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Multicellular simulations with shape and volume constraints using optimal transport.

Antoine Diez^1,2, Jean Feydy³

¹RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan.

Science Advances

|July 10, 2026

Summary

This study presents a new computational framework for modeling complex particle systems, crucial for understanding self-organization in biology and physics. The method efficiently handles volume exclusion and dynamic shapes, advancing biophysics research.

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Area of Science:

Biophysics
Computational Biology
Soft Matter Physics

Background:

Living and physical systems (e.g., cell aggregates, tissues, bacterial colonies) exhibit complex behaviors due to volume exclusion and shape interactions.
Understanding the emergence of macroscopic self-organized structures from these microscopic constraints is a key challenge, particularly in developmental biology.

Purpose of the Study:

To introduce a novel computational framework for modeling particle systems with arbitrary volumes, dynamic shapes, and deformability.
To provide a versatile method grounded in optimal transport theory capable of handling diverse interaction and deformation mechanisms.

Main Methods:

Utilizing optimal transport theory, a mathematical framework inspired by incompressible fluid dynamics, crowd dynamics, and material sciences.
Developing a computational approach that automatically enforces volume exclusion constraints with high numerical performance.
Implementing a model that supports a wide range of particle interaction and shape deformation properties.

Main Results:

Demonstrated the framework's versatility through various experimental simulations.
Showcased the ability to model systems with arbitrary volumes, dynamical shapes, and deformability.
Extended and refined results from previous modeling approaches, particularly in challenging 3D biophysical scenarios.

Conclusions:

The developed framework offers a powerful and efficient tool for simulating complex particle systems with realistic constraints.
This approach advances the study of self-organization in biological and physical systems, offering new insights into phenomena like tissue morphogenesis.
The method's adaptability makes it suitable for a broad spectrum of applications in biophysics and beyond.