Mapping Three-Dimensional Stress and Strain Fields within a Soft Hydrogel Using a Fluorescence Microscope

Three-dimensional cell culture is becoming mainstream as it is recognized that many animal cell types require the biophysical and biochemical cues within the extracellular matrices to perform truly physiologically realistic functions. However, tools for characterizing cellular mechanical environment are largely limited to cell culture plated on a two-dimensional substrate. We present a three-dimensional traction microscopy that is capable of mapping three-dimensional stress and strain within a soft and transparent extracellular matrix using a fluorescence microscope and a simple forward data analysis algorithm. We validated this technique by mapping the strain and stress field within the bulk of a thin polyacrylamide gel layer indented by a millimeter-size glass ball, together with a finite-element analysis. The experimentally measured stress and strain fields are in excellent agreements with results of the finite-element simulation. The unique contributions of the presented three-dimensional traction microscopy technique are: 1), the use of a fluorescence microscope in contrast with the confocal microscope that is required for the current three-dimensional traction microscopes in the literature; 2), the determination of the pressure field of an incompressible gel from strains; and 3), the simple forward-data-analysis algorithm. Future application of this technique for mapping animal cell traction in three-dimensional nonlinear biological gels is discussed.