Osteoblasts infill irregular pores under curvature and porosity controls: a hypothesis-testing analysis of cell behaviours

Abstract

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.

Appendix: Influence of initial porosity on average infilling rate

Figure 10 shows simulations of the infilling of random pore 8 of Fig. 7 scaled down by $70\%$ and scaled up by $130\%$, performed with Model 3 and $D = 0.00075 ~\text {mm}^2 /\text {day}$. The corresponding plot of the average interface velocity versus the average pore radius is shown in Fig. 11.

Fig. 11

Comparison of the average interface velocity versus the average pore radius between different scales of random pore 8 (solid lines) and experimental data (black squares)