The Transport of Insulin-Like Growth Factor through Cartilage - Porous Media: Applications in Biological Systems and Biotechnology - page 429

squares and curve-fitting feature in MATLAB's optimization toolbox [78].
The fitting results through the optimization process are shown in Table 11.3.
Details of this calibration procedure can be found in the work by Zang
et al. [34]. The first thing to note is that the model is able to be fit-
ted to the experimental results of Bhakta et al. [29]. This adds support to
the notion that the differential uptake observed by Bhakta et al. [29] when
the radiolabeled IGF-I or IGF-II was used was due to differences in bind-
ing a nities of these two growth factors for the local IGFBPs [59]. Sec-
ond, the estimates of IGFBP concentrations and the various binding ani-
ties derived from the calibration are consistent with previous experimental
findings [69,72,74-76] showing IGFBP-6 has 20- to 100-fold higher binding
anity for IGF-II than IGF-I and IGFBP-6 is the major IGFBP species
in bovine cartilage with a range of 30-150 nM. Therefore, the competitive
interaction model presented here appears to be consistent with known exper-
imental data and adds support to our current understanding of this system.
Now that we have gained confidence in this competitor model we can begin
to extend our knowledge by combining it with the transport model in a
cartilage undergoing cycle deforming. That is, in the following section, we
will extend our growth factor transport model to see how the presence of a
competitor growth factor influences IGF-I uptake in a cyclically deforming
cartilage.

11.4.2.4 Competitive Binding in a Deforming Cartilage

Assuming the contribution of chondrocyte consumption of IGFs to the IGF
sink are not considered in the model due to the relatively low total-receptor
concentration and binding anities in comparison with that of IGFBPs [27,
58], conservation of mass of free IGF-I and -II can be expressed as

∂ φ f c j
∂t

c j + φ f v f c j =

2

φ f D j ∇

s ji ,j =1 , 2

+ ∇• − − (11.59)

i =1

where s ji is source/sink term for IGF-I and -II, respectively, representing their
interaction with each functional group of IGFBPs attached to the solid phase.
D 1 and D 2 are the effective diffusion coecients for IGF-I and -II in the
uniform cartilage, respectively.
The conservation of mass of the IGF-I and -II attached to the two func-
tional groups on the solid phase is described by

∂ 1 φ f c ji

∂t

−

∇• 1 φ f v s c ji = s ji ,j =1 , 2

+ − (11.60)