Cancer initiation appears to be a phenomenon which involves
some regulatory genes, which can either enhance or inhibit tumor
levels of malignancy and whose micro-scale dynamics is regulated
by mesoscale and macroscale properties and processes. Indeed,
biological tissues are somewhat ordered but complex structures
generating forces exchanged by cells in union with extracellular
matrix surrounding them. These mechanical interactions are super-
imposed to biochemical and electrical ones, in some cases even
back-reacting dynamically as it happens in cardiac tissue for
instance. All of these contributions at the end determine the geo-
metrical features of the tissue and can in many situations define
cells’ final state.
Such communication pathways at the cellular and tissue levels
have an important role in the global tissue organization so that their
impairment results in several cases to be associated with cancer
generation and progression [20, 21]. In this context, we must
point out that specific chemicals known as morphostats are experi-
mentally known [22] to drive “cell to cell” and “tissue to tissue”
communications in a way somewhat very similar to Turing’s acti-
vators and inhibitors activities. These morphostats present dynami-
cally varying concentrations in space and have a great influence on
the tissue expressed phenotype, although a clear understanding of
their underlying mechanistic dynamics is still not present.
It is natural to look for an appropriate conceptual framework
which could analyze and possibly interpret both these phenomen-
ologies. The mainstream nowadays follows as primary candidates
two theories, i.e., the Somatic Mutation Theory or SMT [23] and
the Tissue Organization Field Theory or TOFT [24, 25]. The
former deserves cancer generation to progressive DNA changes
within a single cell. This is an approach in which the main source
of cancer is the cell itself. On the other hand, in TOFT possible
carcinogen factors tend to mismatch cellular communications, in a
fashion similar to Turing morphogens’ theory.
As standard in hard Sciences, it is mandatory often to accom-
modate different perspectives based on empirical facts taking
advantage of an appropriate mathematical framework and compu-
tational resources.
In silico studies do not represent necessarily the starting point
for mathematical modeling, however. For instance, books devoted
to the study of Computational Biology [26] and Evolutionary
dynamics of cancer [27] and Mathematical Biology in general
[6, 28] offer different possible analytical approaches to describe
cancer dynamics. Together with mathematical tools previously dis-
cussed as ordinary and partial differential equations with stochastic,
delay and integrodifferential extensions, also more exotic tools as
maps and cellular automata or even the recently growing field of
complex networks applied to biology can be used to this aim
[29–31].206 Christian Cherubini et al.