Mathematical Optimisation of Magnetic Nanoparticles Diffusion in the Brain White Matter

Magnetic Nanoparticles (MNPs) is a promising technique to cure brain diseases. On the one hand, by serving as drug carriers, they can bypass the blood-brain barrier and deliver drug molecules to the brain parenchyma; on the other hand, their transport trajectory can be manipulated by applying an external magnetic field. However, due to the complex microstructure of brain tissues, e.g. the anisotropy of white matter (WM), how to achieve desired drug distribution patterns, e.g. uniform distribution, by tuning the drug delivery system is largely unknown. Here, in this study, by adopting a mathematical model capable of capturing the diffusion trajectories of MNPs in the microstructures, we systematically investigated the effects of key parameters in the MNPs delivery system on the equivalent diffusion coefficient of MNPs in the microenvironment of brain WM. The results show that uniform distribution of MNPs in anisotropic tissues can be achieved by adjusting the particle size and magnetic field. We have not only obtained a deeper understanding on how to optimise the MNPs delivery system, it can also be anticipated that an improved mathematical model could even help to achieve complex drug distribution patterns in the complicated brain environment by designing an appropriate combination of the key parameters.