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

TL;DR

This paper demonstrates the effectiveness of Physics Informed Neural Networks (PINNs) in accurately solving differential equations modeling drug assimilation in humans, validating PINNs as a powerful tool for dynamical systems.

Contribution

The study applies PINNs to model drug absorption in humans, showing high accuracy and validating PINNs for complex biological differential equations.

Findings

Achieved error as low as 10^(-11) and 10^(-8) in solutions.

Validated PINNs as effective for solving biological differential equations.

Demonstrated PINNs' potential in modeling pharmacokinetics.

Abstract

Differential equations play a pivotal role in modern world ranging from science, engineering, ecology, economics and finance where these can be used to model many physical systems and processes. In this paper, we study two mathematical models of a drug assimilation in the human system using Physics Informed Neural Networks (PINNs). In the first model, we consider the case of single dose of drug in the human system and in the second case, we consider the course of this drug taken at regular intervals. We have used the compartment diagram to model these cases. The resulting differential equations are solved using PINN, where we employ a feed forward multilayer perceptron as function approximator and the network parameters are tuned for minimum error. Further, the network is trained by finding the gradient of the error function with respect to the network parameters. We have employed DeepXDE, a python library for PINNs, to solve the simultaneous first order differential equations describing the two models of drug assimilation. The results show high degree of accuracy between the exact solution and the predicted solution as much as the resulting error reaches10^(-11) for the first model and 10^(-8) for the second model. This validates the use of PINN in solving any dynamical system.