A mathematical multiscale model of bone remodeling, accounting for pore space-specific mechanosensation.

ABSTRACT

While bone tissue is a hierarchically organized material, mathematical formulations of bone remodeling are often defined on the level of a millimeter-sized representative volume element (RVE), "smeared" over all types of bone microstructures seen at lower observation scales. Thus, there is no explicit consideration of the fact that the biological cells and biochemical factors driving bone remodeling are actually located in differently sized pore spaces active osteoblasts and osteoclasts can be found in the vascular pores, whereas the lacunar pores host osteocytes - bone cells originating from former osteoblasts which were then "buried" in newly deposited extracellular bone matrix. We here propose a mathematical description which considers size and shape of the pore spaces where the biological and biochemical events take place. In particular, a previously published systems biology formulation, accounting for biochemical regulatory mechanisms such as the rank-rankl-opg pathway, is cast into a multiscale framework coupled to a poromicromechanical model. The latter gives access to the vascular and lacunar pore pressures arising from macroscopic loading. Extensive experimental data on the biological consequences of this loading strongly suggest that the aforementioned pore pressures, together with the loading frequency, are essential drivers of bone remodeling. The novel approach presented here allows for satisfactory simulation of the evolution of bone tissue under various loading conditions, and for different species; including scenarios such as mechanical dis- and overuse of murine and human bone, or in osteocyte-free bone.