## 3 Results
### Estimation of Shear during the Printing Process and on Cells  
A flow rate of 0.10 mL\(\cdot\)min\({}^{-1}\) during printing was determined for our established printing process [12], reflecting a wall shear stress of 226.0 Pa in the nozzle and a very small Reynolds number indicating laminar flow (Table 4). The residence time in the nozzle at this flow rate was 13.6 s. The shear could be reduced by slowing the flow of bioink, but this increased the residence time to 54.30 s. In contrast, higher flow rates increased the shear and reduced the residence time. The flow profile was universally laminar, with theoretical calculations ruling out turbulent flow conditions within the nozzle. The shear exposure in subsequent experiments was therefore set to the determined residence times in the nozzle: 10 s (100 kPa) and 60 s. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Volume Flow Rate** & \(\tau\) & \(\dot{\gamma}\) & **Reynolds Number** & **Reynolds Number** & **Residence Time \(z\)** \\ (mL\(\cdot\)min\({}^{-1}\)) & **Wall (Pa)** & **Wall (s\({}^{-1}\))** & **Power Law** & **Carreau–Yasuda** & **in Nozzle (s)** \\ \hline
**0.025** & 112.2 & 19.6 & 0.000118 & 0.000014 & 54.30 \\ \hline
**0.05** & 159.3 & 39.3 & 0.000332 & 0.000027 & 27.14 \\ \hline
**0.10 (100 kPa)** & 226.0 & 78.6 & 0.000935 & 0.000054 & 13.60 \\ \hline
**0.50** & 509.5 & 393.0 & 0.010375 & 0.000271 & 2.71 \\ \hline
**0.75** & 625.2 & 589.5 & 0.019022 & 0.000407 & 1.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation of shear intensity, Reynolds number, and residence time at different flow rates in a G20 nozzle (\(\varnothing\) 600 \(\mu\)m, 25 mm length, cylindrical). As reference for the printing process [12], the volume flow rate is presented for 37 \({}^{\circ}\)C and 40 min cooling time. Increasing the shear intensity and exposure time reduced cell viability, as shown in the fluorescence-based Celltox Green assay (Figure 5). The viability during the 10 s exposure was 90.27 \(\pm\) 20.77% (1 Pa) and 91.46 \(\pm\) 16.24% (20 Pa), whereas the viability during the 60 s exposure decreased continuously from 89.46 \(\pm\) 28.46% (1 Pa) to 66.45 \(\pm\) 19.36% (20 Pa). Cell viability therefore appears to depend on the combination of shear intensity and exposure time. Figure 4: Optimization of the mixing process by applying the requirements profile (Table 2) to the Adchem 1:1 system at 28 \({}^{\circ}\)C. (**A**) Rheological assessment of the impact of pipetting strokes on the gelatin solution (\(n=3\); Kruskal–Wallis test * \(p<0.1\)). (**B**) Time-dependent re-establishment of the gelatin solution after 16 strokes compared with one stroke (\(n=3\)). (**C**) Analysis of homogeneity using fluorescein for the three mixing sections (\(n=3\)) with different syringe pump settings. (**D**) Rheological properties after mixing (\(n=6\)) relative to an established printing process (black column). The shear-dependent behavior of the carrier material and corresponding bioink (loaded with 10\({}^{5}\)-10\({}^{6}\) cells\(\cdot\)mL\({}^{-1}\)) at 37 \({}^{\circ}\)C showed a decrease in viscosity as the shear rate increased (Figure 6A), indicating that shear thinning occurred in all samples. The viscosity of the carrier material (Figure 6, black line) started at 30,603 \(\pm\) 1145 mPa\(\cdot\)s (1 s\({}^{-1}\)) and declined to 770 \(\pm\) 20 mPa\(\cdot\)s (1200 s\({}^{-1}\)). Adding cells reduced the viscosity of the low-shear regions (Figure 6B,C) compared with the carrier. The viscosity of the bioink ranged from 24,445 to 25,002 mPa\(\cdot\)s (1 s\({}^{-1}\)), representing decreases of 20.12% and 18.30%, respectively, indicating no direct relationship between cell density and viscosity. The carrier and bioink showed greater similarities in the medium and high shear regions (Figure 6D,E), with cell loading reducing the viscosity of the carrier by only 11.32% (100 s\({}^{-1}\)) and 9.75% (1000 s\({}^{-1}\)).