Systems Biology (Methods in Molecular Biology)

the fractal dimension, and the tumor growth rate. A common

property of invasive cancers is their altered glucose metabolism.

The glycolytic rate in cultured cell lines seems to correlate with

tumor aggressiveness [78]. That an increase in proliferation and a

reduction in apoptosis trigger a maximum of ATP consumption by

the tumor cells has been already confirmed [79]. The tumor meta-

bolome—mainly characterized by the glycolytic phenotype—con-

fers an advantage to the evolving cancer cell population and

contributes to their tissue invasion and the metastasis

spreading [80].

The dissipation function could be evaluated through Eq. (29)

from the data reported by Bru ́[38] for different tumors cell lines

(seeTable2).

During the avascular development the growth rate remains

constant [35], it can be proved from Eq. (29) that the metabolic

rate exhibits a maximum with respect to the fractal dimensions (see

Fig.6).

As other authors have suggested, the thermodynamic dissipa-

tive function is correlated with both the glucose metabolism and

cell shape [76]. We suggest that the latter could interfere with the

metabolic pathways.

In previous works [26, 81, 82] we have shown that the rate of

entropy production is a Lyapunov function (seeEq. ( 18)), in fact we

extended this formalism to the development of cancer [21, 22, 49,

83 ]. The dissipation function is related to the entropy production

rate through Eq. (29), showing that the dissipation function

Ψ¼f ξ_;df



0 is a function of the fractal dimensiondfand of

tumor growth rateξ_. Taking the Eulerian derivative of Eq. (12), we

have

Table 2
Dissipation function for different human tumor cell lines,T¼310 K ,R¼8.31 J/mol K. Reprinted
from [22]

Human tumor cell lines

Growth ratea

ξ_ μm

h

dfa

Metabolic rate

q_Gl

kJμm

molh



AT5 Primary human foreskin fibroblasts Human 8.72 1.23 11.97
C-33a Cervix carcinoma Human 6.40 1.25 8.46
HT-29 Colon adenocarcinoma Human 1.93 1.13 2.98
HT-29 M6 Mucus secreting HT-29 cells Human 1.85 1.12 2.88
HeLa Cervix carcinoma Human 1.34 1.30 1.64
Saos-2 Osteosarcoma Human 0.94 1.34 1.09
a[38]

144 Sheyla Montero et al.