Mathematical model of insulin-like growth factor-1 estimating its cause in human bone cancer arises due to liver cancer

The insulin-like growth factor-1 (IGF-1) is a peptide hormone that is regulated by growth hormone and secreted in the liver; its prime role is to regulate the growth and proliferation of the bone cell. Our study results relate to the cause of bone cancer due to high IGF-1 levels in liver metastatic conditions. Liver cancer increases the liver volume which further increases IGF-1 secretion to a toxic level, which in turn causes uncontrolled bone cell proliferation and maturation thus leading to bone cancer. Thus, the mathematical model was designed to explain the kinetics of IGF-1 from the liver to bone and mathematically simplified using the ordinary differential equation, and IGF-1 concentration was estimated in the normal and cancerous state. The mathematical simulation was done using a high throughput technique using MATLAB (version R2020a). The model parameter condition due to liver cancer is considered as an increase in liver volume (v_L), The initial mass of IGF-1(x₀₁), and the varying rate constants (k_P, k_L, ke₁, and ke₂). The graphical results represent the volume of the liver and synthesis of IGF-1 increases with varying abnormal rate constants giving the estimation of an increase in IGF-1 concentration in plasma, and more IGF-1 deposits over the bone to a toxic level.