Page 366 - IJB-9-4

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

specific for fibroblasts. Oxygen concentration was taken
from McMurtrey . Glucose concentration was taken
[10]
from the data sheet of DMEM, a basic culture medium
commonly used for several cell types, according to the
product catalog . The proliferation rate G was calculated
[25]
based on the exponential cell growth phenomenon,
considering a duplication time of 24 h. A similar approach
was used by Higuera et al. . The death rate H was set in
[20]
order to observe a decrease in cell viability of 90% after
14 days in a hypoxic environment, as considered by Niu
et al. . The maximum cell concentration was imposed
[27]
by considering that a high percentage of the volume of
the bioprinted construct should be occupied by cells
after proliferation. The Michaelis–Menten and Monod
Figure 1. 3X construct modified with nine channels with each having a constants were taken from the literature. The initial values
diameter of 0.4 mm.
of oxygen and glucose concentration were set to zero to
Table 3. Input parameters of the model to simulate the account for the usage of gas and nutrients by cells during
bioprinting applicationa the printing. The initial condition for cell density is given
by the initial concentration of cells inserted into the
Parameter Value Ref bioink. Initial conditions of oxygen and glucose are set to
2
-1
-9
D O2 10 [m ∙ s ] [10] zero, by assuming that cells would consume the available
2
D gl 10 -10 [m ∙ s ] [10] nutrients during the printing phase, while embedded in
-1
m m 2 × 10 -17 [mol ∙ cell ∙ s ] [10] the bioink. The simulations account for 8 days of culture
-1
-1
O2
m m 3.5 × 10 -17 [mol ∙ cell ∙ s ] [10] of the extrusion-bioprinted constructs immersed in fresh
-1
-1
gl culture medium.
m g 3.8 × 10 -17 [mol ∙ cell ∙ s ] [10]
-1
-1
O2
m g gl 1.4 × 10 -16 [mol ∙ cell ∙ s ] [10] 2.5. Statistical analysis
-1
-1
-3
ϕ O2 OUT 0.2 [mol ∙ m ] [10] Raw data of cell concentration resulting from the
ϕ OUT 25 [mol ∙ m ] [10] experimental tests were analyzed in Microsoft Excel. For
-3
gl each bioprinted sample, the cell concentration was obtained
G 6.94 × 10 [s ] [20] by computing the average of the cell concentration values
-6
-1
H 1.9 × 10 [s ] [27] over the 7 layers along the Z direction. For each time point,
-1
-6
ρ 8.8 × 10 [cell ∙ m ] Imposed
13
-3
max the average cell concentration was obtained by computing
-3
K m O2 10 [mol ∙ m ] [24] the average of the three samples.
-3
K m gl 10 [mol ∙ m ] [28]
-3
-1
K g 10 [mol ∙ m ] Imposed 3. Results
-3
-2
O2
K g 10 [mol ∙ m ] [20] 3.1. Experimental validation
0
-3
gl
K 10 [mol ∙ m ] [29] In the following sections, the results of the bioprinting
-4
-3
d
ϕ in O2 0 [mol ∙ m ] Imposed experiment and volume-averaged model validation
-3
ϕ in gl 0 [mol ∙ m ] Imposed are described. Cell concentration over time within the
-3
bioprinted samples was investigated, and the results are
12
-3
ρ 11 × 10 [cell ∙ m ] [30]
in shown in Figure 4A. Each point represents the average cell
concentration of three samples. At day 1, cell concentration
1.1 × 10 cells/m , as suggested by bioprinting protocols . amounted to 1.89414 × 10 cells/m . Cell concentration
13
[30]
3
3
11
The input parameters are summarized in Table 3. The increased rapidly up to day 4, when it reached a value of
diffusivity coefficients for oxygen and glucose in alginate 2.311809 × 10 cells/m . At day 7, cell concentration was
3
12
hydrogel and the oxygen and glucose consumption rates 2.215761 × 10 cells/m .
3
12
by MSCs were taken from McMurtrey . Boundary
[10]
conditions of oxygen and glucose are set according to 3.2. Cell viability from volume-averaged model
their oxygen and glucose concentrations found in the An example of bioprinted specimen and cell imaging are
culture medium in which the bioprinted constructs shown in Figures 2 and 3. In Figure 4B, the results of the
are immersed after being printed. The culture medium volume-averaged numerical model in terms of cell density
consists of a basal medium embedded with supplements as a function of time are shown, when the experimental
Volume 9 Issue 4 (2023) 358 https://doi.org/10.18063/ijb.741