Finite Element Analysis and Empirical Solution for Flexible Substrates Undergoing Large Equibiaxial Strains

Studies of cellular mechanobiology have depended heavily on the use of in vitro experiments. Many devices have been developed to probe those basic physical mechanisms responsible for cell culture mechanostimulus. The work reported here uses a system that imparts equibiaxial loading on a flexible substrate, similar to the Bioflex in Flexcell [1] family of products, to study cell response to mechanical load. The objective of this study is to incorporate an adaptive loading algorithm (ALA) in a finite element analysis (FEA) to update loading conditions, to obtain an accurate correlation between the substrate stain and applied pressure in the culture system. There is a good agreement between the strain predicted from the analysis and that from the direct measurement. Also, based on the mechanistic condition of physical constrains and a regression analysis of finite element results, we have developed an empirical formula to predict the pressure-strain relationship for large substrate strain levels (up to 15 %) to circumvent experimental measurement or FEA for the substrate strain. The results from this study can be used to validate experimental observations and provide a framework for advancing the apparatus to next level involving other loading cases and geometries.