other hand, a nonzeromcreates a nonlinear equation for which the
cancer propagation front is non-smooth.
This is an interesting modification which could be tested exper-
imentally both in vitro and in vivo. The best candidate for this type
of description, always in the context of Neuro-Oncology, would be
glioblastoma multiform cancers for which many data exist both for
cultures and for NMR and TC biomedical images leading to a well-
developed and dynamic sector of mathematical oncology (seeref. 35
and references therein).4 Notes
In the spirit of Systems Biology, we must take into account now the
fact that the presence of tumor masses, for instance in the brain,
requires substantial refinements of the mathematical modeling pre-
sented above. A growing tumor, in fact, leads to significant
mechanical effects on the underlying anatomy. Cancer moves into
a limited region, i.e., the skull, and this leads to the displacement of
anatomical structures, for instance, the ventricular cavities, which
experimentally are well known to collapse resulting in an anoma-
lous hydrodynamics for the brain. Moreover, cancer tends to infil-
trate pre-existing fibred tissues and vascularized structures,
eventually becoming necrotic and leading to an entirely new (path-
ological) anatomy which is revealed by subsequent patient’s bio-
medical imaging. The role of the model is crucial here in giving a
predictive snapshot on what will occur in patients.
Physiology too of course results affected in this quite compli-
cated developmental dynamics. A Systems Biology perspective must
be adopted again by merging these new aspects into a model
possibly (but not necessarily) described by reaction-diffusion partial
differential equations acting into space and time changing domains
ruled both by coupled nonlinear solid mechanics and microfluidics
(seefor instance refs.36, 37). The modeling could be then still
enriched by taking into account the effects of chemotherapy and
radiation therapy, ablation, immunological treatments, tempera-
ture changes, and many others.
A Systems Biology perspective of such a problem, in conclu-
sion, seems to resemble a sort of constructions toy set. Each model
can be expanded and enriched taking advantage of new ingredients
coming from advances not only in experiments and mathematics
but also in computational resources. This refinement process even-
tually should lead to updated “in silico” versions of the system
giving new insights into such a complex problem. Biological and
human sciences in this procedure surely will take advantage of a
mathematical language, mostly free of ambiguity, to find new inter-
pretative frameworks for cancer.Systems Biology Modelling 211