Creating 3D Objects

Abstract

The present invention provides a method for forming a 3D object, comprising the steps of: providing a photocurable resin; providing a print head for transmitting curing radiation to the photocurable resin; introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein the print head has a cavity for containing the gas, where the gas-resin interface is constrained by the print head and defines a printed surface; and projecting curing radiation onto the submerged gas-resin interface to promote curing of the resin on the printed surface; and promoting relative movement between the gas-resin interface and the resin to produce the 3D object. The method may also include the step of transmitting acoustic waves to the submerged gas-resin interface.

Description

[Technical Field]

[0001] The present invention relates, in general terms, to methods and systems for forming 3D objects, and more specifically, to methods and systems for forming 3D objects using photocurable resins. [Background technology]

[0002] Additive manufacturing is a rapidly expanding and multifaceted field that provides tools for producing arbitrary 3D objects with complex outlines. Advances in this field are extending to applications such as rapid prototyping, medical devices, aerospace components, microfabrication strategies, and even artificial organs. Among additive manufacturing techniques, optical printing of photocurable resins, including two-photon polymerization, projection microstereolithography, and volumetric printing, is attracting considerable attention due to their superior spatial resolution and material versatility.

[0003] Conventional optical printing methods, such as stereolithography, typically involve the application of light to induce localized layer-by-layer polymerization of a photocurable resin. While these techniques readily produce dimensionally accurate parts, the printing speed is inherently limited by the need to repeatedly reset the position of the part between printed layers. Furthermore, these techniques do not allow for the printing of free-floating structures because they are limited to bottom-up printing, starting from the layers adhering to the printing stage.

[0004] Continuous Liquid Interface Production (CLIP) is a recently proposed printing technique that achieves higher printing speeds by directly regulating the oxygen concentration within the printing volume. In CLIP, polymerization light is projected upward through an oxygen-permeable window at the bottom of the resin vat (bottom-up configuration). The increased oxygen concentration in the resin layer directly above the window prevents polymerization at the printing boundary, thus enabling high-speed printing of objects that can be sequentially pulled out of the resin vat. However, the need to sequentially extract the printed structure from the resin vat makes it difficult to print extremely soft materials such as hydrogels that lack self-supporting properties.

[0005] The limitations of existing layer-by-layer printing techniques have been partially overcome by recent developments in "volumetric" printing procedures, which enable simultaneous printing of resin volumes on a centimeter scale. An example of volumetric printing is computed axial lithography, in which a target projection is exposed from an azimuthal angle while a vial containing a photopolymer is rotated, thereby inducing polymerization within the resin volume corresponding to the 3D object through the cumulative intersection of light rays. Xolography is a further volumetric technique based on the polymerization of spiropyran photoswitched photoinitiators. This technique requires focusing a 2D projection within the resin volume and intersecting it with two orthogonal sheets of light of different wavelengths, where selective polymerization occurs at the intersection of these two light paths.

[0006] However, while volumetric printing offers free-floating, layerless, and rapid fabrication of flexible structures, it is only effective on highly permeable resin formulations. This essentially hinders high-speed bioprinting, which is primarily performed on resins containing viable organisms (e.g., cells) that scatter light, thus preventing precise optical focusing across the expanded volume of the resin.

[0007] Therefore, there remains an opportunity to develop techniques for creating 3D objects that address one or more limitations of existing methods. [Overview of the Initiative]

[0008] The present invention is a method for forming a 3D object, In the step of providing a photocurable resin, In the step of providing a print head for transmitting curing radiation to the photocurable resin, the print head has a cavity for containing gas. In order to form a submerged gas-resin interface between the gas and the resin, the print head is introduced into the resin, where the gas-resin interface is constrained by the print head and defines the printing surface. In order to promote the curing of the resin on the printed surface, a step is to project curing radiation onto the submerged gas-resin interface. A step to promote relative movement between the gas-resin interface and the resin in order to produce the 3D object. This provides a method for providing this.

[0009] Providing a recessed gas-resin interface constrained to the print head enables precise spatial curing of any volume of resin, regardless of the resin's properties and formulation. Because the gas-resin interface essentially defines the printing surface constrained to the movable print head, the method advantageously provides high-speed, precise, and highly customizable positioning of the printing surface at any point within the resin volume.

[0010] Furthermore, the gas-resin interface provides a mechanical barrier to prevent cured resin from adhering to the print head. As a result, the method enables the precise and high-speed production of self-supporting 3D structures, including flexible structures, at any point within the resin volume.

[0011] From an optical standpoint, providing a printed surface at the gas-resin interface dramatically minimizes the optical defocusing and aberration effects of curing radiation, thereby providing minimal to no refractive index change along the radiation path. This significantly facilitates the rapid creation of arbitrary, supportless structures without the need for complex optical setups.

[0012] In addition, the provision of a printed surface at the gas-resin interface ensures that the proposed method is virtually unaffected by light scattering effects arising from the use of opaque and light-scattering resins. Therefore, the proposed method can be effectively implemented to cure resins containing suspended particulate matter, including biologically relevant entities such as living cells.

[0013] In some embodiments, the submerged gas-resin interface is provided by pressurizing the gas within the cavity of the print head. The pressure within the cavity counteracts the hydrostatic pressure from the resin, thus resulting in control and modulation of the shape and expansion of the gas-resin interface.

[0014] In some embodiments, the gas used to form the gas-resin interface includes oxygen.

[0015] Oxygen can dissolve through the gas-resin interface, creating an oxygen-enriched resin layer near the interface where polymerization is inhibited. This layer is thought to provide a favorable physical distance between the object being formed and the interface, thereby minimizing mechanical interference caused by surface tension effects at the interface. As a result, the polymerization speed can be significantly increased. In some cases, high-speed printing can be achieved by directly regulating the oxygen concentration in the gas. This can be particularly advantageous for, for example, the precise and high-speed printing of self-supporting flexible structures.

[0016] In some embodiments, the method further comprises the step of transmitting acoustic waves to the submerged gas-resin interface.

[0017] The transmission of acoustic waves to the gas-resin interface during printing is considered to be unique in itself. Therefore, the present invention also provides a method of forming a 3D object, comprising the steps of providing a photocurable resin; providing a printing head for transmitting curing radiation to the photocurable resin, the printing head having a cavity for containing a gas; introducing the printing head into the resin to form a sunken gas-resin interface between the gas and the resin, wherein the gas-resin interface is constrained by the printing head and defines a printing surface; projecting curing radiation onto the sunken gas-resin interface to promote curing of the resin at the printing surface; transmitting acoustic waves to the sunken gas-resin interface; and promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

[0018] It has been observed that the gas-resin interface can be sensitive to acoustic stimuli. By transmitting acoustic waves to the sunken gas-resin interface, it is thus possible to impart a rapid modulation of the shape of the interface according to the properties of the acoustic waves. The rapid modulation of the shape of the interface via acoustic excitation can advantageously promote the formation of capillary waves (i.e., surface waves with a wavelength short enough that the restoring force is the surface tension of the resin) on the interface, thereby significantly improving the resin inflow around the interface. The rate and distribution of the material inflow itself can be modulated by controlling parameters such as the properties of the acoustic waves (e.g., amplitude, frequency), the printing head profile, and / or the interface curvature.

[0019] In addition, the provision of vibrational excitation at the gas-resin interface improves the resin transfer across the gas-resin interface, thereby improving the printing speed and fidelity. Furthermore, Faraday waves across the printing interface generate movement of the fluid within most of the resin volume, thereby not only improving mixing but also being used to generate patterning of suspended microobjects across this interface during printing.

[0020] The proposed method is highly versatile across a wide range of materials and intricate geometries, including those that would be impossible to print using a bottom-up configuration.

[0021] The method is also particularly effective at precisely curing a range of resin materials, including soft and biologically relevant hydrogels, at speeds suitable for high-viability tissue engineering, scalable manufacturing, and rapid prototyping. The method of the present invention is thus suitable for achieving in-situ printing, overlay printing, and bioprinting.

[0022] Unlike volumetric approaches, the proposed method also eliminates the need for complex feedback systems, special resin chemistries, or intricate optical systems while maintaining ultra-high printing speeds. Additionally, the method of the present invention can be easily parallelized, thereby enhancing its potential for automation. We expect this approach to be valuable for industries where high resolution, scalable throughput, and biocompatible printing are essential.

[0023] The present invention also provides a system for forming a 3D object, comprising a print head that transmits curing radiation to a photocurable resin, the print head having a cavity for containing a gas, whereby the gas promotes the formation of a gas-resin interface constrained within the print head when the print head is introduced into the photocurable resin. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Embodiments of the present invention are described herein with reference to the following non-limiting drawings.

[0025] [Figure 1]A schematic diagram of an exemplary printing setup for carrying out the method of the present invention is shown (IS, image stack; IO, illumination optics; DMD, digital micromirror device; IL, imaging lens; PC, print head; O2, oxygen inlet; L, 635nm shadowgraph imaging red laser; CL, collimating lens; FL, focusing lens; CCD, charge-coupled device); the inset shows a rendering of the gas-resin interface and a shadowgraph image of the printed structure highlighting the improved contrast. [Figure 2] This shows a side-view time-lapse print of a sample 3D helical stent over a period of 60 seconds. [Figure 3] (a) A side profile of a sample cylindrical hollow printhead having a protruding gas / resin interface generated by pressurizing gas bubbles in the internal cavity of the printhead, showing a model extrapolation of the interface shape as a function of gas pressure; (b) A reconstructed interface displacement map from the side profile of an axisymmetric printhead; and (c) A comparison between non-planar (convex) cross-sectional slices of a 3D object and conventional planar slicing. [Figure 4] A sample print parameter space is shown that can be employed to determine practical combinations of optical output and print speed for effective printing; the inset shows an example of a rectangular test structure used to evaluate the parameter space. [Figure 5] The image shows an exemplary printhead immersed in a glass vial containing a curable resin, printing a simple vascular tree. [Figure 6] (a) Standard polyethylene glycol diacrylate (PEGDA) resin against the “USAF-1951” test pattern exhibiting high light transmittance, (b) Impermeable alginate resin in front of the same “USAF-1951” test pattern exhibiting low light transmittance, and (c) Tricuspid valves successfully printed using the low light transmittance resin. [Figure 7](a) A diagram of the printed tricuspid valve outline shown in Figure 6(c), (b) Multi-component printing of multiple tricuspid valves via print-and-repeat, showing that three complete structures are printed in 120 seconds, and (c) Microcomputer tomography (CT) slices of the obtained tricuspid valve, showing an accurate reproduction of the internal valve leaflets (scale bar 10 mm). [Figure 8] This image shows a composite fluorescence image of a 3D-printed kidney model containing 7.2 million viable cells per mL-1, directly printed into resin contained in a 12-well plate container, demonstrating a high cell viability 24 hours after printing. [Figure 9] (a) A two-step printing procedure for printing a soft buckyball on top of a previously printed, harder stem, and (b) a schematic diagram of the resulting PEGDA buckyball printed on a printed hexanediol diacrylate (HDDA) rod, demonstrating multi-material overprinting. [Figure 10] (a) A multi-interface printhead housing a 3x3 cavity grid for forming a corresponding array of separate gas-resin interfaces, and (b) a photograph of the word “DIP” (“Dynamic Interface Printing,” which may be used herein to identify the proposed method) with characters simultaneously printed using the multi-interface printhead. [Figure 11] This diagram shows a schematic representation of the transmission of acoustic waves to the gas-resin interface, where the acoustic waves are introduced into the cavity of the print head. [Figure 12] (a) A schematic diagram showing the effect of acoustic stimulation on the outline of the submerged gas-resin interface, illustrating how acoustic stimulation can promote improved material inflow through capillary-driven waves; and (b) showing that the instantaneous location of the air-liquid boundary depends on the spatial location of the print head, the internal pressure state, and the acoustic excitation. [Figure 13]The images show different acoustic patterns (A, B, C) formed using a cylindrical print head in different cross-sections of the print through acoustic excitation at different frequencies. [Figure 14] (a) A CAD model of a mechanical component of a 3D printing setup that may be used to carry out the method of the present invention, including an acoustic modulation device for transmitting acoustic waves to the gas-resin interface through the cavity of the print head; (b) A schematic diagram of the gas-resin interface formed at the tip of the print head under acoustic excitation; (c) Exemplifications of the total degrees of freedom (DOF) of the printing interface location under conventional 3D printing (left) and the method described herein (right); and (d) An instantaneous interface location depending on the sum of the locations of the above degrees of freedom. [Figure 15] A schematic diagram of one embodiment of a print head assembly and acoustic airline modulation, i.e., a, b) enlarged half section view of the print head assembly; c) half section view of the airline modulation system; d) showing diaphragm excitation when an electrical signal is applied to the voice coil. [Figure 16] A process flowchart of the slicing algorithm is shown, illustrating both the steps of determining the convex projection and verifying the reconstruction via the Jacquard index J(V,V′). [Figure 17] For a 15mm diameter print head, numerical predictions of interface release dynamic characteristics using a circular print structure with a diameter varying from 4mm to 14mm are shown, which include: a) the location of the interface's central node as a function of time for top-down SLA; b) the location of the interface's central node as a function of time for dynamic interface printing (DIP) without acoustic excitation; c) the location of the interface's central node as a function of time for dynamic interface printing (DIP) with acoustic excitation at a frequency of 40Hz; and d) the location of the interface's central node as a function of time for dynamic interface printing (DIP) with acoustic excitation at a frequency of 100Hz.

[0026] [Figure 18]This shows a numerical prediction of the average inflow fluid velocity for a 15mm diameter print head using a circular print structure with a diameter varying in the range of 4 to 14mm, which is a) the average fluid velocity with respect to increasing structure diameter in a top-down SLA.

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[0027] The present invention provides a method for forming a 3D object. More specifically, the method of the present invention involves forming a 3D object using a photocurable resin.

[0028] In this specification, the term "photocurable resin" is used in its broadest sense to refer to a composition containing components that crosslink upon exposure to radiation, thereby resulting in the curing of the composition.

[0029] Any photocurable resin through which a print head can be introduced to form the required gas-resin interface is suitable for use in the method of the present invention. Typically, the resin will be in a liquid or semi-solid state. In this specification, a “semi-solid” resin means a resin that does not maintain its shape like a solid, but may not flow like a liquid due to its high viscosity.

[0030] Suitable examples of resins for use in the method of the present invention include any photocurable resin used in lithography processes such as photolithography, two-photon lithography, electron beam lithography, 3D direct laser writing, ion beam lithography, and X-ray lithography.

[0031] In some embodiments, the photocurable resin comprises one or more of the following: epoxy monomers and / or oligomers, acrylate monomers and / or oligomers, styrene monomers and / or oligomers, vinyl ether monomers and / or oligomers, urethane monomers and / or oligomers, silicone monomers and / or oligomers, cationic photopolymers, diacrylates or triacrylates, and / or thiol monomers and / or oligomers. The oligomers may be epoxides, urethanes, polyethers, or polyesters. In some embodiments, the photocurable resin comprises norbornene-functionalized monomers and / or oligomers.

[0032] In some embodiments, the resin includes biomaterials. The term “biomaterial” is used herein in its broadest sense and encompasses materials derived from or produced by living organisms (e.g., plants, animals, bacteria, fungi, and other living organisms). Thus, the term includes not only biological entities (e.g., viable cells) but also synthetic or natural substances (e.g., carbohydrates, proteins, etc.) that are suitable for direct interaction with components of a biological system.

[0033] Advantageously, if the resin contains biomaterials, the method of the present invention results in the production of biologically relevant 3D structures, which may find applications in the fields of biomedicine and tissue engineering.

[0034] The biomaterial itself may or may not be crosslinkable. If the biomaterial is not crosslinkable (e.g., viable cells), the resin may also contain crosslinkable components. If the biomaterial itself is crosslinkable (e.g., biopolymers), the resin may or may not contain additional crosslinkable components.

[0035] In some embodiments, the biomaterial includes biopolymers. In this specification, “biopolymer” means a polymer produced from a natural source, either chemically synthesized from biological materials or entirely biosynthesized by living organisms. Examples of suitable biopolymers for use in the resins of the present invention include thiol-based biopolymers (e.g., biopolymers based on thiol-enclic chemistry), alginic acid, hyaluronic acid methacrylate (HAMA), gelatin, gelatin methacryloyl (GelMA), collagen, chitosan, fibrin, elastin, silk, and dextran.

[0036] In some embodiments, the biopolymer contains norbornene groups. For example, the biopolymer may contain one or more of norbornene-functionalized alginic acid (Alg-NOR), norbornene-functionalized gelatin, norbornene-functionalized polyethylene glycol, and norbornene-functionalized hyaluronic acid.

[0037] Upon exposure to radiation, the types of biopolymers described herein may crosslink to form aggregated structures.

[0038] In some embodiments, the biomaterial includes a bioactive agent. Examples of suitable bioactive agents in this regard include growth factors, matrix inhibitors, antibodies, cytokines, heparin, integrins, thrombin, thrombin inhibitors, proteases, anticoagulants, glycosaminoglycans, chemotherapeutic agents, antibiotics, cardiovascular agents, analgesics, central nervous system agents, hormones, enzymes, proteins, insulin, and solutes such as glucose or NaCl.

[0039] In some embodiments, the resin comprises a hydrogel precursor. Hydrogel “precursor” as used herein means a compound that forms a hydrogel upon crosslinking. In this context, the term “hydrogel” means a crosslinked network of hydrophilic polymers (natural or synthetic) that swell in water and can capture many times their original mass without the use of dissolution. In the context of this invention, hydrogels are therefore considered to encompass those based on natural and / or synthetic polymers. Thus, hydrogels in the context of this invention include those obtained using the types of biopolymers described herein or those obtained from synthetic polymers.

[0040] The hydrogel precursor for use in the method of the present invention may comprise one or more crosslinkable hydrogel macromers. "Hydrogel macromer" means a macromolecule comprising a hydrophilic or water-soluble region and one or more crosslinkable regions.

[0041] Hydrogel macromers may be made from multiple hydrophilic polymers. Examples in this regard include polyvinyl alcohol (PVA), polyethylene glycol (PEG), polyvinyl pyrrolidone (PVP), polyalkyl hydroxyacrylates and methacrylates (e.g., hydroxyethyl methacrylate (HEMA), hydroxybutyl methacrylate (HBMA), dimethylaminoethyl methacrylate (DMEMA)), polysaccharides (e.g., cellulose, dextran), polyacrylic acid, polyamino acids (e.g., polylysine, polyethyleneimine, PAMAM dendrimers), and polyacrylamides (e.g., polydimethylacrylamide-co-HEMA, polydimethylacrylamide-co-HBMA, polydimethylacrylamide-co-DMEMA). Hydrogel macromers may be linear, branched, hyperbranched, or have a dendrimer structure.

[0042] In some embodiments, the resin comprises a hydrogel precursor which is a crosslinkable polysaccharide, thereby providing a polysaccharide hydrogel upon exposure to radiation. Examples of polysaccharide hydrogels include hydrogels containing alginic acid, cellulose, and glycosaminoglycans.

[0043] In some embodiments, the resin comprises a hydrogel precursor of a biopolymer of the type described herein.

[0044] In some embodiments, the photocurable resin includes polyethylene glycol diacrylate (PEGDA), gelatin methacryloyl (GelMA), or hexanediol diacrylate (HDDA).

[0045] In some embodiments, the photocurable resin contains viable cells suspended therein. For example, the resin may be a liquid mixture of living cells, biopolymers and / or hydrogels of the types described herein, and cellular nutrients. These resins can provide direct production of 3D structures, for example, enabling cell proliferation to form shape-specific target tissues.

[0046] Therefore, the use of photocurable resins containing the types of biopolymers, bioactive materials, and / or hydrogels described herein leads to the production of 3D objects with high biological relevance.

[0047] For example, the high biocompatibility of these materials, combined with their associated low immune response, leads to the production of highly host-compatible implants with arbitrary shapes. Furthermore, these materials can be effectively used in the production of custom-shaped 3D substrates for tissue growth, including organ tissues. For instance, the excellent biocompatibility of GelMA hydrogels makes them suitable as cell culture matrices mimicking natural extracellular matrices (ECMs). Moreover, biopolymers and hydrogels, more generally, exhibit highly customizable chemical properties, thereby enabling the encoding of bioactive motifs within their chemical structures for the production of function-specific 3D objects. Therefore, the methods of the present invention are particularly useful, for example, in the fabrication of 3D biomedical components aimed at mimicking natural tissue properties to create tissue and organ-like structures that allow living cells to proliferate.

[0048] In some embodiments, the resin further comprises additives. The additives may be any compounds that provide or improve one or more properties of the resin and / or the resulting 3D object.

[0049] In some embodiments, the photocurable resin includes a photoinitiator. The photoinitiator can induce crosslinking of monomers / oligomers forming the resin upon exposure to curing radiation. As they are known in the art, photoinitiators are compounds that, upon emission of light, generate reactive species (e.g., by decomposition and / or activation of compounds present in the system) which activate the polymerization of crosslinkable monomer / oligomer compounds contained in the resin.

[0050] Suitable examples of photoinitiators for use in resins include onium salts (e.g., iodonium and sulfonium salts), organometallic salts (e.g., metal salts having non-nucleophilic counter-anions such as ferrocenium salts), pyridinium salts, abstraction-type photoinitiators (e.g., benzophenone, xanthone, and quinone), and cleavage-type photoinitiators (e.g., benzoin ether, acetophenone, benzoyloxime, and acylphosphine).

[0051] In some embodiments, the photoinitiator is a combination of tris(2,2′-bipyridyl)dichlororuthenium(II) hexahydrate and sodium persulfate (also known as "Ru / SPS"). Upon photoexcitation, the ruthenium metal complex cleaves the OO bond of the persulfate, and the persulfate then proceeds to polymerization of the desired monomer.

[0052] In some embodiments, the photocurable resin includes fillers, which may be in the form of nanoparticles, microparticles, fibers, or flakes. When integrated into the resin formulation, these additives can improve the mechanical properties and dimensional stability of the cured resin. The addition of fillers and reinforcing materials provides increased strength, stiffness, and resistance to deformation, thereby making the resin suitable for forming objects for use in applications requiring high durability and structural integrity.

[0053] In some embodiments, the resin includes additives that introduce controlled optical properties into the cured resin. Examples of suitable additives in this regard include dyes, pigments, or luminescent materials that impart color, translucency, or other aesthetic properties to the resin.

[0054] In some embodiments, the resin includes a surface tension modifier. This class of modifiers can alter the surface energy and wetting properties of the resin, thereby enabling the harmonization of the surface tension properties of the gas-resin interface.

[0055] In some embodiments, the resin contains a thixotropic agent. The thixotropic agent may be added to the resin to modify its viscosity and flow behavior, thereby enabling precise control during the printing process. By incorporating a thixotropic agent, complex shapes can be manufactured with improved accuracy, thereby ensuring the creation of high-quality objects with intricate details.

[0056] The photocurable resin may further contain a solvent selected from water, alcohols (e.g., isopropanol, ethanol), acetone, esters, ketones, toluene, ethyl acetate, methyl acetate, hexane, benzene, and ethane. The specific solvent may be selected so as to be able to dissolve other components of the resin without impairing the structural integrity of the cured resin, provided that the required gas-resin interface is formed. Those skilled in the art will consider whether the use of a solvent is appropriate. For example, a solvent may not be recommended if there is a possibility of off-gas formation during curing or subsequent storage of the 3D object, for example, due to the heat generated during exposure to curing radiation.

[0057] The present invention includes providing a print head for delivering curing radiation to a photocurable resin. In this specification, “print head” means a component or assembly that delivers curing radiation to a photocurable resin such that the resin is locally cured at the location where the radiation is delivered.

[0058] In some embodiments, the print head includes a curing radiation emitter. The emitter may be any component suitable for emitting the curing radiation of the type described herein. For example, the print head may include an optical transmitter for emitting the radiation of the type described herein.

[0059] In some embodiments, the print head transmits curing radiation emitted from a radiation source located outside the print head. One example of such an arrangement is shown in the schematic system depicted in Figure 1.

[0060] In particular, if the print head transmits curing radiation emitted from a radiation source outside the print head, it will be understood that the print head will be transparent to the curing radiation, at least along the principal light transmission axis used to project the curing radiation onto the photocurable resin. In the schematic diagram of Figure 1, the exemplary print head is transparent to curing radiation projected onto the photocurable resin along the vertical axis.

[0061] In some embodiments, the print head includes a photoconductive component. For example, the print head may include an optical fiber for projecting curing radiation onto a photocurable resin.

[0062] In some embodiments, the print head includes a fiber optic system for guiding light and an attachment designed to provide the required gas-resin interface at the fiber tip.

[0063] The print head may be made from any material that allows it to be introduced into the resin without compromising its structural integrity.

[0064] For example, the print head may be made from a material that is chemically inert to the photocurable resin. Suitable examples of print head materials for use in the present invention include polymer materials, metals, and ceramics, such as glass.

[0065] In some embodiments, the print head is made from a polymer material. Examples of suitable polymer materials in this regard include polyethylene, including low-density polyethylene (LDPE) and high-density polyethylene (HDPE), polypropylene (PP), polyvinyl chloride (PVC), polystyrene (PS), nylon, nylon 6, nylon 6, 6, Teflon® (polytetrafluoroethylene), and thermoplastic polyurethanes (TPU). In some embodiments, the polymer material is a composite comprising the types of polymers described herein.

[0066] In some embodiments, the print head is made of metal. Suitable examples of metals in this regard include aluminum, stainless steel, and titanium.

[0067] In some embodiments, the print head is made of glass. For example, the print head may be made entirely of glass.

[0068] In some embodiments, the print head includes one or more articulated regions, for example, in the form of segments connected by joints. This allows for arbitrary positioning of the interface along a desired orientation, for example, by using an internal mirror.

[0069] In some embodiments, the print head includes an LCD panel. In those cases, the print head may be designed such that when the print head is introduced into the resin, the gas-resin interface is formed on, for example, the LCD panel or below the LCD panel.

[0070] In some embodiments, the print head can be rotated around a central axis. In those cases, the print head may be rotated to change its fluid flow profile and the shape of the gas-resin interface during subsequent printing.

[0071] The print head may have any dimensions that contribute to its function as intended. For example, the print head may have the largest dimension of 0.5 cm, 1 cm, 5 cm, 10 cm, or 30 cm.

[0072] In the method of the present invention, the print head has a cavity for containing gas, and the method comprises the step of introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin.

[0073] The expression "gas-containing cavity" refers to an empty space provided within the printhead to contain a gas, such as air. The gas-containing cavity is shaped and oriented so that when the printhead is introduced into the resin, the gas within the cavity prevents the resin from entering the cavity, thereby providing the formation of a submerged gas-resin interface.

[0074] To ensure contact between the gas and the resin, it will be recognized that the printhead cavity will present at least one opening that allows contact between the gas and the resin, ensuring the formation of the required gas-resin interface once the printhead is introduced into the resin.

[0075] In other words, the present invention may also be said to provide a method for forming a 3D object, comprising the steps of: providing a photocurable resin; providing a print head for transmitting curing radiation to the photocurable resin; introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein the print head has an opening cavity for containing the gas, where the gas-resin interface is constrained by the print head and defines a printed surface; and projecting curing radiation onto the submerged gas-resin interface to promote curing of the resin on the printed surface; and promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

[0076] Because it is "sunk," the gas-resin interface is located below the surface level of the resin.

[0077] The proposed principle is similar to inverting an empty glass and pushing it into a volume of water. When the inverted glass is pushed into the water, the air pockets within the empty glass prevent water from entering the glass, thereby effectively resisting the hydrostatic pressure of the water and providing a submerged air-water interface at the opening of the glass.

[0078] Therefore, the formation of a gas-resin interface may be achieved by any cavity design that would suit the purpose.

[0079] In some embodiments, the print head comprises a cavity having a single opening. In those cases, once the print head is introduced into the resin, the gas contained within the cavity induces the formation of a desired gas-resin interface at the opening. An example of one such print head configuration is shown in Figures 1, 2, 3(a), 5, and 7. In those cases, the print head is a hollow component introduced vertically into a photocurable resin. The component is sealed at the top with a radiolucent window and left open at the bottom, so as to define an internal cavity with an opening at the bottom of the print head. The gas within the cavity prevents the resin from entering the cavity. In certain examples of those figures, the gas is pressurized to form a convex gas-resin interface protruding downward from the opening cavity.

[0080] In some embodiments, the print head comprises a cavity having multiple openings. These configurations result in the provision of multiple distinct gas-resin interfaces for the simultaneous curing of different volumes of resin, for example. An example of one such configuration is shown in Figure 10. The figure depicts a print head having an internal cavity with a rectangular cross-section and a 3x3 arrangement of openings, thereby defining a 3x3 arrangement of recessed gas-resin interfaces.

[0081] In some embodiments, the print head comprises multiple cavities and multiple openings. For example, the print head may comprise multiple cavities, each having a corresponding opening. When in use, these print heads advantageously provide multiple gas-resin interfaces, which are useful for the simultaneous curing of different volumes of resin.

[0082] In the method of the present invention, the gas-resin interface is constrained to the print head. Since the gas is contained within the cavity of the print head, the gas-resin interface formed when the print head is introduced into the resin is in close contact with the print head. Because the gas-resin interface is "constrained" to the print head, relative movement between the interface and the print head is restricted, thereby causing the interface and the print head to move together.

[0083] The gas may be any gas that forms a gas-resin interface when it comes into contact with the resin.

[0084] In some embodiments, the gas includes oxygen.

[0085] Advantageously, oxygen can diffuse through the gas-resin interface, creating a passivation layer of resin at the interface where photocuring is inhibited. During projection of curing radiation, the presence of a non-curing layer of resin between the interface and the curing resin improves the physical separation between the object being formed and the print head. This helps minimize the opportunity for physical adhesion between the object being formed and the print head as the print head moves through the resin, thereby enabling faster movement of the print head for faster printing.

[0086] The amount of oxygen in the gas can be controlled to harmonize the thickness of the passivation resin layer at the interface; that is, the higher the oxygen content, the thicker the passivation resin layer. Therefore, in some embodiments, the gas contains at least about 5%, at least about 10%, at least about 20%, at least about 50%, or at least about 75% oxygen (v / v). In some embodiments, the gas is about 100% oxygen (v / v).

[0087] In some embodiments, the gas includes air.

[0088] In some embodiments, the submerged gas-resin interface is provided by pressurizing the gas within the cavity of the print head. The term “pressurizing” is understood to encompass the application of either positive or negative pressure to the gas, thereby resulting in either expansion or contraction of the gas volume. This may be achieved by any means known to those skilled in the art.

[0089] In some embodiments, the print head includes a gas inlet that is fluidly connected to the print head cavity. The gas inlet may be used to introduce gas into and / or extract gas from the print head cavity. Pressurizing the gas in the cavity alters the shape and expansion of the interface, as the gas pressure in the cavity counteracts the hydrostatic pressure of the resin at the gas-resin interface.

[0090] For example, an increase in gas pressure causes the gas to expand and push against the interface, resulting in outward expansion relative to the print head. Conversely, a decrease in pressure results in a contraction of the gas volume, which in turn causes the interface to recede, for example, within the print head boundary.

[0091] Pressurizing the gas within the printhead cavity is advantageous in that it ensures the shape of the gas-resin interface can be maintained during printing, regardless of the depth of the printhead in the resin. In other words, the use of pressurized gas inside the printhead creates and maintains controlled surface tension at the gas-resin interface at any resin depth, thereby helping to maintain the interface shape during printing and printhead movement. This results in an improved resin flow rate compared to conventional "flat" gas-liquid interfaces, whose shape is determined and modulated by the depth-dependent hydrostatic pressure of the resin.

[0092] The gas used to pressurize the gas inside the printhead cavity may be the same as or different from the gas contained within the cavity.

[0093] The gas-resin interface may have any shape and expansion that contributes to equalizing the gas pressure and resin hydrostatic pressure within the print head cavity. Therefore, changes in gas pressure within the print head can result in dynamic deformation of the gas-resin interface, thereby allowing for the inflow of new resin at the interface and thus facilitating the creation of a continuous, layerless structure.

[0094] In some embodiments, the gas-resin interface has a convex shape.

[0095] In some embodiments, the gas-resin interface has a concave shape.

[0096] In some embodiments, the gas-resin interface is substantially flat.

[0097] In this context, the convex or concave nature of the interface will be understood in relation to the gas phase. That is, a convex interface curves / projects outward from the gas phase, while a concave interface curves / projects inward into the gas phase.

[0098] Examples of convex gas-resin interfaces are shown in Figures 3(a) and 3(b). The images show a convex gas-resin interface that protrudes outward relative to the gas phase and outward from the printhead into the resin. As shown in Figure 3(a), the shape and expansion of the printhead can be modulated by changing the gas pressure. The figure shows a side view of an axially symmetric hollow cylindrical printhead immersed in resin. The gas in the printhead cavity is pressurized to create a convex gas-resin interface that protrudes from the bottom aperture of the printhead. The images show multiple sequentially expanding interface boundaries that can be formed by increasing the gas pressure. The side profile of the interface can be extracted and therefore predicted as a function of various pressure values ​​in the printhead cavity.

[0099] Automatic control of the gas-resin interface shape can be implemented by installing a camera that collects images, such as the one shown in Figure 3(a). In these cases (see, for example, the CCD camera in the schematic diagram of Figure 1), the method can be carried out by utilizing camera-based feedback to automatically modulate the shape and expansion of the gas-resin interface (for example, by automatically adjusting the gas pressure in the print head). Therefore, in some embodiments, the method includes automatic modulation of the pressure induced by the pressurized gas in the print head based on image feedback of the gas-resin interface. This may be achieved, for example, by the arrangement shown in Figure 1.

[0100] The method of the present invention involves projecting curing radiation onto a submerged gas-resin interface to accelerate the curing of the resin on the printed surface.

[0101] In the method of the present invention, any curing radiation that accelerates the curing of the resin may be used. The selection of a specific curing radiation may depend on various factors, such as the type of resin, the desired curing speed, the curing depth, and compatibility with the curing apparatus. It should be noted that the following descriptions of curing radiation are provided as examples and are not intended to be limiting.

[0102] In some embodiments, the curing radiation has wavelengths between approximately 190 nm and approximately 2000 nm. For example, the curing radiation may have wavelengths in the range of approximately 290 nm and approximately 600 nm, or between approximately 365 nm and approximately 405 nm.

[0103] In some embodiments, the curing radiation is ultraviolet (UV) radiation. UV radiation is typically in the range of 200–400 nm and can be generated using UV light-emitting diodes (LEDs), mercury vapor lamps, or other UV sources. This radiation can activate photoinitiators present in the resin and / or crosslinkable functional groups in the resin composition, thereby initiating crosslinking reactions that lead to the solidification of the resin in the irradiated volume.

[0104] In some embodiments, the curing radiation is visible light radiation. Visible light, having a wavelength range of approximately 400-700 nm, can penetrate deeper into the resin compared to UV radiation. Light sources such as high-intensity LED arrays or special lamps can emit the desired visible light spectrum. Photoinitiators and / or crosslinkable functional groups present in the resin absorb the visible light and undergo chemical reactions similar to those in the case of UV radiation, thereby leading to the curing of the resin.

[0105] In some embodiments, the curing radiation is infrared (IR) radiation. IR radiation, with wavelengths in the range of approximately 700 nm to 1,100 nm, which are longer than those of visible light, can effectively penetrate deeper into the resin. This deeper penetration allows for the curing of thick or opaque resin layers that may be blocked by UV or visible light. An IR source, such as an IR LED or IR lamp, can provide the necessary radiation to initiate the curing process.

[0106] It should be recognized that the examples of curing radiation described herein are not exhaustive. Other types of radiation, including, for example, X-ray radiation, electron beam radiation, laser radiation, or focused ion beams, may also be suitable for use in the methods of the present invention.

[0107] Furthermore, it is assumed that different combinations of curing radiation may be used in specific embodiments. Sequential or simultaneous exposure to multiple wavelengths or spectral bands may be used to optimize the curing process, improve material properties, or achieve unique curing effects. The intensity, duration, and spatial modulation of the curing radiation may be adjusted to accommodate various resin formulations, printing requirements, or specific design considerations.

[0108] For a given resin composition, the curing radiation is selected to deliver a sufficient optical dose to the printed surface in order to promote local curing of the resin. For example, the curing radiation is approximately 0.1 mW / cm² on the printed surface. 2 and 1.6·10 10 mW / cm 2 To deliver an optical dose between these two points, it may be selected and projected.

[0109] For a given image projection, the curable resin may be projected for any exposure time that contributes to effective curing of the resin. In some embodiments, the exposure time for a given projection is at least 0.1 s, at least 0.5 s, at least 1 s, at least 5 s, at least 10 s, or at least 30 s. In some embodiments, the exposure time for a given projection is from 0.1 s to 60 s.

[0110] One of ordinary skill in the art will recognize that the energy density and exposure time delivered to the resin can be adjusted to meet the requirements of a particular application.

[0111] For example, if the resin contains biological entities (e.g., viable cells), the energy density delivered to the printing surface and the exposure time for a given projection will be adjusted to ensure curing of the resin while maintaining cell viability. For example, the optical dose may remain at the minimum level required to achieve curing of the resin, thereby maximizing the retention of cell viability.

[0112] In some embodiments, the curing radiation is selected and projected to deliver an energy density of from about 0.1 mW / cm 2 to about 150 mW / cm 2 . Considering an exposure time of 0.1 to 10 s, this would correspond to a total energy of from 0.01 mJ / cm 2 to 1.5 J / cm 2 delivered to the printing surface.

[0113] In some embodiments, the curing radiation delivers an energy density of from about 10 mW / cm 2 to about 10,000 mW / cm 2 . These cases are particularly suitable for the formation of 3D objects made from biologically relevant materials.

[0114] For non-biomedical materials, the energy delivered to the printing surface can be higher. For example, for an exposure time of 0.1 to 10 s, the energy delivered at the printing surface is 0.01 mJ / cm2 ~1.6·10 8 J / cm 2 It is possible.

[0115] Curing radiation may be projected by any means known to those skilled in the art, insofar as it reaches the gas-resin interface, in order to accelerate the curing of the resin.

[0116] Typically, curing radiation is generated by a radiation source and directed to a print head that delivers it to the gas-resin interface. Optical parameters of the emitted radiation, such as direction, intensity, collimation, focus, and wavelength, may be controlled along the radiation path by optical components that would be known to those skilled in the art.

[0117] For example, a projection system fabricated from a radiation source, such as a digital optical projector or laser beam emitter, may be used in combination with optical components such as filters, lenses, mirrors, and shutters to guide and control the emitted radiation to a print head, which then delivers it to the gas-resin interface while controlling projection parameters such as the intensity of the projected radiation, the duration of exposure, and the focusing. An example of such an optical device is shown in the schematic diagram of Figure 1.

[0118] In some embodiments, the radiation source comprises a laser scanning system for receiving relevant cross-sectional images of a 3D object onto a gas-resin. One example of such a system is the type of laser scanning system used in two-photon polymerization.

[0119] In those cases where the radiation emitter is integrated with the print head, the radiation may be emitted from within the print head and delivered directly to the gas-resin interface.

[0120] In some embodiments, the print head includes one or more optical components for delivering, focusing, and controlling curing radiation. These components may include one or more optical lenses, one or more mirrors, or other optical components that precisely shape and guide the radiation.

[0121] In some embodiments, the curing radiation is projected by one or more optical fiber means.

[0122] The curing radiation may be projected along any direction that contributes to accelerating the curing of the resin on the printed surface. In some embodiments, the curing radiation is projected along the vertical axis. An example of one such optical apparatus is shown in the schematic diagram of Figure 1.

[0123] In the method of the present invention, the gas-resin interface defines the printed surface. “Printed surface” as used herein means a target area in the resin whose curing is accelerated by curing radiation. While not intended to be constrained by theory, it is assumed that the printing (i.e., local curing) of the resin occurs at the gas-resin interface and resin intersection, which may be flat or curved. Typically, the printed surface would be interpreted as substantially conforming to the shape of the gas-resin interface.

[0124] Therefore, it will be understood that the photocuring energy used in the method of the present invention results in the overall exposure of the gas-resin interface area, and consequently overall curing, in contrast to a single curing point in space (obtained, for example, using a single spot-focused laser).

[0125] In the method of the present invention, local curing of the resin on the printed surface can be achieved by any means known to those skilled in the art. For example, local selective curing of the resin on the printed surface may be achieved by providing the required optical dose on the printed surface to accelerate the curing of the resin. This may be achieved, for example, by optically focusing the curing radiation on the printed surface, across the printed surface, or in front of the printed surface, relative to the optical path of the incoming radiation.

[0126] Therefore, in some embodiments, the step of projecting curing radiation through the submerged gas-resin interface includes the step of focusing the curing radiation onto the gas-resin interface, onto the resin side of the gas-resin interface, or onto the gas side of the gas-resin interface.

[0127] In some embodiments, the hardening radiation has a cross-sectional image of the 3D object.

[0128] Cross-sectional images of a 3D object may be obtained from a digital representation of the target object, which may be acquired or generated by means known to those skilled in the art. These means may include data obtained from computer-aided design (CAD) software, a 3D scanning device, or other 3D digital modeling techniques. The digital representation will typically include a stacking sequence of cross-sectional images that, when stacked together, form a complete 3D optical representation of the target object.

[0129] By employing curing radiation that includes cross-sectional images of a 3D object, the method of the present invention enables the generation of a complete 3D target object by translating the print head along a single directional axis, thereby significantly simplifying the requirements of the printing equipment. In each subsequent translation, sequential cross-sections of the 3D object are projected and thus can be cured at the gas-resin interface, thereby resulting in the layer-by-layer formation of the 3D object. This is a fundamental departure from conventional 3D printing systems based on printing focused to a single spot (e.g., using a single spot-focused laser for spot curing). In those conventional systems, the print head required for printing an entire 3D object must be movable relative to the resin along multiple axial directions to effectively enable point-by-point curing of the entire 3D volume. In this regard, conventional printing systems may be characterized, for example, by having a print head (or resin tank) mounted on a 3-6 DOF ("Degrees-Of-Freedom") robotic arm to allow movement of the focal spot over all points of a given target volume. In this regard, the method of the present invention results in the adoption of a significantly simplified printing system.

[0130] In some embodiments, a cross-sectional image of a 3D object corresponds to a 2D cross-section of the object. In those cases, for example, the gas-resin interface is flat, which is useful when defining a corresponding flat printed surface.

[0131] Therefore, in some embodiments, the curing radiation includes a cross-sectional image of the 3D object, the cross-sectional image representing a flat cross-section of the 3D object that conforms to a flat gas-resin interface.

[0132] In some embodiments, the cross-sectional image of a 3D object corresponds to a non-planar cross-section of the object. For example, the cross-sectional image of a 3D object may correspond to a curved slice of the object, such as a convex or concave slice of the object. These cases are useful, for example, when the gas-resin interface is non-planar, thereby defining corresponding non-planar printed surfaces, such as convex or concave printed surfaces that define the convex or concave gas-resin interface, respectively.

[0133] Therefore, in some embodiments, the curing radiation includes a cross-sectional image of the 3D object, the cross-sectional image representing a convex cross-section of the 3D object that fits a convex gas-resin interface.

[0134] In other embodiments, the curing radiation includes a cross-sectional image of a 3D object, the cross-sectional image representing a concave cross-section of the 3D object that fits a concave gas-resin interface.

[0135] In cases where the gas-resin interface (and the corresponding printed surface) is non-planar (e.g., curved, convex or concave), it is required to project the corresponding non-planar cross-section of the target 3D object in order to achieve correct spatial curing of the resin within the three-dimensional printed surface. That is, each projection should conform to the shape of the gas-resin interface, which requires considering both the in-plane and out-of-plane structures of the 3D object during the slicing process because the interface extends in three dimensions. Consequently, discretization of the printed outline requires the adoption of non-planar methods, as opposed to planar layers. This may be achieved, for example, by means of a customized algorithm for determining the non-planar cross-section of the target object.

[0136] The following paragraphs describe an exemplary procedure for image transposition of one non-planar slice of a target 3D object in the case of an axisymmetric print head (such as the schematic diagram in Figure 1) that projects curing radiation along the z-direction perpendicular to a convex gas-resin interface. Nevertheless, based on this information, those skilled in the art will be able to readily devise suitable image transposition algorithms for differently shaped print heads and gas-resin interfaces.

[0137] As shown in Figure 3(a), by utilizing an axisymmetric cylindrical print head, the shape of the convex layer can be extracted from the interface's side profile for various gas pressures. Once the profile is extracted, a 2D displacement map of the interface can be created as a function of the gas, thereby determining the displacement transformation matrix (r,θ,φ) (Figure 3(b)). By correcting the 3D voxel array using this transformation matrix, an optimized convex projection is created, resulting in an illumination image that follows the interface curvature (Figure 3(c)).

[0138] The proposed method can be generalized to any interface shape. In the simplified version, it is assumed that the print head is axially symmetric, which allows the three-dimensional shape of the interface to be approximated from a single side profile. Using high-contrast images such as those presented in Figure 3(a), a custom script (e.g., a MATLAB® script) extracts the curvature of the interface for different syringe displacement values ​​and identifies the optimal syringe position corresponding to a given print head size. The optimal syringe position (S) minimizes the average piece-wise derivative of the interface profile ((x,y)), thereby resulting in the flattest interface shape while ensuring that the interface is fully developed (i.e., extends across the entire print head dimension).

number

[0139] Using an interface displacement map, a collection of 3D voxel points is displaced in the z direction by the corresponding xy displacement values ​​in the displacement map, thereby producing a collection of voxel points stretched in the z direction according to the interface profile. Once the collection of transformed points is generated, a standard planar slice is performed on the distorted collection of points, resulting in an optimized slice that is then used to create the desired structure.

[0140] Therefore, the method of the present invention may integrate image-based feedback to provide automatic control of the shape and size of the gas-resin interface by modulating the gas pressure within the print head. This can be achieved, for example, by mounting a CCD camera for continuous monitoring of the gas-resin interface shape, and this image data can be used by a feedback controller to act on the gas pressure within the print head to maintain the desired interface shape.

[0141] A more detailed description of air-resin interface modeling for determining relevant cross-sectional image parameters for curing radiation is provided in the examples.

[0142] In the case of a multi-interface arrangement of a print head, a corresponding array displacement map may be used. For example, in the 3x3 array acquired by the print head shown in Figure 10, the "DIP" character was acquired using a 3x3 displacement map instead of a single interface map.

[0143] The method of the present invention also includes a step of facilitating relative movement between the gas-resin interface and the resin in order to produce a 3D object.

[0144] In some embodiments, facilitating relative movement between the gas-resin interface and the resin to produce a 3D object involves moving the print head relative to the resin. For example, the print head may be mounted on a moving structure or stage that moves relative to a static vat containing the resin. The relative movement may advantageously be along a single axial direction during printing, thereby providing a simplified setup compared to conventional multi-degree-of-freedom arrangements.

[0145] In some embodiments, facilitating relative movement between the gas-resin interface and the resin to produce a 3D object involves moving the resin relative to the print head. This may be achieved by placing a vat containing the resin on a moving stage. The relative movement may, advantageously, be along a single axial direction during printing, thereby providing a simplified setup compared to conventional multi-degree-of-freedom arrangements.

[0146] In some embodiments, curing radiation is projected while facilitating relative movement between the gas-resin interface and the print head. In those cases, adjacent volumes of resin can be cured without interruption for the continuous formation of a 3D object. The relative movement may, advantageously, be along a single axial direction during printing, thereby providing a simplified setup compared to conventional multi-degree-of-freedom arrangements.

[0147] In some embodiments, the curing radiation is not projected while facilitating relative movement between the gas-resin interface and the print head. That is, curing radiation is projected when the print head is stationary to cure the first layer of resin, but not when the print head is translating to subsequent projection layers. In those cases, the 3D object may be formed sequentially (i.e., layer by layer) by alternating irradiation and placement of the print head.

[0148] In some embodiments, the relative movement between the gas-resin interface and the resin is facilitated along a single axial direction during printing. This axial direction may be the vertical (z-axis). In those cases, the relative movement between the gas-resin interface and the resin during printing may be facilitated by moving the print head along the axial direction relative to the resin, or alternatively, by moving the resin along the axial direction relative to the print head. Once the first object is fully printed, the print head may then be translated (e.g., along the x and y axes) for printing further objects.

[0149] The relative movement between the gas-resin interface and the resin may be facilitated at any speed that contributes to the formation of the intended 3D object. For example, the interface and the resin may move relative to each other at a relative speed of at least about 0.1 μm / s, for example, at least about 1 μm / s. In some embodiments, the interface and the resin move relative to each other at relative speeds of about 0.1 μm / s to about 1 cm / s, about 0.5 μm / s to about 1 cm / s, about 1 μm / s to about 1 cm / s, or about 1 μm / s to about 0.5 cm / s.

[0150] In some embodiments, relative movement between the gas-resin interface and the resin is achieved by moving the print head relative to the resin-containing vat at a speed of at least about 0.1 μm / s, for example, at least about 1 μm / s. In some embodiments, the print head is moved relative to the resin-containing vat at a speed of about 0.1 μm / s to about 1 cm / s, about 0.5 μm / s to about 1 cm / s, about 1 μm / s to about 1 cm / s, or about 1 μm / s to about 0.5 cm / s. In some embodiments, the above relative speed is obtained by moving the resin-containing vat relative to the print head, which may be static or moving.

[0151] In a typical procedure of the present invention, a photocurable resin, typically transparent or translucent, is positioned in a printing chamber or vat, and a print head may be immersed in the resin. The gas present in the cavity of the print head will create the desired gas-resin interface. The shape and expansion of the print head may be modified, for example, by pressurizing the gas in the cavity by means of a gas inlet provided within the print head and connected to the internal cavity. A cross-sectional image slice determined using, for example, the procedure described herein, is then projected onto the gas-resin interface through the print head using, for example, projection means described herein.

[0152] Each cross-sectional image of the target object is sequentially projected onto the gas-resin interface as the print head moves across the resin. As the print head moves across the resin, the projected light selectively exposes and cures the volume of resin in a pattern corresponding to the shape of the projected cross-section. This curing process may occur layer by layer, with each projected cross-section cured before the next layer is formed.

[0153] To facilitate the accurate projection of each cross-section, the method may include alignment and positioning steps. The digital representation of the target object is aligned to the print coordinates of the print head, thereby ensuring that each projected cross-section is correctly positioned relative to the preceding layer and the overall object. The alignment technique may involve coordinate transformation, image processing algorithms, or fiducial markers placed within the print chamber.

[0154] In some embodiments, the method includes an optimization step to improve the printing process. For example, projection parameters such as the intensity and duration of the projected light may be dynamically adjusted based on the properties of the photocurable resin or specific design requirements. This optimization enables improved curing efficiency, reduced printing time, and improved surface quality of the printed object.

[0155] Figure 1 shows an exemplary printing setup illustrating optical and mechanical components that may be used to carry out the method of the present invention.

[0156] In the schematic diagram of Figure 1, a cylindrical printhead is immersed in a resin vat, and its dimensions can be adapted to various sizes depending on the print volume and the dimensions of the target object. In the schematic diagram, the printhead is a hollow cylinder, which remains open at the bottom and is sealed at the top with a radiolucent glass window. The printhead is therefore designed to be transmissive to curing radiation projected perpendicularly along the z-axis (shown in blue) while maintaining a gas reservoir within its core when immersed in the resin. The gas reservoir is exposed to the resin at the bottom of the printhead, thereby providing the required gas-resin interface.

[0157] The print head is provided with a gas inlet that allows the introduction of a gas, such as air or oxygen at various concentrations, into its internal cavity. After the tip is immersed, the gas (e.g., air, i.e., O2) is pressurized within the internal cavity to create a curved (i.e., convex) fixed interface, which defines the printing surface. Doing so produces a concave resin meniscus at the bottom edge of the print head. Therefore, the shape of the interface (meniscus) can be easily controlled by varying the gas pressure within the print head.

[0158] In the schematic diagram of Figure 1, a 3D object can be printed by illuminating the gas-resin interface at the desired cross-section and continuously translating the print head out of the resin tank along the vertical z-axis. Alternatively, or in addition, to add an extra degree of freedom to the system, the resin tank itself may be moved. For example, the resin tank may be mounted on a three-axis moving stage for additional x-axis, z-axis, and / or z-axis movement. As also shown in Figure 7, the print head may be additionally translated along the horizontal direction for sequential curing of adjacent objects.

[0159] The schematic diagram in Figure 1 also includes a setup of orthogonal illumination paths (highlighted in red) that can be used to image the shadow graph of the structure being formed during printing. An example of one such shadow graph is shown in the lower inset of Figure 1.

[0160] In the method of the present invention, the absence of a solid interface between the print head and the 3D object being formed prevents mechanical adhesion of the object to the print head, while surface tension maintains the interface shape, thereby enabling the rapid production of the structure.

[0161] Furthermore, the method of the present invention results in the high-speed production of 3D objects. By continuously translating and projecting light, centimeter-scale objects can be printed in a timeframe of several tens of seconds. In this regard, Figure 2 shows a collection of photographs taken from the side of the resin tank while printing a spiral stent structure using a setup corresponding to the schematic diagram in Figure 1. The images were taken over a 60-second timeframe and depict the formation of a continuous centimeter-scale structure.

[0162] The method of the present invention can also advantageously result in the formation of large objects. For example, in the case of a vertically mounted print head with z-axis movement, the height of the resulting structure is governed by the focal length of the projection optics, which can allow for the fabrication of a structure with a height of several centimeters in less than two minutes (e.g., 90 seconds). Further vertical translation of the print head can lead to even taller structures. Therefore, there is an essential trade-off between in-plane resolution and total feature height.

[0163] Furthermore, the permeability, or lack of physical interface and contact between the print head and the forming 3D object, facilitates the ability of objects to pass through its surface by relying on the surface tension of the printing fluid. This technique enables the printing of objects onto the tops of pre-existing structures, or the use of these structures as supports for semi-free-floating structures (Figure 9).

[0164] The multi-stage printing process enables the integration of multiple material components, where a single material is printed and removed before a second material is added and printed on a previously printed structure, significantly increasing the complexity of the fabricated component (Figure 9 (a-b)).

[0165] In addition to the demonstrated parallelism through sequential printing, it is possible to engineer printheads that leverage interface control to create arbitrary configurations or multiple print interfaces within a single printhead (Figure 10(a-b)). Generating a global interface displacement map of the printhead facilitates parallel printing of multiple structures, as illustrated by the arrangement of nine individual interfaces creating three sets of the word "DIP" (Figure 10(b)).

[0166] In some embodiments, the method comprises the step of transmitting acoustic waves to the submerged gas-resin interface.

[0167] The term "acoustic wave" refers to all types of elastic waves that can propagate as pressure fluctuations through a transmission medium.

[0168] The transmission of acoustic waves to the gas-resin interface during printing is considered to be independent in itself. Therefore, the present invention may also be said to provide a method for forming a 3D object, comprising the steps of: providing a photocurable resin; providing a print head for transmitting curing radiation to the photocurable resin, the print head having a cavity for containing gas; introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, where the gas-resin interface is constrained by the print head and defines a printing surface; projecting curing radiation onto the submerged gas-resin interface to accelerate the curing of the resin on the printing surface; transmitting acoustic waves to the submerged gas-resin interface; and facilitating relative movement between the gas-resin interface and the resin to produce the 3D object.

[0169] It has been observed that gas-resin interfaces can be sensitive to acoustic stimulation. By transmitting acoustic waves to a submerged gas-resin interface, it is possible to rapidly modulate the shape of the interface according to the properties of the acoustic waves. Rapid modulation of the interface shape via acoustic excitation can advantageously promote the formation of capillary waves (i.e., surface waves with sufficiently short wavelengths where the restoring force is the surface tension of the resin) on the interface, thereby significantly improving the resin inflow around the interface (Figure 12). The speed and distribution of material inflow itself can be modulated by controlling parameters such as the properties of the acoustic waves (e.g., amplitude, frequency), the print head shape, and / or the interface curvature.

[0170] Therefore, in some embodiments, the method includes the step of transmitting acoustic waves to the gas-resin interface in order to induce an acoustic field in the form of Faraday waves on the interface. The application of the above waves to the interface is advantageous in that it improves the resin flow during printing, thereby resulting in a faster printing speed.

[0171] The improved mass transfer at the gas-resin interface, achievable under acoustic excitation, advantageously results in faster and more consistent printing compared to printing in the absence of acoustic excitation. This, in turn, leads to printing of a wider cross-section, along with higher resolution printing.

[0172] The use of acoustic wave excitation during 3D object printing is particularly advantageous in the fabrication of composite objects made from cured resin matrices containing suspended materials, for example, in the context of bioprinting. In these cases, the improved resin inflow at the gas-resin interface under acoustic excitation improves the localization of suspended materials (e.g., viable cells) within the printed volume. This results in the rapid production of 3D objects containing high concentrations of the desired suspended material. Through the use of acoustic modulation, not only can the precipitation of suspended materials in the resin be effectively removed, but an increase in encapsulation efficiency may also be achieved through acoustic focusing. This improvement greatly increases the range of possible biological materials while maintaining biologically relevant processing parameters and cellular homogeneity.

[0173] Figure 13 shows representations of different acoustic patterns (A, B, C) formed using a cylindrical printhead in different cross-sections of the print. The patterns are associated with acoustic excitation at different frequencies. The image on the right of Figure 13 shows the pattern obtained at the gas-resin interface using polystyrene microparticles suspended in resin under acoustic excitation. The pattern is observed through the printhead at three different application frequencies, demonstrating the ability to change the number and location of the collected microobjects along the gas-resin interface.

[0174] Mechanical vibrations at the gas-resin interface resulting from the transmission of acoustic waves may also be used to provide localized mechanical mixing of the uncured resin layer adjacent to the object being formed during printing. In these cases, for example in the context of bioprinting, this further improves the printing efficiency during the production of composite objects made from a cured resin matrix containing suspended material. For example, in a vertical setup, by temporarily stopping the printing process and raising the print head to a set distance from the preceding layer, standing waves can be formed by the hydrodynamic interaction between the gas-resin interface and the underlying structure, thereby promoting the spatial patterning of particles or suspended material. During this process, the suspended material is driven by acoustic radiation forces formed by spatial fluctuations in energy density. Thus, the suspended material moves to either a node or an antinode of the standing wave, depending on whether the acoustic contrast factor of the suspended material to the surrounding fluid is positive or negative, respectively.

[0175] By transmitting acoustic waves over a submerged gas-resin interface, the method of the present invention advantageously provides additional degrees of freedom to the fabricated surface, where the superposition of print head translation, internal pressure, and acoustic drive signals determines the time-dependent location (Figure 12(b)). This additional modality can be used to enhance fabrication speed, material handling range, cell patterning, or fluid handling performance by providing direct control of the wave properties within the fabrication regime. Thus, objects can be created by illuminating the interface at a desired cross-section and continuously modulating the interface shape and position, where the absence of a solid interface avoids mechanical adhesion, thereby enabling the rapid production of structures. This technique results in the reproducible formation of a wide variety of 3D centimeter-scale objects in tens of seconds.

[0176] The transmission of acoustic waves to the submerged gas-resin interface may be achieved by any means known to those skilled in the art.

[0177] For example, acoustic waves may be transmitted to the submerged gas-resin interface by vibrating the print head.

[0178] Acoustic waves may also be transmitted to the submerged gas-resin interface by introducing acoustic waves into the resin, for example, by generating acoustic waves within the resin volume. In these cases, the acoustic waves may be propagated through the resin to the gas-resin interface, thereby resulting in the desired shape modulation of the submerged gas-resin interface.

[0179] In some embodiments, the method of the present invention includes the step of introducing acoustic waves into the cavity of a print head. In those cases, the acoustic waves propagate through the cavity of the print head as pressure waves in a gas contained within the cavity, thereby causing shape modulation of the submerged gas-resin interface.

[0180] Acoustic waves may be generated by any means known to those skilled in the art. For example, acoustic waves may be transmitted to the gas-resin interface by an acoustic generator (e.g., an electroacoustic device such as a voice coil actuator or a surface acoustic wave generator) positioned to emit acoustic waves that can propagate to the gas-resin interface.

[0181] For example, a suitable acoustic generator may be coupled to the cavity of the print head so that emitted acoustic waves propagate through the gas in the cavity and reach the gas-resin interface. In another configuration, the acoustic generator may be submerged in the resin so that the generated acoustic waves propagate through the resin to the gas-resin interface. In yet another configuration, the acoustic wave generator may be coupled to the print head so that emitted acoustic waves propagate through the body of the print head and reach the submerged gas-resin interface. Alternative configurations may be readily devised by those skilled in the art.

[0182] Figure 11 illustrates a schematic diagram of an exemplary print head for performing the method through acoustic stimulation. Acoustic waves are introduced into the cavity of the print head through an opening in the print head. The print head is open at one end and sealed with a transparent glass window to maintain a constant gas volume, while allowing optical projection to pass through. As the print head is submerged vertically in the resin, a gas-resin interface is formed at its base. The interface acts as a fabrication surface used by the patterned projection to locally cure the resin. Acoustic manipulation of the air volume inside the print head facilitates enhanced material inflow through capillary-driven waves propagating across the interface, as shown in Figure 12(a). The instantaneous location of the air-liquid boundary depends on the spatial location of the print head, the internal pressure state, and the acoustic excitation, as shown in Figure 12(b).

[0183] Acoustic excitation at the gas-resin interface results in the formation of capillary-gravity waves and subsurface streaming, significantly enhancing material inflow into the printed volume. The ability to position the print head itself at any point in the resin largely eliminates the essential link between the shape of the material container and the formation of free surface waves. Therefore, acoustic stimulation can be effectively performed regardless of the properties of the resin container. This is particularly important for biological materials printed in saturates in sequential volumes, such as multi-well plates, where the entire process (including all structures subsequently printed) must operate continuously, and prolonged, unnecessary stress could potentially damage the delicate tissue material due to the biological components.

[0184] The shape of the gas-resin interface can be modulated by acting on the properties of acoustic waves. For example, given the shape of the print head and the resin, the shape of the gas-resin interface, and therefore the shape of the print volume, can also be modulated by acting on the frequency and / or amplitude of acoustic waves.

[0185] For example, with cylindrical print heads (such as those depicted in Figures 11 and 12), it was observed that low-frequency acoustic waves form monochromatic modes symmetrical in the azimuthal direction, and that these sequentially evolve to tetragonal symmetry at higher frequencies.

[0186] Furthermore, it was observed that low-amplitude modulation at a frequency synchronized with the projection frame rate significantly increased mass transfer, thereby enabling translational flow across the meniscus. Additionally, centralized jetting was observed at higher drive amplitudes, enabling the creation of structures from the interface and subsequent high-speed injection.

[0187] Therefore, acoustic excitation significantly increases the material inflow during printing, which is further amplified by the meniscus curvature resulting from a secondary streaming effect. To demonstrate this improvement, transient inflow of the new material was captured using high-speed imaging with and without acoustic excitation for various material viscosities and translational velocities. The application of acoustic modulation results in an exponential decrease in the "dry" area beneath the interface. By measuring the instantaneous area of ​​the dry region before acoustic excitation and the duration that fully saturates the interface, the time-averaged rate of the new material under the conditions used (as described in the examples) is approximately 16–40 mms over a range of translational velocities. -1 It was found that this was the case. This heuristic method can be used in combination with the topology of an object to predict and adapt the printing speed based on the length of the fluid path.

[0188] Therefore, in some embodiments, the acoustic wave has a frequency of 1 Hz to 10 MHz, for example, 1 Hz to 20 kHz, or 1 Hz to 1000 Hz. In some embodiments, the acoustic wave has a frequency of 50 Hz to 150 Hz.

[0189] In some embodiments, the acoustic wave, when expressed in terms of pressure amplitude, has an amplitude of 0.1 Pa to 1 MPa, for example, 0.1 Pa to 5 kPa (measured in the medium transmitting the wave, for example, in the gas section of the print head when the acoustic wave is generated in a gas).

[0190] In some embodiments, the acoustic wave has a frequency of 1 Hz to 100 kHz and an amplitude converted to a pressure in the range of 0.1 Pa to 5 kPa.

[0191] It will be understood that the specific effects of acoustic stimulation on the gas-resin interface may be resin-dependent, in that the propagation characteristics of acoustic waves propagating through the resin may vary depending on the density of the resin. Those skilled in the art will be able to fine-tune the frequency and amplitude characteristics of the acoustic waves depending on the intended result.

[0192] Furthermore, the specific effects of acoustic stimulation on the gas-resin interface may depend on the specific shape of the print head. In this regard, selecting different print head shapes, along with custom shapes of the interface under acoustic stimulation, can help create different wave patterns.

[0193] Acoustic wave formation can be used to capture, locate, and trap particles or additives suspended in a resin. This is due to the interaction between the modulated wave and the underlying layer. This technique can be used to pattern particles or cells in a specific arrangement.

[0194] The present invention also provides a system for forming a 3D object, comprising a print head for transmitting curing radiation to a photocurable resin, wherein the print head has a cavity for containing a gas, which in turn facilitates the formation of a gas-resin interface constrained to the print head when the print head is introduced into the photocurable resin.

[0195] The print head in the system of the present invention may be any of the types of print heads described herein.

[0196] In some embodiments, the system includes a tub for containing a photocurable resin.

[0197] In a typical configuration, the vat may be positioned beneath the print head so that the print head can be introduced vertically into the resin contained within the vat.

[0198] Nevertheless, any configuration that allows for the introduction of the print head into the resin to facilitate the formation of the intended gas-resin interface will be understood to be within the scope of the present invention.

[0199] In some embodiments, the system also includes one or more movable stages to facilitate relative movement between the print head and the resin when the print head is introduced into the photocurable resin. This relative movement may be achieved, for example, by moving the print head relative to the resin contained in a vat, or by moving the vat containing the resin relative to the print head.

[0200] In some embodiments, the print head moves only along the vertical axis (z-axis) during printing. Figure 1 shows an exemplary system in which the print head (PC) is introduced into resin housed in a vat in an arrangement that results in vertical movement of the print head along the z-direction. In those cases, printing of multiple objects may be achieved by translating the print head across different printing locations (as shown, for example, in Figure 7) once the initial object has been printed.

[0201] The system of the present invention may further include a source of curing radiation, which may be of the type of curing radiation described herein. The source of curing radiation may be integrated into the print head or be independent of the print head. Therefore, in some embodiments, the print head includes the source of curing radiation.

[0202] In some embodiments, the print head includes an optical fiber for transmitting curing radiation. The optical fiber may be for transmitting curing radiation from a radiation source located outside the print head, or from a radiation source integrated into the print head.

[0203] The printhead cavity may be of any design that facilitates the printhead's operation as intended; that is, when the printhead is introduced into the photocurable resin, the gas within the cavity promotes the formation of a gas-resin interface constrained to the printhead.

[0204] For example, a print head may have an internal cavity with an opening on the bottom side of the print head, so that a gas-resin interface is formed at the opening when the print head is introduced into the photocurable resin.

[0205] In some embodiments, the print head is equipped with a gas inlet for introducing or extracting gas into / from the cavity. In those cases, when the print head is introduced into the resin, the gas in the cavity may be pressurized or depressurized, which results in alteration of the shape and expansion of the gas-resin interface.

[0206] In some embodiments, the print head has an internal cavity having an opening on the bottom side of the print head, thereby forming a gas-resin interface that has a convex shape protruding downward from the opening when the print head is introduced into the photocurable resin and the cavity is filled with pressurized gas.

[0207] The opening may have any dimensions that contribute to the formation of a submerged gas-resin interface, as described herein. In some embodiments, the opening has the largest dimensions in the range of 2 mm to 30 mm, 2 mm to 15 mm, or 5 mm to 15 mm. In some embodiments, the opening has a maximum dimension of 10 mm or 25 mm.

[0208] The opening may be of any shape that contributes to the formation of a submerged gas-resin interface, as described herein. In some embodiments, the opening may be circular, square, or rectangular in shape, having the largest dimension being 2 mm to 30 mm, 2 mm to 15 mm, or 5 mm to 15 mm, for example, 10 mm or 25 mm.

[0209] In some embodiments, the print head includes an opening cavity having a circular opening with a diameter of 2mm to 30mm, 2mm to 15mm, or 5mm to 15mm, for example, 10mm or 25mm.

[0210] An example of a printhead with an opening cavity having a circular opening is shown in Figures 1, 2, 3(a), 5, 7, 11, 12(a), 14(b), and 15. An example of a printhead with an opening cavity having a separate array of square openings (each 8 mm × 8 mm) is shown in Figure 10.

[0211] For simplification, an axisymmetric printhead was used to simplify the calculation of the interface shape, although any arbitrary shape of the printhead is conceivable. Generally, printheads with cavities ranging from 5 mm to 30 mm (the largest dimension) were primarily used. For example, two printhead sizes (D=25 mm and D=10 mm) were used.

[0212] The print head may have any shape that contributes to its intended function.

[0213] In some embodiments, the print head has a tubular shape with an opening at one end and a window at the opposite end that is transparent to curing radiation. The tubular shape may have a circular or square cross-section. An example of a tubular print head with a circular cross-section is shown in the schematic diagram of Figure 1. An example of a tubular print head with a square cross-section is shown in Figure 10.

[0214] In some embodiments, the print head comprises a cavity having multiple openings. When such a print head is used, its configuration results in the provision of multiple distinct gas-resin interfaces, for example, for the simultaneous curing of different volumes of resin. An example of one such configuration is shown in Figure 10. The figure depicts a print head having an internal cavity with a rectangular cross-section and a 3x3 arrangement of openings, which consequently defines a 3x3 arrangement of recessed gas-resin interfaces when in use.

[0215] In some embodiments, the print head comprises multiple cavities and multiple openings. For example, the print head may comprise multiple cavities, each having a corresponding opening. When in use, these print heads advantageously provide multiple gas-resin interfaces, which are useful for the simultaneous curing of different volumes of resin.

[0216] In some embodiments, the system includes optical components for delivering, focusing, and controlling curing radiation. These components may include one or more optical lenses, one or more mirrors, or other optical components that precisely shape and guide the radiation. In some embodiments, the print head includes one or more such optical components.

[0217] In some embodiments, the system further comprises control and feedback mechanisms for monitoring and adjusting the operating parameters of the printing process. These mechanisms may include sensors, actuators, and controllers that provide real-time feedback on resin quantity, radiation intensity, gas pressure in the cavity within the print head, and other relevant parameters. The control and feedback mechanisms ensure the stability and accuracy of the printing process, thereby enabling consistent and reliable production of 3D objects.

[0218] For example, the system may include an image-based feedback control system for automatic modulation and control of the shape and dimensions of the gas-resin interface. The system may include a camera (see, for example, the CCD camera in Figure 1) that continuously monitors the interface profile (see also Figure 3(a)). The camera may supply profile information to a control unit. If the camera detects that the interface shape deviates from the intended configuration, the control unit may act on the gas pressure in the print head to modulate the interface shape to conform to the intended one.

[0219] An example of an exemplary assembly that implements one embodiment of the system of the present invention is shown in the schematic diagram of Figure 1, as described herein.

[0220] In some embodiments, the system includes an acoustic wave generator for transmitting acoustic waves to the gas-resin interface.

[0221] The acoustic generator may be any device capable of transmitting acoustic waves to the gas-resin interface. Suitable examples of acoustic generators in this regard include electroacoustic devices such as voice coil actuators, piezoelectric actuators, magnetostrictive actuators, and capacitive transducers. The transducers may be arranged in a phase array or modified by acoustic holograms or acoustic metamaterials.

[0222] The acoustic wave generator may be positioned within the system to effectively transmit acoustic waves to the gas-resin interface. For example, the acoustic generator may be mounted in communication with a cavity in the print head so that the generated acoustic waves propagate through the gas in the cavity to reach the gas-resin interface. In other configurations, the acoustic generator may be mounted, for example, by being submerged in the resin, so that the acoustic waves are transmitted through the resin to reach the gas-resin interface. In yet another configuration, the acoustic generator may be mechanically coupled to the print head so that the acoustic waves are transmitted to the gas-resin interface as mechanical vibrations of the print head. As long as acoustic waves are transmitted to the gas-resin interface, those skilled in the art will be able to readily devise alternatives to the configurations described herein.

[0223] A schematic diagram of one embodiment of the system of the present invention, including an acoustic generator, is shown in Figure 14(a). Figure 14(a) shows a CAD model of mechanical components of a 3D printing setup that may be used to carry out the method of the present invention, which includes an acoustic modulation device for transmitting acoustic waves to the gas-resin interface through the cavity of the print head.

[0224] A projection module (1) is used to generate 2D optical projections of slices of a target 3D object, which are projected vertically along the z-axis. A z-axis stage (2) is mounted to provide vertical translational movement to the projection lens (3) and the print head assembly (4). In the embodiment shown in the figure, a 12-well plate (5) is located on a multipurpose holder (6), which itself is mounted on the x-axis stage (7) and z-axis stage (8) for lateral movement along the horizontal plane. A pneumatic air line (9) connects the acoustic modulation device (10) to the cavity of the print head assembly (4) to transmit acoustic waves generated by the acoustic modulation device (10) to the gas-resin interface (see also Figure 14(b)). In the embodiment shown in the figure, a 50 mL syringe (11) is mounted on the s-axis stage (12) and may be used to modulate the air pressure in the pneumatic line (9) and the cavity of the print head assembly (4).

[0225] Figure 14(b) shows a schematic diagram of the corresponding gas-resin interface formed at the tip of the print head under acoustic excitation. Figure 14(c) illustrates the total degrees of freedom (DOF) of the print interface location under conventional 3D printing (left) compared with the proposed method and system (right), and Figure 14(d) shows the instantaneous interface location depending on the sum of the DOF locations.

[0226] Alternative arrangements of the elements shown in Figure 14 may also work as intended. For example, the projection module may be mounted to project a 2D optical projection of a slice of the target 3D object horizontally (similar to the arrangement shown in Figure 1). In this case, the horizontally projected beam may be deflected vertically by a beam splitter. The use of a beam splitter may also result in mounting additional optical elements on the opposite side of the projection module, such as a CCD camera with a horizontal focal axis for image feedback control of the gas-resin interface shape. The print head may be mounted vertically below the beam splitter to collect the vertically deflected projections and focus them on the gas-resin interface. Other components may then reflect the mounting of the corresponding components described in relation to Figure 14.

[0227] In summary, we present herein a rapid 3D printing technique based on the generation of a gas-resin interface. The result is an extremely flexible printing method that, when used in conjunction with existing photochemistry, can produce high-resolution structures faster than those demonstrated by previously demonstrated volumetric printing methods.

[0228] Furthermore, we demonstrated that the process can be used to print complex structures, multi-material structures, via two-stage printing and overprinting by leveraging the permeability of the interface.

[0229] Furthermore, we demonstrated that this process can be easily parallelized and is safe for bioprinting applications. We expect that dynamic interface printing methods will offer numerous advantages in fields requiring high-speed, high-resolution fabrication of three-dimensional structures.

[0230] Herein, specific embodiments of the present invention are described with reference to the following non-limiting examples. [Examples] [Example 1]

[0231] [3D Printer Assembly] The system shown in the schematic diagram in Figure 1 was prepared as follows.

[0232] All components shown in the schematic diagram were mounted on two orthogonal optical breadboards to facilitate vertical and horizontal displacement. A patterned cross-section of the target object was projected using a high-power projection module (LRS-WQ, Visitech) with a resolution of 2560 × 1600 pixels and a pixel size of 15.1 μm. The projection module was rigidly mounted to a linear stage (MOX-02-100, Optics Focus) attached to the vertical component of the optical breadboard.

[0233] Direct control of the dynamic interface is achieved via a second linear stage (MOX-02-50, Optics Focus), which controls the displacement of a 10 mL or 50 mL syringe connected to the print head via a silicone hose for pressurizing the gas within the print head.

[0234] An additional pair of linear stages (MOX-02-100, Optics Focus) are used to position cuvettes / well plates under the print head for sequential or multi-stage printing. System control was performed via a custom MATLAB graphical user interface (GUI) that enabled management of the motorized linear stages via RS232, control of the acoustic modulation device, control of projection module parameters, and transmission of cross-sectional images via HDMI®. The Shadowgraph imaging system consists of a 635nm single-mode fiber-coupled laser (635nm SM FC Laser, Civil Laser) collimated using a lens (#32-970, Edmund Optics).

[0235] After passing through a glass cuvette, the shadowgraph is focused using the same collimating lens and imaged onto the CCD of a mirrorless camera (A7 II, Sony) using a third lens (#32-483, Edmund Optics). System control is performed via a custom MATLAB graphical user interface (GUI) that enables management of the motorized linear stage via RS232, acquisition of the shadowgraph, and transmission of cross-sectional images via HDMI.

[0236] To generate target projection, a 405nm digital optical projector with a 2560×1600 pixel array produces an in-plane resolution of 15.1μm, and the projector's maximum radiance is 270mW / cm² at the focal plane. 2 Here, this may be modulated to a lower radiance value. The projection optics are mounted on a z-stage to translate the focal plane during printing, where a further linear stage is used to position the print head in XY space to facilitate sequential printing, and a fourth stage is used for direct control of the printing interface via a syringe. The projection module, laser, camera, and stage are controlled through a custom MATLAB-based interface.

[0237] [Print head] The print heads used in this study can be made to various dimensions depending on the desired size of the resin container. For simplification, an axisymmetric print head was used to simplify the calculation of the interface shape, although any arbitrary shape of the container is possible. Generally, print heads in the range of 30 mm to 5 mm were mainly used. For example, two print head sizes (D=25 mm and D=10 mm) were used.

[0238] In dynamic interface printing, the total size of the object in the x and y directions is limited by the full field of view of the projector in the focal plane, while the total height of the object is limited by the focal length of the projection optics. In our setup, this was approximately 70 mm. The print head was fabricated using a commercially available 3D printing system (Form3+, Formlabs), and a glass window was bonded in place to facilitate light transmission along its center. An internal channel was also fabricated with the print head to allow gas exchange into the print head via a syringe system. [Example 2]

[0239] [Resin composition and preparation] PEGDA-based resins: Various PEGDA materials were used in the range of 10% w / v to 100% w / v. 10 g of PEGDA Mn700 (#455008, Sigma) was dissolved in 40 g of 40°C deionized water (excluding 100% w / v) and thoroughly mixed for 10 minutes. Then, 0.1% w / w (e.g., 500 mg) of tartrazine (#T0388, Sigma) and 0.25% w / w (e.g., 150 mg) of lithium phenyl-2,4,6-trimethylbenzoyl phosphinate (LAP, #900889, Sigma) were added to the mixture and stirred until completely dissolved.

[0240] HDDA-based resin: A solution of 500 mg of phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (511447, Sigma) and 50 g of 1,6-hexanediol diacrylate (#246816, Sigma) was prepared by heating the mixture to 40°C and stirring for 30 minutes. To control the resolution in the z direction, the light absorber Sudan I (#103624, Sigma) was added in 36 different amounts ranging from 0 to 0.04% w / w.

[0241] GelMA-based resin: GelMA was synthesized according to the protocol described in Zhu, M. et al. "Gelatin methacryloyl and its hydrogels with an exceptional degree of controllability and batch-to-batch consistency", Sci Rep9, 6863 (2019), producing a degree of substitution of 93% (confirmed by NMR).

[0242] A 10% w / v GelMA solution was prepared by dissolving 1 g of GelMA in 10 mL of cell culture medium (Freestyle 293 Expression Medium, Thermofisher) preheated to 37°C. After complete dissolution of the GelMA, 100 mg of tartrazine g and 25 mg of LAP were added to the solution, which was then maintained at 37°C until complete dissolution. The mixture was sterilized by passing it through a 0.22 μm sterile filter in a biosafety cabinet and then stored in a refrigerator until use.

[0243] Alginate-based resin: norbornene-functionalized sodium alginate (AN) was synthesized according to the following procedure. 10 g of sodium alginate was dissolved in 500 mL of 0.1 M 2-(N-morpholino)ethanesulfonic acid buffer (#145224-94-8 Research Organics) and fixed to pH 5.0. 9.67 g of 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide·HCl, 2.90 g of N-hydroxysuccinimide, and 3.11 mL of 5-norbornene-2-methylamine were added. The pH was fixed to 7.5 with 1 M NaOH, and the reaction was carried out at room temperature for 20 hours. The mixture was dialyzed against water for 5 days before lyophilization.

[0244] The functionalization degree of norbornene was determined to be 16.2% by 1H NMR. A 7% w / v AN solution was prepared by dissolving 1 g of AN in 14.29 mL of phosphate-buffered saline (PBS). 200 mg of tartrazine, 20 mg of LAP, and 122.7 μl of 2,2'-(ethylenedioxy)diethanethiol were dissolved in 5.59 mL of PBS, added to the AN solution, and mixed until homogeneous. The pH was adjusted with 1 M NaOH until the solution was visibly opaque.

[0245] UDMA support material: A solution of 50 mg of phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (511447, Sigma) and 5 g of diurethane dimethacrylate (#436909, Sigma) was prepared by heating the mixture to 45°C and stirring for 30 minutes. To remove trapped air bubbles, the mixture was then transferred to a light-shielding Falcon tube and centrifuged at 4000 rpm for 10 minutes to remove any remaining air bubbles. This material was then used as a base support for free-floating printing tests.

[0246] [microscope] Using the Phoenix Nanotom M scanner (voxel size = 10 μm) 3 A μCT image was acquired using a 90kV tube voltage, 200μA tube current, and an 8-minute scan time. For hydrogel samples, the structure was briefly dried on tissue paper and mounted in a Falcon tube for imaging. For rigid materials such as HDDA, the structure was placed on top of a plastic cap to provide good contrast between the printed structure and the support medium. For each structure, an STL surface mesh was extracted and imported into Keyshot11 (Keyshot, Luxion) to render the final μCT representation.

[0247] Scanning electron microscope (SEM) images were acquired on a FlexSEM1000 (Hitachi High Technologies, Japan). Printed structures on glass slides were mounted directly onto the microscope stage without further sample preparation. No conductive coatings were applied to the samples. The FlexSEM operated in variable pressure mode at 50 Pa, and images were acquired using a 15 keV beam with an Ultra Variable Detector (UVD). To cover the field of view required for large structures, the working distance was typically 40–50 mm, and multiple images were collected in a tiled manner and stitched together in post-processing. [Example 3]

[0248] The proposed method enables the creation of structures not only in rigid acrylates such as HDDA, but also in common biomaterials such as PEGDA and GelMA. To demonstrate this, we began developing a printing parameter space to determine the maximum achievable printing speed as a function of optical output (Figure 4). Using a PEGDA-based hydrogel material, we achieved 270 mW / cm². 2 At optical doses, speeds exceeding 700 μm / s were achieved, while even at lower optical doses relevant to tissue engineering, high-throughput printing was still facilitated. An example of a helical test structure printed with different power-speed combinations can be seen in Figure 1, where the correct pairing of printing speed and optical dose resulted in high-quality structures.

[0249] To assess the achievable resolution of the dynamic interface system, a series of test structures were fabricated using HDDA (method). To evaluate the minimum in-plane feature size, test structures containing an array of feature parts with specified dimensions and orientations were printed. A scanning electron microscope (SEM) was used to image the test structures, yielding a minimum in-plane resolution of 50 μm, which corresponds to approximately 3 pixels in the plane. To confirm the system's ability to print structures with non-planar feature parts, a gyroid grating and a Kelvin cell were fabricated and subsequently imaged using SEM and micro-computed tomography (microCT). Both structures exhibited feature parts with dimensions less than 100 μm.

[0250] We propose that the proposed method offers significant advantages in the fields of biomedicine and tissue engineering due to its rapid, contactless, and support-free fabrication capabilities. High-fidelity, low-rigidity structures, such as cardiac models (not shown), can be produced in as little as 30 seconds. The ability to change the size of the print head is particularly relevant for producing biologically valid constructs, as working with high cell populations often requires the use of small volumes. To illustrate this, a small-diameter (10 mm) probe was used to print directly into a vial with a total printing volume of 3 mL (Figure 5).

[0251] Furthermore, cell solutions are often opaque due to optical scattering induced by the suspension of cell populations in bio-inks. While this does not pose a problem for low cell populations, matching the refractive indices between the material and the cell medium becomes important for high cell populations, particularly in the context of volumetric printing. Notably, the proposed method does not require light projection to pass through the entire volume of the resin, thereby enabling high-resolution printing of high cell populations or opaque resins.

[0252] A comparison between our standard PEGDA resin and an engineering opaque alginate bioresin that shields a standard United States Air Force (USAF) test pattern is presented in Figures 6(a) and 6(b). Despite the high optical shielding produced by the alginate gel, the method yields an accurate reproduction of the internal structure of the tricuspid valve model (Figure 6(c)).

[0253] Considering that the print head can move more freely in 3D space, it is possible to parallelize the system to sequentially create multiple structures (Figure 7). This is advantageous not only for single-chamber printing applications but also for facilitating the production of multiple structures in multiple volumes (such as well plates) that may accommodate various cell types, materials, or morphologies.

[0254] [Cell printing] To evaluate the preliminary viability of this technique for generating biologically relevant constructs containing cells, a simplified kidney-shaped hydrogel structure was printed using HEK293-F cells at a density of 7.2 million cells / mL. Human Embryonic Kidney (HEK)293-F cells (Freestyle293-F, Thermo Fisher) were used to determine the preliminary viability of the 3D printing system. Unlike other volumetric printing methods, high cell populations can be easily printed without requiring a matching refractive index between the cells and the printing medium.

[0255] A cell solution containing 7.2 million cells / mL was used for both the kidney model and the measurement of cell viability. To determine cell viability, a thin 500 μm wall was printed to minimize the effect of cell death due to insufficient medium diffusion, and this was determined via the LIVE / DEAD viability / toxicity kit (L3224, Invitrogen). Measurements were performed daily over a 5-day cycle, and viability was averaged across four representative regions for each day.

[0256] To create the cell-supported bioink, the GelMA solution was heated to 37°C, followed by resuspending of the cells in the solution. The solution was then passed through a cell strainer (#0877123, Thermo Fisher) and stored in a water tank when not in use. The printing process involved pipetting approximately 3 mL of GelMA ink into a 12-well plate and lowering the print head into the wells. Before each print, an electric syringe was used to resuspend the cells by sequentially applying positive and negative pressure (similar to pipetting a liquid up and down) to prevent cell sedimentation before printing. Each print was performed for approximately 30 seconds, with a linear translational speed of 150 μm / s.

[0257] A fluorescence microscope was used to image the constructs over a 72-hour cycle (Methods), which revealed that the proposed method maintained a high cell viability (>85%) after 24 hours (Figure 8).

[0258] The elimination of the need for fluid handling by using optically transparent materials or a print head as a pipetting tool, along with additional functionalities such as acoustically driving the interface to align cells before encapsulation, opens up a wide path for this system to become a highly beneficial tool for bioengineering. Currently, our system is focused on generating centimeter-scale objects, but future improvements may extend to optical systems with higher numerical apertures, where microscale structures could be created at high speed without the costs associated with two-photon systems. [Example 4]

[0259] [Data Preprocessing, Printing, and Postprocessing] The 3D design models of the helical stent, vascular tree, kidney model, "DIP" lettering, and microfluidic outline shown in the figure were created in Autodesk Inventor. The gyroid grid, fluorite grid, and Kelvin cell were created using nTopology, nTop NY. The tricuspid valve model, heart model, and buckyball were downloaded from Thingiverse.com. For each outline, an STL file was extracted and sliced ​​into a stack of PNG images using Chitubox.

[0260] Because the frame rate of the HDMI signal is limited to 60fps, the layer height depends on the printing speed, i.e.

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[0261] The MATLAB GUI sends a signal to turn on the LED module, and the print head is displaced in the positive z direction at a predetermined print speed. The optical output of the projection module is automatically set according to the user-selected print speed, according to a parameter space matrix. For materials made from HDDA, the printer structure was removed from the print volume and washed with isopropyl alcohol. For soft materials made from PEGDA and GelMA, excess material was gently removed using a pipette, and the structure was resuspended in deionized water to wash away any remaining material. The structure was then gently separated from the bottom of the print head 93 and stored in DI water. [Example 5]

[0262] [Parallel Printing] In addition to the demonstrated parallelization through sequential printing, it is possible to engineer a print head that utilizes interface control to create arbitrary configurations or multiple printing interfaces within a single print head (Figure 10(a)). Generating a global interface displacement map of the print head facilitates the parallel printing of multiple structures, as illustrated by the arrangement of nine individual interfaces creating three sets of the word "DIP" (Figure 10(b)).

[0263] We have successfully demonstrated the capacity for rapid parallelization of the printing process, either by using a multi-interface print head or by sequentially printing multiple structures within the same print volume or across multiple wells. We believe these findings highlight the potential for high levels of automation and rapid generation of multiple structures, which may enable multiple printing parameters or material or cell type variations in the context of multi-well plates to be quickly explored. [Example 6]

[0264] [Microprinting] To assess the ability to produce intricate internal structures, two simple microfluidic structures were printed, exemplifying that small features of 500 μm can be achieved (not shown). Combined with overprinting, this performance may enable the fabrication of integrated microfluidic models, such as directly printing a microfluidic chip onto a perfusion device like a syringe needle. Furthermore, multi-step printing methods may enable the rapid incorporation of multiple cell types or materials into a single model, significantly enhancing the complexity of printed tissue constructs. [Example 7]

[0265] [Acoustic Modulation] In accordance with the systems outlined schematically in Figures 11 - 15, the synthesis of 3D objects was performed while transmitting acoustic waves across the gas-liquid interface of a submerged print head.

[0266] The system configuration relies on an in-plane resolution of 15.1 μm, which is largely defined by the pixel size of the Digital Micromirror Device (DMD) and the magnification of the imaging optical system. The DMD resolution is 2560 × 1600 pixels. This system utilizes a 405 nm LED source, and the radiance at the focal plane is zero to approximately 270 mW / cm². 2 It can be modulated. Projection illumination and optics are mounted on the z-stage to translate the print head during printing. Further stages are used to position the print head in XY space for sequential printing, and another stage is used for controlling the printing interface.

[0267] Additionally, acoustic control of the interface was achieved via volume manipulation of a supply line located outside the system by a voice coil actuator. Acoustic modulation of the interface was also achieved via direct volume manipulation of the gas volume contained within the print head. In practice, a 3-inch 15W speaker driver (Techbrands, AS3034) was mounted on a sealed 3D printing manifold housing the inlet and outlet ports. The speaker was driven by a commercially available amplifier (Adafruit, MAX9744) using a supplied auxiliary port, and a predetermined waveform was transmitted via the MATLAB GUI. A frequency range of 5–500Hz was used, with fixed or transient frequency switching depending on the structure. Synchronizing the acoustic modulation with the rest of the motion and pressure control was straightforward by specifying a waveform for each degree of freedom. The acoustic modulation device operated as an inline control unit, with the inlet port connected to the syringe system and the outlet port connected to the print head. This facilitated modulation around the pressurization and pressurization setpoint of the sealed system.

[0268] The acoustic waves used in the test had frequencies ranging from 1 Hz to 100 kHz, for example, 5 Hz to 500 Hz, and amplitudes converted to pressures in the range of 0.1 Pa to 5 kPa.

[0269] The projection module, acoustic modulation device, and motion control stage are controlled through a custom MATLAB-based graphical user interface.

[0270] Figure 15 shows schematic diagrams of an exemplary printhead assembly and acoustic airline modulation, namely: a) an enlarged half section of the printhead assembly; b) a reduced half section of the printhead assembly, highlighting the formation of a sealed air volume with a transparent glass window at the top; c) a half section of the airline modulation system, where the speaker diaphragm forms one side of the sealed box; and d) an electrical signal applied to the voice coil causing excitation of the diaphragm, which modulates the volume near the setpoint pressure in the air manifold and, consequently, in the printhead.

[0271] The printhead assembly includes a lens mounting adapter (13) with an optical window for mounting a 75 × 50 mm glass slide (14). The printhead thread adapter (16) is sealed to the glass slide (14) and the 25 mm printhead (17) through a gasket (15). As shown in Figures 15(a) and (b), the printhead thread adapter (14) provides an inlet (22) for a pneumatic connection between the cavity of the printhead (17) and the acoustic generator (shown in Figures 15(c) and (d)) through an acoustically modulated air line (23). Figures 15(c) and (d) show schematic diagrams of an exemplary acoustic generator, including a voice coil (18), a suspension (20), and a movable diaphragm (19) connected through a gasket (15). Figure 15(d) shows a schematic diagram of the diaphragm's movement during the generation of acoustic waves that propagate through the inlet (22) to the cavity of the print head (17). [Example 8]

[0272] [Modeling of the Gas-Resin Interface] The shape of the interface can be approximately described by the Young-Laplace equation, which relates the interface curvature to the pressure difference sustained across the boundary. Generally, this can be written as follows. [Number] Here, [Number] represents the Laplace pressure, [Number] is the surface tension, [Number] is the normal vector to the surface. The dimensionless shape of the interface can be obtained by substituting the general formula for the principal curvature of an axisymmetric surface shown below. [Number] The origin of coordinates is taken as the point where the meniscus edge contacts the print head, the positive z-axis is directed downward along the central axis of the print head, and the r-axis is parallel to the diameter of the print head. The prime superscript indicates the differentiation with respect to z, [Number] represents the maximum height of the meniscus given by the following. [Number] Here, [Number] [[ID=5^4]] is the volume [Number] is the radius of the theoretical spherical meniscus having the volume, [Number] This indicates the number of bonds,

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[0273] The shape of the interface is,

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[0274] [Formation of convex interfaces] The proposed method can produce an air-liquid meniscus by pressurizing the cavity within the print head, so the profile of this boundary, and consequently the cured region, is non-planar. Traditional slicing schemes assume that the projected outline is parallel to the construct plane, and therefore will result in reconstructed artifacts. To compensate for this, in the case of an axisymmetric print head, the 3D surface can be reconstructed by rotating the predicted surface around the z-axis using Young-Laplace. A separate interface profile Z(r) is the solution to the boundary value problem, and the parametric representation of the reconstructed 3D surface is given by:

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[0275] To solve the above equation, a cubic Bézier curve is defined along with its first and second derivatives.

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[0276] Besides remapping the outline in 3D Cartesian coordinates to slice the volume at a curved printing interface, the meniscus shape presents additional challenges for the initial layer of printing. If the first layer of printing is defined as the point where the air / liquid interface descends into the container so that the “stable state” meniscus shape is maintained, any outline of the desired object radially beyond the contact point C may not harden properly.

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[0277] The number of interpolation steps used is the discretization of the volume (

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[0278] Therefore, the reconstruction error is a single value.

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[0279] [Theoretical model of optical resolution] The print resolution is determined by the exposure energy density, magnification, spatial distribution of the projection optics, and photopolymerization reactions, which depend on the photoinitiator, monomer, and light absorber concentrations. To quantify the theoretical resolution of the imaging system, we use a similar method outlined by Behroodi et al., which predicts the final energy distribution in the projection plane as the superposition of the point spreading functions of all pixels reflected from the DMD surface via spatial convolution.

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[0280] In an axisymmetric print head, the curvature of the meniscus is the meniscus height.

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[0281] The curvature of the meniscus determines the direction of incoming light.

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[0282] To investigate the effective reduction in resolution across the meniscus, checkerboard patterns were calculated in numerous areas between 0 and 5 mm.

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[0283] [Derivation and modeling of capillary waves at the air-liquid boundary] During printing, a thin fluid volume of uncured material is created between the meniscus and the previously cured regions, its height depending on the oxygen-inhibiting zone of the material and the z-translation of the meniscus. From lubrication theory, a thin fluid volume or film can be described under the assumption that the fluid depth is much shallower than the degree of fluid. Under this assumption, the complete Navier-Stokes equations can be simplified.

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[0284] [Scaling laws for acoustically driven flows] To understand how fluid transfer is affected by different material parameters, we consider the interface height in the ideal case to be

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[0285] [Interface Wetting Model] The printing speed in the methods described herein may depend primarily on two main processing parameters: the light responsiveness of the material and the speed at which new material can penetrate the printing interface. For the former, polymerization kinetics are driven by light intensity, monomer concentration, oxygen inhibition region, light absorber concentration, and photoinitiator concentration. For the latter, the material inflow rate is primarily driven by the interface velocity in the z-direction and the frequency and amplitude of acoustic drive. However, a crucial criterion to be met is ensuring that the interface is completely saturated with new material, independently of the part shape. To predict this filling time for a given shape, we employ a computational method based on distance transformation of voxel arrays. 21 This is used, where the presence of an outline is defined as "1" and the absence of an outline is defined as "0". Therefore, we can treat the "0" region within the voxel array as a resin source that defines the fluid path length. For each voxel in the array, white pixels

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[0286] [Print speed prediction using interfacial wetting model] Using an interface wetting model, the fluid path length and wetting time for a representative slice plane can be determined. By repeating this method for all object planes and taking the maximum value for each plane, the fluid path length can be determined.

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[0287] Figure 16 shows an example of the process flow in the use of a convex slicing algorithm. The figure illustrates the process flow of the slicing algorithm, illustrating the key steps in both the determination of the convex projection Iijk and the reconstruction verification via the Jacquard index J(V,V′). [Example 10]

[0288] Simulations were used to compare and contrast the method proposed herein (also known as "DIP," or Dynamic Interface Printing), which is performed using conventional top-down stereolithography (SLA) and systems based on vertical z-axis lens arrangements (of the type shown in Figures 14-15), with and without acoustic modulation of the gas-resin interface. The data show that DIP is indeed superior to conventional top-down SLA and enables higher throughput fabrication.

[0289] To analyze the effects of curved interfaces and acoustic action on printing speed, the flow of printing material was modeled using the finite element analysis (FEA) software COMSOL Multiphysics 6.1. Resin penetration across the printed structure was investigated for two competing printing schemes: DIP and conventional top-down stereolithography (SLA). We utilize the axial symmetry of the problem by leveraging a 2D axially symmetric modeling domain to dramatically reduce computational effort. The print head and printed structure are treated as impermeable solids and excluded from the modeling.

[0290] The Laminar Flow module is used to model the pressure and velocity fields in the printing material (PEGDA) and air subdomains. Assuming an incompressible Newtonian fluid, this module utilizes the Navier-Stokes equations. No-slip boundary conditions are used for all outer walls of the domains except the free surface and meniscus. Under initial conditions, the velocity component is zero, and a reference pressure of zero is induced at the top boundary. The air property is 1.204 kg / m³. 3 The density and viscosity were set at 18.1 μPas. The density of PEGDA is 1012 kg / m³. 3 The viscosity and surface tension data for PEGDA can be found in the literature.

[0291] The PEGDA-air interface and PEGDA free surface are simulated using a moving mesh module. The boundary conditions for velocity and normal stress on the PEGDA-air interface are set as follows:

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[0292] A preliminary study is conducted to establish the shape of the PEGDA-air meniscus. To do this, we use a domain without a printed structure, and the equilibrium shape of the meniscus is assessed by performing a time-dependent study under static boundary conditions (zero boundary displacement). In subsequent analysis, the shape of the formed meniscus defines the profile of the printed structure.

[0293] A dynamic study is conducted to model transient fluid intrusion during printing. Initially, the interface is assumed to be pressed against the printed structure, forming a uniform 50 μm thick fluid layer. This was chosen to improve the initial computational stability of the solution, particularly under acoustic excitation. The selected boundary is translated downward (along the z-axis) to replicate the displacement of the print head during the printing process. While the print head is translated upward in the experiment, the modeled setup is inverted, with the resin container containing the printed structure being displaced downward instead. The displacement is performed with a 0.1 s delay necessary for stabilizing the computational model. When acoustically driven, the upper part of the air domain is actuated harmonically at f = 100 Hz in addition to the displacement. The wall velocity has an amplitude of 10 mm / s and a 0.1 s delay necessary for model stabilization.

[0294] The computational domain mesh utilizes a hybrid grid with triangular mesh elements for most of the domain, complemented by a structural grid near fluid intrusion areas and non-slip boundaries. The mesh is subdivided to dmesh=8μm at the structural tip and expanded to 72dmesh=0.57mm for most of the domain.

[0295] The air-fluid interface aligns with the printed structure surface at the start of the simulation. Domain deformation drives meniscus separation from the structure. The displacement of the meniscus centroid C is used with a printed structure of SD=10mm. In the time frame 0.1~0.96s, it translates downward according to the boundary displacement. However, fluid penetration along the structure causes meniscus bouncing and subsequent recovery. The bouncing dynamics are used to assess the computational mesh, where a half-size mesh demonstrates the meniscus's virtually identical dynamics.

[0296] Figure 17 shows the spatial tracking of a point located at the center of the gas-resin interface during layer transition. During layer transition, the point initially translates downward (when the layer transition occurs), and then the rebound as the fluid flows across the interface causes the tracked point to return upward. Insets (a-d) show the corresponding point tracking for conventional top-down SLA, DIP, and DIP with 40Hz and 100Hz acoustic modulation of the gas-resin interface. For each simulation configuration (a-d), the size of the printed structure was varied from 4mm to 14mm (when the print head diameter was 15mm). That is, the structure size ranged from approximately 26% to approximately 93% of the diameter.

[0297] Figure 17 shows numerical predictions of interface release dynamic characteristics for a 15 mm diameter print head using a circular print structure with a diameter varying from 4 mm to 14 mm. Figure 17(a) shows the location of the interface center node as a function of time for top-down SLA, Figure 17(b) shows the location of the interface center node as a function of time for dynamic interface printing (DIP) without acoustic excitation, Figure 17(c) shows the location of the interface center node as a function of time for dynamic interface printing (DIP) with acoustic excitation at a frequency of 40 Hz, and Figure 17(d) shows the location of the interface center node as a function of time for dynamic interface printing (DIP) with acoustic excitation at a frequency of 100 Hz. For (c~d), the permeability plot shows the oscillating interface height, and the solid line represents the moving average over a single excitation period.

[0298] This simulation shows that the proposed method (DIP) produces a faster material inflow (due to faster rebound at the tracking point) and is less affected by structure size compared to conventional top-down SLA.

[0299] The model was used to simulate 2D fluid velocity contour plots during layer changes. For conventional top-down SLA and non-acoustic DIP, 2D plots (not shown) were provided in the form of time series of velocity magnitudes during the duration of layer changes, obtained for structure sizes from 4 mm to 14 mm. For top-down SLA and dynamic interface printing using a 15 mm diameter print head, numerical predictions of velocity magnitudes were produced. The simulations were performed to produce (i) the time-sequence velocity field for a 4mm diameter printed structure using top-down SLA from the time of initial displacement (t=100ms) to the release of the central interface (t=190ms), (ii) the time-sequence velocity field for a 14mm diameter printed structure using top-down SLA from the time of initial displacement (t=100ms) to the release of the central interface (t=880ms), (iii) the time-sequence velocity field for a 4mm diameter printed structure using dynamic interface printing without acoustics from the time of displacement (t=100ms) to the release of the central interface (t=190ms), and (iv) the time-sequence velocity field for a 14mm diameter printed structure using dynamic interface printing without acoustics from the time of displacement (t=100ms) to the release of the central interface (t=320ms).

[0300] Each of the simulation plots illustrates that the average and maximum velocities of material flowing across the gas-resin interface are greater in DIP than in conventional top-down SLA. The simulated data also demonstrate concentrated flow within the interface layer adjacent to the structure. Acoustic action was found to induce pressure fluctuations within the air domain with an amplitude of approximately 20 Pa. This pressure oscillation induces capillary-gravity waves at the liquid-air interface.

[0301] Corresponding simulation plots (not shown) were also obtained for DIP systems using acoustic modulation at 40 Hz and 100 Hz. The simulations were used to produce numerical predictions of the magnitude of the velocity for acoustically driven dynamic interface printing using a 15 mm diameter print head. The simulations were performed to produce (i) a time-sequence velocity field for acoustically driven dynamic interface printing at a frequency of 40 Hz and a structural diameter of 4 mm, with a time-sequence velocity field extending from the initial displacement (t=100 ms) to the central interface release (t=150 ms), and (ii) a time-sequence velocity field for acoustically driven dynamic interface printing at a frequency of 40 Hz and a structural diameter of 14 mm. The time sequences are: (iii) for acoustically driven dynamic interface printing, a time sequence velocity field at a frequency of 100 Hz and a structural diameter of 4 mm, with a time sequence extending from the initial displacement (t=100 ms) to the central interface release (t=270 ms); and (iv) for acoustically driven dynamic interface printing, a time sequence velocity field at a frequency of 100 Hz and a structural diameter of 14 mm, with a time sequence extending from the initial displacement (t=100 ms) to the central interface release (t=290 ms). The simulated data demonstrate concentrated flow within the interface layer adjacent to the structure. Acoustic action was found to induce pressure fluctuations in the air domain with an amplitude of approximately 20 Pa. This pressure oscillation induces capillary gravity waves at the liquid-air interface. The data demonstrate the resulting fluid streaming along the acoustically driven fluid-gas interface, which ultimately accelerates the resin inflow. The resin entry then induces recirculation flow within the adjacent gas domain. Acoustic action subsequently reduces the time required for complete wetting of the structure.

[0302] Figure 17 shows a simulation plot of the average velocity under the interface during layer changes as a function of time for each printing technique and object size configuration. This shows that the magnitude of the velocity under the interface is higher for DIP and the group (spread) of the velocity range becomes tighter as the object diameter increases. The second plot shows the average velocity under the interface for each structure size and printing technique. The data again shows that under all conditions DIP performs better than conventional top-down SLA and is less sensitive to structure size compared to top-down SLA. Specifically, Figure 18 presents numerical predictions of the average inflow fluid velocity for a 15 mm diameter print head using circular printed structures with diameters ranging from 4 mm to 14 mm. Figure 18(a) shows the average fluid velocity with respect to increasing structure diameter in top-down SLA.

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[0303] The simulation data in Figure 19 shows the interaction of the structure under acoustic modes during acoustic modulation at 40 Hz and 100 Hz. This indicates that interfaces can be used to trap material at nodal locations. The figure plots the vibration modes of an acoustically actuated meniscus. This visualization demonstrates the complex interaction between meniscus shape, print head size, and printed structure size that governs vibration intensity and ultimately fluid intrusion. While this study is limited to the axially symmetric case, more complex spatial modes may be observed in 3D systems. These findings highlight the importance of multimodal surface actuation to ensure efficient resin inflow.

[0304] Specifically, Figure 19 shows numerical predictions of structure-mode interaction, where Figure 19(a) shows the meniscus resonant mode shape over a single period with 40 Hz acoustic drive for structures with diameters of 10 mm, 12 mm, and 14 mm (shown by solid white lines), and Figure 19(b) shows the meniscus resonant mode shape over a single period with 100 Hz acoustic drive for structures with diameters of 10 mm, 12 mm, and 14 mm (shown by solid white lines). In the figures, white arrows indicate the locations of the nodal points of the induced capillary wave.

[0305] As used herein, the term “approximately” in the context of a number typically means ±5% of the stated value, more typically ±4% of the stated value, more typically ±3% of the stated value, more typically ±2% of the stated value, even more typically ±1% of the stated value, and even more typically ±0.5% of the stated value.

[0306] Throughout this specification and the following claims, unless the context requires otherwise, the word “includes,” and variations such as “includes” and “contains,” will be understood to mean the inclusion of the described component or stage or group of components or stages, but not to mean the exclusion of any other component or stage or group of components or stages.

[0307] No reference in this specification to any prior publication (or information derived therefrom) or any known matter shall be construed as acknowledging, accepting, or in any way suggesting that such prior publication (or information derived therefrom) or known matter constitutes part of the common general knowledge in the art relating to this specification. The claims defining the present invention are as follows:

Claims

1. A method for forming a 3D object, In the step of providing a photocurable resin, In the step of providing a print head for transmitting curing radiation to the photocurable resin, the print head has a cavity for containing gas. In order to form a submerged gas-resin interface between the gas and the resin, the print head is introduced into the resin, where the gas-resin interface is constrained by the print head and defines the printing surface. In order to promote the curing of the resin on the printed surface, a step is to project curing radiation onto the submerged gas-resin interface. A step to promote relative movement between the gas-resin interface and the resin in order to produce the 3D object. A method for providing this.

2. The method according to claim 1, wherein the submerged gas-resin interface is provided by pressurizing the gas in the cavity of the print head.

3. The method according to claim 1, wherein the gas has oxygen.

4. The method according to claim 1, wherein the hardening radiation has a cross-sectional image of the 3D object.

5. The method according to claim 1, wherein the gas-resin interface has a convex shape.

6. The method according to claim 5, wherein the curing radiation has a cross-sectional image of the 3D object, and the cross-sectional image represents a convex cross-section of the 3D object that fits the gas-resin interface.

7. The method according to claim 1, wherein the step of projecting curing radiation through the submerged gas-resin interface comprises the step of focusing the curing radiation onto the gas-resin interface or onto the resin side of the gas-resin interface.

8. The method according to claim 1, wherein the relative movement between the gas-resin interface and the resin is facilitated by moving the print head relative to the resin.

9. The method according to claim 1, wherein the hardening radiation is projected along a vertical axis.

10. The method according to claim 1, further comprising the step of changing the pressure of the gas in the cavity of the print head so as to modulate the expansion of the gas-resin interface.

11. The method according to claim 1, wherein the relative translation between the gas-resin interface and the resin is facilitated by retracting the print head along the vertical direction.

12. The method according to claim 11, wherein the print head is retracted at a retraction speed of approximately 1 μm / s to approximately 5 mm / s.

13. The method according to claim 1, wherein the hardening radiation has wavelengths between approximately 190 nm and approximately 2,000 nm.

14. The curing radiation is approximately 0.1 mW / cm² on the printed surface. ２ and approximately 1.6.10 １０ mW / cm ２ The method according to claim 1, which delivers an optical dose between two intervals.

15. The method according to claim 1, wherein the photocurable resin comprises an acrylate resin, a styrene resin, or a thiol resin.

16. The method according to claim 1, wherein the photocurable resin has a hydrogel precursor.

17. The method according to claim 1, wherein the photocurable resin is polyethylene glycol diacrylate (PEGDA), gelatin methacryloyl (GelMA), or hexanediol diacrylate (HDDA).

18. The method according to claim 1, wherein the photocurable resin has viable cells.

19. The method according to any one of claims 1 to 18, further comprising the step of transmitting acoustic waves to the submerged gas-resin interface.

20. The method according to claim 19, wherein the acoustic waves are transmitted to the submerged gas-resin interface by being introduced into the cavity of the print head, generated within the resin volume, or by vibrating the print head.

21. The method according to claim 19, wherein the acoustic wave has a frequency of 1 Hz to 100 kHz and an amplitude converted to a pressure in the range of 0.1 Pa to 5 kPa.

22. A system for forming a 3D object, comprising a print head for transmitting curing radiation to a photocurable resin, wherein the print head has a cavity for containing a gas, which in turn facilitates the formation of a gas-resin interface constrained to the print head when the print head is introduced into the photocurable resin.

23. The system according to claim 22, wherein the print head is transparent to curing radiation projected vertically.

24. The system according to claim 22, further comprising one or more movable stages for facilitating relative movement between the gas-resin interface and the resin when the print head is introduced into the photocurable resin.

25. The system according to claim 22, wherein the print head is movable along a vertical axis.

26. The system according to claim 22, further comprising a source of hardening radiation.

27. The system according to claim 26, wherein the print head has the source of curing radiation.

28. The system according to claim 22, wherein the print head has an internal cavity having an opening on the bottom side of the print head, and thereby the gas-resin interface formed has a convex shape that protrudes downward from the opening when the print head is introduced into the photocurable resin and the cavity is filled with pressurized gas.

29. The system according to claim 22, wherein the print head has a tubular shape including an opening at the bottom end and a radiolucent window at the top end.

30. The system according to claim 22, wherein the print head has a plurality of cavities, thereby promoting the formation of a plurality of gas-resin interfaces constrained to the print head when the print head is introduced into the photocurable resin.

31. The system according to any one of claims 22 to 30, further comprising an acoustic wave generator for transmitting acoustic waves to the gas-resin interface.

32. The system according to claim 31, wherein the acoustic wave generator is an electroacoustic device selected from a voice coil actuator, a piezoelectric actuator, a magnetostrictive actuator, and a capacitive transducer.

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