Determination of the mechanical behavior of materials requires an understanding of deformation during loading. While this is traditionally accomplished in engineering by examining a force displacement curve for a whole sample, these techniques implicitly ignore local geometric complexities and local material inhomogeneities commonly found in biologic tissues. Techniques such as normalized cross correlation have been classically applied to address this issue and resolve deformation at the local level;​ however, these techniques have proven unreliable when deformations become large, if the sample undergoes a rotation, and/or if strain fields become incompatible (e.g. at or near failure).

Presented here is a toolbox of techniques that addresses the limitations of the prior stateof-the-art for localized strain estimation. The first algorithm, termed 2D direct deformation estimation (2D-DDE), directly incorporates concepts from mechanics into non-rigid registration algorithms from computer vision, eliminating the need to consider displacement fields, as required for all of the prior state-of-the-art techniques. This results in not only an improvement in accuracy and precision of deformation estimation, but also relaxes compatibility of the deformation fields. A second algorithm, 2D Strain Inference with Measures of Probable Local Elevation (2D-SIMPLE), incorporates the results of 2D-DDE with results from algorithms that enforce strain compatibility to develop a robust detector of strain concentrations. While tracking local strain in a vinylidene chloride sheet in tension, 2D-SIMPLE detected strain concentrations which predicted the initiation of a crack in the material and the progression of the crack tip. The third and fourth algorithms generalize the two dimensional algorithms to analyze three dimensional deformations in volumetric images (3D-DDE and 3D-SIMPLE, respectively). Lastly, the 2D-DDE algorithm is modified to estimate two dimensional surface deformation from multi-view imaging systems.

The robustness and adaptability of these techniques was then validated and demonstrated on a wide variety of biomedical applications. Using 2D-DDE, a microscale compliant region was discovered at the tendon-to-bone attachment, local heterogeneity of partially mineralized scaffolds was revealed, and gradients in stiffness of partially mineralized nano-fiber scaffolds were demonstrated. Using 2D-SIMPLE, mechanisms of embryonic wound healing and associated strain localizations were elucidated. 3D-DDE confirmed the existence of strain gradients across chordae tendineae in beating murine hearts as well as demonstrated dramatic localized changes in wall deformation before and after myocardial infarction in murine hearts.

2D-DDE was also used to develop a model system to study the effects of applied stress versus the effects of applied strain on cells. The model system was first theorized by considering a system in which gradients of cross sectional area or scaffold shape were composed with gradients in material stiffness. By combining these gradients in novel ways, it was theoretically determined that stress and strain could be locally isolated. A tensile bioreactor was constructed, techniques for fabricating scaffolds with gradients in stiffness and gradients in cross sectional area were developed, and theoretical strain gradients were confirmed experimentally using 2D-DDE. The model system was then validated for in vitro cell studies. Cell adhesion, proliferation, and viability following a seven day loading protocol were explored. Methods for determining single cell responses, which could be correlated back to a specific stress or strain states, were developed using immunocytochemistry and 2D-DDE approaches. Future studies will apply this model system to determine precise mechanotransduction responses of cells. These studies are critical to optimize stem cell tissue engineering strategies as well inform cell mechanobiology mechanisms.