Mathematical model to describe regulation of carbohydrate metabolism taking into account functional disorders for predicting increased risk of associated diseases

Diseases of the endocrine system, including those associated with increased consumption of carbohydrates and high-calorie foods, are common throughout the world. Existing complex mathematical models for describing carbohydrate metabolism processes contain many parameters, which makes their use difficult at the individual level. The aim of this work is to develop a mathematical model to describe regulation of carbohydrate metabolism, taking into account the endocrine function of the pancreas and functional disorders in the body under various diets. The new basic mathematical formulation proposed by the authors of this article takes into account the main processes in the system of glucose, insulin and glucagon balance in blood and glucose in the liver as well as functional disorders of certain organs (liver, kidneys, pancreas), time delays in the transmission of regulatory signals, as well as various diets (fast food with a high content of fast carbohydrates, high-calorie food, and unbalanced daily diets). A system of differential equations with a delayed argument is used as a mathematical apparatus and the Euler method is used for the numerical solution of the system.

Numerical experiments consider the results for four scenarios: a process without functional disorders in the body; impaired pancreatic and liver function in type I diabetes; impaired insulin-dependent glucose intake in type II diabetes; and unbalanced consumption of fast carbohydrates. In case of diabetes or when consuming fast carbohydrates, periods of elevated blood glucose as well as excess levels themselves (up to 8.8–15 mmol/l) are significantly higher than in case the disease is absent. Elevated glucose levels and periods of exceeding normal levels are the output parameters of the model, risk-inducing factors of diseases of the endocrine and cardiovascular systems. In addition, the carbohydrate balance is violated in scenarios with diabetes. The body begins to store excess glucose in the liver on a daily basis, which can lead to further conversion of carbohydrates into fats, increasing the obesity risk.

Depending on the simulation results, disease prevention measures can include optimal individual recommendations for balancing the amount of consumed carbohydrates and meals per day. In future studies, it is advisable to consider carbohydrate metabolism in combination with fat, which allows for more detailed consideration of pathways typical for diabetes and concomitant pathologies.