An asymptotic slender-body model for predicting print resolution in extrusion-based bioprinting

Bioprinting enables fabrication of three-dimensional, patient-specific, tissue-like structures, for which printing resolution and printability are key determinants of construct fidelity. Achieving consistent control of printed filament dimensions remains challenging due to its strong dependence on interacting process parameters, while existing print-and-test approaches are often time-consuming, expensive, and specific to particular materials and experimental set-ups. This study proposes a generalised, physics-based model to predict printed filament diameters for moderately shear-thinning materials under pneumatic extrusion-based bioprinting. By adopting an arc length coordinate system and exploiting the slender geometry of the extruded filament, asymptotic techniques are employed to reduce the incompressible Navier-Stokes equations to a closed system describing filament radius and centre-line orientation. Non-Newtonian behaviour characteristic of bioinks is captured by modelling the material as a power-law fluid. Applied prior to printing, the model enables identification of process parameter combinations corresponding to a bioink's window of printability, reducing reliance on print-and-test methodologies. Preliminary validation using pneumatically extruded Nivea Crème demonstrates good predictive capability. This work highlights the value of theoretical modelling for supporting optimisation-driven design in extrusion-based bioprinting.

The online version contains supplementary material available at 10.1007/s10665-026-10544-0.