Page 260 - IJB-10-4

International Journal of Bioprinting Cell viability in printing structured inks

to 6.726e+0, 5.183e+0 Pa to 5.336e+0 Pa, and 1.663e+0 Pa The essence of the equivalent analysis is that the fluid
to 1.886e+0 Pa, respectively. Like vascular-like inks, both forces experienced by cells are identical in homogeneous
the maximum shear stresses at the nozzle wall and at the inks and corresponding structured inks. Firstly, we
material phase interfaces display noticeable differences. evaluated the maximum shear stress of homogeneous inks
Whether for vascular-like inks or hepatic lobule with varying viscosity and density for equivalent analysis.
analogue-like inks, pressure and shear stress exhibit similar Figure 10 illustrates the shear stress of homogeneous
trends based on the corresponding geometric parameters inks with varying viscosity and density, with the
of the respective structured inks. For pressure, this trend representative contour of shear stress shown in Figure
is speculated to be attributed to large nozzle volumes S16 (Supplementary File). As illustrated in Figure 10A,
associated with averaging and the constant inlet mass flow maintaining constant viscosity while increasing density
rate corresponding to average and maximum pressures, from 1030 kg/m³ to 1110 kg/m³ resulted in an almost
respectively. For average shear stress, the trend is believed unchanged maximum wall shear stress. For example, at
to be linked to large wall and interface areas corresponding viscosities of 3.23 Pa·s and 3.64 Pa·s, the maximum shear
to averaging. As for maximum shear stress, one plausible stress remained in the range of 1.733e+2 Pa to 1.734e+2
explanation is that the design parameters of the structured Pa and 1.953e+2 Pa to 1.954e+2 Pa, respectively. The
inks influence the distribution of the material phase at the impact of density on maximum shear stress was minimal,
outlet, where velocity changes dramatically. possibly due to the narrow density variation range (close
to 1000 kg/m³), resulting in a constant maximum velocity
The structured inks with two-phase materials were gradient at the outlet. Conversely, when density was held
chosen as case samples for the ensuing equivalent analysis. constant and viscosity increased from 3.23 Pa·s to 3.64
The viscosity and density of the homogeneous inks Pa·s, the maximum shear stress rose. This increase is
between the corresponding properties of the two-phase explained by Equation III, indicating that, with a constant
materials were investigated. In the equivalent analysis, velocity gradient, shear stress rises with an increase in
theoretically, equivalent fluid forces (including average viscosity. The relationship between viscosity and the
pressure, maximum pressure, average shear stress, and maximum shear stress of homogeneous inks is depicted in
maximum shear stress) were required to fall within the Figure S17A (Supplementary File), with an r-value of 1,
respective ranges of fluid forces experienced by cells in signifying a positive correlation between maximum shear
structured inks. The average and maximum pressures stress and viscosity, as shown in Equation IV. Following the
exhibited minimal fluctuations under different structured determination of the maximum shear stress experienced
parameters, while the average shear stress at the wall and by cells using structured inks, the equivalent material
the material phase interface was comparable. Therefore, viscosity can be obtained.
for simplification, only shear stress was considered in
the equivalent analysis. The maximum shear stresses,
encompassing wall shear stress and shear stress at material τ = 53 .61 µ +0 .2097 (IV)
phase interfaces, were chosen as the research target for max
equivalent analysis. Subsequently, the average shear stress
of the equivalent homogeneous inks was validated to assess where τ max and µ represent the maximum shear stress
its reasonability. and dynamic viscosity, respectively.
3.5. Examination of fluid forces for Concerning average wall shear stress, its relationship
equivalent analysis with viscosity and density mirrors that of maximum
The reasons for the equivalent analysis are as follows: The shear stress and viscosity and density (Figure 10B). For
preparation process of structured inks, whether with or instance, with constant viscosity, increasing density from
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without intervals, is not easy; the geometric parameters 1030 kg/m³ to 1110 kg/m³ maintained maximum wall
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of structured inks not only influence the distribution shear stress at a constant level. Within this density range,
of cross-sectional patterns of extruded fibers but also at a viscosity of 3.23 Pa·s, the average wall shear stress was
impact the forces acting on cells. Conventional methods 6.363e+0 Pa, and at a viscosity of 3.64 Pa·s, the average wall
assess cell viability after bioprinting through in vitro cell shear stress was 7.170e+0 Pa. The relationship between
culture and live/dead staining; however, relying solely on viscosity and average shear stress of homogeneous inks, as
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experimental validation may result in time and material shown in Figure S17B (Supplementary File; r-value = 1),
costs, especially in the bioprinting of structured inks. indicated a positive correlation between average wall shear
Considering and predicting cell viability during ink design stress and viscosity when density varied within the given
could potentially help reduce material design costs. range, as expressed in Equation V. After calculating the

Volume 10 Issue 4 (2024) 252 doi: 10.36922/ijb.2362