Glucose control using dual-hormone model predictive control (MPC) with pramlintide compartments

Abstract

Systems and methods are disclosed for managing a person's blood glucose concentration within a predetermined range by co-administration of insulin and pramlintide using an automated insulin delivery system. A model predictive control (MPC) algorithm that includes a glucoregulatory control model augmented with a compartment model of pramlintide pharmacokinetics and pharmacodynamics is utilized. In some embodiments, the person may announce in advance meals to be consumed and the pramlintide-aware MPC algorithm uses this data as input to the glucoregulatory control model. In other embodiments, an automatic meal detection and size estimation algorithm is incorporated into the system to relieve the person of the burden of meal entry and carbohydrate estimation.

Description

GLUCOSE CONTROL USING DUAL-HORMONE MODEL PREDICTIVE CONTROL (MPC) WITH PRAMLINTIDE COMPARTMENTSRELATED APPLICATION

[0001] This application claims priority benefit of U.S. Provisional Patent Application No. 63 / 707,711 filed October 15, 2024, which is hereby incorporated by reference.ACKNOWLEDGEMENT OF GOVERNMENT SUPPORT

[0002] This invention was made with government support under R01 DK129382 awarded by The National Institutes of Health. The government has certain rights in the invention.TECHNICAL FIELD

[0003] This disclosure relates generally to type 1 diabetes (T1D) treatment intervention for a person using an automated insulin delivery system to co-deliver with insulin one or more compositions to improve glucoregulatory control. More particularly, this disclosure relates model predictive control (MPC) approaches that incorporate the pharmacokinetics and pharmacodynamics of a co-administered composition to reduce hyper- and hypo-glycemic excursions.BACKGROUND INFORMATION

[0004] The development of automated insulin delivery (AID) systems for treatment of patients with type 1 diabetes remains an active area of research. With the advent of bodymounted sensors that allow real-time measurement of blood glucose levels and infusion pump technology that can precisely dispense controlled amounts of insulin into the body, the realization of closed-loop and hybrid AID systems has progressed rapidly in recent years. A typical AID system comprises a sensor component for continuous glucose monitoring (CGM) data collection, a control algorithm to receive and operate upon the CGM data, and an insulin infusion pump component to automate delivery of insulin subcutaneously as prescribed by the control algorithm. While fully closed-loop systems with minimal user interaction are pursued as an ideal solution for glucose management, most systems to-date still require some amount of user input to effectively regulate glucose levels within an acceptable range. As an example, most systems perform best when meals are announced to the system (i.e., entered into the AID system via a user interface) with correct carbohydrate amounts entered before or immediately after meal consumption. However, thisrequirement for meal entry poses an additional burden on users of AID systems, and missed announcements and mis-estimates of carbohydrate amounts can cause errors in insulin dosage prediction, potentially leading to serious postprandial hypo- and hyperglycemic outcomes.

[0005] Amylin is a neuroendocrine hormone that is normally co-secreted with insulin from healthy beta cells in response to meal intake. In persons with type 1 diabetes, where amylin production and secretion is diminished or absent, amylin insufficiency contributes to postmeal glucose spikes. In recent years, synthetic amylin analogs such as pramlintide have been identified as effective agents to reduce the severity of post-meal glucose spikes. Part of pramlintide’ s effectiveness in mitigating postprandial hyperglycemic excursions is attributed to its ability to cause delayed gastric emptying. Because absorption of carbohydrates from meals is faster than absorption of insulin delivered subcutaneously, pramlintide has been investigated as a means to slow carbohydrate uptake after meals to blunt post-meal glucose increases. Such research has shown that pramlintide delivered with insulin can, indeed, be used to improve the postprandial glucose response in people with T1D. However, in the context of an AID system, there remains a need for effective control algorithms that can appropriately model the impact of pramlintide pharmacokinetics & pharmacodynamics (PK / PD) on delayed gastric emptying to optimize dosing to improve time in range. Further, there is a need for such pramlintide-aware models to be adaptable over time to match an individual’s own physiology and behavior, and to adjust individualspecific insulin sensitivity parameters during times when no meals are consumed.SUMMARY OF THE DISCLOSURE

[0006] A model-predictive control (MPC) algorithm that provides automated delivery of controlled amounts of insulin and pramlintide to a person with type 1 diabetes using continuous glucose measurements (CGM) sensed from the person’s subcutaneous tissue is disclosed. The MPC algorithm uses a physiologic model of the human glucoregulatory system and employs compartment modeling techniques to simulate pramlintide PK / PD effects. The term compartment may refer to a logical or mathematical representation of a region, volume, or phase within a pharmacokinetic, pharmacodynamic, or physiologic model in which a glucoregulatory hormone or other substance such as insulin, pramlintide, glucose, or a metabolite is assumed to be well mixed and to have uniform concentration. A compartment may correspond to a physical region of the body, such as subcutaneous tissue, plasma, or interstitial fluid, or it may represent an abstract or unobservable state variable that accounts for transport, delay, or metabolic conversion between regions. In someembodiments, compartments may be coupled through transfer coefficients or rate constants that describe exchange of material or information between compartments. Specific model parameters are included to describe a person’s insulin sensitivity, carbohydrate sensitivity, pramlintide sensitivity, and various kinetic and dynamic variables within this glucoregulatory system. When incorporated into an automated delivery system with associated hardware and software elements, the disclosed MPC control algorithm can be used to improve glycemic control in people with type 1 diabetes. Importantly, the control model as formulated herein can appropriately handle and predict the long-term kinetics and dynamics of insulin and pramlintide co-delivered through the subcutaneous route.

[0007] In a particular embodiment, the disclosed MPC algorithm includes a method for automatically detecting meals and meal sizes using an Al algorithm, and dosing insulin and pramlintide in response to those meals. When such meal detection is provided, predicting the glucose trajectory and calculating an appropriate dosing regimen using the disclosed MPC control algorithm can improve post-meal glucose outcomes. An important aspect of the model is its ability to target and provide glucose prediction trajectories during the period of time immediately after a meal and adaptively adjust insulin dosing during this period of time. Whereas other adaptive algorithms modify the manual insulin dose given immediately prior to a meal, the algorithm disclosed herein can be configured to adjust, in real time, the amount and timing of postprandial insulin delivery to better curtail glucose excursions. As used herein, the term postprandial refers to a period beginning upon detection or announcement of a meal and extending for up to approximately four hours thereafter, during which the person’s blood glucose concentration remains affected by the ingested meal.

[0008] In further embodiments, the disclosed MPC algorithm can include a method for adapting postprandial insulin amounts in response to prior postprandial hypoglycemia episodes. This method is called “Adaptive Learning Postprandial Hypoglycemia Prevention Algorithm” (ALPHA). Dosing insulin after meals can be challenging and can lead to hyperglycemia or late-term hypoglycemia if the dosing is not done properly. The ALPHA algorithm detects hypoglycemia after a meal and automatically adjusts the aggressiveness of post-meal insulin dosing to prevent subsequent postprandial hypoglycemia.

[0009] In yet further embodiments, the MPC algorithm may include a safety layer decision tree to prevent dosing of insulin and pramlintide under certain physician-specified conditions. For example, the meal insulin dosed automatically by the algorithm will never dose more insulin than will bring the person’s glucose down to 70 mg / dL when using the person’s correction factor, and assuming that the person has not actually consumed a meal. Another example of a safety layer is to limit the amount of insulin that the MPC deliversduring non-meal periods to no more than a prescribed amount, such as four times their typical (average) pre-specified basal insulin delivery amount. Additional implementations of possible safety layers are described in Mosquera-Lopez, C. et al. (2023) Automated Meal Detection and Meal Size Estimation Using Machine Learning: Towards Artificial - intelligence-enabled Fully Closed-loop Insulin Delivery Systems. Nat NP J Dig 6 (39) 1-7 which is incorporated by reference in its entirety herein.

[0010] In some embodiments, adaptive insulin sensitivity may be incorporated into the MPC algorithm, whereby the control model updates its insulin sensitivity automatically during certain periods of time. The insulin sensitivity of a person can vary in a circadian way, seasonally, and in response to external factors such as sleep, stress, and physical activity. For example, the control model can be configured to adapt the insulin sensitivity component during times when no meals are consumed (e.g. overnight) to help prevent nocturnal hypoglycemia. Insulin sensitivity is represented by the parameters p3 and p2 in Equation Set 3 of the Detailed Description of Embodiments section below. These parameters may be adjusted over time to ensure that the model estimation of the person’s glucose matches the person’s specific glucose responses.

[0011] In one aspect, a method is provided, performed by a computing device executing a model predictive control (MPC) glucoregulatory model, for automating the administration of one or both insulin and pramlintide to a person so as to maintain the person’s blood glucose concentration within a predetermined range. The method comprises receiving glucose data generated by a continuous glucose monitor (CGM) coupled to the person; calculating, using the MPC glucoregulatory model, a dose of insulin and a dose of pramlintide sufficient to maintain the person’s blood glucose within the predetermined range, in which the dose of pramlintide is determined at least in part from a pharmacokinetics and pharmacodynamics (PK / PD) pramlintide sub -model compartment included in the MPC glucoregulatory model and configured to predict an effect of pramlintide on delayed gastric emptying; and delivering, by an infusion pump coupled to the person for subcutaneous delivery, the dose of insulin or the dose of pramlintide or both insulin and pramlintide doses sufficient to maintain the person’s blood glucose within the predetermined range. The method may further comprise receiving meal consumption data entered by the person, the meal consumption representing carbohydrates consumed by the person. The method may further comprise detecting, by an automated algorithm, when the person has consumed a meal, estimating a size of the meal, and providing the size of the meal as input to the MPC model to calculate a dose of insulin and or a dose of pramlintide or both a dose of insulin and pramlintide sufficient to maintain the person’s blood glucosewithin the predetermined range. In one embodiment, a first compartment of the PK / PD pramlintide sub-model compartment tracks subcutaneous pramlintide. In another embodiment, a second compartment of the PK / PD pramlintide sub -model compartment tracks intact blood plasma pramlintide, and a third compartment tracks active metabolite pramlintide. The PK / PD pramlintide sub-model compartment may comprise state variables representing intact plasma pramlintide and a pramlintide metabolite and a term representing a pramlintide-dependent gastric emptying delay. In certain embodiments, calculating the dose of insulin and the dose of pramlintide comprises linearizing the MPC glucoregulatory model using a zero-order hold for pramlintide-related nonlinearities and a first-order hold for insulin-related nonlinearities. The computing device may receive a continuous glucose data stream and recalculate insulin and pramlintide doses at fixed intervals of about five minutes using updated state-space matrices. The method may further comprise automatically detecting a meal using a neural-network -based meal-detection algorithm and estimating a meal size, the meal size being provided as input to the MPC glucoregulatory model. In some examples, the computing device limits post -meal insulin dosing through a safety layer that prevents delivery of insulin predicted to reduce glucose below about 70 mg / dL. Insulin and pramlintide may be delivered as a fixed ratio co-formulation comprising about 6 micrograms of pramlintide per unit of insulin, or alternatively, insulin and pramlintide may be delivered independently through separate infusion channels controlled by the MPC glucoregulatory model. In another embodiment, pramlintide is delivered as a constant basal infusion proportional to an average daily insulin infusion rate while insulin is delivered in both basal and bolus modes. The MPC glucoregulatory model may adaptively update one or more insulin-sensitivity parameters based on one or more glucose measurements collected within a preceding period of several hours that reflect hypo- or hyperglycemia, or glucose responses to meals or physical activity. The MPC glucoregulatory model may include an adaptive postprandial hypoglycemia-prevention algorithm configured to reduce aggressiveness of post-meal insulin dosing following a detected hypoglycemia episode. The computing device may execute the MPC glucoregulatory model on a smartphone, smartwatch, insulin-pump microcontroller, or cloud server communicatively coupled to an infusion pump and a continuous glucose monitor. In some configurations, the computing device outputs insulin and pramlintide dose control signals to a dual -chamber infusion pump for subcutaneous co-delivery of hormones.

[0012] In another aspect, a non-transitory computer-readable medium is provided having stored thereon instructions that, when executed by one or more processors of a computing device, cause the computing device to perform the method described above.

[0013] In another aspect, a system is provided for automating administration of one or both insulin and pramlintide to a person to maintain the person’s blood glucose concentration within a predetermined range. The system comprises a continuous glucose monitor (CGM) configured to generate glucose data from the person; and a computing device communicatively coupled to the CGM, the computing device being programmed to execute a model predictive control (MPC) glucoregulatory model configured to receive the glucose data generated by the CGM; calculate, using the MPC glucoregulatory model, a dose of insulin and a dose of pramlintide sufficient to maintain the person’s blood glucose within the predetermined range, in which the dose of pramlintide is determined at least in part from a pharmacokinetics and pharmacodynamics (PK / PD) pramlintide sub -model compartment included in the MPC glucoregulatory model and configured to predict an effect of pramlintide on delayed gastric emptying; and transmit control information for delivery of one or more calculated doses of a glucoregulatory hormone, including one or both the calculated dose of insulin and the calculated dose of pramlintide. The computing device may be further configured to receive meal consumption data entered by the person, the meal consumption representing carbohydrates consumed by the person. The computing device may be further configured to detect when the person has consumed a meal, estimate a size of the meal, and provide the meal size as input to the MPC glucoregulatory model. In certain embodiments, a first compartment of the PK / PD pramlintide sub -model tracks subcutaneous pramlintide, a second compartment tracks intact plasma pramlintide, and a third compartment tracks active metabolite pramlintide. The PK / PD pramlintide sub-model may comprise state variables representing intact plasma pramlintide and a pramlintide metabolite and includes a term representing a pramlintide-dependent gastric-emptying delay. The computing device may linearize the MPC glucoregulatory model using a zeroorder hold for pramlintide-related nonlinearities and a first-order hold for insulin-related nonlinearities. The computing device may receive a continuous glucose data stream and recalculate insulin and pramlintide doses at fixed intervals of about five minutes using updated state-space matrices. The computing device may execute a neural -network -based meal -detection algorithm to estimate a meal size and provide the estimate as input to the MPC glucoregulatory model. In certain embodiments, the computing device limits postmeal insulin dosing through a safety layer that prevents delivery of insulin predicted to reduce glucose below about 70 mg / dL. The system may further comprise an infusion pump configured to deliver insulin and pramlintide as a fixed-ratio co-formulation comprising about 6 micrograms of pramlintide per unit of insulin, or alternatively, a dual -chamber infusion pump configured to deliver insulin and pramlintide independently through separateinfusion channels under control of the MPC glucoregulatory model. In some embodiments, the computing device controls an infusion pump to deliver pramlintide as a constant basal infusion proportional to an average daily insulin infusion rate while delivering insulin in both basal and bolus modes. The MPC glucoregulatory model may adaptively update one or more insulin-sensitivity parameters based on glucose measurements collected within a preceding period of several hours that reflect hypo- or hyperglycemia, or glucose responses to meals or physical activity. The MPC glucoregulatory model may include an adaptive postprandial hypoglycemia-prevention algorithm configured to reduce aggressiveness of post-meal insulin dosing following a detected hypoglycemia episode. The computing device may comprise a smartphone, smartwatch, glucoregulatory hormone microcontroller, or cloud server communicatively coupled to the glucoregulatory hormone microcontroller and the CGM. In certain embodiments, the computing device outputs insulin and pramlintide dose-control signals to a dual-chamber infusion pump for subcutaneous co-delivery of the hormones.

[0014] Additional aspects and advantages will be apparent from the following detailed description of preferred embodiments, which proceeds with reference to the accompanying drawings.BRIEF DESCRIPTION OF THE DRAWINGS

[0015] To easily identify the discussion of any particular element or act, the most significant digit or digits in a reference number refer to the figure number in which that element is first introduced.

[0016] FIG. 1 is a block diagram of a decision support system in accordance with one embodiment.

[0017] FIG. 2A is a block diagram of a model predictive control (MPC) algorithm in accordance with one embodiment.

[0018] FIG. 2B is a block diagram of an example metabolic model in accordance with one embodiment.

[0019] FIG. 3 is a block diagram of an example metabolic model in accordance with one embodiment.

[0020] FIG. 4 is a set of plots showing example simulation results from in silico subject consuming the same meal under four different scenarios, (1) insulin only AID, (2) pramlintide dosed as 6: 1 fixed ratio with insulin with an AID unaware of the pramlintide,(3) pramlintide dosed as a 6: 1 fixed ratio with MPC aware of the pramlintide in the process model, and (4) dual-hormone MPC independently delivering insulin and pramlintide.

[0021] FIG. 5 is an example interquartile plot of results across 6-day simulations from all participants for an insulin-only MPC (blue) and for AID with pramlintide delivered as a 6: 1 fixed ratio (red).

[0022] FIG. 6 is a time diagram of example CGM traces for a single in silico subject in response to a meal when the person is receiving five different rates of constant basal pramlintide.

[0023] FIG. 7 is a time diagram of an example a CGM trace for a single study participant using the insulin+pramlintide MPC vs. insulin-only.

[0024] FIG. 8 is a set of block diagrams showing example candidate models for insulin PK.

[0025] FIG. 9 is a set of block diagrams showing example candidate models for pramlintide PK.

[0026] FIG. 10 is a set of block diagrams showing example candidate models for glucoregulatory pharmacodynamics.

[0027] FIG. 11 is a block diagram of a system, according to one embodiment.

[0028] FIG. 12 is a block diagram of a computing device, according to one embodiment.DETAILED DESCRIPTION OF EMBODIMENTS

[0029] Disclosed herein is an adaptive model predictive control (MPC) control algorithm to automate the delivery of insulin and pramlintide to a person with type 1 diabetes. The algorithm can be run on a smart phone or alternatively within an insulin infusion pump or on any computing device. Unlike a PID controller, which delivers insulin based on the proportional distance of a person’s glucose from a target glucose level (P = proportional error) and the rate of change of the person’s glucose (D = derivative error), and the duration of time away from a target (I = integral error), an MPC uses a model of the glucoregulatory system and optimization techniques to determine the optimal insulin and pramlintide dosing schedule over a future time horizon sufficient to return the person’s glucose to a desired target level within a certain period of time. An advantage of the MPC is its ability to predict / anticipate long delays in glucose response caused by slow meal kinetics and even slower insulin kinetics for insulin delivered subcutaneously. The disclosed MPC is able to outperform traditional PID algorithms, and, when used within a fully automated system thatdoes not require the user to enter meals, a dual hormone insulin and pramlintide system can greatly improve glucose outcomes for people with type 1 diabetes.

[0030] The disclosed MPC model incorporates a compartment -based mathematical description of pramlintide pharmacokinetics and pharmacodynamics into a glucoregulatory control framework. The model describes how pramlintide is absorbed into the blood when delivered through a subcutaneous route. It also describes how the pramlintide, once in the blood, acts to delay gastric emptying, thereby capturing the dynamics of pramlintide on metabolism. An insulin-only approach to fully automated insulin delivery will inherently struggle with the slow kinetics of subcutaneous insulin infusion relative to the fast kinetics of carbohydrate absorption. The disclosed model incorporating pramlintide kinetics and dynamics is used within the MPC to determine the optimal amount of insulin and pramlintide that should be delivered to a person with type 1 diabetes. This feature can help prevent hypoglycemia or hyperglycemia that may be due to plant -model mismatch that can evolve over time.

[0031] FIG. 1 shows an Automated Dual Hormone Delivery (ADHD) system 100 including a personalized computing device 102 configured (e.g., using a smartphone app 104) to coadminister insulin and pramlintide according to a metabolic model formulated to account for pramlintide PK / PK effects on glucose dynamics 122. As described in this disclosure, ADHD 100 may be used to control delivery of insulin and pramlintide either as a co-formulation or independently (for example, using a dual-chamber infusion pump or two separate pumps).

[0032] Computing device 102 may include a mobile phone, infusion pump, smartwatch, server or combination thereof. In the example of FIG. 1, computing device 102 is shown as a smart phone configured to communicate with wearable glucose sensing and regulating medical devices 106, which include an infusion pump 108 and a continuous glucose monitor (CGM) 110 (or similar device configured to implement features for glucose monitoring). Also shown is an optional fitness tracker 112 (shown here as a smartwatch) for quantifying exercise, heart rate, or other metric of physical activity. In some embodiments, when device 122 is embodied as a watch, it may also serve as a computing device on which an app is executed and configured to present glucose measurements, receive user input, and / or communicate alerts or notifications. Wearable glucose sensing and regulating medical devices 106 may also include a relay personal diabetes manager (PDM) 114 to convey information between glucose sensing and regulating medical devices 106 and personalized computing device 102. Data may be stored locally on personalized computing device 102 and / or transmitted to and stored on a data repository 116 (e.g., to an Amazon Web Services (AWS) Cloud monitoring and data storage).Process Model

[0033] The prediction of blood glucose (BG) in our MPC algorithm is achieved using a glucoregulatory model, comprising a glucose kinetics model, insulin kinetics and dynamics models, and pramlintide kinetics and dynamics models. The model describes the relationship between subcutaneously delivered insulin and pramlintide and blood glucose concentration. The glucose kinetics model defines the effect of the insulin and actions on the blood glucose, as follows:Equation Set 1

[0034] In Equation Set 1, Q1and Q2are the masses of glucose in the accessible and non- accessible compartments, respectively, in mmol / L. xi and I describes the insulin kinetics, X describes the insulin dynamics, ai and a2 describe meal kinetics and lastly, QP1, QP2, and QP3describe the pramlintide kinetics.

[0035] Nonlinearities are apparent in this Equation Set 1, notably, the X*Q1term in the Q1equation and the (QP2+ QP3) term that is multiplied by other state variables in the Q1, ai, and a2 equations. While it is possible to solve for the insulin and pramlintide delivery using nonlinear optimization approaches, one can also linearize the model using, for example,either a zero order hold or a first order hold linearization. For a first order linearization, the following equation is used:Equation 2

[0036] For the insulin effect non-linearity, a first order hold linearization is employed and for the pramlintide effect non-linearity, a zero order hold linearization is employed. Since the model is implemented in discrete time and the states are recalculated every 5 minutes, the error due to the linear approximation is mitigated by recalculating the state space matrices with updated states. The matrix exponential method is used for converting the continuous time state space matrices into discrete time state space matrices, with a sampling time of 5 minutes. Using this approach, Equation Set 1 may be recast as follows:Equation Set 3

[0037] The linearized version of the model is given in Example 2 below, where the states with an asterisk are constants at the time of linearization, not state variables. K is a meal compartment to glucose compartment transfer variable, defined asEquation 4

[0038] Parameters for these equations are given in Table 1 and Table 2 below.Table 1 : Model parameters and example values.Table 2: Model states summary.Model Predictive Controller

[0039] Model predictive control is an optimization-based control algorithm, which considers the dynamic model of the plant. Unlike PID controllers, MPC is able to predict the future outputs and optimize the inputs to the plant accordingly.

[0040] FIG. 2A shows an example structure of an MPC control model 200 in accordance with embodiments described herein. FIG. 2B shows an example flow diagram of a compartment-based glucoregulatory model 250 with associated control equations. Theglucoregulatory model is the MPC process model. Typically, the plant would be the person using the artificial pancreas system. The plant (or person) receives hormones as an insulin infusion rate (IIR) or pramlintide infusion rate (PIR) and has a blood glucose level measured by a sensor (BG). For simulation purposes, the plant is approximated using the same glucoregulatory state equations described above. However, while the process model parameters are kept constant during the simulation and are set to the mean values from prior published studies, the plant model parameters vary for each virtual patient tested during simulation.

[0041] There are 10 state variables, which include state variables from the glucose kinetics model, the insulin kinetics model, the insulin dynamic models, the pramlintide kinetics model and the pramlintide dynamic model. The final linearized form of the MPC equations is as follows:Equation Set 5 xm(k + 1) = Amxm(k) + Bmu(k) + dm(k); y(k) = Cmxm(k);

[0042] In Equation Set 5, xm(k) is the state vector, u(k) is the 2-dimensional input vector (insulin and pramlintide) and d(k) includes the constant terms resulting from the linearization. Since the controller requires a history of the output for future predictions, it is essential to relate the input vector to the output. We define a new vector as follows:Equation 6 x(k) = [Δxm(k)Ty(k)]T

[0043] The augmented state equations are re-arranged as follows:Equation Set 7

[0044] The predicted outputs are calculated as follows:Equation Set 8Yp= Fx(k) + ΦΔU + ΨΔD,YP= [y(k + 1) y(k + 2) • • • y(k + )]T,ΔU = [Δu(k) Δu(k+1) • • • Δu(k+Nc-1)]T,AD = [Δdm(k) Δdm(k+1) Δdm(k+Nc-1)]T,

[0045] In Equation Set 8, the form and description of matrices F, Φ and Ψ are presented in [Wang L. Advances in Industrial Control. Vol. 1. Springer; 2009. Model Predictive Control System Design and Implementation Using Matlab; pp. 1-39], which is incorporated by reference in its entirety herein.

[0046] A prediction horizon of 300-minutes was chosen, given that the action of insulin is several hours. A 20-minute control horizon was chosen, as the results did not change substantially with a longer control horizon. The cost function is defined in Equation 9, which includes the reference trajectory (Rs) and the predicted outputs, and the tuning the control parameteras followsEquation 9

[0047] The output of the optimizer (future inputs) can now be computed by setting the derivative of the cost function with respect to ΔU to zero and; after some calculations, the optimal ΔU is defined in Equation 10 as follows:Equation 10

[0048] At the next step, some optimization constraints are imposed on the insulin and pramlintide delivery. For example, insulin can only be delivered in increments of 0.05 units, since this is the increment size used by commercial insulin infusion pumps. Insulin and pramlintide can also be constrained to only be delivered as a fixed ratio (e.g. 1 unit of insulin : 6 mcg of pramlintide). The maximum amount of insulin to deliver can also be constrained here to be a prescribed amount, for example, four times the average basal insulin amount as a part of the safety layer of the algorithm.Automatic Meal Detection

[0049] In some embodiments, the above-described model may be combined with automatic meal detection algorithms (see for example PCT / US2023 / 066417 “Machine Learning Based Meal Detection and Size Estimation Using Continuous Glucose Monitoring (CGM) andInsulin Data”, incorporated by reference herein) such that insulin and pramlintide can be dosed when meals are detected. In silico results show significant benefit of (1) insulin and pramlintide administered in a 6 mcg pramlintide to 1 u insulin co-formulation ratio, and (2) a model in the MPC that is pramlintide-aware. Delivering pramlintide with insulin into an automated insulin delivery system with meal detection can improve time-in-range (TIR, i.e., 70-80 mg / dL) from 70% to 83%. When PK / PD of pramlintide are included in the model, TIR further improves from 83% to 90%.Adaptive Learning Postprandial Hypoglycemia Prevention Algorithm (ALPHA)

[0050] In some embodiments, the above-described MPC model can be adaptive and change the aggressiveness of insulin dosing for a period of time (tagg_win) after a meal based on prior hypoglycemia episodes that occurred after a meal. This functionality, termed the “Adaptive Learning Post-prandial Hypoglycemia Avoidance” (ALPHA) algorithm, is described in greater detail in following references, both of which are incorporated by reference herein: Resalat, N., El Youssef, J., Reddy, R., Castle, J. & Jacobs, P. G. (2019) Adaptive tuning of basal and bolus insulin to reduce postprandial hypoglycemia in a hybrid artificial pancreas. Journal of Process Control 80 (7) 247-254; and Resalat, N., Hilts, W ., El Youssef, J., Tyler, N., Castle, J. & Jacobs, P. G. (2019) Adaptive Control of an Artificial Pancreas Using Model Identification, Adaptive Postprandial Insulin Delivery, and Heart Rate and Accelerometry as Control Inputs. Journal of Diabetes Science and Technology 13 (6) 1044- 1053. The ALPHA algorithm does not adapt insulin delivery after boluses delivered by the meal detection and dosing algorithm. If the patient’s glucose drops below a minimum glucose level (Gmin upper) between a time interval of tstart to tstop minutes after a meal, the drop in glucose (AG) below Gmin upper will be calculated and used to adjust an aggressiveness factor (Af) of dosing of insulin for the next meal. The aggressiveness factor may be defined as a value between 0 and 1 that can be multiplied by the final algorithm- calculated insulin infusion rate (IIR). If on subsequent meals after a change in Af there is no hypoglycemia between tstart and tstop, then Af will remain unchanged. However, if the patient’s minimum glucose between tstart to tstop is larger than a maximum glucose level (Gmax lower), then the aggressiveness factor may be increased so as to prevent post-prandial hyperglycemia. The increase or decrease in Af may be capped at 1 and 0 that correspond to maximum and minimum glucose levels (Gmax upper and Gmin lower, respectively). The change in the Af value may be programmed to occur for a window of time (tagg_win) after the time of the next meal (t meal).Example 1

[0051] The inventors have previously described the design of a single-hormone MPC and a dual-hormone MPC (insulin and glucagon) in a prior publication (Resalat, N., Youssef, J. E., Reddy, R. & Jacobs, P. G. (2017) Evaluation of model complexity in model predictive control within an exercise-enabled artificial pancreas. IFAC-PapersOnLine 50 (1) 7756- 7761; hereby incorporated by reference in its entirety). In that model a minimal insulin dynamics model and a 2-compartment insulin kinetics model were used to represent insulin PK / PD (Cobelli 1999, Kobayashi 1983). In the present disclosure, the single-hormone insulin-only MPC is extended to include a new model that models how pramlintide impacts a delay on gastric emptying.

[0052] In the description of the mathematical model that follows, several of the equations that were presented in Equations and Equation Sets 1 -10 above are recapitulated and presented in a alternate order to facilitate description of the specific model implementation described in this Example.

[0053] FIG. 3 shows a glucoregulatory model incorporating a specific formulation of a PK / PD compartment model to describe the effect of pramlintide on delayed gastric emptying. This specific pramlintide PK / PD model was selected from a set of candidate compartment model architectures based on goodness-of-fit to an experimental dataset (a description of alternate candidate models and their evaluation for goodness-of-fit to data is provided in Example 2 below). Parameter values and state descriptions for the model of FIG. 3 are the same as those presented previously in Table 1 and Table 2 above, respectively. Note that the dataset that was used to identify the model was collected during a meal tolerance test whereby participants came into a clinic and consumed a meal while receiving a proprietary co-formulation of insulin and pramlintide. Each participant received an 88 g carb meal with 45 mcg pramlintide and 7.5 U insulin. Blood metabolite data including glucose, insulin, and pramlintide (both intact pramlintide and an active metabolite, des-lys pramlintide) was collected for the next several hours.

[0054] In the model depicted in FIG. 3, oral carbohydrates are consumed and move from the gut, M1, into an unobservable compartment, M2, and finally into plasma, Q1. Subcutaneous insulin is infused into compartment Xiand moves into plasma, I. Subcutaneous pramlintide is infused into compartment QP1and then moves into blood plasma as intact pramlintide, denoted, QP2, and then as the active metabolite, denoted QP3. It is noted that the active metabolite has approximately the same physiological effect as intact pramlintide. The effect of pramlintide on the movement of carbohydrates into plasma is represented as the action of P on the gastric emptying coefficient 1 / tmaxG.

[0055] When a person eats a meal, the carbohydrates (Um) enter the gut (M1) and move into M2with a rate of

[0056] The percent of the meal utilized is handled by the variable Agwhereby an Ag of 1.0 indicates full meal utilization, and 0.5 indicates a 50% meal utilization. Agis included in the compartment transfer variable K, which incorporates the person’s body weight and converts the carbohydrate amount to the correct units whereby the 180 is a unit conversion term from mmol / kg into mg / kg.

[0057] The effect of the pramlintide on gastric emptying is given by the sensitivity factors SfP1and SfP2. We assumed that the intact and metabolite pramlintide act equivalently on the gastric emptying. The concentration of active pramlintide (P) is therefore the sum of the metabolite and the intact pramlintide (dividing by the volume of distribution of pramlintide, VP, to convert mass per mass to mass per volume).

[0058] The kinetics of pramlintide moving from subcutaneous into plasma are given by the following equations:

[0059] The effect of pramlintide on gastric emptying is represented by the pramlintide effect variables PEff1and PEff2, which are functions of SfP1and SfP2.

[0060] The meal carbohydrates move from M2into plasma (Q1). Glucose disposal out of Q1happens at a rate of pi which represents combined disposal due to brain and kidney uptake.

[0061] Insulin is delivered (Ui) to the subcutaneous space (Xi) and moves into the insulin in plasma compartment I with a rate constant ka.

[0062] Insulin in plasma (X) acts to mediate disposal of glucose out of Q1according to Equation 10. Insulin also moves into an unobservable compartment Q2at a rate k21.Linearizing the glucoregulatory model

[0063] The model described above is nonlinear in that states are being multiplied together in the state-space equations (e.g. in Equation 10, Q1is being multiplied by X). It is simpler and less computationally complex to integrate a linear model into an MPC framework compared with a nonlinear model. We evaluated two different ways to linearize the model, a zero-order hold approach (ZOH) and a first-order hold (FOH) approach. There are two places in the model where a nonlinearity occurs, the impact of pramlintide on the gastric emptying (Equations 1-2) and the impact of insulin and pramlintide on the glucose disposal (Equation 10).

[0064] Equations 1-14 are put into state-space format in which states Xi through X10 are Q1, Q2, XI, I, X, M1, M2, QP1, QP2, and QP3, respectively. The state-space representation of the system is then given in Equation 15.

[0065] A is the state transition matrix, X is the vector of state values, B represents the impact of the inputs (pramlintide and insulin) on the change in states. G represents the impact of meals (um) on the change in states. The vector D represents terms which are constant with respect to the state variables; these are mostly derived by the linearization process.

[0066] For ZOH linearization, the nonlinear components of the state transition matrix are set to their current value and presume that they remain constant during the prediction horizon.

[0067] For FOH, one can start with the original nonlinear ODEs,

[0068] where the function F is the right-hand side of the system of differential equations. Note that F is a nonlinear function mappingwith n being the number of state variables of the model. To obtain A and d, we will make a first-order approximation, where X* = X(t*) is the point around which the equations are linearized; the linearization time t* is typically the current time when the next control step is to be computed.

[0069] where DXF is the Jacobian matrix of F with respect to X, with the i, j’th element of the DXF equal to dFi / dXj. Equation 17 can be written more briefly as

[0070] Note that the terms A(X*) and d(X*) are only functions of the approximation point X*, so Equation 18 is a linear inhomogeneous ODE for X. The linearized version of the system in equations 1-14 are provided in detail in Example 3 below.

[0071] The state space representation of the MPC process model is given in Equations 19- 20 as xm(k + 1) = Amxm(k) + Bmu(k) + dm(k) (E-19) y(k) = Cmxm(k) (E-20)

[0072] where xm(k) is the state vector, u(k) is the input vector (insulin and pramlintide), and d(k) is the constant term originating from the linearization of the nonlinear interactions between the states using the linearization approaches described above. The linearized process model described above is used to determine the predicted glucose levels over a prediction horizon of 300 minutes (NP), which are then compared with a reference trajectory. When the person’s glucose is above a target glucose level (e.g. 110 mg / dL), then the reference trajectory is a straight line from the current glucose level to the target glucose level across the prediction horizon. When glucose is less than the target glucose level, the reference trajectory exponentially approaches the target as described in Resalat et al (Resalat (2017); supra). Additional description of the MPC methods are detailed in the following two publications, and incorporated by reference herein: Resalat, N., El Youssef, J., Reddy, R. & Jacobs, P. G. (2016) Design of a dual-hormone model predictive control forartificial pancreas with exercise model. Conference proceedings : IEEE Eng Med Bio Conf. 2016 2270-2273, and Resalat, N., El Youssef, J., Tyler, N., Castle, J. & Jacobs, P. G. (2019) A statistical virtual patient population for the glucoregulatory system in type 1 diabetes with integrated exercise model. PloS One 14 (7) 1-17.Meal detection and dosing

[0073] A previously described meal detection and dosing (MDD) algorithm described in Mosquera-Lopez, C. et al. (2023) Automated Meal Detection and Meal Size Estimation Using Machine Learning: Towards Artificial -intelligence-enabled Fully Closed-loop Insulin Delivery Systems. Nat NPJ Dig 6 (39) 1-7 and incorporated by reference herein was used that includes a neural network to estimate the probability of a meal and the meal size. MDD techniques are also a subject of United States Patent Application No. 18 / 858,236 filed October 18, 2024, which is hereby incorporated by reference in its entirety. For instance, an MDD algorithm dosed the amount of insulin that would optimize the benefit using a digital twin to replay various meal doses in response to the detected meal. Examples of digital twin technologies are described in International Application Publication No. WO 2025 / 165924 published August 7, 2025; and U.S. Provisional Patent Application No. 63 / 767,492 filed March 5, 2025; and both aforementioned applications are hereby incorporated by reference in their entireties. The final amount of insulin was limited by a safety layer that would prevent delivery of insulin that would bring the person’s glucose below 70 mg / dL based on their correction factor. An example safety layer would also have a maximum infusion rate of no more than four times a pre-specified basal insulin infusion rate.Results

[0074] Several approaches were evaluated for delivering pramlintide during AID. For all simulations, the OHSU T1D simulator was used (Resalat, et al. (2019); supra) with the addition of the population PK / PD model of pramlintide incorporated. No meal announcements were provided to any of the virtual patients such that we relied on the meal detection and dosing algorithm for all meal insulin. Real-world meals were delivered to the virtual patients and delivery times from the open source type 1 diabetes in exercise initiative data set (Riddell, M. et al. (2023) The Type 1 Diabetes EXercise Initiative (T1DEXI): Examining the acute glycemic effects of different types of structured exercise sessions in type 1 diabetes in a real-world setting. Diab Care 46 (4) 704-713) which includes carbohydrate meal amounts confirmed through food photography. These real -world meals scenarios lasted between 3 and 12 days.Fixed ratio vs independent control of pramlintide

[0075] Three use cases were evaluated for the MPC model described above. In the first case, the performance of the insulin-only MPC was evaluated. In the second case, the MPC was evaluated when pramlintide was dosed at a fixed ratio of 6 mcg of pramlintide per unit of insulin. This delivery approach was designed to emulate an AID that delivers a coformulation of insulin and pramlintide at a ratio of 6: 1. This fixed ratio delivery of insulin was evaluated for an MPC that had a process model that was unaware of the pramlintide delivery (pram-unaware), and also with an MPC that was aware of the pramlintide delivery (pram-aware). In the third case, a dual-hormone MPC that allowed for independent delivery of insulin and pramlintide was evaluated.

[0076] Results from these case experiments are shown in Table 3. The percent time in range (TIR, 70-180 mg / dL) improved from 64.1% in the insulin-only experiment to 91.6% when insulin and pramlintide were delivered at a fixed ratio with the process model in the MPC aware of the pramlintide being delivered. There was significant improvement in TIR when the process model was aware of the pramlintide (78.7% vs 91.6%). Interestingly, the TIR was higher for the insulin and pramlintide delivered as a fixed ratio compared with independent control of the insulin and pramlintide (91.6% vs. 87.5%). While this result was surprising, it was surmised that this behavior was because there was a benefit of having pramlintide on board at the time that the meal was consumed. Since the MPC had no knowledge in advance of a meal being consumed, it was not possible to dose pramlintide in advance of the meal when pramlintide and insulin were dosed independently. Therefore, the pramlintide on board at the time of the meal detection was oftentimes close to zero for the independent control of pramlintide and insulin.

[0077] Table 3: Results comparing an insulin-only MPC with insulin and pramlintide delivered as a fixed ratio of 6 mcg pramlintide: 1 u insulin and when delivered independently.

[0078] FIG.4 shows an example from one participant across each of these conditions in response to a meal. Notice that the peak CGM is significantly lower when pramlintide is delivered compared with the insulin-only example. Notice also that when the MPC process model is unaware of the pramlintide, it is not as successful at bringing the person’s glucose down to baseline following the meal because the process model is not aware that the carbohydrate will be on board for a longer period of time due to the delayed gastric emptying caused by the pramlintide.

[0079] FIG. 5 is an interquartile plot showing how across 99 virtual patients, the pramlintide-aware MPC delivering at a 6: 1 fixed ratio significantly reduced the postprandial glucose spike.

[0080] The meal detection and dosing (MDD) algorithm detected 51% of the meals in the insulin-only study with about 0.81 false positives per day. We defined a true positive meal detection if the meal was detected within 45 minutes following a meal consumption. The sensitivity of the MDD algorithm dropped because the slope of the CGM following a mealwas lower and also because the meal detection was likely detected beyond the 45-minute dosing window.Pramlintide delivery at fixed basal levels

[0081] Pramlintide has the potential to cause nausea. It may be that delivering high doses of pramlintide is what causes the nausea and that if pramlintide were delivered at a constant rate throughout the day, there may be a benefit without the nausea. The impact of different constant basal pramlintide delivery amounts on glucose outcomes were evaluated in a pramlintide-aware MPC. Pramlintide was delivered at a constant rate that was a function of the participant’s average daily insulin infusion rate (IIR) such that basal pramlintide was delivered at either 2, 4, 6, 8, or 10 mcg / hr x IIR. Results shown in Table 4 indicate that TIR improved as more basal pramlintide was delivered compared with the insulin-only arm. The best TIR (89.1%) was achieved for the 10 mcg / hr x IIR delivery rate. This was worse performance than when insulin and pramlintide were delivered as a fixed-ratio with a pramlintide-aware MPC, even though the average total daily pramlintide delivered was more during the constant basal pramlintide delivery.

[0082] Table 4: Mean and standard deviation results comparing an insulin-only MPC with and insulin-only MPC that is aware of the pramlintide delivery and the PK / PD of pramlintide, but when pramlintide is delivered as a fixed basal amount constantly throughout the day and night at different levels as a function of the basal insulin infusion rate (IIR): 2, 4, 6, 8, and 10 mcg / hr times the IIR.

[0083] FIG. 6 shows results from a single subject that shows how the postprandial peak glucose drops as more basal pramlintide is delivered at a constant level. These results are from in silico subject consuming the same meal using an insulin-only MPC with pramlintide delivered at 5 different rates as a multiple of the person’s automated basal insulin infusion rate (IIR): 2 mcg / hr × IIR, 4 mcg / hr × IIR, 6 mcg / hr × IIR, 8 mcg / hr × IIR, 10 mcg / hr × IIR. Meal detection insulin is dosed later as more basal pramlintide is dosed as shown by the blue circle and red star.Evaluation in humans

[0084] A human study (NCT06422325, IRB25279) was conducted to evaluate the pramlintide unaware MPC whereby participants came to the OHSU clinic and consumed two meals either using an insulin-only MPC or a pramlintide unaware MPC that delivered pramlintide at a fixed ratio of 6 mcg pramlintide : 1 u of insulin. Participants consumedapproximately 60 g of carbohydrates for each meal that was a function of their body weight and total daily carbohydrate needs. A preliminary safety analysis was performed on the first several subjects.

[0085] FIG. 7 shows results from one participant the study evaluating the insulin+pramlintide MPC vs. insulin-only. Postprandial glucose is significantly reduced with pramlintide. For this participant, postprandial time in range is nearly 100% when pramlintide is delivered.Discussion

[0086] We have presented in this Example 1 a model that describes PK / PD of pramlintide within a glucoregulatory model. We demonstrate that including this model within the process model of an MPC AID algorithm significantly improves glucose outcomes. While it is important to inform the MPC model of the pramlintide delivery using the PK / PD model of pramlintide, there is not a benefit of independent control of insulin and pramlintide (Table 3). Delivering constant basal pramlintide as a function of daily insulin requirements improves time in range compared with an insulin only MPC. The benefit was not as significant as when pramlintide was delivered as a fixed ratio with insulin that also dosed automated meal insulin using MDD.

[0087] It was surprising that results did not show a very high time below range (70 mg / dL) as is oftentimes observed in people with T1D on AID therapy. This was likely because there were no meal announcements given in this study, meaning that participants’ glucose levels were generally high (FIG. 4).Conclusion

[0088] Pramlintide can improve glucose outcomes in AID therapy. A coformulation of insulin and pramlintide at a ratio of 6: 1 is a promising way to enable automated insulin and pramlintide delivery using current insulin pump technology. Independent delivery of insulin and pramlintide and constant basal delivery of pramlintide also provides benefit.Example 2

[0089] While the glucoregulatory model used in Example 1 employed the architecture depicted in FIG. 3, those skilled in the art will recognize that alternate formulations may also be used, and that for purposes of fitting real world data to an appropriate model it can be advantageous to evaluate several variations of compartment models for their ability to recapitulate results from real world experiments. In this Example 2 section, several nonlimiting examples of candidate model formulations are presented for demonstrativepurposes. These models differ somewhat in structure, and are collectively evaluated towards the goal of designating a preferred model which we may be applied to the problem of glucose control. The model evaluation problem presented in this example is divided into three parts, corresponding to the insulin pharmacokinetics (PK), pramlintide PK, and glucoregulatory pharmacodynamics (PD) subsystems. In the examples provided here, six insulin PK, six pramlintide PK, and eight glucoregulatory PD models are evaluated. However, it will be appreciated by those skilled in the art that the candidate models presented here are non-limiting to the disclosure and that alternate formulations are possible.

[0090] For each subsystem model presented below, best-fitting parameters were found by random sampling (implemented in Stan, as described further below). For each set of parameter values, the system of ODEs for the subsystem was solved, and the estimated values of observable quantities (insulin for insulin PK, intact pramlintide and active pramlintide metabolite for pramlintide PK, and glucose for the glucoregulatory PD) compared with experimental measurements.Candidate models for Insulin PK

[0091] FIG. 8 shows six candidate models for insulin pharmacokinetics that were studied. Compartments Qi 1, Qi 1 a, and Qi 1brepresent a subcutaneous bolus. LD, LDa, and LDb represent local degradation with Michaelis-Menten kinetics. Compartment Qi2represents transport from the subcutaneous region to plasma, and Qi3 represents insulin in plasma. Compartment e is an elimination compartment. 3 The variations which were evaluated are whether there is one pathway or two pathways, in parallel, from subcutaneous bolus to plasma, whether there is local degradation in the one-pathway model, and whether the rate coefficient from the intermediate compartment Qi2to plasma Qi3is an independent free parameter. As with the pramlintide PK models, for each model structure there is a corresponding set of differential equations. For each model in which local degradation (LD) is present, the parameters KMand Vmax have the values KM= 62.6 mU and V max 1.93 mU / min, respectively, and m is body mass in kg.

[0092] * Insulin PK models 1 and 2. Model 1 is the same as model 2, except that model 1 has ki2=ki1

[0093] * Insulin PK models 3 and 4. Model 3 is the same as model 4, except model 3 has ki2=ki1.

[0094] * Insulin PK models 5 and 6. Model 5 is the same as model 6, except model 5 has ki3=ki1.

[0095] The candidate model block diagrams depicted in FIG. 8 and their associated parameters are summarized as follows: Upper Diagram: models 1, 2, 3, and 4 with one pathway and with or without local degradation. Lower Diagram: models 5 and 6, with two pathways and local degradation. Model 1 : ki2 = ki1, no local degradation. Model 2: ki2ki1, no local degradation. Model 3: ki2= ki1, with local degradation. Model 4: ki2ki1, with local degradation. Model 5: ki3= ki1. Model 6: ki3ki1Candidate models for pramlintide PK

[0096] FIG. 9 shows six candidate models for pramlintide pharmacokinetics that were evaluated for suitability in the disclosed MPC framework. Compartment QP1represents a pramlintide bolus delivered subcutaneously, QP2represents intact pramlintide in plasma, and QP3represents pramlintide active metabolite (des-lys pramlintide) in plasma. Qe2and Qe3are elimination compartments. The variations which were evaluated are the presence or absence of a path from compartment QP1to QP3, and from compartment QP2to QP3, and the presence or absence of so-called hidden compartments QP4and QP5, which are not directly connected to an input or elimination compartment. For each model structure, there are similar sets of differential equations:

[0097] * Pramlintide PK model 1

[0098] * Pramlintide PK model 2

[0099] * Pramlintide PK model 3

[0100] * Pramlintide PK model 4

[0101] * Pramlintide PK model 5

[0102] * Pramlintide PK model 6

[0103] The candidate model block diagrams depicted in FIG.9 and their associated parameters are summarized as follows: Upper Diagram: models 1 and 4, with pathway QP1→ QP3, and without pathway QP2→ QP3. Center Diagram: models 2 and 5, with pathways QP1→ QP3and QP2→ QP3. Bottom Diagram: models 3 and 6, without pathway QP1→ QP3, and with pathway QP2→ QP3. Model 1: with pathway QP1→ QP3, and without pathway QP2→ QP3, without hidden compartments. Model 2: with pathways QP1→ QP3and QP2→ QP3, without hidden compartments. Model 3: without pathway QP1→ QP3, and with pathway QP2→ QP3, without hidden compartments. Model 4: with pathway QP1→ QP3, and without pathway QP2→ QP3, with hidden compartments. Model 5: with pathways QP1→ QP3and QP2→ QP3, with hidden compartments. Model 6: without pathway QP1→ QP3, and with pathway QP2→ QP3, with hidden compartments. Candidate models for glucose PD

[0104] FIG.10 shows eight candidate models for glucose pharmacodynamics that were evaluated for suitability in the disclosed MPC framework. Compartment QS0, or QS1if QS0is not present, represents carbohydrate input to the stomach. Compartment QS2represents carbohydrates in the gastrointestinal system. Compartment QG1represents glucose in plasma, while QG2represents glucose in the interstitium. There is an input path in addition to carbohydrates in the digestive system, namely endogenous glucose production (EGP). There are also several output paths. The main glucose pathway leads from the carbohydrate compartments through glucose in plasma to the interstitium and thence to insulin-mediated glucose uptake (IMGU). There is an output pathway for carbohydrate elimination (SE), representing unutilized carbohydrates in the digestive system, and for glucose outputs, renal elimination (RE), and non-insulin-mediated glucose uptake (NIMGU), comprising mostly glucose uptake in the brain.

[0105] The equations for the glucoregulatory models are the following. The factor a appearing in the equations foris the conversion factor for converting glucose to the correct units, a=1000 / 180 mmol / g.

[0106] * Glucoregulatory models 1, 2, 3, 4, 5, and 6: Models 1, 2, and 3 are the same as model 4 with the following differences. Model 1: kG1,S2= kS2,S1, kSEfixed. Model 2: kG1,S2̸= kS2,S1, kSEfixed. Model 3: kG1,S2= kS2,S1, kSEvariable. Model 4: kG1,S2̸= kS2,S1, kSEvariable. Models 5 and 6 have the same structure as model 3, except that SfP1 ̸= SfP2 in both cases; model 5 has no effect of P on kSE, while model 6 does.

[0107] * Glucoregulatory models 7 and 8: Model 7 is the same as model 8, except model 7 is without action of P on kSE.

[0108] The candidate model block diagrams depicted in FIG. 10 and their associated parameters are summarized as follows: Upper Diagram: models 1, 2, 3, and 4, with SfP1= SfP2, without QS0, and without action of P on kSE. Lower Diagram: models 5, 6, 7, and 8, with SfP1SfP2, with or without QS0, and with or without action of P on kSE. Model 1 : kG1,S2= kS2,S1, kSEfixed. Model 2: kG1,S2kS2,S1, kSEfixed. Model 3: kG1,S2= kS2,S1, kSEvariable. Model 4: kG1,S2kS2,S1, kSEvariable. Model 5: SfP1SfP2, without QS0, and without action of P on kSE. Model 6: SfP1SfP2, without QS0, and with action of P on kSE. Model 7: SfP1SfP2, with QS0, and without action of P on kSE. Model 8: SfP1SfP2, with QS0, and with action of P on kSEParameter Inference via Markov Chain Monte Carlo

[0109] For each candidate model, a search was conducted for parameter values to maximize goodness of fit, defined as mean squared error (MSE), the square of the difference between the value predicted by the model at a point in time, and the measured value for the quantity predicted by the model; the predicted quantities are insulin concentration for the insulin PK model, intact pramlintide and pramlintide active metabolite concentrations for the pramlintide PK model, and glucose concentration for the glucoregulatory PD model.Maximum Likelihood and Formal Bayesian Inference

[0110] The software package Stan was used for parameter inference. Stan implements full Bayesian inference, taking both prior and likelihood into account. Stan samples from the posterior of the joint distribution of parameters given the observed data.

[0111] However, in all of the results reported here, the prior for each parameter is a distribution which is uniform over an interval, and the posterior is therefore proportional to just the likelihood and constrained to the support of the prior (the interval over which the prior is nonzero). In effect, then, all inferences are just constrained maximum likelihood. Markov Chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo.

[0112] A central goal in any Bayesian analysis is the construction of the posterior distribution of model parameters. This requires explicit or implicit integration over the parameter space, and, in general, numerical methods are necessary, due to the difficulty of carrying out the required integrations symbolically. When the dimensionality of the parameter space is small (i.e., there are few parameters), direct integration via quadrature rules may be possible. However, the computational burden for quadrature rules grows exponentially with the number of dimensions. When there are any more than a very few (in practice, perhaps about three) dimensions, random sampling is much more efficient. In any number of dimensions, the error of a random sampling estimate decreases proportionally to where n is the number of samples. Markov chain Monte Carlo is a class of relatedalgorithms for random sampling, which have the feature in common that it is possible to sample from a function which is only proportional to the posterior density of the parameters, that is, it is not necessary to normalize the posterior in order to sample from it. Hamiltonian Monte Carlo is a particular variant of MCMC which makes use of an analogy to classical mechanics to 6 define abstract position and momentum variables. The HMC formulation allows for faster exploration of the parameter space.

[0113] To carry out sampling for model parameters, the software package Stan was employed. Stan is a widely-used open source implementation of Hamiltonian Monte Carlo and other sampling algorithms. The following sampling parameters were applied for each modeling task.• Pramlintide PK: 1000 warmup samples, 4000 samples post -warmup• Insulin PK: 500 warmup samples, 4000 samples post-warmup• Glucoregulatory PD: 500 warmup samples, 2000 samples post-warmup

[0114] To gain insight about the sampling process, so-called f diagnostic was used. The R diagnostic is defined, for each sampled parameter, as a function of the ratio of within-chains variance to between-chains variance:

[0115] Where are the per-chain mean and overall mean, respectively, andis the per-chain sample variance.

[0116] For well-mixed chains, the mean of each chain will converge to the posterior mean of the parameter, and therefore the overall mean will likewise converge, and the numerator of the fraction in the equation forwill converge to zero. The sample variance for each chain will converge to the posterior variance of the parameter, so the fraction (between - chains variance) / (within-chains variance) converges to zero, andconverges to 1. On the other hand, when chains are sampling substantially different regions in the parameter space and not overlapping, the between-chains variance does not converge to zero, anddoes not converge to 1. A value of< 1.1 is considered to indicate acceptable mixing; otherwise, the diagnostic criterion indicates a sampling problem.Example 3

[0117] The process for linearizing the final model that is given in Equations E-1 through E-14 in the manuscript is shown below. These state equations are presented again in this section for readability and continuity.whereby the 10 state variables are Q1, Q2, xl, I, X, M1, M2, QP 1, QP2, and QP3.

[0118] The linearized right-hand side, DxF(X*)X, is:The constant terms, F(X*) — DxF(X*)X*, areWhereby the terms have been defined for brevity.Example 4

[0119] FIG. 11 shows a system 1100 for supporting glucoregulatory management to predict and control blood glucose using a MPC model that includes pramlintide kinetics and dynamics. System 1100 includes a medical device 1102 (e.g., CGM 1108 or insulin or pramlintide infusion pump 1110), a user's software application 1104 (e.g., an iPhone app, smartwatch app, or other smart device app) running on associated user equipment, and a cloud-based software application 1106 running on associated computing devices. Medical device 1102 communicates user data over a personal area network (PAN) connection 1112 (e.g., Bluetooth) with software application 1104.

[0120] Software applications 1104 generates a user interface 1114 that presents to a user feedback from ADHD system 100 (FIG. 1), which is partly represented in FIG. 11 as a set of algorithms 1116 including PK / PD MPC model 1118, insulin sensitivity adaptation model 1120, and meal detection 1122, but may further include other algorithms such as, for example, a safely layer and / or and ALPHA algorithm to adjust the aggressiveness of insulin dosing. For completeness, software applications 1104 also shows lower-layer OS components such as network stack 1124.

[0121] Software application 1106 is configured to receive data from software applications 1104 through a secure internet connection 1146. The data may then be stored in data storage 1128 used to generate a data visualization 1130 for display on user interface 1114.

[0122] FIG. 12 is a block diagram illustrating components 1200, according to some example embodiments, able to read instructions from a machine-readable or computer- readable medium (e.g., a non -transitory machine-readable storage medium), and perform any one or more of the methods discussed herein. For example, hardware resources 1202 may be embodied in a smartwatch, server, tablet computer, or patient-connected device that provides the ability to measure a physiological signal, provide some analysis of that signal, transmit information about that signal, and / or support a user interface to provide information about that signal. This includes an equivalent functional combination, for example a watch that can measure a physiological signal and transmit the data to a computer(including a smartphone), where the computer provides analysis and user interface functions.

[0123] Specifically, FIG. 12 shows a diagrammatic representation of hardware resources 1202 including one or more processors 1206 (or processor cores), one or more memory / storage devices 1214, and one or more communication resources 1222, each of which may be communicatively coupled via a bus 1216.

[0124] Processors 1206 (e.g., a central processing unit (CPU), a reduced instruction set computing (RISC) processor, a complex instruction set computing (CISC) processor, a graphics processing unit (GPU), a digital signal processor (DSP) such as a baseband processor, an application specific integrated circuit (ASIC), another processor, or any suitable combination thereof) may include, for example, a processor 1208 and a processor 1210.

[0125] Memory / storage devices 1214 may include main memory, disk storage, or any suitable combination thereof. Memory / storage devices 1214 may include, but are not limited to any type of volatile or non-volatile memory such as dynamic random access memory (DRAM), static random-access memory (SRAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), Flash memory, solid-state storage, etc.

[0126] Communication resources 1222 may include interconnection or network interface components or other suitable devices to communicate with one or more peripheral devices 1204 or one or more databases 1220 via a network 1218. For example, communication resources 1222 may include wired communication components (e.g., for coupling via a Universal Serial Bus (USB)), cellular communication components, NFC components, Bluetooth® components (e.g., Bluetooth® Low Energy), Wi-Fi® components, and other communication components.

[0127] Instructions 1212 may comprise software, a program, an application, an applet, an app, or other executable code for causing at least any of processors 1206 to perform any one or more of the methods discussed herein. In some embodiments, instructions 1212 include executable code to run a pramlintide-aware glucoregulatory control model as described in the Equation sets described herein, which are stored in memory / storage devices 1214.

[0128] Instructions 1212 may reside, completely or partially, within at least one of processors 1206 (e.g., within the processor’s cache memory), memory / storage devices 1214, or any suitable combination thereof. Furthermore, any portion of instructions 1212 may be transferred to hardware resources 1202 from any combination of the peripheral devices 1204or the databases 1220. Accordingly, the memory of processors 1206, memory / storage devices 1214, peripheral devices 1204, and databases 1220 are examples of computer- readable and machine-readable media.

[0129] In other embodiments, computing device 102 receives data and transmits it to a remote server for further processing. In that embodiment, the remote server performs calculations using a programmed glucoregulatory model, returns results to computing device 102, and so forth. In still other embodiments, different processing steps are performed by each of computing device 102 and remote server, depending on the particular configuration.

[0130] Skilled persons will appreciate that many changes may be made to the details of the above-described embodiments without departing from the underlying principles of the invention. The scope of the present invention should, therefore, be determined only by claimed inventions and equivalents thereof.

Claims

CLAIMSWhat is claimed is:

1. A method, performed by a computing device executing a model predictive control (MPC) glucoregulatory model, for automating the administration of one or both insulin and pramlintide to a person so as to maintain the person’s blood glucose concentration within a predetermined range, the method comprising: receiving glucose data generated by a continuous glucose monitor (CGM) coupled to the person; calculating, using the MPC glucoregulatory model, a dose of insulin and a dose of pramlintide sufficient to maintain the person’s blood glucose within the predetermined range, in which the dose of pramlintide is determined at least in part from a pharmacokinetics and pharmacodynamics (PK / PD) pramlintide sub-model compartment included in the MPC glucoregulatory model and configured to predict an effect of pramlintide on delayed gastric emptying; and delivering, by an infusion pump coupled to the person for subcutaneous delivery, the dose of insulin or the dose of pramlintide or both insulin and pramlintide doses sufficient to maintain the person’s blood glucose within the predetermined range.

2. The method of claim 1, further comprising receiving meal consumption data entered by the person, the meal consumption representing carbohydrates consumed by the person.

3. The method of claim 1, further comprising: detecting, by an automated algorithm, when the person has consumed a meal; estimating a size of the meal; and providing the size of the meal as input to the MPC model to calculate a dose of insulin and or a dose of pramlintide or both a dose of insulin and pramlintide sufficient to maintain the person’s blood glucose within the predetermined range.

4. The method of claim 1, in which a first compartment of the PK / PD pramlintide sub-model compartment tracks subcutaneous pramlintide.

5. The method of claim 1, in which a second compartment of the PK / PD pramlintide sub-model compartment tracks intact blood plasma pramlintide.

6. The method of claim 1, in which a third compartment of the PK / PD pramlintide sub-model compartment tracks active metabolite pramlintide.

7. The method of claim 1, in which the PK / PD pramlintide sub -model compartment comprises state variables representing intact plasma pramlintide and a pramlintide metabolite and a term representing a pramlintide-dependent gastric emptying delay.

8. The method of claim 1, in which calculating the dose of insulin and the dose of pramlintide comprises linearizing the MPC glucoregulatory model using a zero-order hold for pramlintide-related nonlinearities and a first-order hold for insulin-related nonlinearities.

9. The method of claim 1, in which the computing device receives a continuous glucose data stream and recalculates insulin and pramlintide doses at fixed intervals of about five minutes using updated state-space matrices.

10. The method of claim 1, further comprising automatically detecting a meal using a neural-network-based meal-detection algorithm and estimating a meal size, the meal size being provided as input to the MPC glucoregulatory model.

11. The method of claim 10, in which the computing device limits post-meal insulin dosing through a safety layer that prevents delivery of insulin predicted to reduce glucose below about 70 mg / dL.

12. The method of claim 1, in which insulin and pramlintide are delivered as a fixed ratio co-formulation comprising about 6 micrograms of pramlintide per unit of insulin.

13. The method of claim 1, in which insulin and pramlintide are delivered independently through separate infusion channels controlled by the MPC glucoregulatory model14. The method of claim 1, in which pramlintide is delivered as a constant basal infusion proportional to an average daily insulin infusion rate while insulin is delivered in both basal and bolus modes.

15. The method of claim 1, in which the MPC glucoregulatory model adaptively updates one or more insulin-sensitivity parameters based on one or more glucose measurements collected within a preceding period of several hours that reflect hypo- or hyperglycemia, or glucose responses to meals or physical activity.

16. The method of claim 1, in which the MPC glucoregulatory model includes an adaptive postprandial hypoglycemia-prevention algorithm configured to reduce aggressiveness of post-meal insulin dosing following a detected hypoglycemia episode.

17. The method of claim 1, in which the computing device executes the MPC glucoregulatory model on a smartphone, smartwatch, insulin-pump microcontroller, or cloud server communicatively coupled to an infusion pump and a continuous glucose monitor.

18. The method of claim 1, in which the computing device outputs insulin and pramlintide dose control signals to a dual -chamber infusion pump for subcutaneous codelivery of hormones.

19. A system for automating administration of one or both insulin and pramlintide to a person to maintain the person’s blood glucose concentration within a predetermined range, the system comprising: a continuous glucose monitor (CGM) configured to generate glucose data from the person; a computing device communicatively coupled to the CGM, the computing device being programmed to execute a model predictive control (MPC) glucoregulatory model configured to: receive the glucose data generated by the CGM; calculate, using the MPC glucoregulatory model, a dose of insulin and a dose of pramlintide sufficient to maintain the person’s blood glucose within the predetermined range, in which the dose of pramlintide is determined at least in part from a pharmacokinetics and pharmacodynamics (PK / PD) pramlintide sub -model compartment included in the MPC glucoregulatory model and configured to predict an effect of pramlintide on delayed gastric emptying; and transmit control information for delivery of one or more calculated doses of a glucoregulatory hormone, including one or both the calculated dose of insulin and the calculated dose of pramlintide.

20. The system of claim 19, in which the computing device is further configured to receive meal consumption data entered by the person, the meal consumption representing carbohydrates consumed by the person.

21. The system of claim 19, in which the computing device is further configured to detect when the person has consumed a meal, estimate a size of the meal, and provide the meal size as input to the MPC glucoregulatory model.

22. The system of claim 19, in which a first compartment of the PK / PD pramlintide sub-model tracks subcutaneous pramlintide, a second compartment tracks intact plasma pramlintide, and a third compartment tracks active metabolite pramlintide.

23. The system of claim 19, in which the PK / PD pramlintide sub-model comprises state variables representing intact plasma pramlintide and a pramlintide metabolite and includes a term representing a pramlintide-dependent gastric-emptying delay.

24. The system of claim 19, in which the computing device linearizes the MPC glucoregulatory model using a zero-order hold for pramlintide-related nonlinearities and a first-order hold for insulin-related nonlinearities.

25. The system of claim 19, in which the computing device receives a continuous glucose data stream and recalculates insulin and pramlintide doses at fixed intervals of about five minutes using updated state-space matrices.

26. The system of claim 19, in which the computing device executes a neural- network-based meal-detection algorithm to estimate a meal size and provide the estimate as input to the MPC glucoregulatory model.

27. The system of claim 26, in which the computing device limits post-meal insulin dosing through a safety layer that prevents delivery of insulin predicted to reduce glucose below about 70 mg / dL.

28. The system of claim 19, further comprising an infusion pump configured to deliver insulin and pramlintide as a fixed-ratio co-formulation comprising about 6 micrograms of pramlintide per unit of insulin.

29. The system of claim 19, further comprising a dual-chamber infusion pump configured to deliver insulin and pramlintide independently through separate infusion channels under control of the MPC glucoregulatory model.

30. The system of claim 19, in which the computing device controls an infusion pump to deliver pramlintide as a constant basal infusion proportional to an average daily insulin infusion rate while delivering insulin in both basal and bolus modes.

31. The system of claim 19, in which the MPC glucoregulatory model adaptively updates one or more insulin-sensitivity parameters based on glucose measurements collected within a preceding period of several hours that reflect hypo- or hyperglycemia, or glucose responses to meals or physical activity.

32. The system of claim 19, in which the MPC glucoregulatory model includes an adaptive postprandial hypoglycemia-prevention algorithm configured to reduce aggressiveness of post-meal insulin dosing following a detected hypoglycemia episode.

33. The system of claim 19, in which the computing device comprises a smartphone, smartwatch, glucoregulatory hormone microcontroller, or cloud server communicatively coupled to the glucoregulatory hormone microcontroller and the CGM.

34. The system of claim 19, in which the computing device outputs insulin and pramlintide dose-control signals to a dual-chamber infusion pump for subcutaneous codelivery of the hormones.

Images