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International Journal of Bioprinting Cell viability in printing structured inks
including computer configuration and computation time. phases are common, and typically, there is a gradient
Free tetrahedral and hexahedral elements were used for distribution of velocity from the center of the pipes to the
meshing the models. The reasons are as follows: due to the walls. Therefore, shear stress at interfaces was considered a
presence of curved boundaries in the fluid models (e.g., crucial parameter for assessing fluid forces in the relevant
as in the case of fluid sudden expansion when the fluid flow domains. Shear stress is calculated as the product of
entered the nozzles) and high-velocity gradients near the the fluid dynamic viscosity and the corresponding velocity
nozzle tips, free tetrahedral meshing was employed in gradient, with shear stress components present in the xy,
these regions to ensure computational accuracy. For other yz, and xz planes. A user-defined function in Fluent was
regions, free hexahedral meshing was employed to reduce employed to calculate shear stress within the interior fluid
computational expenses. as follows :
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2.8. Simulation boundary conditions ∂u ∂ 2 ∂v ∂ 2 ∂u ∂ 2
v
w
w
The simulated boundary conditions were established to τ = µ ∗ ∂y + ∂x + ∂z + ∂y + ∂z + x (III)
replicate the ink flow into the cartridge and its outflow ∂
through the nozzle, as shown in Figure S2 (Supplementary
File). The boundary condition parameters used in the where u, v, and w represent the fluid velocity
investigation are listed in Table S1 (Supplementary File). In components in the x, y, and z directions, while τ and μ
the subsequent simulations, the viscosity values of 3% w/v denote the respective shear stress and dynamic viscosity.
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alginate, respectively combined with two gelatin solutions The CFD-Post package enables the calculations of
of different concentrations, were referenced. We selected pressure and wall shear stress by utilizing its built-in
these combinations due to their demonstrated feasibility in functions. For the actual fluid domains, relevant 3D
extrusion-based 3D co-printing, and we conducted initial bodies corresponding to simplified models were created by
simulations of the extruded fiber distribution in structured applying reflection transformations with chosen mirrored
inks using these combinations. Furthermore, the flow symmetry planes, and then qualitative cloud images can be
velocities of fluid models for the 18G nozzle, as well as displayed. Fluid forces were computed by combining the
the 27G and 32G nozzles, were determined, based on related functions with their respective fluid domains. Then,
flow velocities reported in other studies, 34,38,39 to replicate results for fluid forces were quantified. Fluid domains at
equivalent heterogeneous structures. The inlet velocity was the nozzle were mainly considered, given the higher shear
configured with normal directional conditions, considering rate at these positions.
the fluid extrusion. Both hydrogels for simulation were
assumed to be incompressible. The outlets were connected 2.10. Evaluation of cell viability
40
to the air, and consequently, boundary condition of Sodium alginate and calcium chloride (CaCl ) were
2
pressure outlet was applied. The relative pressure at the purchased from Aladdin Chemical Reagent Co., Ltd.
outlet was set to 0 Pa. The fluid flow was constrained by the (Shanghai, China). Gelatin was sourced from Sinopharm
inner walls of the cartridge and nozzle, and therefore, the Chemical Reagent Co., Ltd. (Shanghai, China). LIVE/
relevant inner walls were indicated as fluid walls, and were DEAD assay reagents were obtained from Solarbio Science
treated as no-slip walls, as the fluid velocity at the walls is & Technology Co., Ltd. (Beijing, China). Deionized water
zero. Symmetry planes were used to replicate the 3D body was used for preparing solutions. Human umbilical vein
by mirroring symmetric 3D models. Before evaluating endothelial cells (HUVECs) were cultured in a medium
the fluid forces generated during the flow of various inks supplemented with 10% fetal bovine serum and 1%
from cartridge inlets to nozzle outlets, the accuracy of the penicillin and 1% streptomycin, and incubated at 37°C
computational results must be ensured. Since these were and 5% CO . The medium was replaced every 2 days, and
2
transient computations, in addition to residual evaluation, cells were passaged every 4 days. Subsequently, a cell-
the temporal evolution of material phase volume fractions, laden bioink comprising 3% w/v sodium alginate and
outlet velocities, and inlet and outlet mass flow rates were 7.5% w/v gelatin was prepared for printing, using methods
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analyzed to verify the attainment of a steady state. referenced from previous research. A cell-free solution
used in structured inks, with the same composition as the
2.9. Measuring procedures post-simulation bioink except for the cells, was also prepared. A 4% w/v
The solution data obtained from Fluent were exported CaCl solution was prepared for crosslinking. To fabricate
2
in cdat format, which was then imported into the CFD- vascular-like fiber structures with inner, middle, and
Post package for measurements of pressure, wall shear outer layer distances in a 2:1:1 ratio, two types of vascular-
stress, and shear stress at material phase interfaces. For like inks were developed using a mold-assisted method
multiphase flows, velocity differences between different combined with casting techniques. One of them had cells
Volume 10 Issue 4 (2024) 244 doi: 10.36922/ijb.2362
