Traction Force Microscopy for Viscoelastic Substrates: A Semi-Analytical Method

Area of Science:

• Biophysics
• Cellular Mechanics
• Materials Science

Background:

• Traction Force Microscopy (TFM) is vital for measuring cellular forces.
• Elastic TFM formulations are limited on viscoelastic substrates, potentially misinterpreting cellular forces.
• Viscous dissipation is often neglected in standard TFM.

Purpose of the Study:

• Introduce a semi-analytical 2D viscoelastic TFM (veTFM) for accurate force quantification on viscoelastic substrates.
• Generalize the Boussinesq framework to accommodate Generalized Maxwell (GMX) substrates.
• Provide criteria for determining the validity of elastic TFM regimes.

Main Methods:

• Developed a semi-analytical 2D viscoelastic TFM (veTFM).
• Combined Fourier and Laplace transforms for time-resolved traction analysis.
• Applied veTFM to cardiomyocytes, epithelial cells, and fibroblasts on viscoelastic hydrogels.

Main Results:

• veTFM quantifies time-resolved tractions and resolves substrate pre-stress.
• Cellular regime (elastic vs. viscoelastic) depends on timescale matching between cell loading and substrate relaxation.
• Viscoelastic traction magnitude scales with total substrate dissipation for GMX substrates.

Conclusions:

• veTFM offers a scalable extension of elastic TFM to viscoelastic materials.
• Identifies when standard TFM is sufficient and when viscoelastic analysis is necessary.
• Demonstrates the importance of timescale matching and total dissipation in cellular force transmission.