Using a Hopfield Iterative Neural Network to Explain Diffusion in the Brain’s Extracellular Space Structure

Abstract

Many therapies for drug delivery to the brain are based on diffusion, and diffusion in this extracellular space is based on micro-techniques that can be modelled with classical differential equations such as the point source diffusion equation. In this paper an energy function is constructed using a finite-difference approximation to the governing diffusion equation and then minimized by a Hopfield neural network. The synergy of Hopfield neural networks with finite difference approximation is promising. The neural network approach is capable of giving insight to the complex brain activity better than any other classical numerical method and the parallelism nature of the Hopfield neural networks approach is easier to implement on fast parallel computers and this will make them faster than the traditional methods for modelling this complex problem. Moreover, the effect of the involved parameters on the diffusion distribution and drug delivery in the ECS is investigated.