# How do vibration stimulation frequencies affect the nonlinear dynamics and mechanical characterization of breast cancer cells?

## TL;DR

This study explores how different vibration frequencies affect the mechanical behavior of breast cancer cells and healthy mammary cells, revealing insights into their nonlinear dynamics and potential for noninvasive therapies.

## Contribution

The study introduces a novel approach combining mechanical testing, finite element modeling, and nonlinear dynamics to analyze cancer cell behavior at specific frequencies.

## Key findings

- MCF-10 cells were stiffer than MCF-7 cells, with significant differences observed at higher frequencies.
- FEM simulations provided detailed stress distribution and deformation patterns in both cell types.
- Chaotic behavior in cancer cells was identified at frequencies between 22–36 kHz.

## Abstract

Understanding the mechanical properties of cells is crucial for gaining insights into their physiological and pathological states. This study focuses on the mechanical behavior of human mammary epithelial cells (MCF-10) and human breast cancer cells (MCF-7), emphasizing mechanical frequencies, finite element modeling (FEM), and nonlinear dynamics of the cells.

Cells were cultured and subjected to mechanical testing using Atomic Force Microscopy (AFM) and Magnetic Tweezer Cytometry (MTC). The elastic and viscoelastic properties were analyzed, and FEMs were developed to simulate cell behavior under various mechanical stimuli. The nonlinear dynamic behavior was examined using the Duffing model, and chaos was assessed using the Largest Lyapunov exponent (LLE).

MCF-10 cells exhibited higher stiffness than MCF-7 cells. The mechanical frequencies of both cell types were determined, and significant differences were observed at higher frequencies. FEM simulations provided detailed insights into the stress distribution and deformation patterns within cells. The nonlinear analysis revealed chaotic behavior at specific frequencies, particularly in the range of 22–36 kHz.

Identifying the mechanical frequencies and responses of cancer cells, including their nonlinear and chaotic behaviors, can inform the development of noninvasive therapeutic strategies. Further research is required to refine these models and explore the potential of mechanical forces in cancer treatment.

•Investigated mechanical properties of MCF-10 and MCF-7 cells using AFM and MTC.•Analyzed nonlinear dynamics and chaos in cell mechanics using the Duffing model and Largest Lyapunov exponent.•FEM simulations revealed stress distribution and deformation patterns in epithelial and cancer cells.•Identified chaotic behavior in cancer cells at mechanical frequencies (22–36 kHz).•Findings suggest potential applications of mechanical forces in non-invasive cancer therapies.

Investigated mechanical properties of MCF-10 and MCF-7 cells using AFM and MTC.

Analyzed nonlinear dynamics and chaos in cell mechanics using the Duffing model and Largest Lyapunov exponent.

FEM simulations revealed stress distribution and deformation patterns in epithelial and cancer cells.

Identified chaotic behavior in cancer cells at mechanical frequencies (22–36 kHz).

Findings suggest potential applications of mechanical forces in non-invasive cancer therapies.