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Animal cells use traction forces to sense the mechanics and geometry of theirenvironment. Measuring these traction forces requires a workflow combining cellexperiments, image processing and force reconstruction based on elasticitytheory. Such procedures have been established before mainly for planarsubstrates, in which case one can use the Green's function formalism. Here weintroduce a worksflow to measure traction forces of cardiac myofibroblasts onnon-planar elastic substrates. Soft elastic substrates with a wave-liketopology were micromolded from polydimethylsiloxane (PDMS) and fluorescentmarker beads were distributed homogeneously in the substrate. Using featurevector based tracking of these marker beads, we first constructed a hexahedralmesh for the substrate. We then solved the direct elastic boundary volumeproblem on this mesh using the finite element method (FEM). Using datasimulations, we show that the traction forces can be reconstructed from thesubstrate deformations by solving the corresponding inverse problem with aL1-norm for the residue and a L2-norm for 0th order Tikhonov regularization.Applying this procedure to the experimental data, we find that cardiacmyofibroblast cells tend to align both their shapes and their forces with thelong axis of the deformable wavy substrate.

Measuring cellular traction forces on non-planar substrates