Biomedical Engineering Reference
In-Depth Information
One advantage of the static coupling strategy consists in the fact that different
calls to the microscale model, i.e.
micro
=
⇒
P
, are inde-
pendent and thus can be performed in parallel on CPU or GPU clusters. By this way,
the computational time needed for the miscroscale simulations is considerably re-
duced. Furthermore, the cost of the miscroscale model does not affect the macroscale
computations, that could be extended to a more realistic three-dimensional setting
without compromising the applicability of the entire model.
F
(
ϒ
p
)
D
(
F
(
ϒ
p
))
for
p
=
1
,...,
11.5 Computational analysis of polymer degradation
11.5.1 Computational results of the microscale model
The diffusion of water in PLA matrices is modelled considering monodisperse sys-
tems with different level of PLA degradation and swelling (i.e., water content). We
generated 30 different molecular models of PLA matrices, characterized by differ-
ent degree of polymerization (monodisperse systems with 600, 300, 150, 75, 30 and
1 monomers per chain, respectively) (see Fig. 11.2) and different degree of swelling
(with 2 %, 20 %, 40 %, 60 % and 80 % of water). Additionally, we studied a system
containing pure water for validating reasons.
As a preliminary validation of the atomistic models we analyze the density of
the quasi-dry PLA matrices, see Table 11.2, showing that the predicted density
(
cm
3
) is close to experimental density of PLA (1
cm
3
). On the other
1
.
18
g
/
.
24
g
/
cm
3
) well matches the wa-
ter density. For the systems with intermediate water content the density decrease
linearly from the density of quasi-dry PLA to the density of pure water.
We then proceed with the calculation of the water diffusivity in PLA matrices
by means of in silico experiments run for a simulated time of 7 ns. As a validation
of the approach we calculated the self diffusion coefficient of water, obtaining a
value of 42
hand, the final density of the pure water systems (0
.
98
g
/
10
−
6
cm
2
10
−
6
cm
2
s
). The
analysis of the water diffusivity values in PLA (see Table 11.3) shows that the dif-
fusivity coefficient spans two orders of magnitude (from 10
−
7
.
0
·
/
s
, close to the experimental value (22
.
7
·
/
to 10
−
5
cm
2
s
)and
is mainly affected by the water content. Indeed, the diffusion coefficient increases
/
Fig. 11.2.
Sketch of the quasi-dry PLA matrices (2 % water) studied in this work, from non de-
graded matrix (A) to partially degraded (B and C) and highly degraded (D)
