Biomedical Engineering Reference
In-Depth Information
a
3
Cartilage spilt line
Cartilage
a
2
a
1
Bone
FIGURE 11.2
Application of orthotropic Conewise Linear Elasticity model [55] in the solid
phase of cartilage. Three preferred directions of material symmetry:
a
1
parallel
to the split line direction;
a
2
perpendicular to the split line direction; and
a
3
normal to the articular cartilage surface.
11.2.2.3
Model Geometry for Radial Solute Transport in
Cartilage under Unconfined Cyclic Compression
One common experimental method for testing cartilage is the unconfined com-
pression test [9,54,56,57] (as shown in Figure 11.3). Typically, a thin, cylin-
drical cartilage disc explant is obtained (to minimize inhomogeneities in car-
tilage properties) [57]. For experiments investigating the role of cyclic loading
on nutrient uptake, the cartilage disc is loaded between two impermeable
platens in a bathing solution containing IGF-I [58]. Under this configuration,
the radial expansion (
r
) caused by compression applied along the
z
direction
is unconstrained and fluid can either be exuded or imbibed across the outer
surface of the cartilage disc [57]. As the axial normal strain is homogeneous,
due to effectively frictionless platens the system is symmetrical about the z-
axis, as demonstrated below, the problem can be reduced to a one-dimensional
problem in the radial coordinate.
Due to symmetry, it can be assumed that
∂
()
/∂θ
= 0 and
u
θ
= 0. Thus,
u
r
=
u
r
(
r, t
)
,
r
=
∂u
r
∂t
,p
=
p
(
r, t
)
,
z
(
t
)=
∂u
z
I
=
c
I
(
r, t
)
(11.22)
∂z
,
where
r
and
z
are radial and axial coordinates, respectively, and
t
is time.
ε
z
is the axial strain due to the applied axial load, and is therefore assumed to
take a sinusoidal form,
ε
z
=
ε
0
2
[1
−
cos (2
πft
)]
(11.23)
where
ε
0
is the peak-to-peak strain amplitude and
f
is the frequency of the
axial strain.
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