Factors influencing the determination of cell traction forces

Methods summarized by the term Traction Force Microscopy are widely used to quantify cellular forces in mechanobiological studies. These methods are inverse, in the sense that forces must be determined such that they comply with a measured displacement field. This study investigates how several experimental and analytical factors, originating in the realization of the experiments and the procedures for the analysis, affect the determined traction forces. The present results demonstrate that even for very high resolution measurements free of noise, traction forces can be significantly underestimated, while traction peaks are typically overestimated by 50% or more, even in the noise free case. Compared to this errors, which are inherent to the nature of the mechanical problem and its discretization, the effect of ignoring the out-of-plane displacement component, the interpolation scheme used between the discrete measurement points and the disregard of the geometrical non-linearities when using a nearly linear substrate material are less consequential. Nevertheless, a nonlinear elastic substrate, with strain-stiffening response and some degree of compressibility, can substantially improve the robustness of the reconstruction of traction forces over a wide range of magnitudes. This poses the need for a correct mechanical representation of these non-linearities during the traction reconstruction and a correct mechanical characterization of the substrate itself, especially for the large strain shear domain which is shown to plays a major role in the deformations induced by cells.