HYPOTHYROID MATHEMATICAL MODEL: ANALYTICAL AND NUMERICAL SOLUTION USING THE LAPLACE Key TRANSFORMATION

Abstract

Hypothyroidism, one of the most prevalent endocrine disorders in the world, results from the insufficient production of thyroid hormones, thyroxine (T4) and triiodothyronine (T3), by the thyroid gland. This work utilizes a mathematical model of the hypothalamic-pituitary-thyroid (HPT) axis to describe the development of hypothyroidism, specifically the development of thyroid stimulating hormone (TSH), T4 and T3 levels within the thyroid gland. The model uses the formulation established by Pandiyan et al. and employs the Laplace Transform to convert the system of differential equations into an algebraic one in the complex frequency field. The solutions to this system of differential equations were obtained using standard inversion techniques and partial fraction decomposition. The results of this model were tabulated for a 50-day period with biologically reasonable parameter values. Sensitivity plots of each variable to the rate parameter of that variable were created to examine the sensitivity of each of the variables within the model. The efficacy of the Laplace-based method for compartmental modeling of biological systems is confirmed by the development of solutions to the model that exhibit the characteristics of hypothyroidism, including elevated TSH levels and suppressed levels of T4 and T3