The Transport of Insulin-Like Growth Factor through Cartilage - Porous Media: Applications in Biological Systems and Biotechnology - page 437

∂c I
∂t

+ v r ∂c I
∂r

= k +1 φ f c I c BP − k − 1 c I (11.74)

dc BP
dt

k +1 φ f c I c BP + k − 1 c I = − (11.75)

dc R 1
dt

k +2 φ f c I c R 1 +( k − 2 + k 0 ) c R 1 I = − (11.76)

dc R 1 I
dt

= k +2 φ f c I c R 1 − ( k − 2 + k 0 ) c R 1 I (11.77)

11.5.2.2 Cartilage ECM Biosynthesis

As a first estimate, the total aggrecan biosynthesis rate is assumed to be a
sum of the basal production rate s p 0 [80], the matrix production rate induced
by IGF-I ( s pI ) and the mechanical-stimuli-induced production rate ( s pm ),
respectively. Further experiments have suggested that aggrecan biosynthesis
is limited by the possible maximum allowable aggrecan concentration (i.e.,
c a max ) in cartilage tissue [30,84,85]. Thus, the total aggrecan biosynthesis
rate s p may be expressed as
s p =( s p 0 + s pI + s pm ) 1

c a + c a
c a max

− (11.78)

where c a max is the maximum allowable maximum aggrecan content in carti-

lage.
Following the experimental result of Sah et al . [86] the basal rate of aggre-
can is assumed to be 1 . 9 10 − 8 . ×

11.5.2.3 IGF-I Mediated Aggrecan Biosynthesis

IGF-I mediated production rate ( s pI ) depends on the concentration of com-
plex IGF-I/R1 (i.e., c R 1 I ) and as a first approximation the link between s pI
and IGF-I/R1 complex concentration can be described by an activator Hill
function [87]. That is, s pI may be expressed as
s pI = β

c R 1 I
K n + c R 1 I

(11.79)

where parameter K is the “activation coecient” and determines the threshold
IGF-I/R1 complex concentration at which aggrecan biosynthesis is “switched
on.” The smaller the K , the lower the IGF-I/R1 concentration required to
initiate biosynthesis. K can be directly related to receptor occupancy. The
index n defines the steepness of the Hill function when K = c R 1 I and usually
takes between 1 and 5. Hence when n = 1 aggrecan production is largely dose
dependent, whereas n = 5 corresponds to threshold or “on-off” dependency of
aggrecan production with an increase in c R 1 I . Finally, β is the IGF-I mediated
maximum production rate.