Solutions for determining equibiaxial substrate strain for dynamic cell culture

In this work, empirical and analytical solutions of equibiaxial strain on a flexible substrate are derived for a dynamic cell culture system. The empirical formula, which fulfills the mechanistic conditions of the culture system, is based on a regression analysis from finite element analyses 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 from the direct measurement. Using material and geometric properties of the culture system, the solutions developed here are straightforward and can be used to circumvent experimental measurements or finite element analysis to establish substrate pressure–strain relationships.