Biomedical Engineering Reference
In-Depth Information
Fig. 21.9
Effect of cell migration from regions of high compressive stress to regions of lower
compression/tension, modeled as pressure gradient driven advection
modeled as pressure gradient driven advection (Eq. (
21.15
)), was considered. The
results in Fig.
21.9
show that such a stress-driven migratory behavior of cells can
lead to preferred growth directions and thus may be a possible explanation for
development of ellipsoidal tumor shapes.
Extension of the above formulation to 3D is only limited by available compu-
tational resources. A representative simulation of 3D tumor growth is shown in
Fig.
21.10
.
21.5 Discussion
The mathematical formulation based on multi-species reaction-transport equations
and chemomechanical coupling presented here is to be seen as a generic framework
for simulating tumor growth dynamics. The specific details of the source terms,
transport properties and the influence of mechanics will depend on the type of the
tumor, and one needs an extensive experimental program to fine tune various pa-
rameters and assumptions of inter-species interactions. The work presented here
was part of a larger experimental program to investigate the growth of human colon
adenocarcinoma tumors in agarose hydrogels, and thus the
in vitro
observations of
tumor growth allowed us to set bounds on various chemical, transport and mechan-
ical parameters. The simulations presented compared well with
in vitro
observa-
tions of tumor growth dynamics (tumor size and shape evolution, cell population
distribution, etc.) (Mills et al.,
2011
,
2012
). As a natural second step, this simula-
tion framework is now being used to probe the possible mechanisms driving tumor
growth, and our current interests include the evolution of various tumor shapes and
effects of initial cell distributions (single cells, distributed colonies, secondary stem
cell population, etc.). The results presented here seem to suggest that mechanics
plays a critical role in evolution of these tumor shapes and various mechanics driven
phenomena could possible explain some of the
in vitro
observations. One possible
