Advances in carbon-based bioinks for bioprinting: Rheology, printability, and applications

1. Introduction

1.1. History of Bioprinting

Additive manufacturing, more commonly called three-dimensional (3D) printing, is a manufacturing technique that places single layers of material on top of one another until the desired shape or part has been produced. Each layer is dispensed onto a platform, frequently called the print bed. Print beds typically move in the z-direction, allowing the layers to be stacked, while the print nozzle typically moves in the x- and y-directions. These shapes and parts are first modeled in a computer-aided design (CAD) software. The CAD part is then processed and turned into G-code that informs the 3D printer the exact location that each layer should be deposited. 3D printing technology was developed in the 1980s and has been increasing in popularity since then [1]. 3D printing uses materials such as plastics, metals, or ceramics and has made its way into a variety of fields such as engineering, manufacturing, and the medical field [1, 2]. 3D printing enables the rapid creation of prototypes, accurate and precise models, and personalized products while also allowing for parts to be made quickly and repeatably. After 20 years, additive manufacturing made its way into the field of tissue engineering. 3D printing was adopted as a technique to produce 3D scaffolds with embedded cells; this process is called bioprinting [3]. Similarly, to traditional 3D printing, bioprinting is a technique that places single layers of material on top of one another to produce the desired shape. A big advantage that bioprinting has over other tissue engineering techniques, it allows for the control of cell placement and cell density within a printed construct [4, 5]. Bioprinting utilizes materials that are biocompatible and often biomimetic as a measure to keep the cells alive and allowing them to adhere and proliferate after being bioprinted. These materials, called bioinks, are typically hydrogels, which are materials consisting mostly of water. Hydrogels can be made from a variety of materials, each having different properties, making them suitable for different applications. Before bioprinting, cells are mixed into the bioink. The bioink and cells are then printed together to form a scaffold, which supports the cells as they grow and eventually take over the construct. Some bioprinters allow for two or more different inks to be extruded at the same time [6], enabling ink combinations to be used to create scaffolds with higher degrees of customization.

In recent years, carbon-based nanomaterials, including graphene, graphene oxide (GO), carbon nanotubes (CNTs), carbon dots (CDs), and nanodiamonds (NDs), have gained increasing attention as multifunctional additives in hydrogel-based bioinks [7-12]. These nanomaterials have been shown to significantly enhance the mechanical strength, electrical conductivity, and rheological stability of bioinks, while also promoting improved cellular responses such as adhesion, proliferation, and differentiation. Additionally, their high surface area, tunable surface chemistry, and the ability to interact with polymer networks enable precise modulation of printability and structural fidelity, making carbon-based nanomaterials promising components for advanced bioprinting applications, particularly in electrically active and mechanically demanding tissues.

1.2. Bioprinters

There are different types of bioprinters used in bioprinting, including inkjet, extrusion, laser-assisted, and stereolithography (SLA) systems. Each type of printer has pros and cons when it comes to bioprinting applications. Different types of bioprinters can handle a different range of bioink viscosities, cell densities and printing speeds [13]. An overview of printer properties can be seen in table 1.

Table 1. A comparison of bioprinters with respect to their cost, cell viability, print resolution, and print speed [13]. The values represent general ranges and are not device specific.

Property	Inkjet	Extrusion	Laser	SLA
Cost	Low	Medium	High	Low
Cell Viability	>85%	40%–80%	>95%	>85%
Resolution	High	Medium	High	High
Print Speed	Fast	Slow	Medium	Fast

Inkjet bioprinters work in a way that is similar to traditional desktop inkjet printers. Inkjet bioprinters dispense successive drops of bioink onto the print bed, using heat or piezoelectric actuation to expel the drops, as seen in Figure 1. The printer dispenses the droplets in a pattern specified by a CAD model. These printers lack precision, as the printer struggles to dispense each bioink drop in an exact location. While inkjet printers are relatively safe for cells and are available at a low cost, they require bioinks with low viscosities, limiting the materials that can be used [1, 3, 14]. Low viscosity materials are required to prevent the nozzle from getting clogged.

Extrusion bioprinters push the bioink out of the nozzle in a continuous stream directly onto the print bed following the CAD specified pattern. Unlike inkjet bioprinters, extrusion bioprinters can handle viscous bioinks [2].

Extrusion bioprinters are the most commonly used type of bioprinter [2]. There are different types of extrusion bioprinters, characterized based on the way the extrusion force is produced. One type of extrusion bioprinter uses a pneumatic force, also known as air pressure, to push the bioink through the nozzle. Another type of extrusion bioprinter uses a piston to produce a mechanical force on the bioink to extrude it through the nozzle [3, 15]. The third type of extrusion bioprinter utilizes a threaded screw mechanism to feed the bioink through the nozzle and onto the platform. Each type of extrusion bioprinter can be seen in Figure 2. Extrusion bioprinters are more precise than inkjet bioprinters but exert a higher force onto the bioink as it is pushed through the nozzle, which in turn subjects the cells to high forces [16]. These forces can decrease cellular viability, which decreases the viable cell density in the printed construct. On the other hand, extrusion bioprinters allow for the use of multiple printing techniques. Direct bioprinting is the most used technique and is the layer-by-layer deposition of the bioink directly onto the print bed. Coaxial printing is the use of a nozzle with a concentric tube in the center. As the bioink is extruded out, the center tube prevents the center of the layer from being filled, like a donut. This allows for the printing of tubular structures, which can be used to mimic vasculature [3, 17, 18]. Sacrificial bioprinting, also called indirect bioprinting utilizes two different bioinks, a scaffold material and a sacrificial material, to create hollow or porous structures. In sacrificial bioprinting, the scaffold and the sacrificial ink are used to print one construct. The scaffold is cured and then the construct is placed in a solution that will dissolve the sacrificial ink. Once the sacrificial ink is dissolved, the construct is removed from the solution and often rinsed with saline or phosphate buffered saline (PBS) to remove any remaining sacrificial ink [3, 19-21].

Another type of bioprinter is the laser-assisted bioprinter. This type of bioprinter utilizes a laser pulse to propel bioink droplets off a ribbon and onto the print bed, which can be seen in Figure 3 [15]. Laser-assisted bioprinting is very precise and is nozzle free, so it is able to print with viscous bioinks. Laser-assisted bioprinting is very expensive compared to other bioprinting methods and can result in low cell viability due to the cells’ exposure to the high energy laser pulses.

The last type of bioprinter is stereolithography (SLA). SLA uses lasers or ultraviolet (UV) light to polymerize, or harden, a liquid polymer. As each layer is polymerized, the platform is lowered to allow more liquid to flood the platform and be polymerized in a CAD specified pattern. This can be seen in Figure 4. While this method is very precise, SLA exposes cells to high levels of radiation, which can affect cell viability. SLA bioprinting also has a limited number of compatible bioinks, due to the need for photosensitive materials [22].

2. Bioinks

Bioinks are the materials used for bioprinting and are typically hydrogel-based systems [23]. Hydrogels are materials that have an ability to absorb a water, giving them a high water content [24]. Bioinks must undergo physical or covalent crosslinking to form three dimensional constructs and be able to maintain their shape [3, 25, 26]. A variety of materials can be made into hydrogels, and it is often a combination of materials that allows for the hydrogel to be printable while also promoting cellular activity [1]. There are two types of materials that can be used to make hydrogels, synthetic and natural materials [19, 27]. Synthetic materials are man-made while natural materials are derived from plants or animals. Each type of material has properties that are advantageous for bioprinting and some that are disadvantageous.

2.1. Bioink properties

Many bioinks are designed to recreate the in vivo environment by mimicking the structural, chemical, and biological properties of the extracellular matrix [16, 28, 29]. Bioinks also tend to be viscoelastic, meaning they exhibit both solid and liquid behaviors [23]. While many materials with excellent mechanical properties and high printability exist for traditional 3D printing, there is still room to improve the properties of bioinks [2]. 3D bioprinted constructs must have some degree of mechanical strength to prevent the construct from collapsing on itself. Printed constructs must also be mechanically stable enough to support cell adhesion and growth [23]. The degree of mechanical stiffness and stability required varies depending on the application [2]. Rheological properties describe the viscoelasticity and flow dynamics of hydrogels [26]. There are multiple rheological properties that indicate if a bioink can be printed [23]. Hydrogels suitable for bioprinting must exhibit shear-thinning behavior, meaning that as the force or shear stress on the materials increases, the viscosity decreases [25, 26]. Shear-thinning behavior allows the bioink to be easily extruded through the printer nozzle, where forces are high, while allowing the construct to keep its shape after being printed when the forces are low. Yield stress is another important rheological property in bioprinting. Yield stress is the point at which a hydrogel no longer behaves elastically, and it starts to flow [26]. High yield stress has been linked to high quality printed constructs. This is due to the material’s ability to maintain its elasticity as it experiences the weight of successively printed layers. Bioinks with a low yield stress are more prone to losing their shape once under the weight of the rest of the printed construct [30]. Viscosity recovery is another rheological property important to bioprinting. As a bioink is printed it experiences very little shear stress, then a high shear stress while being printed, and then another period of low shear stress after being printed. If the bioink is shear-thinning, the viscosity will decrease during printing. After printing, the viscosity should return to its pre-printed value; if this does not occur, then the bioink will not be able to hold its shape, resulting in poor printability [26]. Biocompatibility is a term used to describe materials that do not cause adverse effects on cells [2]. All bioinks must be biocompatible, but bioinks should have positive effects on cells, such as promoting adhesion and proliferation while mimicking native extracellular matrix [1, 27, 31, 32]. Creating an environment that closely resembles a cell’s native environment is known as biomimicry. Biomimicry enables cells to behave as they would in in vivo environments, allowing them to thrive [2]. A summary of these properties can be seen in Table 2.

Table 2. Ideal bioink properties [2].

Property	Description
Printability	Properties that describe how the bioink is deposited and is impacted by multiple factors including rheological properties.
Biocompatibility	Cells and tissues should not be adversely affected by the material in use.
Degradation Kinetics	The rate at which the bioink degrades should be the same rate at which the cells are taking over the construct.
Structural and Mechanical	Materials used should be strong enough to support cellular activity and the weight of the bioprinted construct.
Biomimicry	The material properties should contribute to the microenvironment and be chosen with specific cell types or tissues in mind.

2.2. Carbon-based bioinks

Carbon-based nanomaterials, such as graphene, graphene oxide (GO), carbon nanotubes (CNTs), carbon dots (CDs), and nanodiamonds (NDs), have emerged as multifunctional additives for hydrogel bioinks. Even at low concentrations, typically below 0.5 wt%, these fillers markedly enhance rheological behavior, print fidelity, mechanical robustness, and in some cases electrical conductivity—properties that are crucial for electroactive tissue constructs and cell viability [8, 10, 12]. GO in particular improves viscosity and resolution in alginate/gelatin, gellan gum, and collagen systems, supporting high cell viability and microarchitecture fidelity [8, 10]. CNTs act as conductive reinforcers, with hyaluronic-acid/MWCNT bioinks demonstrating superior mechanical strength and cell compatibility for cartilage constructs when dispersion and endotoxin levels are properly controlled [9]. Carbon dots extend functionality further by serving as visible-light photoinitiators for protein-based hydrogels such as silk fibroin, enabling gentle crosslinking and intrinsic fluorescence for bioimaging [11]. Nanodiamonds, being sp³-bonded and chemically inert, improve the toughness and cell adhesion of gelatin hydrogels, showing promise for long-term stability in extrusion-printed scaffolds [7]. Thus, carbon nanomaterials offer a powerful toolbox for tailoring the mechanical, electrical, and biological performance of next-generation bioinks aimed at functional tissue manufacturing.

2.3. Natural bioinks

Natural bioinks frequently used in bioprinting include collagen, alginate, gelatin, agarose, and hyaluronic acid [2, 23]. Natural bioinks are advantageous because they are biocompatible, closely mimic in vivo environments, and promote cellular activity such as adherence, maturation, differentiation, and proliferation [16, 28, 29]. From a biocompatibility and cell health perspective, natural bioinks seem to be the perfect group of materials for bioprinting, but natural hydrogels often lack the mechanical and rheological properties needed for constructs to keep their shape after bioprinting [2].

2.3.1. Matrigel

Matrigel is a natural material derived from the basement-membrane of Engelbreth-Holm-Swarm (EHS) mouse sarcoma, containing important components of the ECM surrounding tumors [3, 33]. Matrigel is frequently used in cancer cell culture because it closely mimics the in vivo environment consisting of laminin, collagen IV, and entactin among many other components [34-36]. Cancers most commonly start in epithelial cells, which grow on and interact with the basement-membrane. Cancer cells then have to penetrate the membrane to reach vasculature and spread throughout the body [37]. Due to the importance of the basement membrane in the development of cancer, Matrigel is a seemingly good material to choose, but the material composition varies from lot to lot, making it unreliable to use in experiments as it cannot be proven whether a change in cellular response is due to the variability in the material or the treatment given to the cells [35, 38]. Aside from Matrigel’s variable composition, it can contain contaminants from mice, and it has poor mechanical and rheological properties meaning it cannot be printed on its own or produce large-scale products [33, 36].

2.3.2. Gelatin

Gelatin is a denatured protein, derived from collagen and is frequently used in bioprinting due to its non-toxic and non-immunogenic effect on cells, while also promoting cell adhesion and migration [13, 22, 39]. Like many other natural hydrogels, gelatin has poor mechanical properties; thus, it is frequently used in combination with other materials to increase its printability [22, 40]. Methacrylamide and methacrylate groups are frequently used with gelatin to improve its mechanical properties, while keeping its biocompatibility and biomimetic properties. When the methacrylamide and methacrylate groups are added the bioink becomes semi-synthetic and photocrosslinkable [41]. The improved mechanical properties, photocrosslinkability, and gelatin’s ability to form gels at relatively low temperatures increase the shape fidelity of the printed construct [39]. Gelatin is also frequently used in combination with alginate, another natural hydrogel. Gelatin-alginate bioinks have the added benefit of increased biocompatibility and biomimetic properties, as well as allowing for multiple crosslinking agents to be used, slightly increasing the mechanical properties [42].

2.3.3. Alginate

Alginate is another commonly used natural biomaterial that is derived from bacteria and marine algae [13, 22]. Alginate is biomimetic, promotes cell adhesion, and only creates a minimal inflammatory response [43]. While alginate’s biological properties are not as favorable as those of gelatin or collagen, it has better mechanical properties, resulting in higher print fidelity [13, 22, 43]. Alginate can gel quickly when exposed to Ca²⁺, often in the form of calcium chloride (CaCl₂), an ionic crosslinking agent [39, 42, 44]. Alginate is typically used in combination with other natural hydrogels to improve its biological properties [13]. To enhance the mechanical properties of hydrogels, alginate is often added to a blend to allow additional crosslinking methods to be utilized, such as UV crosslinking. Dual crosslinking creates more stable structures [43].

2.3.4. Collagen

Collagen is the most abundant protein in mammals, typically found in skin, bones, tendons, and connective tissue [25]. Collagen is a natural bioink and is classified into 28 different types, each type is given a Roman numeral [13]. Types I-III are the most prevalent in the human body [45]. Collagen type I is one of the most important components of the extracellular matrix and is used most often in bioprinting [22]. Collagen has many cell binding sites, high cell viability, and promotes cell proliferation [25], but hydrogels made with very high percentages of collagen lead to negative effects on cell proliferation and differentiation [45]. On its own, collagen has a low viscosity and weak mechanical properties, making it a poor candidate for bioprinting in its unmodified state [25, 45]. To allow for the printing of collagen, it is typically used in combination with other natural materials such as alginate, gelatin methacrylate, hyaluronic acid, or a combination of two or three materials [13, 25].

2.4. Synthetic bioinks

Synthetic bioinks come from man-made materials. The most commonly used synthetic bioinks include poly (ethylene glycol), poly (lactic acid), and poly (glycolic acid) [3]. While synthetic bioinks aren’t as commonly used in bioprinting, they do have some advantages [22]. Synthetic bioinks have good mechanical properties for bioprinting and their mechanical and rheological properties can be tuned by changing the molecular weight. The disadvantages of synthetic bioinks are that they are generally not biomimetic, meaning they cannot support cellular activity on their own [2, 22, 33].

Poly(ethylene glycol) diacrylate (PEGDA) is a synthetic hydrogel synthesized by adding acrylate groups to both ends of the poly(ethylene glycol) (PEG) polymer and is available at a low cost [22, 46]. With properties such as high biocompatibility, low immunogenicity, and tunable mechanical properties, PEGDA is one of the most frequently used synthetic bioinks for bioprinting [22, 33, 46]. PEGDA is crosslinked using a photoinitiator along with exposure to UV light, a process that typically isn’t toxic to cells [33, 47]. While PEGDA is biocompatible and non-toxic, it lacks biomimetic properties, meaning biological and chemical signaling molecules must be added in order to support cellular adhesion, proliferation and other activities [33]. Poly (L-lactic) acid is another synthetic material used as a bioink in bioprinting. Although it is not used as frequently as PEGDA, poly(L-lactic) acid is biocompatible and non- toxic. Like most other synthetic hydrogels, poly(L-lactic) acid is not biomimetic and cannot support cellular activity without the addition of biological factors [22]. A comparison of natural and synthetic bioinks can be seen in Table 3.

Table 3. Advantages and disadvantages of natural and synthetic bioinks [1, 2, 48, 49].

	Natural	Synthetic
Description	Derived from natural materials like plants and animals	Man-made
Advantages	·  Biocompatible and usually biomimetic	·  Tailorable to specific applications by changing functional groups and molecular weight ·  Non-immunogenic
Disadvantages	·  Not tailorable	·  Not biologically active

3. Bioink characterization

Bioinks have been characterized in a variety of ways, including the investigation of rheological properties, mechanical properties, and degradation kinetics, as well as compression testing and swelling ratios. Of these, rheology is one of the most important in the ability to predict the quality of the resulting bioprinted construct [31].

3.1. Rheological properties

Rheology is the study of the deformation and flow of a material in response to applied forces [26]. These responses give insights on material behavior, including viscoelasticity and thixotropy [23]. The materials that are typically subject to rheological testing are those that are non-Newtonian, as Newtonian fluids have rheological properties that are independent of shear [23, 26]. The rheological properties of bioinks are studied because they are known to impact cell behavior such as proliferation and differentiation, and the overall performance and quality of the end 3D printed construct [23, 31, 50, 51]. Properties such as viscosity, viscoelastic shear moduli, viscosity recovery, and shear stress can be linked to a hydrogel’s performance during all stages of printing [26, 52-54]. Bioinks must have a dominant elastic behavior, except during extrusion [23]. They must also be viscous enough to be extruded by a bioprinter and maintain their shape after being printed [31, 55]. Although its potential isn’t always fully utilized in experimental work, rheology is an important tool used to evaluate properties that have impacts on the overall outcomes of printed constructs and the bioprinting process, which can be seen in Figure 5 [23, 26].

3.1.1. Viscoelastic properties

Bioinks are typically viscoelastic materials. The elastic or solid part of the material’s behavior is described by the storage modulus (G’), also called the elastic modulus. The viscous or liquid part of the behavior is described by the loss or viscous modulus (G”). A balance between the storage and loss modulus is necessary for hydrogels to be able to produce quality 3D bioprinted constructs [26]. A dominant storage modulus is desirable for bioinks because the hydrogel must be able to maintain its shape after being printed [45]. Another measurement related to viscoelastic behavior is the loss factor (tan(δ)), which can be calculated by dividing the loss modulus by the storage modulus [26]. When the phase angle (δ) is equal to zero, the material is ideally elastic. Viscous materials have a phase angle of 90 degrees. Viscoelastic materials have a phase angle between 0 and 90 degrees [57]. Gao et al. found that bioinks with low loss factors have an increased print accuracy in the vertical (z) direction and a high loss factor resulted in increased print precision [26, 58].

3.1.2. Flow behavior

The flow behavior of bioinks is an important property to understand as it greatly affects how the material behaves during the bioprinting process. A material’s flow behavior is a result of multiple material properties, including its viscoelastic properties and viscosity [23]. Bioinks with predominantly viscous behavior flow easily and are unable to maintain their shape. On the other hand, bioinks that are close to ideal elastic materials cannot be printed because they are brittle and will fracture under the stress of being extruded [23]. A happy medium is required for successful bioinks.

Viscosity, the resistance of fluid to flow under stress, is another important rheological property and is one of the most studied in relation to bioprinting [23, 26]. As a function of shear rate, viscosity can provide a lot of information on material behavior. Print accuracy, print fidelity, and extrudability are influenced by viscosity. High viscosity bioinks have been known to increase print accuracy and increase yield stress [26, 56]. When the viscosity of a material increases as the shear rate increases, the material is shear-thickening. When the viscosity decreases as the shear rate is increased, the material is shear-thinning. Shear-thinning occurs because the internal bonds of the material start to break as stress increases, causing the polymer chains to disentangle, allowing the material to flow more easily [23, 59]. High degrees of shear-thinning are associated with poor mechanical strength because the secondary bonds within the material structure are weak [60]. Shear-thinning and shear-thickening behaviors are time independent and are frequently modeled using the power law, Equation 1, also known as the Ostwald-de-Waele model, where η() is the viscosity, m is the consistency index, is the shear rate, and n is the flow index [26, 61].

When the value of n is equal to one, then the material is Newtonian. The further the value is from one, the higher the degree of shear-thinning or shear-thickening. Values of n less than one indicate the material is shear-thinning and values of n greater than one indicate shear-thickening [23, 26]. Shear-thinning is an important property of bioinks. Shear-thinning bioinks prevent nozzle clogging in extrusion bioprinters, because the material flows more easily in the nozzle where stress is the highest and give the material the ability to be stacked on itself [62-64]. This property also reduces stress on cells during extrusion [23].

Viscosity recovery is another property related to flow behavior. Viscosity recovery is a measure of how viscosity changes with alternating periods of low and high shear stress [26]. During the first period, when the shear stress is low, it is expected that the bioink will have a relatively high viscosity. Then, during the period of high shear, the viscosity is expected to decrease due to its shear-thinning properties. The third period is one of low shear. If the viscosity during the third period reaches at least 80% of the original viscosity, then the material has sufficient viscosity recovery [23, 65]. Rapid and high viscosity recovery enables bioinks to flow through the nozzle easily and helps create constructs with higher print resolution and shape fidelity [52].

3.1.3. Yield stress

The yield stress, or yield point, of a hydrogel is the stress at which the hydrogel starts to flow [23, 26]. The Herschel-Bulkley law states that below the yield stress, the hydrogel will behave elastically, and above, the material behaves in accordance with the power law in Equation 1 [23]. In bioprinting, the yield stress of a bioink has multiple implications. The yield stress of a bioink is not only a predictor of the required printing pressure needed to extrude the bioink, but it can also be a telling sign of how well the bioink will be able to support the layers being stacked on itself [23, 30]. Bioinks with a very low yield stress are unable to support the weight of subsequently stacked layers which leads to low quality printed [23, 26, 52]. On the other hand, high yield stress enables the first printed layers to keep their shape and support each layer printed after [26]. The yield stress of a bioink is unaffected when cells are added [23].

3.2. Rheological testing

The testing used for rheological characterization in bioprinting consists of two types of measurements, continuous and oscillatory. Measurements are continuous if the shear rate as a function of time is constant [23]. During continuous measurements, stresses and shear rates are measured once steady state flow is reached after the respective stress or shear rate is applied [23]. In oscillatory measurements shear stress or strain vary with time and either have a controlled stress or strain. Oscillatory measurements are used to look at time dependent behavior. Small-amplitude oscillatory shear (SAOS) measurements are used to investigate viscoelastic behavior, having the ability to look at the elastic behavior and viscous behavior separately [23].

3.2.1. Oscillation amplitude sweep

The oscillation amplitude sweep is an oscillatory test used to determine the linear viscoelastic region (LVR), which is the range of strain values where G’ and G” act independently of strain [23, 26, 52]. The LVR is an important value to obtain at the beginning of rheological testing, as subsequent tests use strain as a constant parameter and it is important to ensure that G’ and G” are independent of strain in other tests so the changes in viscoelastic behavior can be attributed to the independent variable instead of strain [23].

Oscillation amplitude sweeps are conducted by subjecting a hydrogel to a wide range of strains with a constant angular frequency [23]. Du et al. performed an oscillation amplitude sweep on their hydrogel with a gap of 200 μm at 25°C. They used a strain range of 0.01% to 100% and chose a fixed frequency of 1 rad/s [45]. Hu et al. selected a gap of 0.35 mm and a strain range of 0.01% to 500% with a fixed frequency of 10 rad/s [52]. The results of a standard oscillation amplitude sweep can be seen in Figure 6.

The linear viscoelastic range is the point at which the storage modulus starts to decrease, and the loss modulus starts to increase [52]. The point where G’ and G” cross over is known as the flow point and is the point where the dominant behavior switches from being elastic to being viscous [23].

3.2.2. Oscillation frequency sweep

An oscillation frequency sweep is an oscillatory rheological test used to individually look at the storage and loss moduli as functions of frequency. This test allows for analysis of how G’ and G” change with frequency and which behavior is dominant. In bioprinting, it is important that bioinks have a dominant elastic behavior, as a bioink’s elasticity is one of the factors that allows it to maintain its shape after being bioprinted [23].

Oscillation frequency sweeps are conducted with a constant strain that is within the LVR, and a range of frequencies. Hu et al. performed their oscillation frequency sweep with a strain of 0.1% and a frequency range of 0.1 to 100 rad/s, the results of which can be seen in Figure 7 [52]. Minjares-Fuentes et al. performed the same test [61].

When looking at the results of an oscillation frequency sweep, a storage modulus that is much greater than the loss modulus without the two crossing over indicates that bioink has a stable, solid-like behavior, which is ideal for bioinks because it allows the printed construct to keep its shape [23, 52]. This type of solid, frequency independent behavior is expected in gels due to their supramolecular structure [23].

3.2.3. Shear rate sweep

Shear rate sweeps are continuous measurements that examine how viscosity behaves as a function of shear rate [23]. This test is used to identify shear-thinning behavior. As discussed previously, a material has shear-thinning behavior if its viscosity decreases as shear rate is increased. This behavior can be seen in Figure 8.

Shear rate sweeps consist of subjecting the material to a range of shear rates while all other parameters are kept constant. Bociaga et al. chose a shear rate range from 0 to 160 1/s at room temperature [24]. Hu et al. and Minjares-Fuentes et al. used similar protocols but used shear rate ranges of 0.01 to 1000 1/s and 0.01 to 300 1/s, respectively [52, 61]. The decreasing line on a shear rate versus viscosity graph is indicative of shear-thinning behavior and is often modeled using the previously described power law.

3.2.4. Yield stress determination

A steady shear or strain sweep is used to study the yield point of a hydrogel [53]. During a steady shear rate sweep, the yield stress is defined as the stress at which viscosity decreases by several orders of magnitude. Yield stress can also be determined by performing a dynamic oscillatory stress sweep. In this test the yield stress is the point at which G’ and G” crossover, indicating a change from dominantly elastic behavior to dominantly viscous behavior [52]. Minjares-Fuentes et al. conducted a steady shear sweep using a shear rate range of 0.1 to 300 1/s [61]. Ning et al. used a shear rate range of 0.1 to 1000 1/s to conduct a steady shear sweep [53].

3.2.5. Time sweep

Time sweeps are occasionally used to study if and how a hydrogels viscoelastic behavior changes over time as well as determining gelation time [23]. Flores-Torres et al. used a time sweep to determine gelation time. The hydrogel was loaded at 37°C and quickly cooled to 25°C to simulate the temperature change at the time of printing. The test was run for 2 hours, collecting G’ and G” once every minute. The results showed that Matrigel accelerated the gelation process [68].

3.2.6. Viscosity recovery

The viscosity recovery test, also known as the three interval thixotropy test (3ITT), is used to measure how much of the material’s original viscosity can be recovered after a period of high shear [23]. This is an important property to study in bioprinting as it allows the flow behavior of the bioink to be studied under conditions which mimic those of the bioprinting process [26].

The viscosity recovery test, which is a continuous measurement test, consists of alternating periods of low and high shear rate. The first period, one of low shear stress, is designed to mimic the conditions of the bioink in the printer cartridge prior to bioprinting. The next period is one of a high shear rate, which is meant to reflect the high shear rates that bioinks experience while being extruded through the printer nozzle. The last period, one of low stress is reflective of the bioink sitting statically on the print bed [23, 26, 69].

Hu et al. conducted a three interval thixotropy test, with periods of low shear were at a rate of 0.1 1/s and high shear rate at 100 1/s [52]. Davila et al. set the rest period shear rates to 1 1/s and high shear periods had various shear rates for different runs ranging from 50 1/s to 700 1/s [69]. As seen in Figure 9, when the shear rate increases, the viscosity decreases due to the shear- thinning properties of bioinks. It is the behavior of the viscosity after the shear rate has been greatly reduced that is important to the quantification of viscosity recovery. Ideal bioinks can fully recover their viscosity in a very short period of time, with adequate recovery being 80% [23, 65].

3.2.7. Temperature sweep

Temperature sweeps are oscillatory measurements used to investigate how a bioink’s behavior changes when temperature is not constant. They can also be used to determine the sol- gel transition temperature, which helps find the temperature range at which the material behaves like a solid [23]. Du et al. cooled a bioink from 40°C to 4°C with a constant strain of 0.5% and an angular frequency of 1 rad/s [70]. Ning et al. also used cooling to study the effects of temperature change on a hydrogel, cooling it from 30°C to 5°C at a rate of -1°C/min with a constant frequency of 1 Hz and constant strain of 1% [53]. Park et al. also cooled hydrogels during the temperature sweep but did so at three different rates, 0.3°C/min, 0.6°C/min, 2.5°C/min, and 10°C/ min. This resulted in the conclusion that the higher the cooling rate, the lower the temperature needed to cause increases in G’ and G” and to cause gelation. This result was also reflected with changes in heating rates [26, 71]. Hu et al. took the approach of heating the bioink and carried out the test under a constant frequency of 10 rad/s and a strain of 0.5%. The bioink was heated from 5°C to 45°C at a rate of 0.05°C/s [52]. It should be noted that the temperature should not be increased at a rate faster than 2°C/min, as the bioink may not fully reach the desired temperature [26, 72].

3.3. Print quality

As the field of bioprinting is relatively new, there has not been a consensus on how to quantify the overall quality of bioprinted constructs. The term ‘printability’ is frequently used when defining the quality of a bioprinted construct, but the definition varies greatly throughout the literature [23, 26, 73-78]. Some definitions of printability stem from rheological properties, while others are influenced by crosslinking, nozzle size, printed pore and bioink dimensions, how well the printed construct mimics the CAD model, filament spreading ratio, or the mechanical properties of the final printed construct [26, 73, 77, 79]. Bom et al. set forth some definitions for printability, extrudability, print accuracy, print fidelity, and print precision based on what was found in the literature, which can be seen in Table 4 [26]. These definitions and their applications in current literature will be discussed further in the later sections.

Table 4. Print quality terms and definitions. Adapted from Ref [26], copyright Elsevier.

Concept	Definition
Printability	The ability of a certain ink to achieve extrusion and maintain shape fidelity with high printing accuracy, which is influenced by pre-printing (rheological and nozzle features), printing (design, slicing, g-code (e.g., pressure, temperature and feed rate) and non-g-code parameters (e.g., environmental conditions)) and post- printing parameters (e.g., crosslinking, coating or drying techniques).
Extrudability	The capability of achieving extrusion, which is influenced by rheological parameters, printing parameters and environmental conditions.
Printing accuracy	Degree to which the 3D printed construct matches their size and spatial location, with respect to the original CAD model in terms of length, width, and height.
Printing fidelity	Degree to which the 3D printed construct matches their geometry with respect to the original design file in terms of length and width.
Printing precision	Measures the repeatability or reproducibility of a print in terms of size, geometry, and spatial location.

3.3.1. Printability

Printability is one of the most commonly used terms to describe bioprinted constructs in literature, but the term has a lot of ambiguity [26]. Bom et al. put forth the definition that printability is the ability of a bioink to be used to create a 3D construct layer by layer following a CAD model [26]. He et al. set forth two parameters for the definition of printability, including the ability to form filament and the ability be stacked in a layer by layer manner to create 3D structures as similar to the 3D model as possible [23, 73]. Li et al. do not give a quantitative definition of printability but state that it is determined by a combination of factors, including rheological properties, cross-linking, and printing parameters [74]. Naghieh et al. define printability as a hydrogel’s ability to form a reproducible 3D printed construct that maintains its shape [75]. Gillispie et al. provide a rather abstract definition, defining printability as the ability to achieve desirable printing outcomes [80]. Godoi et al. state that the printability of a bioink depends on the bioink’s material properties and crosslinking mechanisms [78].

Along with the multiple proposed definitions for printability, there are also multiple proposed tests to quantify printability. Ouyang et al. developed a test for quantifying printability. The test is conducted by printing a square grid and measuring the perimeter and area of each grid pore. The measurements are then used in the printability equation (Pr) where C is the circularity of an enclosed area (C = 4πA L²), L is the perimeter, and A is for area shown in Equation 2. When using the printability equation, printability values closer to 1 indicate better printability as seen in Figure 10 [26, 36, 76, 77, 81, 82].

Naghieh uses multiple tests to measure printability. First, the strand diameter was calculated using the Equations 3, 4, and 5 where ρ is the density, Q is the flow rate, and Ds is the standard strand diameter [75].

Once the strand diameter was determined, strand printability was calculated using the strand printability equation in Equation 6 where Dexp is the experimental strand diameter. Values for strand printability closer to 1 indicate better strand printability [75].

3.3.2. Print accuracy

Print accuracy describes how well the printed construct matches the designed CAD model, including the size, shape, and location [26, 80]. Others have described print accuracy through a theoretical calculation called the Parameter Optimization Index (POI). The POI equation, Equation 7, considers factors such as nozzle gauge (D_G), printing pressure (p), and printed line thickness (t_line) [26, 31, 83]. Increased POI indicates greater print accuracy.

Multiple tests have been used to quantify print accuracy. Kang et al. used unitless indexes of L’, W’, and H’ to investigate the print accuracy of the length, width, and heigh of the construct, as seen in Figure 11. In the L’ index equation, A is the average under printed length, B is the overlapping printed length, and C is the overprinted length. L’ can range from zero to one, with a value of 1 indicating the best print accuracy. For equation W’, W_avg is the average construct width and D is the nozzle diameter. In the H’ index equation H is the construct height and T the average thickness [26, 84].

De Stefano et al., as well as Giuseppe, printed multiple single layer square grids with varying pore sizes. Photos were taken of the printed constructs and analyzed using ImageJ software. A print accuracy percentage calculation was then used to quantify the results. In the print accuracy equation, Equation 8, A_i is the printed area of each pore and A is the originally designed pore area, with high printer accuracy values indicating higher quality prints [31, 36].

3.3.3. Print fidelity

Print fidelity, also referred to as shape fidelity, is a printed construct’s ability to retain its shape after being printed [26]. The rheological properties of yield stress and viscosity influence print fidelity. Higher yield stress and viscosity are associated with better shape fidelity because the bioink is more resistant to flow [23, 26, 85]. The main phenomenon that affects shape fidelity is bioink spreading, which is when the bioink spreads out and flattens once it is deposited on the print bed [26].

To investigate the shape fidelity of individually printed strands, Soltan et al. developed a strand uniformity test. The test consisted of printing multiple strands and imaging them. ImageJ was then used to measure the length of the outer edge. The uniformity factor equation in Figure 12 quantifies how similar the printed strand was to a perfect strand. Strands with a uniformity factor of 1 represent strands that are the same as the theoretical strand [26, 82].

He et al. used a grid to evaluate the print fidelity of grid structures (Figure 13). This test was conducted by printing a square pore with a known pore area (Art). Once the construct was bioprinted, the experimental pore area (Are) was calculated. The equation in Figure 13 is then used to calculate print fidelity [73].