The geometric control of bone tissue growth plays a significant role in bone
remodelling, age-related bone loss, and tissue engineering. However, how
exactly geometry influences the behaviour of bone-forming cells remains
elusive. Geometry modulates cell populations collectively through the evolving
space available to the cells, but it may also modulate the individual
behaviours of cells. To factor out the collective influence of geometry and
gain access to the geometric regulation of individual cell behaviours, we
develop a mathematical model of the infilling of cortical bone pores and use it
with available experimental data on cortical infilling rates. Testing different
possible modes of geometric controls of individual cell behaviours consistent
with the experimental data, we find that efficient smoothing of irregular pores
only occurs when cell secretory rate is controlled by porosity rather than
curvature. This porosity control suggests the convergence of a large scale of
intercellular signalling to single bone-forming cells, consistent with that
provided by the osteocyte network in response to mechanical stimulus. After
validating the mathematical model with the histological record of a real
cortical pore infilling, we explore the infilling of a population of randomly
generated initial pore shapes. We find that amongst all the geometric
regulations considered, the collective influence of curvature on cell crowding
is a dominant factor for how fast cortical bone pores infill, and we suggest
that the irregularity of cement lines thereby explains some of the variability
in double labelling data as well as the overall speed of osteon infilling.Comment: 14 pages, 11 figures, Appendi