A data driven nonlinear stochastic model for blood glucose dynamics

A simple modeling framework for prediction in the human glucose-insulin system

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

A Glucose-Only Model to Extract Physiological Information from Postprandial Glucose Profiles in Subjects with Normal Glucose Tolerance

BACKGROUND

Current mathematical models of postprandial glucose metabolism in people with normal and impaired glucose tolerance rely on insulin measurements and are therefore not applicable in clinical practice. This research aims to develop a model that only requires glucose data for parameter estimation while also providing useful information on insulin sensitivity, insulin dynamics and the meal-related glucose appearance (GA).

METHODS

The proposed glucose-only model (GOM) is based on the oral minimal model (OMM) of glucose dynamics and substitutes the insulin dynamics with a novel function dependant on glucose levels and GA. A Bayesian method and glucose data from 22 subjects with normal glucose tolerance are utilised for parameter estimation. To validate the results of the GOM, a comparison to the results of the OMM, obtained by using glucose and insulin data from the same subjects is carried out.

RESULTS

The proposed GOM describes the glucose dynamics with comparable precision to the OMM with an RMSE of 5.1 ± 2.3 mg/dL and 5.3 ± 2.4 mg/dL, respectively and contains a parameter that is significantly correlated to the insulin sensitivity estimated by the OMM (r = 0.7) Furthermore, the dynamic properties of the time profiles of GA and insulin dynamics inferred by the GOM show high similarity to the corresponding results of the OMM.

CONCLUSIONS

The proposed GOM can be used to extract useful physiological information on glucose metabolism in subjects with normal glucose tolerance. The model can be further developed for clinical applications to patients with impaired glucose tolerance under the use of continuous glucose monitoring data.

Bayesian analysis of Glucose dynamics during the Oral Glucose Tolerance Test (OGTT)

This paper proposes a model that considers the action and timing of insulin and glucagon in glucose homeostasis after an oral stimulus. We use the Bayesian paradigm to infer kinetic rates, namely insulin and glucagon secretion, gastrointestinal emptying, and basal glucose concentration in blood. We identify two insulin scores related to glucose concentration in both blood and the gastrointestinal tract. The scores allow us to suggest a classification for individuals with impaired insulin sensitivity.

Bayesian parameter estimation in the oral minimal model of glucose dynamics from non-fasting conditions using a new function of glucose appearance

BACKGROUND AND OBJECTIVE

The oral minimal model (OMM) of glucose dynamics is a prominent method for assessing postprandial glucose metabolism. The model yields estimates of insulin sensitivity and the meal-related appearance of glucose from insulin and glucose data after an oral glucose challenge. Despite its success, the OMM approach has several weaknesses that this paper addresses.

METHODS

A novel procedure introducing three methodological adaptations to the OMM approach is proposed. These are: (1) the use of a fully Bayesian and efficient method for parameter estimation, (2) the model identification from non-fasting conditions using a generalised model formulation and (3) the introduction of a novel function to represent the meal-related glucose appearance based on two superimposed components utilising a modified structure of the log-normal distribution. The proposed modelling procedure is applied to glucose and insulin data from subjects with normal glucose tolerance consuming three consecutive meals in intervals of four hours.

RESULTS

It is shown that the glucose effectiveness parameter of the OMM is, contrary to previous results, structurally globally identifiable. In comparison to results from existing studies that use the conventional identification procedure, the proposed approach yields an equivalent level of model fit and a similar precision of insulin sensitivity estimates. Furthermore, the new procedure shows no deterioration of model fit when data from non-fasting conditions are used. In comparison to the conventional, piecewise linear function of glucose appearance, the novel log-normally based function provides an improved model fit in the first 30 min of the response and thus a more realistic estimation of glucose appearance during this period. The identification procedure is implemented in freely accesible MATLAB and Python software packages.

CONCLUSIONS

We propose an improved and freely available method for the identification of the OMM which could become the future standardard for the oral minimal modelling method of glucose dynamics.

Hypoglycemia Prevention via Personalized Glucose-Insulin Models Identified in Free-Living Conditions

BACKGROUND

The objective of this research is to show the effectiveness of individualized hypoglycemia predictive alerts (IHPAs) based on patient-tailored glucose-insulin models (PTMs) for different subjects. Interpatient variability calls for PTMs that have been identified from data collected in free-living conditions during a one-month trial.

METHODS

A new impulse-response (IR) identification technique has been applied to free-living data in order to identify PTMs that are able to predict the future glucose trends and prevent hypoglycemia events. Impulse response has been applied to seven patients with type 1 diabetes (T1D) of the University of Amsterdam Medical Centre. Individualized hypoglycemia predictive alert has been designed for each patient thanks to the good prediction capabilities of PTMs.

RESULTS

The PTMs performance is evaluated in terms of index of fitting (FIT), coefficient of determination, and Pearson's correlation coefficient with a population FIT of 63.74%. The IHPAs are evaluated on seven patients with T1D with the aim of predicting in advance (between 45 and 10 minutes) the unavoidable hypoglycemia events; these systems show better performance in terms of sensitivity, precision, and accuracy with respect to previously published results.

CONCLUSION

The proposed work shows the successful results obtained applying the IR to an entire set of patients, participants of a one-month trial. Individualized hypoglycemia predictive alerts are evaluated in terms of hypoglycemia prevention: the use of a PTM allows to detect 84.67% of the hypoglycemia events occurred during a one-month trial on average with less than 0.4% of false alarms. The promising prediction capabilities of PTMs can be a key ingredient for new generations of individualized model predictive control for artificial pancreas.

A Minimal Model Approach for the Description of Postprandial Glucose Responses from Glucose Sensor Data in Diabetes Mellitus

Modelling of the gluco-regulatory system in response to an oral glucose tolerance test (OGTT) has been the subject of research for decades. This paper presents an adaptation to the well-established oral minimal model that is identifiable from glucose data only and is able to capture the dynamics of glucose following both OGTT and mixed meal consumption. The model is in the form of low-dimensional differential equations with a recently introduced input function consisting of Gaussian shaped components. It was identified from glucose data recorded from six subjects without diabetes, prediabetes and type 2 diabetes under controlled conditions. The inferred parameters of the model are shown to have physiological meaning and produce realistic steady state behavior. This model may be useful in the development of clinical advisory tools for the treatment and prevention of non-insulin dependent type 2 diabetes mellitus.

Chaos, mitochondria and type 2 diabetes; does type 2 diabetes arise from a metabolic dysrhythmia?

The increasing incidence of type 2 diabetes transcends all cultures, largely due to populations transitioning from traditional diets and manual occupations, to sedentary, calorific lifestyles. Excess calorie intake leads to intramuscular fat accumulation and insulin resistance. Physical inactivity causes underutilization of mitochondria causing dysfunction and inflammation. Both insulin resistance and mitochondrial dysfunction mechanisms are known to be closely related and to antagonise one another, although the precise nature of the relationship has eluded characterization. It is poorly understood why this mutual dysfunction progresses on to clinical diabetes in only some patients, why progression is often stepwise and why diabetes control only weakly predicts future cardiovascular disease in individuals. Clinical prediction in patients is therefore currently unsatisfactory and current linear assumptions require challenging. Cells contain networks of oscillating ionic fluxes. Cellular activity is characterised by complex patterns of fluctuation with sudden transitions between patterns. The non-linear nature of these oscillations is well characterised in neuronal activity, cardiac impulses and more recently mitochondria, but not previously in relation to diabetes. Cells under metabolic stress demonstrate complex fluctuations of mitochondrial distribution, coupling strength and synchronisation resulting in periodic or chaotic oscillations of function, causing accumulation of intracellular fat and excess reactive oxygen species (ROS), which exacerbates insulin resistance. Glucose, insulin and HbA1c in patients are also known to oscillate in complex patterns but the mechanisms and significance are largely unknown. Drawing on existing evidence and models from other diseases, a nonlinear, dynamical hypothesis of diabetes onset and progression is proposed. Insulin receptor pathways and mitochondria are treated as two populations of coupled, phase oscillators. Health or disease states depend on system stability or instability and reflect the balance of substrate supply and energy demand. The implication of this novel mechanism is that diabetes and the complications are not the consequence of a distinct pathological agent or pathway, but more an evolving dysrhythmia of normal cellular energetics systems, resulting from accumulated adverse lifestyle conditions. This hypothesis is proposed with the intention of stimulating research into non-linear dynamical constructs as an alternative to current linear models, to improve risk prediction and trajectory analysis in type 2 diabetes.

Statistical Modeling of Trivariate Static Systems: Isotonic Models

This paper presents an improved version of a statistical trivariate modeling algorithm introduced in a short Letter by the first author. This paper recalls the fundamental concepts behind the proposed algorithm, evidences its criticalities and illustrates a number of improvements which lead to a functioning modeling algorithm. The present paper also illustrates the features of the improved statistical modeling algorithm through a comprehensive set of numerical experiments performed on four synthetic and five natural datasets. The obtained results confirm that the proposed algorithm is able to model the considered synthetic and the natural datasets faithfully.

A review of personalized blood glucose prediction strategies for T1DM patients

This paper presents a methodological review of models for predicting blood glucose (BG) concentration, risks and BG events. The surveyed models are classified into three categories, and they are presented in summary tables containing the most relevant data regarding the experimental setup for fitting and testing each model as well as the input signals and the performance metrics. Each category exhibits trends that are presented and discussed. This document aims to be a compact guide to determine the modeling options that are currently being exploited for personalized BG prediction.

Personalized glucose forecasting for type 2 diabetes using data assimilation

Type 2 diabetes leads to premature death and reduced quality of life for 8% of Americans. Nutrition management is critical to maintaining glycemic control, yet it is difficult to achieve due to the high individual differences in glycemic response to nutrition. Anticipating glycemic impact of different meals can be challenging not only for individuals with diabetes, but also for expert diabetes educators. Personalized computational models that can accurately forecast an impact of a given meal on an individual's blood glucose levels can serve as the engine for a new generation of decision support tools for individuals with diabetes. However, to be useful in practice, these computational engines need to generate accurate forecasts based on limited datasets consistent with typical self-monitoring practices of individuals with type 2 diabetes. This paper uses three forecasting machines: (i) data assimilation, a technique borrowed from atmospheric physics and engineering that uses Bayesian modeling to infuse data with human knowledge represented in a mechanistic model, to generate real-time, personalized, adaptable glucose forecasts; (ii) model averaging of data assimilation output; and (iii) dynamical Gaussian process model regression. The proposed data assimilation machine, the primary focus of the paper, uses a modified dual unscented Kalman filter to estimate states and parameters, personalizing the mechanistic models. Model selection is used to make a personalized model selection for the individual and their measurement characteristics. The data assimilation forecasts are empirically evaluated against actual postprandial glucose measurements captured by individuals with type 2 diabetes, and against predictions generated by experienced diabetes educators after reviewing a set of historical nutritional records and glucose measurements for the same individual. The evaluation suggests that the data assimilation forecasts compare well with specific glucose measurements and match or exceed in accuracy expert forecasts. We conclude by examining ways to present predictions as forecast-derived range quantities and evaluate the comparative advantages of these ranges.