Systems Biology (Methods in Molecular Biology)

dΨ

dt

¼

∂Ψ

∂_ξ



df

dξ_

dt

þ

∂Ψ

∂df



ξ_

ddðÞf

dt

ð 30 Þ

Taking tumor growth rateξ_ constant as in [38] and taking

fractal dimensiondfas a control parameter, Eq. (30) can be rewrit-

ten as

dΨ

dt

¼

∂Ψ

∂df



ξ_

ddðÞf

dt

, ð 31 Þ

In previous work [49] we obtained the analytical solution of the

Gompertz equation for LNCaP tumor cell line (seeEq. ( 23)).

Substituting Eq. (23) into Eq. (29) it can be verified that

∂Ψ

∂df



ξÄn

<ξ_ξ

Än

0, and asddðÞdtf 0[49] we have

dΨ

dt

 0 ð 32 Þ

This shows that the dissipation functionΨ is a Lyapunov

function of the control parameterdf.

4 Complexity of Cancer Glycolysis

In the last years, cancer glycolysis has been a target in oncology

research [78]. Most of tumor cells show a high glycolytic rate

compared with normal cells. This phenomenon is known in the

literature as Warburg’s effect and is observed without an increase in

the tricarboxylic acid cycle (TAC) or the electron transport chain

(ETC) rate [84]. The significant increase in glycolysis rate observed

in tumors has been recently verified, yet few oncologists or cancer

Fig. 6Relationship between metabolic rateqGl, fractal dimensiondf, and tumor growth rateξ. Reprinted from
[22]

Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate... 145