A cellular-meso-macro three-scale approach captures remodelling of cancellous bone in health and disease.

Remodelling of cancellous bone due to the combined activity of osteoclasts and osteoblasts at the cellular scale has notable repercussions both at the meso (tissue) as well as the macro (organ) scale. At the meso scale, trabeculae adapt their geometry, typically in terms of their cross section, whereas the nominal bone density evolves at the macro scale, all in response to habitual mechanical loading and its perturbations. To capture this intricate scale coupling, we here propose a novel conceptual three-scale approach to the remodelling of cancellous bone. Therein, we combine a detailed bone cell population model at the cellular scale with an idealised trabecular truss network model with adaptive cross sections, that are driven by the cell population model, at the meso scale, which is eventually upscaled to a continuum bone density adaption model at the macro scale. Algorithmically, we solve the meso and macro problems concurrently within a finite element setting and update the cell activity in a staggered fashion. Our benchmark simulations demonstrate the applicability and effectivity of the three-scale approach to analyse bone remodelling in health and disease (here exemplified for the example of osteoporosis) with rich details, e.g. evolving anisotropy, resolved at each scale.