Experimental and numerical determination of cellular traction force on polymeric hydrogels

Anchorage-dependent cells such as smooth muscle cells (SMCs) rely on the transmission of actomyosin-generated traction forces to adhere and migrate on the extracellular matrix. The cellular traction forces exerted by SMCs on substrate can be measured from the deformation of substrate with embedded fluorescent markers. With the synchronous use of phase-contrast and fluorescent microscopy, the deformation of polyacrylamide (PAM) gel substrate can be quantitatively determined using particle image velocimetry. This displacement map is then input as boundary conditions for the stress analysis on PAM gel by the finite-element method. In addition to optical microscopy, atomic force microscopy was also used to characterize the PAM substrate using the contact mode, from which the elasticity of PAM can be quantified using Hertzian theory. This provides baseline information for the stress analysis of PAM gel deformation. The material model introduced for the computational part is the Mooney-Rivlin constitutive law because of its long proven usefulness in predicting polymers' mechanical behaviour. Numerical results showed that adhesive stresses are high around the cell edges, which is in accordance with the general phenomena of cellular focal adhesion. Further calculations on the total traction forces indicate a slightly contact-dominated regime for a broad range of Mooney-Rivlin stiffnesses.