Pore-scale analysis of nanoparticle diffusion in brain tumours

Nanoparticles have emerged as a promising platform for drug delivery to brain tumours. Despite their ability to successfully traverse the blood–brain barrier, nanoparticle penetration in tumour tissues, primarily governed by diffusion, remains significantly limited, posing a major challenge to effective delivery. The diffusion of nanoparticles in tumour tissues is determined by complex interactions between nanoparticles and the tumour microenvironment, a process that remains insufficiently understood. This study employs a mechanics-based model at the pore-scale to address this gap. After validation with reported experimental results, the model is applied to investigate nanoparticle diffusion across different grades of brain tumours under various conditions, with the 3D geometries of tumour microstructures mathematically reconstructed based on their morphological characteristics. The results indicate nanoparticles diffuse slowly in high-grade tumours despite their loose cell arrangements. This implies that the density of hyaluronic acid, the key tumour extracellular matrix component, surpasses tissue porosity in determining nanoparticle diffusion. To quantify nanoparticle diffusion, for each grade of brain tumours empirical formulas are developed to express the relationships between nanoparticle diffusion coefficient and hyaluronic acid concentration, as well as with nanoparticle size and zeta potential. Furthermore, the results demonstrate the Einstein-Stokes equation can be used to estimate nanoparticle diffusion coefficient at different temperatures by scaling the values at normal body temperature, whereas using it to directly calculate nanoparticle diffusivity would result in substantial errors. The developed model and empirical formulas provide effective tools for rapidly predicting nanoparticle diffusion, offering insights for drug nanocarriers’ design to improve brain tumour treatment.