Page 21 - Mathematical Techniques of Fractional Order Systems

Variable Order Fractional Derivatives and Bone Remodeling Chapter | 1 11

TABLE 1.1 (Continued)
Parameters Description Units

r BB OB tumorous autocrine regulation —
L T Maximum size of bone metastases %
Metastases growth rate % Day 21
γ T
Cð0Þ=Cð0;xÞ Initial distribution of osteoclasts —
Bð0Þ=Bð0;xÞ Initial distribution of osteoblasts —
zð0Þ=zð0;xÞ Initial bone mass percentage %
Tð0Þ=Tð0;xÞ Initial tumorous mass percentage %
C ss Steady-state OC number —
B ss Steady-state OB number —
D 0 Drug dosage mg
τ Drug administration time interval Day
F Bioavailability —
V d Volume distribution L
κ g Drug absorption rate Day 21
κ p Drug elimination rate Day 21
50=base Initial drug concentration for 50% mg/L
C p
of its maximum effect
K r Drug resistance capacity —
Maximum effect of denosumab —
K s 1
Maximum effect of zoledronic acid —
K s 2
Maximum effect of paclitaxel —
K i 3
OC stands for Osteoclasts, and OB for Osteoblasts.

mechanism between the different clusters of bone cells is involved. It acts
through the combined influence of autocrine and paracrine factors (Raggatt
and Partridge, 2010). An active BMU can travel across the tissue at a con-
stant speed of 20 40 μm/day for up to 6 months. It comprises 10 20 osteo-
clasts that remove old and damaged tissue, and around 1000 2000
osteoblasts that secrete and deposit unmineralized bone matrix, directing its
formation and mineralization into mature lamellar bone (Ryser, 2011). The
BMU can be seen as a mediator mechanism, as it bridges individual cellular
activity to whole bone morphology (Raggatt and Partridge, 2010).