Research on the flow behavior of bio-ink inside the extrusion nozzle during printing

As we all know, the rise and development of 3D bio-printing technology has brought convenience to the reconstruction of tissue engineered artificial tissues and organs,^1,2 the controlled release of drugs,^3,4 and the preparation of biological scaffolds.^5,6 Especially in the research and clinical application of tissue engineered living tissues and organs,^7–9 3D bio-printing technology has evolved into a necessary tool or method due to its ability to manufacture complex and high-precision tissue constructs. Bio-inks embedded with bioactive substances (active proteins, growth factors, and functional cells) combined with the extrusion based 3D bio-printing technology can deposit the active substances to the pre-specified position and finally, complete the accurate assembly of the bio-inks to realize the printing of the precursors of active tissues and organs.¹⁰ 

Up to now, a large number of researchers have conducted research around bio-printed living tissues and organs, and most of these investigations have gained promising progress. For instance, extrusion bio-printing technology has been applied to print cartilage for the regeneration of full-thickness chondral defect by Idaszek et al.¹¹ In his research, bone marrow-derived human mesenchymal stem cells (BM-hMSCs) have been encapsulated in different zone-specific bio-inks, deposited layer-by-layer to form a bio-construct with a unidirectional gradient of cell instructive stimuli. Neural tissues¹² were also assembled with defined human neural cell types in a desired dimension using a commercial bio-printer, and the printed neuronal progenitors differentiate into neurons and form functional neural circuits within and between tissue layers with specificity within weeks. Pourchet et al.¹³ prepared a full-layer skin with anatomical similarity to human skin by extrusion bio-printing using fibroblasts, gelatin, alginate, and fibronectin as bio-inks, and the epidermis could be fully differentiated. In terms of the cardiac scaffolds containing cells, Zou et al.¹⁴ prepared sacrificial scaffolds with multiple network pores using PVA as the sacrificial material and then filled the scaffold pores with sodium alginate, agarose, PRP, cardiomyocytes (H9c2), and HUVECs mixed bio-ink. The simplified aortic valve and anatomical heart scaffolds with multistage fluid channels can be fabricated by this method, and the cell viability is more than 90%. In addition, the academic research studies and application explorations focused on bio-printing have also been carried out in the airway,¹⁵ blood vessels,¹⁶ muscles,¹⁷ liver,¹⁸ and other aspects, and a large number of fruitful results have been achieved.

From the existing studies, it can be found that most of the current studies usually focus on material modification, processing methods, and printing equipment, but few studies pay attention to the effect of extrusion printing needles on cell activity. But in fact, the reproduction of physiological functions of tissue and organ precursors printed by bio-printing mainly depends on the activity of functional seed cells embedded in biological materials, and the shear stress caused by the extrusion flow of bio-ink inside the printing needle is the main factor causing cell damage during bio-printing.¹⁹ However, in the actual bio-printing process, researchers often choose and use needle types unthinkingly and randomly, almost without considering the effect of the needle types (cylindrical and conical) on cell damage. Some studies have shown that the maximum shear stress that cells can withstand is generally about 100 Pa, and the peak shear stress inside the needle in the printing process can easily reach the level of KPa.²⁰ Therefore, under the premise of meeting the requirements of printing manufacturing, it is important to reduce the shear stress caused by the extrusion flow of bio-ink as much as possible to reduce cell damage.

However, the flow behavior and shear stress distribution of the bio-inks inside the tiny printing needle are difficult to directly observe and measure by traditional experimental methods because of their microscopic and complex characteristics.²¹ To address this issue, in this research, the finite element simulation software COMSOL based on fluid dynamics theory was used to simulate the extrusion flow behavior of the bio-ink inside the printing needle. By establishing the flow models of two commonly used needles (cylindrical and conical needles), taking sodium alginate solution as bio-ink, the extrusion flow behavior of bio-ink inside the printing needle was simulated. Following, taking steady pressure, flow rate, and fluid shear stress as the research objectives, the response effects of nozzle geometry parameters, including shape, size, and feeding pressure, on the flow behavior of bio-ink were analyzed. This work not only provides a theoretical basis for the selection of an extrusion nozzle but also helps researchers to further understand the flow behavior of bio-ink inside the extrusion needle and reduce the damage caused by shear stress to cells in the extrusion printing process.

When using the numerical simulation method, the parameters of the power-law model of the pseudo-plastic non-Newtonian fluid such as bio-ink have great influence on the results of the subsequent simulation, so it is important to determine the parameters of the power-law model. In this research, a rotary rheometer was used to test the viscosity of bio-ink under different shear rates at 30 °C, and the shear rate was in the range of 50–900 s⁻¹. The measured data points were fitted with a pseudo-plastic non-Newtonian fluid power-law model, and the test and fitting results were shown in Fig. 1. From the distribution and change trend of the experimental data, it can be clearly judged that the sodium alginate solution belongs to the typical pseudoplastic non-Newtonian fluid. The fluid consistency coefficient of 10% sodium alginate solution is K = 10.231, and the flow index is n = 0.39.

Because the real flow situation of the fluid inside the nozzle is very complicated, a series of basic assumptions about the actual flow field is needed to make it conform to the actual flow situation and facilitate the establishment and calculation of the subsequent simulation model.^21,24 The specific assumptions are as follows: (1) continuous medium: it is assumed that the fluid is composed of an infinite number of fluid particles that are continuously connected to each other, with no gaps between them, so the fluid’s physical properties are distributed continuously within the medium. (2) Homogeneity and isotropy: that is, the properties of the fluid material at any location are the same, and the material properties are independent of direction. (3) Incompressibility: non-Newtonian fluids are all in the liquid state, and the volumetric elastic modulus of liquids is very large and the compressibility is very small. It is generally believed that its volume remains unchanged during flow and its density is a constant.

The hopper and nozzle in the bio-printing feeding device can be abstracted as an injection syringe. The bio-ink is pre-stored in a cylindrical hopper with a circular cross section. When a certain pressure P is applied to the hopper, the bio-ink flows from the hopper into the nozzle under the action of pressure. With the coordination of the movement of the nozzle, it is printed into a specific scaffold structure according to a certain trajectory. This study is based on the rheological characteristics and basic equations of alginate solution flow and analyzes the fluid flow model in cylindrical nozzles and conical nozzles, establishing fluid flow equations.

The cylindrical nozzle used in the air-extrusion molding system can be abstracted as an injection model, and the simplified model of the cylindrical nozzle model is shown in Fig. 2(a). The end of the cylindrical nozzle model can be regarded as a rigid cylindrical tube with a small inner diameter, the cross-sectional radius of which is R₂. It is assumed that there is a cylindrical body with an axial radius of r and a length of L inside the tube, the tangential stress on the surface of the cylindrical body is $τ$⁠, and the pressure on the two end faces is P and P + ΔP, as shown in Fig. 2(b).

It can be seen from formulas (6) and (8) that when the fluid reaches a stable state, the driving force acting on the microcylinder is in a balanced state with the resistance existing in the adjacent liquid layer. The stress and velocity distributions are shown in Fig. 2(b).

When the conical nozzle is connected to the cylinder, the feeding pressure extrudes the bio-ink inside the cylinder from the conical nozzle with an outlet radius of R₂. Because the diameter and height of the cylinder are much larger than the diameter of the nozzle outlet, the bio-ink in the cylinder can be approximately simplified to be in a static state, and the changes in velocity and flow rate are ignored. The simplified process of the calculation model of the cylinder and conical needle is shown in Fig. 3.

Equations (17) and (18) show that the flow velocity of the bio-ink inside the needle is a function of flow behavior and nozzle geometry parameters.

Bio-ink achieves a dynamic balance of fluid flow under pressure gradient transmission. Part of the internal fluid stress of bio-ink is the shear stress caused by the different velocities between adjacent layers in the fluid. In addition to the shear stress, the tensile flow between fluid layers will produce tensile stress due to the sharp reduction of the nozzle shape.

Bio-ink is a non-Newtonian fluid, and its power-law coefficient K and fluid flow index n are both positive numbers. It can be seen from Eq. (20) that the shear stress is positively correlated with the shear rate.

In the measurement of stress, the tensile stress $σ E$ is generally taken as the stress $ε ˙$ generated by the normal second stress difference $( τ z z − τ r r)$⁠.

Experimental studies show that when the power-law fluid is in the critical state of laminar to turbulent flow, Z = 808; when Z < 808, it is laminar flow; and when Z > 808, it is turbulent.

Substituting the flow characteristic parameters of bio-ink into Eq. (24), the feeding pressure was set to 0.6 MPa. For the cylindrical nozzle and conical nozzle, the maximum Z values calculated are 327.13 and 492.97, respectively, which are less than 808. In the printing experiment, the gas pressure used in the system is less than 0.6 MPa, so the hydrogel material is in a laminar flow state from the end of the hopper to the outlet of the nozzle. That is, the squeezing flow in the hopper and nozzle is also in a laminar flow state.

In this research, the COMSOL software was applied to investigate the flow behavior of the bio-ink inside the extrusion needle. The fluid model of the bio-ink inside the nozzle can be simplified into a two-dimensional axisymmetric model. The appropriate physical field was selected and the corresponding material parameters and boundary conditions were input. The grid division of the model is based on an ultra-fine element grid. Wall is the wall boundary condition, and Axis is the axisymmetric boundary condition. “In” is the pressure inlet, and “Out” is the pressure outlet. The inlet pressure is p_in and the outlet pressure is set to 0.

The flow of bio-ink inside the nozzle depends on the driving force resulting from the pressure difference between the inlet pressure and the outlet pressure. During the flow process, the pressure difference resists the viscous force between the biological materials inside nozzle and is passed down step by step until the dynamic equilibrium of the fluid flow is reached, at which time the pressure inside the fluid is called the steady-state pressure. The steady-state pressure is affected by the geometric parameters of the nozzle and the feeding pressure and determines the change in fluid stress and flow rate.

To reveal the distribution law of steady-state pressure in the flow channel of the nozzle, the nozzle radius d_out and inlet pressure p_in of cylindrical and conical nozzles were parameterized. When d_out was 0.84 mm and p_in was 0.3 MPa, the internal steady-state pressure distribution cloud map and isosurface distribution were viewed. In order to better observe the steady-state pressure change process of different structures and better highlight the contrast, the two key parts at the corner of the cylindrical nozzle and the exit of the conical nozzle were locally enlarged, and the steady-state pressure distribution diagram is shown in Fig. 4(a).

For the cylindrical nozzle, the internal steady-state pressure is evenly distributed between the pressure inlet and the transition section of the nozzle (z = 9 mm); from z = 9 mm to the nozzle outlet, the internal steady-state pressure gradually decreases; and the internal steady-state pressure at the outlet is 0 (the external atmospheric pressure). For the conical nozzle, the internal steady-state pressure distribution is similar to that of the cylindrical nozzle. From the pressure inlet to the transition stage of the nozzle, the internal steady-state pressure distribution is relatively uniform with little difference. The difference is that the internal steady-state pressure of the transition section of the cone nozzle changes slowly at first, but drops sharply at the exit. The amplification diagrams of the isoplane of the transition section for two nozzles show that on the same isoplane, the pressure distribution does not coincide with the horizontal plane, but is depressed downward, which indicates that the change of shape leads to uneven changes in pressure, and easily lead to a large local shear stress.

In order to more directly observe the pressure changes inside the flow channel of the nozzle, the pressure values on the internal axis of the nozzle were calculated to study the influence of the feeding pressure and nozzle diameter on the steady-state pressure. As shown in Figs. 4(b) and 4(c), the steady-state pressure of the cylindrical nozzle at the transition section turns to linear decline due to the abrupt flow channel at the transition section. The steady pressure of the conical nozzle decreases exponentially because the diameter of the transition section decreases gradually. In addition, comparing the internal steady-state pressure values of the two needles under the same conditions, it can be concluded that (1) the internal steady-state pressure of the conical nozzle is greater than that of the cylindrical nozzle from the transition section to the exit, and it will not be equal until the exit and (2) compared with the influence of inlet pressure, the change of nozzle diameter has little influence on the steady-state pressure of the nozzle.

In the printing process of the scaffold based on air-driven extrusion molding, the quality of the scaffold is directly affected by the flow rate and flux of bio-ink, especially the internal pore structure and printing accuracy of the printed scaffold. While the flow state of the bio-ink inside the nozzle is affected by the inlet pressure, the shape and diameter of the nozzle, as well as some other factors. Herein, a flow model of the bio-ink inside the nozzle was established to study the effects of inlet pressure, nozzle shape, and diameter on the flow velocity distribution, axial flow velocity, and outlet flux of the bio-ink. The simulated results are shown in Fig. 5.

Figure 5(a) shows the flow velocity distribution maps of the cylindrical nozzle and the conical nozzle. It can be judged from the result that the flow velocity of the bio-ink inside two nozzles is gradually increasing during the process of the inlet to the outlet. The flow velocity of the cylindrical nozzle in the first half of the inlet maintains a low speed. In the transition section, the flow velocity increases sharply with the shrinking of the flow channel diameter. After reaching the outlet section, the flow velocity changes little. For the conical nozzle, the flow velocity steadily rises along the flow channel, and finally, the flow velocity suddenly rises at the exit. Moreover, it can be seen from the velocity distribution diagram of the flow in the cross section that the flow velocity in the nozzle of both shapes gradually decreases from the central axis to the nozzle wall along the radius direction, that is, the velocity is maximum at the center and the velocity is minimum at the nozzle wall. This is resulted by the adhesion of the bio-ink to the wall of the flow channel, and the closer to the nozzle wall, the greater the viscous effect, resulting in a smaller velocity.

In order to clarify the effects of nozzle shape, diameter, and feeding pressure on the flow velocity and flow flux of bio-ink inside the nozzle. The flow velocity value of the bio-ink was obtained along the central axis of the nozzle, and Fig. 5(b) shows the flow velocity of the bio-ink inside the two nozzles under different inlet pressure when the nozzle diameter is 0.84 mm. It can be found that for the cylindrical nozzle, the flow velocity at the center increases exponentially from the inlet to the transition section, reaches the maximum velocity at the end of the transition section (z = 9 mm), and then maintains the same velocity. For the conical nozzle, the flow velocity increases exponentially from the inlet to the outlet until the velocity reaches the maximum at the outlet, which is 1.5 times the maximum velocity of the cylindrical nozzle under the same conditions. For both types of nozzle, the maximum flow velocity of the outlet increases with the increase of the inlet pressure. Figure 5(c) shows the flow velocities at the center of the nozzles with different outlet diameters when the inlet pressure is 0.3 MPa. The results show that the larger the nozzle outlet diameter, the higher the flow velocity.

The outlet flux presented in Fig. 5(d) was obtained by theoretical calculation and simulation. From the figure, we can judge that the size and variation trend of theoretical calculation results are very close to those of simulation results, which further indicates the reliability and accuracy of the simulation results in this work. For both nozzles, their outlet flux tends to change exponentially with inlet pressure, and the larger the outlet diameter, the more obvious the exponential relationship is. That is to say, the larger the outlet diameter, the stronger the sensitivity of the outlet flux to the inlet pressure.

Therefore, under the same conditions, the flow velocity and flux at the outlet of the conical nozzle are larger and more stable than that of the cylindrical nozzle, which indicates that if a high flow velocity is required, the conical nozzle will be the first choice. That is to say, the same flow velocity can be obtained with the conical nozzle at a lower pressure, which also means that the cone nozzle can choose a smaller feed pressure and a smaller size of the nozzle, which is beneficial to meet the basic requirements of high throughput and stability in bioprinting.

Researchers have found that the stress generated by stress transfer during the flow of bio-ink directly affects the processes of cell flocculation and suspension, causing damage to cells or active factors.²⁶ In the process of pneumatic extrusion printing, fluid shear stress will inevitably occur due to the different pressure and flow velocities of bio-ink inside the nozzle. If the magnitude or duration of the stress exceeds a certain level,²⁷ some damage will be caused to the cells or active substances contained in the bio-ink. In order to meet the printing requirements of bioactive substances, it is necessary to adhere to the bio-friendly design concept to select the geometric parameters and feeding pressure of the nozzle and then guide the selection of the nozzle and printing parameters. In order to meet the printing requirements of bioactive substances, the choice of the nozzle geometric parameters and its feeding pressure must adhere to the bio-friendly design concept.

Figure 6 shows the distributions of shear stress and tensile stress of the bio-ink inside the nozzle under the feeding pressure of 0.15 and 1.2 MPa. It can be seen from the figure that during the printing process, the shear stress and tensile stress inside the nozzle exist simultaneously. The shear stress is mainly distributed from the nozzle transition section to the needle outlet, the closer to the nozzle wall, the greater the shear stress is, and the minimum shear stress is at the center of the nozzle. This is mainly because the speed of bio-ink at the same level is different [Fig. 5(a)], and shear stress is generated between the layers and between the bio-ink and the inner wall of the nozzle. The tensile stress is concentrated in the transition section of the nozzle, and the tensile stress is maximum at the central axis, which is different from the shear stress. For cylindrical nozzles, the maximum tensile stress occurs at the end of the transition phase, and tensile stress at the outlet can be negligible, while for conical nozzles, the maximum tensile stress does not reach until the end of the nozzle outlet. The tensile stress is mainly caused by the contraction of the nozzle channel. According to results in Sec. III B, the larger the feeding pressure, the faster the flow velocity. By comparing the size of fluid stress in the two kinds of nozzle under different feeding pressures (flow velocity), it can be seen that the fluid stress generated in the nozzle is mainly shear stress at low speed. With the increase of flow velocity, the tensile stress is strengthened and gradually becomes the dominant stress. Under the same feeding pressure condition, the maximum stress of the conical nozzle is significantly higher than that of the cylindrical nozzle, which is completely consistent with the flow velocity distribution of the bio-ink inside the nozzle.

In order to ensure sufficient deposition of bio-ink, the extrusion speed of bio-ink in the actual bio-printing process is relatively low, so the shear stress is the dominant stress during the printing process. Figure 7 shows the calculation results of the wall shear stress distribution of two types of nozzle under different conditions.

For the cylindrical nozzle [Figs. 7(a) and 7(c)], its wall shear stress rises almost exponentially along the axis from the inlet and drops sharply after reaching a maximum value at the end of the transition segment (Z = 9 mm), and then maintains a constant value along the axis until the exit. The shear stress distribution curve has two obvious fluctuations, which are caused by the size change of the flow channel inside the cylinder. For the conical nozzle [Figs. 7(b) and 7(d)], its wall shear stress rises exponentially along the axis from the inlet to the outlet and reaches the maximum value until the exit position. Subsequently, the wall shear force suddenly drops at the outlet due to the angle shape of the conical nozzle. In addition, for both types of nozzles, the greater the inlet pressure, the greater the wall shear stress [Figs. 7(a) and 7(b)], which is consistent with the analysis results of the steady-state pressure and fluid flow velocity. When the inlet pressure is 0.3 MPa, the wall shear stress of the cylindrical nozzle increases with the increase of the nozzle outlet diameter [Fig. 7(c)], while the wall shear stress of the conical nozzle increases with the increase of the nozzle outlet diameter before approaching the outlet, but the maximum wall shear stress near the outlet decreases with the increase of the outlet diameter [Fig. 7(d)].

The magnitude and duration of the wall shear force are the key factors that affect the activity of cells and growth factors inside the bio-ink during printing. Here, we calculated the change curve of wall shear force on a unit volume of bio-ink in two nozzles with the inlet pressure of 0.3 MPa and nozzle outlet diameter of 0.84 mm over time. Then, the obtained curves were integrated with the time, that is, the area between the curve and the time axis, which can be used to evaluate the cumulative damage of the active substance passing through the nozzle during the extrusion printing process, a larger integral value means larger damage. From the calculation results in Fig. 8, it can be clearly seen that under the same conditions, the maximum wall shear stress generated in the conical nozzle is about twice that of the cylindrical nozzle, but the active substance stays in the cylinder nozzle for a longer time. The shear stress action time of the conical needle is 280 ms, and the shear force action time of the cylindrical nozzle is 700 ms. The time integral of the wall shear stress of the cylindrical nozzle is 29.65 Pa s and that of the conical nozzle is 18.25 Pa s, which indicates that the cumulative damage of the active substance in the cylindrical nozzle is obviously greater than that in the conical nozzle.

To further verify the above obtained conclusion, the 10 wt. % sodium alginate blending with mouse embryonic osteoblasts (MC3T3-E1) was used as the bio-ink, the nozzles with the inlet pressure of 0.3 MPa and outlet diameter of 0.84 mm were used for printing test, and the cell concentration was 1.5 × 10⁴ cells/ml. 5 ml of bio-ink was extruded through the nozzle into a Petri dish, and each group contained five parallel tests. Considering the delayed effect of cell damage, after a 6 h culture of the printed bio-ink, the live and dead cell staining, alkaline phosphatase activity (ALP), and MTT cell activity assay were conducted. All the experimental processes were carried out following the standard requirements and will not be introduced in detail here. The statistical results of living and dead cell staining, ALP activity, and MTT activity assay of the bio-ink printed by two types of nozzles are shown in Fig. 9.

Figures 9(a) and 9(b) show living and dead cell staining images, from the fluorescent images of the living cell staining, it is difficult to tell the damage of the cells in bio-ink, but the dead cell staining images show that the dead cell inside the bio-ink printed by the cylindrical nozzle is more than that of the bio-ink printed by the conical nozzle. This indicates that compared with the conical nozzle, cells are more damaged when printed through a cylindrical nozzle. Moreover, the ALP and MTT activity of the cells [Figs. 9(c) and 9(d)] printed by the conical nozzle is obviously higher than those printed by the cylindrical nozzle. A larger value of ALP and MTT activity indicates a smaller cell damage. It also means that a smaller damage will be caused by the conical nozzle than the cylindrical nozzle, which shows a good line with the simulation results and also proves the reliability and accuracy of the simulation results to a certain extent.

Therefore, based on the above analysis results, from the perspective of bio-friendliness, although the maximum stress of the cylindrical nozzle is lower than that of the conical nozzle when the feeding pressure and nozzle diameter are the same, the wall shear stress value of the cylindrical nozzle changes sharply at the transition section, where the active substances contained in bio-ink containing is most vulnerable to damage. Due to the structural characteristics of the conical nozzle, the nozzle flow channel changes slowly, the flow velocity of the bio-ink changes in the transition section tends to be stable, and the cumulative damage is less than that of the cylindrical nozzle, so the biological friendliness is better. Moreover, compared with the cylindrical nozzle, under the condition of meeting the flow velocity and printing accuracy, the conical nozzle can choose a smaller inlet pressure and a larger outlet diameter, which further reduces the wall shear stress on the bio-ink and reduces the damage to the active substances inside bio-ink to maintain their activity. This research result has important guiding significance for the selection of the nozzle.

During the bio-printing process, the bio-ink will suffer the action of fluid shear stress during the process of extrusion through the nozzle, which is the main reason for the damage of the active substances inside the bio-ink. To address the issue mentioned above, two types of commonly used nozzles (cylindrical and conical needles) were simplified and applied to investigate the flow behavior of bio-ink inside the nozzle in terms of the steady pressure, flow velocity, and shear stress by using the finite element simulation method. Moreover, the effects of nozzle geometry parameters (shape, size, and inlet pressure) on the flow behavior of bio-ink were demonstrated. Finally, combining the analysis results, a method based on the idea of integration for evaluating the cumulative damage to the active substances inside the bio-ink has been proposed and applied to evaluate the biofriendliness of the nozzle. The analyzed results show that compared with the cylindrical nozzle, when the inlet pressure and outlet diameter are the same, the steady-state pressure of the bio-ink in the conical nozzle changes steadily, which is conducive to the dynamic balance adjustment of the bio-ink. Moreover, the flow velocity and flux of the bio-ink at the outlet are larger, and the flow velocity changes are relatively stable. Under a certain inlet pressure, the steady-state pressure inside the conical nozzle decreases exponentially. With the increase of the outlet diameter, the steady-state pressure changes more smoothly, and the flow rate at the outlet also increases, which is conducive to realizing the stability and high throughput requirements of bioprinting. In addition, at the low speed flow where the bioprinting is located, the shear stress inside the two shapes of the nozzles is dominant, and the closer the nozzle is to the wall, the greater the value. The maximum wall shear stress generated in the conical nozzle is about twice that of the cylindrical nozzle, but the active substance stays in the cylinder nozzle for a longer time. The time integral of the wall shear stress of the cylindrical nozzle is 29.65 Pa·s and that of the conical nozzle is 18.25 Pa·s, indicating that the cumulative damage of the active substance in the cylindrical nozzle is significantly greater than that in the conical nozzle, which has been verified by the cell printing tests. Thus, the selection of the conical nozzle is conducive to the biofriendliness of the bioprinting process. This work not only provides a theoretical basis for the selection of the extrusion nozzle but also helps researchers to further understand the flow behavior of bio-ink inside the extrusion nozzle and reduce the damage caused by shear stress to cells in the extrusion printing process.

This project was sponsored by the National Natural Science Foundation of China (NNSFC) (Grant No. 52275292), the Key Research and Development Program of Shaanxi Province (Grant No. 2022GY-228), the Fundamental Research Funds for the Central Universities (Grant No. D5000230084), the National Key Research and Development Program of China [Grant No. 2019QY(Y)0502]. We would like to thank the Analytical AND Testing Center of Northwestern Polytechnical University.

The authors have no conflicts to disclose.

Qinghua Wei: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Visualization (lead); Writing – original draft (lead). Yalong An: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal). Mingyang Li: Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal). Xudong Zhao: Methodology (equal); Resources (equal); Software (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.