Improving alginate printability for biofabrication: establishment of a universal and homogeneous pre-crosslinking technique

Many different biofabrication approaches as well as a variety of bioinks have been developed by researchers working in the field of tissue engineering. A main challenge for bioinks often remains the difficulty to achieve shape fidelity after printing. In order to overcome this issue, a homogeneous pre-crosslinking technique, which is universally applicable to all alginate-based materials, was developed. In this study, the Young’s Modulus after post-crosslinking of selected hydrogels, as well as the chemical characterization of alginate in terms of M/G ratio and molecular weight, were determined. With our technique it was possible to markedly enhance the printability of a 2% (w/v) alginate solution, without using a higher polymer content, fillers or support structures. 3D porous scaffolds with a height of around 5 mm were printed. Furthermore, the rheological behavior of different pre-crosslinking degrees was studied. Shear forces on cells as well as the flow profile of the bioink inside the printing nozzle during the process were estimated. A high cell viability of printed NIH/3T3 cells embedded in the novel bioink of more than 85% over a time period of two weeks could be observed.


Introduction
The fields of regenerative medicine, cell therapy and tissue engineering (TE) have been growing constantly in recent years. Especially in soft tissue engineering approaches, naturally occurring polymeric materials are used to create scaffolds, as they often show biocompatibility and suitable biodegradability [1]. Moreover, their features to mimic the native extracellular matrix due to their hydrophilicity, high water content and physical characteristics, render them suitable as matrix for biofabrication approaches [2].
In this study, we used alginate as a base material for the development of bioinks; a material that has been broadly characterized in literature [3][4][5][6][7][8][9][10][11][12]. Alginate based bioinks are commonly used for dispense plotting, which requires to join various property requirements at once [13,14]. Li et al have 5 Author to whom any correspondence should be addressed. summarized those requirements and divided them into two main categories: Properties of bioink vs. properties of constructs. Those categories can be then further divided into rheological properties, adhesion between layers, shape fidelity, cell viability and degradability [15].
In order to adapt the mechanical properties and printability of alginate based bioinks, mostly (1) multi-material bioinks [16][17][18][19], (2) non-degradable particle or fiber filled systems [20][21][22][23] or (3) printing with support (sacrificial) material [24,25] are utilized. All those approaches have the common goal of overcoming the lack of shape fidelity of pure alginate solutions, which is due to the mostly viscous characteristics dominating over the elastic behavior of non-crosslinked polymer solutions. Although these methods work well, in general they also face certain challenges. When using multi-material bioinks for example, the solid content of those hydrogels often exceeds 10% (w/v) or the bioinks are still deficient in terms of printability. The drawback of such high polymer concentrations is that the mesh size of the polymer network decreases, resulting in significant barriers to diffusive transport of soluble factors and nutrients [26][27][28]. Moreover, in case of non-or comparably slow degrading fillers the question arises, whether residual filler particles will lead to interactions with the surrounding tissue, once the matrix is degraded. When considering sacrificial support materials, depending on the size of the printed structure, it can be challenging to remove all of the support material sufficiently. Furthermore, usually one additional step after crosslinking has to be conducted. Moreover, the 3rd dimension, meaning the actual height of the printed constructs, is often not shown or specified. Thus, in our approach, we aimed to design an alginate-based bioink with low polymer content which is capable to form high volume, porous, cellladen 3D structures without deploying a second matrix material, thickeners, non-degradable fillers or sacrificial support materials.
In order to achieve this goal, we had the intention to create a loosely pre-crosslinked alginate network, giving just enough stability to preserve its shape after printing. Apart from this, an important aspect of such a bioink is its homogeneity. This is why a homogeneous pre-crosslinking technique, which is universally applicable to all alginate-based bioinks was developed, combining the following ideas. On the one hand, it could already be shown, that CaCl 2 pre-crosslinked alginate bioinks can be applied for bioprinting [29,30]. However, due to the rapid reaction of free Ca 2+ -ions with alginate, it is very difficult to achieve homogeneously crosslinked hydrogels and thus also bioinks [31]. Marchioli et al [29] for example reported viscosity data of their CaCl 2 precrosslinked bioink with a marked standard deviation (η = 2923.33 ± 958.45 Pas) and found it to be nonsuitable for bioprinting compared to other bioinks prepared in their work. Furthermore, Chung et al [32] and Paxton et al [30] reported printing of 3-4 layered scaffolds with CaCl 2 pre-crosslinked alginate hydrogels, but the images reveal rather uneven, inhomogeneous strands. On the other hand, an internal gelation method has been used previously in order to create homogeneously crosslinked alginate structures. In comparison to external gelation, where ions are first crosslinking the structure on the surface and then diffusing into the bulk, ions are released all over the bulk structure during internal gelation. All such structures were shaped by mold casting or membrane emulsification [5,[33][34][35]. In order to control the crosslinking kinetics and thus, to produce more homogeneous bioinks, the internal gelation method was chosen in the current study for pre-crosslinking. Figure 1 illustrates the application of pre-crosslinked alginate bioinks schematically and gives an overview of the appropriated volume ratios during preparation, as well as the processing parameters.

Chemical characterization of alginate
Sodium alginate powder (VIVAPHARM® alginate PH176) from brown algae, with approval as pharmaceutical excipient, was purchased from JRS PHARMA GmbH & Co. KG (Rosenberg, Germany). The particle size distribution is declared between 150-200 µm, whereas the viscosity of a 1% (w/v) solution of the sodium salt lies in the range of 550-750 mPas, according to the supplier.

Chain composition.
In order to investigate the M/G ratio of alginate, a reduction of the molecular weight by partial hydrolysis was performed, according to Jensen et al [36]. Firstly, 100 mg of alginate were dispersed in 2 ml ethanol and dissolved in 100 ml H 2 O. After adjusting the pH to 5.6 by adding HCl the solution was refluxed at 100 • C for 1 h. Subsequently, the pH was decreased to 3.8 by addition of HCl and refluxed for further 20 min. After cooling down to 0 • C, NaOH was used to finally neutralize the solution. 1 H nuclear magnetic resonance (NMR) spectra of 5 mg lyophilized alginate sample in 0.5 ml D 2 O were recorded on a Bruker Advance 500 spectrometer (Bruker Biospin, GmbH, Rheinstettem, Germany) operating at 400 MHz. In order to obtain the M/G ratio, the relative integrals of the three signals in the anomeric region were calculated which contain specific information about the chain composition. Signals of the region A, B and C according to Jensen et al were integrated and the M/G ratio could be determined with the equation deduced by Grasdalen (equation (5)) [37]:  the containers were additionally sealed with PARA-FILM® (Pecheney Plastics Packaging, Chicago, USA), to prevent solvent evaporation. The alginate concentration was set to 2% (w/v).

Pre-crosslinked alginate hydrogels
In order to fabricate pre-crosslinked alginate hydrogels for bioprinting, first alginate solutions with a concentration of 4% (w/v) were prepared as described in section 2.2.1. Subsequently, CaCO 3 (Calcium carbonate precipitated for analysis EMSURE®, CAS 471-34-1, Merck KGaA, Darmstadt, Germany) and D-Glucono-δ-lactone (CAS 90-80-2, Merck KGaA, Darmstadt, Germany) were mixed with ultrapure water type 1 separately and then slowly added to the alginate solution while stirring. CaCO 3 dispersions were added first and D-Glucono-δ-lactone (GDL) solutions were afterwards added dropwise, using a micro-pipette. GDL was chosen, as it is already used in some medical products, where it serves as irrigation solution to prevent clogs in bladder catheters and is applied for hydrofluoric acid burn management in the form of calcium gluconate gels [38,39]. The initial concentrations of CaCO 3 dispersions were 20, 50 and 80 mM and corresponding GDL solutions always had twice the concentration (40, 100 and 160 mM respectively), leading to the final values seen in table 1. This ratio was on the one hand chosen for all experiments due to the fact that CaCO 3 needs two protons to dissolve. On the other hand, GDL will undergo hydrolysis when dissolved in water to form gluconic acid, which then has one carboxylic acid group to release one proton [40,41]. Thus, in theory this ratio would serve to exactly dissolve the CaCO 3 particles, without further decrease of the pH. Preliminary results also showed that around 4 mM of CaCO 3 particles remain undissolved. However, CaCO 3 particles were already shown to be resorbable in scaffolds by MSCs as well as osteoclasts and are not suspected to have a negative influence on other cell types [42,43].The volume ratio between alginate-, CaCO 3 -and GDL-solutions/dispersions was kept constant at 2:1:1, resulting in concentrations in the prepared bioinks, according to table 1. This table also serves to show the labeling system of the different bioinks analyzed in this work, including their different compositions and crosslinking environments. During the gelation time of two days, the hydrogel was either kept at room temperature or in a temperaturecontrolled room at 4 • C, with and without stirring.

3D printing
For 3D-printing, a BioScaffolder 2.1 (GeSIM, Radeberg, Germany) and polypropylene needles with a stainless-steel cannula with an inner diameter of 410 µm (All-purpose dispensing tips 7 018 272, Nordson EFD, Apex Business Centre Boscombe Road Dunstable, Bedfordshire, England) were used. With this setup, squared structures with a side length of 15 mm were printed at a pressure of 17 kPa, regulated by the F-Box and a print velocity of 4 mm s −1 .

Post-crosslinking
In order to fully solidify the 3D-printed structures, a post-crosslinking step was performed. In this step, the alginate hydrogels were slowly covered with CaCl 2 (Calcium chloride dihydrate, CAS 10 035-04-8, Merck KGaA, Darmstadt, Germany) solution of 100 mM concentration and left to crosslink for 10 min. Afterwards, the CaCl 2 -solution was removed and replaced by DPBS or Dulbecco's Modified Eagle Medium and additions (further specified in section 2.6) in the case of cell culture studies. , with the idea to prevent slippage at the specimen geometry interface during the measurements. All solutions and hydrogels were rheologically investigated before the postcrosslinking step. For this purpose, the respective test samples were filled into a syringe, dispensed on the bottom plate geometry and finally trimmed, once the upper geometry was in place. Additionally, the upper geometries' trough was filled with distilled water and a solvent trap covered the upper and lower geometries during the measurements to avoid solvent evaporation. Each experiment was conducted three times and the arithmetic mean as well as the standard deviation (SD) were calculated. At a gap width of 0.5 mm with a pre conditioning step (120 s; 20 • C; no strain), all samples were examined with three different methods: oscillation amplitude sweep (20 • C; 10 rad * s −1 frequency; 0.1%-500% strain), oscillation frequency sweep (20 • C; 0.25-100 rad * s −1 frequency; 1.0% strain), and flow sweep (20 • C, 0.8-1000 s −1 shear rate). The measurements were performed using direct-strain control in either continuous rotation or oscillation mode.
The measurements were chosen based on the work of Paxton et al [30], but adapted to the current parameters. For analyzing the viscosity data in dependence of shear rate, either the Carreau-Yasuda or power-law model were used [44,45]. These models and the importance in the field of biofabrication were comprehensively discussed by the group of Akhilesh K. Gaharwar [46,47], also pointing out their limitations as well as alternative models. With those models, the velocity, residence time, shear rate and shear stress profiles in the tip could then be calculated.

Printability and shrinkage
In order to evaluate the different alginate hydrogels in terms of printability and shrinkage, an evaluation strategy was created. Images of the hydrogels were taken directly after printing with a Sony NEX-5 digital system camera and after post-crosslinking with a Stereolupe Stemi 508 light microscope. By using Fiji ImageJ software version 1.51 n, the size of all 3D printed structures was quantified [48]. Here, either the scale bar or the diameter of the well plate of 37 mm were used to set a scale in pixels/mm for microscope and digital camera images, respectively. In the images, the printed structures in cuboid shape, were overlaid with a grid of six by six lines in order to allow consistent length measurements. The arithmetic means of those measurements are indicated with an overline.
To calculate the shrinkageS of the hydrogels during post-crosslinking, the arithmetic means of the shrinkageS x (x-direction) andS y (y-direction), were averaged.S x andS y can be calculated by subtracting the averaged side length in the respective direction, before (L bx andL by ) and after (L ax andL ay ) post-crosslinking from each other, setting them in relation with the corresponding length before postcrosslinking and multiplying them by 100 %: (1) Additionally, a general evaluation system for the printability of pre-crosslinked hydrogels was introduced. Here, two main aspects were considered. On the one hand, the aspect of size and on the other hand, the edge sharpness were addressed. This could be achieved by calculating a value P for printability in the range of 0 < P ≤ 1, according to equation (2):

SD by L0y
(2) L 0x and L 0y are the provided side lengths to the printing system (in this case 15 mm),L bx andL by the arithmetic means and SD bx and SD by the standard deviations of the length measurements before postcrosslinking in x-and y-direction, respectively. As the squared structures were kept the same throughout this work, the printability P is only dependent on L bx ,L by , SD bx and SD by . Those values can therefore be assigned to the observed size (L bx andL by ) and to the sharpness of the contour (SD bx and SD by ), respectively.

Nanoindentation
A Piuma Nanoindenter (Optics11, Amsterdam, Netherlands) was used for mechanical testing of the hydrogels to examine the effective Young's modulus (E eff ). For all measurements a boro-silicate glass tip featuring 0.46 N m −1 stiffness and 61 µm radius (Optics11, Amsterdam, Netherlands) was mounted to the Nanoindenter. The samples were casted, crosslinked (10 min in 0.1 M CaCl 2 solution) and measured in plastic petri dishes right after crosslinking (SARSTEDT AG & Co. KG, Nürnmbrecht, Germany). Hanks' Balanced Salt solution (HBSS, Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) was added on top of the samples in order to prevent desiccation of the hydrogels during the measurements. A total number of at least 22 indentations were performed for each material and equation (3) [49] was applied: where E eff is the measured effective Young's Modulus of the sample, E is the real Young's Modulus of the sample, E i the Young's Modulus of the indenter tip, ν the Poisson ratio of the sample and ν i the Poisson ratio of the indenter tip. With the assumption, that E i ≫ (1 − ν i ), the last term of equation (3) can be neglected. For our calculations, the Poisson ratio of all hydrogels was given an estimated value of 0.5, which leads to the following correction factor to calculate the Young's Modulus: . In order to concentrate the cells in cell culture medium to a total number of 11 Mio. cells/ml, they were centrifuged for three minutes at 500 rpm and the supernatant was discarded. After that, cells were resuspended in the medium. In order to prepare the bioinks, the initial inks were prepared under sterile conditions and allowed to reach room temperature before mixing. Those inks were filled into a syringe and subsequently mixed with the concentrated cell suspension by connecting the two syringe openings and carefully pushing the material back and forth several (at least five) times, to ensure homogeneity of the cell mixture. A volume ratio of ten to one (ink to cell suspension) was chosen, in order to achieve a final cell concentration in the bioinks of Rhodamine-Phalloidin at 620/60 nm (ET620/60 m) through an HC Fluotar L16x/0.6 CORR VISIR objective [50]. The excitation light power was 150 mW on average, the intensity was attenuated according to an exponential function in correlation to the penetration depth starting with 100 mW at the sample surface and ending at about 250 mW for the deepest image slice, to compensate for light scattering and absorption in the sample and keep fluorescence emission intensity constant over sample depth. Recording was performed with a typical voxel size of 0.4 × 0.4 × 1 µm and a field of view of 600 × 600 µm. The images were only taken with well printable samples including NIH/3T3 cells after 14 d of cell culture, to visualize the difference of cell morphology deep inside the sample and close to the surface, as 2D images did not give enough information on this issue.

Statistical analysis
For the evaluation of Nanoindentation, at least 22 measurements were performed, and one-way ANOVA was used in order to find statistically significant differences on the 0.005 level. In contrast to that, the population variances of cell viability tests were significantly different on the 0.05 level according to Levene's Test. Due to this, a nonparametric Friedman ANOVA was performed in this case.

Results and discussion
As the method used in this paper utilizes CaCO 3 particles as inactive Ca 2+ source, those particles can be distributed in any alginate-based solution without leading to a crosslinking reaction. By adding D-Glucono-δ-lactone (GDL), the mixture is acidified in a slow manner, leading to the dissolution of CaCO 3particles and consequently crosslinking of the alginate solution, as previously reported [5,33,34]. In order to evaluate most requirements of bioinks [15], rheological measurements, printability studies, as well as cell viability tests were performed. In contrast to our first hypothesis that protons released by gluconic acid and used by CaCO 3 for dissolution should compensate one another and thus not decrease the pH level, a decrease of pH in the range from 4.96-6.05 after pre-crosslinking could be determined. The initial values of pH lay between 7.39-7.50 before precrosslinking. A more detailed trend of the pH level over a time period of 21 h for one specific hydrogel during pre-crosslinking can be found in section 5.3 (supplementary material). Due to the addition of a volume fraction of 1:10 of DMEM buffer solution to the bioink when cells are added, the pH increases to a value of around 6.2. After a maximum of one hour at this pH, printing was completed, followed by the crosslinking step which had no significant effect on pH. Finally, the hydrogel samples were covered with cell culture medium, which potentially leads to a further gradual increase of pH, to a value of 7.4, over time. Kruse et al showed that after up to 5 d at pH 6.5, cell viability of fibroblasts was above 70% [51]. The short-term effects are assumed to be significantly lower, but the shortest time period covered by Kruse et al was one day. Additionally, Geum-Hwa Lee et al observed similar results for MG63 osteoblast cell line, but covered shorter time frames down to 12 h, where cell viability was shown to be around 85% at pH 6.4 [52]. Thus, we considered that a pH level of around 6.2 affecting the cells for one hour did not decrease cell viability markedly. In addition, the potential precipitation of calcium phosphate particulates is discussed in section 5.4 (supplementary material) and it is concluded that no relevant amount of calcium phosphate is precipitated. Through GPC analysis a weight average molecular weight (M w ) of around 250 kg mol −1 could be determined for alginate. Moreover, NMR spectroscopy revealed a mannuronic (≈54 %) to guluronic acid (≈46 %) ratio of 1.19.

Strain amplitude sweeps
With the help of amplitude sweeps, the linear viscoelastic regions of alginate hydrogels and solutions were determined and are shown in figure 2. Below strains of approximately 10% all investigated inks behave linearly viscoelastic. Thus, the amplitude for frequency sweeps was chosen to be 1.0 %, one order of magnitude below this value. Moreover, the difference in storage and loss moduli for varying parameters is shown. It can be observed that the loss moduli within the linear viscoelastic region are only dependent on the amount of CaCO 3 used for the pre-crosslinking and are rising with increasing amount of the latter.
In contrast to that, storage moduli are not only dependent on the amount of CaCO 3 used, but also on the applied preparation and conditions. Similar to the behavior of loss moduli, the storage moduli increase with the amount of CaCO 3 , as expected. The increasing number of physical Ca 2+ crosslinks in the hydrogels at growing CaCO 3 concentrations is thought to be responsible for the growing elastic response. When comparing the different methods of crosslinking at a total CaCO 3 concentration of 12.5 mM, it can be noticed that crosslinking at room temperature, as compared to crosslinking at 4 • C, leads to a slightly increased elastic behavior. Moreover, fabricating a pre-crosslinked alginate hydrogel with a concentration of 12.5 mM CaCO 3 , but without stirring during the crosslinking process, increases the elastic behavior markedly, even exceeding the storage modulus of hydrogels with 20 mM total CaCO 3 concentration. In this case, too, it is supposed that the network formation plays the most important role for the change in the elastic behavior. When the hydrogels are not stirred during the pre-crosslinking process, there is no obstruction to the crosslinking mechanism. Thus, a hydrogel with a completely interconnected 3D structure will form. Compared to this, under the condition of stirring, an overall 3D network formation is hindered, leading to less elastic, i.e. more viscous, behavior. Moreover, it was observed that at higher temperatures the main proportion of material transition from solution to hydrogel (=network formation) occurs within a shorter period of time (section 5.3, supplementary information (available online at stacks.iop.org/BF/12/045004/mmedia)). It is assumed that with a smaller timeframe of crosslinking (e.g. RT), the alginate will be able to generate a stronger connected network, as the ratio between competing mechanisms of crosslinking (influenced by temperature; results in ↑G') and shearing (influenced by stirring; results in ↓G') is shifted. Due to this interplay, we hypothesize that G' of Alg _12.5mM_4 • C will not reach the one of Alg _12.5mM_RT when stirred for a prolonged time. An increase in loss moduli at high oscillation amplitudes can be noticed for inks Alg _20mM_4 • C and Alg _12.5mM_4 • C_w/o stirring . In conformity with this observation, those two inks are also the ones which have the highest storage moduli. Thus, the growing amount of dissipated energy at high strains could either be explained by ripping off the strong network or by slippage at the geometry surface due to stiffer gels [53].

Oscillation frequency and shear flow sweeps
Additionally to amplitude sweeps, frequency sweeps and shear flow sweeps were conducted with all hydrogels, according to section 2.3. Figure 3 shows the values of viscosity η in dependence of the shear rate (flow sweep), as well as the tangent of the loss angle δ (frequency sweep).
Firstly, and most importantly, it can be observed, that all samples in figure 3(a) show shear thinning behavior, although different characteristics of the graphs can be observed. Characteristic for noncrosslinked polymer solutions, the pure alginate solution (Alg _0mM_RT ) shows a Newtonian plateau region at low shear rates, and shear thinning behavior at high shear rates. This trend is often described with a Carreau-Yasuda or Cross-Model in literature [44]. However, those models are not suitable for crosslinked polymer-networks (Alg _5mM_4 • C , Alg _12.5mM_4 • C , Alg _20mM_4 • C , Alg _12.5mM_RT and Alg _12.5mM_4 • C_w/o stirring ). In case of crosslinking with the lowest amount of crosslinking agent (Alg _5mM_4 • C ), the trend of the curve in figure 3(a) is still comparable to the non-crosslinked alginate solution (Alg _0mM_RT ). The main difference is that at low shear rates, no obvious plateau is reached due to the formation of a lose network of crosslinks. All other materials (Alg _20mM_4 • C , Alg _12.5mM_RT and Alg _12.5mM_4 • C_w/o stirring ) show a markedly different, almost linear trend in the double-logarithmic plot. By comparing samples Alg _0mM_RT , Alg _5mM_4 • C , Alg _12.5mM_4 • C , Alg _20mM_4 • C with increasing CaCO 3 contents, figure 3(a) clearly shows the increase in viscosity at low shear rates. At the lowest measured shear rate of 0.8 s −1 , a 100-fold increase in the viscosity can be achieved by pre-crosslinking. Due to the beneficial shear thinning behavior, the increase in viscosity at 1000 s −1 is only around three times. This is a first indication that the performance of the inks is increased by the pre-crosslinking, due to high and shape preserving viscosities at rest, but low and more cell friendly viscosities at high shear rates. Moreover, a slope of close to minus one in the double logarithmic plot can be observed at low shear rates for samples Alg _12.5mM_4 • C , Alg _20mM_4 • C , Alg _12.5mM_RT and Alg _12.5mM_4 • C_w/o stirring . This result indicates the presence of a yield point τ y . In order to find the values for τ y of the different inks, a simplified Ponslinki model was used to fit the graphs [44]: Here, η 0 is the zero shear viscosity,γ c the critical shear rate, α the transition control factor and β the exponent which can be described as: with the power-law index n. The resulting fit functions can be observed in the top right corner of figure 3(a). For the pure alginate solution without a yield point, τ y was fixed to the value zero, resulting in a simplified Carreau-Yasuda model. For all other samples, τ y was determined via the fitting function with the restriction that η 0 was fixed to the value of 1.44 Pas, which equals the zero shear viscosity of the non-crosslinked alginate solution. The yield points obtained are shown in the supplementary information (table 3 in the supplementary materials) in combination with the quality of the related fit function (R-Squared) and viscosities at a shear rate of 0.8 s −1 . The yield points indicate the presence of an increasingly strong network when increasing the amount of CaCO 3 or the temperature, as well as when switching the processing conditions from stirring to non-stirring.
Considering figure 3(b), it can be observed that the non-crosslinked and weakly crosslinked samples (Alg _0mM_RT , Alg _5mM_4 • C ), have a tan(δ) > 1 over the whole frequency range measured. This shows the dominance of the fluid-like behavior and thus it correlates well with the observation of an indicated plateau region of the weakly-crosslinked sample (Alg _5mM_4 • C ) in figure 3(a). In comparison to that, all samples which show an almost linear trend in figure 3(a) also show a tan(δ) < 1 over the whole frequency range. Thus, these samples are dominated by their elastic behavior which indicates a stronger and denser crosslinking network.
Considering all these observations, the results show that pre-crosslinking with CaCO 3 and GDL has a strong influence on shear-dependent viscosity and leads to an increased network formation with increasing amounts of added calcium.

Shear stress, shear rate, velocity and residence time flow profiles
In this section, the rheological data of the bioinks including cells (according to section 2.6 In vitro studies) are analyzed. From the obtained parameters, an estimate of the velocity, shear rate, shear force and residence time profiles could be calculated for these bioinks which were also used for cell viability tests. When comparing the shear flow measurements with cells (figure 8-supplementary information) to those without cells, no substantial change in the trend of the curves can be observed. Slight changes in the viscosity values might occur due to the dilution of the hydrogel with DMEM or by the effect of cells acting as soft particle fillers.
In order to fit the graphs and create model functions, two different equations were chosen. On the one hand, for Alg _20mM_4 • C where no plateau region at low shear rates was observed, a simple power-law model was used [45]: with the viscosity η, shear rateγ, shear thinning coefficient K and exponent n. This model was chosen with the assumption of wall adhesion and real flow inside the tip channel. As the latter was revealed by preliminary flow experiments the power-law appeared as a simple model to estimate the flow properties of the pre-crosslinked ink. Although the appearance of wall slip is still to be examined, all following calculations were performed without taking it into account. The reason behind is that in the case of wall slip, the flow profile would result in a plug flow and thus highly reduced shear stresses on embedded cells. In the unfavorable scenario of wall adhesion, higher shear stresses will occur and thus it will be discussed in the following.
On the other hand, in the case of Alg _0mM_RT with a clearly visible plateau region, the Carreau-Yasuda model was chosen for fitting the function [44]: where η 0 is the zero shear and η ∞ the infinite shear viscosity,γ c the critical shear rate, a the transition control factor and N the power-law index.
The resulting model functions and parameters when fitting with those equations can be found in section 5.2, supplementary information, which are necessary to calculate flow profiles from the rheological data. The profiles in figures 4(a) and (b) were calculated according to Paxton et al [30] Figure 4(a) shows that the velocity of the pure alginate bioink is distinctly higher than that of the pre-crosslinked bioink. As the two bioinks were printed with the same pressure and nozzle, this behavior can simply be explained by the increased viscosity of the pre-crosslinked bioink. At the center of the nozzle, where the maximum velocity is reached, this results in values of 15.2 mm s −1 and 2.6 mm s −1 for non-crosslinked and pre-crosslinked bioink, respectively. Accordingly, the shear rate profiles of the noncrosslinked bioink shows higher values than the precrosslinked one.
However, the more important parameters in terms of cell damage and survival are given in figure 4(b). On the one hand, the shear stress profile is given which is, in the case of our model, only dependent on the die geometry and printing parameters, but not on the material properties themselves [30,54]. It results in linearly increasing shear stresses from the center of the nozzle (τ = 0 Pa), towards the wall, where a maximum value of τ = 137 Pa is reached. On the other hand, the residence time which is dependent on the materials flow properties is shown in figure 4(b). Thus, the flow properties play a crucial role in how strong the cells will be damaged during printing, as they determine the residence time during which the cells are exposed to increased shear stresses. More precisely, it was shown before by Snyder et al [55] that apart from printing at higher stress intensity, also increased residence times lead to necrosis in a larger subpopulation of cells. Furthermore, they hypothesized that the increased number of necrotic cells might affect cell viability and differentiation of the local cell population [55]. Another study showed  that shear stresses < 5 kPa in the nozzle hardly have any effect on the cell viability directly after printing resulting in an average cell viability of 96 %. In that paper, also alginate solutions (0.5, 1.0 and 1.5% (w/v)) were used for the experiments, in combination with L929 mouse fibroblasts [56]. When translating these previous observations to our results, a high cell viability after printing is expected for both materials due to very low maximum shear forces of around 0.14 kPa. The pre-crosslinked bioink would be more likely to damage the cells, as the average residence time of 9.6 s is around three-fold the residence time of the non-crosslinked bioink with an average residence time of 3.3 s. However, the cell viability after printing will be further discussed in section 3.4.

Printability and shrinkage
The following section serves to visualize the influence of pre-crosslinking on the rheological behavior (section 3.1 Rheology) and connect those values to the printability. Moreover, the shrinkage of different bioink formulations will be compared.
First of all, the printability values (P) and shrinkages (S) calculated according to section 2.4, as well as the viscosity values from shear flow graphs at 0.8 s −1 for three selected bioinks, are given in table 2. Those bioinks were chosen as they represent one bioink which lacks printability due to low viscosity, one with good printability and one which lacks printability due to strong crosslinking.
It can be observed that the shrinkage of the scaffolds during post-crosslinking is reduced markedly by the pre-crosslinking. The pure alginate solution shows a shrinkage of almost 50% while the shrinkage of pre-crosslinked bioinks is reduced to around 32-33 %. This observation substantiates the hypothesis that physical Ca 2+ crosslinks are present in the precrosslinked hydrogels. Thus, less new cross-links will be formed during the post-crosslinking process of the latter, leading to less shrinkage. With respect to the printability values, it should be highlighted that, theoretically, printability can vary in the range 0 < P ≤ 1, but, practically, no values below 0.6 were measured. As the shear thinning behavior was already shown and discussed in section 3.1.2, table 2 only provides the viscosity of the bioinks at a shear rate of 0.8 s −1 , representing an estimate of the viscosity at rest. In addition, the loss angle tan(δ) is given, in order to show if either the elastic behavior (tan(δ) < 1) or the viscous behavior (tan(δ) > 1) of the material dominates. In conclusion, it can be shown that the viscosity as well as tan(δ) can be connected to the printability, indicating a window of good printability at a viscosity of around 150 Pas (γ = 0.8 s −1 ) and tan(δ) of 0.34 (1% strain, 10 rad s −1 frequency), which is in good accordance with the reported data and conclusion by Gao et al [57]. Moreover, the viscosity data and/or storage and loss moduli of Alg _20mM_4 • C , are comparable to these of other well printable alginate-based bioinks [58][59][60][61]. When under-gelation (Alg _0mM_RT ) or overgelation (Alg _12.5mM_4 • C_w/o stirring ) occurs, the printability decreases due to either too low or too high viscosities at low shear rates, respectively. Moreover, the values of tan(δ) show that the flow property of pure alginate solution is dominated by viscous behavior, leading to viscous flow of the scaffold after printing. Contrary to this, the well printable bioink with 20 mM CaCO 3 pre-crosslinking is dominated by elastic behavior, indicated by a tan(δ) of 0.34. The elastic component (due to the formation of a network) leads to the ability of the material to store energy and thus, to an increased shape fidelity. However, when the network formation is too strong and insufficient viscous flow occurs in the bioink, the printability also decreases, which can be observed for sample Alg _12.5mM_4 • C_w/o stirring . A similar and even more pronounced effect occurred when a comparison bioink, pre-crosslinked with CaCl 2 at the same concentrations, was supposed to be printed under similar conditions. For this purpose, a 4% (w/v) alginate solution and a 40 mM CaCl 2 solution were prepared separately. Then, with a volume fraction of 1:1, CaCl 2 solution was added to the alginate solution dropwise at 4 • C and stirred for 48 h. Due to the rapid crosslinking, a strongly crosslinked alginate bulk, immersed in CaCl 2 solution, formed. This alginate hydrogel bulk could not be printed with a comparable nozzle, even at the maximum available pressure of 6 bar.
These results are further visualized in figure 5 which shows printed cuboids and parallel strands of the formulations given in table 2. The images illustrate the effect of pre-crosslinking on the printability. When looking at panels a and b, a lack of shape fidelity can be clearly observed for the pure alginate solution. The surface tension leads to the formation of a round shaped droplet in figure 5(a), although a cuboid was supposed to be printed. Moreover, in figure 5(b), the surface tension of the liquid also leads to droplet formation of the strands, which consequently merge. Thus, a very poor shape fidelity is given which matches with the dominating loss modulus (G") of this formulation. When inspecting figure 5(c), a cuboid structure with an almost exact side length of 15 mm can be perceived. Furthermore, figure 5(d) shows nicely aligned strands in horizontal direction, which do not merge or have any protrusions. Both of the latter figures show that the high value for printability P of 0.953 for this bioink is justified. With increasing viscosity and decreasing tan(δ) however, the printability drops down to 0.898. In figures 5(e) and (f), the decreased printability can clearly be observed. Due to the highly elasticity dominated property of this ink, the material behaves solidlike. Thus, during printing and undergoing high shear strains, the material rips apart unevenly which results in abrasive edges and inhomogeneous strands.
In order to further emphasize the printability and shape fidelity of the best printable bioink, figures 5(g)-(i) shows a variety of different perspectives and magnifications of bioink IV, which was well printable. In figures 5(g) and (h), a porous scaffold with 5 mm in height is shown. It can be observed that the pores reach through the whole height of the scaffold, speaking for good shape fidelity. However, no porosity in z-dimension could be observed. By further developing the method, especially investigating different methods of stirring for high viscosity materials, it is assumed that rheological properties can further be improved, which might even lead to z-dimensional porosity. The microscopy image in figure 5(i), shows the pore structure of such scaffolds from a top view. With those images, an average pore size of 1.10 mm and strut width of 0.74 mm could be determined. Although the 3D structure looks promising, the pores show slightly rounded edges and the ones on the extreme edge of the scaffolds are smaller in size, which might be an artefact of the printer.

Mechanical properties of post-crosslinked matrix materials
A crucial factor for cell viability and differentiation is given by the mechanical properties of the matrix wherein the cells are embedded. As shown by Huebsch et al [62], stem cells do not only sense, but also respond to the mechanical properties of their surrounding extracellular matrix. However, it is also important to control the Young's Modulus of the matrix that is used to embed fully differentiated cells.
In figure 6, the Young's moduli of the two material compositions which were also used for cell viability tests are given. Although the concentration of alginate inside the hydrogel and the CaCl 2 concentration for post-crosslinking were the same, significantly different values can be observed. The Young's modulus of pure alginate hydrogels with 17.7 kPa is significantly higher (more than two times) than that of the pre-crosslinked hydrogels with 7.3 kPa.
So far, this reduction cannot be explained with certainty. However, even if a relatively high calcium concentration of around 20 mM is already present inside the pre-crosslinked hydrogel, the formation of an overall 3D network was hindered due to stirring. As the particle current density and thus the diffusion rate are dependent on the concentration gradient (Fick's law), one hypothesis is that less calcium ions interpenetrate the pre-crosslinked hydrogels during the post-crosslinking time of ten minutes. In order to gain the same Young's moduli for both materials, preliminary results showed that longer post-crosslinking durations are necesarry. Apart from the reduced diffusion rate, the different stiffness could also be caused by the fact that many crosslinks have already been formed inside the pre-crosslinked hydrogel, which reduces the mobility of alginate chains. Thus, the process of forming new crosslinks might be extended. When comparing the obtained values with data reported by Liu et al [63], it turns out that the Young's modulus of our material is comparable to a range of soft tissues like spleen, skin or muscles.

Cell viability and morphology post-printing
The aim of this part of the study was to investigate the influence of printing with either pure alginate solution or pre-crosslinked alginate on the viability of NIH/3T3 murine fibroblast cells. The cell tests were conducted according to section 2.6. Similar and homogeneous cell distributions were observed visually for both materials during 2D imaging of the constructs, confirming a homogenous cell distribution inside the bioink owing to the mixing procedure.
Live and dead stainings, as well as light microscopy images were captured after 1 d, 3 d, 7 d and 14 d after printing. These images showed roundly shaped cell morphology for cells embedded in pure alginate hydrogels over the whole period of time. Moreover, the vast majority of cells were separated from each other and did not show agglomerates on day one and three of cell culture. After seven days of cell culture, the cell spots showed an increased diameter, which was even more pronounced after 14 d. This might be a sign of proliferating cells which are not able to grow through the hydrogel, either due to an excessive stiffness of the surrounding material, a lack of celladhesive moieties in the material, or a combination of both. In general, this observation was expected and is in agreement with literature, as native alginate is a bioinert material which does not have any binding sites where cells can directly attach to [64]. Moreover, unmodified alginate is known to show slow degradation rates and thus, will maintain its initial stiffness over long periods of time [65,66].
In cell culture of pre-crosslinked alginate samples, the same observation was made on day one and three in 2D bright field imaging. However, after 7 and 14 d, the morphology of cells started to be more elongated and agglomerates could be observed. Due to this rather unexpected behavior, 3D images with cell nucleus and actin-filament staining were captured with a multi-photon microscope. Figure 7(a) shows such a 3D stack of cells embedded inside the precrosslinked hydrogel sample, after 14 d of cell culture. The very top of the image displays the hydrogel surface, whereas everything below that shows the interior of the hydrogel. It can be observed that the hydrogel surface is covered with many cells compared to the interior. This observation is further highlighted in figures 7(b)-(e). Figure 7(b) shows a vertical cross section view of the 3D stack, whereas figures 7(c)-(e) shows horizontal cross sections at depths of 90 µm, 1000 µm and 1690 µm. Those images reveal that the cells on the surface show an interconnected actinfilament network. In contrast to that, the cells which are situated 1000 µm or deeper inside the hydrogel are separated from each other and no actin-filaments can be observed between the cell nuclei. Thus, one can conclude that the observations of cell spreading made in 2D were surface-related effects.Those effects might have occurred in the pre-crosslinked hydrogels but not in the pure alginate hydrogels due to the reduced stiffness (section 3.3). Embedded in less stiff hydrogels, cells would have the possibility to move through the hydrogel. Especially close to the surface, cells have very good supply of nutrition and on the surface itself also the opportunity to reach out easily to each other to form spread structures as observed in figure 7(c). Moreover, the cell density in dependence of the depth is shown in figure 7(f) and clarifies the trend of fewer cells in the depth of the structure (0.42 * 10 6 cells ml −1 ) compared to the surface (0.88 * 10 6 cells ml −1 ). Interestingly, when comparing the counted cell density to the initial cell density (1.0 * 10 6 cells ml −1 ), it becomes apparent that fewer cells were counted inside the construct. Conceivable hypotheses to explain this observation could be that either the cells were not evenly distributed in the first place, or that the counting based on image data is not capable to separate cell nuclei which lie close to each other in cell agglomerates.
In addition, cell viability was considered. Figure  7(g) shows the percentage of living cells compared to dead cells for the pure as well as for the precrosslinked alginate hydrogel after 1 d, 3 d, 7 d and 14 d. Figure 7(g) shows that the mean cell viability for both tested materials is above 90% over a period of seven days. Apart from this, the cell viability in precrosslinked alginate exceeds the one in pure alginate during this time period. Significant differences between the samples on the 0.05 level were found between 1 d and 7 d as well as 1 d and 14 d samples in non-crosslinked alginate bioink, as well as between 7 d and 14 d in pre-crosslinked alginate. The strong decrease of cell viability between 7 d and 14 d of the pre-crosslinked samples is assumed to be due to a slightly misleading read out of counting live and dead cells. As discussed before, especially after 14 d of cell culture in pre-crosslinked hydrogel, the cells started to spread significantly. Thus, it was not possible to separate living cells in ImageJ software with absolute certainty, possibly leading to a lower number of detections than actual living cells inside the hydrogels. In general, a trend for decreasing cell viability over time can be noticed which is not questioned, as the adhesive fibroblast cells do not have any cell-adhesive moieties to attach to. In order to incorporate cell adhesive motifs, native alginate can be chemically modified with RGD-sequences [67,68] or with proteins containing such motifs [69,70]. Although the rheological properties are most likely to change by any type of modification, it is assumed that the universal pre-crosslinking technique could help to increase the printability of other alginate-based hydrogels, too.
However, the main goal of this experiment was to determine whether the pre-crosslinking of alginate has an influence on the cell viability after printing. Due to the fact that the mean value of cell viability in pre-crosslinked alginate exceeds the one in pure alginate throughout the first week, it can be concluded that the pre-crosslinking process itself, as well as different residence times during printing, did not harm the cells. Consequently, NIH/3T3 cells were not affected by the increased viscosity, nor the decreased pH values which they were exposed to for a short period of time.

Conclusions
Advanced bioinks for biofabrication need to fulfil a variety of material properties and requirements. Hence, this study addressed a range of those properties, such as shear thinning behavior, shape fidelity and cell viability of different bioinks.
From a rheological point of view, the transition from a solution to a crosslinked hydrogel could be shown, also revealing different kinetics at room temperature and at 4 • C. The increasing viscosity at low shear rates due to pre-crosslinking can therefore be clearly ascribed to the network formation, whereas particle reinforcement due to undissolved CaCO 3 or precipitated calcium phosphate particulates is very unlikely. Moreover, all tested bioinks showed shear thinning behavior which is very advantageous in terms of 3D bioprinting, as cells will 'suffer' less from long residence times under high shear stress conditions [30]. Rheological key parameters, namely the viscosity (atγ = 0.8 s −1 ), tan(δ) (at 1% strain; 10 rad s −1 ), the yield stress τ y and the shear thinning coefficient n, could be linked to the printability of printed cuboid structures. It was ascertained that the alginate based bioinks were best printable with a viscosity of around 150 Pas (γ = 0.8 s −1 ), tan(δ) of 0.34 (1% strain; 10 rad s −1 ), yield stress of 170 Pa and shear thinning coefficient n = 0.23. For extrusionbased bioprinting of pre-crosslinked alginate, those values lie close to the optimum. These beneficial printing properties were achieved by pre-crosslinking with a molar concentration of 20 mM CaCO 3 while constantly stirring the bioink, in order to have a homogeneous distribution of CaCO 3 particles and to preserve the viscous behavior of the bioink. On the contrary, it was not possible to print a comparison bioink pre-crosslinked with CaCl 2 (instead of CaCO 3 ), even using the same salt concentrations.
Furthermore, rheological flow-sweep graphs could be used to estimate shear force, shear rate, residence time and velocity profiles in the nozzle. However, it is important to keep in mind that all calculations performed to generate the different profiles are based on the assumption of linear, steady flow and no slip between bioink and nozzle wall. In case of predominant yield stresses and resulting plug flow, the stress on cells would be reduced markedly. Thus, the absolute values should be used with caution, and they show the least favorable case in terms of stresses affecting the cells. The power-law model is restricted to describe the measured region of shear rates. As it is only an empiric model without underlying physical theory, it cannot describe the low-shear and high-shear rate constant viscosity data. Nevertheless, considering the cell viability studies, it could be proven that the increased residence time at the same pressure does not negatively affect the cell viability when pre-crosslinking the alginate. Moreover, the pre-crosslinking procedure and all components do not significantly affect viability of NIH/3T3 cells in a negative manner over a period of seven days.
Hence, the pre-crosslinking technique used in this paper was proven to be suitable for significantly enhancing the printability of alginate based bioinks without losses in the viability of NIH/3T3 cells. Thus, this technique comprises the possibility to improve the printability of alginate based bioinks in general and is therefore extremely useful in the field of biofabrication.