Simulation Model for Hashimoto Autoimmune Thyroiditis Disease

Abstract

Hashimoto thyroiditis (HT) is a pathology that often causes a gradual thyroid insufficiency in affected patients due to the autoimmune destruction of this gland. The cellular immune response mediated by T helper lymphocytes TH1 and TH17 can induce the HT disease. In this pathologic condition, there is an imbalance between the TH17 and Treg lymphocytes as well as a gut microbiota dysfunction. The objective of this work was to describe the interactions of the cell subpopulations that participate in HT. To achieve this goal, we generated a mathematical model that allowed the simulation of different scenarios for the dynamic interaction between thyroid cells, the immune system, and the gut microbiota. We used a hypothetical-deductive design of mathematical modeling based on a system of ordinary differential equations, where the state variables are the TH1, TH17, and Treg lymphocytes, the thyrocytes, and the bacteria from gut microbiota. This work generated a compartmental model of the cellular immune response occurring in the thyroid gland. It was observed that TH1 and TH17 lymphocytes could increase the immune cells' activity, as well as activate effector cells directly and trigger the apoptosis and inflammation processes of healthy thyrocytes indirectly. Likewise, the model showed that a reduction in Treg lymphocytes could increase the activity of TH17 lymphocytes when an imbalance of the gut microbiota composition occurred. The numerical results highlight the TH1, TH17, and bacterial balance of the gut microbiota activities as important factors for the development of HT disease.

Keywords: T helper cells; autoimmune hypothyroidism; dynamic systems; gut microbiota; mathematical modeling; thyrocytes.

Figure 1.

Schematic representation of simulation model for the Hashimoto autoimmune thyroiditis disease process. In the thyroid gland, thyrocytes mediate the differentiation of CD4+ T-helper (TH) cells into subpopulations of specific T cells (TH1, TH17, and Treg). The proliferation of TH1 and TH17 lymphocytes activate apoptosis and inflammation of the thyroid tissue, respectively. The gut microbiota regulates the relationship between the effector (TH17) and regulator (Treg) lymphocytes, leading to greater differentiation of pathogenic TH17 lymphocytes and subsequent inflammation. The model also assumes that thyrocytes, TH17 lymphocytes and TH1 lymphocytes have mortality rates β ₁, β ₂, and β ₃. The lymphocytic differentiation process φ ₁ and φ ₂. The Treg and φ ₃ parameters stimulate the differentiation of TH17 lymphocytes.

Figure 2.

The numerical simulation of the model parameters satisfies the condition of the disease state. The orange line represents the behavior of thyrocytes; the gray line shows the bacterial growth in the gastrointestinal tract; the blue and red lines represent the growth dynamics of TH17 and TH1 lymphocytes, respectively. Graphs A to C illustrate the interaction dynamics of the state variables, where the increase of the balance between Treg lymphocytes and the gut bacteria stimulates a higher differentiation of TH17 lymphocytes. In the different simulation scenarios shown in A to C, it is assumed that α = 0.25, β ₁ = 0.05, β = 0.092, γ = 0.05, φ ₁ = 0.05, Treg = 0.7, β ₂ = 0.05, φ ₂ = 0.05, β ₃ = 0.05, α ₁ = 0.09; and the value of φ ₃ in the distinct scenarios A to C is φ ₃ = 0.01, φ ₃ = 0.2, and φ ₃ = 0.3, respectively.

Figure 3.

The numerical simulation of the model parameters satisfies stability condition of disease free. The orange line represents the behavior of thyrocytes; the gray line shows bacterial growth in the gastrointestinal tract; the blue and red lines show the growth dynamics of TH17 and TH1 lymphocytes, respectively. Graphs A and B illustrate the interaction dynamics of the state variables, where the increase in the balance between Treg lymphocytes and the bacteria of the intestinal microbiota stimulates a higher differentiation of TH17 lymphocytes. In the different simulation scenarios shown in A and B it is assumed that α = 0.25, β ₁ = 0.05, β = 0.092, γ = 0.05, φ ₁ = 0.05, Treg = 0.7, β ₂ = 0.05, φ ₂ = 0.05, β ₃ = 0.05, α ₁ = 0.09; and the value of φ ₃ in the distinct scenarios A and B is φ ₃ = 0.05 and φ ₃ = 0.1, respectively.

Figure 4.

Numerical simulation for the state variable thyrocytes with the parameter values of Table 1, in identical initial condition. The orange line represents the behavior of the thyrocytes in different simulation scenarios. A to E illustrate the behavior of thyrocytes, as the balance between Treg lymphocytes and the bacteria of the intestinal microbiota, which increases their contribution percentage to TH17 lymphocyte differentiation. For all simulation scenarios, A-E assumes that α = 0.25, β ₁ = 0.05, β = 0.092, γ = 0.05, φ ₁ = 0.05, Treg = 0.7, β ₂ = 0.05, φ ₂ = 0.05, β ₃ = 0.05, α ₁ = 0.09; and the value of φ ₃ in the different scenarios represented by A-E is φ ₃ = 0.01, φ ₃ = 0.05, φ ₃ = 0.1, φ ₃ = 0.2, and φ ₃ = 0.3, respectively.