Self-Excited Oscillations in a System Model of the Human Thyroid

Abstract

The thyroid, the largest gland in the endocrine system, secretes hormones that regulate homeostatic functions within the body and promote normal growth and development. Recently, a detailed computational model of the thyroid gland has been derived and used to explain clinical observations regarding the thyroid gland’s ability to maintain its hormonal secretion target in the face of uncertain dietary iodine intake levels. In this paper we probe deeper into the thyroid’s nonlinear dynamics. We first reduce the original model to an eight-order dynamical system, analytically determine that a Hopf mechanism governs the loss of stability of thyroid equilibrium, culminating with numerically obtained periodic limit-cycle behavior beyond the critical threshold. We numerically investigate the orbital stability of periodic thyroid dynamics via its harmonic perturbation and construct a bifurcation structure that includes both periodic and subharmonic mode-locked solutions embedded within a set of quasiperiodic tori. An increase of the perturbation parameter reveals a similar and structurally stable bifurcation structure. Thus, the analysis of our nonlinear thyroid model shows that the gland can exhibit both a stable equilibrium and periodic limit-cycle behavior which can lose its orbital stability due to small harmonic perturbations.