Biomedical Engineering Reference
In-Depth Information
that, although their model allows cell migration through continuous diffusion, at
the core theirs is proliferation-focused, with a cursory treatment on tumor cell
invasion. Researches that focus on
invasive
expansion can also be broken down
into deterministic-continuum (e.g. (26,27,30)) and stochastic-discrete ap-
proaches (e.g. (23)). In a deterministic-continuum model, multicellular patterns
typically emerge from the dynamic evolution of population density functions
satisfying second-order nonlinear differential equations of reaction-diffusion and
wave propagation. For example, (30) successfully simulates the branching pat-
tern on a tumor surface using a continuum model whereby migrating cells fol-
low the gradients of diffusive substrates.
As an attempt to generalize, (28) considers both proliferation and migration
within a three-dimensional diffusion framework. All these continuum models
emphasize the interaction of cells with the environment, but usually cannot iden-
tify the individual cell
itself
. In addition, incorporating stochastic cell behavior
within a reaction-diffusion framework is a daunting task. Perhaps more impor-
tantly, such models are not suitable for modeling the early stages of tumorigene-
sis when only a small number of tumor cells are present. At that stage, the
progression of tumor growth depends on the discrete history of each individual
cell and its local interactions with the environmental variables as well as with
neighboring tumor cells. (23) therefore develops a
hybrid
discrete-continuum
model to account for the importance of tumor cells to be treated as discrete
units. This study shows that the formation of (experimentally observed)
"branches" on the surface of a multicellular tumor spheroid may require both
heterotype and homotype
chemoattraction
, i.e., toward distinct signals that are
released by nutrient sources as well as produced by the tumor cells themselves
(i.e., paracrine). (29) employs a discrete model to replicate the spatiotemporal
pattern of malignant cell invasion into the surrounding extracellular matrix
(ECM). However, in their model cancer cells migrate to minimize their collec-
tive energy expenditures, implying that each cell endeavors to minimize the sur-
face energy of the entire tumor domain. Their model therefore does not qualify
as a true agent-based framework since the latter by definition must be based on
individual-level "decisions" rather than community-level considerations on the
part of tumor cells. Nonetheless, their work underscores the critical role of
minimal energy expenditure
for tumor expansion, which also influences our
work (6-9).
For example, in the agent-based model presented in (6), due to a cascading
information structure, tumor cells gradually "learn" information content about a
particular location in two stages. In the first stage, signal content is global (based
on the assumption that cells can upregulate their receptor sensitivity) but incom-
plete, while in the second stage detailed local information is complete. Guiding
the migratory behavior of tumor cells is the principle of "least resistance, most
permission,
1
and highest attraction," which classifies the attractiveness of the
microenvironmental conditions. The key finding of this study is the emergence
