Biomedical Engineering Reference
In-Depth Information
Fig. 21.1
Time progression of the growth of an LS174T tumor embedded in a 0
.
5 % agarose gel
mor colonies (metastasis). All these processes can be mathematically modeled as
reaction-transport phenomena coupled with growth induced mechanics and mechan-
ical interactions at the tumor scale, where the complex biophysical interactions be-
tween these processes are more broadly observable than in single-cell studies.
In vitro
observations of prevascular tumor growth of human colon adenocarci-
noma (LS174T, trypsinized variant of LS180) cells, involving multicellular tumor
spheroids embedded in a tissue-mechanics-mimicking hydrogel (Mills et al.,
2011
,
2012
), have shown strong influence of growth induced mechanics on the tumor scale
growth dynamics, such as rate of tumor growth (Fig.
21.1
) and evolution of different
tumor shapes (Fig.
21.2
). Our motivation in this work is to develop a quantitative
understanding of these
in vitro
observations. The underlying physical processes that
lead to these observations are also of interest because of their potential influence on
the progression of the cancer. Towards this goal, we have been developing a coupled
reaction-transport and finite deformation framework. The mathematical formulation
and numerical implementation of this framework and a discussion of potential un-
derlying mechanisms are presented here.
21.2 Mathematical Formulation
The formulation presented here is based on a broader treatment that was developed
for the growth and remodeling of biological tissue. It is based on the continuum the-
ory of mixtures and has been detailed in Garikipati et al. (
2004
) and Narayanan et
al. (
2009
,
2010
). The first step in this formulation is the identification of the various
biological and chemical species involved and characterizing their sources, transport
behavior and external interactions. The primary biological species are the cancer
cells, represented as a concentration at the tumor scale. The two chemical species
considered are the critical nutrients: oxygen and glucose. Over time, the cancer cells
consume oxygen and glucose and produce many byproducts. In this study, the pro-
duction of metabolic byproducts is not modeled; however, the production of ECM
is modeled as it has an important role in the calculation of available free volume and
the elastic compliance of the growth matrix. Cell death is tracked by considering
