Model-based data analysis of tissue growth in thin 3D printed scaffolds
Tissue growth in three-dimensional (3D) printed scaffolds enables exploration and control of cell behaviour in biologically realistic geometries. Cell proliferation and migration in these experiments have yet to be explicitly characterised, limiting the ability of experimentalists to determine the effects of various experimental conditions, such as scaffold geometry, on cell behaviour. We consider tissue growth by osteoblastic cells in melt electro-written scaffolds that comprise thin square pores with sizes that we deliberately vary. We collect highly detailed temporal measurements of the average cell density, tissue coverage, and tissue geometry. To quantify tissue growth in terms of the underlying cell proliferation and migration processes, we introduce and calibrate a mechanistic mathematical model based on the Porous-Fisher reaction-diffusion equation. Parameter estimates and uncertainty quantification through profile likelihood analysis reveal consistency in the rate of cell proliferation and steady-state cell density between pore sizes. This analysis also serves as an important model verification tool: while the use of reaction-diffusion models in biology is widespread, the appropriateness of these models to describe tissue growth in 3D scaffolds has yet to be explored. We find that the Porous-Fisher model is able to capture features relating to the cell density and tissue coverage, but is not able to capture geometric features relating to the circularity of the tissue interface. Our analysis identifies two distinct stages of tissue growth, suggests several areas for model refinement, and provides guidance for future experimental work that explores tissue growth in 3D printed scaffolds. Author SummaryAdvances in 3D printing technology have led to cell culture experiments that realistically capture natural biological environments. Despite the necessity of quantifying cell behaviour with parameters that can be compared between experiments, many existing mathematical models of tissue growth in these experiments neglect information relating to population size. We consider tissue growth by cells on 3D printed scaffolds that comprise square pores of various sizes in this work. We apply a relatively simple mathematical model based on the Porous-Fisher reaction-diffusion equation to interpret highly detailed measurements relating to both the cell density and the quantity of tissue deposited. We analyse the efficacy of such a model in capturing cell behaviour seen in the experiments and quantify cell behaviour in terms of parameters that carry a biologically meaningful interpretation. Our analysis identifies important areas for model refinement and provides guidance for future data-collection and experimentation that explores tissue growth in 3D printed scaffolds.