1 research outputs found
A Simple Modeling Framework For Prediction In The Human Glucose-Insulin System
In this paper, we build a new, simple, and interpretable mathematical model
to describe the human glucose-insulin system. Our ultimate goal is the robust
control of the blood glucose (BG) level of individuals to a desired healthy
range, by means of adjusting the amount of nutrition and/or external insulin
appropriately. By constructing a simple yet flexible model class, with
interpretable parameters, this general model can be specialized to work in
different settings, such as type 2 diabetes mellitus (T2DM) and intensive care
unit (ICU); different choices of appropriate model functions describing uptake
of nutrition and removal of glucose differentiate between the models. In both
cases, the available data is sparse and collected in clinical settings, major
factors that have constrained our model choice to the simple form adopted.
The model has the form of a linear stochastic differential equation (SDE) to
describe the evolution of the BG level. The model includes a term quantifying
glucose removal from the bloodstream through the regulation system of the human
body, and another two terms representing the effect of nutrition and externally
delivered insulin. The parameters entering the equation must be learned in a
patient-specific fashion, leading to personalized models. We present numerical
results on patient-specific parameter estimation and future BG level
forecasting in T2DM and ICU settings. The resulting model leads to the
prediction of the BG level as an expected value accompanied by a band around
this value which accounts for uncertainties in the prediction. Such
predictions, then, have the potential for use as part of control systems which
are robust to model imperfections and noisy data. Finally, a comparison of the
predictive capability of the model with two different models specifically built
for T2DM and ICU contexts is also performed.Comment: 47 pages, 9 figures, 7 table