The influence of bone surface availability in bone remodelling—A mathematical model including coupled geometrical and biomechanical regulations of bone cells

Abstract

Bone is a biomaterial undergoing continuous renewal. The renewal process is known as bone remodelling and is operated by bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts). An important function of bone remodelling is the repair of microcracks accumulating in the bone matrix due to mechanical loading. Cell–cell communication between cells of the osteoclastic lineage and cells of the osteoblastic lineage is thought to couple resorption and formation so as to preserve bone integrity and achieve homeostatic bone renewal. Both biochemical and biomechanical regulatory mechanisms have been identified in this coupling. Many bone pathologies are associated with an alteration of bone cell interactions and a consequent disruption of bone homeostasis. In osteoporosis, for example, this disruption leads to long-term bone loss and increased fragility, and can ultimately result in fractures.Here we focus on an additional and poorly understood potential regulatory mechanism of bone cells, that involves the morphology of the microstructure of bone. Bone cells can only remove and replace bone at a bone surface. However, the microscopic availability of bone surface depends in turn on the ever-changing bone microstructure. The importance of this geometrical dependence is unknown and difficult to quantify experimentally. Therefore, we develop a sophisticated mathematical model of bone cell interactions that takes into account biochemical, biomechanical and geometrical regulations. We then investigate numerically the influence of bone surface availability in bone remodelling within a representative bone tissue sample. Biochemical regulations included in the model involve signalling molecules of the receptor–activator nuclear factor κB pathway (rank–rankl–opg), macrophage colony-stimulating factor (mcsf), transforming growth factor β(tgfβ), and parathyroid hormone (pth). For the biomechanical regulation of bone cells, a multiscale homogenisation scheme is used to determine the microscopic strains generated at the level of the extravascular matrix hosting the osteocytes by macroscopic loading. The interdependence between the bone cells’ activity, which modifies the bone microstructure, and changes in the microscopic bone surface availability, which in turn influences bone cell development and activity, is implemented using a remarkable experimental relationship between bone specific surface and bone porosity. Our model suggests that geometrical regulation of the activation of new remodelling events could have a significant effect on bone porosity and bone stiffness in osteoporosis. On the other hand, geometrical regulation of late stages of osteoblast and osteoclast differentiation seems less significant. We conclude that the development of osteoporosis is probably accelerated by this geometrical regulation in cortical bone, but probably slowed down in trabecular bone.