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Traction force microscopy 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…

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory.…

Quantitative Methods · Quantitative Biology 2016-08-24 Jerome R. Soine , Nils Hersch , Georg Dreissen , Nico Hampe , Bernd Hoffmann , Rudolf Merkel , Ulrich S. Schwarz

Mechanobiology is gaining more and more traction as the fundamental role of physical forces in biological function becomes clearer. Forces at the microscale are often measured indirectly using inverse problems such as Traction Force…

Biological Physics · Physics 2025-03-21 Aleix Boquet-Pujadas

Combining experiments with artificial intelligence algorithms, we propose a new machine learning based approach to extract the cellular force distributions from the microscope images. The full process can be divided into three steps. First,…

The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates.…

Biological Physics · Physics 2019-10-25 Luca Giomi

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation…

Adherent cells exert traction forces on to their environment, which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures. This traction can be measured in a perturbation-free manner with…

Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft…

Cell Behavior · Quantitative Biology 2015-06-19 Philipp J. Albert , Ulrich S. Schwarz

Adherent biological cells generate traction forces on a substrate that play a central role for migration, mechanosensing, differentiation, and collective behavior. The established method for quantifying this cell-substrate interaction is…

Cell Behavior · Quantitative Biology 2020-05-05 Yunfei Huang , Gerhard Gompper , Benedikt Sabass

Traction Force Microscopy (TFM) is a technique used to determine the tensions that a biological cell conveys to the underlying surface. Typically, TFM requires culturing cells on gels with fluorescent beads, followed by bead displacement…

Image and Video Processing · Electrical Eng. & Systems 2019-10-17 Nicolas Pielawski , Jianjiang Hu , Staffan Strömblad , Carolina Wählby

Traction Force Microscopy (TFM) computes the forces exerted at the surface of an elastic material by measuring induced deformations in volume. It is used to determine the pattern of the adhesion forces exerted by cells or by cellular…

Biological Physics · Physics 2018-02-09 Stanislav Makarchuk , Nicolas Beyer , Christian Gaiddon , Wilfried Grange , Pascal Hébraud

Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance and repair. Here we show analytically that the experimentally observed…

Tissues and Organs · Quantitative Biology 2012-01-16 Carina M. Edwards , Ulrich S. Schwarz

Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular…

Biological Physics · Physics 2015-06-23 Ariel Livne , Eran Bouchbinder , Benjamin Geiger

Using a minimal model of cells or cohesive cell layers as continuum active elastic media, we examine the effect of substrate thickness and stiffness on traction forces exerted by strongly adhering cells. We obtain a simple expression for…

Soft Condensed Matter · Physics 2015-06-04 Shiladitya Banerjee , M. Cristina Marchetti

A living cell actively generates traction forces on its environment with its actin cytoskeleton. These forces deform the cell elastic substrate which, in turn, affects the traction forces exerted by the cell and can consequently modify the…

Biological Physics · Physics 2022-02-03 H. Chelly , A. Jahangiri , M. Mireux , J. Étienne , D. K. Dysthe , C. Verdier , P. Recho

The importance of molecular-scale forces in sculpting biological form and function has been acknowledged for more than a century. Accounting for forces in biology is a problem that lies at the intersection of soft condensed matter physics,…

Soft Condensed Matter · Physics 2025-12-10 K. Vijay Kumar , Mandar M. Inamdar , Pramod A. Pullarkat , Gautam I. Menon

This study presents a novel, versatile traction force microscopy framework for quantifying three-dimensional (3D) interfacial forces during bio-adhesion by integrating in situ stereo digital image correlation with finite element (FE)…

Instrumentation and Detectors · Physics 2026-01-09 Yingwei Hou , Fusheng Wang , Tao Liu

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living…

Soft Condensed Matter · Physics 2025-02-13 Michael Chiang , Austin Hopkins , Benjamin Loewe , Davide Marenduzzo , M. Cristina Marchetti

Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…

Soft Condensed Matter · Physics 2009-11-07 U. S. Schwarz , S. A. Safran

Anchorage-dependent cells collect information on the mechanical properties of the environment through their contractile machineries and use this information to position and orient themselves. Since the probing process is anisotropic,…

Soft Condensed Matter · Physics 2007-05-23 I. B. Bischofs , S. A. Safran , U. S. Schwarz
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