Transport properties of the brain tissues, especially the hydraulic permeability, play a key role in the development of brain diseases, including Parkinson’s Disease, Alzheimer’s Disease, and drug delivery to the brain [1, 2]. However, non-invasively characterising the permeability of brain is still a challenge. Furthermore, neurons are very easily deformable and little is known about the interplay between neurons and their surrounding fluid and its impact on mass transport in the brain on the macroscale [3,4]. Misrepresenting these relationships may lead to the erroneous prediction of, e.g. disease spread, drug delivery, and nerve injury in the brain. To solve these problems, we derived a mathematical relationship between porosity and permeability of the brain white matter (WM). Then, we numerically characterised the coefficients in the derived formulas by adopting high-fidelity microstructures of brain WM and computational fluid dynamics (CFD). Finally, we obtained an anisotropic permeability tensor of the brain WM as a function of the tissue porosity [5]. To further consider the axonal deformation, we explicitly modelled the transient fluid-solid interaction between the fluid and axons. We then establish the first microstructurally based permeability tensor as a function of local interstitial pressure and pressure gradients for macroscopic brain modelling with a higher resolution [6]. These newly developed porosity-permeability tensor and pressure-permeability tensor relationships have been validated by a group of sheep brain infusion experiments. Since advanced imaging techniques have enabled non-invasive characterisation of porosity distribution in the brain [7], this newly developed porosity-permeability tensor relationship will provide possibilities to non-invasively characterise the hydraulic permeability of brain tissues. This will lead to the provision of better patient-specific medical treatments, such as drug delivery. Considering fluid-axon interactions further reveals that (i) the brain’s transport properties strongly depend on the two-way interactions between neurons and interstitial fluids, and (ii) the pressure-dependent permeability tensor can inherently capture the dynamic transport property of the brain.