Nonlinear Dynamics and Complexity of the Thyroid Homeostatic Mechanism

ABSTRACT

The thyroid homeostatic mechanism (Danziger & Elmergreen, 1956) is a neuroendocrine control system regulating the delicate equilibrium governing human body growth as well as metabolism. Triiodothyronine (T3) and thyroxine (T4) are the key species secreted by the thyroid gland into the blood due to thyroid stimulating hormone (TSH) excitation and then transported to tissues. Stable hormone concentrations in blood plasma are normally regulated within narrow bounds by a complex feedback control system involving the brain (hypothalamus, pituitary) and the thyroid. The study and elucidation of T3, T4 and TSH secretory dynamics concern biochemists, molecular biologists and clinical endocrinologists alike because they affect millions of patients. Numerous thyroid function and texture pathological conditions have been recognized as named (Basedow, Plummer, Graves and Hashimoto) diseases and induce a considerable societal impact. Computing optimal hormone dosage profiles in silico and verifying the efficient therapies in vivo requires reliable computational models without parametric uncertainty and/or state multiplicity.

Pathological states of thyroid hormone excess or deficiency lead to predictable TSH fluctuations: in primary hypothyroidism (a condition characterized by an absolute deficiency of T3 and T4), the signal species (TSH) is expected to be significantly elevated as a physiologic attempt to stimulate the thyroid so as to increase its thyroid hormone production to compensate for the lack. Conversely, thyrotoxicosis, which is a pathological state of thyroid hormone excess, can either be due to overproduction of the hormones by the thyroid gland (termed hyperthyroidism) or due to elevated circulating thyroid hormones despite suppressed thyroid output of thyroid hormones due to of leakage of thyroid hormones from an inflamed thyroid, consumption of excess exogenous thyroid hormones, or uncontrolled secretion of thyroid hormones in certain tumors (Leow, 2007).

This paper presents a rigorous structural and computational analysis of a reliable dynamic model (DiStefano III et al., 1975) which comprises 6 ordinary differential equations and 17 parameters. This established dynamic model has been selected as the starting point for this study because it has been developed with a consistent and systematic parameterization, thus avoiding heuristics; also, it is the basis of subsequent optimal hormone dosage studies (Mak & DiStefano III, 1978). Nonlinear dynamics may explain the significant clinical response variability observed in patients who receive slightly different thyroid hormone/iodine dosage therapies for the same disease. Critical thyroid mechanism nonlinearities are illustrated by means of dynamic simulation studies. A bifurcation analysis (Seydel, 1994) is performed via MATCONT (Dhooge et al., 2003) in order to understand the hitherto unclear effect of parameters on system response and state trajectories.  

Augmented mathematical models of thyroid dynamics which encapsulate multiple organ effects and consider multiple biochemical and cellular species explicitly have also appeared in the literature: they may contain organ-specific time delays (Mukhopadhyay & Bhattacharyya, 2006) as well as several additional state variables and widely uncertain parameters (Degon et al., 2008), but may admittedly suffer with respect to parameter identifiability (DiStefano III & Mori, 1977).

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