Study of Drug Assimilation in Human System using Physics Informed Neural Networks

The ADME (T) (absorption, distribution, metabolism, excretion and toxicity) is a term used for regulation of drugs in clinical applications, delineating pharmacokinetics studies over the last 5 decades. However, mathematical insights in quantitative descriptions to ADME(T) appears promising and provide a suitable way of offering therapeutic targets. Recently, deep learning emerged as a powerful tool to solve physical systems. In this paper, based on the potential of mathematical modelling and deep learning, the assimilation, distribution and elimination of the drugs in the human system in the form of two mathematical models over a period of time has been studied. The aim to study these models is to see how these drugs are absorbed into the human system, which would be valuable in assessing the therapeutic value of a drug. The resulting differential equations which describe the rate of change of drug as it diffuses through the human system are solved using Physics Informed Neural Networks. Deep XDE, a python library for Physics Informed Neural networks is employed to solve the system of differential equations describing the two models of drug assimilation. The results obtained show a high degree of accuracy between the exact solution and the predicted solution of these models. The network is modelled for two activation functions and their results are compared. This approach which is mesh free as compared to other approaches validates the use of Physics Informed neural networks for solving dynamical system of drug diffusion model.