Biomedical Engineering Reference
In-Depth Information
extracellular matrix molecules underlying the monolayer become exposed, al-
lowing the spheroids to grow and to form large foci of invasion that appear to
grow laterally, almost within the same plane of the layer (Figure 3.4(B)). The
area occupied by the original spheroids progressively increases in size, as the
mesothelial cells recede and are overtaken and replaced by the malignant mass
(disruptive invasion; see Figure 3.4(C-D)). The invasion is regulated by the
proteases secreted and activated by the tumor cells. Indeed, some experimen-
tal data indicate that ovarian cancer spheroids secrete much greater amounts
of both pro-MMP-2 and MMP-9 compared to cells grown as a monolayer, and
that both MMPs are present in the active form [53, 127, 136].
Quantitative studies evaluating the percentage of invasion demonstrate
that tumor spheroids plated in the same well do not exhibit the same invasive
properties despite sharing an identical environment, since only a proportion
of them establishes foci of invasion. These data imply that the metastatic
potential is not merely induced by the microenvironment, but likely relies on
physiological differences in the invasive characteristics of every single spheroid.
3.2 Mathematical Model
The model aims to reproduce a typical in vitro experiment of ovarian cancer
transmesothelial migration, characterizing the principal biological aspects. In
particular, we focus on the differences between the invasion of a single cell and
of cells aggregated in a spheroid. The simulation environment involves more
entities with respect to the previous application: two cell populations, tumor
( = C) and mesothelial cells ( = M), and two types of substrate objects,
matrix bers ( = E) and the experimental dish ( = S), used only to indicate
the low boundary of the domain, in addition to the interstitial/peritoneal
uid, isotropically distributed ( = F). Continuous elds are instead used to
represent the evolution of chemotactic factors and tumor MMPs.
The system evolves following the usual rule given in relation (1.2). How-
ever, with respect to the previous example, we no longer use a single overall
motility of the entire pattern, but T is specific for each type of individual, i.e.,
T = T .
The Hamiltonian includes surface and perimeter constraints for cells, terms
for the adhesion between individuals, and the energetic counterpart of the
cancer chemotactic movement:
H(t) = H adhesion (t) + H shape (t) + H chemotaxis (t):
(3.1)
The form of H adhesion is the same as in Equation (1.5): the Js, as usu-
ally measuring the level of the expression of specific adhesion molecules.
They are spatially homogeneous, meaning that the coupling strengths are
 
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