Linear time-varying model predictive control of an artificial pancreas with blood glucose predictors

Abstract

A blood glucose monitoring system having an insulin pump operational to administer insulin to the subject, sensors associated with the subject and operational to measure the blood glucose levels of a subject, and a computing device in electronic communication with the insulin pump. The computing device includes computer readable storage mediums having program code embodied therewith. The computing device includes a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject. The algorithm includes a data-driven multi-step- ahead blood glucose predictor integrated with a linear time-varying model predictive control law. The computing device includes programming instructions for feeding the subject's blood glucose level into the algorithm, using the algorithm to predict if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia, and transmitting insulin administration instructions to the insulin pump based on the prediction.

Description

PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 TITLE LINEAR TIME-VARYING (LTV) MODEL PREDICTIVE CONTROL (MPC) OF AN ARTIFICIAL PANCREAS WITH DATA-DRIVEN NEURAL MULTI-STEP AHEAD AFFINE BLOOD GLUCOSE PREDICTORS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 536,660, filed on September 5, 2023. The entirety of which is incorporated herein by reference. BACKGROUND

[0002] A need exists for more effective methods of predicting blood glucose levels for the treatment of hyperglycemia and / or hypoglycemia. Numerous embodiments of the present disclosure aim to address the aforementioned need. SUMMARY

[0003] In an embodiment, the present disclosure pertains to a blood glucose monitoring system having an insulin pump associated with a subject and operational to administer insulin to the subject, one or more sensors associated with the subject and operational to measure the blood glucose levels of the subject, and a computing device in electronic communication with the insulin pump. The computing device includes a non-transitory computer-usable medium having computer-readable program code embodied therein, a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject, where the algorithm includes a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law, and programming instructions operable to implement a method. The method includes feeding the subject’s blood glucose level into the algorithm, predicting if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia using the algorithm, and transmitting insulin administration instructions to the insulin pump based on the prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] FIG.1 illustrates a method of monitoring blood glucose levels of a subject in accordance with various embodiments of the present disclosure.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0005] FIG. 2 illustrates a blood glucose monitoring system in accordance with various embodiments of the present disclosure.

[0006] FIG.3 illustrates the architecture of a computing device of the present disclosure.

[0007] FIG. 4 illustrates the proposed model architecture for blood glucose prediction. Input samples are processed through Long Short-Term Memory (LSTM) layers to capture temporal dependencies, and the output is mapped to a suitable format for prediction using fully connected (FC) layers.

[0008] FIGS. 5A-5B illustrate the mean and standard deviation of the predicted blood glucose concentrations obtained by the 1-step ahead auto-regressive with exogenous (ARX) predictor and the proposed multi-step ahead affine predictors on the validation dataset. The black solid line represents the mean of the actual continuous glucose monitor (CGM) measurements, and the black dashed line represents the standard deviation of the actual CGM measurements. Model predictions are reported for each prediction step ^^· ^ = 15, 30... , 120 minutes.

[0009] FIG.6 illustrates Scenario A, as described in Example 1. Top: Mean and standard deviation of glucose concentration [md / dL] using the proposed Model Predictive Control (MPC) based on the multi-step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC; Bottom: Mean and standard deviation of insulin delivery [pmol / kg] using the proposed MPC based on the multi-step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC. The shaded area denotes the euglycemic range, 70-180 mg / dL.

[0010] FIG. 7 illustrates Scenario B, as described in Example 1. Top: Mean and standard deviation of glucose concentration [md / dL] using the proposed MPC based on the multi-step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC; Bottom: Mean and standard deviation of insulin delivery [pmol / kg] using the proposed MPC based on the multi- step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC. The shaded area denotes the euglycemic range, 70-180 mg / dL.

[0011] FIG.8 illustrates Scenario C, as described in Example 1. Top: Mean and standard deviation of glucose concentration [md / dL] using the proposed MPC based on the multi-step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC; Bottom: Mean and standard deviation of insulin delivery [pmol / kg] using the proposed MPC based on the multi-step predictorPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 vs. the reference MPC based on the 1-step ahead ARX predictor MPC . The shaded area denotes the euglycemic range, 70-180 mg / dL.

[0012] FIG.9 illustrates Scenario D. Top: Mean and standard deviation of glucose concentration [md / dL] using the proposed MPC based on the multi-step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC; Bottom: Mean and standard deviation of insulin delivery [pmol / kg] using the proposed MPC based on the multi-step predictor vs. the reference MPC based on the 1-step ahead ARX predictor MPC. The shaded area denotes the euglycemic range, 70-180 mg / dL.

[0013] FIG. 10 illustrates mean and standard deviation of glucose concentration [md / dL] using the proposed MPC based on the multi-step predictor vs. the conventional therapy ; Bottom: Mean and standard deviation of insulin delivery [Ui] using the proposed MPC based on the multi-step predictor vs. the conventional therapy. The black line denotes the delivery of long-acting analog once a day. FIGS. 6-9 are related to continuous subcutaneous insulin infusion (CSII) therapy while FIG.10 is related to multiple daily injection (MDI) therapy. DETAILED DESCRIPTION

[0014] It is to be understood that both the foregoing general description and the following detailed description are illustrative and explanatory, and are not restrictive of the subject matter, as claimed. In this application, the use of the singular includes the plural, the word “a” or “an” means “at least one”, and the use of “or” means “and / or”, unless specifically stated otherwise. Furthermore, the use of the term “including”, as well as other forms, such as “includes” and “included”, is not limiting. Also, terms such as “element” or “component” encompass both elements or components comprising one unit and elements or components that include more than one unit unless specifically stated otherwise.

[0015] The section headings used herein are for organizational purposes and are not to be construed as limiting the subject matter described. All documents, or portions of documents, cited in this application, including, but not limited to, patents, patent applications, articles, books, and treatises, are hereby expressly incorporated herein by reference in their entirety for any purpose.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 If one or more of the incorporated literature and similar materials defines a term in a manner that contradicts the definition of that term in this application, this application controls.

[0016] Type 1 diabetes (T1D) is a metabolic condition characterized by high blood glucose (BG) levels (hyperglycemia), caused by the autoimmune irreversible destruction of the pancreatic β- cells, which are responsible for the production and release of the hormone insulin. The chronic diabetes hyperglycemia leads to an increased risk of life-threatening events, such as diabetes ketoacidosis, and has serious long-term complications associated with damage, dysfunction and failure of various organs. Exogenous insulin is therefore required for individuals with T1D to adequately regulate their BG concentration in the euglycemic range. Despite burdensome insulin treatment, however, individuals with T1D experience difficulties in maintaining healthy BG levels and fail to meet the recommended glycemic targets.

[0017] Over the past 40 years, significant effort has been directed toward the automated control of blood glucose concentration. Due to the recent technological advances in glucose sensing devices and insulin infusion mechanisms, effective glucose regulation is becoming increasingly possible. Model predictive control (MPC) is an attractive control strategy for closed loop insulin delivery and has been considered in this context, showing promising results in the management of diabetes in a hybrid fashion (so-called hybrid closed-loop systems).

[0018] In the hybrid setting, the MPC algorithm oversees adjusting the clinical defined basal insulin profile during fasting periods based on real-time measurements from continuous glucose monitoring (CGM) device, while a linear feed-forward control action is included in the control scheme based on the announcement of the disturbances provided by the user. The MPC algorithms currently adopted in clinical trials rely on linear models to describe the process under control, to optimize the control performance and ensure constraint satisfaction over a prediction horizon.

[0019] From the algorithmic point of view, the major limitation affecting glucose control schemes lies in the inaccuracies of the linear models used for generating the BG predictions. The use of a linear model is justified by its simplicity and small computational load, but a linear model can only approximate the complex non-linear dynamic of the human metabolism.

[0020] Specifically, long prediction horizons of the same length of hyperglycemic perturbations ( e.g., after a mixed meal) introduce large errors due to large plant-model mismatch, and arePCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 therefore not advantageous. However, shorter prediction horizons yield control laws that persist to command insulin delivery beyond what is required, especially when a hyperglycemic state is in the process of correcting itself. Similar observations can be made when dealing with glycemic perturbations arising from stress, illness, hormonal variations and physical activity, which are not captured by the available linear models. The resulting insulin administration is inadequate and contributes to the risk of dangerous controller-induced hypoglycemia and increased time outside of the target range.

[0021] As such, a need exists for more effective methods of predicting blood glucose levels for the treatment of hyperglycemia and / or hypoglycemia. In particular, a need exists for a different way of approaching blood glucose modeling steps. Numerous embodiments of the present disclosure aim to address the aforementioned need.

[0022] Methods of Monitoring Blood Glucose Levels

[0023] In some embodiments, the present disclosure pertains to a computer-implemented method of monitoring blood glucose levels of a subject. In some embodiments illustrated in FIG.1, the methods of the present disclosure include: feeding the subject’s blood glucose level into a closed- loop insulin delivery algorithm trained to predict the blood glucose level of the subject, where the algorithm includes a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law (step 10); using the algorithm to predict if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia (step 12); and transmitting insulin administration instructions based on the prediction.

[0024] In some embodiments, the methods of the present disclosure occur in real-time. In some embodiments, the methods of the present disclosure occur continuously. Additionally, the methods of the present disclosure may transmit various insulin administration instructions.

[0025] For instance, in some embodiments, the insulin administration instructions are based on the solution of a receding horizon (RH) optimal control problem carried out by the LTV-MPC. In some embodiments where no prediction of hypoglycemia or hyperglycemia is made by the algorithm (step 14), the method of the present disclosure may not command a change in insulin delivery (step 16). In some embodiments where the blood glucose level of the subject is expectedPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 to reach a level representing hyperglycemia (step 18), the insulin administration instructions include increasing insulin administration to the subject (step 20). Thereafter, the method of the present disclosure may command a change in insulin administration (step 16). In some embodiments where the blood glucose level of the subject is expected to reach a level representing hypoglycemia (step 22), the insulin administration instructions include decreasing or suspending insulin administration to the subject (step 22). Thereafter, the method of the present disclosure may command a change in insulin administration (step 16).

[0026] In some embodiments, the methods of the present disclosure also include a step of administering insulin based on the insulin administration instructions. In some embodiments, the insulin is administered by a user. In some embodiments, the administration occurs by a method that includes, without limitation, intravenous administration, subcutaneous administration, transdermal administration, percutaneous administration, topical administration, intraarterial administration, intrathecal administration, oral administration, or combinations thereof. In some preferred embodiments, the administration occurs by subcutaneous administration.

[0027] In some embodiments, the insulin administration instructions are transmitted to an insulin pump associated with the subject. Thereafter, the insulin pump implements the instructions. In some embodiments, the insulin pump is in the form of a patch. In some embodiments, the insulin pump is operable for subcutaneous insulin administration.

[0028] The methods of the present disclosure may utilize various types of pumps. For instance, in some embodiments, the insulin pumps include tethered pumps.

[0029] In some embodiments, the insulin pump includes an insulin reservoir and a processor. In some embodiments, the processor is in electronic communication with the algorithm. In some embodiments, the processor actuates or withholds the release of insulin from the insulin reservoir based on received instructions from the algorithm.

[0030] In some embodiments, the methods of the present disclosure also include a step of measuring the blood glucose levels of the subject. In some embodiments, the methods of the present disclosure include a step of obtaining a blood sample from the subject and measuring the blood glucose levels from the blood sample.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0031] In some embodiments, the blood glucose levels of the subject is measured by a sensor that is associated with the subject. In some embodiments, the sensor transmits the measured blood glucose levels to the algorithm.

[0032] The methods of the present disclosure may be utilized to monitor the blood glucose levels of various subjects. For instance, in some embodiments, the subject is a human being suffering from type 1 diabetes. In some embodiments, the methods of the present disclosure may be used to treat or prevent type 1 diabetes. In some embodiments, the methods of the present disclosure are used to treat type 1 diabetes or prevent the complications arising from type 1 diabetes.

[0033] The methods of the present disclosure may utilize various types of LTV-MPC models. For instance, in some embodiments, the LTV-MPC models include parameters that vary with time according to previously specified laws. In some embodiments, the LTV-MPC models are also capable of controlling a process while satisfying a set of constraints. In some embodiments, the LTV-MPC models are also capable of controlling a process while satisfying a set of constraints that aim to limit the amount of commanded insulin dose to the maximum insulin delivery and limit the glucose levels to the maximum reading value on the glucose sensor.

[0034] The methods of the present disclosure may utilize various types of algorithms. In some embodiments, the algorithm includes a machine learning algorithm. In some embodiments, the machine learning algorithm is a Root Mean Square Propagation (RMSProp) training algorithm. In some embodiments, the machine learning algorithm is a Long Short-Term Memory (LSTM) network.

[0035] In some embodiments, the algorithm does not identify an open-loop algorithm of the glucoregulatory system from available data. In some embodiments, the algorithm directly fits the entire BG trajectory over a predefined prediction horizon to be used in the MPC law as a nonlinear function of past input-output data and an affine function of future insulin control inputs. In some embodiments, a Long Short-Term Memory (LSTM) network is used to fit the component of the BG trajectory nonlinear in the state to a predictive nonlinear function incorporated into the algorithm. In some embodiments, a linear regression model is used to fit the future insulin control inputs to an affine function incorporated into the algorithm.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0036] In some embodiments, the BG trajectory is implemented as a nonlinear function of past input-output data and an affine function of future insulin control inputs. In some embodiments, the algorithm includes customizable user parameters. In some embodiments, the customizable user parameters include, without limitation, length of prediction horizon, weight matrices, setpoints, or combinations thereof.

[0037] Blood Glucose Monitoring Systems

[0038] Additional embodiments of the present disclosure pertain to blood glucose monitoring systems. In some embodiments, the blood glucose monitoring systems of the present disclosure are operational to monitor blood glucose levels in accordance with the methods of the present disclosure. An example of a blood glucose monitoring system is illustrated in FIG. 2 as blood glucose monitoring system 30. Blood glucose monitoring system 30 generally includes: an insulin pump 32 associated with a subject 34 and operational to administer insulin to the subject; one or more sensors 33 associated with the subject 34 and operational to measure the blood glucose levels of the subject; and a computing device 40 in electronic communication with insulin pump 32. In some embodiments, computing device 40 is in electronic communication with insulin pump 32 through a wireless network 39.

[0039] In some embodiments, computing device 40 is also in electronic communication with one or more sensors 33 through a wireless network 39. In some embodiments, one or more sensors 33 are operational to transmit the subject’s blood glucose levels to computing device 40.

[0040] In some embodiments, insulin pump 32 includes an insulin reservoir 36 and a processor 38 that is in electronic communication with computing device 40. In some embodiments, processor 38 is operational to actuate or withhold the release of insulin from insulin reservoir 36 upon receiving instructions from computing device 40.

[0041] The computing devices of the present disclosure generally include one or more computer readable storage mediums having at least one program code embodied therewith. The computing devices of the present disclosure also include a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject, where the algorithm includes a data-driven multi- step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0042] Additionally, the computing devices of the present disclosure include programming instructions for: feeding the subject’s blood glucose level into the algorithm (e.g., via sensors 33); using the algorithm to predict if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia; and transmitting insulin administration instructions to the insulin pump (e.g., insulin pump 32) based on the prediction. For instance, in some embodiments, the insulin administration instructions include increasing insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hyperglycemia. In some embodiments, the insulin administration instructions include decreasing or suspending insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hypoglycemia. In some embodiments, the insulin administration instructions are based on the solution of a receding horizon (RH) optimal control problem carried out by the LTV-MPC.

[0043] The blood glucose monitoring systems of the present disclosure may include various insulin pumps. For instance, in some embodiments, the insulin pump is in the form of a patch. In some embodiments, the insulin pump is operable for subcutaneous insulin administration. In some embodiments, the insulin pumps include tethered pumps.

[0044] The blood glucose monitoring systems of the present disclosure may also include various types of computing devices. For instance, in some embodiments, the computing device includes a computer. In some embodiments, the computing device includes a mobile device. In some embodiments, the computing device includes an app on a mobile device. In some embodiments, the computing device is in electronic communication with the insulin pump through a wireless network. In some embodiments, the computing device includes a chip on the insulin pump.

[0045] The blood glucose monitoring systems of the present disclosure may also include various types of algorithms. Suitable algorithms were described supra and are incorporated herein by reference.

[0046] The blood glucose monitoring systems of the present disclosure may be suitable for use in monitoring the blood glucose levels of various subjects. For instance, in some embodiments, the subject is a human being suffering from type 1 diabetes.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0047] In a particular embodiment, the present disclosure relates to a blood glucose monitoring system having an insulin pump associated with a subject and operational to administer insulin to the subject, one or more sensors associated with the subject and operational to measure the blood glucose levels of the subject, and a computing device in electronic communication with the insulin pump. In some embodiments, the computing device includes a non-transitory computer-usable medium having computer-readable program code embodied therein and a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject. In some embodiments, the algorithm comprises a data-driven multi-step-ahead BG predictor integrated with an LTV- MPC law. In some embodiments, the computing device further includes programming instructions operable to implement a method. In some embodiments, the method includes feeding the subject’s blood glucose level into the algorithm, predicting if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia using the algorithm, and transmitting insulin administration instructions to the insulin pump based on the prediction.

[0048] In some embodiments, the insulin administration instructions are based on the solution of a RH optimal control problem carried out by the LTV-MPC. In some embodiments, the algorithm is a machine learning algorithm. In some embodiments, the machine learning algorithm is an LSTM network. In some embodiments, the algorithm does not identify an open-loop algorithm of the glucoregulatory system from available data.

[0049] In some embodiments, the algorithm directly fits the entire BG trajectory over a predefined prediction horizon to be used in the MPC law as a nonlinear function of past input-output data and an affine function of future insulin control inputs. In some embodiments, an LSTM network is used to the component of the BG trajectory nonlinear in the state to a predictive nonlinear function incorporated into the algorithm. In some embodiments, a linear regression model is used to fit the future insulin control inputs to an affine function incorporated into the algorithm. In some embodiments, the BG prediction is implemented as a nonlinear function of past input-output data and an affine function of future insulin control inputs. In some embodiments, the feeding of the subject’s blood glucose level into the algorithm occurs in real-time.

[0050] In some embodiments, the insulin pump includes an insulin reservoir and a processor. In some embodiments, the processor is in electronic communication with the computing device. In some embodiments, the processor is operational to actuate or withhold the release of insulin fromPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 the insulin reservoir. In some embodiments, the computing device is a mobile device. In some embodiments, the computing device is an app on a mobile device. In some embodiments, the computing device is a chip on an insulin pump. In some embodiments, the computing device is in electronic communication with the insulin pump through a wireless network. In some embodiments, the insulin pump is operable for subcutaneous insulin administration.

[0051] Computing Devices

[0052] Additional embodiments of the present disclosure pertain to computing devices that include one or more computer readable storage mediums having at least one program code embodied therewith. In some embodiments, the computing device includes a closed-loop insulin delivery algorithm trained to predict the blood glucose level of a subject, where the algorithm includes a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law. In some embodiments, the computing device also includes programming instructions for: feeding the subject’s blood glucose level into the algorithm; using the algorithm to predict if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia; and transmitting insulin administration instructions based on the prediction.

[0053] As set forth in more detail herein, the computing devices of the present disclosure can have numerous architectures. The computing device of the present disclosure can include various types of computer readable storage mediums. For instance, in some embodiments, the computer readable storage mediums can be a tangible device that can retain and store instructions for use by an instruction execution device. In some embodiments, the computer readable storage medium may include, without limitation, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or combinations thereof. A non-exhaustive list of more specific examples of suitable computer readable storage medium includes, without limitation, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device, or combinations thereof.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0054] A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se. Such transitory signals may be represented by radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0055] In some embodiments, computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network and / or a wireless network. In some embodiments, the network may include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. In some embodiments, a network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0056] In some embodiments, computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the "C" programming language or similar programming languages.

[0057] In some embodiments, the computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected in some embodiments to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitryPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry to perform aspects of the present disclosure.

[0058] Embodiments of the present disclosure for monitoring blood glucose levels as discussed herein may be implemented using a computing device illustrated in FIG.3. FIG.3 illustrates an embodiment of the present disclosure of the hardware configuration of a computing device 50, which is representative of a hardware environment for practicing various embodiments of the present disclosure. Computing device 50 has a processor 51 connected to various other components by system bus 52. An operating system 53 runs on processor 51 and provides control and coordinates the functions of the various components of FIG. 3. An application 54 in accordance with the principles of the present disclosure runs in conjunction with operating system 53 and provides calls to operating system 53, where the calls implement the various functions or services to be performed by application 54. Application 54 may include, for example, a program for monitoring blood glucose levels of a subject, as discussed in the present disclosure, such as in connection with FIGS.1-2.

[0059] Referring again to FIG.3, read-only memory ("ROM") 55 is connected to system bus 52 and includes a basic input / output system ("BIOS") that controls certain basic functions of computing device 50. Random access memory ("RAM") 56 and disk adapter 57 are also connected to system bus 52. It should be noted that software components including operating system 53 and application 54 may be loaded into RAM 56, which may be computing device’s 50 main memory for execution. Disk adapter 57 may be an integrated drive electronics ("IDE") adapter that communicates with a disk unit 58 (e.g., a disk drive). It is noted that the program for monitoring blood glucose levels of a subject, as discussed in the present disclosure, such as in connection with FIGS.1-2, may reside in disk unit 58 or in application 54.

[0060] Computing device 50 may further include a communications adapter 59 connected to bus 52. Communications adapter 59 interconnects bus 52 with an outside network (e.g., wide area network) to communicate with other devices.

[0061] Aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computing devicesPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0062] These computer readable program instructions may be provided to a processor of a computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein includes an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks. The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0063] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computing devices according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which includes one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be accomplished as one step, executed concurrently, substantially concurrently, in a partially or wholly temporally overlapping manner, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform thePCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0064] Additional Embodiments

[0065] Reference will now be made to more specific embodiments of the present disclosure and experimental results that provide support for such embodiments. However, Applicant notes that the disclosure below is for illustrative purposes only and is not intended to limit the scope of the claimed subject matter in any way.

[0066] Example 1. Model Predictive Control (MPC) of an Artificial Pancreas with Data- Driven Learning of Multi-Step-Ahead Blood Glucose Predictors

[0067] Applicants present the design and in-silico evaluation of a closed-loop insulin delivery algorithm to treat type 1 diabetes (T1D) in a data-driven multi-step-ahead blood glucose (BG) predictor integrated into a linear time-varying (LTV) model predictive control (MPC) framework. Instead of identifying an open-loop model of the glucoregulatory system from available data, Applicants propose to directly fit the entire BG prediction over a predefined prediction horizon to be used in the MPC, as a nonlinear function of past input-output data and an affine function of future insulin control inputs. For the nonlinear part, a Long Short-Term Memory (LSTM) network is proposed, while for the affine component a linear regression model is chosen. To assess benefits and drawbacks when compared to a traditional linear MPC based on an auto-regressive with exogenous (ARX) input model identified from data, Applicants evaluated the proposed LSTM- MPC controller in four simulation scenarios: a nominal case with 3 meals per day, a random meal disturbances case where meals were generated with a recently published meal generator, a case with ± 25% decrease in the insulin sensitivity and a case with ± 25 % error on the estimated meal amounts. Further, in all the scenarios, no feedforward meal bolus was administered. For the more challenging random meal generation scenario, the mean ± standard deviation percent time in the range 70-180 [mg / dL] was 74.99 ± 7.09 vs.54.15 ± 14.89, the mean ± standard deviation percent time in the tighter range 70-140 [mg / dL] was 47.78 ± 8.55 vs. 34.62 ± 9.04, while the mean ± standard deviation percent time in sever hypoglycemia, i.e., < 54 [mg / dl] was 1.00 ± 3.18 vs.9.45 ± 11.71, for the proposed LSTM-MPC controller and the traditional ARX-MPC, respectively. This approach provided accurate predictions of future glucose concentrations and good closed-loop performances of the overall MPC controller.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0068] Example 1.1. Introduction

[0069] Type 1 diabetes (T1D) is a metabolic condition characterized by high blood glucose levels (hyperglycemia), caused by the autoimmune irreversible destruction of the pancreatic β-cells, which are responsible for the production and release of the hormone insulin. The chronic diabetes hyperglycemia, i.e. blood glucose (BG) levels ≥ 180 mg / dL, leads to an increased risk of life- threatening events, such as diabetes ketoacidosis, and has serious long-term complications associated with damage, dysfunction and failure of various organs. Exogenous insulin is therefore required for individuals with T1D to adequately regulate their BG concentration in the euglycemic range, i.e.70-180 mg / dL. Despite burdensome insulin treatment, however, individuals with T1D experience difficulties in maintaining healthy BG levels and fail to meet the recommended glycemic targets. Over the past 40 years, significant effort has been directed toward the automated control of blood glucose concentration, and thanks to the recent technological advances in glucose sensing devices and insulin infusion mechanisms, effective glucose regulation is becoming increasingly possible. Model predictive control (MPC) is an attractive control strategy for closed loop insulin delivery and has been considered in this context showing promising results in the management of diabetes in a hybrid fashion (so-called hybrid closed-loop systems). In the hybrid setting, the MPC algorithm oversees adjusting the clinical defined basal insulin profile during fasting periods based on real-time measurements from continuous glucose monitoring (CGM) device, while a linear feed-forward control action is included in the control scheme based on the announcement of the disturbances provided by the user. The MPC algorithms currently adopted in clinical trials rely on linear models to describe the process under control, to optimize the control performance and ensure constraint satisfaction over a prediction horizon. From the algorithmic point of view, the major limitation affecting glucose control schemes, lies in the inaccuracies of the linear models used for generating the BG predictions. The use of a linear model is justified by its simplicity and small computational load, but a linear model can only approximate the complex non-linear dynamic of the human metabolism. Specifically, long prediction horizons of the same length of hyperglycemic perturbations, e.g., after a mixed meal, introduce large errors due to large plant-model mismatch, and are therefore not advantageous. However, on the other hand, shorter prediction horizons yield control laws that persist to command insulin delivery beyond what is required, especially when a hyperglycemic state is in the process of correcting itself. Similar observations can be made when dealing with glycemic perturbations arising from stress, illness,PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 hormonal variations and physical activity, which are not captured by the available linear models. The resulting insulin administration is inadequate and contributes to the risk of dangerous controller-induced hypoglycemia and increased time outside of the target range. That said, in this Example, Applicants explore a different way of approaching the modeling step in a linear time- varying (LTV) MPC framework. In particular, Applicants consider the estimation of long-term horizons multi-step ahead predictors of BG dynamics for receding horizon control starting from input-output data, with the goal of increasing the prediction accuracy for longer prediction horizons. Given the inherent physiological nonlinearity in the underlying glucose metabolism, data-driven approaches based on Artificial Neural Networks (ANNs) can achieve remarkable performance over traditional linear models thanks to their ability to perform automatic feature extraction, and hence eliminating the need of feature engineering. In particular, unlike traditional Recursive Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks are specifically designed to learn and retain information over long sequences and were successfully applied for blood glucose predictions. In this Example, Applicants build predictors as the superposition of a nonlinear function of past inputs and past outputs and an affine function of future control moves. This predictor construction allows Applicants to solve the MPC problem via quadratic programming (QP) despite the nonlinearity of the system. Applicants propose a LSTM network for the nonlinear part, and a linear regression model for the affine component of the predictor. The performance of the proposed approach is demonstrated on four real-life use-case scenarios using a widely accepted metabolic model of glucose metabolism equipped with ten in-silico adult subjects and compared against a linear autoregressive exogenous (ARX) model.

[0070] Example 1.2. Data-Driven Multi-Step-Ahead Blood Glucose Predictors for MPC

[0071] A predictor structure affine in the future inputs. Let an unknown, non-linear discrete-time system ^ be described by the dynamical model:where ^ is the discrete-time instant, ^^∈ ^^^the state of the system at time ^, ^^∈ ^^^and ^^∈ ^^^input and output at time ^, respectively, ^^: ^^^×^^→ ^^^, and ℎ^: ^^^→ ^^^.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0072] The aim is to design ^ predictors of the system output ^^ !, based on input-output data available from the system ^ at time ^, where ^ = 1, … , ^ denotes the prediction step and ^ ∈ # is the prediction horizon in the MPC problem. Note that here Applicants propose to learn one predictor per each prediction step ^, as opposed to the traditional approach in the process control literature prescribing the iteration of the system equations for the derivation of output predictions beyond one-step ahead. Stacking all the predicted sequences on top of each other, Applicants obtain: where $%: ^^^×%&^→ ^%&^is the multi-step predictor, comprised of one predictor for each (( (, prediction step, '%= )'^ *, … , '^ %+ , is the predicted output sequence, and -%.*= [^^, … , ^^ % *]′future input sequence, along the prediction horizon.

[0073] The multi-step predictor described in Eq.2 is intended to be used as the process model for an MPC formulation. Note that, when choosing a quadratic cost function and linear constraints in the MPC, an input-affine formulation of the predictor is preferable, as the resulting Finite Horizon Optimal Control Problem (FHOCP) in this case turns out to be a quadratic program, which can be efficiently solved using ad-hoc solvers. For this reason, the general multi-step predictor formulation of Eq.2 is then specialized to an affine form with respect to the future control moves:where -%.*is a nominal input sequence and is assumed to be equal to the steady-state nominal input, 2%: ^^^→ ^%&^and 3%: ^^^→ ^%&^×%&^. Additionally, to reduce the predictor complexity, a recursive structure is adopted, with 2%and 3%defined as follows:PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0074] In thisdata (^456), the past injected insulin (^7^8) and the past and current ingested carbohydrates (94:;):

[0075] Note that meal information in the future prediction horizon is not part of the state vector. The nominal input sequence -%.*is chosen to be the basal insulin, which is a constant amount of insulin in charge of maintaining the glucose levels in the euglycemic range during fasting periods. Insulin variations, -%.*− -%.*, are obtained by injecting insulin boluses, and aim at minimizing the occurrence of hypo- and hyperglycemia in presence of disturbances (e.g., meals, physical activity).

[0076] Learning predictors. The problem of learning the maps 2%and 3%in Eqs.4-5 can be posed as two separate learning problems, and the prediction '(%can be seen as the sum of two contributions, which Applicants propose to identify separately. To ease the two-steps identification procedure, Applicants generated two training datasets in-silico using the metabolic model and a 10-subject adult cohort with different insulin therapies: (Scenario-I) insulin therapy based only on the administration of the basal insulin throughout the day; and (Scenario-II) insulin therapy based on the administration of basal insulin together with insulin boluses at mealtimes.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0077] Both scenarios have the same sequence of meals, however only Scenario-II includes an insulin bolus at mealtime to compensate for the induced prandial glucose rise. Following conventional therapy, the insulin bolus dose is computed as the ratio between the meal amount and the carbohydrate-to-insulin (CR) factor. Additionally, Scenario-I and Scenario-II include a ± 10% error in the basal insulin therapy to mimic the mismatch that often occurs in real-life. Since Scenario-I corresponds to the condition of having -%.*= -%.*, Applicants used this dataset to identify 2%, which models the dynamics of the system from past input-output sequences collected in quasi open-loop conditions, i.e., without applying any control action to reject meal disturbances. On the other side, the dataset generated with the second insulin therapy was exploited to identify 3%, which represents the effect of any control action on the glucose predictions. The sampling time ^8chosen for the overall T-step-ahead predictor is 15 minutes, which provides a sufficiently accurate reproduction of the continuous time dynamics of the system and allows spanning over a long time with a reasonable number of predictors. The system under control typically settles in 2 to 4 hours.

[0078] Modeling 2%via LSTMs. Applicants designed the ^ functions ^!with ^ = 1, … , ^ as a 2- layer stacked LSTM model as illustrated in FIG. 4. As described previously, each predictor is trained using the synthetic dataset where the insulin therapy includes only the administration of the basal insulin, i.e. Scenario-I. This assumption implies that -%.*= -%.*, and consequently,='%= 2(^^).

[0079] Each LSTM layer receives input from the previous layer, enabling the model to learn hierarchical representations of the data. The output of the last LSTM layer is then passed to a stack of two fully connected (FC) layers. The FC layers are responsible for mapping the LSTM’s hidden representations to a suitable format for prediction. They introduce additional nonlinearity and complexity to the model, enabling it to capture more intricate patterns in the data. The output size of each predictor ^!is set equal to j such that the number of neurons in the output layer equals the number of samples up to ^. Finally, as Applicants combine each ^!into a T-step-ahead predictor, then '(^ !is the ^@:sample from ^!(^^). The training process uses a Mean Absolute Error (MAE) loss function, with the Root Mean Square Propagation (RMSProp) algorithm to minimize the loss function and update the model’s parameters. The MAE loss function is defined as:PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 where ABCDis the loss, Edataset, ^7and ^ GFare the actual and the predicted glucose samples, respectively. The learning rate was set to 0.0001 to ensure stable and effective convergence during training.

[0080] The forward chaining methodology was applied for training and validation of each ^!by using the entire 10-adult cohort. This approach is specifically designed to handle temporal dependencies and ensures realistic evaluation of the model’s performance. Forward chaining involves iteratively training the model on a subset of the subjects’ data and testing it on remaining subjects of the cohort. For each iteration in the training, the model is recalibrated using all available subjects in the training set, which means to use the overall data cohort for the identification of the model. This validation step assesses the model’s ability to generalize and make accurate predictions for new patients. To enhance the performance of the LSTM model for blood glucose prediction, Applicants undertook a comprehensive process involving hyperparameter tuning, early stopping, and meticulous model evaluation. In the pursuit of optimal hyperparameters, Applicants explored different batch sizes (64, 128, and 256) and the number of training epochs (ranging from 200 to 400). These selections were made based on the dataset’s characteristics, considering the length of the dataset and the number of patients involved in training. This exploration allowed Applicants to identify the most effective combination of batch size and training epochs that yielded superior predictive capabilities. To mitigate the risk of overfitting and promote generalization, Applicants implemented the early-stopping-point approach. The early stopping point strategy halts the training process if the model failed to demonstrate improvement within a specific threshold on the validation data. Specifically, Applicants employed a patience value of 20 epochs in the changes in the loss defined in Eq.9. This technique safeguarded against excessive adaptation to the training data, ensuring robust performance on testing data.

[0081] Modelling GT via a linear regression model. Applicants modelled the ^ functions H!, with ^ = 1, … , ^ as linear regression models able to describe the relation between glucose concentration and injected bolus insulin. As described above, each component H!has to model the effect of any control action on the glucose predictions. Specifically, 3%has to describe the glucose response to the variation in insulin dose with respect to the basal insulin rate, defined as ∆- ∶=PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 -%.*− -%.*. To capture this relationship, Applicants rely on the concept of the correction factor (CF. The CF is a clinical parameter that describes how much 1 unit of rapid-acting insulin will reduce the blood glucose from the current level. The CF is an estimate of the so-called insulin sensitivity, which is unknown, but it affects the observed blood glucose trends. That is, the following is assumed: the flatter the glucose trend, the lower the insulin sensitivity. Assuming 2%has been identified and hence available, the mismatch between the glucose data generated in Scenario-II and the predicted open-loop glucose excursions can be calculated as: the error samples at time instant ^, andsamples at time instant ^. From Eq.3, Applicants can derive that 3%describes the ratio between K'456,LMand K-. This implies that 3%plays the role of the correction factor. Since the correction factor can be indirectly estimated by observing the past glucose trend, the proposed regressors for 3%are the past and current CGM data, which are a subset of the variables of the state vector ^^, as described in Eq.6:

[0082] Because of the recursive structure of 3%described in Eq.5, Applicants obtain the following structure:the administration of basal insulin and the insulin boluses at mealtimes.

[0083] Example 1.3. Implementation in an MPCPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0084] Let S(·) be the cost function of the MPC problem: where ^ > 0along the horizon ^, U = VW%and ^ = XW%are tuning parameters, V > 0, X > 0, W%∈ ^%×%is the identity matrix. The basal insulin -%.*is the subject-dependent basal insulin rate. A time-dependent set point '%was employed and set to 110 mg / dl during the day, and 125 mg / dl at night. Daytime is defined to be the interval 5:00 am to 10:00 pm. All other times are nighttime and there is no transition period. This trade-off helps to reduce the chance of immediately dangerous nocturnal hypoglycemic events, i.e. glucose levels below 70 mg / dL. The proposed MPC law uses ^ ∶= 8, i.e.120 minutes, V: = 1, and X: = 10. Then, the resulting FHOCP is reported in Eqs.15-17:subject to

[0085] The constraint values are defined according to hardware limitations of the insulin pump and the CGM:

[0086] The receding horizon (RH) principal is then applied so that the actual control action given as output, ^6Z4, is the first element of the optimal control sequence -%∗.*at each time instant ^.

[0087] Example 1.4. In-Silico Performance EvaluationPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0088] Evaluation of the predictors. In this Example, two different scenarios were designed for the identification, i.e., Scenario-I and Scenario-II, and a separate scenario (Scenario-III) was designed for the validation of the T-step-ahead predictors. In both identification and validation scenarios, the mealtimes and corresponding amounts were defined by using a stochastic meal generator, which was designed for an accurate reproducibility of eating habits of a cohort of subjects with T1D. The stochastic meal generator is based on a Markov Chain, whose state is the fasting period, and the transition probabilities depend on daytime and carbohydrate intake of the previous meal. The use of a stochastic generator choice removes the arbitrariness of the scenario design process and provides enough variability in the synthetic data. Consequently, identification and validation scenarios have different sequences of meals: different food habits imply different insulin therapies, which in turn impact differently on glucose levels, as observed in standard clinical practice. All scenarios last 28 days.

[0089] In this Example, Applicants considered a prediction horizon ^ = 120 minutes, with a sampling time of ^^= 15 minutes. Denoting with ^\ the model prediction and y the measured glucose level in the validation scenario, the accuracy of the model predictions of each single predictor composing the overall T-step-ahead predictor, is computed in terms of mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean squared error (RMSE), defined as:

[0090] Evaluation of the controller. The evaluation of control performances was carried out using the in-silico subjects. Simulations were 48 h in duration, starting at midnight. With the aim to test the controller in different but realistic conditions, including real-life food habits and unknown changes in insulin sensitivity, Applicants considered four scenarios: (Scenario A) a comparatively standard scenario where each subject consumes three meals per day, including breakfast of 50 g atPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 8 AM, lunch of 75 g at 1 PM, dinner of 75 g at 7 PM; (Scenario B) this scenario aims at mimicking realistic meal habits, with meal time and amounts defined by using a stochastic meal generator; (Scenario C) this scenario aims at reproducing the uncertainties due to unknown factors, typically encountered in real-life conditions, with a random ± 25% variation of the nominal insulin sensitivity; and (Scenario D) this scenario aims at simulating under- or over-estimation errors of carbohydrate intakes, with a random ± 25% error on the estimated meal amounts.

[0091] Applicants evaluated the controller for each scenario based on the metrics that are considered most relevant in clinical practice, including mean glucose (mg / dL), glycemic variability, i.e. coefficient of variation (CV), (mg / dl), percent time above 250 mg / dL, percent time above 180 mg / dL, percent time in range, i.e. between 70-180 mg / dL, percent time below 70 mg / dl, and percent time below 54 mg / dl. Recommended glucose targets include percent time in range of 70-180 mg / dL > 70%, percent time below 70 mg / dL < 4%, and percent time above 180 mg / dL < 25%.

[0092] Identification of the ARX predictor for comparison purposes. For comparison purposes, Applicants considered a linear, 1-step-ahead predictor because it represents the most widely applied solution in clinical applications for automated insulin delivery systems. It is worthy to note that the controllers that have been tested in clinical trials have a certain level of individualization to deal with the inter-patient variability. However, the proposed non-linear, multi-step-ahead predictor is a population model and a comparison with a population linear, 1-step-ahead predictor identified can truly help to gauge the impact of the model structure on the control performance without any additional confounding factor.

[0093] Applicants identified a linear, 1-step-ahead predictor of blood glucose evolution with an autoregressive model with exogenous inputs describing the system dynamics around a nominal working point. Hence, denoting with ]^7^8= ^7^8− ^7^8the injected insulin variation with respect to the nominal insulin basal rate, ^7^8, and ]94:;= 94:;− 94:;the ingested carbohydrate with 94:;= 0, and ]^456= ^456− ^456the measured glucose variation with the nominal basal glucose, ^456, the predicted glucose variation ]^\^C^_is obtained as:PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 where E`is the numberinputs, and E^is the pure time delay. The proposed ARX model uses E`: = 3, and Ea: = 3, and E^: = 1, respectively, to achieve a flexible, yet parsimonious, description of the system dynamics. Using a Prediction Error Method (PEM) the parameters of the proposed ARX are identified, using the identification data from Scenario-II, for consistency with the training of the T-step-ahead predictor. The identified parameters are:

[0094] The ARX has a sampling time ^^= 15 minutes, that is the sampling time chosen for the control action, as described above. To design a linear MPC, a state space realization of the proposed ARX is required. Applicants chose the realization corresponding to the canonical controllability form. The state vector of the ARX model is not measurable, thus a steady-state Kalman filter has been incorporated.

[0095] The process noise covariance UbLis set to the identity matrix, WQ, and the measurement noise covariance ^bLis defined equal to 1c.d.

[0096] In the MPC formulation, a standard quadratic cost function was used, with weights VC^_for the system output tracking error ]^C^_− ]^ where ]^ is the glucose variation with respect to the set points, i.e. ]^ = ^%− ^456. Consistently with the cost function defined in Eq.3, the weight rARX always penalizes the deviation of the control action from the basal rate, i.e. δuins. In this formulation, the MPC parameters are defined as VC^_= 1, VC^_= 1.5, and the prediction horizon ^C^_is set equal to ^ = 8. The input and output constraints are consistent with those defined in Eq.18.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0097] Applicants conduct statistical analyses for each metric and scenario to evaluate the significance of the difference between controller designs. The significance is evaluated based on the average outcomes per subject via paired t-test using two-sided p-value ≤ 0.05 significance threshold for # = 10.

[0098] Example 1.5 Results

[0099] Accuracy of predictions. Applicants compare the performance of the proposed multi-step predictor with that of the ARX model-based predictor on the validation dataset (Scenario-III) as a function of the step ahead index, i.e., ^ = 1, ... , 8. FIGS. 5A-5B illustrate the predicted population-level CGM time-series on a representative day of the validation dataset. Meals occur at 7 PM, at 8 AM, and 1 PM, respectively. An increase in the step ahead index leads to a deterioration in the accuracy of the prediction for a given model, as shown in FIGS.5A-5B. With 1-step ahead, i.e.15 minutes, the ARX and multi-step predictions are overlapping with the CGM data: this result is expected because the ARX predictor was identified to maximize the 1-step ahead prediction performance. With 2-step ahead, i.e. 30 minutes, the ARX and multi-step predictions are almost overlapping, but the prediction of the ARX model slightly tends to underestimate the glucose excursion around the postprandial phase. This holds also for 3-step ahead case, i.e. 45 minutes, where the ARX model starts to underestimate the glucose level also during the nocturnal period. With 4-step ahead, i.e.60 minutes, the predictions capabilities of both predictors start to degrade. Around meals, the multi-step predictor shows a faster response to insulin bolus than to meal intake. From 75 up 120 minutes, the aforementioned issues become more evident: the ARX predictor heavily underestimates the glucose levels, while the multistep predictor captures the glucose trend but with an wider excursion around the meals. In particular, it is important to note is that the proposed multi-step predictor is able to capture the downward slope of a prandial hyperglycemic excursion as well as the overnight steady-state equilibrium glucose concentration consistently well, regardless of prediction horizon. The presence of a pronounced undershoot in the glucose response produced by the proposed predictor can be attributed to the fact that the predictor is a population model, and it does not consider the well-known inter-patient variability in the insulin sensitivity. A conservative tuning of the aggressiveness of the controller was considered to address this limitation. The mean and standard deviation outcomes across the 10- adult 325 in-silico cohort are presented in Table 1.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061a metabolic model with a trial-and-error approach. As discussed above, the 1-step ahead ARX predictor tends to underestimate the glucose concentrations, while Applicants’ multi-step predictor tends to enlarge the dynamic range of glucose responses. Thus, the best tuning of the ARX-based MPC resulted in being more aggressive with respect to the best tuning of the multi-step-based MPC. Applicants compared the performance of the MPC constructed with the proposed multi-step predictors with those of the ARX-based MPC for each scenario, i.e., Scenario A, Scenario B, Scenario C, and Scenario D. In the clinical practice, the effect of the meal disturbance is rejected with a static feed-forward action based on the conventional therapy, which relies on clinical parameters. In this case, to stress the controller capabilities, although the meal is announced to the controller, no additional feed-forward control action is included in the control scheme and the both MPC are completely in charge of disturbance rejection.

[0101] FIGS.6-9 show population-level trajectories on Scenario A, Scenario B, Scenario C, and Scenario D, respectively. Compared to the ARX-based MPC, the proposed MPC results in BG curves that are less steep from peak to through, and generally in tighter standard-deviation and min-max envelopes. After correction of meal-induced hyperglycemia, the controller shows a steady insulin delivery with no suspension. In the prandial phase, the ARX-based MPC tends to command extremely large insulin boluses to compensate the meal effect, followed by periods of suspension of insulin delivery, which is an undesirable situation in this application. Suspension of insulin delivery, especially when prolonged, inevitably results in BG rebounds which lead to oscillations and increased glycemic variability and risk of hyperglycemia. It is worthy to note that Applicants could not improve this aspect even with less aggressive tuning of the ARX-based MPC.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0102] Numerical results are tabulated in Table 2, where each block of rows list glycemic metrics for the scenarios, reported as mean and standard deviation across the in-silico population. The proposed controller structure yields a significant reduction in CV for all simulation scenarios. Further, the percentage time spent in hypoglycemia is also significantly reduced in all the cases tested. An important observation to make, in this regard, is that the lower hypoglycemia risk is achieved without enforcing pump suspensions at all. In both Scenario A and Scenario B, time in severe hyperglycemia is reduced and time in the acceptable ranges, i.e., 70-140 mg / dl and 70-180 mg / dl, are increased. However, the time above 180 mg / dl is slightly elevated, most likely due to a conservative tuning of the controller gains for the prevention of hypoglycemia. Scenario C mimics a challenging condition with both positive and negative variations of the insulin sensitivity. The proposed controller achieves a significant decrease in the coefficient of variation in the glucose outcome, as reported in Table 2. Compared to the ARX-based MPC, the proposed MPC resulted in a significant reduction in hypoglycemia risk at the cost of a non-significant increase in the time in hyperglycemia and a slight reduction in the time in acceptable ranges. The notable fact here is that the controller avoided over-delivery of insulin and prevented the dangerously low glucose levels in situation of potential increase of the insulin sensitivity. In Scenario D, compared to the ARX-based MPC, the proposed MPC achieved a significant reduction in the coefficient of variation and in the percentage of time in the hypoglycemic zone, i.e. below 70 mg / dL, as well as an increase in the percentage of time between 70 and 180 mg / dL, with a non-significant increase in the time in hyperglycemic zone, i.e. above 180 mg / dL, as reported in Table 2.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061

[0103] Example 1.6. Summary and Conclusions

[0104] In this Example, Applicants proposed a novel closed-loop insulin delivery algorithm for the treatment of T1D. The novelty in the approach lies in the modeling step of the model-based control architecture. Applicants learn a multi-step-ahead predictor of the output which is affine in the control input via a LSTM network. The predictor structure is conceived to increase the accuracy of long-term predictions, allowing at the same time for an efficientPCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 formulation and solution of the resulting LTV-MPC. Applicants showed in numerical simulations the better performances of the proposed predictor, compared to that of an ARX-based. As for control performances, Applicants have demonstrated an improvement overall, increased time in target range with significant reduction in glucose variability and both hypo- and hyperglycemia risks, for a nominal scenario and a scenario testing the robustness against random meal disturbances. In the case of increased insulin resistance, the proposed approach significantly reduced hypoglycemia risk. However, a population predictor could ideally limit the performance since it describes the average dynamics of the population. The well-known inter-patient variability increases the need of patient-tailored models as an individualized description of the glucose metabolism can improve the effectiveness of the control algorithm. However, training the model using data from a single patient may result in a lack of generalization for the model. A trade-off may be achieved by pre-training the multi-step-ahead predictor using the population data and then fine-tuning the model parameters with individual data. The same approach can be replicated in an in vivo setting with a first phase during which the model is pre-trained using in silico data to maximize the generalization capability of the predictor and a second phase of fine-tuning by using the clinical data collected in a real-life setting.

[0105] Example 2. Multiple Daily Injection (MDI) Treatment Regime

[0106] In the context of type 1 diabetes (T1D), the most common platforms adopted for sensing and actuation, respectively, are continuous glucose monitors (CGM) and continuous subcutaneous insulin infusion (CSII) pumps. However, there is a large group of subjects with T1D following the multiple daily injection (MDI) treatment regime.

[0107] The MDI treatment comprises the delivery of two types of insulin formulations: (1) a long-acting analog once per day, e.g., every morning before breakfast; and (2) a rapid-acting analog at mealtimes.

[0108] Applicants envision automated adjustments on the insulin therapy for subjects with T1D following the MDI therapy. Specifically, Applicants currently envision the use of the disclosed technology, i.e. model predictive control approach with data-driven multi-step ahead affine blood glucose predictors, to compute the optimal dose for the rapid-acting analog at mealtimes. Currently, the calculation for the dose for the rapid-acting analog is based on the so-PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 called conventional therapy, which is generally performed by considering the Carbohydrate-to- insulin Ratio (CR), a clinical parameter identified by the physician from subject history / habits.

[0109] Applicants tested the proposed strategy on a population of 10 in-silico MDI patients on a comparatively standard scenario where each subject consumes three meals per day, including breakfast of 50 g at 8 AM, lunch of 75 g at 1 PM, dinner of 75 g at 7 PM.

[0110] FIG.10 displays the preliminary results showing that the injection policy improves desired glucose regulation with respect to conventional therapy. The proposed technology improves the postprandial glucose regulation by reducing the time spent in hyperglycemic range (>180 mg / dL) and increasing the time in euglycemic range (70-180 mg / dL), as reported in Table 3.

[0111] Additional embodiments of the present disclosure are provided herein below: Embodiment 1. A computer-implemented method of monitoring blood glucose levels of a subject, said method comprising: feeding the subject’s blood glucose level into a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject, wherein the algorithm comprises a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a Linear time-varying (LTV) model predictive control (MPC) law; using the algorithm to predict if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia; and transmitting insulin administration instructions based on the prediction. Embodiment 2. The method of Embodiment 1, wherein the insulin administration instructions are based on the solution of a receding horizon (RH) optimal control problem carried out by the LTV- MPC.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 3. The method of Embodiment 1, wherein the insulin administration instructions comprise increasing insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hyperglycemia. Embodiment 4. The method of Embodiment 1, wherein the insulin administration instructions comprise decreasing or suspending insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hypoglycemia. Embodiment 5. The method of Embodiment 1, wherein the method further comprises a step of measuring the blood glucose levels of the subject. Embodiment 6. The method of Embodiment 1, wherein the method further comprises a step of obtaining a blood sample from the subject and measuring the blood glucose levels from the blood sample. Embodiment 7. The method of Embodiment 6, wherein the blood glucose levels of the subject is measured by a sensor associated with the subject, wherein the sensor transmits the measured blood glucose levels to the algorithm. Embodiment 8. The method of Embodiment 1, wherein the method occurs in real-time. Embodiment 9. The method of Embodiment 1, wherein the method occurs continuously. Embodiment 10. The method of Embodiment 1, further comprising a step of administering insulin based on the instructions. Embodiment 11. The method of Embodiment 10, wherein the insulin is administered by a user. Embodiment 12. The method of Embodiment 10, wherein the administration occurs by a method selected from the group consisting of intravenous administration, subcutaneous administration, transdermal administration, percutaneous administration, topical administration, intraarterial administration, intrathecal administration, oral administration, or combinations thereof. Embodiment 13. The method of Embodiment 1, wherein the insulin administration instructions are transmitted to an insulin pump associated with the subject, wherein the insulin pump implements the instructions. Embodiment 14. The method of Embodiment 13, wherein the insulin pump is in the form of a patch. Embodiment 15. The method of Embodiment 13, wherein the insulin pump is operable for subcutaneous insulin administration.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 16. The method of Embodiment 13, wherein the insulin pump comprises an insulin reservoir and a processor. Embodiment 17. The method of Embodiment 16, wherein the processor is in electronic communication with the algorithm, and wherein the processor actuates or withholds the release of insulin from the insulin reservoir based on received instructions from the algorithm. Embodiment 18. The method of Embodiment 1, wherein the algorithm comprises a machine learning algorithm. Embodiment 19. The method of Embodiment 18, wherein the machine learning algorithm is a Root Mean Square Propagation (RMSProp) training algorithm. Embodiment 20. The method of Embodiment 18, wherein the machine learning algorithm is a Long Short-Term Memory (LSTM) network. Embodiment 21. The method of Embodiment 1, wherein the algorithm does not identify an open- loop algorithm of the glucoregulatory system from available data. Embodiment 22. The method of Embodiment 1, wherein the algorithm directly fits the entire BG trajectory over a predefined prediction horizon to be used in the MPC law as a nonlinear function of past input-output data and an affine function of future insulin control inputs. Embodiment 23. The method of Embodiment 22, wherein a Long Short-Term Memory (LSTM) network is used to fit the component of the BG trajectory nonlinear in the state to a predictive nonlinear function incorporated into the algorithm. Embodiment 24. The method of Embodiment 22, wherein a linear regression model is used to fit the future insulin control inputs to an affine function incorporated into the algorithm. Embodiment 25. The method of Embodiment 1, wherein the algorithm comprises customizable user parameters. Embodiment 26. The method of Embodiment 25, wherein the customizable user parameters are selected from the group consisting of length of prediction horizon, weight matrices, setpoints, or combinations thereof. Embodiment 27. The method of Embodiment 1, wherein the BG trajectory is implemented as a nonlinear function of past input-output data and an affine function of future insulin control inputs. Embodiment 28. The method of Embodiment 1, wherein the subject is a human being suffering from type 1 diabetes.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 29. The method of Embodiment 28, wherein the method is used to treat type 1 diabetes or prevent the complications arising from type 1 diabetes. Embodiment 30. A blood glucose monitoring system comprising: an insulin pump associated with a subject and operational to administer insulin to the subject; one or more sensors associated with the subject and operational to measure the blood glucose levels of the subject; and a computing device in electronic communication with the insulin pump, the computing device comprising: a non-transitory computer-usable medium having computer-readable program code embodied therein; a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject, wherein the algorithm comprises a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law; and programming instructions operable to implement a method comprising: feeding the subject’s blood glucose level into the algorithm; predicting if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia using the algorithm; and transmitting insulin administration instructions to the insulin pump based on the prediction. Embodiment 31. The system of Embodiment 30, wherein the insulin administration instructions are based on the solution of a receding horizon (RH) optimal control problem carried out by the LTV-MPC. Embodiment 32. The system of Embodiment 30, wherein the insulin administration instructions comprise increasing insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hyperglycemia. Embodiment 33. The system of Embodiment 30, wherein the insulin administration instructions comprise decreasing or suspending insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hypoglycemia. Embodiment 34. The system of Embodiment 30, wherein the insulin pump is in the form of a patch. Embodiment 35. The system of Embodiment 30, wherein the insulin pump is operable for subcutaneous insulin administration. Embodiment 36. The system of Embodiment 30, wherein the insulin pump comprises an insulin reservoir and a processor, wherein the processor is in electronic communication with the computing device, and wherein the processor is operational to actuate or withhold the release of insulin from the insulin reservoir.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 37. The system of Embodiment 30, wherein the one or more sensors are operational to transmit the subject’s blood glucose levels to the computing device. Embodiment 38. The system of Embodiment 30, wherein the computing device comprises a computer. Embodiment 39. The system of Embodiment 30, wherein the computing device comprises a mobile device. Embodiment 40. The system of Embodiment 30, wherein the computing device comprises an app on a mobile device. Embodiment 41. The system of Embodiment 30, wherein the computing device comprises a chip on an insulin pump. Embodiment 42. The system of Embodiment 30, wherein the computing device is in electronic communication with the insulin pump through a wireless network. Embodiment 43. The system of Embodiment 30, wherein the algorithm is a machine learning algorithm. Embodiment 44. The system of Embodiment 43, wherein the machine learning algorithm is a Root Mean Square Propagation (RMSProp) training algorithm. Embodiment 45. The system of Embodiment 43, wherein the machine learning algorithm is a Long Short-Term Memory (LSTM) network. Embodiment 46. The system of Embodiment 30, wherein the algorithm does not identify an open- loop algorithm of the glucoregulatory system from available data. Embodiment 47. The system of Embodiment 30, wherein the algorithm directly fits the entire BG trajectory over a predefined prediction horizon to be used in the MPC law as a nonlinear function of past input-output data and an affine function of future insulin control inputs. Embodiment 48. The system of Embodiment 47, wherein a Long Short-Term Memory (LSTM) network is used to the component of the BG trajectory nonlinear in the state to a predictive nonlinear function incorporated into the algorithm. Embodiment 49. The system of Embodiment 47, wherein a linear regression model is used to fit the future insulin control inputs to an affine function incorporated into the algorithm. Embodiment 50. The system of Embodiment 30, wherein the algorithm comprises customizable user parameters.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 51. The system of Embodiment 50, wherein the customizable user parameters are selected from the group consisting of length of prediction horizon, weight matrices, setpoints, or combinations thereof. Embodiment 52. The system of Embodiment 50, wherein the customizable user parameters comprise length of prediction horizon. Embodiment 53. The system of Embodiment 30, wherein the BG prediction is implemented as a nonlinear function of past input-output data and an affine function of future insulin control inputs. Embodiment 54. The system of Embodiment 30, wherein the feeding of the subject’s blood glucose level into the algorithm occurs in real-time. Embodiment 55. The system of Embodiment 30, wherein the system is suitable for use in monitoring the blood glucose levels of the subject. Embodiment 56. The system of Embodiment 30, wherein the subject is a human being suffering from type 1 diabetes. Embodiment 57. A computing device comprising one or more computer readable storage mediums having at least one program code embodied therewith, wherein the computing device comprises: a closed-loop insulin delivery algorithm trained to predict the blood glucose level of a subject, wherein the algorithm comprises a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law; and programming instructions for: feeding the subject’s blood glucose level into the algorithm, using the algorithm to predict if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia, and transmitting insulin administration instructions based on the prediction. Embodiment 58. The computing device of Embodiment 57, wherein the insulin administration instructions are based on the solution of a receding horizon (RH) optimal control problem carried out by the LTV-MPC. Embodiment 59. The computing device of Embodiment 57, wherein the insulin administration instructions comprise increasing insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hyperglycemia. Embodiment 60. The computing device of Embodiment 57, wherein the insulin administration instructions comprise decreasing or suspending insulin administration to the subject if the blood glucose level of the subject is expected to reach a level representing hypoglycemia.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 61. The computing device of Embodiment 57, wherein the computing device comprises a computer. Embodiment 62. The computing device of Embodiment 57, wherein the computing device comprises a mobile device. Embodiment 63. The computing device of Embodiment 57, wherein the computing device comprises an app on a mobile device. Embodiment 64. The computing device of Embodiment 57, wherein the computing device comprises a chip on an insulin pump. Embodiment 65. The computing device of Embodiment 57, wherein the computing device is in electronic communication with the insulin pump through a wireless network. Embodiment 66. The computing device of Embodiment 57, wherein the algorithm is a machine learning algorithm. Embodiment 67. The computing device of Embodiment 66, wherein the machine learning algorithm is a Root Mean Square Propagation (RMSProp) training algorithm. Embodiment 68. The computing device of Embodiment 66, wherein the machine learning algorithm is a Long Short-Term Memory (LSTM) network. Embodiment 69. The computing device of Embodiment 57, wherein the algorithm does not identify an open-loop algorithm of the glucoregulatory system from available data. Embodiment 70. The computing device of Embodiment 57, wherein the algorithm directly fits the entire BG prediction over a predefined prediction horizon to be used in the MPC law as a nonlinear function of past input-output data and an affine function of future insulin control inputs. Embodiment 71. The computing device of Embodiment 70, wherein a Long Short-Term Memory (LSTM) network is used to fit the component of the BG trajectory nonlinear in the state to a predictive nonlinear function incorporated into the algorithm. Embodiment 72. The computing device of Embodiment 70, wherein a linear regression model is used to fit the future insulin control inputs to an affine function incorporated into the algorithm. Embodiment 73. The computing device of Embodiment 57, wherein the algorithm comprises customizable user parameters.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 Embodiment 74. The computing device of Embodiment 73, wherein the customizable user parameters are selected from the group consisting of length of prediction horizon, weight matrices, setpoints, or combinations thereof. Embodiment 75. The computing device of Embodiment 74, wherein the customizable user parameters comprise length of prediction horizon. Embodiment 76. The computing device of Embodiment 57, wherein the BG prediction is implemented as a nonlinear function of past input-output data and an affine function of future insulin control inputs. Embodiment 77. The computing device of Embodiment 57, wherein the feeding of the subject’s blood glucose level into the algorithm occurs in real-time. Embodiment 78. The computing device of Embodiment 57, wherein the computing device is suitable for use in monitoring the blood glucose levels of the subject. Embodiment 79. The computing device of Embodiment 78, wherein the subject is a human being suffering from type 1 diabetes.

[0112] Without further elaboration, it is believed that one skilled in the art can, using the description herein, utilize the present disclosure to its fullest extent. The embodiments described herein are to be construed as illustrative and not as constraining the remainder of the disclosure in any way whatsoever. While the embodiments have been shown and described, many variations and modifications thereof can be made by one skilled in the art without departing from the spirit and teachings of the invention. Accordingly, the scope of protection is not limited by the description set out above, but is only limited by the claims, including all equivalents of the subject matter of the claims. The disclosures of all patents, patent applications and publications cited herein are hereby incorporated herein by reference, to the extent that they provide procedural or other details consistent with and supplementary to those set forth herein.

Claims

PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 CLAIMS 1. A blood glucose monitoring system comprising: an insulin pump associated with a subject and operational to administer insulin to the subject; one or more sensors associated with the subject and operational to measure the blood glucose levels of the subject; and a computing device in electronic communication with the insulin pump, the computing device comprising: a non-transitory computer-usable medium having computer-readable program code embodied therein; a closed-loop insulin delivery algorithm trained to predict the blood glucose level of the subject, wherein the algorithm comprises a data-driven multi-step-ahead blood glucose (BG) predictor integrated with a linear time-varying (LTV) model predictive control (MPC) law; and programming instructions operable to implement a method comprising: feeding the subject’s blood glucose level into the algorithm; predicting if the blood glucose level of the subject is expected to reach a level representing hypoglycemia or hyperglycemia using the algorithm; and transmitting insulin administration instructions to the insulin pump based on the prediction.

2. The system of claim 1, wherein the insulin administration instructions are based on the solution of a receding horizon (RH) optimal control problem carried out by the LTV-MPC.

4. The system of claim 1, wherein the algorithm is a machine learning algorithm.

5. The system of claim 4, wherein the machine learning algorithm is a Root Mean Square Propagation (RMSProp) training algorithm.

6. The system of claim 4, wherein the machine learning algorithm is a Long Short-Term Memory (LSTM) network.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 7. The system of claim 1, wherein the algorithm does not identify an open-loop algorithm of the glucoregulatory system from available data.

8. The system of claim 1, wherein the algorithm directly fits the entire BG trajectory over a predefined prediction horizon to be used in the MPC law as a nonlinear function of past input- output data and an affine function of future insulin control inputs.

9. The system of claim 8, wherein a Long Short-Term Memory (LSTM) network is used to the component of the BG trajectory nonlinear in the state to a predictive nonlinear function incorporated into the algorithm.

10. The system of claim 8, wherein a linear regression model is used to fit the future insulin control inputs to an affine function incorporated into the algorithm.

11. The system of claim 1, wherein the BG prediction is implemented as a nonlinear function of past input-output data and an affine function of future insulin control inputs.

12. The system of claim 1, wherein the feeding of the subject’s blood glucose level into the algorithm occurs in real-time.

13. The system of claim 1, wherein the insulin pump comprises an insulin reservoir and a processor, wherein the processor is in electronic communication with the computing device, and wherein the processor is operational to actuate or withhold the release of insulin from the insulin reservoir.

14. The system of claim 1, wherein the computing device comprises a mobile device.

15. The system of claim 1, wherein the computing device comprises an app on a mobile device.

16. The system of claim 1, wherein the computing device comprises a chip on an insulin pump.

17. The system of claim 1, wherein the computing device is in electronic communication with the insulin pump through a wireless network.PCT Application Attorney Docket No. AF23853.P198WO UH ID No.2023-061 18. The system of claim 1, wherein the insulin pump is operable for subcutaneous insulin administration.

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