(714e) Nonlinear Dynamics and Complexity of the Thyroid Homeostatic Mechanism

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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