Finite Element Analysis of Traction Force Microscopy: Influence of Cell Mechanics, Adhesion, and Morphology

Abstract

The interactions between adherent cells and their extracellular matrix (ECM) have been shown to play an important role in many biological processes, such as wound healing, morphogenesis, differentiation, and cell migration. Cells attach to the ECM at focal adhesion sites and transmit contractile forces to the substrate via cytoskeletal actin stress fibers. This contraction results in traction stresses within the substrate/ECM. Traction force microscopy (TFM) is an experimental technique used to quantify the contractile forces generated by adherent cells. In TFM, cells are seeded on a flexible substrate and displacements of the substrate caused by cell contraction are tracked and converted to a traction stress field. The magnitude of these traction stresses are normally used as a surrogate measure of internal cell contractile force or contractility. We hypothesize that in addition to contractile force, other biomechanical properties including cell stiffness, adhesion energy density, and cell morphology may affect the traction stresses measured by TFM. In this study, we developed finite element models of the 2D and 3D TFM techniques to investigate how changes in several biomechanical properties alter the traction stresses measured by TFM. We independently varied cell stiffness, cell-ECM adhesion energy density, cell aspect ratio, and contractility and performed a sensitivity analysis to determine which parameters significantly contribute to the measured maximum traction stress and net contractile moment. Results suggest that changes in cell stiffness and adhesion energy density can significantly alter measured tractions, independent of contractility. Based on a sensitivity analysis, we developed a correction factor to account for changes in cell stiffness and adhesion and successfully applied this correction factor algorithm to experimental TFM measurements in invasive and noninvasive cancer cells. Therefore, application of these types of corrections to TFM measurements can yield more accurate estimates of cell contractility.