A model for the testosterone regulation taking into account the presence of two types of testosterone hormones

Abstract

The purpose of this paper is to study the effect of sex hormone binding globulin (SHBG) on the mathematical model of the hypothalamic-pituitary-gonadal (HPG) endocrine cycle which regulates the production of the male hormone testosterone. Large amounts of total circulating testosterone are bound to SHBG making them. Standard analytical techniques are used to analyze the modified mathematical model which includes a delay to account for the time required for luteinizing hormone emitted by the pituitary gland to reach the testis, to determine the steady state, its stability and the critical delay needed for the bifurcation. Numerical simulation of the solutions of the model is performed to illustrate the possible behaviors.