Differences in boundary behavior in the 3D vertex and Voronoi models.

Area of Science:

• Computational Biology
• Biophysics
• Tissue Engineering

Background:

• Coarse-graining scales and degrees of freedom are critical in biological tissue modeling.
• Vertex and Voronoi models are established methods for simulating confluent tissues in 2D.
• Recent 2D studies suggest potential model discrepancies at heterotypic interfaces, prompting 3D investigation.

Purpose of the Study:

• To compare the geometric structure and dynamic sorting in 3D mixtures of two cell types using vertex and Voronoi models.
• To identify differences in how these models represent cell interactions and tissue behavior in three dimensions.
• To determine the suitability of each model for simulating complex 3D biological tissues.

Main Methods:

• Simulated mixtures of two cell types in 3D using both vertex and Voronoi models.
• Analyzed cell shape indices, cell center registration, and cell orientation at boundaries.
• Investigated the influence of model-specific forces on tissue dynamics.

Main Results:

• Cell shape indices showed similar trends across both models.
• Significant differences were observed in cell center registration and boundary orientation between vertex and Voronoi models.
• Macroscopic differences were attributed to cusp-like restoring forces arising from the distinct representations of degrees of freedom.

Conclusions:

• The Voronoi model exhibits stronger constraints due to representational artifacts.
• Vertex models may offer a more accurate representation for 3D simulations of tissues with heterotypic contacts.
• The choice of model significantly impacts the simulation of 3D tissue dynamics and structure.