Modelo de glicose-insulina com medicamento

Abstract

Diabetes mellitus is a metabolic disease caused by the lack or inefficiency of insulin function, a hormone responsible for blood sugar balance. Since the last century, this disease has been investigated through experimental studies and mathematical models, which depict its behavior. In this work, we analyze the function of the glucose-insulin system through several mathematical models related to different symptoms and characteristics of diabetes, such as high blood sugar concentration, known as hyperglycemia. The starting point in this work was proposed by Ackerman in 1964; the model consists of two differential equations related to glucose and insulin concentration, applied to hyperglycemia symptoms. Subsequently, a third equation was implemented by Bajaj in 1987, in a study representing insulin-producing cells in cases of diabetes with deficient insulin release. In order to find a solution to reduce blood sugar levels, we added an equation in the 1987 model associated with the medication dimethylbiguanide, used to reduce blood glucose concentration. Results obtained by the model show that the presence of different medication doses reduces glucose concentration levels. Furthermore, we determined glucose control by the amount of medication the body can absorb. Low medication absorption values imply longer times to reduce glucose concentration, requiring higher doses to compensate for low absorption. Using the model, it was possible to study the medication characteristic related to the time the medication concentration remains in the body, called half-life. It is possible to find a treatment combination related to the medication dose and the time it will stay in the organism. Our results show that medication reduces glycemia and that there are different possibilities for treating diabetes, such as low doses of the medicine with longer duration in the body or high doses of the medication with short periods of time in the body. Both treatments resulting in hyperglycemia control, but with possibilities to adapt the medication for different types of organisms.