Liquid trap phenomenon in the 3D micromesh structure
Liquid maintains its shape below a certain pressure limit due to the surface tension between the liquid and the solid surface of the microstructures. The micromesh structure was developed to handle the behavior of microliquids or droplets in a three-dimensional channel. The micromesh was made of photocurable polymer resin using a DLP 3D printer, and for this reason, the minimum structures that could be produced were determined. In the 3D-MMP, the thickness of the smallest rectangular frame was 200 μm, and the hole size varied from 400 μm to 800 μm. Figure 1 shows an overview of the 3D micromesh channel. The liquid trapped in the structure is outwardly convex due to surface tension. In this case, the pressure acting on the fluid is determined by the radius of curvature of the surface. When the pressure applied to the liquid was smaller than the capillary busting pressure (CBP) of the micromesh, the liquid was trapped. Especially for a stationary state, the height difference between the lowest and highest level of the liquid determines the pressure exerted on the fluid according to Pascal’s law. In other words, if the height difference in the vertical direction of the overall shape of the channel constituting the micromesh exceeds a certain value, the liquid cannot maintain its shape and begins to burst. Based on this design rule, Fig. 1B shows an example of this phenomenon by creating a trapezoidal cube and a Möbius band, which are three-dimensionally twisted structures with a height of 3 cm and a gap size of 400 μm. In the scanning electron microscopy image, the micromesh was generated without defects and with high accuracy. Thanks to the development of 3D printing and computer-aided design (CAD) technology, it has become possible to quickly and precisely fabricate complicated 3D structures that could not otherwise be obtained through conventional manufacturing methods such as soft lithography or injection molding. Using this 3D printing technology, microchannels with a complex Möbius band structure with a curved as well as a planar surface could be fabricated, and channel bundles with dimensions ranging from several hundred micrometers to several tens of millimeters can also be produced, depending on the particular applications or functions.
A Schematic explanation of the liquid patterning of post-based 2D microchannels to 3D micromesh guided patterning using Hy-MAP. The liquid was patterned in 3D mesh channel structure by surface tension. B Photograph and scanning electron microscope images of a cubic trefoil and Möbius’ twisted structure, which were difficult to fabricate with conventional manufacturing methods. The size of the gap is 800 μm and the thickness of the line structure is 200 μm.
Theoretical and experimental analysis in the liquid trap
In this study, we applied fluid dynamics and tissue engineering cell studies by expanding the phenomenon of pinning and filling fluid in 3 dimensions. To fill the liquid in designated positions, the pressure applied to the micromesh should be below the CBP. The experimental results in Fig. 2 show that the CBP increases as the size of the hole decreases and the polygon approaches the circle. Regardless of how flawless and accurate the 3D printing was, the SEM image in Fig. 1B shows that the micromesh lacked sharpness during the printing process, which caused errors between the experimental and theoretical values.
A When the size of gap is increased from 400 μm to 800 μm in size, the tendency of decreasing CBP is similar in experimental and theoretical values. B CBP increases with increasing number of sides of regular polyhedral in all sizes, and it is confirmed that the effect of shape decreases as gap size increases. C Based on CBP data, shape factors (k) were calculated for regular polygon shapes, which numerical values is used in designing other microfluidic 3D mesh structure.
We examined how the CBP varied with the size of the gap from both analytical and experimental perspectives. For the experimental setup, we fabricated simple micromesh units of different shapes and sizes and connected them with a water reservoir. We slowly elevated the level of the water reservoir to sustain the quasi-static status and recorded the water level when the liquid burst out of the micromesh. Just before the fluid burst out of the microhole or post structure, the fluid maintained a convex shape outward in the solid-liquid-gas three-phase interface according to the Young-Laplace equation (Fig. S1). In this equation, the equilibrium pressure of the fluid could be predicted according to the two radius curvatures in the direction perpendicular to the fluid at any given point. Figure 2 shows the comparison of the calculated CBP values and the experimental values when the shape of the mesh was circular. The results show that when the gap size increased from 400 μm to 800 μm, the CBP was observed at both the expected and measured values. A mesh structure with a gap size of 200 μm or less could not be fabricated due to the resolution of the 3D printer used in this work. From the analytical and experimental data, it can be inferred that with a smaller gap size, a higher structure can be patterned (approximately from 20 mm to 40 mm).
If the gap consisting of meshes is circular, the radius of curvature in both vertical directions is constant regardless of the observation direction. Therefore, it is possible to predict at what pressure the fluid will burst, as in the following equation. However, when the 3D shape of the hole or gap is a general shape other than a circle, this value is difficult to predict because the shape of the fluid just before the explosion is difficult to predict. To predict the CBP held in the polygon shape of the gap, we defined the shape factor for polygons and approximated the value through experiments. We defined a shape factor (k) by comparing the CBP in a circular gap with a diameter ({boldsymbol{a}}) and CBP in a polygon gap circumscribed to this circle for shape interpolation in a regular polygon. In addition, the size of an imaginary circle corresponding to the size of each polygon was calculated and defined as lambda (equivalent diameter). Shape factor values for triangular, rectangular, pentagonal, and hexagonal gap shapes are listed in Fig. 2C, and the values decrease as the number of sides increases.
Open channel application
Using these liquid patterning principles of micromesh, we produced a wide variety of microfluidic channels. First, a cell culture chamber with a relatively large channel size of ~5 mm was fabricated. Despite having a relatively large amount of water and increased water pressure, the gap size of ~400 μm could be reliably filled because it could theoretically hold a fluid more than 30 mm high, as calculated from Fig. 2 above (10 Pa = 1 mmH2O). By utilizing the advantage of being able to design with a 3D printer, we fabricated various types of microfluidic channels; for example, a microchannel with a width of 5 mm and a length of 20 mm and a cube with a 5-mm width and 5-mm crossing cells were fabricated. Moreover, we were able to fabricate a channel with a width and height of 1 mm using a platform with a micromesh. A 3D microchannel with a gap size of 400 μm and a frame thickness of 200 μm was designed to form two individual three-dimensionally twisted channels (Fig. 3A).
A Fabrication of microfluidic channel by injecting liquid into a micromesh and channel with width and height of 1 mm and a gap of 400 μm to trap liquid inside the microfluidic 3D channel, three-dimensionally twisted microfluidic channel (gap: 400 μm and 1000 μm). Liquid inlets are marked with black arrows. B Method of selectively filling liquid by increasing the pressure applied to the mesh by gradually increasing and immersed depths when it starts to fill liquid according to the micromesh gap size. Scale bar = 1 cm.
Hy-MAP has the advantages of not only stably filling the fluid with the pipette but also handling the surface tension of the fluid. We proposed an application that can take advantage of open microfluidic channels. Three different channels that had gap sizes of 400 μm, 600 μm, and 800 μm each were composed in one plane, and the structure was gradually immersed in the water reservoir. The pressure applied to the channel gradually increased, and the three different channels were filled to different levels with water. Based on this patterning principle, we proposed a method for selective fluid patterning by dipping the whole mesh structure in a liquid or hydrogel reservoir (Fig. 3B). In conclusion, the micromesh structure-based microfluidic channel can be manufactured by choosing a size relatively freely for selective liquid patterning, and it is possible to fabricate a channel that is complicatedly entangled in three dimensions at once.
Liquid patterning via a simple rotating micromesh structure
When filling 3D-MMP, the micromesh acts as both an inlet through which the fluid can enter and a virtual wall that prevents fluid from bursting out. The liquid is captured when the hydrostatic pressure is greater than the CBP of the composing gap size, while liquid bursts out and drains if the hydrostatic pressure increases and exceeds the critical CBP of the gap size. Hydrostatic pressure is determined by the total height of the device. The effective height determined by gravitational direction can be modified by rotating the 3D-MMP with a geometrically asymmetric structure. In Fig. 4B, the length and width and height of the 3D-MMP are 40 mm, 1.4 mm, and 17 mm, respectively, the gap sizes of S, N, and U are 400 μm, and the gap size of the background is 1000 μm. When the device was dipped into liquid, the whole channel was filled with liquid (Fig. 4B-(i)). After the device was lifted from the liquid reservoir, the liquid remained in the whole channel because the hydrostatic force from 17 mm of height does not exceed the CBP of the 1000 μm gap. However, if the device is rotated 90°, the height and length of the device become interchanged. Since the hydrostatic pressure of 40 mm is greater than the CBP of the 1000-μm gap and smaller than the CBP of 400 μm, the liquid in the letter(SNU) remains still, and the liquid in the background bursts out (Fig. 4B-(ii)). Using this simple dipping, rotating, and draining process, liquid can be patterned in the designated area much faster than injection through pipettes or syringes. One microliter droplet array (24) was formed inside the channel by applying this patterning method in Fig. 4C, which is expected to be applied in further multiple cell coculture or organoid research.
A The process of liquid patterning. Since the effective height and length interchanges in rotation procedure, liquid bursts out except for designated area. B This patterning method was demonstrated by patterning typical words in Hy-MAP. C Liquid droplet patterning by selective draining of liquid after filling liquid in whole structure. Scale bar = 1 cm (ii), 1 mm (iii).
Cell patterning and tissue engineering applications
Various approaches toward 3D patterning of fluids and hydrogels/cells have been presented in a wide variety of ways, including two-dimensional hydrogel/cell patterning inside a microfluidic chip and 3D bioprinting techniques. In this study, we developed a technique of 3D patterning by trapping hydrogels and cells using a technique that can hold liquid inside a 3D micromesh structure. We suggest several liquid patterning methods: (1) direct injection, (2) serial dipping, and (3) dipping and draining, as shown in Figs. 3 and 4. This Hy-MAP method can be applied to sophisticated cell patterning and may be an alternative to 3D bioprinting. For the cell culture study, we fabricated a micromesh-based compartmentalized structure that enabled the selective patterning of multiple cell types. Then, the device was coated with Parylene at a height of ~2 μm by the oxygen plasma-enhanced CVD method to reduce the toxicity of uncured 3D printer resin and to ensure biocompatibility for cell culture35,36. Since 3D vasculature formation is a key element of most tissues or organs, blood vessels, and stromal cells were used. Furthermore, cancer cells or spheroids were cocultured with endothelial cells, which replicates the microphysiological system of a tumor. A cell and hydrogel mixture prior to enzymatic gelation was first filled and then cured sequentially to form a cocultured structure.
To demonstrate applications of the Hy-MAP, we performed a series of coculture models including endothelial cells, stromal cells, and cancer cells. In Figure S2, a 3D vascular network was cultured in a simple three-channel micromesh platform by injecting cell-laden fibrin gel directly with a pipette. Then, the whole 3D-MMP was immersed in a 24-well plate with endothelial cell growth medium and cultured for 5 days. These coculture conditions were demonstrated in a previous study by our group37,38,39. As shown in Figure S2, vasculogenesis was confirmed in the middle region. In the fluorescence confocal microscope photographs, red-dyed sections were stained actin filaments, and lectin was stained green. To confirm the perfusion, sectional images were analyzed to confirm that the tube had a height of 10 to 50 μm.
In Fig. 5, a 3D micromesh platform with two patterning areas was fabricated for tumor-vasculature coculture experiments. Two preliminary works are required for this experiment: one is a 400–500 μm spheroid cultured on a U-shaped plate, and the other is a mixture of HUVECs, LFs, and fibrin gel in a 24-well plate. In the first step, tumor spheroids with 2 μl of cell culture medium were introduced in the inner zone, which had a 400-μm gap. Since the size of the spheroids was >400 μm, the spheroids could be stably trapped in the micromesh. Then, the micromesh platforms were simply dipped into the 24-well plate, which filled the outer zone with the HUVEC, LF, and fibrin gel mixture. As can be inferred from Fig. 2, the outer zone was composed of a 1-mm gap, which theoretically can withstand 144 kPa when it is a circle and can withstand a pressure of 123 kPa by applying the shape factor of the square (1.163). In other words, this outer mesh could hold fluid 12.3 mm high on a mmH2O scale. Since the total height of the micromesh platform was 3.8 mm, the mixture of cells and fibrin gel could stay in the micro mesh even after dipping and raising. Patterning was complete after dipping the whole platform in and out of the fibrin gel, so it was possible to perform the experiment very quickly (~10 platforms per minute) compared to most organ-on-a-chip or 3D bioprinting methods that directly inject or dispense the hydrogel. After 5 days of incubation, it was confirmed that blood vessels were formed as a monolayer around the spheroids and that the spheroids remained spherical in shape. In addition, compared to the control group in which only spheroids were cultured, it was confirmed that spheroids cultured alone without blood vessels hardly maintain a spherical shape but instead spread throughout the inner zone, whereas in the model cocultured with blood vessels, the spheroids grew while maintaining their original shape. With this series of experiments, we demonstrated that cells could be cultured through various methods, such as direct injection, dipping, dipping and draining, and confirmed the possibility of introducing spheroids or organoids through the Hy-MAP method.
A Detailed design and patterning procedure of 3D-MMP. Cancer zone (inner mesh) consists of 400 μm gap, vascular zone (outer mesh) consists of 1000 μm gap. U-87 MG spheroid was placed in cancer zone by direct injection, HUVECs and LFs are patterned in vascular zone by dipping. B, C Confocal microscope images of both experimental group (HUVECs and LFs exist in the vascular zone) and control group (Only fibrin gel exists in the vascular zone) in Day 5. D Section view of vascularized tumor spheroid. Spheroid maintains spherical form on micro vascular bed. Scale bar = 200 μm (B), Scale bar = 400 μm (C).
