  Tumor spheroids are in vitro three-dimensional, cellular collectives
consisting of cancerous cells. Embedding these spheroids in an in vitro fibrous
environment, such as a collagen network, to mimic the extracellular matrix
(ECM) provides an essential platform to quantitatively investigate the
biophysical mechanisms leading to tumor invasion of the ECM. To understand the
mechanical interplay between tumor spheroids and the ECM, we computationally
construct and study a three-dimensional vertex model for a tumor spheroid that
is mechanically coupled to a cross-linked network of fibers. In such a vertex
model, cells are represented as deformable polyhedrons that share faces. Some
fraction of the boundary faces of the tumor spheroid contain linker springs
connecting the center of the boundary face to the nearest node in the fiber
network. As these linker springs actively contract, the fiber network remodels.
By toggling between fluid-like and solid-like spheroids via changing the
dimensionless cell shape index, we find that the spheroid rheology affects the
remodeling of the fiber network. More precisely, fluid-like spheroids displace
the fiber network more on average near the vicinity of the spheroid than
solid-like spheroids. We also find more densification of the fiber network near
the spheroid for the fluid-like spheroids. These spheroid rheology-dependent
effects are the result of cellular motility due to active cellular
rearrangements that emerge over time in the fluid-like spheroids to generate
spheroid shape fluctuations. Our results uncover intricate
morphological-mechanical interplay between an embedded spheroid and its
surrounding fiber network with both spheroid contractile strength and spheroid
shape fluctuations playing important roles in the pre-invasion stages of tumor
invasion.
