Inverse problems for the determination of traction forces by cells on a substrate: a comparison of two methods

Abstract

Traction forces exerted by cells on soft elastic substrates are important for characterizing the types of mechanisms used for cell migration. Classical tools for the determination of traction forces include the knowledge of the displacement field thanks to fluorescent beads embedded into the substrate. Then, from the discrete beads displacements, an inverse problem is solved to obtain the stress field. Two currently used methods in the literature are the well-known Fourier Transform Traction Cytometry (FTTC) method and the adjoint method (AM), which are compared here. A real case is presented where the displacement field is known from cancer cell migration study. The two methods allow the recovery of the traction stresses and their results are compared. Similar results are seen as long as an adequate projection technique is used (zero force imposed outside the cell). It is found that the AM allows a finer resolution of the traction forces, in particular at the cell edge. This is a strong incentive to use this method for the investigation of cancer cell migration on soft substrates.