The hallmark of malignant tumors is their invasion of local tissue and infiltration
of distant organs (metastasis). A defining characteristic of aggressive tumors
is an unstable morphology, including invasive fingers and protrusions. Shape
instabilities (growing protrusions) are associated with local invasiveness, also
often a precursor to tumor metastasis. We study tumor morphological stability
by employing three mathematical models to gain insight into tumor invasion
and metastasis. Using linear theory, we study the tumor morphological stability
described by each model and evaluate the consistency between theoretical
model predictions and experimental data from in vitro 3D multicellular tumor
spheroids. We will discuss the results and show that it is feasible to extract parameter
values from a limited set of data and create a self-consistent modeling
framework that can be extended to the multiscale study of cancer. Numerical
methods are used to simulate the nonlinear effects of stress on solid tumor
growth and invasiveness.