Purpose: Tissue hydraulic permeability of brain tumours can vary considerably depending on the tissue microstructure, compositions in interstitium and tumour cells. Its effects on drug transport and accumulation remain poorly understood. Methods: Mathematical modelling is applied to predict the drug delivery outcomes in tumours with different tissue permeability upon convection-enhanced delivery. The modelling is based on a 3-D realistic tumour model that is extracted from patient magnetic resonance images. Results: Modelling results show that infusing drugs into a permeable tumour can facilitate a more favourable hydraulic environment for drug transport. The infused drugs will exhibit a relatively uniform distribution and cover a larger tumour volume for effective cell killing. Cross-comparisons show the delivery outcomes are more sensitive to the changes in tissue hydraulic permeability and blood pressure than the fluid flow from the brain ventricle. Quantitative analyses demonstrate that increasing the fluid gain from both the blood and brain ventricle can further improve the interstitial fluid flow, and thereby enhance the delivery outcomes. Furthermore, similar responses to the changes in tissue hydraulic permeability can be found for different types of drugs. Conclusions: Tissue hydraulic permeability as an intrinsic property can influence drug accumulation and distribution. Results from this study can deepen the understanding of the interplays between drug and tissues that are involved in the drug delivery processes in chemotherapy.

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.

Unresolved digital rock images are often used to avoid high computational costs and limited field of views associated with processing fine‐resolution rock images. However, segmentation of unresolved images using classical methods is suboptimal due to the presence of the partial‐volume effect. Suboptimal segmentations can significantly influence the geometry and effective properties of the reconstructed models. This study reveals that partial‐volume pixels with high pore fractions remain as regional minima in intensity levels in unresolved images. By identifying these regional‐minima pixels, we can effectively extract pore space obscured by the partial‐volume effect. Based on this observation, we propose a novel segmentation method capable of identifying these regional‐minima partial‐volume pixels and converting them to pure pore pixels, thereby binarizing the digital rock images. The method is validated on sandstone and carbonate rock samples. Our method demonstrates a notable improvement in modeled permeability accuracy, surpassing 50% compared to the thresholding method and over 30% compared to the watershed method. Moreover, models segmented by this approach exhibit smaller pore and throat sizes compared to the substantially overestimated results obtained by classical methods. These findings suggest that the regional‐minima segmentation method effectively corrects for the partial‐volume effect and preserves more detailed pore structures. Consequently, it enhances the quality of binarized rock geometries, leading to improved accuracy in fluid‐flow simulations.

Convection-enhanced delivery (CED) can effectively overcome the blood–brain barrier by infusing drugs directly into diseased sites in the brain using a catheter, but its clinical performance still needs to be improved. This is strongly related to the highly anisotropic characteristics of brain white matter, which results in difficulties in controlling drug transport and distribution in space. In this study, the potential to improve the delivery of six drugs by adjusting the placement of the infusion catheter is examined using a mathematical model and accurate numerical simulations that account simultaneously for the interstitial fluid (ISF) flow and drug transport processes in CED. The results demonstrate the ability of this direct infusion to enhance ISF flow and therefore facilitate drug transport. However, this enhancement is highly anisotropic, subject to the orientation of local axon bundles and is limited within a small region close to the infusion site. Drugs respond in different ways to infusion direction: the results of our simulations show that while some drugs are almost insensitive to infusion direction, this strongly affects other compounds in terms of isotropy of drug distribution from the catheter. These findings can serve as a reference for planning treatments using CED.