Predicting Bone Formation in Mesenchymal Stromal Cell-Seeded Hydrogels Using Experiment-Based Mathematical Modeling

In vitro bone formation by mesenchymal stromal cells encapsulated in type-1 collagen hydrogels is demonstrated after a 28-day in vitro culture period. Analysis of the hydrogels is carried out by X-ray microcomputed tomography, histology, and immunohistochemistry, which collectively demonstrates that bone formation in the hydrogels was quantifiably proportional to the initial collagen concentration, and subsequently the population density of seeded cells. This was established by varying the initial collagen concentration at a constant cell seeding density (3 × 10⁵ cells/0.3 mL hydrogel), and separately varying cell seeding density at a constant collagen concentration (1 mg/mL). Using these data, a mathematical model is presented for the total hydrogel volume and mineralization volume based on the observed linear contraction dynamics of cell-seeded collagen gels. The model parameters are fitted by comparing the predictions of the mathematical model for the hydrogel and mineralized volumes on day 28 with the experimental data. The model is then used to predict the hydrogel and mineralization volumes for a range of hydrogel collagen concentrations and cell seeding densities, providing comprehensive input/output descriptors for generating mineralized hydrogels for bone tissue engineering. It is proposed that this quantitative approach will be a useful tool for generating in vitro manufactured bone tissue, defining input parameters that yield predictable output measures of tissue maturation. Impact statement This article describes a simple yet powerful quantitative description of in vitro tissue-engineered bone by combining experimental data with mathematical modeling. The overall aim of the article is to examine what is currently known about cell-mediated collagen contraction, and demonstrate that this phenomenon can be exploited to tailor bone formation by choosing a specific set of input parameters in the form of cell seeding density and collagen hydrogel concentration. Our study utilizes a clinically relevant cell source (human mesenchymal stem cells) with a biomaterial that has received regulatory approval for use in humans (collagen type 1), and hence could be useful for clinical applications, as well as furthering our understanding of cell/extracellular matrix interactions in determining in vitro bone tissue formation.