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Integrative Toolkit to Analyze Cellular Signals: Forces, Motion, Morphology, and Fluorescence
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Traction Force Microscopy for Viscoelastic Substrates: A Semi-Analytical Method.

Adrià Villacrosa-Ribas1,2,3, Daniëlle C A Duffhues1,2, Pim van den Bersselaar1,2

  • 1Department of Biomedical Engineering, Eindhoven University of Technology (TU/e), Eindhoven, Netherlands.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|May 28, 2026
PubMed
Summary
This summary is machine-generated.

Viscoelastic traction force microscopy (veTFM) accurately quantifies cellular forces on complex substrates. This method distinguishes between elastic and viscoelastic responses, crucial for understanding cell-matrix interactions.

Keywords:
cell–material interactionssemi‐analytical methodsstress relaxationviscoelastic hydrogelsviscoelastic traction force microscopy

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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.