Endocrine systems modeling: Towards personalized treatment of thyroid diseases

Thyroid hormones are fundamental in the development and function of the human body. They are produced by the thyroid and their concentration is regulated by a negative feedback loop involving also the hypothalamus and the pituitary. Many studies have shown that each individual has a unique HPT axis set-point, which means that everyone has his or her own personal level of thyroid hormones. However, when the thyroid is affected by a disease, such as hypothyroidism, a change in the thyroid function modifies the levels of thyroid hormones, therefore they do not match the patient’s set-point anymore. Hence, the aim of this thesis is to investigate the relationship between the thyroid hormones TSH and FT4 in order to predict each individual’s set-point. Moreover, the variation in time of the two hormones in patients under medication is studied as well, which allows to determine around which values the concentrations of TSH and FT4 will stabilize and, if these are not matching the set-point, to adjust the patient’s medication dosage. This research was conducted using patients’ datasets from different hospitals. In particular, datasets of hypothyroid and thyroidectomized patients were included in this study. The analysis of hypothyroid patients’ measurements shows that TSH can be expressed as a negative exponential function of FT4. Furthermore, the individual set-point can be predicted as the point of maximum curvature of that function and this has been validated using data from thyroidectomized patients. Finally, a model of coupled differential equations, taking into account the effects of medication, has been developed to describe how the concentrations of the hormones are changing in time after a patient starts the treatment.Applied Mathematic