  The formation of new bone involves both the deposition of bone matrix, and
the formation of a network of cells embedded within the bone matrix, called
osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that
become buried in bone matrix during bone deposition. The generation of
osteocytes is a complex process that remains incompletely understood. Whilst
osteoblast burial determines the density of osteocytes, the expanding network
of osteocytes regulates in turn osteoblast activity and osteoblast burial. In
this paper, a spatiotemporal continuous model is proposed to investigate the
osteoblast-to-osteocyte transition. The aims of the model are (i) to link
dynamic properties of osteocyte generation with properties of the osteocyte
network imprinted in bone, and (ii) to investigate Marotti's hypothesis that
osteocytes prompt the burial of osteoblasts when they become covered with
sufficient bone matrix. Osteocyte density is assumed in the model to be
generated at the moving bone surface by a combination of osteoblast density,
matrix secretory rate, rate of entrapment, and curvature of the bone substrate,
but is found to be determined solely by the ratio of the instantaneous burial
rate and matrix secretory rate. Osteocyte density does not explicitly depend on
osteoblast density nor curvature. Osteocyte apoptosis is also included to
distinguish between the density of osteocyte lacuna and the density of live
osteocytes. Experimental measurements of osteocyte lacuna densities are used to
estimate the rate of burial of osteoblasts in bone matrix. These results
suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the
control of osteoblast burial by osteocytes is likely to emanate as a collective
signal from a large group of osteocytes, rather than from the osteocytes
closest to the bone deposition front.
