this context, $d (t)$ is assumed as a disturbance that includes the unmodeled phenomena directly affecting glucose dynamics, modeled to have constant dynamics, that is, $d_{k + 1} = d_{k},$ allowing the state estimator to correct the disturbance entering the main glucose dynamics.³ This estimation is used within the linear, discrete model to generate the predictions in the MPC algorithm.

To modify the action of the MPC based on IS, we consider two modifications: (1) $S I_{e s t}$ is used in the prediction model (Equation [2]) within the KF and MPC, and (2) the basal operating point $(u_{o p})$ for linearization is modified to be a function of the $S I_{r a t i o}$ defined in Equation (3). In this regard, we considered the values for $J_{b}$ obtained in “Estimation of IS” section, to obtain a description of its variation with factor $α,$ as follows:

u_{o p}^{I S} = u_{o p, r a t i o} * {u_{o p} |}_{α = 1},

(4)

where $u_{o p}^{I S}$ is the modified basal operating point, and ${u_{o p} |}_{α = 1}$ is the subject-specific basal insulin rate at nominal conditions. In this way, $u_{o p, r a t i o}$ is defined as the ratio between $J_{b}$ at each $α$ by $J_{b}$ under nominal conditions (ie, for $α = 1) .$ Considering that this value is not available in real settings, we characterize the relationship between $S I_{r a t i o}$ and $u_{o p, r a t i o},$ to tailor the modifications to the system solely with respect to $S I_{r a t i o} .$ Figure 2 presents the relationship between these ratios for all the in silico subjects, and its variation with factor $α$

Figure 2.

Relation with $S I_{r a t i o}$ and $u_{o p, r a t i o}$ for the different $α$ values considered. Colored dots are the observed ${S I_{r a t i o}, u_{o p, r a t i o}}$ pairs for each subject for each value of $α .$ The line represents the linear relation described in Equation (5). Color bar indicates the values of $α .$

It is observed that the modification of basal insulin needs $(J_{b})$ as IS changes is not constant for all values of $S I_{r a t i o},$ mainly due to nonlinearity in the model and, possibly, the modification selected for the parameters in the UVA/Padova simulator in the experiments. However, we can simplify the relationship through the following linear relation between $S I_{r a t i o}$ and $u_{o p, r a t i o} :$

u_{o p, r a t i o} = 0.5 (S I_{r a t i o} + 1), u_{o p, r a t i o} \leq 2 .

(5)

The correlation obtained for the linear definition is 0.8859 (P value < 10⁻⁴), indicating a significant, strong positive correlation. According to Equation (5), the operating point is increased as IS decreases, to compensate for the increased insulin requirements. Similarly, the operating point is decreased when insulin requirements are lower due to increased IS. However, the linear description offers a better fit for lower values of $S I_{r a t i o},$ that is, for the increased sensitivity cases.

HMS and BPS

In these modules, boluses are dependent on the subject’s TDI. For HMS, they are computed with CF estimates from the 1800-rule, that is, CF = 1800/TDI.³⁵ In turn, for BPS, they are computed as a percentage of the subject’s TDI. The integration of the IS estimate is thus made by computing TDI with the same scheme as the basal Operating point (OP). In this way, the TDI parameter for these modules is obtained as follows:

T D I^{I S} = 0.5 (S I_{r a t i o} + 1) {T D I |}_{α = 1},

(6)

where $T D I^{I S}$ is the modified TDI, and ${T D I |}_{α = 1}$ is the subject-specific TDI at the nominal conditions (average IS). The correlation obtained for the linear definition is 0.8859 (P value = 0), indicating a significant, strong positive correlation. As for the basal operating point, a safety bound was defined for $T D I^{I S}$ to be 50% higher than the one at nominal conditions.

BC

This module is used only for HCL and requires a meal announcement. Using the estimated CHO content of the meal, boluses are computed according to the following:

M e a l B o l u s = (\frac{C H O}{C R} + \frac{B G - B G_{t g t}}{C F}) - I O B .

(7)

The IS-informed BC would then modify the amount obtained through⁷ by a factor of $S I_{r a t i o},$ in a similar manner as the method used in Fabris et al.¹ Note that this would imply a proportional modification of both CR and CF, instead of solely modifying the correction element in the meal bolus as proposed for bolus calculators in Schmidt and Norgaard.³⁶

Performance Analysis of Personalized AID System

Performance of the HCL/FCL system when not informed (naïve) versus informed with changing IS levels was assessed using a novel performance metric penalizing the time outside the target glucose range. The index, $M P C_{r i s k},$ is given by the following:

M P C_{r i s k} = \sum_{j = 1}^{N_{s u b j}} 2 L B G I_{j}^{70} + H B G I_{j}^{180} + \frac{N_{j, H T}}{N_{D a y s}},

(8)

where $N_{s u b j}$ is the number of subjects considered, $N_{d a y s}$ is the number of days considered during the experiment, $N_{H T}$ is the number of hypoglycemic treatments per day, and $L B G I^{70}$ and $H B G I^{180}$ are modified low and high blood glycemic indices based on the high blood glucose index and low blood glucose index as defined in Kovatchev,³⁷ respectively. Such modification is introduced to emphasize the time spent in target glycemic range (TIR, $70 < B G < 180 m g / d L$ ) while penalizing deviations from it, as follows:

R i s k_{k} = \log B G_{k}^{1.084} - 5.381,

(9)

L B G I_{j}^{70} = \sum_{k = 1}^{N_{s a m p l e s}} 22.77 * R i s k_{k}^{2} \forall R i s k_{k} \leq 0 a n d B G_{k} < 70,

(10)

H B G I_{j}^{180} = \sum_{k = 1}^{N_{s a m p l e s}} 22.77 * R i s k_{k}^{2} \forall R i s k_{k} > 0 a n d B G_{k} > 180,

(11)

with $N_{s a m p l e s} = 288,$ the number of samples per day considering a sampling time equal to five minutes. As defined, a better performance is indicated by a lower value of $M P C_{r i s k}$

For this analysis, one-day simulations are performed for each value of $α,$ which is kept constant throughout the entire simulation. Although this represents a very simple scenario, it allows the examination of the effect of informing the IS that matches the physiological state of the individual to the controller, without other confounding factors present.

Three meals are provided at 7:00, 13:00, and 19:00 hours, with 80, 70, and 60 g of CHO respectively, considering that in FCL meals are unannounced. Intraday variability in IS and dawn phenomenon were not included. Hypoglycemia treatments (15 g CHO) were administered for BG lower than 60 g/dL, waiting 15 minutes before administering a new treatment, if needed.

Results

IS Estimation

Distribution of IS across the different values for $α$ is presented in Figure 3, where a pattern of increasing SI is observed as $α$ increases. It is worth noting that the obtained values of estimated IS are within physiological values for this parameter.^1,32 Ratio of the estimated IS by the value obtained at nominal conditions (ie, $α = 1$ ) is also presented in Figure 3. The figure shows that, by modifying $V_{m 0}$ and $V_{m x}$ as described above, we were able to induce changes in IS for each subject ranging from 0.3 to 3.5 times their nominal IS value. These ranges are consistent with intrasubject IS variation observed in the results of mixed meal glucose tolerance tests reported by Hinshaw et al.³⁸

Figure 3.

Top: Distribution of insulin sensitivity estimates across the different variation scenarios considered. Bottom: Ratio of insulin sensitivity with its value obtained at nominal conditions.

Performance Evaluation of Model and Controller Individualization

The variation of showing the effect of informing IS to the different modules of the AID system is presented in Figure 4.

Figure 4.

Performance index (left panels) and delta in performance with respect to the naïve controller (right panels) for the different stages of the adaptation strategy for the hybrid closed-loop (top) and fully closed-loop (bottom) systems. Solid black: Naïve (baseline) controller. Dashed orange: Model personalization with insulin sensitivity. Dotted blue: Model personalization with insulin sensitivity and individualized basal operating point. Dashed dotted purple: Model personalization with insulin sensitivity and individualized basal operating point and boluses.

The first observation is that solely informing the MPC prediction model improves the AID system’s performance, which is in line with findings that the quality of the prediction model is crucial to the performance of MPC algorithms.³⁹ According to this, improving the prediction model is also beneficial when using the disturbance input $d (t)$ that intends to capture unmodeled phenomena both in the HCL and in the FCL configurations. Updating the basal operating point, $u_{o p},$ does not provide a significant improvement on performance in the FCL case. For the HCL configuration, this update causes the performance index to increase, being similar to that of the naïve controller for the more resistant scenarios. The modification proposed for TDI in the HMS and BPS modules also presents the same effect as the basal operating point.

Glycemic outcomes for the naïve and IS-informed HCL and FCL systems are presented in Figures 5 and 6, respectively. A comparable or increased TIR is obtained by the informed controller in all cases, indicating better average performance than the naïve controller. For the increased sensitivity cases $(α > 1),$ a significant reduction in time spent below 70 mg/dL (TBR) is achieved without significantly increasing time spent in glycemic range above 180 mg/dL (TAR). In addition, we observe that there is not much difference in TIR between all stages of the adaptation. Analyzing the more resistant cases $(α < 1),$ the increased TIR is accompanied by a significant decrease in TAR, at the expense of an increase in TBR. It is also shown that for situations when the individual is more resistant, the effect of informing both basal operating point and boluses is larger than that of solely informing parameter SI in the model.

Figure 5.

Mean outcome metrics for the hybrid closed-loop system: naïve (empty black circles), insulin sensitivity–informed model (filled orange squares), insulin sensitivity–informed model and basal operating point (blue filled circles) and insulin sensitivity–informed model, basal operating point, and boluses (purple diamonds).

Figure 6.

Discussion

Insulin dosing is complicated due to several reasons such as user involvement to dose insulin for meals, education for carbohydrate counting to correctly dose insulin, and many other behavioral and metabolic factors that affect insulin needs. Such metabolic factors, as circadian rhythms, physical activity, psychological stress, menstrual cycle, and so on, vary greatly among the T1D population, but also among the same individual, mostly mediated by IS.

It has been shown that IS-informed bolus calculators improve outcomes for open loop and HCL therapy.^1,10,40 In this work, we find evidence that this advantage might also be appreciated when using IS to update the MPC’s internal model, basal operating point, and boluses in closed-loop systems, noting that the feedback action of AID system provides a degree of robustness to increased sensitivity up to 50% in terms of hypo-protection. To be noted, this evidence was obtained without temporal changes in SI, but rather a constant value for the duration of the experiments. Further work involves assessing the effects of these system modifications within a time-varying framework and developing the method for estimating IS in real time within our FCL/HCL system. In this regard, we intend to extend the method used in Fabris et al,¹ to include the estimation of IS within the FCL/HCL AID system and optimize insulin dosing modulation while removing the necessity of having accurate meal information as an input to track IS in the FCL framework. Moreover, this integration would also require modifying the characterization of the disturbance input and adding the estimation of IS in the Kalman filter as a separate state, to track both acute (induced by physical activity, for example) and longer-term IS fluctuations (intraday and interday variations).

From the proposed experiments, it could be noted that adapting all modules of our AID system is beneficial for glucose control. When analyzing the value of the $M P C_{r i s k},$ the most relevant improvements happen while solely informing the prediction model, while performance is degraded with the adaptation of the basal operating point and bolus calculations. While these adaptations still provide improvements over the naïve controller for increased IS scenarios, this is not the case for the increased resistance ones. In these cases, although the effect of adapting $u_{o p}$ and TDI for boluses has a larger effect in reducing hyperglycemia than solely updating the model, the sharp increase in hypoglycemia indicates that these modifications are too aggressive for some subjects, which would be expected from Figure 2, as for some subjects, the proposed relation for $u_{o p, r a t i o}$ is greater than the value observed for them. In addition, with these modifications an increase in TAR is obtained for the more sensitive cases driven by the same issue with the linear fit defined for $u_{o p, r a t i o},$ as for some subjects, the proposed relation yields a lower value than the observed for them. This could be improved by further personalizing the adaptation of the basal operating point for each subject, especially considering that for these scenarios the fit with the proposed linear relation was worse than for the increased IS cases and the detrimental effects in performance that were observed for both cases.

The proposed performance index based on hypoglycemia and hyperglycemia risks allows obtaining a condensed representation of the glycemic control achieved by the system using a single index. Moreover, although it is well known that risks are good indicators of glycemic control, the number of hypoglycemic treatments was also included in the performance index to avoid unreliable TBR values, as overly aggressive controllers can provide lower TAR and TIR but at the expense of increased hypoglycemia treatments, which in turn is detrimental to the individual’s quality of life. It is worth highlighting that for more resistant cases, including the adaptation of the basal operating point did not modify the value for the $M P C_{r i s k} .$ However, when looking at the glycemic outcome metrics we see that this modification implies a reduced time in TAR with increased TBR. The lowering impact that the reduced TAR implies in the proposed $M P C_{r i s k}$ is annulled by the increase in hypoglycemia that this modification causes, thus highlighting the ability of the proposed index to capture the quality of glucose control.

Finally, the controller’s tuning was optimized using $J_{p e r f}$ for the nominal naïve scenario, and thus, further improvement in terms of hypoglycemia protection might be achieved if it is also modified to consider the IS-based adaptation. Given that a controller’s robustness and achievable performance are a tradeoff, reducing uncertainty by informing IS could allow for improved performance.

Conclusions

Feedback in AID systems provides a certain degree of tolerance to changes in IS. However, IS-informed systems improve glycemic outcomes, providing increased protection against hypoglycemia and hyperglycemia according to the person’s physiological state. This proof-of-concept analysis highlights the beneficial effects of integrating accurate IS estimates into AID systems. These findings underscore the importance of considering IS fluctuations in MPC-based AID algorithms, offering valuable insights for optimizing T1D management. Further research is warranted to explore real-time methods for continuously updating IS estimates and refining their integration into AID systems. Clinical trials are also needed to validate the efficacy and safety of IS-informed MPC algorithms in real-world settings.

Footnotes

Abbreviations

AID, automated insulin delivery; BG, blood glucose; BW, body weight; BC, bolus calculator; BPS, Bolus Priming System; CHO, carbohydrates; CR, correction factor; FDA, Food and Drug Administration; FCL, fully closed loop; HBGI, high blood glucose index; HCL, hybrid closed loop; HMS, Hyperglycemia Mitigation System; IS, insulin sensitivity; KF, Kalman filter; LBGI, low blood glucose index; MPC, model predictive control; SSM, safety system mechanism; SOGMM, Subcutaneous Oral Glucose Minimal Model; TAR, time spent in glycemic range above 180 mg/dL; TBR2, time spent in glycemic range above 250 mg/dL; TBR2, time spent in level 2 hypoglycemia; TIR, time spent in target glycemic range; TDB, total daily basal; TDI, total daily insulin; T1D, type 1 diabetes; UVA, University of Virginia.

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: M.M-.V. receives research support and royalties through her institution from Dexcom. C.F. receives royalties from Dexcom and Novo Nordisk managed through her institution. M.D.B. receives research support through his institution from Tandem, Dexcom, and Novo Nordisk; M.D.B. received honorarium and travel compensation from Sanofi and Tandem; M.D.B. consults for Dexcom and Sanofi.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been supported by Dexcom, Inc (San Diego, California) and National Institutes of Health under Grant R01-DK-129553.

ORCID iDs

Marcela Moscoso-Vasquez

Marc D. Breton

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