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

Abstract

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 methodology of phenotyping ICU patients from EHR data: High-fidelity, personalized, and interpretable phenotypes estimation

“…The phenotyping knowledge extraction problem with clinical data in EHR can also be seen as a classic inverse problem [ 18 - 21 ]. This paradigm begins by calculating from explicitly measurable data, e.g., blood glucose, the unmeasurable but implicitly quantifiable properties, e.g., insulin secretion, by estimating a model of glucose-insulin mechanics [ 22 - 25 ]. Usually, but not always, this nonlinear model consists of a set of ordinary differential equations that represent our mathematized knowledge of a physical system, e.g., a mathematical physiological model [ 26 ].…”

Nonlinear Mathematical Analysis based on an Insulin-Pancreatic Cells Model in the Presence of Epinephrine

“…Es importante destacar que recientemente en [7] , se ha reportado un modelo que conduce a la predicción del nivel de glucemia, donde tales predicciones tienen el potencial de ser utilizadas como parte de sistemas de control las cuales pueden ser robustos para modelar imperfecciones y datos ruidosos. Lo interesante de este modelo es que su capacidad predictiva se compara con modelos enfocados a diabetes mellitus tipo 2 (DMT2).…”