Thermodynamically Consistent Diffuse Interface Model for Cell Adhesion and Aggregation

TL;DR

This paper introduces a thermodynamically consistent phase-field model for simulating multicellular deformation and aggregation, incorporating cell interactions and flow effects, with a focus on numerical stability and biological applications.

Contribution

The paper presents a novel phase-field model with a Lennard-Jones potential for cell interactions and a second-order accurate finite element method, ensuring energy stability and convergence.

Findings

Model accurately simulates cell deformation and aggregation.

Numerical tests confirm convergence and energy stability.

Application to sickle cell disease vesicles explains pathological risks.

Abstract

A thermodynamically consistent phase-field model is introduced for simulating multicellular deformation, and aggregation under flow conditions. In particular, a Lennard-Jones type potential is proposed under the phase-field framework for cell-cell, cell-wall interactions. A second-order accurate in both space and time $C^0$ finite element method is proposed to solve the model governing equations. Various numerical tests confirm the convergence, energy stability, and nonlinear mechanical properties of cells of the proposed scheme. Vesicles with different adhesion are also used to explain the pathological risk for patients with sickle cell disease.