Embedded 3D Bioprinting for Perfusable Vascular Networks: Supporting-Bath Materials, Structural Fidelity, and Functional Validation

Vascularization remains the principal bottleneck preventing engineered tissues from reaching clinically relevant thickness, and conventional extrusion printing cannot reconcile the low-viscosity, cell-rich bioinks required for biological function with the mechanical support needed to build suspended, branched, and hollow architectures. Embedded bioprinting resolves this conflict by transferring structural support from the ink to a yield-stress bath that locally fluidizes around the moving needle and self-heals behind it, thereby decoupling printability from ink rheology. This review presents a unified parameter-to-function analysis of extrusion-based embedded bioprinting for perfusable vascular networks. We first classify support baths along two orthogonal dimensions—post-printing fate (temporary support versus retained matrix) and physical form (granular, continuous-phase, or liquid)—and distill their behavior into four coupled rheological descriptors: yield stress, shear thinning, thixotropic recovery, and storage modulus. These parameters, together with ink–bath compatibility and process conditions, are then linked to structural fidelity in both its static (geometric accuracy) and dynamic (shape retention during crosslinking and culture) senses, and reported failure modes are consolidated into a parameter–defect–countermeasure matrix. Vascular fabrication strategies are organized into sacrificial-lumen and functional-ink direct-writing routes, and the strength of published validation is appraised through a three-level evidence framework spanning structural patency, biological maturation, and direct function, with direct embedded evidence explicitly separated from benchmarks borrowed from adjacent technologies. Persistent challenges—including the resolution gap relative to capillary dimensions, bath removal and residue control, non-transferable rheological windows, and the scarcity of long-term and interlaboratory functional data—are critically examined. Finally, we outline priorities in closed-loop intelligent process control, function-oriented design, tunable and responsive support baths, hybrid fabrication, and standardized quantitative reporting, charting a path from printable structures to predictable vascular function.