Date of Award

Summer 2011

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics, Statistics and Computer Science

First Advisor

Merrill, Stephen J.

Second Advisor

Krenz, Gary

Third Advisor

Bansal, Naveen


This thesis is a mathematical modeling study of the operation of the negative feedback control through the hypothalamus-pituitary- thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis. Negative feedback control through the HPT axis is a mechanism in which the high levels of thyroid hormone; free thyroxine (FT4) in the blood inhibits the secretion of the pituitary hormone, thyroid stimulating hormone (TSH) into the blood. Similarly, the low levels of free thyroxine (FT4) sensed by the pituitary gland and then it secretes thyroid stimulating hormone (TSH) into the blood. Autoimmune (Hashimoto's) thyroiditis is a disease in which the immune system turns against the thyroid follicle cells and destroys them slowly for a long period of time. This in turn interrupts the operation of the negative feedback control, in fact, the HPT axis. The half-life of thyroid stimulating hormone (TSH) and free thyroxine (FT4) is one hour and seven days respectively in the blood. This implies that thyroid stimulating hormone (TSH) changes in a faster time scale than free thyroxine (FT4) both in the healthy and diseased thyroid gland. Thus, the operation of negative feedback control is at least in two different time scales. The normal reference range for TSH and FT4 is used in this thesis are(0.4-2.5) mU/L and (7-18) pg/mL respectively. In thyroid clinics, in general, physicians see three different kinds of patients with autoimmune (Hashimoto's) thyroiditis with or without goiter (enlarged thyroid gland).

Patients with euthyroidism (normal FT4 and TSH levels).Patients with subclinical hypothyroidism (normal FT4 but TSH above normal levels).Patients with overt (clinical) hypothyroidism (low FT4 and TSH above normal levels).Usually patients with euthyroidism progress to subclinical hypothyroidism and then progress to overt hypothyroidism. This is a sequential event, but in some patients' cases, it is not true. To describe the operation of the feedback control in autoimmune (Hashimoto's) thyroiditis, we developed a mathematical model in this thesis involving four clinical (state) variables, thyroid stimulating hormone (TSH), free thyroxine (FT4), anti-thyroid antibodies (TPOAb and TGAb), and the functional size of the thyroid gland (T). The first three variables are regularly measured in thyroid clinics to determine the function of negative feedback control and the status of the thyroid gland in autoimmune thyroiditis. The last variable is determined through relationships between the other three variables and is required for this work to accurately track the output of the gland. The problem of two different time scales is addressed using singularly perturbation theory. Also, the analysis of the mathematical model establishes stability and conditions under which the diseased state can be maintained the slow movement of the functioning of the negative feedback control toward the diseased state equilibrium.

In this thesis, the purpose of modeling the operation of negative feedback control is to describe the natural history of autoimmune (Hashimoto's) thyroiditis. This means to describe the natural course of euthyroidism, subclinical hypothyroidism or overt hypothyroidism for every patient with autoimmune thyroiditis. Although, we have used four variables in modeling the feedback control through the HPT axis, the end product depends on the levels of thyroid stimulating hormone (TSH) and free thyroxine (FT4). In addition, the clinical chart is developed based on the levels of thyroid stimulating hormone (TSH) and time. To validate the model description, patient's dataset are employed in chapter 5. For this thesis, the dataset is obtained from Sicilian adult population, Italy through our clinical collaborator.