Cross-linkable microgel composite matrix bath for embedded bioprinting of perfusable tissue constructs

Described herein are apparatuses, systems, and methods for fabricating tissue constructs, such as by fabricating perfusable tissue constructs by embedding a sacrificial material into a composite matrix yield stress support bath. A composite matrix bath can include a microgel filler and a hydrogel precursor. An extrusion tip can be used for embedded printing of perfusable tissue constructs by disposing sacrificial material into the composite matrix bath while the extrusion tip travels along a predefined course through the composite matrix bath. This sacrificial material can be the printed tissue construct or can be removed to render the matrix bath a perfusable tissue construct. The composite matrix bath can include acellular or cell-laden hydrogels. The sacrificial material can include a salt and a physiological buffer or a non-cytotoxic porogen material. The hydrogel precursor can include at least one of gellan and gelatin. Cross-linking can be carried out chemically, thermally, enzymatically, or physically.