Brittle-to-ductile cell escape from a two-dimensional spheroid

For cancer to metastasize, i.e. spread to other parts of the body, cancer cells must first escape from a localized tumor and invade their surroundings. Cancer cells exhibit many invasion strategies that are challenging to predict in vivo. Therefore, this phenomenon is studied in vitro using tumor spheroids, multi-cellular aggregates embedded in a collagen matrix. To determine how the geometry and the rheology of the spheroid affects how cells escape a tumor, we construct and study a minimal computational model in two dimensions for the outer edge of a spheroid that allows us to connect larger-scale geometric and rheological properties of the spheroid to the shapes of individual cells. More specifically, we implement a two-dimensional vertex model with mechanosensitive activity and impose a local pulling force, simulating a leader cell escaping from the spheroid. We test the hypothesis that rigid spheroids undergo brittle, single cell break-out, whereas more fluid spheroids exhibit more ductile, multi-cell break-out to allow us to formulate experimentally-testable predictions for the metastatic potential of spheroids and, ultimately, cancerous tumors.