Bifurcation in the healing or fibrotic response in a network model of fibrosis: role of the initial injury structure.

Introduction: Pulmonary fibrosis (PF) is a heterogeneous progressive lung disease characterized by excessive extracellular matrix (ECM) deposition and cross-linking, leading to irreversible tissue stiffening and loss of function. Previous evidence suggests that percolation behavior, where increasing local stiffness facilitates the emergence of stiff regions that span the tissue, underlies the stiffening of the ECM and drives the irreversible mechanical dysfunction. However, it is not fully understood how percolation emerges from the complex interactions between cells and the ECM. Methods: In this study, we investigated a previously published agent-based spring network model of PF that exhibited bifurcation behavior between healing and fully developed fibrosis as network members were gradually stiffened. By systematically analyzing the configuration of the initial tissue injury, we identify key structural determinants that govern whether an injury heals or transitions into fibrosis. Results: Results demonstrate that fibrosis is strongly associated with increased initial clustering of injured springs, reduced intercluster distances, and the presence of critical stiffening sites, or hotspots, that act as bifurcation points for disease progression. Furthermore, we show that selectively modifying the stiffness of pivotal network regions at the time of injury can shift the network's trajectory from fibrosis to healing, highlighting potential intervention targets. These findings suggest that the network structure of tissue injury may serve as a predictive marker for fibrosis susceptibility and provide a mechanistic basis for understanding the nonlinear progression of PF.