A Porous Media Model for the Description of Adaptive Bone Remodelling

Abstract

AbstractBones are strong and lightweight structures, which mainly consist of extracellular bone matrix. The bone remodelling is a process of resorption followed by replacement of the bone matrix with small changes in shape, which allow the bones to adapt according to the local loading situation.In the context of the Theory of Porous Media (TPM), a consistent model of bone tissue is introduced, which is able to describe the local accretion and reduction of the extracellular bone matrix. To this end, the bone is treated as an aggregate of two immiscible constituents. In this biphasic macroscopic model, the aggregate consists of the extracellular bone matrix and cells summarised to a solid phase and an interstitial fluid phase comprising nutrients, metabolites and bone precursors. The addition and removal of bone matrix is described by a mass exchange between the constituents, which depends upon the local strain of the material. Additionally, the growth energy is introduced as a non‐mechanical quantity, which measures the average amount of chemical energy available for cell metabolism [1, 2], and thus, controls the growth process. The presented numerical example illustrates the fundamental effects of bone remodelling under varying boundary conditions. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)