Modelagem matemática para otimização de dietas de portadores de Diabetes Mellitus

Abstract

Diabetes Mellitus is a disease that affects millions of people around the world and presents itself in several ways, the main types 1 and 2 of the disease. Type 1 occurs when the production of the hormone insulin by the pancreas is insufficient and is often diagnosed in children and adolescents. Type 2 is responsible for more than 90% of diabetes cases, characterized by malfunctioning of insulin receptors, being more common in adults and related to overweight, sedentary lifestyle and inadequate diet. In all forms of the disease there is an increased concentration of glucose levels in the bloodstream, being important the observation of the amount and type of carbohydrate present in the diet, the glycemic index of the food to be ingested by the individual among other factors to decrease its undesirable effects on the body of the Diabetes Mellitus carrier. The search for viable methods of diabetes control as well as patient adherence has encouraged the development of research and innovation of existing methodologies. This work aims to present a mathematical model that is able to allow assistance to the diet planning of Diabetes Mellitus carriers through Linear Programming. In order to do so, tables with sufficient data bases were developed for the elaboration of generic food plans in the GAMS® software where food and their respective nutritional values are considered. Three generic case studies were performed simulating hypothetical choices of users/patients of different sexes, heights and intensity levels of physical activity performed, in order to verify the use of this mathematical modeling in compliance with the pertinent nutritional recommendations. The model was generated from parameters related to the observance of nutritional recommendations, identifying the best combinations that make possible the minimization of daily carbohydrate consumption, resulting in optimal solutions of the diets obtained.