Applied Math Seminar

Date: April 14, 2025

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: John Lowengrub, UC Irvine

Title: Thermodynamically consistent modeling of the chemomechanical regulation of growing tumors

Abstract: 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 models 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. We consider both sharp and diffuse interface approaches. Additionally, we implement efficient numerical methods with a special boundary treatment to incorporate applied forces. We compare the model results to experimental data on tumor spheroid growth under varying mechanical conditions and find good agreement between the two. We confirm the validity of our diffuse interface (phase-field) model by demonstrating its convergence to the 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. Zoom: https://tamu.zoom.us/j/94220070032

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