Systems Biology (Methods in Molecular Biology)

Each of these has its specific advantage and limitations and

must be carefully chosen depending on the particular problem

that one wants to investigate. Another key ingredient to take into

account is the geometry on which the model lives, whether an

idealized one or a realistic domain imported in the computer

from specific biomedical datasets coming from histological,

NMR, CT scans, or others.

Traditional physicists and mathematicians often feel themselves

more comfortable with the former case, thinking about cancer for

instance as a sphere of a cube so that they can take advantage of the

geometrical symmetries to facilitate the study both analytically and

numerically. On the other hand engineers and computer scientists

are happy with complex situations. This approach takes advantage

of the incredible boost in performance of nowadays computers

which use multiprocessing technology and powerful graphic pro-

cessing units (also present in commercial smartphones, video games

consoles, smart tv, etc.), which 15 years ago were found in particu-

lar academic or industrial contexts only. While the latter situation is

more in the spirit of Systems Biology, we have to say that the

formerly described use of simplified scenarios (often called toy

models) can be extremely useful to orientate and interpret complex

numerical simulations.

2 Experimental Research

As an example, in Fig.1 we show the simulation at a given time of a

brain cancer cells growth in a realistic NMR imported geometry.

In this work, we shall focus on a particular subset of these

possibilities, i.e. the case of solid cancer dynamics described by a

single nonlinear reaction-diffusion equation, mostly on the lines of

previous studies by some of the authors [32]. This approach,

although minimalist in its toy model nature, will accommodate

both points of view of SMT and TOFT conceptually. It moreover

represents a simple example of a Systems Biology activity which

merges somewhat together the knowledge of mathematics, bio-

physics and philosophy of science.

Specifically, the proposed model for the tumor cell concentra-

tion in space and timectðÞ¼;x;y;z ct;x

⇀



is governed by the

following reaction-diffusion type partial differential equation (∇

⇀

is

the Laplacian operator, andR¼F(c) is the reaction term):

∂c

∂t

þ∇

⇀

J

⇀

¼R

which, by using Fick’s law for the matter flux vectorJ

⇀

¼D∇

⇀

c,

results, in Cartesian coordinates, in:

Systems Biology Modelling 207