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research-article

Displacement propagation and nonaffinity in collagen networks due to local contraction

[+] Author and Article Information
Peter Grimmer

Department of Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI, 53706
pgrimmer@wisc.edu

Jacob Notbohm

Department of Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI, 53706
jknotbohm@wisc.edu

1Corresponding author.

ASME doi:10.1115/1.4038744 History: Received June 19, 2017; Revised November 19, 2017

Abstract

The extracellular matrix provides macroscale structure to tissues and microscale guidance for cell contraction, adhesion, and migration. The matrix is composed of a network of fibers, which each deform by stretching, bending, and buckling. Whereas the mechanics has been well characterized in uniform shear and extension, the response to more general loading conditions remains less clear, because the associated displacement fields cannot be predicted a priori. Studies simulating contraction, such as due to a cell, have observed displacements that propagate over a long range, suggesting mechanisms such as reorientation of fibers toward directions of tensile force and nonlinearity due to buckling of fibers under compression. It remains unclear which of these two mechanisms produces the long-range displacements and how properties like fiber bending stiffness and fiber length affect the displacement field. Here we simulate contraction of an inclusion within a fibrous network and fit the resulting radial displacements to ur ~ r^{-n} where the power n quantifies the decay of displacements over distance, and a value of n less than that predicted by classical linear elasticity indicates displacements that propagate over a long range. We observed displacements to propagate over a longer range for greater contraction of the inclusion, for networks having longer fibers, and for networks with lower fiber bending stiffness. Contraction of the inclusion also caused fibers to reorient into the radial direction, but, surprisingly, the reorientation was minimally affected by bending stiffness. We conclude that both reorientation and nonlinearity are responsible for the long-range displacements.

Copyright (c) 2017 by ASME
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