Relationship between shear-thinning rheological properties of bioinks and bioprinting parameters

Abstract

Three-dimensional bioprinting is a technology in constant development, mainly due to its extraordinary potential to revolutionize regenerative medicine. It allows fabrication through the additive deposition of biochemical products, biological materials, and living cells for the generation of structures in bioengineering. There are various techniques and biomaterials or bioinks that are suitable for bioprinting. Their rheological properties are directly related to the quality of these processes. In this study, alginate-based hydrogels were prepared using CaCl₂ as ionic crosslinking agent. Their rheological behavior was studied, and simulations of the bioprinting processes under predetermined conditions were carried out, looking for possible relationships between the rheological parameters and the variables used in the bioprinting processes. A clear linear relationship was found between the extrusion pressure and the flow consistency index rheological parameter, k, and between the extrusion time and the flow behavior index rheological parameter, n. This would allow simplification of the repetitive processes currently applied to optimize the extrusion pressure and dispensing head displacement speed, thereby helping to reduce the time and material used as well as to optimize the required bioprinting results.

1. Introduction

The evolution of the layer-by-layer material deposition technology called three-dimensional (3D) printing or additive manufacturing[1] has led to its implementation (as 3D bioprinting) in the health field. The principal motivation has been the limited availability of organs for transplantation[2]. 3D bioprinting is a constantly developing technology with the potential to revolutionize regenerative medicine[3].

Bioprinting can be defined as the deposition of biochemicals, biological materials, and living cells through additive manufacturing for the generation of bioengineered structures, which are made of biological and biologically relevant materials[4]. It allows cells, tissues, and organs to be printed at will depending on the needs, although this technology is currently not mature enough to printing structures for use in humans. Some of the most sought after applications are the bioprinting of skin[5,6], heart tissue[7], vascular grafts[4], cartilage[8], and hard tissues such as bone[9,10].

In bioprinting techniques, generating the desired geometry in 3D models using tissue engineering is as important as cell proliferation in the subsequent step, both of which are the key to the survival of the printed tissue and its functional success. The selected bioprinting technology also influences the strategy taken to approach the bioprinting process and the selection of the materials to be used. Bioprinting techniques are classified into inkjet, microextrusion (μ-extrusion), and laser-assisted techniques[11]. The most widely used by the scientific community is microextrusion[12], which is one of the reasons why this technology was chosen for simulation in the present study.

An important aspect of bioprinting process is to use materials that allow the native extracellular matrix (ECM) to be reproduced as a medium for cell development, that is, a medium that has the ideal biological, physical, and mechanical properties for a good bioprinting process to take place and finally that emulate the development of the desired system. Specifically, the definition of bioink is attributed to a biomaterial that contains a certain cellular load.

The materials most used as bioinks to make 3D structures are polymers, ceramics, lipids, elastomers, and hydrogels[13]. Hydrogels stand out from the rest as being the materials that best simulate the ECM and have become established as the practically universal option for bioprinting processes[14-16].

Biomaterials made of polymer chains do not usually have very good mechanical properties as they do not have any well-formed 3D structures. This is often remedied by applying a cross-linking process. This involves a reaction, in which a 3Dl network is formed by intertwining different linear or sparsely-branched polymer chains. One of the most commonly used processes is based on ionic cross-linking,[17] in which the addition of multivalent cations to the polymer solution leads to rapid gelation due to the cations’ high solubility in aqueous solutions[18]. The cross-linking agent most widely used with alginate, for example, is calcium chloride (CaCl₂).

The resulting final composition of the hydrogels directly influences the quality of bioprinting and indicates the steps to achieve a certain 3D structure. Thorough rheological characterization is therefore necessary. Thanks to rheology, the behavior of fluids can be analyzed, and different parameters obtained allow the fluids to be classified, their properties known, and their applications predicted. Thus, a specific hydrogel, such as alginate, is considered thixotropic[19-22], viscoelastic[23-25], and shear-thinning[26-30].

These properties turn out to be very interesting for bioprinting. An ideal printable hydrogel should be highly thixotropic, meaning that the viscosity of the hydrogel decreases rapidly when a shear force is applied, but recovers rapidly after the shear force is removed. It is also important to know how the viscosity behaves as the hydrogel dries before starting to print the next layer[31].

The viscoelastic behavior will favor the fluid’s maintaining the displacement properties typical of a fluid while having the structural properties of an elastic solid. In this way, it will be capable of flowing when a deformation force is applied, thus allowing the extrusion process to be achieved while also recovering part of the energy absorbed due to the characteristics of the elastic solid to form a consistent 3D structure.

Shear-thinning fluids become less viscous when a deforming force is applied. This implies that when the hydrogel is subjected to pressure in the bioprinter, these forces lead to a deformation in the fluid, reducing its viscosity, and thus resulting in a fluid that flows more readily through the printing nozzle. Once the fluid has been extruded, it is no longer subjected to the deformation force and returns to its viscous consistency.

Fluids with this shear-thinning property are governed by the mathematical model of the Ostwald–de Waele power law[32]. The equation as represented in either linear or logarithmic scales is shown in Equation I:

Where τ and γ are the shear stress and shear rate, respectively. These variables are, in turn, related to the viscosity of the fluid, and k and n are the rheological parameters of the model representing the flow consistency and the flow behavior indices, respectively. The index, n, serves to classify fluids according to their behavior so that if n is equal to unity, the fluid is said to have a Newtonian behavior, and when it is less than unity, the fluid will present shear-thinning properties.

From the above, the rheological properties are directly related to the bioprinting quality. However, the treatment and mathematical deduction of the bioprinting geometry and the application conditions for each type of hydrogel constitute a long and tedious process. This has led to increasing use of the resources provided by simulation, with which complex calculations can be carried out at high speeds, shortening the computation times and reducing or simplifying routine tests.

Computer simulations use mathematical techniques that allow the behavior of practically any type of process to be imitated. It also allows the behavior of various real systems to be studied by constructing models that manage to imitate the desired scenario. In the present study, we used the COMSOL multiphysics software package. This allows the model to be defined in terms of its geometry and constraints and the fluid’s physical conditions. It applies adaptive meshing to allow the problem to be solved through use of finite element method calculations.

In short, the purpose of this study was to form and characterize different alginate-based hydrogels, determine and catalogue their rheological behavior parameters, and finally simulate bioprinting processes under certain conditions. The intention was to analyze the possible existence of relationships between the rheological parameters or behavior of the hydrogel and the parameters of the bioprinting processes used.

2. Materials and methods

2.1. Reconstitution of hydrogels

Alginate-based hydrogels were selected and used, because they are the most widely used hydrogels by the scientific community for bioprinting[12]. The proportions of 3.5%, 4.0%, and 5.0%, combined with 3.5% CaCl₂, were chosen to study the influence of these variations since these proportions are commonly used.

The main materials to reconstitute the biomaterial were lyophilized alginate, a type-M reconstitution agent (buffer solution was prepared so that the final solution has physiological pH, making the resulting bioink suitable for cell culture), and the ionic crosslinking agent CaCl₂, all of them of the Cellink^® brand.

The protocol followed to conform the alginate-based hydrogel with CaCl₂ ionic crosslinking agent begins by preparing 2 mL of the reconstitution agent M. This solution was mixed with 70 mg of CaCl₂ to achieve a proportion of 3.5% w/v. Once mixed, the solution was filtered into a sterile 15-mL Falcon tube using a syringe and a sterile 0.22-µm syringe filter. Then, 2 mL of the resulting filtered solution was mixed with 100 mg of lyophilized alginate, previously tempered at room temperature, to obtain the alginate-based hydrogel at 5% w/v. This mixture was stirred with a magnetic stirrer at room temperature for 1 h or until the lyophilized material has completely dissolved. To obtain hydrogels in other proportions, the corresponding proportions were modified and mixed accordingly.

Once the hydrogel was formed, the pH was measured and adjusted to within the physiological range of between 7.0 and 7.4. The pH is also an important factor for obtaining appropriate viscosity of the material. The resulting materials are listed in Table 1.

Table 1.

Composition and pH of the hydrogels used

Hydrogel nomenclature	% alginate	% calcium chloride	pH
Alginate 3.5% (3.5% CaCl2)	3.5	3.5	7.23
Alginate 4.0% (3.5% CaCl2)	4.0	3.5	7.21
Alginate 5.0% (3.5% CaCl2)	5.0	3.5	7.19

2.2. Rheological characterization

The rheological properties of the hydrogels were determined with a rotational rheometer (Discovery DHR-2, TA Instruments), using a 40 mm parallel plate with a gap of 550 µm. Before testing, the samples were left to stand for 5 min to allow them to reach mechanical and temperature equilibrium.

Shear viscosity experiments were carried out with shear rates between 0.01 and 1000 s^-1, at a temperature of 37°C, to obtain the mathematical relationship between shear stress and shear rate and hence the dynamic viscosity of the hydrogels.

2.3. Modeling

COMSOL multiphysics were used to construct a 2D axisymmetric model together with a two-phase flow level set interface. We started from the real model (Figure 1) which consists of the union of the syringe containing the biomaterial, where the bioprinter exerts pressure, the nozzle (model 22G, Cellink^®), and the extrusion zone of air at ambient conditions. The geometry was modeled using trapezoids, rectangles, and ellipses, taking into account different subdivisions of the extrusion zone to give an adaptive mesh.

Figure 1.

(A) Real model. (B) The COMSOL multiphysics representation of the model.

2.4. Domains and boundary conditions

The model considers two domains. The first refers to the union of the syringe and the nozzle where the biomaterial is located, and the second to the outside of the nozzle in the extrusion zone.

The characteristic parameters of the materials were configured in the selected domains. In that of the syringe and the nozzle, the corresponding densities and rheological parameters were specified, and in the second domain, the conditions of the air. The rheological parameters were obtained through rheological characterization tests and a fit to the Newtonian power-law (Equation I), where k and n are the model’s rheological parameters, representing the flow consistency and flow behavior indices, respectively.

In addition, the edges of the geometries corresponding to the system input, output, walls, and the initial interface were defined in the boundary conditions.

2.5. Meshing

A 2D triangular-type mesh was created for the model simulations, opting for adaptive meshing since this type allows for higher resolution results in the extrusion zone of the biomaterial and coarser meshing for the zones, where no measurable or precision results are required, thus reducing the simulation’s computational load.

2.6. Simulation

Numerous simulations were carried out for the different materials, varying the system’s inlet pressure, which corresponds to the pressure exerted by the bioprinter on the biomaterial. The pressure range used was from 400 kPa to 1200 kPa, reflecting very different results for the various biomaterials studied.

These simulations provided such results as the volumetric fraction of fluid in extrusion. At low pressures, there occurs detachment of a droplet, contrary to the case at high pressures. For this reason, the inlet pressure corresponding to reaching the droplet detachment limit was evaluated for each biomaterial.

Dispensing head displacement speed is another bioprinter’s variable that needs to be controlled, since the faster the movement, the thinner the deposited line of printing, and vice versa. To this end, once the pressures are defined and set, the extrusion time with which the samples result in a similar geometry, that is, reaching a certain thickness or level, is obtained. It will thus be possible to determine how rapidly or slowly each material is extruded, and this can be related to the head’s displacement speed.

3. Results and discussion

Alginate-based hydrogels were prepared with CaCl₂ cross-linking agent with varied alginate concentrations (Table 1). The samples were light yellowish and transparent in appearance. Numerous samples of hydrogels were used, and preliminary tests were carried out varying the composition and proportions of CaCl₂ and alginate. In some cases, the hydrogels did not show significant differences in their rheological behavior. Therefore, for the benefit of a better representative and computational clarity, the results of the hydrogels that offered the most relevant results are shown.

3.1. Rheological characterization

The steady-state flow curves showed the alginate-based hydrogels to present shear rate dependence and thinning behavior characteristic of shear-thinning fluids. All three viscosity curves showed similar trends (Figure 2), but the apparent viscosity increased with increasing proportion of alginate.

Figure 2.

Viscosity versus shear rate of the 3.5%, 4%, and 5% (w/v) alginate-based hydrogels, which contain 3.5% CaCl₂ each.

By way of example, Figure 3 shows a plot of shear stress versus shear rate for the 4% alginate sample. One sees that the hydrogels show a markedly shear-thinning evolution conforming to a Newtonian power-law. From the corresponding fit, one can determine the parameters, that is, the consistency index, k, and the behavior index, n, that characterize the fluid’s viscosity behavior. These, together with the datum corresponding to the density of the hydrogels, constitute the values representative of the behavior of the materials used in the simulation.

Figure 3.

Response of the 4% alginate (w/v) and 3.5% CaCl₂ (w/v) hydrogel.

The flow consistency index, k, increased and the flow behavior index, n, decreased with increasing percentage of alginate (Table 2). Thus, the lower the alginate percentage, the closer the behavior index approaching unity – behavior typical of a Newtonian fluid. This is attributable to the properties and influence of the proportion of water present in the samples. The density of the hydrogels also increased slightly with increasing percentage of alginate.

Table 2.

Hydrogel density and power-law parameters (Equation I)

Hydrogels	Density (kg/m3)	k	n
Alginate 3.5% (3.5% CaCl2)	1009.9	0.05321	0.92846
Alginate 4% (3.5% CaCl2)	1010.8	0.32461	0.87092
Alginate 5% (3.5% CaCl2)	1016.6	2.10303	0.75444

3.2. Computer simulation

The objective was to relate the rheological data that characterize the hydrogels with those simulation parameters that have a possible relationship with those programmed in the bioprinter. To this end, it was necessary to create a model of the bioprinter using the COMSOL Multiphysics software package, as described above.

First, an adaptive mesh was set up to achieve a balance between good model resolution and acceptable computational load to differentiate the volumetric fraction of the hydrogel from that of the air. The simulation time was in the range of 6 – 10 h.

It was found that for low pressures (around 200 kPa), the sample created a droplet at the nozzle outlet that ended up falling off. For high pressures, however (around 5000 kPa), a uniform flow was created to end by being deposited onto the simulated bioprinting bed. To be able to compare the pressures at which the hydrogels exhibited this behavior, the droplet detachment limit was sought.

To compare the results of the extrusion of the different hydrogels, it was necessary to apply different pressures to the inlet in the range of 650 – 1000 kPa and to analyze the geometries of the resulting extrusion patterns so that they would be similar to each other. Figure 4 shows the most significant results of the samples with different percentages of alginate and CaCl₂.

Figure 4.

Volumetric fraction in the nozzle’s extrusion zone for the different hydrogels for different inlet pressures. Dark red represents the hydrogel, and dark blue represents the presence of air.

The observations and data show that the droplet detachment limit occurs at lower pressures the greater the percentage of alginate in the samples. In particular, the sample with 5% alginate plus CaCl₂ needs less pressure than that with 4% plus CaCl₂ to reach the droplet detachment limit. In addition, it can be seen that the samples with greater alginate percentage present a change in extrusion behavior that is less sensitive to pressure than those with a lower percentage. In particular, when the pressure at the inlet increases by 50 kPa, the sample with 5% alginate undergoes less variation in the extrusion geometry than that shown by the samples with 4% and 3.5% alginate. This is consistent with the increase in viscosity with increasing alginate percentage.

By comparing extrusion geometries of the different hydrogels at the droplet detachment limit that are the most similar (Figure 5), one obtains the pressures that would be necessary to apply to each biomaterial to achieve the same bioprinting flow. Another of the bioprinter variables to control is the head displacement speed – the faster the speed, the thinner the printing line that is deposited. For this reason, the extrusion time at which the 3 mm height mark is reached (ordinate scale in Figure 6) was determined for samples defined with the pressures set so that they would result in similar geometries. It would then be found how much faster or slower the extrusion is performed, and this could be related to the head’s speed of movement.

Figure 5.

Volumetric fraction and extrusion geometry of the hydrogels studied at the droplet detachment limit achieved at different pressures.

Figure 6.

Time for extrusion to reach the 3 mm mark in samples of hydrogel with 3.5% alginate with CaCl₂ at an inlet pressure of 950 kPa (A), of hydrogel with 4% alginate with CaCl₂ at an inlet pressure of 930 kPa (B), and of hydrogel with 5% alginate with CaCl₂ at an inlet pressure of 750 kPa (C).

The times required to pass the mark were set at 0.395 s for the 3.5% alginate sample, 0.780 s for the 4% alginate sample, and 1.610 s for the 5% alginate sample. In other words, to achieve the same line thickness in the 4% alginate sample, it is necessary to apply 1.97 times the speed defined for the 3.5% sample, and 4.07 times for the 5% alginate sample.

The resulting pressure and time parameters related to bioprinting for the different hydrogels are listed in Table 3.

Table 3.

Parameters related to bioprinting of the hydrogels

Hydrogels	Pressure (kPa)	Time (s)
Alginate 3.5% (3.5% CaCl2)	950	0.395
Alginate 4% (3.5% CaCl2)	930	0.780
Alginate 5% (3.5% CaCl2)	750	1.610

3.3. Relationship between the rheology parameters and the bioprinting

Once the rheological parameters of the hydrogels had been characterized and obtained (Table 2) and the values related to bioprinting were found for similar extrusion of the different biomaterials (Table 3), the possible existence of a relationship between these was sought.

First, a relationship was sought between the pressure applied by the bioprinter at the inlet and the flow behavior index, n, presented by various samples. Figure 7 shows a straight-line fit for this relationship.

Figure 7.

Relationship between the pressure applied by the bioprinter at the system inlet and the flow behavior index, n, presented by the biomaterials studied.

As shown in Figure 7, the linear fit is insufficiently acceptable to affirm that there is a clear relationship between the two parameters. Similarly, a relationship was sought between this pressure and the second rheological parameter obtained, that is, the consistency index, k (see Figure 8).

Figure 8.

Relationship between the pressure applied by the bioprinter at the system inlet and the flow consistency index, k, presented by the biomaterials studied.

According to Figure 8, which shows a good linear fit for such parameters, it can be said that the consistency index rheological parameter, k, is directly related to the pressure that the bioprinter must apply to the biomaterial for extrusion. In this way, with just one rheological test that uses 0.620 mL of material, it is possible to determine the input pressure that will allow good bioprinting with any bioink. A present, a trial-and-error technique is usually applied to find the said inlet pressure, leading to a large amount of wasted biomaterial. By applying the relationship presented above, the amount of material and the time used can be reduced.

The second parameter that we intended to relate is the dispensing head displacement speed that allows the line of extruded material to have the desired thickness. This variable is linked to the extrusion time reflected in Table 3, and the possible relationship was sought with the aforementioned rheological parameters.

Figure 9 represents the extrusion time versus the consistency index rheological parameter, k. No clearly conclusive relationship is apparent.

Figure 9.

Relationship between the hydrogel extrusion time and the consistency index, k, presented by the biomaterials studied.

Finally, the possible relationship with the behavior index rheological parameter, n, was sought. As shown in Figure 10, there is a clear linear relationship between the extrusion time (and therefore the head displacement speed) with the behavior index, n. Through this relationship, with just one rheological test, it is possible to calculate the equivalent speed for different biomaterials to achieve the same line thickness in the bioprinting process.

Figure 10.

Relationship between the hydrogel extrusion time and the behavior index, n, presented by the biomaterials studied.

4. Conclusion

In view of the results obtained in this study, in which the behavior of different alginate-based hydrogels with 3.5% of CaCl₂ were characterized rheologically and simulated, the following conclusions were drawn:

Alginate-based hydrogels with cross-linking agent, consisting of 3.5%, 4.0%, and 5.0% (w/v) of alginate and 3.5% (w/v) of CaCl₂, show behavior typical of a non-Newtonian, shear-thinning fluid. Furthermore, the viscosity and density increase with increasing alginate proportion.

These hydrogels present a flow consistency index, k, that increases with the alginate proportion, and a flow behavior index, n, that decreases. Thus, the lower the proportion of alginate, the closer the behavior index, n, to unity, that is, the more it corresponds to Newtonian fluid behavior.

Correct bioprinting requires an optimal extrusion pressure to be found. On the one hand, hydrogels extruded at a low pressure give rise to droplets that are released later. On the other hand, if the extrusion pressure is excessive, the speed at which the fluid comes out is so high that it produces splashes when it is deposited onto the plate. Likewise, hydrogels with lower proportions of alginate present higher sensitivity to the pressure applied at the inlet so that when the pressure is increased in smaller ranges, they present greater variation in the extrusion flow, unlike the case with higher alginate percentage samples.

Biomaterials with lower alginate percentages need higher bioprinting pressures to achieve uniform flow. With this, the extrusion times, which are directly related to the head displacement speed needed to achieve a certain line thickness, are shorter than those of hydrogels with higher alginate percentage.

It has been verified that there is a clear linear relationship between the pressure that must be applied to the biomaterial at the inlet of the system and the flow consistency index rheological parameter, k. Likewise, there is also a linear relationship between the extrusion time, related in turn to the dispensing head displacement speed, and the flow behavior index rheological parameter, n. This allows reduction and simplification of the currently repetitive processes employed to optimize the extrusion pressure and head displacement speed needed to achieve the required bioprinting results.

A new and useful way is proposed to obtain the most suitable bioprinting conditions for any hydrogel or bioink. In this way, numerous repetitive and costly tests can be avoided for the determination of the key parameters to carry out bioprinting of complex structures. The results and conclusions are supported by the simulations carried out and contrasted by experimental bioprinting tests with the prepared hydrogels. Such tests and bioprinting results will be the subject of future publications.

Funding

This research was financially supported by the European Regional Development Fund (ERDF) within the framework of the Interreg VA Spain – Portugal (POCTEP) 2014-2020 program, project number 0633_BIOIMPACE_4_A.

Conflict of interest

The authors declare no conflicts of interest

Author contributions

Raúl Sánchez Sánchez: Investigation, Writing-original draft

Jesús Manuel Rodríguez Rego: Investigation, Methodology, review & editing

Antonio Macías García: Funding acquisition, Project administration, Suppervision

Laura Mendoza Cerezo: review & editing

Antonio Díaz Parralejo: Writing-original draft, review & editing, Supervision.

Ethics approval and consent to participate

Not applicable.

Consent for publication

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Availability of data

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