1 research outputs found
Nonlinear simulation of an elastic tumor-host interface
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