Biomedical Engineering Reference
In-Depth Information
hollow structures are formed as a consequence [
16
]. A more complex model, with
more parameters, is necessary to describe this phenomenon. This implies an exten-
sive experimental characterization. However, this hollow formation occurs in the
late stages of erosion, when molecular weight becomes greatly reduced. The mod-
els presented in the following section, to describe strength decrease and stress-strain
plot evolution during degradation are only valid for the initial phase of erosion, i.e.
for hydrolytic damage of about 50 %. Hence, these models neglect the hollow for-
mation effect, since this phenomenon may be neglected during the first 50 % of
strength loss, i.e. the mass loss and oligomer diffusion are neglected (as will be
showed in the following sections).
Some authors claim that the local raise of degradation rate can also be explained
by the local increase of hydrophilicity. The hydrophilicity involves the build-up of
acid and alcohol groups, much more hydrophilic than the initial ester group [
49
].
An increasing water equilibrium concentration with time can thus be expected. It is
quite simple to solve the problem, as Bellenger et al. [
4
] have shown, if it were con-
sidered, with Van Krevelen, that the water equilibrium concentration is an additive
function, thus,
w
=
b
+
an
t
, and:
dC
dt
=
dn
t
dt
=
kE(C
0
+
n
t
)(b
+
an
t
)
(15)
Solving Eq. (
15
), as demonstrated by Bellenger et al. [
4
], leads to:
C
0
1
aC
0
be
−
kE(b
−
aC
0
)t
b
−
n
r
=
aC
0
−
(16)
−
were
a
and
b
are material parameters. Accordingly to Bellenger et al. [
4
], this equa-
tion gives a good quantitative description of the auto-accelerated character of the
degradation. If the auto-accelerated character is not due to increasing hydrophilic-
ity, it is probably because its origin is in the hydrolysis mechanism. Alcohol groups
and especially acid groups coming from the first degradation steps can catalyze later
hydrolysis reactions.
7 Tuning Hydrolytic Rate According to Scaffold Requirements
To control the hydrolytic rate, in order to match the dimensioning requests during all
the healing process, the project designer can combine different materials with differ-
ent hydrolytic rates. A wide range of degradation times and mechanical properties
are possible, using different commercial available materials and varying dimensions
and 3D architecture. One possible approach is the composite concept, making use
of the broad range of material properties to construct a multilayer device, each layer
possessing its own degradation rate. The mixture law may also be applied to hy-
drolytic rate, assuming homogeneous degradation:
n
u
c
=
u
1
∗
V
1
+
u
2
∗
V
2
+···+
u
i
∗
V
i
+···+
u
n
∗
V
n
=
u
n
∗
V
n
(17)
i
=
1
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