Traction force microscopy for linear and nonlinear elastic materials as a parameter identification inverse problem

Abstract Traction force microscopy (TFM) is a method widely used in biophysics and cell biology to determine forces that biological cells apply to their environment. In the experiment, the cells adhere to a soft elastic substrate, which is then deformed in response to cellular traction forces. The inverse problem consists in computing the traction stress applied by the cell from microscopy measurements of the substrate deformations. In this work, we consider a linear model, in which 3D forces are applied at a 2D interface, called 2.5D TFM, and a nonlinear pure 2D model, from which we directly obtain a linear pure 2D model. All models lead to a linear resp. nonlinear parameter identification problem for a boundary value problem of elasticity. We analyze the respective forward operators and conclude with some numerical experiments for simulated and experimental data.

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Publication Details

Journal
Inverse Problems
Published
2025-04-25
DOI
https://doi.org/10.1088/1361-6420/add0d5
Citations
3
Primary Topic
Force Microscopy Techniques and Applications
Type
article
Field-Weighted Citation Impact
3.74

Funders

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article

Traction force microscopy for linear and nonlinear elastic materials as a parameter identification inverse problem

Anne Wald, Timo Betz, Tram Thi Ngoc Nguyen, Stephen Koester et al.
3 citations
Inverse Problems
Force Microscopy Techniques and Applications
3.74
article

Traction force microscopy for linear and nonlinear elastic materials as a parameter identification inverse problem

Anne Wald, Timo Betz, Tram Thi Ngoc Nguyen, Stephen Koester, Thorsten Hohage, Ulrich S. Schwarz, Manisha Sinha, Gesa Sarnighausen
article en
3 citations

Abstract

Abstract Traction force microscopy (TFM) is a method widely used in biophysics and cell biology to determine forces that biological cells apply to their environment. In the experiment, the cells adhere to a soft elastic substrate, which is then deformed in response to cellular traction forces. The inverse problem consists in computing the traction stress applied by the cell from microscopy measurements of the substrate deformations. In this work, we consider a linear model, in which 3D forces are applied at a 2D interface, called 2.5D TFM, and a nonlinear pure 2D model, from which we directly obtain a linear pure 2D model. All models lead to a linear resp. nonlinear parameter identification problem for a boundary value problem of elasticity. We analyze the respective forward operators and conclude with some numerical experiments for simulated and experimental data.

Inverse ProblemsVol. 41(6)
Heidelberg University (DE), Max Planck Institute for Solar System Research (DE), European Neuroscience Institute Göttingen (DE), Nanoscale Microscopy and Molecular Physiology of the Brain Cluster of Excellence 171 — DFG Research Center 103 (DE), Heidelberg Institute for Theoretical Studies (DE), University of Göttingen (DE)
Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, Max-Planck-Gesellschaft
Openalex Percentile: Top 8%
Force Microscopy Techniques and Applications
3.74
DOIOpen Access PDFOpenAlex
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