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 simple 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 pointwise addition and removal of osteocytes significantly affects signalling molecules propagating to the bone surface, which in turn affects the dynamics of bone formation and bone resorption. The explicit consideration of signal propagation through a dynamic network leads to new behaviours compared to previous models, such as partial bone recovery after an unloading and reloading cycle, and a minimum loading threshold below which all bone is resorbed when osteocytes are stimulated by mechanical stress (but not when they are stimulated by the strain energy density). While many extensions of this mathematical model are possible, it provides a first illustration of how the osteocyte network can act as a dynamic embedded control network for bone adaptation to mechanical loads.