Hybrid bioprinting of hierarchical vascular networks at capillary-scale resolution

Abstract

Replicating the intricate hierarchical architecture of natural vascular networks, especially at capillary-scale resolution, remains a pivotal challenge in organ fabrication. Here we present a machine learning-enhanced hybrid bioprinting strategy that combines high-resolution aerosol jet printing of sacrificial materials and high-throughput extrusion printing of tissue matrices. This integrated approach enables sub-10 μm of resolution, achieving capillary-like channels and allowing on-demand modulation of vessel diameters in real time. Constrained Bayesian optimization rapidly identify optimal printing parameters, ensuring reliable, high-fidelity attainment of target channel sizes without exhaustive trial-and-error. This streamlined workflow supports the fabrication from 1D conduits to 3D multibranch hierarchical networks with tunable geometries. Endothelial cells seeded into these channels form continuous, functional monolayers, significantly reducing permeability while maintaining high cell viability and proliferation. By transcending the resolution limits of conventional sacrificial printing, this bioprinting method establishes a new route for producing biomimetic vasculature. Its unique combination of rapid optimization, real-time tunability, and microcapillary-scale precision holds exceptional promise for tissue engineering, regenerative medicine, and drug discovery.

1. Introduction

In recent decades, the emergence and rapid development of three-dimensional (3D) engineered tissues have made significant strides in diverse research areas, including disease modeling¹, tissue engineering^2,3, organ fabrication⁴, and bio-hybrid robotics⁵. The viability and functionality of these engineered tissue constructs are intimately tied to vascularization. Vascular networks, crucial for ensuring tissue survival, facilitate nutrient and oxygen supplies and metabolic waste removal⁶. A notable aspect of natural vasculature is its hierarchical branching structure, with a network of vessels ranging from large arteries and veins down to the minutest capillaries. This hierarchy is not solely a consequence of biological evolution but serves functional purposes. Hierarchical vascular networks maximize the surface area for efficient nutrient and gas exchange while optimizing hydrodynamic flows, reducing flow resistance, as well as ensuring adequate perfusion and diffusion to even the innermost embedded cells within the tissues^7,8. Mimicking this hierarchical structure in 3D tissue constructs is of paramount importance to achieving true physiological functionality. However, replicating the intricate sizes and hierarchical structures of natural vascular networks presents formidable challenges.

Although vascular networks can form naturally through cell migration and self-organization, these processes lack deterministic control over vessel size, geometry, and branching, making it difficult to create predefined structures within engineered tissues⁹. Therefore, to directly construct tissues with controllable embedded vascularized structures, various biofabrication techniques have been explored. Light-based bioprinting is favored for its ability to generate complex 3D structures¹⁰. Nevertheless, such approaches are usually hindered by challenges in building channels smaller than 100 μm in diameter especially when producing soft volumetric constructs¹¹, necessitating adaptations in material properties for finer vascular structures^12,13. Alternatively, the deposition of sacrificial materials within a tissue matrix to create microscale channels offers a viable approach. Typically, these sacrificial materials are first fabricated and then embedded within the tissue matrix. Techniques like extrusion-based printing^14,15, melt-electrowriting¹⁶, and selective laser sintering⁸ are employed to construct complex 3D sacrificial templates. Most recently, microchannels with cellular-scale features were fabricated by employing liquid metal sacrificial structures, which are cast using molds fabricated through two-photon laser printing¹⁷. However, these strategies require delicate multi-step pre- and post-assembly processes to generate the sacrificial templates and position them accurately and safely within the tissue matrix, which pose significant challenges in the fabrication of interconnected networks and limit their practical applications. Embedded extrusion printing, which uses a supportive liquid or gel-like bath, allows for direct printing of sophisticated sacrificial structures within the tissue matrix, eliminating the need for post-assembly^18,19. Still, the success of these techniques heavily depends on precise control of the bath’s rheological and mechanical properties, and the achievable resolution remains closely contingent upon the nozzle’s size²⁰. Furthermore, because the supporting bath must be confined within a container, the overall geometry of the tissue matrix is restricted by the container’s shape and size.

Herein we report a hybrid bioprinting technique to fabricate 3D hierarchical vascular networks with high spatial resolutions by synergistically integrating the unique strengths of aerosol jet printing (AJP) and extrusion printing (EP) (Fig. 1a). Though unconventional and underexplored in bioprinting, AJP enables precise deposition of sacrificial materials with ultrahigh spatial resolution at sub-10 μm and thus enables the creation of capillary-scale vasculature (Fig. 1c). This ability is facilitated by a sheath gas flow surrounding the aerosolized ink stream, which not only achieves aerodynamic focusing for fine feature sizes while preventing ink clogging and eliminating the need for extremely fine nozzles, but also enables real-time modulation of sacrificial channel sizes during printing by simply adjusting the sheath gas flow rate²¹. Concurrently, EP deposits matrix materials to create customizable 3D matrices around sacrificial channels for cell seeding, while its integration with AJP enables the conformal deposition of sacrificial materials in 3D spaces.

Fig. 1 ∣. Machine learning-enhanced high-resolution hybrid bioprinting approach.

a, Schematic of the hybrid bioprinting process integrating AJP and EP, guided by the constrained Bayesian optimization. b, Hybrid printing workflow of the 3D vasculatures. c, Schematic of the printed matrix with embedded sacrificial channels, ranging from a few micrometers to several hundred micrometers, and the endothelialized vessels after cell seeding.

Importantly, unlike prior work that fabricated polydimethylsiloxane-based microfluidic devices²², the present work establishes a fully hydrogel-based bioprinting platform in which gelatin-based sacrificial materials are directly deposited within a soft hydrogel matrix, introducing fundamentally different material interactions and process requirements. This synergy allows the direct and integrated fabrication of complex 3D vascularized constructs, including capillary-scale features, through a single coordinated AJP-EP hybrid printing step without the pre-fabrication or assembly of sacrificial templates required in conventional methods. Leveraging Bayesian optimization, a powerful tool for optimizing expensive-to-evaluate functions^23,24, we developed an intelligent and efficient hybrid bioprinting workflow that can rapidly identify the optimal printing parameters to realize the target channel sizes and desired printing qualities, marking a clear advancement over previous AJP implementations. Advancing further, we demonstrated the effectiveness of this printing method in constructing 1D, 2D, and 3D hierarchical vasculature. Finally, the functionality of the printed vasculature was validated by seeding endothelial cells through infusion, successfully forming an endothelial barrier.

2. Results

2.1. Hybrid bioprinting of 3D vascularized tissues

AJP is utilized to deposit sacrificial materials in order to produce the vascularized structures (Fig. 1b). These materials, composed of a fugitive ink formulated from gelatin, are atomized by an ultrasonic atomizer during the printing process. The choice of gelatin as the sacrificial material is due to its ease of printing and removal under mild conditions²⁵. Upon immersion in warm deionized (DI) water, buffer, or culture medium at or below body temperature (37 °C), the AJP-printed gelatin filaments transit into a liquid phase for the ease of removal (Supplementary Fig. 1). In addition, the gelatin-based filaments exhibit markedly improved surface smoothness, structural stability, and spatial resolution within the hydrogel matrix compared to the salt-based sacrificial materials used in previous work²², which often suffer from surface roughness and poor compatibility with soft, aqueous environments. To mitigate rapid evaporation of the ink droplets during the aerosol printing process, the ink’s solvent is mixed with glycerol (a biocompatible humectant²⁶). After experimenting with various gelatin ink formulations, it was found that a mixture containing 1.5 wt% gelatin dissolved in glycerol-water (5.0 vol%) and mildly heated at 55 °C for 12 hours, achieved a low viscosity towards optimal printability at ~40 °C (for viscosity, Supplementary Fig. 2 and Supplementary Fig. 3; and for printability, Supplementary Fig. 4). Furthermore, this formulation allows the deposited ink to form a physical gel at room temperature. To construct tissue matrices, we employ EP to fabricate 3D structures, capitalizing on its ability to handle larger ink output rates and more viscous inks (Fig. 1b).

Gelatin methacryloyl (GelMA) is selected as the matrix material due to its cyto/biocompatibility^27,28. To determine the suitable GelMA concentration range for hybrid printing, formulations from 5 wt% to 12.5 wt% were tested (Supplementary Fig. 5). Matrices containing 7.5 wt% GelMA or higher provided stable surfaces that enabled accurate AJP filament placement and perfusable channels, while the 5 wt% formulation was prone to rapid dehydration during AJP deposition due to too high-water content and a more porous network. The rheological behavior was characterized to further evaluate the printability of the 12.5 wt% formulation (Supplementary Fig. 6a-c). The ink exhibited strong shear-thinning and rapid viscosity recovery under step-shear cycling, supporting smooth extrusion and stabilization of deposited filaments. The storage and loss moduli remained relatively constant across the room-temperature printing window, consistent with a weakly viscoelastic precursor capable of maintaining layer cohesion prior to photocrosslinking. These rheological characteristics enabled reliable extrusion of the GelMA into free-standing 3D structures with good shape fidelity (Supplementary Fig. 6d), confirming its printability as a matrix ink for hybrid printing. In addition, atomic force microscopy measurements confirmed that exposure to the AJP process did not compromise the mechanical integrity of the GelMA matrix, with only negligible changes in local stiffness observed between AJP-exposed and unexposed regions (Supplementary Fig. 7 and Supplementary Discussion 3).

During the hybrid printing process, the gelatin sacrificial channels and GelMA matrices are sequentially printed by alternating AJP and EP. This is coordinated autonomously through an in-house developed program tailored for our multi-method, multi-material hybrid printer. After the entire structure is printed, the GelMA matrix is photocrosslinked under ultraviolet (UV) light to ensure sufficient mechanical integrity and prevent deformation during subsequent washing. After photocrosslinking, the construct is immersed in warm DI water, following which warm DI water is also injected into the channels to completely remove the sacrificial materials, effectively leaving behind the intended 3D vascular network (Fig. 1c). After the washing process, quantitative analysis using a glycerol assay revealed that 91.4 % of the glycerol introduced by the sacrificial gelatin ink was removed (Supplementary Fig. 8). The residual glycerol concentration in the GelMA matrix was 0.662 mM at a vascular channel density of 0.56%. Even when the vessel density was increased to 10%, the residual glycerol level remained below 10 mM, comparable to the physiological glycerol concentration in human tissues (0.6–3 mM²⁹) and far below the cytotoxic threshold for cells (~700 mM³⁰).

2.2. Machine-learning guided optimization of printing parameters

The AJP method is governed by several key processing parameters, including carrier gas flow rate, sheath gas flow rate, printing speed (the speed of nozzle motion relative to the print bed), the number of printing layers, and nozzle size²². Notably, these parameters are not full independent. For example, the sheath-to-carrier gas flow ratio govens aerodynamic focuing, while carrier gas flow rate and printing speed together determines material deposition per unit length. These parameters are vital for determining the quality and dimensions of the printed filaments. Here we systematically investigated the impact of these high-dimensional parameters on the geometry and quality of the printed sacrificial gelatin materials, for which we devised a highly efficient constrained Bayesian optimization framework to rapidly optimize them and achieve target channel sizes with desired printing qualities.

Fig. 2a displays four gelatin filaments printed on glass slides, with line widths ranging from 5 to 100 μm. The optical profilometry image of the 100-μm gelatin filament is shown in Supplementary Fig. 9. To refine the dimensions of the microchannels, we extensively investigated the effects of these printing parameters on the size of the sacrificial filament. All the detailed experimental settings are provided in Supplementary Table 1. The influence of sheath gas flow rates on the filament’s line width, when analyzed for three distinct nozzle sizes (50 μm, 100 μm, and 234 μm), is depicted in Fig. 2b. Across those nozzle sizes, the same trend emerges: an initial sharp reduction in line width as the sheath gas flow rate rises due to the increasing aerodynamic focusing effect²¹, which tapers off as the sheath gas flow rate reaches saturation point. Fig. 2c illustrates the effect of the carrier gas flow rate on the filament’s line width and thickness. A surge in the carrier gas flow rate results in augmented line width and thickness, attributed to the increased ink deposition rate and a declining focusing ratio (the ratio of sheath gas flow rate to carrier gas flow rate).

Fig. 2 ∣. Processing-property relationships and constrained Bayesian optimization of AJP of sacrificial materials.

a, Images of printed gelatin filaments with line widths ranging from around 5 μm to 100 μm. b, Effect of sheath gas flow rate on the line width for three different nozzle sizes (50 μm, 100 μm, and 234 μm). c, Impact of carrier gas flow rate on the line width and thickness for those nozzles. d, Range of achievable line widths for six different nozzles (diameters ranging from 50 μm to 564 μm). e, Correlation between the number of printing layers and filament thickness. f, Normalized printing quality scores under various sheath and carrier gas flow rates. g, Comparison of target and achieved line widths across 16 Bayesian optimization guided experiments, with marker colors indicating the experiment iteration number after the initial phase. h, Example of an optimization process. i, Image of the gelatin filament from the first trial. j, Image of the gelatin filament after the optimization process is complete. Data in (b-e) are presented as mean ± s.d. n = 5 measurements on different sample locations.

The range of filament widths achievable through a series of nozzle diameters (ranging from 50 μm to 564 μm) is shown in Fig. 2d. Smaller nozzle diameters permit the attainment of finer filaments with narrowed range of line width adjustment. Notably, using a 50-μm nozzle, the smallest achieved filament width reaches a remarkably small value of 5 μm as a result of strong aerodynamic focusing under a high sheath gas flow rate. For each distinctive nozzle diameter, the printed gelatin line width can be tuned from ~10% to 40-85% of the nozzle diameter simply by changing the sheath and carrier gas flow rates. The maximum ratio of achievable line width to nozzle diameter decreases as the nozzle diameter increases. This trend is attributed to the reduced aerodynamic focusing capability with larger nozzles, which often leads to the unsuccessful formation of continuous filaments, particularly at very low sheath gas flow rates. Predictably, ramping up the printing layers correspondingly boosts the filament’s thickness, a linear association illustrated in Fig. 2e. Increasing printing speed leads to diminished ink deposition, subsequently scaling down both line width and thickness (Supplementary Fig. 10).

Our final exploration centered on the interplay between the sheath gas flow rate and the carrier gas flow rate as well as their impact on printing quality, evaluated using metrics including edge roughness and overspray. To better compare printing qualities, we developed an automated image-processing algorithm that analyzes the printed filament and quantifies printing quality with scores, as shown in Supplementary Fig. 11. Fig. 2f presents the normalized printing quality scores for various sheath and carrier gas flow rates. It reveals a specific zone of sheath and carrier gas flow rates that allows high-quality filament deposition. Conversely, deviating from this optimal range can lead to undesired features such as excessive overspray or pronounced edge roughness, as depicted in Supplementary Fig. 12.

While the thickness of the deposited gelatin line is directly proportional to the number of printing layers which facilitate easy control over the thickness by adjusting the number of layers, the line width and printing quality are influenced by a multitude of parameters interwoven in a complex manner. Pinpointing the optimal printing process parameters for a filament to achieve both the desired size and quality can be a daunting task using a trial-and-error approach. To navigate this challenge, we harnessed the constrained Bayesian optimization method³¹, a specialized Bayesian optimization approach designed for optimizing functions under expensive-to-evaluate constraints, to accelerate the AJP process optimization (Supplementary Fig. 13). In practice, the aerosolized ink transport and deposition in AJP can be sensitive to variations in ink formulation and environmental factors such as ambient temperature and humidity. Compared with previous works^32-34, this constrained Bayesian optimization strategy trains a new model for each time and does not rely on previous data, ensuring the algorithm to automatically adapt to the current printing and environmental conditions and remain robust against slight variations of environmental conditions. In this study, we set the printing line width as the optimization objective while enforcing printing line quality as a constraint.

To demonstrate the efficacy of this constrained Bayesian optimization method, we first conducted 16 tests with target line widths ranging from 30 to 100 μm under the standard printing condition, as shown in Fig. 2g. It took only an average number of 8 trials during the refinement process to find the optimized printing parameters, as revealed in Supplementary Fig. 14 and Supplementary Table 2. All optimized results exhibited 95% conformity to the target line width yet maintained high printing qualities. An example of this optimization process is illustrated in Fig. 2h and Supplementary Fig. 15. After 10 trials, the constrained Bayesian optimization achieved a 99% conformity in line width (45.2 μm compared to the target width of 45.0 μm) with satisfactory printing quality score (larger than −5, indicating low overspray and edge roughness), as shown in Fig. 2i. This result significantly outperformed the initial refinement trial, as depicted in Fig. 2j.

To further evaluate the robustness of the constrained Bayesian optimization strategy, we performed 24 additional optimization tests under three different conditions with altered ink formulations and environmental conditions (Supplementary Fig. 14). These conditions intentionally introduced variations in printing behaviors, including changes in gelatin concentration, printing bed temperature, and ambient humidity. Despite these variations, the optimization process converged consistently across all tested conditions, requiring an average of 8-9 refinement trails to reach the target line widths and printing quality, comparable to the standard condition. Statistical analysis revealed no significant differences in the number of optimization iterations among the four conditions (one-way ANOVA, P-value = 0.327; Supplementary Table 2), indicating that the constrained Bayesian optimization method remains robust despite variations in ink formulations and environmental conditions.

Beyond optimizing sacrificial filament deposition using AJP, this closed-loop constrained Bayesian optimization strategy provides a generalizable route for autonomous optimization of processing parameters in multi-material and multi-process additive manufacturing. Its sample-efficiency, ability to handle constraints, and adaptability to variations in ink formulation or environmental conditions make it well-suited for systems operating within a consistent underlying physical regime. Under such conditions, it can be applied to a broad range of engineering-relevant systems such as printing energy-storage materials, catalytic lattices, separation membranes, and drug-delivery structures beyond tissue biofabrication.

2.3. Printing 1D, 2D, and 3D vascular structures

To demonstrate the hybrid printing method, we printed 1D, 2D, and 3D vascular structures embedded within the GelMA matrices. One example of the construction process was recorded in Supplementary Video 1. For reliable connection to external infusion pumps, the vascularized matrices were directly printed onto customized GelMA bases with quick connectors (Supplementary Fig. 16).

Within the 1D domain, employing a single 234-μm nozzle, we printed three linear microchannels with varying widths ranging from 40 μm to 140 μm simply by changing the sheath and carrier gas flow rates, as depicted in Fig. 3a-b. Additionally, using a 50-μm nozzle, we successfully printed an ultrafine sacrificial gelatin filament and achieved a 5.6-μm channel width (Supplementary Fig. 17), demonstrating the high resolution of AJP. Moreover, we replicated a stenotic vascular pattern commonly used to model constricted vessels in cardiovascular disease³⁵, featuring a significant decrease in channel width from 160 μm to 80 μm within a span of 600 μm via changing the sheath and carrier gas flow rates. Such precision is challenging to achieve with conventional extrusion-based printing techniques for the sacrificial materials, highlighting our method’s capability in producing microscale vascular structures with varying sizes.

Fig. 3 ∣. Bright-field and fluorescence images of printed 1D, 2D, and 3D vascular networks.

a,b, Bright-field images of straight gelatin filaments with widths ranging from 40 μm to 140 μm and a stenotic structure for 1D vascular structures (a), along with corresponding channels perfused with a fluorescent dye (b). c-h, Gelatin filaments forming 2D hierarchical and branched vascular networks, with channels as small as 9 μm perfused with a fluorescent dye. i-m, Schematics and images of the printed matrix with a 3D dual-channel vascular network, demonstrating the spatial positioning of microchannels perfused with two differently colored fluorescent dyes. n-p, Schematics and fluorescence visualization of an intricate 3D hierarchical vascular network.

Transitioning to 2D vascular networks, we utilized a 234-μm nozzle to build a representative hierarchical network that begins with a large channel with 200-μm width and then bifurcates into four smaller channels with 100-μm width, as presented in Fig. 3c-d. The channel dimensions were designed to follow Murray’s law³⁶, ensuring approximately balanced hydraulic resistance across successive bifurcations. Computational fluid dynamic (CFD) analysis and perfusion experiments further confirm that this design promotes near-uniform flow distribution among branches (Supplementary Fig. 18 and Supplementary Video 4). A more intricate 2D hierarchical design is displayed in Fig. 3e-f, featuring bifurcated channels with the maximum gaps between each channel <300 μm, which is comparable to the critical oxygen diffusion distance in a 3D tissue^37,38. Complementary measurements confirmed that adjacent channels could be spaced as closely as ~5 μm (Supplementary Fig. 19), enabling dense, high-resolution vascular layouts. Thus, our method is validated for its high resolution and potential for creating physiologically relevant tissue models. Further advancing our capabilities, we employed a 50-μm nozzle to print a tree branch-like pattern with one inlet and 32 outlets, as illustrated in Fig. 3g-h. The widths of these channels decrease gradually from 190 μm at the inlet to as narrow as approximately 9 μm at the outlets. Additionally, we demonstrate the fabrication of the same branched pattern with minimum channel widths approaching ~6 μm (Supplementary Fig. 17b), extending capillary-scale resolution from straight channels to 2D network architectures. At this ultrafine scale, reproduction of complex geometries becomes increasingly sensitive to high-speed stage dynamics during simultaneous X-Y motion, which can introduce minor lateral deviations from the designed path. These effects arise from mechanical limitations of the current motion system rather than the intrinsic resolution of AJP.

Delving into 3D, we printed a vascular network comprising two spatially distinct microchannels at different heights within the 3D volume (Fig. 3i-k). Two contrasting fluorescent dyes were sequentially introduced to illuminate the channels for enhanced visual clarity (Fig. 3l-m and Supplementary Video 2). Additionally, measurements of the extrusion-printed GelMA layers indicated a minimum achievable layer thickness of ~85 μm (Supplementary Fig. 20), which defines the vertical spacing limit for channel stacking. Advancing further, an intricate 3D vascular network was constructed to demonstrate our method’s capability to create multi-layered, spatially complex 3D hierarchical vasculature. This design is initiated with a single channel (237 μm) and bifurcates into 19 subchannels, each around 50 μm and positioned within a defined 3D space, as shown in Fig. 3n and detailed in Supplementary Fig. 21. Fluorescence images of the printed channels are depicted in Fig. 3o-p and Supplementary Video 3.

Beyond the constructs printed on customized GelMA bases with integrated quick connectors for perfusion testing, we further validated the hybrid printing process by printing free-standing GelMA constructs without any external support. Both 2D and 3D vascular channel networks were successfully printed. The printed constructs maintained structural stability and channel fidelity (Supplementary Fig. 22), confirming that the hybrid approach can be readily applied to self-supporting 3D architecture.

A detailed comparison of our hybrid bioprinting method against state-of-the-art 3D printing techniques is provided in Supplementary Table 4, which evaluates various aspects such as printing resolution and achievable geometries. Our hybrid printing method offers a versatile platform for creating a wide range of vascular structures, from simple 1D channels to 3D layered and oblique networks (e.g., Supplementary Fig. 23). The ability of the AJP system to tolerate angular misalignment between the nozzle and substrate enables the fabrication of such 3D oblique branches. However, fully 3D entangled networks remain challenging. Although AJP can deposit pillar-like or angled filaments, achieving seamless integration between these sacrificial filaments and the extrusion-printed matrix requires careful optimization to prevent deformation, incomplete embedding, or interfacial gaps. Notably, our method achieves superior spatial resolution of sub-10 μm and eliminates the need for post-assembly, streamlining the fabrication process. Those capabilities are crucial for advancing tissue engineering, particularly in creating realistic in vitro tissue models and potentially implantable tissue grafts.

2.4. Proof-of-concept biofunctional assessment

To highlight the benefits of our printing strategy, we performed endothelialization by infusing human umbilical vein endothelial cells (HUVECs) through the lumen of the printed channels spanning multiple geometries and dimensions. Following cell infusion, the channels became uniformly lined with HUVECs, which began to attach and spread within the first 6 hours after seeding. This rapid cell adhesion underscores the bioactive contribution of the arginine-glycine-aspartic acid (RGD) motifs present in the GelMA hydrogels. In our experiments, the semicircular channel geometry generated upon printing did not affect cell viability nor cell spreading (Fig. 4a and Supplementary Fig. 24), consistent with literature³⁹. For instance, we conducted CFD simulations to estimate shear stresses in different channel diameters (80-μm, 120-μm, and 240-μm) and geometries (circular and semi-circular). The estimated shear stresses fall within the range of 0.2-10 dynes cm⁻² (Supplementary Fig. 25), which are the typical values of vascular wall shear stresses in vivo³⁹. We further identified consistent results and the same trends of endothelialized non-circular channels that aligned with previously reported findings^40-42.

Fig. 4 ∣. Vascularization and cell seeding of the printed channels.

a, Live/Dead assay and cell viability analyses of HUVECs for up to day 10 of culture after seeding in single straight channels (diameters: 240 μm (i) and 120 μm (ii)). b, Confocal micrographs depicting staining of HUVECs: nuclei/F-actin/CD31 in channel with a diameter of 240 μm, and nuclei/F-actin in channel with a diameter of 120 μm. c, 3D-printed branched-like structures with continuous channel width reduction from 200 μm to 120 μm and down to 80 μm (i). Nucleus/F-actin staining micrographs of HUVECs at different locations including channel bifurcations (ii-iii). Data are presented as mean ± s.d. n = 3 independent samples. P-values are determined by one-way ANOVA and Tukey post hoc test. NS, not significant.

As culture time progressed, endothelial cells proliferated and elongated, forming a homogeneous endothelial layer throughout the channels (Supplementary Video 5) as confirmed by F-actin and nucleus staining. Additionally, Live/Dead assays and image analyses further demonstrated high cell viability ranging from 85 to 95% after 1, 3, and 10 days for both 240-μm and 120-μm channel diameters (Fig. 4a). A slight, non-significant reduction in viability was observed at early time points (day 3), likely reflecting initial cellular adaptation to the GelMA matrix. When HUVECs are transferred from 2D cell culture to GelMA hydrogel, cells need to adapt to a new environment with different mechanical stiffness, diffusion limits and adhesion motifs availability, which can temporarily reduce viability⁴³. Notably, cell viability stabilized or increased during longer culture periods, suggesting that any residual glycerol from AJP or hypoxic conditions exerted negligible cytotoxic effects. Confocal micrographs revealed cellular alignment along the longitudinal axis of the channels (Fig. 4b, Supplementary Figs. 26-28, and Supplementary Videos 6-7) and immunostaining for CD31 and VE-cadherin further confirmed the establishment of endothelial tight junctions and cell adhesion to the GelMA substrate (Fig. 4b and Supplementary Fig. 27, 29).

In addition, we successfully fabricated hierarchical vascular architectures comprising branched endothelialized channels with diameters of 200 μm, 100 μm, and 85 μm. These sizes are markedly smaller than the range typically achieved using conventional extrusion-based methods with sacrificial materials^44-46. The printed pattern consisted of a tree-like branching network with a continuous s reduction in channel size (Fig. 4c and Supplementary Videos 8). To assess patency, fluorescein isothiocyanate (FITC)-dextran was continuously perfused through the branched channels, confirming uninterrupted lumen continuity and uniform transport across the entire hierarchical network (Supplementary Fig. 30). Consistent with the behavior observed in straight channels, the HUVECs proliferated and spread throughout the different channel sizes of the branch-like structure, showcasing a promising strategy to enable the formation of complex hierarchical vascular networks within soft hydrogels.

We finally performed functional assays to assess the permeability of biomacromolecules across the walls of endothelialized 3D-printed channels. Each mold device was connected to a syringe pump and perfused with 0.1 mg mL⁻¹ of FITC-dextran 10 kDa at a flow rate of 2 μL minute⁻¹ (Supplementary Figs. 31, 32). FITC-dextran diffusion was recorded for 15 minutes with 3 seconds of intervals between the imaging frames. As anticipated, permeability coefficients measured at 15 minutes were higher in empty channels (72.3 ± 5.26 μm second⁻¹) than endothelialized channels at day 3 (45.8 ± 4.84 μm second⁻¹). Notably, endothelialized channels maintained in culture for extended periods (14 days) exhibited further reduction in diffusive permeability to 17.8 ± 8.01 μm second⁻¹. These findings suggest a consistent progressive functional improvement of the endothelial barrier (Fig. 5a) and are in line with the data shown in literature^47,48. Together, these experiments show that endothelial cell layers form well and remain viable within the printed channels. However, we recognize that further long-term functional tests are necessary to fully assess the durability and physiological function of these engineered vessels. As a next step, our future research will emphasize extended culture periods and more thorough functional assays, such as evaluating barrier integrity, low-density lipoprotein transport, and nitric oxide production, to gain a deeper understanding of the system’s overall capacity.

Fig. 5 ∣. Functional assessment of endothelial barrier permeability and responsiveness.

a, FITC-dextran (10 kDa) diffusion assay in 120-μm channels that are empty (acellular) and endothelialized (cell-lined) (i). Fluorescence intensity profiles in acellular channels at different time points (ii). Diffusive permeability coefficients of the empty and endothelialized (3 and 14 days) channels at 15 minutes (iii). b, Functional assays showing barrier selectivity and responsiveness. Nucleus/F-actin staining of control and histamine-treated endothelialized channels (i). FITC-dextran diffusion assay and diffusive permeability coefficients of control and histamine-treated endothelialized channels (ii-iii). Data are presented as mean ± s.d. n = 3 independent samples. P-values are determined by one-way ANOVA and Tukey post hoc test.

To further demonstrate the biofunctional properties of our 3D-printed patterns, we exposed endothelialized channels to histamine, a vasoactive mediator known to disrupt endothelial integrity and modulate vascular permeability in vivo and in vitro^49,50. Histamine treatment induced marked changes in cell morphology and cytoskeletal organization, accompanied by compromised barrier function and increased FITC-dextran permeability, at 60.47 ± 7.27 μm second⁻¹ relative to untreated controls at 42.9 ± 4.01 μm second⁻¹ (Fig. 5b). The latter process is consistent with in vivo and in vitro models, where histamine elevates intracellular Ca²⁺ levels, leading to actomyosin contraction and cytoskeletal remodeling^51,52. These sets of experiments demonstrated the biofunctional features present in our bioengineered endothelialized channels showcasing potential applications for tissue engineering. For instance, as proof of concept, we bioprinted a vascularized tissue with NIH/3T3 fibroblasts embedded in GelMA containing an endothelialized channel. F-actin/nucleus staining depicted the co-existence of HUVEC lining the lumen of the channel and NIH/3T3 fibroblasts within the surrounding matrix areas (Supplementary Fig. 33).

3. Discussion

Despite recent advances in bioprinting that led to sophisticated volumetric vascular architectures^{17,18,19,53,54}, existing approaches often involve trade-offs between achievable resolution and workflow efficiency when constructing complex 3D hierarchical vascular networks. Our hybrid bioprinting method provides capacity to achieve sub-10 μm spatial resolutions while dynamically adjusting channel widths on the fly, all in a single fabrication step with no post-printing assembly. Moreover, constrained Bayesian optimization streamlines the identification of optimal printing parameters, allowing targeted channel dimensions with high fidelity within minutes, paving the way for autonomous and intelligent bioprinting processes. Endothelial cells seeded into the printed channels form continuous layers with favorable viability and proliferation, as evidenced by FITC-dextran diffusion assays that highlight distinct permeability profiles between empty and cell-lined channels, an indicator of functional endothelial barriers. In addition, our hybrid bioprinting produces branched endothelialized channels as narrow as 85 μm, surpassing conventional extrusion-based sacrificial methods, which typically achieve channels above 200 μm^44,45.

While capillary-scale channels can be printed using our approach, cell seeding within these ultrafine structures remains challenging due to increased hydrodynamic resistance and cell aggregation during perfusion-based seeding. Nevertheless, prior studies have shown that endothelial cells can spontaneously colonize sub-10-μm capillary-like channels over extended culture periods¹⁷, indicating a feasible pathway for future cellularization of these architectures. Scaling toward organ-level constructs also presents challenges related to throughput and matrix volume. Integrating multi-nozzle AJP and EP could enhance deposition speed, while coupling with digital light processing would enable rapid photopolymerization of large and complex architectures. Beyond fabrication throughput, a recent model-guided vascular design framework has demonstrated rapid generation of organ-scale, perfusable vascular trees with physiologically realistic hierarchical branching and closed-loop topology⁵⁵, which are critical for maintaining uniform perfusion in large tissues. Such a framework could define global vascular architectures, while AJP resolves local capillary-scale features. We also demonstrated direct bioprinting of cell-laden GelMA matrices to achieve vascularization, which can be expanded to complex, multicellular architectures in future works. Looking ahead, translating this hybrid bioprinting strategy toward in vivo applications will require addressing challenges in vascular–host integration, long-term stability, and immune compatibility, while ensuring scalable and reproducible fabrication. Overcoming these barriers will advance the platform from engineered vascular scaffolds to functional, implantable tissue and organ constructs, ultimately contributing to the broader goal of regenerative organ fabrication.

Our machine learning-guided hybrid printing strategy enables the autonomous fabrication of hierarchical microchannel architectures with capillary-scale resolution. These capabilities support a broad spectrum of systems that rely on controlled microscale flow and mass transfer, including vascularized tissue engineering, organ fabrication, drug screening, as well as microreactors^56,57 and lab-on-chip devices⁵⁸, highlighting the relevance of this approach across both biomedical and chemical engineering applications.

4. Methods

4.1. Ink formulations

To prepare the matrix materials, GelMA foam was synthesized according to our reported methods^20,59,60. The GelMA ink for EP was prepared by dissolving 12.5 wt% GelMA foam (unless otherwise specified) in DI water, with the addition of 0.5 wt% photoinitiator, lithium phenyl-2,4,6-trimethylbenzoylphosphinate (LAP, MilliporeSigma, cat.no. 900889). The mixture was heated at 55 °C for 1 hour to ensure complete dissolution of the GelMA foam. For tissue matrices prepared for the cell seeding experiments, 1 vol% antibiotic-antimycotic (Gibco) was added to the GelMA ink and homogenized using a vortex mixer. Before loading the GelMA ink into the EP syringe, the ink was centrifuged at 3000 RPM (~ 1,200g) for 3 minutes to remove air bubbles. The degradation behavior of the GelMA formulation is characterized in detail in Supplementary Discussion 1, including hydrolytic stability prior to cell culture and enzymatic degradation under HUVEC culture conditions.

The sacrificial gelatin ink was prepared by dissolving 1.5 wt% porcine skin gelatin (MilliporeSigma, cat.no. G2500) in a solution containing 5.0 vol% glycerol (Lab Alley) and DI water. This mixture was then heated at 55 °C for 12 hours. For better visualization of the printed filament, 1 vol% red food dye (Kroger) was added to the ink before printing.

4.2. Characterizations of aerosol jet printed sacrificial filaments

The dimensions of the AJP-produced sacrificial filament, specifically its thickness and width, were quantified using a 3D optical profilometer (Profilm3D, Filmetrics). The profilometry scans underwent post-processing steps including plane leveling, noise reduction, and void compensation. Measurements for thickness and width were derived from the software’s step-height measurement functionality. To assess printing quality, images of the printed filament were captured using an optical microscope (Olympus CX31) at 10× magnification. These images were analyzed using a custom Python image-processing algorithm (Supplementary Fig. 11).

4.3. Constrained Bayesian optimization implementation

To implement the constrained Bayesian optimization, as illustrated in Supplementary Fig. 13, a custom Python code was utilized alongside the Bayesian optimization package⁶¹. The “expected improvement” was selected as the exploration strategy. The optimization was performed using a 234-μm nozzle with predefined boundaries for three parameters: sheath gas flow rate (10-110 sccm), carrier gas flow rate (15-35 sccm), and printing speed (1-3 mm second⁻¹). The target line width was set to range from 30 to 100 μm with the constraint that the printing line quality score, $Q$, must be greater than −5, which is considered acceptable based on experimental results. The optimization process was considered successful when the printed line width conformity reached at least 95% of the target and $Q$ was greater than −5, at which point the algorithm would stop further iterations. The conformity, $C$, is calculated by:

$$C=1-\frac{\mid W_{Target}-W_{Printed}\mid }{W_{Target}},$$ (1)

where $W_{Target}$ is the target line width and $W_{Printed}$ is the measured printed line width.

4.4. Fabrication of GelMA base

To avoid the need for inserting a nozzle into microchannels, which often leads to sealing issues and alignment challenges, customized GelMA bases were prepared to ensure reliable connection between the printed vascular channels and external infusion pumps (Supplementary Fig. 16). Rigid molds were printed using an SLA printer (Form 3, Formlabs). Two different mold designs were created for distinct applications (Supplementary Fig. 16a-b). The first type was designed for general use, while the second was optimized for cell seeding experiments. The latter was printed using a biocompatible resin (BioMed Clear Resin) and featured an open bottom, where a glass coverslip was attached post-printing. The coverslip was attached using the same resin precursor as an adhesive. It was pressed against the mold and cured under UV light for 15 seconds to ensure a strong seal, followed by rinsing with DI water to confirm that no leakage occurred. Post-treatment steps, including alcohol washing, DI water washing, dehydration in the oven, and post-curing by UV light were performed to remove residual monomers and thus improve cytocompatibility. The use of glass coverslips, instead of printing the entire mold with resin, was necessary to prevent imaging interference, as the biocompatible resin introduces noise in bright-field and fluorescence microscopy.

After the rigid molds were completed, the same GelMA ink used for EP was poured into the molds until it reached the level of the quick connectors, covering only the lower half of each connector while leaving the upper half exposed to air. During the casting process, metal rods were inserted into the quick connectors to prevent uncured GelMA from filling the voids. The GelMA was then exposed to UV light for 30 seconds to initiate gelation. Then, the metal rods were removed, and another sacrificial gelatin ink, comprising 8.0 wt% gelatin dissolved in DI water, was used to seal the connectors. Following these preparations, the GelMA base was ready for the subsequent printing process. For the following AJP printing process, printing was initiated from the exposed ends of the connectors, where the injected gelatin remained open to the air, ensuring precise alignment and continuous connection between the printed filaments and the connectors.

4.5. Hybrid printing of vascularized matrices

A custom-built 3D aerosol jet printer reported in our previous work²² was optimized and further substantially redesigned to integrate the EP method. All printing experiments were conducted under standard laboratory conditions (approximately 23 °C and 30% relative humidity).

For the AJP method, 1.4 mL of gelatin ink was loaded into the ink vial. The ultrasonic atomizer voltage was set at 36 V, and the atomization bath temperature was kept at 40 °C. Stainless steel nozzles (QuantX Micron-S Precision, Fisnar) with 50-μm and 234-μm inner diameter were used. After a 10-minute pre-printing phase to stabilize the system, continuous printing was initiated. The printing parameters are listed in Supplementary Table 3.

For the EP method, 6 mL of GelMA ink was loaded into the extrusion syringe, maintained room temperature (23 °C). Both 101-μm and 406-μm nozzles (QuantX blunt end, Fisnar) were attached using a luer-lok connections. The printing and extrusion speeds were set to 4-20 mm second⁻¹ and 2-5 mm second⁻¹, respectively.

After all preparations, the digital model was printed. The printed structure was exposed to UV light (365 nm) for 30 seconds after each new GelMA layer was deposited. After the printing process finished, the printed matrix underwent further curing under UV light for 3 minutes. Subsequently, the matrix was immersed in warm DI water at 37°C for 30 minutes. After this immersion, warm DI water was infused through the microchannels to remove the liquid-phase gelatin, using a syringe pump (AL-300, World Precision Instrument).

4.6. Cell culture experiments

HUVECs were acquired from ScienCell (cat. no. 8000), NIH/3T3 fibroblasts were acquired from American Type Cell Culture (ATCC, Cat. no. CRL 1658 and HB-8065 respectively). For HUVEC cell culture and maintenance, we employed endothelial basal medium (EBM-2) (Lonza, cat. no. CC-3156) supplemented with endothelial cell growth medium BulletKits (EGM-2) (Lonza, cat. no. CC-4176). For NIH/3T3, we used Dulbeco Modified Eagle’s medium (Gibco, cat. No. 11965118) supplemented with 10% fetal bovine serum (Gibco, cat. No. A5256701). Low cell passages (<4) and T75 flasks (Corning) were used and placed in an incubator under humidified conditions with 5% CO₂ at 37 °C (Sanyo). Cell passages were performed using 1× trypsin-EDTA (Gibco, cat. no. 15400054) in 1X Dulbecco’s phosphate-buffered saline (DPBS, Gibco). For cell counting we used a hemocytometer chamber (MilliporeSigma) and trypan blue staining to estimate cell viability (ThermoFisher, cat. no. 152561).

4.7. Cell seeding in printed hollow channels

First, the molds were cleaned and washed with 1× DPBS and 1× antibiotic-antimycotic for 20 minutes. Hollow channels were then perfused with 1× DPBS employing a syringe pump (New Era Pump Systems) at a flow rate of 20 μL minute⁻¹ for 1 hour. Subsequently, 5 × 10⁶ cells mL⁻¹ was infused through the channels of both 240-μm and 120-μm diameters (Supplementary Fig. 34). For the 240-μm channel size, a 10-μL micropipette tip (Eppendorf) was directly connected to the device’s inlet and gently perfused through the channel until medium was observed at the outlet. For 120-μm channels, a syringe pump was used at a flow rate of 20 μL minute⁻¹ for 20 minutes. To visualize the cells, devices were mounted on an inverted fluorescence microscope (Axiovert, Zeiss).

4.8. Cell viability assay and immunostaining

To confirm cell viability, Live/Dead assay (Invitrogen) was performed. In brief, calcein-AM (2 μM) and ethidium homodimer (1 μM) were resuspended in 1× DPBS. The devices were first washed three times with 1× DPBS, then perfused with Live/Dead working solution and placed in an incubator (5% CO₂ at 37 °C) for 40 minutes. The devices were washed three times with 1× DPBS. To visualize the cells, the inverted fluorescence microscope was used. For data analyses, we performed image segmentation and quantified independently red and green fluorescence readouts using FIJI (Image J, National Institutes of Health).

For immunostaining, the devices were first washed with 1× DPBS, fixed with 4% paraformaldehyde (MilliporeSigma) for 15 minutes following three 1× DPBS washes, and later added with a blocking buffer (3% bovine serum albumin + 0.1% triton X-100) in DPBS for 4 hours. We employed primary antibodies mouse anti-CD31 and rabbit anti-VE cadherin (Abcam, cat. no. ab9498 and ab33168) at a dilution of 1:200 in the blocking buffer overnight. Then we used secondary antibodies rabbit anti-mouse IgG-594 nm and goat anti-rabbit IgG 488 nm (Abcam, cat. no. ab150125 and ab150077) at a dilution of 1:400 for at least 4 hours. For F-actin/nucleus staining, we prepared a working solution which consisted of phalloidin 488 or 594 nm at a concentration of 200 nM (Invitrogen) and (4’,6-diamidino-2-phenylindole (DAPI, Invitrogen) at 300 nM. The samples were soaked in this working solution and placed in an incubator at 37 °C for 1 hour. To visualize the cells, we employed a confocal laser scanning microscope (LSM880, Zeiss).

4.9. Permeability tests FITC-dextran

Diffusion tests were performed using FITC–dextran (10 kDa; Sigma–Aldrich). Diffusion was evaluated in both acellular and endothelialized channels with a diameter of 120 μm. The inlet of the device was connected to a syringe pump (Harvard Instruments) via 3 mm silicone tubing (Masterflex). FITC–dextran (0.1 mg mL⁻¹) was continuously perfused through the channel at a flow rate of 2 μL minute⁻¹, and fluorescence was monitored using a fluorescence microscope. Because FITC–dextran diffuses relatively rapidly through the hydrogel matrix, fluorescence imaging was initiated immediately after the onset of perfusion rather than after reaching a steady-state within the lumen. This approach allowed us to capture the early dynamics of diffusion from the channel into the surrounding hydrogel. For data analysis, fluorescence images were converted to grayscale in FIJI at defined time points (0, 3, 6, 9, 12, and 15 minutes), as shown in Supplementary Fig. 35. Prior to quantitative analysis, background correction was applied to minimize variations in illumination. Line profiles perpendicular to the channel wall were extracted to obtain fluorescence intensity distributions across both the lumen and the surrounding GelMA hydrogel. Regions of interest were defined within the hydrogel immediately adjacent to the vessel wall, and the fluorescence intensity in this region was quantified at each time point to evaluate the increase in FITC–dextran diffusion outside the channel. The rate of fluorescence increase was determined from the initial linear portion of the intensity–time curve, while the initial intensity difference between the lumen and the surrounding matrix was defined immediately after the onset of perfusion, and permeability coefficients were calculated according to the following equation¹⁶:

$$P_D=(\frac{2r}{I_0})\frac{dI}{dt},$$ (2)

where $P_D$ is the permeability coefficient, $I_0$ is the average fluorescence intensity of the channel, $I$ is the intensity at specific time point, $t$ is the experimental time and $r$ is the channel radius.

4.10. Biofunctional assay

We exposed endothelialized channels to histamine (Sigma-Aldrich, cat. no. H7250), an organic component that disrupts the endothelial barrier and highly influences vascular permeability. In these sets of experiments, we perfused 100 μM of histamine hydrochloride (in EBM-2) to single straight channels (240 μm), maintained the treatment for 4 hours, and compared to control groups without histamine treatment.

4.11. Shear stress simulations

We conducted CFD simulations to estimate the shear stress values in the 3D-printed channels. CFD was implemented in SolidWorks using laminar flow and Navier Stokes equations. Computational aided design (CAD) models corresponding to the actual dimensions of the 3D-printed mold and channel sizes (240 μm, 120 μm and 80 μm) with circular and semi-circular geometries were designed and discretized with tetrahedral elements. The fluid properties were considered to resemble those of water with a density of 997 kg m⁻³, heat conductivity 0.6 W m⁻¹ k⁻¹ and dynamic viscosity of 0.89 mPa s. A tight fluid volume was created by sealing the channel inlets and outlets. The computational domain was then generated automatically and an internal flow analysis was performed allowing laminar flow regime and accounting for gravitational forces acting along the Z axis. Finally, the boundary conditions consisted of an inlet flow rate of 2 μL minute⁻¹ and an outlet set to atmospheric pressure. CFD simulations enabled the determination of internal shear stress values.

4.12. Statistical analyses

Data were expressed as mean ± standard deviation (s.d.). Experiments were conducted at least in triplicate. The statistical analyses for this study were conducted with GraphPad Prism Software using one-way (ANOVA), followed by a post hoc Tukey test. P-values <0.05 were considered statistically significant.

Data availability

All data are available within the article and its supplementary information. Source data are provided with this paper.

Code availability

The custom code used in this study is available from the corresponding author upon reasonable request.