Numerical simulation of stress fiber orientation in cultured endothelial cells under biaxial cyclic deformation using the strain limit hypothesis

This paper verifies the hypothesis that a stress fiber (SF) will only be oriented in the direction in which the fiber strain does not exceed a limit for the maximally deformed state of the substrate. We assume three-dimensional and uniform deformation of a cell on a substrate and predict the three-dimensional orientations of the SFs during cyclic deformation tests of the substrate. These predictions are in good agreement with experimental data for the basal membrane under simple cyclic elongations, and reproduce an observation of the three-dimensional orientation of actin filaments under equibiaxial cyclic stretching. Results from a stress analysis using a finite element model of an adherent cell with a nucleus show that a tensile stress develops in the direction transverse to the stretch axis under pure uniaxial stretching. This indicates that SFs are oriented to minimize strain, not the stress, and that a nucleus complicates the stress distribution in a cell.