Modelling glucose dynamics during moderate exercise in individuals with type 1 diabetes

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.

Management of Glycemia during Acute Aerobic and Resistance Training in Patients with Diabetes Type 1: A Croatian Pilot Study

(1) Background: The increased risk of developing hypoglycemia and worsening of glycemic stability during exercise is a major cause of concern for patients with type 1 diabetes mellitus (T1DM). (2) Aim: This pilot study aimed to assess glycemic stability and hypoglycemic episodes during and after aerobic versus resistance exercises using a flash glucose monitoring system in patients with T1DM. (3) Participants and Methods: We conducted a randomized crossover prospective study including 14 adult patients with T1DM. Patients were randomized according to the type of exercise (aerobic vs. resistance) with a recovery period of three days between a change of groups. Glucose stability and hypoglycemic episodes were evaluated during and 24 h after the exercise. Growth hormone (GH), cortisol, and lactate levels were determined at rest, 0, 30, and 60 min post-exercise period. (4) Results: The median age of patients was 53 years, with a median HbA1c of 7.1% and a duration of diabetes of 30 years. During both training sessions, there was a drop in glucose levels immediately after the exercise (0'), followed by an increase at 30' and 60', although the difference was not statistically significant. However, glucose levels significantly decreased from 60' to 24 h in the post-exercise period (p = 0.001) for both types of exercise. Glycemic stability was comparable prior to and after exercise for both training sessions. No differences in the number of hypoglycemic episodes, duration of hypoglycemia, and average glucose level in 24 h post-exercise period were observed between groups. Time to hypoglycemia onset was prolonged after the resistance as opposed to aerobic training (13 vs. 8 h, p = NS). There were no nocturnal hypoglycemic episodes (between 0 and 6 a.m.) after the resistance compared to aerobic exercise (4 vs. 0, p = NS). GH and cortisol responses were similar between the two sessions, while lactate levels were significantly more increased after resistance training. (5) Conclusion: Both exercise regimes induced similar blood glucose responses during and immediately following acute exercise.

A physical activity-intensity driven glycemic model for type 1 diabetes

BACKGROUND AND OBJECTIVE

The glucose response to physical activity for a person with type 1 diabetes (T1D) depends upon the intensity and duration of the physical activity, plasma insulin concentrations, and the individual physical fitness level. To accurately model the glycemic response to physical activity, these factors must be considered.

METHODS

Several physiological models describing the glycemic response to physical activity are proposed by incorporating model terms proportional to the physical activity intensity and duration describing endogenous glucose production (EGP), glucose utilization, and glucose transfer from the plasma to tissues. Leveraging clinical data of T1D during physical activity, each model fit is assessed.

RESULTS

The proposed model with terms accommodating EGP, glucose transfer, and insulin-independent glucose utilization allow for an improved simulation of physical activity glycemic responses with the greatest reduction in model error (mean absolute percentage error: 16.11 ± 4.82 vs. 19.49 ± 5.87, p = 0.002).

CONCLUSIONS

The development of a physiologically plausible model with model terms representing each major contributor to glucose metabolism during physical activity can outperform traditional models with physical activity described through glucose utilization alone. This model accurately describes the relation of plasma insulin and physical activity intensity on glucose production and glucose utilization to generate the appropriately increasing, decreasing or stable glucose response for each physical activity condition. The proposed model will enable the in silico evaluation of automated insulin dosing algorithms designed to mitigate the effects of physical activity with the appropriate relationship between the reduction in basal insulin and the corresponding glycemic excursion.

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

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.

Dynamic of Glucose Homeostasis in Virtual Patients: A Comparison between Different Behaviors

This work presents a mathematical model of homeostasis dynamics in healthy individuals, focusing on the generation of conductive data on glucose homeostasis throughout the day under dietary and physical activity factors. Two case studies on glucose dynamics for populations under conditions of physical activity and sedentary lifestyle were developed. For this purpose, two types of virtual populations were generated, the first population was developed according to the data of a total of 89 physical persons between 20 and 75 years old and the second was developed using the Monte Carlo approach, obtaining a total of 200 virtual patients. In both populations, each participant was classified as an active or sedentary person depending on the physical activity performed. The results obtained demonstrate the capacity of virtual populations in the generation of in-silico approximations similar to those obtained from in-vivo studies. Obtaining information that is only achievable through specific in-vivo experiments. Being a tool that generates information for the approach of alternatives in the prevention of the development of type 2 Diabetes.

Virtual diabetic patient with physical activity dynamics

BACKGROUND AND OBJECTIVE

Diabetes is a disease of impaired blood glucose regulation due to the absence or insufficient secretion of insulin hormone or insulin resistance induced in the human body. In literature, the impact of exercise is considered in few models based on the minimal representation of glucose dynamics along with the assumption that no endogenous insulin is produced in the body. Hence these models are not capable of describing diabetic behavior which is independent of exogenous insulin. This type of diabetes, known as type-2, affects almost 90% of the total diabetes population. In this article, a constraint-based comprehensive physiological model of blood glucose dynamics is aimed to build for filling up the gap in the literature.

METHODS

For physiological comprehensiveness, the model is considered to consist of several compartments separately connected with a common compartment named 'plasma'. Plasma is the only accessible compartment and contains the state variables. Plasma variables are the integrated result of the net change in rates of metabolic processes and basal rates are influenced between two saturation constraints for an operating range of each plasma variable. The influence of a plasma variable on a metabolic rate is represented using a form of the hyperbolic tangent function. Validation is done by fitting the model with clinical experiments and continuous glucose monitoring data of a free-living environment.

RESULTS

The proposed model generates an average correlation coefficient of 0.85 ± 0.13 on all simulated responses with the target in the fitting experiments. Besides this, the model can produce a spectrum of metabolic effects of plasma variables for showing more insight into glucose metabolism.

CONCLUSIONS

A constraint-based comprehensive glucose regulation with exercise dynamics for modeling diabetes is pursued. The model doesn't consider age, gender, physical, and mental condition of the human body but can be applied in operation research by mathematical programming.

Simulation-Based Evaluation of Treatment Adjustment to Exercise in Type 1 Diabetes

Regular exercise is beneficial and recommended for people with type 1 diabetes, but increased glucose demand and changes in insulin sensitivity require treatment adjustments to prevent exercise-induced hypoglycemia. Several different adjustment strategies based on insulin bolus reductions and additional carbohydrate intake have been proposed, but large inter- and intraindividual variability and studies using different exercise duration, intensity, and timing impede a direct comparison of their effects. In this study, we use a mathematical model of the glucoregulatory system and implement published guidelines and strategies in-silico to provide a direct comparison on a single 'typical' person on a standard day with three meals. We augment this day by a broad range of exercise scenarios combining different intensity and duration of the exercise session, and different timing with respect to adjacent meals. We compare the resulting blood glucose trajectories and use summary measures to evaluate the time-in-range and risk scores for hypo- and hyperglycemic events for each simulation scenario, and to determine factors that impede prevention of hypoglycemia events. Our simulations suggest that the considered strategies and guidelines successfully minimize the risk for acute hypoglycemia. At the same time, all adjustments substantially increase the risk of late-onset hypoglycemia compared to no adjustment in many cases. We also find that timing between exercise and meals and additional carbohydrate intake during exercise can lead to non-intuitive behavior due to superposition of meal- and exercise-related glucose dynamics. Increased insulin sensitivity appears as a major driver of non-acute hypoglycemic events. Overall, our results indicate that further treatment adjustment might be required both immediately following exercise and up to several hours later, but that the intricate interplay between different dynamics makes it difficult to provide generic recommendations. However, our simulation scenarios extend substantially beyond the original scope of each model component and proper model validation is warranted before applying our in-silico results in a clinical setting.