Multiscale Poroelastic Modelling Linking Brain Tissue Cellular and Capillary Scales using Sequential Homogenization

Human brain exhibits a complex hierarchical structure spanning cellular, microvascular, and tissue scales, which governs its mechanical and transport behaviour, particularly under pathological conditions such as ischaemic stroke. In this study, a three-scale poroelastic model is developed using sequential asymptotic homogenization to link together pore scale, microscale, and macroscale brain behaviour. At the pore scale, brain cells are modelled as a linear elastic solid matrix permeated by interstitial fluid. Applying homogenization at the pore scale results in a homogenized microscale poroelastic brain tissue, which then interacts with a capillary network. Applying homogenization again at the microscale results in a double poroelastic model that describes the brain at the macroscale. Effective parameters at each scale are obtained by solving the corresponding cell problems on idealized pore structure and microstructure. The results show that the effective macroscale brain elasticity, interstitial fluid and blood permeabilities and transport properties are highly sensitive to both pore structure and micros porosity and structural arrangement. Under the assumptions of brain ischaemia, the macroscale double poroelastic model can be reduced to a single poroelastic formulation. The proposed framework thus provides a rigorous multiscale approach for linking microscale structural variations to macroscale brain mechanics and fluid transport in both healthy and pathological conditions, with potential applications in understanding neurological diseases.