A mathematical model of osteocyte network control of bone mechanical adaptation.

The osteocyte network embedded in bone tissues plays a central role in the control of bone adaptation to mechanical loads and micro-damage repair. However, much remains to be understood about the precise mechanisms by which the osteocyte network regulates bone formation and bone resorption based on the propagation of biochemical signals emitted in response to mechanical stimulus. In this work, we propose a one-dimensional computational model of bone mechanical adaptation based on the propagation of signalling molecules through a dynamic osteocyte network. The osteocyte network is extended during bone formation and reduced during bone resorption, which affects the generation and propagation of the signalling molecules to the bone surface. We explore how this osteocyte-based model of bone mechanosensation and mechanoresponse gives rise to effective Wolff's laws, in which overloaded bone is consolidated and underloaded bone is removed. We find that the discrete addition and removal of osteocytes significantly affects signalling molecules propagating to the bone surface and leads to new bone adaptation behaviours compared to earlier models, including partial bone recovery following an unloading and reloading cycle and the emergence of a minimum threshold of mechanical stress below which all bone is resorbed. While many extensions of this mathematical model are possible, it provides a first illustration of how the osteocyte network could act as a dynamic embedded control network for bone adaptation to mechanical loads.