A metamodel-based flexible insulin therapy for type 1 diabetes patients subjected to aerobic physical activity

Abstract

Patients with type 1 diabetes are subject to exogenous insulin injections, whether manually or through (semi)automated insulin pumps. Basic knowledge of the patient's characteristics and flexible insulin therapy (FIT) parameters are then needed. Specifically, artificial pancreas-like closed-loop insulin delivery systems are some of the most promising devices for substituting for endogenous insulin secretion in type 1 diabetes patients. However, these devices require self-reported information such as carbohydrates or physical activity from the patient, introducing potential miscalculations and delays that can have life-threatening consequences. Here, we display a metamodel for glucose-insulin dynamics that is subject to carbohydrate ingestion and aerobic physical activity. This metamodel incorporates major existing knowledge-based models. We derive comprehensive and universal definitions of the underlying FIT parameters to form an insulin sensitivity factor (ISF). In addition, the relevance of physical activity modelling is assessed, and the FIT is updated to take physical exercise into account. Specifically, we cope with physical activity by using heart rate sensors (watches) with a fully automated closed insulin loop, aiming to maximize the time spent in the glycaemic range (75.5% in the range and 1.3% below the range for hypoglycaemia on a virtual patient simulator).These mathematical parameter definitions are interesting on their own, may be new tools for assessing mathematical models and can ultimately be used in closed-loop artificial pancreas algorithms or to extend distinguished FIT.

Trial registration: ClinicalTrials.gov NCT04572009.

Figure 1

Metamodel of the glucose dynamics subject to insulin injection and physical activity. (A) Top: A metamodel based on the Bergman minimal model. The black bold scheme represents the core that is common to three specific models, namely Roy and Parker in blue, Breton in red and Alkhateeb in green. The most exhaustive model in terms of biological processes considers the factthat physical activity increases hepatic glucose production, also causes a depletion of glycogen stocks leading to a decrease in the glycogenolysis rate and finally increasing the glucose uptake of working tissues. Other models synthesize these three mechanisms in one module by considering only the increase in the glucose uptake. The ingested carbohydrates can be easily added to these schemes as a third input channel. (B) Bottom: A multicompartment metamodel for the diffusion of carbohydrates, insulin and physical activity and their effects on glycaemia. These multiple compartments act as a ’buffer’ for the diffusion of the primary input. Their behaviours are described in mathematical diffusion equations, which are linear in the case of injected insulin diffusion or in the case of carbohydrates digestion. However, they are nonlinear for some physical activity models.

Figure 2

The extended FIT model and control law behaviour in the simulation. (A) Simulation scenario used to assess the extended FIT model behaviour in reaction to different disturbances. $U_i$ stands for the insulin input flow and is in [U/min], $U_c$ corresponds to the ingested carbohydrates’ flow in [g/min] and $U_{\mathit{hr}}$ is the heart rate in [beats/min] or [bpm]. (B) Diagram highlighting the benefits of a control law with a physical activity variable (in green) and with only a glycaemic regulation term (in blue). In response to aerobic activity, the use of data such as heart rate can enable a quicker reactions to glycaemia decreases. (C) The extended FIT model structure, each block represents a subsystem of differential equations.

Figure 3

The identification procedure led by clinical data with a physical activity period. The upper panel represents the insulin input in [U/min]. These input data are retrieved from the patient’s insulin pump. The second panel pictures meal intakes in [g/min] which are declared by the patient. The third graph and last input is the heart rate, which is acquired using a smartwatch with a plethysmograph. During the first 15 h, the heart rate sensor malfunctions, and we assume that the heart rate remains at a reference value of 55 bpm as the actimetry data show no exertion. The fourth panel shows an identification procedure performed over 48 h via a model without physical activity equations followed by a crossed-validation of 24 h, showing that the model fails and quickly diverges after the onset of exertion. The last graph considers the same 72 h of data while conducting identification on the whole data set with the extended FIT model (including physical activity). The four red vertical lines the delimit two physical activity periods where exertion is deemed significant.

Figure 4

Control law performance comparison on a cohort of virtual patients and a simulator from the literature. (A) Simulation scenario and the results of our 10 virtual patients obtained by using our state-feedback controller. The horizontal dashed-lines represent the hypoglycaemia and hyperglycaemia thresholds (resp. 70 mg/dl and 180 mg/dl), respectively. The red-coloured area corresponds to the physical activity period. The 48-h scenario presented here included 3 meals on the first day, followed by an exercise bout and 3 more meals the next day. (B) Simulation of the 99-patient cohort from the OHSU simulator using our control algorithm and the same scenario as above. The horizontal dashed-lines have the same meanings as those in panel (A). (C) Control-variability grid analysis for our patient cohort with each black dot representing a patient according to their time spent in and out of the glycaemic range with a 95% confidence interval. All patients remained in the B-zone meaning that the control law kept glycaemia within the target range. (D) Control-variability grid analysis for the OHSU simulator.