The Transport of Insulin-Like Growth Factor through Cartilage - Porous Media: Applications in Biological Systems and Biotechnology - page 440

1

φ f ∂c a
∂t

s d 1 φ f c a

= s b φ f c a − − − (11.86)

φ f K d D a ∂ 2 c a
∂r 2

+ K a φ f v r − ∂c a

∂r

φ f ∂c a

∂c a
∂r

= s d 1 φ f c a

(11.87)

+ 1
r

κ r ∂p
∂r ∂t −

−

The normalized average free, bound, and degraded aggrecan in the radial
direction can be defined using the following equations as:

r 0 2 πrc a dr

1
c a 0

c aavg =

r 0
0

(11.88a)

2 πrdr

r 0 2 πrc a dr

1
c a 0

c aavg =

r 0
0

(11.88b)

2 πrdr

r 0 2 πrc a dr

1
c a 0

c aavg =

r 0
0

(11.88c)

2 πrdr

11.5.3 Biosynthesis Model Validation and Predictions
The developed numerical model is validated by using the experimental data
from Bonassar et al. [30], Jin et al. [31], and Buschmann et al. [32]. In
experiments investigating the aggrecan synthesis when cartilage explants were
exposed to a range of IGF-I concentrations under conditions of free diffu-
sion, Bonassar et al. [30] treated cartilage discs with IGF-I ranging from 0
to 300 ng/mL for 48 h with the 35 S-sulfate only present in the final 24 h,
while in Jin et al.'s [31] experiment, cartilage explants were exposed to IGF-
I in the range of 0-300 ng/mL together with 35 S-sulfate for the first 24 h.
The 35 S-sulfate incorporation was later used to assess the effect of IGF-I on
aggrecan synthesis. Differing from the experiments of Bonassar et al. [30] and
Jin et al. [31], the study of Buschmann et al. [32] focused on understanding
the correlation between cyclic loading and the spatial distribution of biosyn-
thesis in the cartilage explants. The rate of aggrecan synthesis was assessed
by measuring the 35 S-sulfate incorporation during the last 8 h after cartilage
explants were under cyclic mechanical loading at frequencies of 0.01-0.1 Hz
at displacement of amplitude of 50 m for 23 h. Thus, these experimental

studies provide three sets of independent biosynthesis data on similar carti-
lage explants but under different experimental conditions. The model should
be able to reproduce these experimental observations.
The rate of aggrecan formation is determined by currently unknown model
parameters, namely the coecient n , the activation coecient K in equation
(11.79), the IGF-I mediated maximum production rate β , and mechanical-
stimuli-mediated production rate λ , as well as estimating the initial aggrecan

µ