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, which has attracted significant attention for the advancement of novel materials. However, in comparison with other materials, biomaterials, especially natural and artificial tissues, have more complex microstructures e.g. high anisotropy, high randomness of cell/fibre dimensions/position and very low porosity. Consequently, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive. To fill this gap, we start a 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. A versatile microstructure generation software (MicroFiM) for fibrous biomaterial with complex microstructure and low porosity was built accordingly and made freely accessible here. Moreover, we propose an anisotropic poro-hyperelastic model enhanced by the newly defined porosity-permeability tensor relationship which precisely captures the tissues macro-scale permeability changes due to the microstructural deformation in an infusion scenario. The constitutive model, 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. STATEMENT OF SIGNIFICANCE: Due to the microstructural complexity, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive, which hinders our way of tuning the fluid transport property of the biomaterials by directly programming their microstructure. The same problem hinders non-invasive characterisations of fluid transport properties in biological tissues, which can significantly improve the efficiency of treatments e.g. drug delivery, directly from the tissues accessible microstructural information, e.g. porosity. Here, we developed a validated mathematical formulation to link the random microstructure to a fibrous material's macroscale permeability tensor. This will advance our capability to design complex biomaterials and make it possible to non-invasively characterise the permeability of living tissues for precise treatment planning. The newly established theory and protocol can be easily adapted to various types of fibrous biomaterials.

Keywords: Biomaterial; Computational fluid dynamics; Fluid transport; Microstructure; Permeability; Poro-hyperelastic model.