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International Journal of Bioprinting A computational model of cell viability and proliferation of 3D-bioprinted constructs

the environmental conditions to which cells are subjected metabolism of cells in 3D environments, especially in the
in bioprinted samples are modeled, as opposed to the plane first days after bioprinting. The maximum cell density is
2D cultures. A cell density of 2 × 10 cells/m was selected important because it provides an asymptote to the value
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3
based on other works found in the literature with similar that cell density can reach and is therefore linked to the
values . The bioink of alginate and gelatin was chosen maximum number of cells observed. The maximum cell
[31]
due to the good properties of gelatin since it promotes density after the optimization process was found to be half
cell viability and proliferation, combined with alginate to of the assumed one. In the original setting, cell density
obtain better printability properties. Similar combinations increases until the last day of observation, whereas in the
of alginate and gelatin are found in other works [32,33] . The optimized setting, the increase of cell density is limited by
initial value of cell density of day 1 measured was lower this parameter. The Monod constants have some limited
than the nominal one, which was set to 2 × 10 cells/m . effects on the outcome of the model. When comparing
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The causes of such cell loss are not completely clear. It their values in the original and optimized configurations,
could be partially due to the rate of death during the they are found within the same ranges. Given these results,
printing phase, where cells are subjected to high shear the growth rate and the maximum cell density need to be
stresses. Besides, many intermediate steps take place before chosen accurately.
the printing stage is reached; therefore, cell loss is plausible. The parameters of the model are influenced by many
The first days of culture did not result in substantial cell factors. In fact, different cells have a different growth rate,
proliferation, which is possibly due to damage to cells of which also depends on the environmental conditions, such
extrusion-based bioprinting or due to a lag time to find as 2D versus 3D culture, bioink formulation, and stiffness
attachment sites. A decrease of cell concentration was of the material. The surface occupied by cells and thus the
reported by Sarker et al. , who observed this reduction maximum cell concentration also changes according to
[34]
when RGD attachment sites of gelatin are released over the cell type. Therefore, when using a numerical model of the
incubation time, pointing out the issue of cell attachment type developed in this study, one must invest some effort
in 3D matrices. Cell density then shows a steep increase in defining the proper values of growth rate and maximum
up to day 4 and consequent stabilization up to day 7. The cell density. Other printing sessions will follow, in order
model, provided with input parameters corresponding to explore different conditions and assess the predictive
to the experimental conditions, predicts a monotonic capability of the model.
increase in cell density over time. The mismatch between
the experimental and numerical outcomes consists A further step was made with the simulation of a
primarily in the observation of a plateau in the experiment plausible bioprinting experiment. We were interested in
versus a continuous cell growth in the simulation. Since understanding the phenomena of nutrient diffusion and
the input parameters taken from the literature do not consumption that lead to impaired cell proliferation far
assume specific values but are found within wide ranges from vascular channels. For this reason, small samples
and display uncertainty in their measurement, a parameter in a size range of 1.5–4.5 mm were analyzed. Bioprinted
optimization step was introduced. In particular, the growth constructs made of alginate embedded with MSCs were
rate, the death rate, and the maximum number of cells modeled. MSCs represent one of the most eligible cell
turned out to be lower than were assumed. The model does types for bioprinting, since they can be differentiated
not include the aspects of cell damage and cell attachment, into other cell types by applying specific stimuli. A future
which we believe to be the reason why the horizontal perspective of bioprinting is in fact to regenerate patients’
pattern between day 1 and day 2 is not met by the model. injured tissues by using their own stem cells. Alginate
Yet, when correctly calibrating the model parameters, a was chosen due to its high versatility and good printing
much more similar pattern is found. properties. One of the main implications of bioprinting is
the possibility to create constructs with high cell density.
Moreover, the parameters affecting the outcome of For this reason, a cell density of 1.1 × 10 cells/m was
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the model the most were identified through a sensitivity considered, as also suggested by bioprinting protocols .
[30]
analysis step. The growth rate and the maximum cell density Constructs of different sizes were modeled. Different
were observed as the most important ones; therefore, they sizes of the constructs resulted in different distributions
need to be chosen accurately. The growth rate being one of nutrients and cells within the constructs. Areas with
g
of the most important parameters is reasonable since it oxygen concentration lower than K are associated with
O2
appears in the mass balance equation and affects the change areas where cell density does not increase. Moreover,
in cell density directly. The optimized value of the growth in areas where oxygen concentration is even lower than
m
rate was found to be half the one found in the literature. K , cell density starts to decrease abruptly, and cell death
O2
This is consistent with the assumption of decreased occurs, leading to a necrotic region. This proves that oxygen
Volume 9 Issue 4 (2023) 363 https://doi.org/10.18063/ijb.741