The Micromechanics of Three Dimensional Collagen-I Gels

TL;DR

This paper develops a 3D micromechanical model of collagen-I gels that aligns well with experimental data, revealing how network geometry and fiber mechanics contribute to strain stiffening.

Contribution

It introduces a realistic 3D network model of collagen-I gels that explains strain stiffening through geometric realignment rather than fiber entropic effects.

Findings

Model agrees with rheology measurements

Strain stiffening driven by network realignment

Cross-link deformation dominates at small strains

Abstract

We study the micromechanics of collagen-I gel with the goal of bridging the gap between theory and experiment in the study of biopolymer networks. Three-dimensional images of fluorescently labeled collagen are obtained by confocal microscopy and the network geometry is extracted using a 3d network skeletonization algorithm. Each fiber is modeled as a worm-like-chain that resists stretching and bending, and each cross-link is modeled as torsional spring. The stress-strain curves of networks at three different densities are compared to rheology measurements. The model shows good agreement with experiment, confirming that strain stiffening of collagen can be explained entirely by geometric realignment of the network, as opposed to entropic stiffening of individual fibers. The model also suggests that at small strains, cross-link deformation is the main contributer to network stiffness whereas at large strains, fiber stretching dominates. Since this modeling effort uses networks with realistic geometries, this analysis can ultimately serve as a tool for understanding how the mechanics of fibers and cross-links at the microscopic level produce the macroscopic properties of the network. While the focus of this paper is on the mechanics of collagen, we demonstrate a framework that can be applied to many biopolymer networks.