Dynamic analysis of Hashimoto’s Thyroiditis bio-mathematical model using artificial neural network

Abstract

This article establishes an efficient solution scheme for a mathematical model of Hashimoto’s Thyroiditis (HT) employing artificial neural networks. HT is an auto-immune disorder hostile to the thyroid follicle cells, effectuating hypothyroid or hyperthyroidism. Under this condition, the thyroid-stimulating hormone (TSH) alters incomparably to the free thyroxine (FT4) interrupts the functioning of the hypothalamus-pituitary-thyroid (HPT) axis, implicating the thyroid follicle cells getting destroyed. We primarily focus on utilizing artificial neural network (ANN) to perform numerical simulations for the system of ordinary differential equations describing the dynamics of an existing 4D model of HT. The presented model comprises four time-dependent variables: TSH, FT4, anti-thyroid antibodies (Ab), and size of the thyroid gland (T). We utilize ND-Solver and ANN scheme in the Mathematica software to acquire the computational data and illustrate thus retrieved results with essential performance plots. Further, mean square error has been considered in validating the proposed ANN-based approach accurately. The plot for training and validation loss exhibits the effectiveness of the proposed methodology, and substantiate that the suggested ANN approach is a good fit for the solving the mathematical model of HT.