Page 444 - IJB-9-5

International Journal of Bioprinting Core-shell bioarchitectures

Figure 2. (A) Selected material combinations for the experimental CSCs characterization. The condition tested in the presence of cells is highlighted in
blue. (B) Schematic of the cellular models investigated as a preliminary proof of concept.

D (Equation II) was introduced to couple reaction– A time-dependent study (see Section S4 in
app
diffusion and crosslinking phenomena: Supplementary File for more details on the numerical
algorithm adopted) was used to consider different
D abD 0 (II) crosslinking times and obtain the concentrations of un-
t
app
where: crosslinked and crosslinked alginate gel and calcium ions
kT diffusing within the structure. The final core radius after
D b (III) the crosslinking process (R , VI) was derived as the radius
6 R H corresponding to C for which α is below α*.
0
c
n gel

t
*
r
e 1 R = | (VI)
a 1 (IV) c αα *
1
<
n Finally, the shell thickness was computed as the difference
e * 1 between the R (estimated from drop formation theory) and
s
1 1 the R . These results were used to define the experimental
R 2 2 1 R 2 c

b 1 H H (V) working window on the basis of crosslinking times,

t 3
t material properties, and extrusion parameters.

2.2. Experimental fabrication and characterization
D (Equation III) represents the value of the free diffusion of the CSCs
0
coefficient, controlled by the size of the macromolecule The in silico results were used to identify the material
as described by the Einstein–Stokes equation, where k is and extrusion conditions (reported in Figure 2A), which
b
Boltzmann’s constant, T the temperature in Kelvin, m the guarantee an optimal structure in terms of distinction of
solvent viscosity, and R is the hydrodynamic radius. a core and shell and roundness. All solutions were prepared
H
(Equation IV) represents the time-dependent coefficient in deionized water. In particular, alginate (A0682, average
that considers the effect of the degree of gelation α, defined molecular weight 12–80 kDa, R 200 nm, Sigma Aldrich)
as the ratio between the calcium- and time-dependent was mixed with 1:100 w/w fluorescein isothiocyanate
h
concentration of crosslinked alginate and the initial (FITC)-alginate (Creative PEGWorks) to improve the
concentration of free alginate [30,31] and b (Equation V) is distinction between core and shell for image analysis.
the Brinkmann coefficient which considers the influence
of hindered diffusion in the spherical gel structure . κ(α) The CSCs were fabricated with COSMIC, a bioprinter
[32]
represents the permeability of the structure as a function with an aluminum stand (height = 47 cm, width = 25 cm)
of α. Section S3 (Supplementary File) details how b and housing two stepper motors that actuate two syringes
κ were estimated on the basis of the Brinkmann and connected to a coaxial needle. In this study, we used
Carman–Kozeny equations . The values for α* (gelation two commercial coaxial needles (Ramé-hart Instrument
[32]
value corresponding to the liquid-like to solid-like Co., USA): needle 1 with an inner diameter = 26 Gauge
transition), δ (diffusion coefficient ratio before and after (0.254 mm) and an outer diameter = 19 Gauge (0.69 mm),
the crosslinking process), n (model parameter governing and needle 2 with the same inner diameter and an outer
the rate of diffusivity change ) and R were adapted diameter = 16 Gauge (1.19 mm). Support elements for
[31]
H
from the literature and optimized on the basis of the motors, syringes, and needle were printed in acrylonitrile
experimental results performing least-square minimization butadiene styrene (Stratasys Fortus 250mc, USA). A 0.1 M
(see Section S3 and Table S6 in Supplementary File). calcium chloride bath was placed at a fixed distance (30 cm)
Volume 9 Issue 5 (2023) 436 https://doi.org/10.18063/ijb.771