Mathematical model of thyroid gland functioning as a follicles system

Abstract

The thyroid gland represents one of the endocrine glands. Despite the relatively small size of the gland, it plays an essential role in controlling the regulation of metabolism and individual cells' growth using hormones. The main component of the hormones is iodine. The gland consists of follicles that are the organ's structural elements, in which the synthesized thyroid hormone accumulates in a state associated with protein. To construct a model in which the rate of iodine metabolism is set in dependence on the concentration of substances in the colloid. To investigate the change in the size of the follicle and the entire thyroid gland from the concentration of iodine using a mathematical model. The entire thyroid glands work is considered a mega-system, consisting of individual follicles having different volumes. The mathematical model represents a boundary value problem for a system of nonlinear differential equations for concentrations of substances in the follicle. The dynamics of changes in the size of both an individual follicle and the system as a whole is considered under various initial and external conditions. The degree of influence of follicle volume on the level of iodine in the follicle as well as on the production of the thyroid hormone is assessed. The thyroid gland's work is studied, and a mathematical model of the thyroid gland is constructed, which considers the thyroid gland as a mega-system consisting of a certain number of follicles. According to the results of studies, this approach allows more accurate tracking of changes occurring with a single follicle and, consequently, the work of the entire organ. If the thyroid gland is healthy, the follicle size distribution is lognormal.