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.

Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size

“…While the Porous-Fisher model allows proliferation to occur wherever cells occupy space with lower density than the carrying capacity, in effect, geometric control of cell proliferation is concentrated in a region near the tissue interface where there are large density inhomogeneities. The Porous-Fisher model is similar in this respect to the cellular models of surface growth of Refs [24,22,25]. A common feature in these cell-based models is that an influence of local curvature on tissue growth rate is not necessarily indicative of changes in cell-level behaviour.…”

“…An often overlooked factor of the geometric control of tissue growth is the mechanistic influence of tissue crowding or spreading in confined spaces. The progression rate of the tissue interface is determined both by how much new tissue is produced locally, and by the availability of space around where this tissue is produced [24,22,25]. The former is related to cell behaviour, but the latter is a purely geometric influence.…”

“…In contrast, there is more space available to accommodate new tissue in a convex region, so that tissue progression in the normal direction is slower as the new tissue needs to fill space laterally too. When new tissue production is confined in a very narrow band near the tissue interface (a situation called 'surface growth', such as that which occurs during bone formation, and the growth of seashells [47]), the mechanistic influence of space constraints on growth rates lead mathematically to a type of hyperbolic curvature flow in which the normal acceleration of the tissue is proportional to curvature [24,22,25]. In the Porous-Fisher model considered here, proliferation is not strictly confined to the tissue interface.…”

“…It is therefore expected that tissue curvature influences cell proliferation and thus tissue growth. The crowding and spreading of tissue material near concavities and convexities of bone tissue was also found to involve curvaturedependent cell behaviours [22]. Curvature, in turn, is affected by the overall size of a pore: the larger a pore is, the smaller its curvature on average.…”

“…Several mathematical modelling strategies have been developed to explore the interplay between tissue growth and curvature effects [16], such as models based on the idea of mean curvature flow, that borrow ideas from fluid mechanics and the role of surface tension, but that do not consider cells explicitly [11][12][13][14][15]. Other modelling approaches consider the effects of cell-level behaviour and tissue crowding and spreading during surface growth, which lead to hyperbolic curvature flow models [24,22,25].…”