A phase-field model of mechanically biased cell migration in enzyme-sensitive hydrogels

Durotactic cell migration plays a fundamental role in many processes, like tumor invasion, wound healing, and tissue engineering applications. This work presents a novel computational model for durotaxis-mediated cell migration within enzyme-sensitive scaffolds. Cell motion is described as an advective-diffusive process through a multi-phase-field formulation and is driven by the mechanical interplay between cells and substrate. The model couples cell migration with enzyme production and diffusion, which cause hydrogel degradation and the associated spatio-temporal evolution of viscosity and stiffness. Mechanical sensing is triggered by cell contraction, which generates a stress field in the surrounding scaffold that is then evaluated to identify the preferred migration direction. The resulting durotactic cue regulates the transition from random motion to a mechanically biased migration regime, while cell velocity is derived from a force balance involving stochastic protrusion, stress-driven polarization, and traction forces generated at the cell-matrix interface. The model is implemented in a finite-element framework and applied to several representative scenarios, in which cell durotaxis is induced by spatial variations in substrate stiffness or/and by externally applied mechanical loads, remarkably reconciled within a single modeling framework. The numerical results show that the model captures the occurrence of directional migration toward mechanically favorable regions, predicts cell speed and traction force values consistent with experimental evidence, and provides quantitative insights into the coupled evolution of cell motion, substrate degradation, and stress redistribution.