MATLAB Program for Traction Force Measurement

This repository contains a custom MATLAB program for traction force microscopy (TFM) analysis of cells cultured on polyacrylamide (PAA) hydrogels. The software reconstructs 3-component (2.5D) traction stresses (σx,σy,σz) at the cell–substrate interface from 3D bead-displacement measurements. Displacements are calculated relative to relaxed reference images using either an Elastix-based free-form deformation approach or, for specific applications such as larger-scale embryo and spheroid experiments, PIV- and subpixel registration-based methods. Traction stresses are obtained by solving a Tikhonov-regularized inverse elasticity problem for finite-thickness substrates in the Fourier domain. The software outputs quantitative lateral and normal traction stresses at the cell–gel interface. The archive further provides a comprehensive README file outlining system requirements, Elastix installation on Windows and Linux, and detailed usage instructions illustrated with screenshots of the graphical user interface. Example TIFF images and corresponding analysis results are also included to demonstrate the workflow and facilitate reproduction of the analysis.