Computational Simulation of Charged Nanoparticles Diffusion in Vascular Tissue

Abstract

Apparition of abnormal vasculature is common at the first phases of tumor growth. It is known as angiogenesis having the whole process various phases. This is also seen as a random migration of cells that require the flux of blood in order to accomplish the consolidation of tumor. This paper provides a hybrid approach by the which it is assumd that sprouting angiogenesis has a well-defined part that would have to be described by classical electrodynamics. A closed-form model that allows to perform computational simulations is presented. In this manner, while the electrically charged compounds such as ions (cations and anions) are described by Coulomb forces, nano particles can be well described by the diffusion equation. According to the model nanoparticles would interact to ions by generating an electric work to cancel cell-ion interactions at the tubular formation of angiogenesis. With this the period of interaction with nano particles is estimated theoretically.