Porosity-permeability tensor relationship of closely and randomly packed fibrous biomaterials and biological tissues: Application to the brain white matter

Abstract

The constitutive model for the porosity-permeability relationship is a powerful tool to estimate and design the transport properties of porous materials, and has thus attracted a significant number of attention for the advancement of composite materials. However, in comparison with engineering composite materials, biomaterials, especially natural and artificial tissues, have more complex micro-structures such as high anisotropy, high randomness of cell/fibre dimensions and very low porosity. Consequently, these properties of the biomaterial make the porosity-permeability relationship more difficult to obtain than traditional composites. To fill this gap, we start the mathematical derivation from the fundamental brain white matter (WM) formed by nerve fibres. This is augmented by a numerical characterisation and experimental validations to obtain an anisotropic permeability tensor of the brain WM as a function of the tissue porosity. Moreover, we propose an anisotropic poroelastic model enhanced by the newly defined porosity-permeability tensor relationship which precisely captures the tissue's macro-scale permeability changes due to the micro-structural deformation in an infusion scenario. The constitutive model, the theories and protocols established in this study will both provide improved design strategies to tailor the transport properties of fibrous biomaterials and enable the non-invasive characterisation of the transport properties of biological tissues. This will lead to the provision of better patient-specific medical treatments, such as drug delivery.