Analysis of brain tissue poroelastic properties using multiscale modelling - Abbas, Shabudin; Mohd Jamil, Mohamed Mokhtarudin; Nik Mohd Zuki, Nik Mohamed; Mohd Akramin, Romlay (International Islamic University Malaysia-IIUM, 2025)
Mathematical models are developed to understand ischaemic stroke formation further and achieve treatment effectiveness. The existing poroelastic model of the brain assumed the brain as a homogenized structure with uniform capillary distribution. This paper describes using a multiscale modeling technique known as asymptotic expansion homogenization (AEH) to derive a new poroelastic model of brain tissue. The model consists of a homogenized governing macroscale model with the effective parameters determined from the microscale cell equations. The microscale cell equations are solved on a representative volume element (RVE) comprising brain tissue embedded with a capillary. Here, the effect of capillary tortuosity and radius on the effective parameters, which are the hydraulic conductivity of the capillary and interstitial space ( and ), homogenous Biot's coefficient of the blood and interstitial space ( and ), Young's modulus and Poisson's ratio, are investigated. From the results, it is found that the percentage difference of is 97.98% with increasing tortuosity, which suggests that is significantly influenced by the shape of the capillary. Whereas the percentage difference of is only 0.25%, which shows that it is unaffected by the shape of the capillary. Meanwhile, and decreases and increases withincreasing tortuosity, respectively. Both and are not significantly affected by tortuosity, as the percentage difference for each is just 0.14% and 0.03%, respectively. In terms of capillary radius, it is found that increases and decreases with the increase of radius. Meanwhile, increases with increasing radius while instead shows the opposite trend. The percentage differences of 18.26% and 14.55% are observed for and, respectively, implying that both parameters are significantly affected by the capillary radius. In conclusion, including capillary in the brain model significantly affects the effective parameters. Hence, important properties of the capillary, including shape and size, should be carefully emphasized so that accurate findings can be obtained when solving the poroelastic model of the brain