Chaotic Model of Brownian Motion in Relation to Drug Delivery Systems Using Ferromagnetic Particles

Abstract

Deterministic and stochastic models of Brownian motion in ferrofluids are of interest to researchers, especially those related to drug delivery systems. The Brownian motion of nanoparticles in a ferrofluid environment was theoretically analyzed in this research. The state of the art in clinical drug delivery systems using ferromagnetic particles is briefly presented. The motion of the nanoparticles in an external field and as a random variable is elaborated by presenting a theoretical model. We analyzed the theoretical model and performed computer simulation by using Maple software. We used simple low-dimensional deterministic systems that can exhibit diffusive behavior. The ferrofluid in the gravitational field without the presence of an external magnetic field in the xy plane was observed. Control parameter p was mapped as related to the fluid viscosity. Computer simulation showed that nanoparticles can exhibit deterministic patterns in a chaotic model for certain values of the control parameter p. Linear motion of the particles was observed for certain values of the parameter p, and for other values of p, the particles move randomly without any rule. Based on our numerical simulation, it can be concluded that the motion of nanoparticles could be controlled by inherent material properties and properties of the surrounding media, meaning that the delivery of drugs could possibly be executed by a ferrofluid without an exogenous power propulsion strategy. However, further studies are still needed.