Mechanics of a two-fiber model with one nested fiber network, as applied to the collagen-fibrin system

The mechanical behavior of collagen-fibrin (col-fib) co-gels is both scientifically interesting and clinically relevant. Collagen-fibrin networks are a staple of tissue engineering research, but the mechanical consequences of changes in co-gel composition have remained difficult to predict or even explain. We previously observed fundamental differences in failure behavior between collagen-rich and fibrin-rich co-gels, suggesting an essential change in how the two components interact as the co-gel's composition changes. In this work, we explored the hypothesis that the co-gel behavior is due to a lack of percolation by the dilute component. We generated a series of computational models based on interpenetrating fiber networks. In these models, the major network component percolated the model space but the minor component did not, instead occupying a small island embedded within the larger network. Each component was assigned properties based on a fit of single-component gel data. Island size was varied to match the relative concentrations of the two components. The model predicted that networks rich in collagen, the stiffer component, would roughly match pure-collagen gel behavior with little additional stress due to the fibrin, as seen experimentally. For fibrin-rich gels, however, the model predicted a smooth increase in the overall network strength with added collagen, as seen experimentally but not consistent with an additive parallel model. We thus conclude that incomplete percolation by the low-concentration component of a co-gel is a major determinant of its macroscopic properties, especially if the low-concentration component is the stiffer component. Statement of significance: Models for the behavior of fibrous networks have useful applications in many different fields, including polymer science, textiles, and tissue engineering. In addition to being important structural components in soft tissues and blood clots, these protein networks can serve as scaffolds for bioartificial tissues. Thus, their mechanical behavior, especially in co-gels, is both interesting from a materials science standpoint and significant with regard to tissue engineering.