Correlating linear rheology and filament fidelity in bioinks: A combined modeling and experimental approach

The rheological behavior of bioinks critically influences their printability, yet current models rely heavily on empirical fits that do not account for or ignore the underlying molecular mechanisms. In this study, we introduce a physically grounded transient network model that links polymer chain attachment-detachment kinetics to small-amplitude oscillatory shear (SAOS) moduli. By resolving chain populations across a spectrum of detachment rates, the model captures the power-law scaling of storage and loss moduli observed in alginate and carboxymethyl cellulose hydrogels. Unlike multimode Maxwell or fractional viscoelastic models, our framework assigns kinetic significance to each network relaxation mode, enabling mechanistic interpretation of viscoelastic behavior. Experimental rheology and filament printing tests further confirm that formulations with higher elastic moduli and lower loss tangents exhibit superior shape fidelity. The model fits SAOS data with high fidelity, replicating G ′ and G ′ ′ (storage and loss moduli) within ± 2% across the analyzed frequency range under analysis, while yielding interpretable parameters such as chain stiffness, relaxation time, and reattachment rate. This work establishes a foundation for predictive bioink design, bridging molecular kinetics and macroscopic rheology in a way that supports rational formulation strategies for extrusion-based bioprinting.