Page 333 - Advances in Biomechanics and Tissue Regeneration

16.6 SOME APPLICATIONS OF INTEREST 331

1.2 1.2
1 1

0.8 0.8
f−(x) 0.6 f+(x) 0.6
0.4 0.4

0.2 0.2
0 0
0 0.5 1 1.5 0 0.5 1 1.5
x x
(A) (B)

1.2
1
d = 0.1
1
0.5
0.8
d =1
s (x) 0.6 d =10 r(x) 0
0.4
−0.5
0.2
−1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5
x x
(C) (D)
1.2
1
0.8
g(x) 0.6

0.4
0.2

0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
(E) x
FIG. 16.4 Different activation functions for phenomenological models. (A) ϕ function. (B) ϕ + function. (C) σ function. (D) ρ function.
(E) r function.

Fig. 16.4 shows functions ϕ , ϕ + , ρ, and r for β ¼ 1.0 (for both ϕ , ϕ + , and σ ), δ ¼ 0.1, 1, 10, α ¼ 1, and K ¼ 0.1. It is
clear that these functions try to model cell adaptation to the environment. In principle, to define these functions, six
parameters are needed (θ 1 , θ 2 , θ 3 , δ, C, and K) but due to the “go or grow” assumption, it is assumed that θ 1 ¼ θ 2 ¼ O so
∗
2
finally:
β 1 ¼ O ∗ 2
β ¼ O ∗
2 2
β ¼ O d
3 2
δ ¼ δO 2
α ¼ C sat
K ¼ O K (16.108)
2
The entire set of parameters is listed in Table 16.1, where the bibliographic source of each parameter is also
included.

II. MECHANOBIOLOGY AND TISSUE REGENERATION