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  1. Abstract Soft bioinspired fiber networks offer great potential in biomedical engineering and material design due to their adjustable mechanical behaviors. However, existing strategies to integrate modeling and manufacturing of bioinspired networks do not consider the intrinsic microstructural disorder of biopolymer networks, which limits the ability to tune their mechanical properties. To fill in this gap, we developed a method to generate computer models of aperiodic fiber networks mimicking type I collagen ready to be submitted for additive manufacturing. The models of fiber networks were created in a scripting language wherein key geometric features like connectivity, fiber length, and fiber cross section could be easily tuned to achieve desired mechanical behavior, namely, pretension-induced shear stiffening. The stiffening was first predicted using finite element software, and then a representative network was fabricated using a commercial 3D printer based on digital light processing technology using a soft resin. The stiffening response of the fabricated network was verified experimentally on a novel test device capable of testing the shear stiffness of the specimen under varying levels of uniaxial pretension. The resulting data demonstrated clear pretension-induced stiffening in shear in the fabricated network, with uniaxial pretension of 40% resulting in a factor of 2.65 increase in the small strain shear stiffness. The strategy described in this article addresses current challenges in modeling bioinspired fiber networks and can be readily integrated with advances in fabrication technology to fabricate materials truly replicating the mechanical response of biopolymer networks. 
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    Free, publicly-accessible full text available August 1, 2024
  2. Free, publicly-accessible full text available November 1, 2023
  3. Abstract Fiber networks are the primary structural components of many biological structures, including the cell cytoskeleton and the extracellular matrix. These materials exhibit global nonlinearities, such as stiffening in extension and shear, during which the fibers bend and align with the direction of applied loading. Precise details of deformations at the scale of the fibers during strain stiffening are still lacking, however, as prior work has studied fiber alignment primarily from a qualitative perspective, which leaves incomplete the understanding of how the local microstructural evolution leads to the global mechanical behavior. To fill this gap, we studied how axial forces are transmitted inside the fiber network along paths called force chains, which continuously evolve during the course of deformation. We performed numerical simulations on two-dimensional networks of random fibers under uniaxial extension and shear, modeling the fibers using beam elements in finite element software. To quantify the force chains, we identified all chains of connected fibers for which the axial force was larger than a preset threshold and computed the total length of all such chains. To study the evolution of force chains during loading, we computed the derivative of the total length of all force chains with respect to the applied engineering strain. Results showed that the highest rate of evolution of force chains coincided with the global critical strain for strain stiffening of the fiber network. Therefore, force chains are an important factor connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network. 
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    Free, publicly-accessible full text available November 1, 2023
  4. Background. An assumption of Digital Image Correlation (DIC) is that the displacement field within each subset is relatively smooth, captured with reasonable accuracy by, for example, linear or quadratic shape functions. Although this assumption works well for many materials, it becomes problematic for heterogeneous materials, such as fiber networks, wherein the length scale of heterogeneity matches the size of a subset. Objective. Here we applied DIC to fibrous networks made of collagen, for which displacements at the scale of a subset are highly heterogeneous, but errors caused by the heterogeneity are difficult to quantify. We developed a method to quantify such errors. Methods. We began by generating a synthetic three-dimensional fiber network with structure matching that of gels made of fibrous collagen. We then formulated an algorithm to mimic the way in which a confocal microscope images the fibers at its focal plane, thereby generating synthetic images similar to those obtained in experiments. Displacement boundary conditions were applied to the synthetic fiber networks, and the resulting displacement fields were computed using a finite element solver. DIC was applied to the synthetic images, and displacements were compared to the data from the finite element method, enabling rigorous quantification of error. Results. Point-wise errors in the DIC-measured displacements were substantial, often exceeding 40%, but over regions far larger than the length scales of heterogeneity or the DIC subset size, errors were modest, e.g., ≤15%. Conclusions. Although DIC can accurately measure displacements of fiber networks at length scales larger than the subset window, quantification of mechanical behavior at the scale of material heterogeneity will require new methods to complement or replace the use of DIC. 
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    Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers—tracts of high densification and fibre alignment—form between cells, thinner bands emanate from cell clusters. While tethers facilitate cell migration and communication, how they form is unclear. Combining modelling, simulation and experiment, we show that tether formation is a densification phase transition of the extracellular matrix, caused by buckling instability of network fibres under cell-induced compression, featuring unexpected similarities with martensitic microstructures. Multiscale averaging yields a two-phase, bistable continuum energy landscape for fibrous collagen, with a densified/aligned second phase. Simulations predict strain discontinuities between the undensified and densified phase, which localizes within tethers as experimentally observed. In our experiments, active particles induce similar localized patterns as cells. This shows how cells exploit an instability to mechanically remodel the extracellular matrix simply by contracting, thereby facilitating mechanosensing, invasion and metastasis. 
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    Cells sense mechanical signals within the extracellular matrix, the most familiar being stiffness, but matrix stiffness cannot be simply described by a single value. Randomness in matrix structure causes stiffness at the scale of a cell to vary by more than an order of magnitude. Additionally, the extracellular matrix contains ducts, blood vessels, and, in cancer or fibrosis, regions with abnormally high stiffness. These different features could alter the stiffness sensed by a cell, but it is unclear whether the change in stiffness is large enough to overcome the noise caused by heterogeneity due to the random fibrous structure. Here we used a combination of experiments and modeling to determine the extent to which matrix heterogeneity disrupts the potential for cell sensing of a locally stiff feature in the matrix. Results showed that, at the scale of a single cell, spatial heterogeneity in local stiffness was larger than the increase in stiffness due to a stiff feature. The heterogeneity was reduced only for large length scales compared to the fiber length. Experiments verified this conclusion, showing spheroids of cells, which were large compared to the average fiber length, spreading preferentially toward stiff inclusions. Hence, the propagation of mechanical cues through the matrix depends on length scale, with single cells being able to sense only the stiffness of the nearby fibers and multicellular structures, such as tumors, also sensing the stiffness of distant matrix features. 
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  8. The extracellular matrix provides macroscale structural support to tissues as well as microscale mechanical cues, like stiffness, to the resident cells. As those cues modulate gene expression, proliferation, differentiation, and motility, quantifying the stiffness that cells sense is crucial to understanding cell behavior. Whereas the macroscopic modulus of a collagen network can be measured in uniform extension or shear, quantifying the local stiffness sensed by a cell remains a challenge due to the inhomogeneous and nonlinear nature of the fiber network at the scale of the cell. To address this challenge, we designed an experimental method to measure the modulus of a network of collagen fibers at this scale. We used spherical particles of an active hydrogel (poly N-isopropylacrylamide) that contract when heated, thereby applying local forces to the collagen matrix and mimicking the contractile forces of a cell. After measuring the particles’ bulk modulus and contraction in networks of collagen fibers, we applied a nonlinear model for fibrous materials to compute the modulus of the local region surrounding each particle. We found the modulus at this length scale to be highly heterogeneous, with modulus varying by a factor of 3. In addition, at different values of applied strain, we observed both strain stiffening and strain softening, indicating nonlinearity of the collagen network. Thus, this experimental method quantifies local mechanical properties in a fibrous network at the scale of a cell, while also accounting for inherent nonlinearity. 
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