Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials

Javier Palacio Torralba, A. Jorge-Peñas, Arrate Muñoz-Barrutia, Carlos Ortiz-de-Solorzano, Elena de Juan-Pardo, José Manuel García-Aznar

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

Original languageEnglish
Pages (from-to)50-55
Number of pages6
JournalJournal of Biomechanics
Issue number1
Publication statusPublished - 4 Jan 2013


  • Finite element modeling
  • Inverse analysis
  • Mechano-sensing
  • Non-linear mechanics
  • Traction Force Microscopy

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Rehabilitation
  • Biophysics
  • Biomedical Engineering


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