Enhancing shape fidelity in bioprinting: Modeling die swell through rheological and process interaction analysis

Achieving high shape fidelity remains a primary challenge in extrusion-based bioprinting, where the viscoelastic nature of hydrogels typically leads to "die swell", a post-extrusion expansion that compromises structural accuracy. This study presents a systematic investigation into the die swell phenomenon by analyzing the complex interplay between process parameters (pressure, temperature, nozzle diameter) and material rheology. Using a Design of Experiments (DOE) approach on functionalized collagen hydrogels, we isolated the main effects of process variables and identified significant interactions that modulate the swelling behavior. Crucially, by integrating rheological data, specifically the ratio between the first normal stress difference (N 1 ) and shear stress (τ), with process kinematics, we developed a robust numerical model capable of predicting the extent of die swell. This model not only validates the theoretical framework of Tanner's law in a bioprinting context but also provides a predictive tool for process optimization. These findings offer a foundational dataset and a mathematical framework that pave the way for future AI-driven strategies and machine learning algorithms aimed at real-time error correction in biofabrication.