## 4 Discussion
We predicted a laminar flow profile (Re <<1), which agrees with previous studies on the behavior of other hydrogels in capillaries [24; 25]. Mathematical models can be used for the precise calculation of flow profiles in a nozzle [24]. The maximum wall shear intensity and the residence time of the fluid were also important criteria for cell survival. Based on the residence time data, we assessed cell viability following the application of different shear rates in the culture medium, revealing a loss of up to 35% of the cells. Generally, the greater the shear intensity and/or exposure time, the greater the loss of cell viability. This was previously demonstrated by comparing different nozzles, revealing that nozzle geometry and length both influence the degree of cell lysis [26]. Hydrogels with a high concentration of gelling agent (14.4% \(w/v\) total) appear to protect the cells from shear stress and maintain viability at levels exceeding 90% [27]. This has been described as the guarding effect [28]. The carrier material we used has a gelling agent content of 7.9% (\(w/v\)) [12] and the power law regression model at 20 Pa resulted in shear rates below 1 s\({}^{-1}\), confirming the ability to protect cells. Intense and/or prolonged shear stress on the cell membrane cause mechanochemical transduction [8], which induces the expression of protective factors and inhibits cell proliferation, alignment, and survival. It is therefore important to evaluate the status of cells during and after printing. Shear stress is well understood as a critical process parameter during bioprinting [29], with higher extrusion forces leading to more cell death [10; 30]. Nozzle geometry, especially the inner diameter, seems to have a major impact on cell viability at medium to high extrusion rates by increasing the shear forces [26; 30]. Moreover, the shear rates applied in a previous study caused more cells to undergo apoptosis rather than necrosis, leading the authors to develop an empirical equation system to predict cell viability for different nozzles [26]. We adapted this approach for the calculation of cell viability in BIOINK4 (2% fibrinogen, 2% alginate, and 5% \(w/v\) gelatin) [26] for our bioink and printing process [12], indicating a viability of 118.4% at a flow rate of 0.1 mL\(\cdot\)min\({}^{-1}\). We assumed a 600 \(\upmu\)m diameter nozzle (compared with the G20 cylindrical nozzle we used) and extrapolated the residence time values at the wall (adapting the nozzle size from 400 to 600 \(\upmu\)m and the length from 6 mm to 25 mm by a scale factor, and adapting our flow rate to their value of 5 \(\mu\)L-s\({}^{-1}\) by a scale factor). We found that the shear forces generated during our printing process had a low impact on cell viability. Cells suspended in the bioink also influence the rheology of the carrier and thus its flow behavior during biofabrication. We observed a maximum viscosity of 20.12% at low shear rates (1-10 s\({}^{-1}\)) following cell loading, but there was less impact at medium and high shear rates. The temperature profile of the bioink was very similar to the carrier. Higher cell concentrations were previously found to stiffen a collagen hydrogel before gelation but reduce the stiffness after gelation, although the bioink and carrier material were almost identical in terms of the crossover of the storage and loss moduli [11]. In partial agreement with our results, cell loading caused the viscosity of a gelatin methacrylamide hydrogel to decrease, although this was observed in all shear regions, and the temperature profile was only minimally affected [10], as previously reported [31]. The crossing point of the mixture during the temperature sweep was also very similar before and after cell loading [10], as reported for the collagen hydrogel [11]. After the mixing process, we were able to produce 3D-printed grids with continuous and visually equal strand widths using our established bioprinting procedure [12].