Poroelastic Models of Bone Tissue

Stephen C. Cowin

Biomedical and Mechanical Engineering

City College of the City University of New York

            This contribution is a review of the application of poroelasticity theory to the modeling of the mechanical behavior of bone fluid in living bone tissue. The models reviewed, while seeking to present an accurate representation of the porous architecture of bone tissue, extend classical Biot theory in two distinct new directions associated with the more precise modeling of material microstructure. The first new direction is to nested porosities. The applications of poroelasticity to fluid movement in biological tissues have transferred to tissues the models of the pore structure employed in geomechanics. Existing theories of the poroelasticity of materials with multiple connected porosities with different characteristic sizes and therefore different permeabilities do not address the case of nested porosities. These existing theories are appropriate for their intended use, fractured porous geological structures, but they are not appropriate for the biological tissues of interest; the nested porosities in biological tissue are hierarchical based on the average diameters of their fluid transport channels while the multiple porosity poroelasticity theories for fractured geological structures are democratic; their fluid transport channels of a particular size may exchange fluid with transport channels of any pore size. A model of a poroelastic pore structure appropriate for bone tissue is described; it is a model that is easily extended to other tissues such as the tendon and the meniscus. The second new direction is the use of a fabric tensor to characterize cancellous bone architecture. Fabric is a quantitative stereological measure of the anisotropy of the structure of the pores in the porous medium and is a concept that originated with geologists.

References

Cowin, S. C. (1999). Bone Poroelasticity. J. Biomechanics 32, 218-238

Cowin SC, Doty, SB. (2007). Tissue Mechanics. Springer

Cowin SC, Mehrabadi MM. (2007). Compressible and incompressible constituents in anisotropic poroelasticity: The problem of unconfined compression of a disk. J. Mech. Phys. Solids, 55:161-193

Cowin, S. C., Gailani, G. and Benalla, M. (2009), Hierarchical Poroelasticity: Movement of interstitial fluid between porosity levels in bones, Phil. Trans. Roy. Soc. A, in press