Theoretical analysis of the spatio-temporal structure of bone multicellular units

Bone multicellular units (BMUs) maintain the viability of the skeletal tissue by coordinating locally the sequence of bone resorption and bone formation performed by cells of the osteoclastic and osteoblastic lineage. Understanding the emergence and the net bone balance of such structured microsystems out of the complex network of biochemical interactions between bone cells is fundamental for many bone-related diseases and the evaluation of fracture risk. Based on current experimental knowledge, we propose a spatio-temporal continuum model describing the interactions of osteoblastic and osteoclastic cells. We show that this model admits travelling-wave-like solutions with well-confined cell profiles upon specifying external conditions mimicking the environment encountered in cortical bone remodelling. The shapes of the various cell concentration profiles within this travelling structure are intrinsically linked to the parameters of the model such as differentiation, proliferation, and apoptosis rates of bone cells. The internal structure of BMUs is reproduced, allowing for experimental calibration. The spatial distribution of the key regulatory factors can also be exhibited, which in diseased states could give hints as to the biochemical agent most accountable for the disorder.