Analysis of geometric fidelity in protein-based 3D printing via coupled pressure-flow dynamics

In extrusion-based food 3D printing, geometric fidelity depends not only on the material's rheological properties but also on the stability of pressure–flow dynamics during deposition. This study aimed to interpret the 3D printing process of a rice protein ink through coupled pressure–flow dynamics analysis and to evaluate the ability of partial least squares (PLS) and machine learning (ML) models to predict geometric fidelity. A 3 2 factorial design was implemented, with real-time extrusion pressure monitoring, flow, oscillatory, and apparent rheological characterization, and image analysis. Mass flow rate ranged from 9.23 to 66.64 mg/s, and maximum pressures ranged from 227 to 237 kPa at 50 mm/s, with AUC reductions of up to 71.4% when increasing nozzle diameter (0.85 to 1.55) at 20 mm/s. The results revealed that printability is governed by two independent mechanisms: lateral redistribution and vertical stability. Lateral expansions reached +19.37% in frontal area and + 17.52% in top area, while maximum height reduction was −12.85%. The combination of 1.55 mm nozzle at 50 mm/s achieved the highest global fidelity (PFI >97%). PLS models showed limited predictive capacity (R 2 = 0.21–0.33), whereas the Random Forest algorithm substantially outperformed them (R 2 = 0.82–0.91), identifying printing speed, mass flow rate, apparent viscosity, and pressure variability as dominant predictors. These findings confirm that geometric fidelity depends on the dynamic balance between volumetric supply and pressure stability, validating ML as a tool to resolve the multivariable complexity of food 3D printing.