A patient-specific model of the negative-feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis (Q2922510)

The authors suggest a patient-specific model for the analysis of the negative feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis. The model is represented by a system of four nonlinear ordinary differential equations containing eleven parameters. The four variables \(x,\) \(y,\) \(z,\) \(w\) represent, respectively, concentrations of thyroid-stimulating hormone (TSH), the unbound T4 (FT4), anti-thyroid peroxidase antibodies (TPOAb) and the functional size of the thyroid gland. A healthy HPT axis maintains negative feedback control in a normal steady state (euthyroid). In the course of an autoimmune disease on the thyroid gland, the control is being lost and a shift from the steady state to a disease state occurs. Each autoimmune thyroiditis patient falls into one of the three categories: (i) euthyroidism to euthyroidism, (ii) euthyroidism to subclinical hypothyroidism, or (iii) euthyroidism to subclinical hypothyroidism and then to overt hypothyroidism.NEWLINENEWLINEThe model has been constructed on a slower scale and it has been rewritten to reflect the structure of a singularly perturbed initial value problem whose dimension was then reduced. The reduced model is also on the same slower time scale. The Hoppensteadt's theorem has been employed to describe asymptotic behavior of solutions and explore the relationship between solutions of the singularly perturbed initial value problem and those of the reduced model for the values of parameter \(\varepsilon\) close to zero.NEWLINENEWLINETheoretical analysis of the model has been conducted and \(k_{7}\) has been identified as a bifurcation parameter for all individuals. Remarkably, each individual has a unique \(k_{7}\) value which allows to describe the patient's group of euthyroidism to euthyroidism and determines the course of disease -- the disease dynamics for two individuals with the same \(k_{7}\) value is just the same. This is the major contribution of the paper, which allows the authors to develop a TSH versus time chart.