Analytical Solutions of Single Dose Drug Models with Injection Administration: Literature Review

Abstract

This literature review aims to explore the development the Single Dose Injection Models by finding their Analytical Solutions. The most very known single-compartment pharmacokinetic model with first-order elimination was developed by Tang & Xiao in 2007, where the elimination part is modified by the Michaelis-Menten kinetics. Years later, in 2015 Wu, Li, & Nekka developed the model by considering simultaneous elimination and drug distribution in the body, then they modified the more complex model through incorporating the endogenous production in 2018. These three models employ differential equations to depict changes in drug concentration, and not only utilize the Lambert W function, the models also introduce the X function to obtain the analytical solutions. The results are expected to provide a deeper understanding of drug dynamics in the body and to serve as a basis for further research and clinical applications in pharmacokinetics as well as to offer the deeper insights into drug delivery within the human body.