Solutions for Determining Equibiaxial Substrate Strain for Dynamic Cell Culture
Martin Y. Chiang, Tianle Cheng, Lisa Pakstis, Joy P. Dunkers
Empirical and analytical solutions are derived in this study to determine the equibiaxial strain on a flexible substrate upon which the cells can be cultured. The empirical formula is based on the mechanistic constraint and a regression analysis of results from finite element analyses with updated loading conditions for a substrate undergoing large strains (<15 %). The analytical (closed-form) solution is derived from the superposition of two elastic responses induced in the equibiaxial strain culture system after applying pressure to a substrate undergoing small strains (microstrains). There is good agreement between the strain predicted from the solutions and that from the direct measurement. Using easily measured material and geometric properties in the culture system, the solutions developed in this study are straightforward and can be used to circumvent experimental measurements or finite element analysis to establish the pressure-strain relationship for substrates under a large range of strains.