Biomedical Engineering Reference
In-Depth Information
0.1 Hz results in the greatest fluid velocity and the mechanical stimulation is
localized to the periphery domain. For the intermediate frequency of 0.01 Hz,
the region experiencing mechanical stimulation extends into the inner region
of the domain, whereas a low frequency at 0.001 Hz there was no stimulatory
effect.
11.5.2.5
Aggrecan Molecule Transport in Cartilage
Newly synthesized matrix molecules are initially mobile after secretion by
chondrocytes. They are then transported into the surrounding matrix, and
can become either bound to hyaluronan as immobile proteoglycan aggregates,
be degraded, or potentially be released from the cartilage matrix [20] into the
synovial fluid. The total matrix aggrecan concentration in cartilage (
c
a
)is
the sum of chondrocyte-derived mobile component transported in fluid phase
(
c
a
); “immobilized” proteoglycan component effectively “bound” within ECM
(
c
a
), and finally the mobile component degraded from the ECM structure (
c
a
)
(which may escape from the cartilage altogether). Therefore the total aggrecan
concentration is given by
c
a
=
c
a
+
c
a
+
c
a
(11.81)
The transport equation of each component is represented as
∇•
−
c
a
+
K
a
v
f
c
a
=
s
p
−
dc
a
dt
s
b
c
a
+
K
d
D
a
∇
(11.82)
dc
a
dt
=
s
b
c
a
−
s
d
c
a
(11.83)
∇•
−
c
a
+
K
a
v
f
c
a
=
s
d
c
a
dc
a
∂t
+
K
d
D
a
∇
(11.84)
where
D
a
is diffusion coecient of free aggrecan and
s
b
and
s
d
are aggrecan
binding and degradation rates, respectively, which are obtained from experi-
mental studies [20,80].
K
d
and
K
a
are the dimensionless tortuosity and hin-
drance coecient, respectively, and their values depend on molecular size and
shape of the molecule being transported through the ECM. Newly synthesized
mobile aggrecans are large molecules with very small diffusion coecients in
the range of 10
−
10
-10
−
9
cm
2
/s [88], and so cartilage ECM may decrease the
mobility of macromolecules and limit their transport. For this reason hindered
advective transport of these matrix molecules is adopted.
Equations (11.82)-(11.84) can be presented in radial coordinates as
∂t
− φ
f
K
d
D
a
∂
2
c
a
+
K
a
φ
f
v
r
−
∂c
a
∂r
φ
f
∂c
a
∂c
a
∂r
+
1
r
κ
r
∂p
∂r
∂r
2
=
s
p
0
+
βc
R
1
I
K
n
+
c
R
1
I
+
λ
1
φ
f
c
a
+(1
φ
f
)
c
a
−
s
b
φ
f
c
a
−
−
(11.85)
c
a
max
Search WWH ::
Custom Search