Combining in silico and in vitro models to inform cell seeding strategies in tissue engineering

Abstract

The seeding density of therapeutic cells in engineered tissue impacts both cell survival and vascularization. Excessively high seeded cell densities can result in increased death and thus waste of valuable cells, whereas lower seeded cell densities may not provide sufficient support for the tissue in vivo, reducing efficacy. Additionally, the production of growth factors by therapeutic cells in low oxygen environments offers a way of generating growth factor gradients, which are important for vascularization, but hypoxia can also induce unwanted levels of cell death. This is a complex problem that lends itself to a combination of computational modelling and experimentation. Here, we present a spatio-temporal mathematical model parametrized using in vitro data capable of simulating the interactions between a therapeutic cell population, oxygen concentrations and vascular endothelial growth factor (VEGF) concentrations in engineered tissues. Simulations of collagen nerve repair constructs suggest that specific seeded cell densities and non-uniform spatial distributions of seeded cells could enhance cell survival and the generation of VEGF gradients. These predictions can now be tested using targeted experiments.

Keywords: interdisciplinary; mathematical modelling; nerve; oxygen; tissue engineering.

Figure 1.

The multidisciplinary method presented here involves close integration between theoretical and experimental work through the use of in vitro experiments specifically designed for the purpose of parametrization. Model predictions can be used to test and form new hypotheses and thereby direct the course of future experiments.

Figure 2.

Flow diagram demonstrating the relationships between the variables in the model.

Figure 3.

In vitro 96-well plate schematic showing a single well containing a cell-seeded collagen gel and media (left) and corresponding geometry created in COMSOL (right). Here, the sample oxygen distribution ranges from 10% at the top of the well, according to the applied boundary condition, to 9.6% at the bottom.

Figure 4.

Comparison of simulated mean viable cell density over collagen gel after 24 h and experimental means, plotted against ambient oxygen concentration. Error bars denote the standard deviations of the experimental data subsets used to calculate each of the means. R² values indicate the accuracy of the model fit to data: (a) training dataset and (b) validation dataset.

Figure 5.

Comparison of simulated mean VEGF concentration over media after 24 h and experimental means, plotted against ambient oxygen concentration. Error bars denote the standard deviations of the experimental data subsets used to calculate each of the means. R² values indicate the accuracy of the model fit to data: (a) training dataset and (b) validation dataset.

Figure 6.

Model simulation results demonstrate the potential impact of different seeded cell densities. (a) Mean viable cell density over the construct has a maximum at n₀ = 95 million cells ml⁻¹ (white point). (b) Median viable cell densities decrease with time. (c) Visual demonstration of the increase in viable cell density across the construct at 95 million cells ml⁻¹. Viable cell densities remain predominantly uniform across the construct geometry independent of the initial cell density, with the exception of an increase in viable cell density at the proximal and distal ends, corresponding to higher oxygen concentrations at these locations. (d) Mean VEGF concentration over the construct has a maximum at n₀ = 245 million cells ml⁻¹ (white point). (e) An initial cell density of 170 million cells ml⁻¹ provides a balance of high viable cell density after 24 h, and high VEGF concentrations with a relatively large range after 24 h, suggesting elevated gradients of VEGF. (f) Visual demonstration of the increase in VEGF quantity and range at n₀ = 245 million cells ml⁻¹ in comparison to both lower initial cell densities. This initial seeding cell density results in greater gradients of VEGF, with higher concentrations in the centre, as well as higher overall concentrations over the length of the construct when compared to other seeding cell densities.

Figure 7.

(a) Example of a range of non-uniform initial distributions of seeded cells, where the total number of seeded cells is 50 000. The case where Sc = 1 corresponds to a uniform distribution. (b) The total number of viable cells in a construct after 24 h depends upon the distribution of the initial seeded cells. The optimal distribution for the maximization of the total number of viable cells after 24 h is approximately uniform (Sc = 1) regardless of the total number of cells used. (c) Simulations suggest that the mean VEGF concentration across the construct after 24 h is lower when there are fewer cells seeded in the centre than in the proximal and distal thirds (Sc < 1). For Sc > 1, the maximum VEGF concentration in the construct increases slightly with Sc, but the mean VEGF concentration remains similar to the uniform case, Sc = 1.

Figure 8.

Different seeding cell strategies result in varying (a) cell density, (b) VEGF concentration and (c) oxygen concentration profiles along the length of the NRC geometry at different time points. In particular, non-uniform-seeded cell distributions (Sc = 3) result in more pronounced VEGF gradients in the centre of the constructs than uniform distributions (Sc = 1), although this varies over time and according the total number of cells seeded. Simulations suggest that the impact of the initial seeded cell distribution upon the VEGF and viable cell density distributions after 24 h varies according to the total number of cells seeded. Seeding 500 000 cells uniformly (Sc = 1) generates a steeper VEGF concentration gradient after 24 h than seeding more cells in the centre (Sc = 3); whereas the converse is true, when seeding 100 000 cells.