Page 446 - IJB-9-5

International Journal of Bioprinting Core-shell bioarchitectures

Figure 3. In silico results. (A) Predicted average degree of gelation (α) as a function of shell alginate viscosity (for 1 mg/mL Pluronic in the core) after
2+
2+
15 min in Ca medium crosslinking. (B) Predicted average α as a function of core Pluronic concentration after 15 min in Ca crosslinking (*p < 0.05).
(C) Computational simulation of alginate shell formation as a function of crosslinking time (for 20 mg/mL alginate in the shell and 1 mg/mL Pluronic in
the core). (D) Comparison of experimental shell thickness (black dotted line) and computational values, for the same condition in C, estimated with (blue
line) and without (orange line) accounting for the Brinkman coefficient b.
3. Results crosslinking time for all the experiments. As an example,
for the condition shown in Figure 3C, the average
3.1. In silico results alginate concentration in the shell (C ) = 0.47 mol/m ,
3
The reaction diffusion models show that the degree of corresponding to α = 0.68 (see Section S5 in Supplementary
gel
gelation in the shell (α) increases as a function of alginate File).
viscosity (and hence concentration), up to a viscosity
corresponding to that of 20 mg/mL alginate. After this In addition, our computations showed that after
point, α decreases with increasing alginate viscosity 15 min under the crosslinking process, the Ca diffusion
2+
because Ca ion diffusion is inhibited (Figure 3A). time within the alginate network is lower than that of un-
2+
[36]
Moreover, Figure 3B shows that the presence of Pluronic in crosslinked alginate and Pluronic (see Section S3 and
the core significantly increases α (0.63 ± 0.06 for 1 mg/mL Table S5 in Supplementary File). This suggests that alginate
Pluronic, 0.71 ± 0.03 for 10 mg/mL Pluronic) with respect crosslinking occurs before core and shell material become
to a water core (0.4 ± 0.03, p < 0.05). However, no significant a continuum and thus the bead structure is conserved.
differences in the degree of gelation were observed
between the two Pluronic concentrations investigated. A Finally, Figure 3D shows that the shell thicknesses
crosslinking degree of α = 0.6 corresponding to complete estimated considering the hindered diffusion were
alginate gelation at the end of the crosslinking kinetics more similar to the experimental data with respect to
in the alginate shell occurred within 15 min in all the the computational data derived without considering
conditions [30,31] . Thus, this time was selected as optimal Brinkmann’s coefficient b. This demonstrates that the

Volume 9 Issue 5 (2023) 438 https://doi.org/10.18063/ijb.771