# Structure--property relationships of cell clusters in biotissues: 2D analysis

## TL;DR

This study investigates the relationship between cell cluster structures and biotissue properties using a detailed cell adhesion model, deriving analytical solutions and simulating complex shapes to connect microstructure with macro-mechanical behavior.

## Contribution

It introduces a comprehensive 2D cell adhesion model to analyze biotissue structures, providing analytical and numerical insights into their mechanical and morphological properties.

## Key findings

- Derived equilibrium shape equations for symmetrical structures.
- Obtained analytical expressions for Young's modulus, bulk modulus, and failure strength.
- Simulated stable multicellular structures and observed symmetry-breaking phenomena.

## Abstract

To insight the relationships between the self-organizing structures of cells, such as the cell clusters, and the properties of biotissues is helpful in revealing the function and designing biomaterial. Traditional random foam model neglects several important details of the frameworks of cell clusters, in this study we use a more complete model, cell adhesion model, to investigate the mechanical and morphological properties of the two-dimensional (2D) dry foams composed by cells. Supposing these structures are formed due to adhesion between cells, the equilibrium formations result from the minimum of the free energy. The equilibrium shape equations for high symmetrical structures without the volume constraint are derived, and the analytical results of the corresponding mechanical parameters, such as the Young's modulus, bulk modulus and failure strength, are obtained. Numerical simulation method is applied to study the complex shapes with the volume constraint and several stable multicellular structures are obtained. Symmetry-breaking due to the volume change is founded and typical periodic shapes and the corresponding phase transformations are explored. Our study provides a potential method to connect the microstructure with the macro-mechanical parameters of biotissues. The results also are helpful to understand the physical mechanism of how the structures of biotissues are formed.