Page 20 - Mathematical Techniques of Fractional Order Systems
P. 20
10 Mathematical Techniques of Fractional Order Systems
TABLE 1.1 Summary and Description of the Variables and Parameters of
the Models of Eqs. (1.19) (1.22) (in the case of non-integer models, units
-α
-1
of Day are replaced by pseudo-units Day )
Variables Description Units
t Time Day
x Distance xA½0; 1
Cðt; xÞ Osteoclast population —
Bðt; xÞ Osteoblast population —
zðt; xÞ Bone mass density %
Tðt; xÞ Bone metastases density %
αðtÞ=αðt; xÞ Variable order expression —
d 1 ðtÞ Effect of denosumab —
d 2 ðtÞ Effect of zoledronic acid —
d 3 ðtÞ Effect of paclitaxel —
Parameters Description Units
α C OC activation rate Day 21
α B OB activation rate Day 21
OC apoptosis rate Day 21
β C
β B OB apoptosis rate Day 21
g CC OC autocrine regulator —
g BC OC paracrine regulator —
g CB OB paracrine regulator —
g BB OB autocrine regulator —
κ C Bone resorption rate Day 21
κ B Bone formation rate Day 21
σ C Diffusion coefficient for OC Day 21
σ B Diffusion coefficient for OB Day 21
σ z Diffusion coefficient for bone mass Day 21
σ T Diffusion coefficient for metastases Day 21
r CC OC tumorous autocrine regulation —
r BC OC tumorous paracrine regulation —
r CB OB tumorous paracrine regulation —
(Continued)
