Models for remodelling in porous bone reconstructed tissues saturated with interstitial fluids

In [1, 2] mathematical models for describing resorption and synthesis phenomena in reconstructed bone tissues are presented and studied. The presence of interstitial fluids in bone pores was there neglected: only in [3] poro-elastic phenomena were partially taken into account. The present paper is a first step towards a more complete modeling of the complex bio-mechanical phenomena involved in tissue remodeling, which seems to be driven by interstitial fluid flow [4, 5]. It has to be remarked that at least two time scales are of relevance in the considered context: the characteristic time of bone growth and resorption and the characteristic time of varying externally applied loads. In the first approximation which we will consider the second time scale will be assumed to be negligible and mechanical phenomena will be assumed to be quasi-static. [1] T. Lekszycki and F. dell’Isola. A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials. J. Applied Math and Mech. (ZAMM), 92:426–444, 2012. [2] A. Madeo, T. Lekszycki, and F. dell’Isola. A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery. Comptes Rendus Mécanique, 339:625–640, 2011.