Mathematical Optimisation of Magnetic Nanoparticle Diffusion in the Brain White Matter

Tian Yuan, Yi Yang, Wenbo Zhan, Daniele Dini* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
4 Downloads (Pure)


Magnetic nanoparticles (MNPs) are a promising drug delivery system to treat brain diseases, as the particle transport trajectory can be manipulated by an external magnetic field. However, due to the complex microstructure of brain tissues, particularly the arrangement of nerve fibres in the white matter (WM), how to achieve desired drug distribution patterns, e.g., uniform distribution, is largely unknown. In this study, by adopting a mathematical model capable of capturing the diffusion trajectories of MNPs, we conducted a pilot study to investigate the effects of key parameters in the MNP delivery on the particle diffusion behaviours in the brain WM microstructures. The results show that (i) a uniform distribution of MNPs can be achieved in anisotropic tissues by adjusting the particle size and magnetic field; (ii) particle size plays a key role in determining MNPs' diffusion behaviours. The magnitude of MNP equivalent diffusivity is reversely correlated to the particle size. The MNPs with a dimension greater than 90 nm cannot reach a uniform distribution in the brain WM even in an external magnitude field; (iii) axon tortuosity may lead to transversely anisotropic MNP transport in the brain WM; however, this effect can be mitigated by applying an external magnetic field perpendicular to the local axon track. This study not only advances understanding to answer the question of how to optimise MNP delivery, but also demonstrates the potential of mathematical modelling to help achieve desired drug distributions in biological tissues with a complex microstructure.

Original languageEnglish
Article number2534
Number of pages15
Journal International Journal of Molecular Sciences
Issue number3
Publication statusPublished - 28 Jan 2023

Bibliographical note

European Unions Horizon 2020 research and innovation programme under Grant Agreement No. 688279. EPSRC Established Career Fellowship Grant No. EP/N025954/1. Children with Cancer UK Grant No. 16-224.

Data Availability Statement

Data available on request from the authors.


  • Diffusion
  • Drug Delivery Systems
  • Magnetite Nanoparticles/chemistry
  • Pilot Projects
  • White Matter
  • Brain tissue


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