Model predictive control of type 1 diabetes: an in silico trial

Offline reinforcement learning for safer blood glucose control in people with type 1 diabetes

The widespread adoption of effective hybrid closed loop systems would represent an important milestone of care for people living with type 1 diabetes (T1D). These devices typically utilise simple control algorithms to select the optimal insulin dose for maintaining blood glucose levels within a healthy range. Online reinforcement learning (RL) has been utilised as a method for further enhancing glucose control in these devices. Previous approaches have been shown to reduce patient risk and improve time spent in the target range when compared to classical control algorithms, but are prone to instability in the learning process, often resulting in the selection of unsafe actions. This work presents an evaluation of offline RL for developing effective dosing policies without the need for potentially dangerous patient interaction during training. This paper examines the utility of BCQ, CQL and TD3-BC in managing the blood glucose of the 30 virtual patients available within the FDA-approved UVA/Padova glucose dynamics simulator. When trained on less than a tenth of the total training samples required by online RL to achieve stable performance, this work shows that offline RL can significantly increase time in the healthy blood glucose range from 61.6±0.3% to 65.3±0.5% when compared to the strongest state-of-art baseline (p<0.001). This is achieved without any associated increase in low blood glucose events. Offline RL is also shown to be able to correct for common and challenging control scenarios such as incorrect bolus dosing, irregular meal timings and compression errors. The code for this work is available at: https://github.com/hemerson1/offline-glucose.

Enabling fully automated insulin delivery through meal detection and size estimation using Artificial Intelligence

We present a robust insulin delivery system that includes automated meal detection and carbohydrate content estimation using machine learning for meal insulin dosing called robust artificial pancreas (RAP). We conducted a randomized, single-center crossover trial to compare postprandial glucose control in the four hours following unannounced meals using a hybrid model predictive control (MPC) algorithm and the RAP system. The RAP system includes a neural network model to automatically detect meals and deliver a recommended meal insulin dose. The meal detection algorithm has a sensitivity of 83.3%, false discovery rate of 16.6%, and mean detection time of 25.9 minutes. While there is no significant difference in incremental area under the curve of glucose, RAP significantly reduces time above range (glucose >180 mg/dL) by 10.8% (P = 0.04) and trends toward increasing time in range (70-180 mg/dL) by 9.1% compared with MPC. Time below range (glucose <70 mg/dL) is not significantly different between RAP and MPC.

Near-optimal feedback control for postprandial glucose regulation in type 1 diabetes

This paper is focused on feedback control of postprandial glucose levels for patients with type 1 Diabetes Mellitus. There are two important limitations that make this a challenging problem. First, the slow subcutaneous insulin pharmacokinetics that introduces a significant lag into the control loop. Second, the positivity constraint on the control action, meaning that it is not possible to remove insulin from the body. In this paper, both issues are explicitly considered in the design process using the internal model control framework, to derive a near-optimal feedback controller. Optimality is understood here as minimizing the blood glucose peak after a meal intake and, at the same time, preventing glucose values below a prescribed threshold. It is shown how the proposed controller approaches the optimal closed-loop performance as a limit case. The theoretical results are supported by a numerical example and the feasibility of the overall strategy under uncertainties is illustrated using an extended version UVa/Padova metabolic simulator.

Adaptive Personalized Prior-Knowledge-Informed Model Predictive Control for Type 1 Diabetes

This work considers the problem of adaptive prior-informed model predictive control (MPC) formulations that explicitly incorporate prior knowledge in the model development and is robust to missing data in the output measurements. The proposed prediction model is based on a latent variables model to extract glycemic dynamics from highly-correlated data and incorporates prior knowledge of exponential stability to improve the prediction ability. Missing data structures are formulated to enable model predictions when output measurements are missing for short periods of time. Based on the latent variables model, the MPC strategy and adaptive rules are developed to automatically tune the aggressiveness of the MPC. The adaptive prior-knowledge-informed MPC is evaluated with computer simulations for the control of blood glucose concentrations in people with Type 1 diabetes (T1D) using simulated virtual patients. Due to the variability among people with T1D, the hyperparameters of the prior-knowledge-informed model are personalized to individual subjects. The percentage of time spent in the target range is 76.48% when there are no missing data and 76.52% when there are missing data episodes lasting up to 30 mins (6 samples). Incorporating the adaptive rules further improves the percentage of time in target range to 84.58% and 84.88% for cases with no missing data and missing data, respectively. The proposed adaptive prior-informed MPC formulation provides robust, effective, and safe regulation of glucose concentration in T1D despite disturbances and missing measurements.

Evaluation of blood glucose level control in type 1 diabetic patients using deep reinforcement learning

Diabetes mellitus is a disease associated with abnormally high levels of blood glucose due to a lack of insulin. Combining an insulin pump and continuous glucose monitor with a control algorithm to deliver insulin is an alternative to patient self-management of insulin doses to control blood glucose levels in diabetes mellitus patients. In this work, we propose a closed-loop control for blood glucose levels based on deep reinforcement learning. We describe the initial evaluation of several alternatives conducted on a realistic simulator of the glucoregulatory system and propose a particular implementation strategy based on reducing the frequency of the observations and rewards passed to the agent, and using a simple reward function. We train agents with that strategy for three groups of patient classes, evaluate and compare it with alternative control baselines. Our results show that our method is able to outperform baselines as well as similar recent proposals, by achieving longer periods of safe glycemic state and low risk.

Control of blood glucose induced by meals for type-1 diabetics using an adaptive backstepping algorithm

In this study, an adaptive backstepping method is proposed to regulate the blood glucose induced by meals for type-1 diabetic patients. The backstepping controller is used to control the blood glucose level and an adaptive algorithm is utilized to compensate for the blood glucose induced by meals. Moreover, the effectiveness of the proposed method is evaluated by comparing results in two different case studies: in the presence of actuator faults and the loss of control input for a short while during treatment. Effects of unannounced meals three times a day are investigated for a nominal patient in every case. It is argued that adaptive backstepping is the preferred control method in either case. The Lyapunov theory is used to prove the stability of the proposed method. Obtained results, indicated that the adaptive backstepping controller is stable, and the desired level of glucose concentration is being tracked efficiently.

Prior Informed Regularization of Recursively Updated Latent-Variables-Based Models with Missing Observations

Many data-driven modeling techniques identify locally valid, linear representations of time-varying or nonlinear systems, and thus the model parameters must be adaptively updated as the operating conditions of the system vary, though the model identification typically does not consider prior knowledge. In this work, we propose a new regularized partial least squares (rPLS) algorithm that incorporates prior knowledge in the model identification and can handle missing data in the independent covariates. This latent variable (LV) based modeling technique consists of three steps. First, a LV-based model is developed on the historical time series data. In the second step, the missing observations in the new incomplete data sample are estimated. Finally, the future values of the outputs are predicted as a linear combination of estimated scores and loadings. The model is recursively updated as new data are obtained from the system. The performance of the proposed rPLS and rPLS with exogenous inputs (rPLSX) algorithms are evaluated by modeling variations in glucose concentration (GC) of people with Type 1 diabetes (T1D) in response to meals and physical activities for prediction windows up to one hour, or 12 sampling instances, into the future. The proposed rPLS family of GC prediction models are evaluated with both in-silico and clinical experiment data and compared with the performance of recursive time series and kernel-based models. The root mean squared error (RMSE) with simulated subjects in the multivariable T1D simulator where physical activity effects are incorporated in GC variations are 2.52 and 5.81 mg/dL for 30 and 60 mins ahead predictions (respectively) when information for all meals and physical activities are used, increasing to 2.70 and 6.54 mg/dL (respectively) when meals and activities occurred, but the information is with-held from the modeling algorithms. The RMSE is 10.45 and 14.48 mg/dL for clinical study with prediction horizons of 30 and 60 mins, respectively. The low RMSE values demonstrate the effectiveness of the proposed rPLS approach compared to the conventional recursive modeling algorithms.

MPC based optimization applied to treatment of HCV infections

BACKGROUND AND OBJECTIVE

The recent introduction of antivirals for the treatment of the hepatitis C virus opens new frontiers but also poses a significant burden on public health systems. This paper presents a simulation study in which model predictive control (MPC) is proposed for optimizing the therapy aiming to obtain a reduction of the costs of therapy, while maintaining the best pharmacological control of the infection.

METHODS

A dynamic model describing the evolution of hepatitis C is deployed as internal model for MPC implementation, using nominal values of parameters. Different closed-loop simulations are presented both in nominal and in mismatch conditions. In addition, a more easily implementable treatment is proposed, which is based on a discrete dosage approach, where days on/off therapy are considered instead of continuous therapy modulation.

RESULTS

Results show that therapy modulation allows one to achieve the same infection evolution as with full therapy, with a reduction of drug consumption between 10% and 40%. The alternative discrete dosage approach shows similar results achieved with therapy modulation, both in terms of therapy effectiveness and drug consumption reduction.

CONCLUSIONS

The proposed model predictive control therapy optimization strategies appear to be effective, implementable and robust to model errors. It therefore represents a potentially useful approach to alleviate the burden of HCV therapy cost on national health systems.

Analysis and Design Process for Predicting and Controlling Blood Glucose in Type 1 Diabetic Patients

Engineering smart software that can monitor, predict, and control blood glucose is critical to improving patients' quality of treatments with type 1 Diabetic Mellitus (T1DM). However, ensuring a reasonable glycemic level in diabetic patients is quite challenging, as many methods do not adequately capture the complexities involved in glycemic control. This problem introduces a new level of complexity and uncertainty to the patient's psychological state, thereby making this problem nonlinear and unobservable. In this paper, we formulated a mathematical model using carbohydrate counting, insulin requirements, and the Harris-Benedict energy equations to establish the framework for predicting and controlling blood glucose level regulation in T1DM. We implemented the framework and evaluated its performance using root mean square error (RMSE) and mean absolute error (MAE) on a case study. Our framework had less error rate in terms of RMSE and MAE, which indicates a better fit with reasonable accuracy.

H∞ controller and observer synthesis with delay and nonlinear perturbation of double diabetes systems

Patient having type 1 diabetes mellitus (having insulin resistance experience) cannot be treated solely by treatment procedure of type 1 patient nor does treatment employed for type 2 diabetes work for such patient. This type of diabetes patient needs a specific insulin injection procedure. For continuous insulin injection, the patient has to be classified as a different group from type 1 and type 2 patient. The patients experiencing both type 1 and 2 are called double diabetes mellitus (DDM) patient. Dynamic behavior of the patient was presented in delay differential equation (DDE). Based on the developed DDE of DDM model, controllers and observers fulfilling H_∞ norm bound are designed for this specific group of diabetes mellitus patient. Also, a nominal controller and a nominal observer are synthesized to check the proposed controller's ability for disturbance rejection, which is the glucose intake. The performance of the designed controller and observer is evaluated for a population of simulated patients. It shows that controller and observer are able to regulate and estimate, respectively, glycaemic for population of double diabetes patients.

Modeling Ketogenesis for Use in Pediatric Diabetes Simulation

BACKGROUND

Simulation is being increasingly integrated into medical education. Diabetes simulation is well-received by trainees and has demonstrated improved clinical results, including reduced adult inpatient hyperglycemia. However, no pediatric-specific diabetes simulation programs exist for use in medical education. None of the existing diabetes models incorporate ketones as an input or an output, which is essential for use in teaching pediatric diabetes management.

METHODS

We created a pediatric diabetes simulation incorporating both blood sugar and urine ketones as output. Ketone output is implemented as a state variable but is obfuscated to simulate hospital experience. Blood sugar output is similar to other models and incorporates the current blood sugar, insulin on board (IOB) and carbohydrates on board (COB), and insulin and carbohydrate sensitivities. The program calculates all IOB and COB every 15 minutes based on user input and provides written summary feedback at the end of the simulation about inaccurate dosing and timing.

RESULTS

The simulation realistically incorporated both blood glucose and urine ketones in clinically valid and actionable formats. After completing this simulation, 16/17 pediatric residents indicated that they wanted more simulated diabetes cases integrated into their curriculum.

CONCLUSION

Implementing simulation into pediatric diabetes education was feasible and well-received. More work is needed to further study the role of simulation in pediatric diabetes education when used adjunctively or in lieu of lectures when time or resources are limited.

An Adaptive Control Scheme for Interleukin-2 Therapy

Regulatory T cells (Treg) are suppressor cells that control self-reactive and excessive effector conventional T helper cell (Tconv) responses. Breakdown of the balance between Tregs and Tconvs is a hallmark of autoimmune and inflammatory diseases. Interleukin-2 (IL-2) is a growth factor for both populations and subtle leverage to restore the healthy immune balance in IL-2 therapy. By using a mechanistic mathematical model, we introduced an adaptive control strategy to design the minimal therapeutic IL-2 dosage required to increase and stabilize Treg population and restrict inflammatory response. This adaptive protocol allows for dose adjustments based on the feedback of the immune kinetics of the patient. Our simulation results showed that a minimal Treg population was required to restrict the transient side effect of IL-2 injections on the effector Tconv response. In silico results suggested that a combination of IL-2 and adoptive Treg transfer therapies can limit this side effect.

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An adaptive dosing strategy for IL-2 therapy is introduced and analyzed in silico

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IL-2 injections can be tuned to increase and stabilize regulatory T-cell numbers

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Immunosuppressive IL-2 therapy may transiently exacerbate effector T-cell responses

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Combined IL-2 and adoptive regulatory T-cell therapy can safely limit inflammation

Novel algebraic meal disturbance estimation based adaptive robust control design for blood glucose regulation in type 1 diabetes patients

This study designs a robust closed-loop control algorithm for elevated blood glucose level stabilisation in type 1 diabetic patients. The control algorithm is based on a novel control action resulting from integrating algebraic meal disturbance estimator with back-stepping integral sliding mode control (BISMC) technique. The estimator shows finite time convergence leading to accurate and fast estimation of meal disturbance. Moreover, compensation of the estimated disturbance in controller provides significant reduction in chattering phenomenon, which is inherent drawback of sliding mode control (SMC). The controller is applied to one of the most reliable models of type 1 diabetic patients, named Bergman's minimal model. The effectiveness and superiority of the designed controller is shown by comparing it to classical SMC and super-twisting sliding mode control. The designed controller is subject to three different cases for detailed analysis of the controller's robustness against meal disturbance. The three cases considered are hyperglycaemia, hyperglycaemia combined with meal disturbance and three meal disturbance. The simulation results confirm superior performance of algebraic disturbance estimator based BISMC controller for all the cases mentioned above.

A Data-Driven Personalized Model of Glucose Dynamics Taking Account of the Effects of Physical Activity for Type 1 Diabetes: An In Silico Study

This paper aims to develop a data-driven model for glucose dynamics taking into account the effects of physical activity (PA) through a numerical study. It intends to investigate PA's immediate effect on insulin-independent glucose variation and PA's prolonged effect on insulin sensitivity. We proposed a nonlinear model with PA (NLPA), consisting of a linear regression of PA and a bilinear regression of insulin and PA. The model was identified and evaluated using data generated from a physiological PA-glucose model by Dalla Man et al. integrated with the uva/padova Simulator. Three metrics were computed to compare blood glucose (BG) predictions by NLPA, a linear model with PA (LPA), and a linear model with no PA (LOPA). For PA's immediate effect on glucose, NLPA and LPA showed 45-160% higher mean goodness of fit (FIT) than LOPA under 30 min-ahead glucose prediction (P < 0.05). For the prolonged PA effect on glucose, NLPA showed 87% higher FIT than LPA (P < 0.05) for simulations using no previous measurements. NLPA had 25-37% and 31-54% higher sensitivity in predicting postexercise hypoglycemia than LPA and LOPA, respectively. This study demonstrated the following qualitative trends: (1) for moderate-intensity exercise, accuracy of BG prediction was improved by explicitly accounting for PA's effect; and (2) accounting for PA's prolonged effect on insulin sensitivity can increase the chance of early prediction of postexercise hypoglycemia. Such observations will need to be further evaluated through human subjects in the future.

Simulation Software for Assessment of Nonlinear and Adaptive Multivariable Control Algorithms: Glucose - Insulin Dynamics in Type 1 Diabetes

A simulator for testing automatic control algorithms for nonlinear systems with time-varying parameters, variable time delays, and uncertainties is developed. It is based on simulation of virtual patients with Type 1 diabetes (T1D). Nonlinear models are developed to describe glucose concentration (GC) variations based on user-defined scenarios for meal consumption, insulin administration, and physical activity. They compute GC values and physiological variables, such as heart rate, skin temperature, accelerometer, and energy expenditure, that are indicative of physical activities affecting GC dynamics. This is the first simulator designed for assessment of multivariable controllers that consider supplemental physiological variables in addition to GC measurements to improve glycemic control. Virtual patients are generated from distributions of identified model parameters using clinical data. The simulator will enable testing and evaluation of new control algorithms proposed for automated insulin delivery as well as various control algorithms for nonlinear systems with uncertainties, time-varying parameters and delays.

Adaptive Control of an Artificial Pancreas Using Model Identification, Adaptive Postprandial Insulin Delivery, and Heart Rate and Accelerometry as Control Inputs

BACKGROUND

People with type 1 diabetes (T1D) have varying sensitivities to insulin and also varying responses to meals and exercise. We introduce a new adaptive run-to-run model predictive control (MPC) algorithm that can be used to help people with T1D better manage their glucose levels using an artificial pancreas (AP). The algorithm adapts to individuals' different insulin sensitivities, glycemic response to meals, and adjustment during exercise as a continuous input during free-living conditions.

METHODS

A new insulin sensitivity adaptation (ISA) algorithm is presented that updates each patient's insulin sensitivity during nonmeal periods to reduce the error between the actual glucose levels and the process model. We further demonstrate how an adaptive learning postprandial hypoglycemia prevention algorithm (ALPHA) presented in the previous work can complement the ISA algorithm, and the algorithm can adapt in several days. We further show that if physical activity is incorporated as a continuous input (heart rate and accelerometry), performance is improved. The contribution of this work is the description of the ISA algorithm and the evaluation of how ISA, ALPHA, and incorporation of exercise metrics as a continuous input can impact glycemic control.

RESULTS

Incorporating ALPHA, ISA, and physical activity into the MPC improved glycemic outcome measures. The adaptive learning postprandial hypoglycemia prevention algorithm combined with ISA significantly reduced time spent in hypoglycemia by 71.7% and the total number of rescue carbs by 67.8% to 0.37% events/day/patient. Insulin sensitivity adaptation significantly reduced model-actual mismatch by 12.2% compared to an AP without ISA. Incorporating physical activity as a continuous input modestly improved time in the range 70 to 180 mg/dL during high physical activity days from 84.4% to 84.9% and reduced the percentage time in hypoglycemia by 23.8% from 2.1% to 1.6%.

CONCLUSION

Adapting postprandial insulin delivery, insulin sensitivity, and adapting to physical exercise in an MPC-based AP systems can improve glycemic outcomes.

Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach

Anemia management with erythropoiesis stimulating agents is a challenging task in hemodialysis patients since their response to treatment varies highly. In general, it is difficult to achieve and maintain the predefined hemoglobin (Hgb) target levels in clinical practice. The aim of this study is to develop a fully personalizable controller scheme to stabilize Hgb levels within a narrow target window while keeping drug doses low to mitigate side effects. First in-silico results of this framework are presented in this paper. Based on a model of erythropoiesis we formulate a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. Previous to this work, model parameters were estimated for individual patients using clinical data. The optimal control problem is formulated for a continuous drug administration. This is currently a hypothetical form of drug administration for EPO as it would require a programmable EPO pump similar to insulin pumps used to treat patients with diabetes mellitus. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. An appropriate control is feasible in the tested patients under the assumption that the controlled quantity is measured regularly and that continuous EPO administration is adjusted on a daily, weekly or monthly basis. Further, the controller satisfactorily handles the following challenging problems in simulations: bleedings, missed administrations and dosing errors.

Closed-Loop Control with Unannounced Exercise for Adults with Type 1 Diabetes using the Ensemble Model Predictive Control

This paper presents an individualized Ensemble Model Predictive Control (EnMPC) algorithm for blood glucose (BG) stabilization and hypoglycemia prevention in people with type 1 diabetes (T1D) who exercise regularly. The EnMPC formulation can be regarded as a simplified multi-stage MPC allowing for the consideration of N _en scenarios gathered from the patient's recent behavior. The patient's physical activity behavior is characterized by an exercise-specific input signal derived from the deconvolution of the patient's continuous glucose monitor (CGM), accounting for known inputs such as meal, and insulin pump records. The EnMPC controller was tested in a cohort of in silico patients with representative inter-subject and intra-subject variability from the FDA-accepted UVA/Padova simulation platform. Results show a significant improvement on hypoglycemia prevention after 30 min of mild to moderate exercise in comparison to a similarly tuned baseline controller (rMPC); with a reduction in hypoglycemia occurrences (< 70 mg/dL), from 3.08% ± 3.55 with rMPC to 0.78% ± 2.04 with EnMPC (P < 0.05).

Robust multi-objective blood glucose control in Type-1 diabetic patient

In this study, an automatic robust multi‐objective controller has been proposed for blood glucose (BG) regulation in Type‐1 Diabetic Mellitus (T1DM) patient through subcutaneous route. The main objective of this work is to control the BG level in T1DM patient in the presence of unannounced meal disturbances and other external noises with a minimum amount of insulin infusion rate. The multi‐objective output‐feedback controller with H_∞, H₂ and pole‐placement constraints has been designed using linear matrix inequality technique. The designed controller for subcutaneous insulin delivery was tested on in silico adult and adolescent subjects of UVa/Padova T1DM metabolic simulator. The experimental results show that the closed‐loop system tracks the reference BG level very well and does not show any hypoglycaemia effect even during the long gap of a meal at night both for in silico adults and adolescent. In the presence of 50 gm meal disturbance, average adult experience normoglycaemia 92% of the total simulation time and hypoglycaemia 0% of total simulation time. The robustness of the controller has been tested in the presence of irregular meals and insulin pump noise and error. The controller yielded robust performance with a lesser amount of insulin infusion rate than the other designed controllers reported earlier.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Model individualization for artificial pancreas

BACKGROUND AND OBJECTIVE

The inter-subject variability characterizing the patients affected by type 1 diabetes mellitus makes automatic blood glucose control very challenging. Different patients have different insulin responses, and a control law based on a non-individualized model could be ineffective. The definition of an individualized control law in the context of artificial pancreas is currently an open research topic. In this work we consider two novel identification approaches that can be used for individualizing linear glucose-insulin models to a specific patient.

METHODS

The first approach belongs to the class of black-box identification and is based on a novel kernel-based nonparametric approach, whereas the second is a gray-box identification technique which relies on a constrained optimization and requires to postulate a model structure as prior knowledge. The latter is derived from the linearization of the average nonlinear adult virtual patient of the UVA/Padova simulator. Model identification and validation are based on in silico data collected during simulations of clinical protocols designed to produce a sufficient signal excitation without compromising patient safety. The identified models are evaluated in terms of prediction performance by means of the coefficient of determination, fit, positive and negative max errors, and root mean square error.

RESULTS

Both identification approaches were used to identify a linear individualized glucose-insulin model for each adult virtual patient of the UVA/Padova simulator. The resulting model simulation performance is significantly improved with respect to the performance achieved by a linear average model.

CONCLUSIONS

The approaches proposed in this work have shown a good potential to identify glucose-insulin models for designing individualized control laws for artificial pancreas.

Design of an online-tuned model based compound controller for a fully automated artificial pancreas

This paper deals with the development of a control algorithm that can predict optimal insulin doses without patients' intervention in fully automated artificial pancreas system. An online-tuned model based compound controller comprising an online-tuned internal model control (IMC) algorithm and an enhanced IMC (eIMC) algorithm along with a meal detection module is proposed. Volterra models, used to develop IMC and eIMC algorithms, are developed online using recursive least squares (RLS) filter. The time domain kernels, computed online using RLS filter, are converted into frequency domain to obtain Volterra transfer function (VTF). VTFs are used to develop both IMC and eIMC algorithms. The compound controller is designed in such a way that eIMC predicts insulin doses when the glucose rate increase detector of meal detection module is positive, otherwise conventional IMC takes the control action. Experimental results show that the compound controller performs robustly in the presence of higher and irregular amounts of meal disturbances at random times, very high actuator and sensor noises and also with the variation in insulin sensitivity. The combination of compound control strategy and meal detection module compensates the shortcomings of both slow subcutaneous insulin action that causes postprandial hyperglycemia, and delayed peak of action that causes hypoglycaemia. Graphical Abstract A fully-automated artificial pancreas system containing glucose sensor, insulin pump and control algorithm. Block diagram showing the control algorithm i.e., online-tuned compound IMC comprising enhanced IMC, conventional IMC and meal detection module, developed in the present work.

Blood Glucose Regulation for Post-Operative Patients with Diabetics and Hypertension Continuum: A Cascade Control-Based Approach

Management of glycemic level in post-operative condition is critical for hypertensive patients and the post-operative stress may results in hyperglycemia, hyper insulin and osmotic diuresis. Recent medical research shows that diabetic and hypertension hands together in a significant overlap in its etiology and its disease mechanism. It is clear that there is a call for monitoring in the parameter and controlling the glucose level particularly in the presence of hypertension. This paper proposes the novel complex (cascade) control system to control the insulin infusion level particularly in the presence of hypertension. Based on the requirements the structure has been designed and the simulation results indicates that the proposed control strategy shows better results and may achieve potentially better glycemic control to the hypersensitive diabetic patients.

Mathematical modeling of septic shock based on clinical data

BACKGROUND

Mathematical models of diseases may provide a unified approach for establishing effective treatment strategies based on fundamental pathophysiology. However, models that are useful for clinical practice must overcome the massive complexity of human physiology and the diversity of patients' environmental conditions. With the aim of modeling a complex disease, we choose sepsis, which is highly complex, life-threatening systemic disease with high mortality. In particular, we focused on septic shock, a subset of sepsis in which underlying circulatory and cellular/metabolic abnormalities are profound enough to substantially increase mortality. Our model includes cardiovascular, immune, nervous system models and a pharmacological model as submodels and integrates them to create a sepsis model based on pathological facts.

RESULTS

Model validation was done in two steps. First, we established a model for a standard patient in order to confirm the validity of our approach in general aspects. For this, we checked the correspondence between the severity of infection defined in terms of pathogen growth rate and the ease of recovery defined in terms of the intensity of treatment required for recovery. The simulations for a standard patient showed good correspondence. We then applied the same simulations to a patient with heart failure as an underlying disease. The model showed that spontaneous recovery would not occur without treatment, even for a very mild infection. This is consistent with clinical experience. We next validated the model using clinical data of three sepsis patients. The model parameters were tuned for these patients based on the model for the standard patient used in the first part of the validation. In these cases, the simulations agreed well with clinical data. In fact, only a handful parameters need to be tuned for the simulations to match with the data.

CONCLUSIONS

We have constructed a model of septic shock and have shown that it can reproduce well the time courses of treatment and disease progression. Tuning of model parameters for each patient could be easily done. This study demonstrates the feasibility of disease models, suggesting the possibility of clinical use in the prediction of disease progression, decisions on the timing of drug dosages, and the estimation of time of infection.

Automated closed-loop control of diabetes: the artificial pancreas

The incidence of Diabetes Mellitus is on the rise worldwide, which exerts enormous health toll on the population and enormous pressure on the healthcare systems. Now, almost hundred years after the discovery of insulin in 1921, the optimization problem of diabetes is well formulated as maintenance of strict glycemic control without increasing the risk for hypoglycemia. External insulin administration is mandatory for people with type 1 diabetes; various medications, as well as basal and prandial insulin, are included in the daily treatment of type 2 diabetes. This review follows the development of the Diabetes Technology field which, since the 1970s, progressed remarkably through continuous subcutaneous insulin infusion (CSII), mathematical models and computer simulation of the human metabolic system, real-time continuous glucose monitoring (CGM), and control algorithms driving closed-loop control systems known as the "artificial pancreas" (AP). All of these developments included significant engineering advances and substantial bioelectronics progress in the sensing of blood glucose levels, insulin delivery, and control design. The key technologies that enabled contemporary AP systems are CSII and CGM, both of which became available and sufficiently portable in the beginning of this century. This powered the quest for wearable home-use AP, which is now under way with prototypes tested in outpatient studies during the past 6 years. Pivotal trials of new AP technologies are ongoing, and the first hybrid closed-loop system has been approved by the FDA for clinical use. Thus, the closed-loop AP is well on its way to become the digital-age treatment of diabetes.

Postprandial fuzzy adaptive strategy for a hybrid proportional derivative controller for the artificial pancreas

This paper presents a support fuzzy adaptive system for a hybrid proportional derivative controller that will refine its parameters during postprandial periods to enhance performance. Even though glucose controllers have improved over the last decade, tuning them and keeping them tuned are still major challenges. Changes in a patient's lifestyle, stress, exercise, or other activities may modify their blood glucose system, making it necessary to retune or change the insulin dosing algorithm. This paper presents a strategy to adjust the parameters of a proportional derivative controller using the so-called safety auxiliary feedback element loop for type 1 diabetic patients. The main parameters, such as the insulin on board limit and proportional gain are tuned using postprandial performance indexes and the information given by the controller itself. The adaptive and robust performance of the control algorithm was assessed "in silico" on a cohort of virtual patients under challenging realistic scenarios considering mixed meals, circadian variations, time-varying uncertainties, sensor errors, and other disturbances. The results showed that an adaptive strategy can significantly improve the performance of postprandial glucose control, individualizing the tuning by directly taking into account the intra-patient variability of type 1 patients. Graphical Abstract title: Postprandial glycaemia improvement via fuzzy adaptive control A fuzzy inference engine was implemented within a clinically tested artificial pancreas control system. The aim of the fuzzy system was to adapt controller parameters to improve postprandial blood glucose control while ensuring safety. Results show a significant improvement over time of the postprandial glucose response due to the adaptation, thus demonstrating the usefulness of the fuzzy adaptive system.

Identifiability Analysis of Three Control-Oriented Models for Use in Artificial Pancreas Systems

OBJECTIVE

Our aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).

METHODS

Structural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.

RESULTS

A reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.

CONCLUSION

This study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

A mathematical model of type 1 diabetes involving leptin effects on glucose metabolism

Leptin, a hormone released from fat cells in adipose tissues, was recently found to be capable of normalizing glucose metabolism in animals. Clinical data on patients with lipodystrophy indicates that leptin may have a positive effect on glucose metabolism in individuals with diabetes. There are growing expectations that leptin can improve the current insulin treatment for patients with type 1 diabetes. We investigated this possibility through in silico experiments based on a mathematical model of diabetes, which is currently the only mode of research that eliminates human risk. A model of the brain-centered glucoregulatory system, in which leptin plays a central role, was constructed and integrated within a conventional model of insulin/glucose dynamics. The model has been validated using experimental data from animal studies. The in silico combination experiments showed excellent therapeutic performance over insulin monotherapy.

Neural network-based model predictive control for type 1 diabetic rats on artificial pancreas system

Artificial pancreas system (APS) is a viable option to treat diabetic patients. Researchers, however, have not conclusively determined the best control method for APS. Due to intra-/inter-variability of insulin absorption and action, an individualized algorithm is required to control blood glucose level (BGL) for each patient. To this end, we developed model predictive control (MPC) based on artificial neural networks (ANNs), which combines ANN for BGL prediction based on inputs and MPC for BGL control based on the ANN (NN-MPC). First, we developed a mathematical model for diabetic rats, which was used to identify individual virtual subjects by fitting to empirical data collected through an APS, including BGL data, insulin injection, and food intake. Then, the virtual subjects were used to generate datasets for training ANNs. The NN-MPC determines control actions (insulin injection) based on BGL predicted by the ANN. To evaluate the NN-MPC, we conducted experiments using four virtual subjects under three different scenarios. Overall, the NN-MPC maintained BGL within the normal range about 90% of the time with a mean absolute deviation of 4.7 mg/dl from a desired BGL. Our findings suggest that the NN-MPC can provide subject-specific BGL control in conjunction with a closed-loop APS. Graphical abstract ᅟ.

Multi-level Supervision and Modification of Artificial Pancreas Control System

Artificial pancreas (AP) systems provide automated regulation of blood glucose concentration (BGC) for people with type 1 diabetes (T1D). An AP includes three components: a continuous glucose monitoring (CGM) sensor, a controller calculating insulin infusion rate based on the CGM signal, and a pump delivering the insulin amount calculated by the controller to the patient. The performance of the AP system depends on successful operation of these three components. Many APs use model predictive controllers that rely on models to predict BGC and to calculate the optimal insulin infusion rate. The performance of model-based controllers depends on the accuracy of the models that is affected by large dynamic changes in glucose-insulin metabolism or equipment performance that may move the operating conditions away from those used in developing the models and designing the control system. Sensor errors and missing signals will cause calculation of erroneous insulin infusion rates. And the performance of the controller may vary at each sampling step and each period (meal, exercise, and sleep), and from day to day. Here we describe a multi-level supervision and controller modification (ML-SCM) module is developed to supervise the performance of the AP system and retune the controller. It supervises AP performance in 3 time windows: sample level, period level, and day level. At sample level, an online controller performance assessment sub-module will generate controller performance indexes to evaluate various components of the AP system and conservatively modify the controller. A sensor error detection and signal reconciliation module will detect sensor error and reconcile the CGM sensor signal at each sample. At period level, the controller performance is evaluated with information collected during a certain time period and the controller is tuned more aggressively. At the day level, the daily CGM ranges are further analyzed to determine the adjustable range of controller parameters used for sample level and period level. Thirty subjects in the UVa/Padova metabolic simulator were used to evaluate the performance of the ML-SCM module and one clinical experiment is used to illustrate its performance in a clinical environment. The results indicate that the AP system with an ML-SCM module has a safer range of glucose concentration distribution and more appropriate insulin infusion rate suggestions than an AP system without the ML-SCM module.

Stochastic Seasonal Models for Glucose Prediction in the Artificial Pancreas

BACKGROUND

Linear empirical dynamic models have been widely used for glucose prediction. The extension of the concept of seasonality, characteristic of other domains, is explored here for the improvement of prediction accuracy.

METHODS

Twenty time series of 8-hour postprandial periods (PP) for a same 60g-carbohydrate meal were collected from a closed-loop controller validation study. A single concatenated time series was produced representing a collection of data from similar scenarios, resulting in seasonality. Variability in the resulting time series was representative of worst-case intrasubject variability. Following a leave-one-out cross-validation, seasonal and nonseasonal autoregressive integrated moving average models (SARIMA and ARIMA) were built to analyze the effect of seasonality in the model prediction accuracy. Further improvement achieved from the inclusion of insulin infusion rate as exogenous variable was also analyzed. Prediction horizons (PHs) from 30 to 300 min were considered.

RESULTS

SARIMA outperformed ARIMA revealing a significant role of seasonality. For a 5-h PH, average MAPE was reduced in 26.62%. Considering individual runs, the improvement ranged from 6.3% to 54.52%. In the best-performing case this reduction amounted to 29.45%. The benefit of seasonality was consistent among different PHs, although lower PHs benefited more, with MAPE reduction over 50% for PHs of 60 and 120 minutes, and over 40% for 180 min. Consideration of insulin infusion rate into the seasonal model further improved performance, with a 61.89% reduction in MAPE for 30-min PH and reductions over 20% for PHs over 180 min.

CONCLUSIONS

Seasonality improved model accuracy allowing for the extension of the PH significantly.

A self-assessment predictive model for type 2 diabetes or impaired fasting glycaemia derived from a population-based survey

AIMS

There is no cure for diabetes and its prevention is interesting for both people and health policy makers. The aim of this study was to construct a simple scoring system to predict diabetes and suggest a self assessment predictive model for type 2 diabetes in Iran.

METHODS

This study was a part of a comprehensive population based survey performed in Ilam province during 2011-2012, including 2158 cases≥25years. All demographic and laboratory results were entered into the prepared sheets and were analysed using SPSS 16. By identification of relative risks of diabetes and IFG, a predictive model was constructed and proposed for these abnormalities.

RESULTS

Totally, 2158 people comprising 72% female, 60% from urban regions, mean age of 45.5±14years were investigated and the average height, weight, FBS and waist of participants were as follows respectively: 164±8.9cm, 68.4±12.3kg, 5.7±2.8mmol/l (102.6±49.9mg/dl) and 82.3±14.3cm. The prevalence of IFG, diabetes and hyperglycaemia among all participants were 7.8%, 11.8% and 19.6% respectively. Regression analysis revealed familial history of diabetes, place of life, age, hypertension, daily exercise, marital status, gender, waist size, smoking, and BMI as the most relevant risk factors for diabetes and hyperglycemia.

CONCLUSION

A self-assessment predictive model was constructed for general population living in the west of Iran. This is the first self-assessment predictive model for diabetes in Iran.

Manual Closed-Loop Insulin Delivery Using a Saddle Point Model Predictive Control Algorithm: Results of a Crossover Randomized Overnight Study

BACKGROUND

The purpose was to assess the efficacy of a new closed-loop algorithm (Saddle Point Model Predictive Control, SP-MPC) in achieving nocturnal normoglycemia while reducing the risk of hypoglycemia in patients with type 1 diabetes.

METHOD

In this randomized crossover study, 10 adult patients (mean hemoglobin A1c 7.35 ± 1.04%) were assigned to be treated overnight by open loop using sensor-augmented pump therapy (open-loop SAP) or manual closed-loop delivery. During closed loop, insulin doses were calculated using the SP-MPC algorithm and administered as manual boluses every 15 minutes from 9:00 pm to 8:00 am. Patients consumed a self-selected meal (65-125 g of carbohydrates) at 7:00 pm accompanied by their usual prandial bolus. Blood glucose was measured every 30 minutes. The primary endpoints were the time spent in target (70-145 mg/dl) and time spent below 70 mg/dl from 11:00 pm to 8:00 am.

RESULTS

Time spent in target did not differ between closed-loop and open-loop SAP. The number of hypoglycemic events (<70 mg/dl) was reduced 2.8-fold in closed loop (n = 5, median = 0/patient/hour; interquartile range: 0-0.11) as compared to open-loop SAP (n = 14, median = 0.22/patient/hour, 0.02-0.22) ( P = .02). The area under the curve for sensor glucose values >145 mg/dl was significantly lower during closed-loop than during open-loop SAP ( P = .03) as well as HBGI ( P = .02).

CONCLUSIONS

This pilot study suggests that the use of the SP-MPC algorithm may improve mean overnight glucose control and reduce the number of hypoglycemic events as compared to SAP therapy.

Design of a dual-hormone model predictive control for artificial pancreas with exercise model

The Artificial Pancreas (AP) is a new technology for helping people with type 1 diabetes to better control their glucose levels through automated delivery of insulin and optionally glucagon in response to sensed glucose levels. In a dual hormone AP, insulin and glucagon are delivered automatically to the body based on glucose sensor measurements using a control algorithm that calculates the amount of hormones to be infused. A dual-hormone MPC may deliver insulin continuously; however, it must avoid continuous delivery of glucagon because nausea can occur from too much glucagon. In this paper, we propose a novel dual-hormone (DH) switching model predictive control and compare it with a single-hormone (SH) MPC. We extended both MPCs by integrating an exercise model and compared performance with and without the exercise model included. Results were obtained on a virtual patient population undergoing a simulated exercise event using a mathematical glucoregulatory model that includes exercise. Time spent in hypoglycemia is significantly less with the DH-MPC than the SH-MPC (p=0.0022). Additionally, including the exercise model in the DH-MPC can help prevent hypoglycemia (p <; 0.001).

Personalization of a compartmental physiological model for an artificial pancreas through integration of patient's state estimation

Artificial Pancreas (AP) are developed for patients with Type 1 diabetes. This medical device system consists in the association of a subcutaneous continuous glucose monitor (CGM) providing a proxy of the patient's glycaemia and a control algorithm offering the real-time modification of the insulin delivery with an automatic command of the subcutaneous insulin pump. The most complex algorithms are based on a compartmental model of the glucoregulatory system of the patient coupled to an approach of MPC (Model-Predictive-Control) for the command. The automatic and unsupervised control of insulin regulation constitutes a major challenge in AP projects. A given model with its parameterization on the shelf will not directly represent the patient's data behavior and the personalization of the model is a prerequisite before using it in a MPC. The present paper focuses on the personalization of a compartmental showing a method where taking into account the estimation of the patient's state in addition to the parameter estimation improves the results in terms of mean quadratic error.

Model Free iPID Control for Glycemia Regulation of Type-1 Diabetes

OBJECTIVE

The objective is to design a fully automated glycemia controller of Type-1 Diabetes (T1D) in both fasting and postprandial phases on a large number of virtual patients.

METHODS

A model-free intelligent proportional-integral-derivative (iPID) is used to infuse insulin. The feasibility of iPID is tested in silico on two simulators with and without measurement noise. The first simulator is derived from a long-term linear time-invariant model. The controller is also validated on the UVa/Padova metabolic simulator on 10 adults under 25 runs/subject for noise robustness test.

RESULTS

It was shown that without measurement noise, iPID mimicked the normal pancreatic secretion with a relatively fast reaction to meals as compared to a standard PID. With the UVa/Padova simulator, the robustness against CGM noise was tested. A higher percentage of time in target was obtained with iPID as compared to standard PID with reduced time spent in hyperglycemia.

CONCLUSION

Two different T1D simulators tests showed that iPID detects meals and reacts faster to meal perturbations as compared to a classic PID. The intelligent part turns the controller to be more aggressive immediately after meals without neglecting safety. Further research is suggested to improve the computation of the intelligent part of iPID for such systems under actuator constraints. Any improvement can impact the overall performance of the model-free controller.

SIGNIFICANCE

The simple structure iPID is a step for PID-like controllers since it combines the classic PID nice properties with new adaptive features.

An Enhanced Model Predictive Control for the Artificial Pancreas Using a Confidence Index Based on Residual Analysis of Past Predictions

BACKGROUND

Model predictive control (MPC) performance depends on the accuracy of the prediction model implemented by the controller. Complex physiology and modeling limitations often prevent the ability to provide long and accurate glucose predictions, which results in the need to account for prediction errors.

METHOD

Optimal insulin dosage by Zone-MPC is calculated by solving an optimization problem in which a scalar index is minimized by penalizing relative input deviations and glucose predictions out of the reference zone. The controller's tuning parameters are the penalties on the input variable (insulin). Positive and negative relative inputs are penalized differently. A dynamic adaptation of the tuning parameters based on the accuracy of the model in recent history is implemented in this article and compared in silico to aggressive and conservative tunings of the same controller structure.

RESULTS

Similar average glucose and time in the safe glucose range (70-180 mg/dL) are achieved for the adaptive design and traditional controller configurations. However, percentage time under 70 mg/dL is significantly reduced, both for announced meals using bolus compensation and unannounced meals with a meal detection algorithm triggered bolus. No differences in the average insulin delivered were observed between the adaptive design and the conservative or aggressive tuning for the bolus strategy, and the adaptive controller delivered less insulin in the other scenario considered.

CONCLUSIONS

The adaptive strategy provides safe and effective glucose management as well as significant reduction of hypoglycemia events. No abnormal insulin delivery profiles were observed upon the application of the adaptive strategy.

Physiology-Invariant Meal Detection for Type 1 Diabetes

BACKGROUND

Fully automated artificial pancreas systems require meal detectors to supplement blood glucose level regulation, where false meal detections can cause unnecessary insulin delivery with potentially fatal consequences, and missed detections may cause the patient to experience extreme hyperglycemia. Most existing meal detectors monitor various measures of glucose rate-of-change to detect meals where varying physiology and meal content complicate balancing detector sensitivity versus specificity.

METHODS

We developed a novel meal detector based on a minimal glucose-insulin metabolism model and show that the detector is, by design, invariant to patient-specific physiological parameters in the minimal model. Our physiological parameter-invariant (PAIN) detector achieves a near-constant false alarm rate across all individuals and is evaluated against three other major existing meal detectors on a clinical type 1 diabetes data set.

RESULTS

In the clinical evaluation, the PAIN-based detector achieves an 86.9% sensitivity for an average false alarm rate of two alarms per day. In addition, for all false alarm rates, the PAIN-based detector performance is significantly better than three other existing meal detectors. In addition, the evaluation results show that the PAIN-based detector uniquely (as compared with the other meal detectors) has low variance in detection and false alarm rates across all patients, without patient-specific personalization.

CONCLUSIONS

The PAIN-based meal detector has demonstrated better detection performance than existing meal detectors, and it has the unique strength of achieving a consistent performance across a population with varying physiology without any individual-level parameter tuning or training.