Chemotaxis Model for Drug Delivery Using Turing’s Instability and Non-Linear Diffusion
This paper is devoted to the study of the chemotaxis model for drug delivery purposes. The pattern formation for a volume-filling with nonlinear diffusive terms is investigated. The proposed mathematical model is governed by a reaction–diffusion system modeling the interaction between the cell density and the concentration of the chemoattractant. We investigate the pattern formation for the model using Turing’s principle and linear stability analysis. An asymptotic expansion is used to linearize the nonlinear diffusive terms. Next, we introduce an implicit finite volume scheme; it is presented on a triangular mesh satisfying the orthogonality condition. Finally, numerical results showing the formation of the spatial pattern for the chemotaxis model are presented and analyzed. The results demonstrate promising progress in understanding the process of controlling and designing targeted drug delivery.
In this paper, we are concerned with the convergence analysis of a combined finite volume-non-conforming finite element scheme, to approximate the two incompressible phase flow with dynamic…
The purpose of this paper was to detect and separate the cluster intensity provided by Iron oxide nanoparticles (IO-NPs), in the MRI images, to investigate the drug delivery effectiveness. IO-NPs…
This paper is devoted to the study of the chemotaxis model for drug delivery purposes. The pattern formation for a volume-filling with nonlinear diffusive terms is investigated.