Toroidal indentation for measuring cell and tissue mechanical anisotropy.

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.