Systems Biology (Methods in Molecular Biology)

the primary site with the secondary tumors being too small to be

clinically detected.

The model proposed (seeFig. 3) contains as a particular case the

avascular growth discussed previously [21]. Starting from the pro-

posed model (Fig.3) and under the Law of Mass Action, the system

of ODEs is obtained:

0.0

1.00

1.10

1.20

1.30

1.40

1.50

1.00

0.90

1.10

1.20

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

1.30

1.40

1.50

s = 0.08945229

r = 0.87898465

s = 0.02539552

r = 0.99327575

1.60

1.70

1.80

PC3

df

df

LNCaP

time [days]

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Fig. 2 Dependence of fractal dimension df with the growth time of the tumor cell lines: LNCaP
(bA¼ 0 :2524,α¼ 0 :1466,K¼ 1 :8384) and PC3 (bA¼ 0 :3335,α¼ 0 :1944,K¼ 1 :4924). Reprinted from
[49]

Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate... 137