Quantification of Errors in Applying DIC to Fiber Networks Imaged by Confocal Microscopy

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