A Revision of the Bernoulli Equation as a Controller of the Fick's Diffusion Equation in Drug Delivery Modeling

TL;DR

This paper proposes a novel mathematical approach combining the Bernoulli and Fick's equations to better model and control drug diffusion in vascular systems, enhancing understanding of drug delivery mechanisms.

Contribution

It introduces a revised Bernoulli equation as a controller for Fick's diffusion equation in drug delivery modeling, providing a new method to optimize drug transport direction.

Findings

The combined equation effectively predicts diffusion direction.

The method improves control over drug carrier divergence.

It offers a theoretical framework for drug delivery optimization.

Abstract

Mathematical equations can be used as effectual tools in drug delivery systems modeling and are also highly helpful to have a theoretical understanding of controlled drug release and diffusion mechanisms. In this study we aim to present a mathematical combination between the Bernoulli equation and the Fick's equation as a diffusion controller in drug delivery systems. For this propose we have revised the Bernoulli equation as an additional, controller and complementary method of the Fick's diffusion equation to detect the optimal delivery direction to control the diffusion divergence of the drug carrier in vascular systems during the transportation process in biological tissues. Therefore, by utilizing the Bernoulli equation we could determine the real direction by the route function f.