The purpose of modelling the negative-feedback control mechanism of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis is to describe the clinical course of euthyroidism, subclinical hypothyroidism and overt hypothyroidism for patients. Thyroid hormone thyroxine (T4) and triiodothyronine (T3) levels are controlled by negative-feedback control through thyroid-stimulating hormone (TSH). T4, like other hormones, can be bound or unbound; the unbound T4 (FT4) is used as a marker for hypothyroidism. Autoimmune thyroiditis is a disease in which the thyroid-infiltrating lymphocytes attack autoantigens in follicle cells, destroying them over a long time. To describe the operation of the feedback control, we developed a mathematical model involving four clinical variables: TSH, FT4, anti-thyroid peroxidase antibodies and the thyroid gland's functional size. The first three variables are regularly measured while the last variable is determined through relationships between the other three variables. The problem of two different time scales for circulating hormones and thyroid damage is addressed using singular perturbation theory. Analysis of the mathematical model establishes stability and conditions under which the diseased state can maintain the slow movement toward diseased state equilibrium. Although we have used four variables in modelling the feedback control through the HPT axis, the predicted clinical course given any set of parameters is shown to depend on the steady-state levels of TSH and FT4. This observation makes possible the development of the clinical charts based only on the levels of TSH, time and potential steady-state values. To validate the model predictions, a dataset obtained from a Sicilian adult population has been employed.

BackgroundGraves’ is disease an autoimmune disorder of the thyroid gland causedby circulating anti-thyroid receptor antibodies (TRAb) in the serum. TRAb mimics the action of thyroid stimulating hormone (TSH) and stimulates the thyroid hormone receptor (TSHR), which results in hyperthyroidism (overactive thyroid gland) and goiter. Methimazole (MMI) is used for hyperthyroidism treatment for patients with Graves’ disease.MethodsWe have developed a model using a system of ordinary differential equations for hyperthyroidism treatment with MMI. The model has four state variables, namely concentration of MMI (in mg/L), concentration of free thyroxine - FT4 (in pg/mL), and concentration of TRAb (in U/mL) and the functional size of the thyroid gland (in mL) with thirteen parameters. With a treatment parameter, we simulate the time-course of patients’ progression from hyperthyroidism to euthyroidism (normal condition). We validated the model predictions with data from four patients.ResultsWhen there is no MMI treatment, there is a unique asymptotically stable hyperthyroid state. After the initiation of MMI treatment, the hyperthyroid state moves towards subclinical hyperthyroidism and then euthyroidism.ConclusionWe can use the model to describe or test and predict patient treatment schedules. More specifically, we can fit the model to individual patients’ data including loading and maintenance doses and describe the mechanism, hyperthyroidism→euthyroidism. The model can be used to predict when to discontinue the treatment based on FT4 levels within the physiological range, which in turn help maintain the remittance of euthyroidism and avoid relapses of hyperthyroidism. Basically, the model can guide with decision-making on oral intake of MMI based on FT4 levels.Electronic supplementary materialThe online version of this article (doi:10.1186/s12976-017-0073-6) contains supplementary material, which is available to authorized users.

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Thyroid autoimmunity is characterized by a large number of identified factors, and determining the relative importance of genetics and environment, for instance, can be difficult. In addition, the definition and progression of the individual diseases can also be challenging, and questions such as "when to begin treatment" or even "should treatment be begun" can be problematic. One approach to handling situations in which there are many factors is utilizing mathematical modeling. In a model, quantities that are clinically measurable are related through equations, based on known and inferred relationships between the systems involved. ations where these relationships are complicated, the resulting simulations can provide information not previous recognized as logically resulting from those relationships. One advantage of this approach is that patient-specific parameter estimates can be used to personalize disease monitoring and treatment. In this paper, models involving Hashimoto's (autoimmune) thyroiditis, Graves' disease, and the roles of leptin, vitamin D, and adipose tissue are described. In the case of Hashimoto's, a model consisting of a system of differential equations is presented which allows a patient specific description of the progression of the disease. The conditions leading to Hashitoxicosis are also described through that model. The patient specific model of the treatment of Graves' disease is also described. Finally, the roles of the inflammatory adipokines, especially leptin, and vitamin D is explored as it relates to the initiation of thyroid autoimmunity. The result of this approach is an enhanced view of the initiation and progression of autoimmunity in the thyroid.

This chapter is devoted to studying the physiology of the pituitary-thyroid axis and thyroid size in autoimmune thyroiditis via modeling. The pituitary-thyroid axis consists of a feed forward and backward loop in humans, which is responsible for maintaining the body's metabolism. Under a disease situation, the dynamics of the axis becomes more complex and unique among patients. Hashimoto's autoimmune thyroiditis disrupts the normal operation of the axis by slowly destroying the thyroid follicle cells through complex immune mechanisms. So, the size of thyroid and the axis operation are fully, partly, or totally not functional in this disease. Basically, the patient situation in the disease process is unique in describing the diffused goiter and/or a clinical symptom of hashitoxicosis, euthyroidism, subclinical hypothyroidism, or overt hypothyroidism. Using patient-specific modeling, we can predict the hidden dynamics of the natural history of autoimmune thyroiditis and test hypothesis on the operation of axis. In addition, we unfold case studies of three patients from the thyroid literature through the modeling viewpoint and describe their hidden dynamics.