Nonlinear simulation of an elastic tumor-host interface

TL;DR

This paper introduces a computational method to simulate nonlinear elastic tumor-host interface dynamics, revealing how curvature weakening influences metastasis patterns and tumor morphology evolution.

Contribution

It develops a novel numerical approach for simulating elastic tumor interfaces with bending energy, exploring nonlinear dynamics and metastasis patterns.

Findings

Curvature weakening promotes branching tumor patterns.

Self-similar shrinking morphologies are observed with non-weakened bending rigidity.

Numerical method accurately captures complex interface behaviors.

Abstract

We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D. Unlike the classic tumor model with surface tension, the elastic interface condition is numerically challenging due to the 4th order derivative from the Helfrich bending energy. Here we are interested in exploring the nonlinear interface dynamics in a sharp interface framework. We consider a curvature dependent bending rigidity (curvature weakening) to investigate metastasis patterns such as chains or fingers that invade the host environment. We solve the nutrient field and the Stokes flow field using a spectrally accurate boundary integral method, and update the interface using a nonstiff semi-implicit approach. Numerical results suggest curvature weakening promotes the development of branching patterns instead of encapsulated morphologies in a long period of time. For non-weakened bending rigidity, we are able to find self-similar shrinking morphologies based on marginally stable value of the apoptosis rate.