A new general glucose homeostatic model using a proportional-integral-derivative controller

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.

Dynamical compensation and structural identifiability of biological models: Analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. However, the original definition of dynamical compensation amounts to lack of structural identifiability. This is relevant if model parameters need to be estimated, as is often the case in biological modelling. Care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability.

A robust behaviour is a desirable feature in many biological systems. The study of mechanisms capable of maintaining the transient response unchanged despite environmental disturbances has recently motivated the introduction of a new concept: Dynamical Compensation (DC). However, the original definition of DC with respect to a parameter amounts to structural unidentifiability of that parameter, which means that it cannot be estimated by measuring the model output. Since most biological models have unknown parameters that need to be estimated, DC can be considered a negative property for the purpose of model identification. In this paper we reconcile these two conflicting views by proposing a new definition of DC that captures its intended biological meaning (i.e. robustness, which should be a systemic property, intrinsic to the dynamics) while making it distinct from structural unidentifiability (which is a modelling property that depends on decisions made by the modeller, such as the choice of model outputs or unknown parameters, and on experimental constraints). Our definition enables a model to have DC with respect to a structurally identifiable parameter, thus increasing the applicability of the concept.

Choosing an optimal input for an intravenous glucose tolerance test to aid parameter identification

OBJECTIVE

The minimal model is used to estimate insulin sensitivity in patients with diabetes, following an intravenous glucose tolerance test (IVGTT). Issues have been reported regarding parameter estimation, including correlation between insulin sensitivity and action parameters. The objective was to reduce these issues, by modifying the input of glucose in the test.

METHODS

Data were available for 24 volunteers following an IVGTT and glucose clamp test. Correlation between parameters was explored using likelihood heatmaps. An integrated glucose-insulin model was used to simulate glucose and insulin concentrations following new glucose inputs. The improved input for the test was selected by finding the minimum inverse of the determinant of the Fisher information matrix.

KEY FINDINGS

When the minimal model was fitted to the IVGTT data, there was clear correlation between the insulin parameters. With the glucose clamp, all parameters were correlated and badly estimated. The modified input, a bolus dose followed by constant infusion, resulted in improvement in parameter estimation and reduction in parameter correlation.

CONCLUSIONS

It is possible to reduce the issues with parameter estimation in the minimal model by modifying the glucose input, leading to a simplified test deign and a reduction in the total amount of glucose infused.

Modeling of free fatty acid dynamics: insulin and nicotinic acid resistance under acute and chronic treatments

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc–FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague–Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{\text{max}}$$\end{document}Imax model. Insulin was incorporated in parallel with NiAc as the main endogenous co-variate of FFA dynamics. The model captured profound insulin resistance and complete drug resistance in obese rats. The efficacy of NiAc as an inhibitor of FFA release went from 1 to approximately 0 during sustained exposure in obese rats. The potency of NiAc as an inhibitor of insulin and of FFA release was estimated to be 0.338 and 0.436 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upmu {\text{M}}}$$\end{document}μM, respectively, in obese rats. A range of dosing regimens was analyzed and predictions made for optimizing NiAc delivery to minimize FFA exposure. Given the exposure levels of the experiments, the importance of washout periods in-between NiAc infusions was illustrated. The washout periods should be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}∼2 h longer than the infusions in order to optimize 24 h lowering of FFA in rats. However, the predicted concentration-response relationships suggests that higher AUC reductions might be attained at lower NiAc exposures.

A data driven nonlinear stochastic model for blood glucose dynamics

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.

A Unifying Organ Model of Pancreatic Insulin Secretion

The secretion of insulin by the pancreas has been the object of much attention over the past several decades. Insulin is known to be secreted by pancreatic β-cells in response to hyperglycemia: its blood concentrations however exhibit both high-frequency (period approx. 10 minutes) and low-frequency oscillations (period approx. 1.5 hours). Furthermore, characteristic insulin secretory response to challenge maneuvers have been described, such as frequency entrainment upon sinusoidal glycemic stimulation; substantial insulin peaks following minimal glucose administration; progressively strengthened insulin secretion response after repeated administration of the same amount of glucose; insulin and glucose characteristic curves after Intra-Venous administration of glucose boli in healthy and pre-diabetic subjects as well as in Type 2 Diabetes Mellitus. Previous modeling of β-cell physiology has been mainly directed to the intracellular chain of events giving rise to single-cell or cell-cluster hormone release oscillations, but the large size, long period and complex morphology of the diverse responses to whole-body glucose stimuli has not yet been coherently explained. Starting with the seminal work of Grodsky it was hypothesized that the population of pancreatic β-cells, possibly functionally aggregated in islets of Langerhans, could be viewed as a set of independent, similar, but not identical controllers (firing units) with distributed functional parameters. The present work shows how a single model based on a population of independent islet controllers can reproduce very closely a diverse array of actually observed experimental results, with the same set of working parameters. The model's success in reproducing a diverse array of experiments implies that, in order to understand the macroscopic behaviour of the endocrine pancreas in regulating glycemia, there is no need to hypothesize intrapancreatic pacemakers, influences between different islets of Langerhans, glycolitic-induced oscillations or β-cell sensitivity to the rate of change of glycemia.

An Improved PID Algorithm Based on Insulin-on-Board Estimate for Blood Glucose Control with Type 1 Diabetes

Automated closed-loop insulin infusion therapy has been studied for many years. In closed-loop system, the control algorithm is the key technique of precise insulin infusion. The control algorithm needs to be designed and validated. In this paper, an improved PID algorithm based on insulin-on-board estimate is proposed and computer simulations are done using a combinational mathematical model of the dynamics of blood glucose-insulin regulation in the blood system. The simulation results demonstrate that the improved PID algorithm can perform well in different carbohydrate ingestion and different insulin sensitivity situations. Compared with the traditional PID algorithm, the control performance is improved obviously and hypoglycemia can be avoided. To verify the effectiveness of the proposed control algorithm, in silico testing is done using the UVa/Padova virtual patient software.

Fabrication of a Flexible Amperometric Glucose Sensor Using Additive Processes

This study details the use of printing and other additive processes to fabricate a novel amperometric glucose sensor. The sensor was fabricated using a Au coated 12.7 μm thick polyimide substrate as a starting material, where micro-contact printing, electrochemical plating, chloridization, electrohydrodynamic jet (e-jet) printing, and spin coating were used to pattern, deposit, chloridize, print, and coat functional materials, respectively. We have found that e-jet printing was effective for the deposition and patterning of glucose oxidase inks with lateral feature sizes between ~5 to 1000 μm in width, and that the glucose oxidase was still active after printing. The thickness of the permselective layer was optimized to obtain a linear response for glucose concentrations up to 32 mM and no response to acetaminophen, a common interfering compound, was observed. The use of such thin polyimide substrates allow wrapping of the sensors around catheters with high radius of curvature ~250 μm, where additive and microfabrication methods may allow significant cost reductions.

Prediction model for glucose metabolism based on lipid metabolism

OBJECTIVES

We developed a robust, long-term clinical prediction model to predict conditions leading to early diabetes using laboratory values other than blood glucose and insulin levels. Our model protects against missing data and noise that occur during long-term analysis.

METHODS

RESULTS of a 75-g oral glucose tolerance test (OGTT) were divided into three groups: diabetes, impaired glucose tolerance (IGT), and normal (n = 114, 235, and 325, respectively). For glucose metabolic and lipid metabolic parameters, near 30-day mean values and 10-year integrated values were compared. The relation between high-density lipoprotein cholesterol (HDL-C) and variations in HbA1c was analyzed in 158 patients. We also constructed a state space model consisting of an observation model (HDL-C and HbA1c) and an internal model (disorders of lipid metabolism and glucose metabolism) and applied this model to 116 cases.

RESULTS

The root mean square error between the observed HbA1c and predicted HbA1c was 0.25.

CONCLUSIONS

In the observation model, HDL-C levels were useful for prediction of increases in HbA1c. Even with numerous missing values over time, as occurs in clinical practice, clinically valid predictions can be made using this state space model.

Automated control of an adaptive bihormonal, dual-sensor artificial pancreas and evaluation during inpatient studies

Automated control of blood glucose in patients with type-1 diabetes has not yet been fully implemented. The aim of this study was to design and clinically evaluate a system that integrates a control algorithm with off-the-shelf subcutaneous sensors and pumps to automate the delivery of the hormones glucagon and insulin in response to continuous glucose sensor measurements. The automated component of the system runs an adaptive proportional derivative control algorithm which determines hormone delivery rates based on the sensed glucose measurements and the meal announcements by the patient. We provide details about the system design and the control algorithm, which incorporates both a fading memory proportional derivative controller (FMPD) and an adaptive system for estimating changing sensitivity to insulin based on a glucoregulatory model of insulin action. For an inpatient study carried out in eight subjects using Dexcom SEVEN PLUS sensors, prestudy HbA1c averaged 7.6, which translates to an estimated average glucose of 171 mg/dL. In contrast, during use of the automated system, after initial stabilization, glucose averaged 145 mg/dL and subjects were kept within the euglycemic range (between 70 and 180 mg/dL) for 73.1% of the time, indicating improved glycemic control. A further study on five additional subjects in which we used a newer and more reliable glucose sensor (Dexcom G4 PLATINUM) and made improvements to the insulin and glucagon pump communication system resulted in elimination of hypoglycemic events. For this G4 study, the system was able to maintain subjects' glucose levels within the near-euglycemic range for 71.6% of the study duration and the mean venous glucose level was 151 mg/dL.

Reducing risk of closed loop control of blood glucose in artificial pancreas using fractional calculus

Healthcare costs in the US are among the highest in the world. Chronic diseases such as diabetes significantly contribute to these extensive costs. Despite technological advances to improve sensing and actuation devices, we still lack a coherent theory that facilitates the design and optimization of efficient and robust medical cyber-physical systems for managing chronic diseases. In this paper, we propose a mathematical model for capturing the complex dynamics of blood glucose time series (e.g., time dependent and fractal behavior) observed in real world measurements via fractional calculus concepts. Building upon our time dependent fractal model, we propose a novel model predictive controller for an artificial pancreas that regulates insulin injection. We verify the accuracy of our controller by comparing it to conventional non-fractal models using real world measurements and show how the nonlinear optimal controller based on fractal calculus concepts is superior to non-fractal controllers in terms of average risk index and prediction accuracy.

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

Continuous glucose monitoring is increasingly used in the management of diabetes. Subcutaneous glucose profiles are characterised by a strong non-stationarity, which limits the application of correlation-spectral analysis. We derived an index of linear predictability by calculating the autocorrelation function of time series increments and applied detrended fluctuation analysis to assess the non-stationarity of the profiles. Time series from volunteers with both type 1 and type 2 diabetes and from control subjects were analysed. The results suggest that in control subjects, blood glucose variation is relatively uncorrelated, and this variation could be modelled as a random walk with no retention of 'memory' of previous values. In diabetes, variation is both greater and smoother, with retention of inter-dependence between neighbouring values. Essential components for adequate longer term prediction were identified via a decomposition of time series into a slow trend and responses to external stimuli. Implications for diabetes management are discussed.

Estimating insulin sensitivity from glucose levels only: Use of a non-linear mixed effects approach and maximum a posteriori (MAP) estimation

Insulin Sensitivity is an important parameter for the management of Diabetes. It can be derived for a particular patient using data derived from some glucose challenge tests using measured glucose and insulin levels at various times. Whilst a useful approach, deriving insulin sensitivities to inform insulin dosing in other settings such as Intensive Care Units can be more challenging - especially as insulin levels have to be assayed in a laboratory, not at the bedside. This paper investigates an approach to measure insulin sensitivity from glucose levels only. Estimates of mean and between individual parameter variances are used to derive conditional estimates of insulin sensitivity. The method is demonstrated to perform reasonably well, with conditional estimates comparing well with estimates derived from insulin data as well.

A novel computerized fading memory algorithm for glycemic control in postoperative surgical patients

BACKGROUND

Hyperglycemia is commonly encountered in critically ill patients and is associated with increased mortality and morbidity. To better control blood glucose levels, we previously developed a new computerized fading memory (FM) algorithm. In this study we evaluated the safety and efficacy of this algorithm in surgical intensive care unit (SICU) patients and compared its performance against the existing insulin-infusion algorithm (named VA algorithm) used in our institution.

METHODS

A computer program was developed to run the FM and VA algorithms. Forty eight patients, who were scheduled to have elective surgery, were randomly assigned to receive insulin infusion on the basis of either the FM or VA algorithm. On SICU admission, an insulin infusion was either continued from the operating room or initiated when the glucose level exceeded the target level of 140 mg/dL. Hourly blood glucose measurements were performed and entered into the computer program, which then prescribed the next insulin dose. The randomly assigned algorithm was applied for the first 8 hours of SICU stay, after which the VA algorithm was used. The number of episodes of hypoglycemia (glucose <60 mg/dL) and excessive hyperglycemia (>300 mg/dL) were noted. Additionally, the time required to bring the glucose level within target range (140 ± 20 mg/dL), the number of glucose measurements within the target range, glycemic variability, and insulin usage were analyzed and compared between the 2 algorithms.

RESULTS

Patient demographics and starting glucose levels were similar between the groups. With the existing VA algorithm, 1 episode of severe hypoglycemia was observed. Three patients did not reach the target range within 8 hours. With the FM algorithm no hypoglycemia occurred, and all patients achieved the target range within 8 hours. Glycemic variability measured by the SD of mean glucose levels was 28% (95% confidence interval, 14% to 39%) lower for the FM algorithm (P < 0.001). The FM algorithm used 1.1 U/h less insulin than did the VA algorithm (P = 0.043).

CONCLUSION

The novel computerized FM algorithm for glycemic control, which emulates physiologic biphasic insulin secretion, managed glucose better than the existing algorithm without any episodes of hypoglycemia. The FM algorithm had less glycemic variability and used less insulin when compared to the conventional clinical algorithm.

Wherefore art thou, homeo(stasis)? Functional diversity in homeostatic synaptic plasticity

Homeostatic plasticity has emerged as a fundamental regulatory principle that strives to maintain neuronal activity within optimal ranges by altering diverse aspects of neuronal function. Adaptation to network activity is often viewed as an essential negative feedback restraint that prevents runaway excitation or inhibition. However, the precise importance of these homeostatic functions is often theoretical rather than empirically derived. Moreover, a remarkable multiplicity of homeostatic adaptations has been observed. To clarify these issues, it may prove useful to ask: why do homeostatic mechanisms exist, what advantages do these adaptive responses confer on a given cell population, and why are there so many seemingly divergent effects? Here, we approach these questions by applying the principles of control theory to homeostatic synaptic plasticity of mammalian neurons and suggest that the varied responses observed may represent distinct functional classes of control mechanisms directed toward disparate physiological goals.