Analytical method for reconstructing the stress on a spherical particle from its surface deformation

Area of Science:

• Biophysics
• Cell Biology
• Materials Science

Background:

• Mechanical forces from surrounding tissues significantly influence cell behavior and development.
• Measuring these forces experimentally is essential for biological studies.
• Bead deformation analysis is a common method, but existing reconstruction techniques are slow or limited.

Purpose of the Study:

• To present a novel analytical approach for reconstructing mechanical stress in tissues from bead deformation.
• To develop a method that is both computationally efficient and broadly applicable.

Main Methods:

• Utilized an analytical approach based on solid spherical harmonics expansion.
• Employed a specialized ansatz for deformed spherical bodies within the linear theory of elasticity.
• Validated the method's applicability to arbitrary radial deformations and low computational requirements.

Main Results:

• Developed a method to reconstruct the complete stress tensor acting on tissues.
• The approach is significantly faster and more general than existing methods.
• Demonstrated the method's effectiveness through application to experimental data.

Conclusions:

• The new analytical method provides an efficient and versatile tool for measuring mechanical forces in biological tissues.
• This advancement aids in understanding the role of mechanical forces in cell development and behavior.
• The clarified conditions for the ansatz enhance its utility in various scientific contexts.