The focus of this mini-symposium is on the measurement and incorporation of pore structure and anisotropy parameters into quasi-static poroelasticity and dynamic poroelasticity with particular application to bone tissue. The plan is to cover this topic in 3 sessions. The tentative titles of the 3 sessions consisting of six 20 min. presentations in this mini symposium are:
1. Measurement and modeling of the pore architecture and anisotropy of bone tissue
Within certain limits, the pore architecture and anisotropy of bone tissue are more homogeneous than the pore architecture and anisotropy of geological materials and therefore somewhat easier to measure and model. However the porosities in biological materials are nested in orderly hierarchical structures, ordered and nested by pore size. To further complicate the life of the analyst all the nested hierarchical pore levels are intertwined, but the pore fluids may only flow to or from a porosity at the next largest or the next smallest pore size; both of these features better serve the biological function. The range of porosities observed in normal bone tissue is much wider than those observed in the usual geological materials. Contributions expected include those associated with recent advances determining the quantitative stereology of bone tissue at the macroscopic (trabecular and cortical bone), mesoscopic (osteon) and microscopic (lacunar-canalicular) levels.
2. The dependence of the physical properties of a porous medium upon pore architecture and anisotropy in bone tissue
The content of this session is expected to be incorporation of the measures of pore architecture and anisotropy into continuum models for the physical properties of the porous medium being considered. Of particular interest will be the advances in the application of Biot poroelasticity theory and experimental measurement of pore hierarchical architecture and anisotropy to better understand bone poromechanics, mechanotransduction and the diseases associated to this porous medium. Again, the emphasis will be on bone tissue, but the extension to geological materials is straightforward.
3. Consequences of the incorporation of microarchitecture measures into quasi-static and dynamic poroelasticity theories
The focus of this session is on the inclusion of microstructural measures in the general theories of quasi-static poroelasticity and dynamic poroelasticity and the application of these theories to obtaining specific results. Studies combining Biot poroelasticity theory, numerical and experimental approaches to better understand both quasi-static and dynamic properties of porous media will be included. Also, the interaction between nested porosities and the frequency dependence of mechanical properties and pore fluid flow in nested porosities will be among the topics covered in this session.