[MS11] Dynamics of Pattern Formation and Morphogenesis in Biological Systems

[MS11-09] Phase-field method for simulating growing tumors with the chemomechanical regulation

*Sungha Yoon¹, Min-Jhe Lu², Nonthakorn Olaranont³, Min Wu³, John Lowengrub¹ (1. University of California at Irvine (United States of America), 2. National Tsinghua University (Taiwan), 3. Worcester Polytechnic Institute (United States of America))

Keywords:

phase-field method,Eulerian framework,chemomechanical regulation

Mechanical forces and biochemical signaling networks play a crucial role in cell behavior in growing tissues. The nonlinear dynamics of tissue growth arises from complex interactions between cells and their surroundings. However, the role of chemomechanical regulation which governs the size, shape, and structure of multicellular tissues remains insufficiently understood. To investigate this, we develop a thermodynamically consistent phase-field model in the Eulerian framework to simulate nonlinear tissue growth in confined geometries. Our formulation integrates both elastic and chemical energies through an energy variational approach. Additionally, we implement an efficient finite difference based multigrid method with a special boundary treatment to incorporate applied forces. We confirm the validity of our phase-field model by demonstrating its convergence to an experimentally supported sharp-interface model. Furthermore, we examine how elastic forces, variations in tumor and host stiffness, and external forces influence the evolution of single and multifocal tumors in confined geometries.