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Bone is a biomaterial undergoing continuous renewal. The renewal process isknown as bone remodelling and is operated by bone-resorbing cells (osteoclasts)and bone-forming cells (osteoblasts). Both biochemical and biomechanicalregulatory mechanisms have been identified in the interaction betweenosteoclasts and osteoblasts. Here we focus on an additional and poorlyunderstood potential regulatory mechanism of bone cells, that involves themorphology of the microstructure of bone. Bone cells can only remove andreplace bone at a bone surface. However, the microscopic availability of bonesurface depends in turn on the ever-changing bone microstructure. Theimportance of this geometrical dependence is unknown and difficult to quantifyexperimentally. Therefore, we develop a sophisticated mathematical model ofbone cell interactions that takes into account biochemical, biomechanical andgeometrical regulations. We then investigate numerically the influence of bonesurface availability in bone remodelling within a representative bone tissuesample. The interdependence between the bone cells' activity, which modifiesthe bone microstructure, and changes in the microscopic bone surfaceavailability, which in turn influences bone cell development and activity, isimplemented using a remarkable experimental relationship between bone specificsurface and bone porosity. Our model suggests that geometrical regulation ofthe activation of new remodelling events could have a significant effect onbone porosity and bone stiffness. On the other hand, geometrical regulation oflate stages of osteoblast and osteoclast differentiation seems lesssignificant. We conclude that the development of osteoporosis is probablyaccelerated by this geometrical regulation in cortical bone, but probablyslowed down in trabecular bone.

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