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  1. 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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  2. 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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  3. Well-controlled 2D cell culture systems advance basic investigations in cell biology and provide innovative platforms for drug development, toxicity testing, and diagnostic assays. These cell culture systems have become more advanced in order to provide and to quantify the appropriate biomechanical and biochemical cues that mimic the milieu of conditions present in vivo. Here we present an innovative 2D cell culture system to investigate human stem cell-derived cardiomyocytes, the muscle cells of the heart responsible for pumping blood throughout the body. We designed our 2D cell culture platform to control intracellular features to produce adult-like cardiomyocyte organization with connectivity and anisotropic conduction comparable to the native heart, and combined it with optical microscopy to quantify cell-cell and cell-substrate mechanical interactions. We show the measurement of forces and displacements that occur within individual cells, between neighboring cells, and between cells and their surrounding matrix. This system has broad potential to expand our understanding of tissue physiology, with particular advantages for the study of the mechanically active heart. Furthermore, this technique should prove valuable in screening potential drugs for efficacy and testing for toxicity. 
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