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

Abstract

Tissue growth in bioscaffolds can be influenced significantly by pore geometry, but how this geometric dependence emerges from dynamic cellular processes such as cell proliferation and cell migration remains poorly understood. Here we investigate the influence of pore size on the time required to bridge pores in a 3D printed scaffold by analysing experiments with a mathematical model. Experimentally, the new tissue infills the pore continually from the pore perimeter under strong curvature control, which leads to rounding off of the initial pore shape. Despite the varied shapes assumed by the tissue during this evolution, we find that time to bridge the pore simply increases linearly with the overall pore size. To disentangle the biological influence of cell behaviour and the mechanistic influence of geometry in this experimental observation, we propose a simple reaction-diffusion model of tissue growth based on Porous-Fisher invasion of cells into the pores. First, this model provides a good qualitative representation of the evolution of the tissue; new cellular tissue in the model grows at a rate that depends on the local curvature of the tissue substrate. Second, the model suggests that a linear dependence of bridging time with pore size arises due to geometric reasons alone, not to differences in cell behaviours across pores of different sizes. Our analysis therefore suggests that tissue growth dynamics in these experimental constructs is dominated by mechanistic cell proliferation and cell diffusion processes. The rates of these processes are unaffected by pore geometry, and can be predicted by simple reaction-diffusion models of cells that have robust, consistent behaviours.

Porous Geometry Guided Micro-mechanical Environment Within Scaffolds for Cell Mechanobiology Study in Bone Tissue Engineering

“…Whereas after fitting these constants to experimental results these equations thus may well describe the effect of changes made within that specific experiment, they may not well describe the outcome of other experiments. To reduce the number of parameters in the tissue growth model, recent computational studies have employed second order diffusion equations to model tissue growth kinetics ( Buenzli et al, 2020 ; Zhao et al, 2020a ). The main advantage of using this diffusion equations over the LS method is that fewer parameters need to be determined.…”

“…The main advantage of using this diffusion equations over the LS method is that fewer parameters need to be determined. For example, diffusion equations can already model the curvature – dependent tissue growth without adding the curvature parameter κ in the equation as that in LS method ( Buenzli et al, 2020 ). Therefore, in modelling the scaffold pore geometry for tissue growth kinetics, if the curvature is not a parameter that needs to be explicitly assessed, a computational model based on a diffusion equation will be a good choice.…”