Remodelling Processes in Bones: A Biphasic Porous Media Model



In the context of the Theory of Porous Media (TPM), a continuum-mechanical model is introduced to describe the complex fluid-structure interaction in bone tissue on the macro-scale. The tissue is treated as an aggregate of two immiscible constituents, where the cells and the bone matrix are summarised to the solid phase, and the fluid phase summarises the extracellular fluids and their components. The remodelling process is described on the macro-scale by a distinct mass exchange that also causes a change of the constituents' material properties. In addition to the mechanical description, systems-biological control mechanisms are included into the model by evaluating a systems-biological cell interaction model at every integration point of the spatially discretised domain.

Here, an integrative solution strategy is presented for this combined mechanical and systems-biological problem. Therein, the mechanical problem is treated using the Finite-Element Method (FEM), where the systems-biological problem is solved locally on integration point level in the sense of a collocation method. To reveal the whole capability of this approach, a 3-dimensional numerical example of the remodelling process in the upper human femur under physiological loading conditions is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)