Hydraulic permeability is a topic of deep interest in biological materials because of its important role in a range of drug delivery-based therapies. The strong dependence of permeability on the geometry and topology of pore structure and the lack of detailed knowledge of these parameters in the case of brain tissue makes the study more challenging. Although theoretical models have been developed for hydraulic permeability, there is limited consensus on the validity of existing experimental evidence to complement these models. In the present study, we measure the permeability of white matter (WM) of fresh ovine brain tissue considering the localised heterogeneities in the medium using an infusion based experimental set up, iPerfusion. We measure the flow across different parts of the WM in response to applied pressures for a sample of specific dimensions and calculate the permeability from directly measured parameters. Furthermore, we directly probe the effect of anisotropy of the tissue on permeability by considering the directionality of tissue on the obtained values. Additionally, we investigate whether WM hydraulic permeability changes with post-mortem time. To our knowledge, this is the first report of experimental measurements of the localised WM permeability, showing the effect of axon directionality on permeability. This work provides a significant contribution to the successful development of intra-tumoural infusion-based technologies, such as convection-enhanced delivery (CED), which are based on the delivery of drugs directly by injection under positive pressure into the brain.

Glioblastomas represent a challenging problem with an extremely poor survival rate. Since these tumour cells have a highly invasive character, an effective surgical resection as well as chemotherapy and radiotherapy is very difficult. Convection-enhanced delivery (CED), a technique that consists in the injection of a therapeutic agent directly into the parenchyma, has shown encouraging results. Its efficacy depends on the ability to predict, in the pre-operative phase, the distribution of the drug inside the tumour. This paper proposes a method to compute a fundamental parameter for CED modelling outcomes, the hydraulic permeability, in three brain structures. Therefore, a bidimensional brain-like structure was built out of the main geometrical features of the white matter: axon diameter distribution extrapolated from electron microscopy images, extracellular space (ECS) volume fraction and ECS width. The axons were randomly allocated inside a defined border, and the ECS volume fraction as well as the ECS width maintained in a physiological range. To achieve this result, an outward packing method coupled with a disc shrinking technique was implemented. The fluid flow through the axons was computed by solving Navier–Stokes equations within the computational fluid dynamics solver ANSYS. From the fluid and pressure fields, an homogenisation technique allowed establishing the optimal representative volume element (RVE) size. The hydraulic permeability computed on the RVE was found in good agreement with experimental data from the literature.

Brain microstructure plays a key role in driving the transport of drug molecules directly administered to the brain tissue, as in Convection-Enhanced Delivery procedures. The proposed research analyzes the hydraulic permeability of two white matter (WM) areas (corpus callosum and fornix) whose three-dimensional microstructure was reconstructed starting from the acquisition of electron microscopy images. We cut the two volumes with 20 equally spaced planes distributed along two perpendicular directions, and, on each plane, we computed the corresponding permeability vector. Then, we considered that the WM structure is mainly composed of elongated and parallel axons, and, using a principal component analysis, we defined two principal directions, parallel and perpendicular, with respect to the axons’ main direction. The latter were used to define a reference frame onto which the permeability vectors were projected to finally obtain the permeability along the parallel and perpendicular directions. The results show a statistically significant difference between parallel and perpendicular permeability, with a ratio of about two in both the WM structures analyzed, thus demonstrating their anisotropic behavior. Moreover, we find a significant difference between permeability in corpus callosum and fornix, which suggests that the WM heterogeneity should also be considered when modeling drug transport in the brain. Our findings, which demonstrate and quantify the anisotropic and heterogeneous character of the WM, represent a fundamental contribution not only for drug-delivery modeling, but also for shedding light on the interstitial transport mechanisms in the extracellular space.