Measuring cellular traction forces on non-planar substrates

TL;DR

This paper presents a novel workflow for measuring cellular traction forces on non-planar elastic substrates, combining experimental techniques, image processing, and finite element modeling to analyze cell mechanics in complex geometries.

Contribution

It introduces a new method for quantifying traction forces on non-planar substrates using FEM and bead tracking, extending prior planar-focused techniques.

Findings

Cardiac myofibroblasts align their shape and forces with substrate geometry.

The workflow successfully reconstructs traction forces from substrate deformations.

The method enables force measurement on complex, non-flat surfaces.

Abstract

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have been established before mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a worksflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite element method (FEM). Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with a L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.