Development of process design tools for extrusion-based bioprinting: From numerical simulations to nomograms through reduced-order modeling

The planning of a bioprinting procedure requires the definition of several process variables. In extrusion-based bioprinting these are, for instance, the printing pressure, the nozzle diameter, the target extrusion velocity and/or mass flow rate. They should be properly set in order to allow printability of the bio-ink, as well as to ensure high cell viability at the end of the process. In fact, printing procedures expose cells to shear and extensional stresses that can lead to mechanobiological damage mechanisms. Bioprinting planning is then a challenging task since process variables are closely interconnected each other through the physical response of bio-inks. Non-Newtonian characteristics of bio-inks, together with possible complex geometries of the extruding system, generally introduce a strong non-linear coupling among process variables. To date, the bioprinting planning in laboratory practice is generally performed via expensive and time-consuming trial-and-error procedures. The aim of this work is the development of novel methodological approaches for an informed definition of printing process variables such to guarantee target conditions of the outcome. The non-linear coupling among dominant process variables is described via a semi-analytical approach, calibrated through high-fidelity numerical solutions and defined via a reduced-order modeling strategy. A cell damage law depending on bioprinting conditions is also introduced, generalizing state-of-the-art approaches on the basis of available experimental evidence. The proposed framework allows to build operative nomograms, whose practical utility is confirmed via some exemplary applications. The latter address the prediction of extrusion velocity, mass flow rate and cell viability, when both the printing pressure and nozzle diameter vary within typically-adopted ranges. The analyzed case studies highlight soundness and effectiveness of such a modeling strategy in providing a clear and straight pathway for planning and setup of bioprinting processes.