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Fibre topography of the extracellular matrix governs local mechanical properties and cellular behaviour including migration and gene expression. While quantifying properties of the fibrous network provides valuable data that could be used across a breadth of biomedical disciplines, most available techniques are limited to two dimensions and, therefore, do not fully capture the architecture of three-dimensional (3D) tissue. The currently available 3D techniques have limited accuracy and applicability and many are restricted to a specific imaging modality. To address this need, we developed a novel fibre analysis algorithm capable of determining fibre orientation, fibre diameter and fibre branching on a voxel-wise basis in image stacks with distinct fibre populations. The accuracy of the technique is demonstrated on computer-generated phantom image stacks spanning a range of features and complexities, as well as on two-photon microscopy image stacks of elastic fibres in bovine tendon and dermis. Additionally, we propose a measure of axial spherical variance which can be used to define the degree of fibre alignment in a distribution of 3D orientations. This method provides a useful tool to quantify orientation distributions and variance on image stacks with distinguishable fibres or fibre-like structures.
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Hyperelastic continuum models for isotropic athermal fibrous networks
Many biological materials contain fibrous protein networks as their main structural components. Understanding the mechanical properties of such networks is important for creating biomimicking materials for cell and tissue engineering, and for developing novel tools for detecting and diagnosing disease. In this work, we develop continuum models for isotropic, athermal fibrous networks by combining a single-fibre model that describes the axial response of individual fibres, with network models that assemble individual fibre properties into overall network behaviour. In particular, we consider four different network models, including the affine, three-chain, eight-chain, and micro-sphere models, which employ different assumptions about network structure and kinematics. We systematically investigate the ability of these models to describe the mechanical response of athermal collagen and fibrin networks by comparing model predictions with experimental data. We test how each model captures network behaviour under three different loading conditions: uniaxial tension, simple shear, and combined tension and shear. We find that the affine and three-chain models can accurately describe both the axial and shear behaviour, whereas the eight-chain and micro-sphere models fail to capture the shear response, leading to unphysical zero shear moduli at infinitesimal strains. Our study is the first to systematically investigate the applicability of popular network models for describing the macroscopic behaviour of athermal fibrous networks, offering insights for selecting efficient models that can be used for large-scale, finite-element simulations of athermal networks.
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- Award ID(s):
- 1720530
- PAR ID:
- 10415112
- Date Published:
- Journal Name:
- Interface Focus
- Volume:
- 12
- Issue:
- 6
- ISSN:
- 2042-8901
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rsfs.2022.0043
