[SY-F14] Symposium F-14

[SY-F14] Numerical simulation of ionic transport through deformable porous media: application to cortical bone tissue modeling

^○Jana Turjanicova^1,2, Eduard Rohan^1,2, Vladimír Lukeš² (1.Dept. of Mechanis, Univ. of West Bohemia in Pilsen, Czech Republic, 2.NTIS - New technologies for information society, Czech Republic)

Cortical bone tissue is known to have a strictly hierarchical porous structure on multiple scales. On the canalicular-lacunar scale, it consist of two phases: deformable collagen-apatite matrix charged by a small electric charge and bone fluid filling the pore space created by network of small interconnected channels. Bone fluid is considered an electrolyte solution of two species of charged monovalent ions of opposite polarizations. Due to the potential differences, the electrical double layer occurs in the proximity of the solid-fluid interface. Considering its effect, the transport of such electrolyte through a network of small channels with charged surface is controlled by coupling between the electric field , Stokes flow, the migration-diffusion process and deformation of solid matrix.
In order to describe cortical bone effective properties on the macroscopic scale, the unfolding homogenization method is applied on the model of ionic transport through deformable porous media. The microstructure on canalicular-lacunar scale is simplified by assumption of its periodicity and is represented by so-called representative periodic cell. The characteristic responses on this cell are used to compute the effective coefficients describing cortical bone behavior on the macroscopic scale (scale of one osteon). Macroscopic model behavior was tested on the simple boundary value problem. Implementation of upscaling process as well as numerical simulation on the macroscopic model was made in in-house developed python based FEM software SfePy.