3D bioprinting is a novel promising solution for living tissue fabrication, with several potential advantages in many different applicative sectors. However, the implementation of complex vascular networks remains as one of the limiting factors for the production of complex tissues and for bioprinting scale-up. In this work, a physics-based computational model is presented to describe nutrients diffusion and consumption phenomena in bioprinted constructs. The model-a system of partial differential equations that is approximated by means of the finite element method- allows for the description of cell viability and proliferation, and it can be easily adapted to different cell types, densities, biomaterials, and 3D-printed geometries, thus allowing a preassessment of cell viability within the bioprinted construct. The experimental validation is performed on bioprinted specimens to assess the ability of the model to predict changes in cell viability. The proposed model constitutes a proof of concept of digital twinning of biofabricated constructs that can be suitably included in the basic toolkit for tissue bioprinting.