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Measuring the Mechanical Properties of Living Cells Using Atomic Force Microscopy
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Toroidal indentation for measuring cell and tissue mechanical anisotropy.

Juanyong Li1, Chaokai Zhang1, Habibeh Ashouri2

  • 1Department of Biomedical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA.

Acta Biomaterialia
|August 1, 2025
PubMed
Summary

This study introduces a new, low-cost toroidal indentation method to measure the anisotropic stiffness of biological materials, from tissues to cells. This accessible technique overcomes limitations of traditional methods, enabling broader biomechanical research.

Keywords:
AnisotropyCell mechanicsDeep learningFinite element modelingIndentationMechanical characterization

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Area of Science:

  • Biomechanics
  • Cellular Mechanobiology
  • Biomaterials Science

Background:

  • Indentation tests measure tissue and cell stiffness but typically assume isotropic material properties.
  • Standard methods using spherical or pyramidal probes and Hertzian analysis fail to capture direction-dependent properties of fibrous tissues and polarized cells.
  • Measuring anisotropic mechanical properties across scales has been challenging without advanced imaging or specialized equipment.

Purpose of the Study:

  • To develop a generalized, accessible indentation method for estimating anisotropic elastic moduli of biomaterials.
  • To create torus-shaped indenter probes suitable for various scales, from millimeters to microns.
  • To establish a computational framework combining finite element modeling and deep learning for modulus calculation.

Main Methods:

  • Fabrication of torus-shaped indenter probes with varying aspect ratios.
  • Indentation of anisotropic biological samples (muscle tissue, cell monolayers, single cells) along and perpendicular to fiber orientation.
  • Development of a linear incompressible transversely isotropic material model and finite element simulations.
  • Training a deep learning model on simulated data to calculate anisotropic moduli (E1 and E2).

Main Results:

  • The developed toroidal indentation method successfully estimated anisotropic moduli for muscle tissue, cell monolayers, and single cells.
  • The measured degrees of anisotropy (E1:E2) aligned with previously published values for these biological systems.
  • The method demonstrated comparability to existing techniques while being more accessible and cost-effective.

Conclusions:

  • The toroidal indentation method offers a generalized, accessible, and low-cost approach to measure anisotropic stiffness in biological materials across scales.
  • This technique overcomes limitations of isotropic assumptions in traditional indentation methods.
  • The study provides a valuable tool for advancing research in tissue engineering, biomechanics, and mechanobiology by enabling the study of anisotropic biological systems.