Biomedical Engineering Reference
In-Depth Information
Fig. 6.7.
Images of medial collagen in a rabbit carotid artery wall taken with the UA-MPM system
under circumferential stretches of 1.4 (left) and 2.0 (right) and analyzed with a custom MATLAB
program to give tortuosity values of 1.1 and 1.0, respectively
Fig. 6.8.
Results for sample 2 of rabbit artery under uniaxial loading showing (a) Mean tortuosity
(
, (error bars = standard deviation) and (b) Stress
versus stretch as well as slope of stress versus stretch
L
/
L
0
)
as a function of circumferential stretch,
λ
Collagen fibre distribution
A custom program was used to evaluated fibre angle distribution using a method in-
troduced by Courtney for tissue-engineered constructs [23]. To avoid artifacts from
fibre waviness, collagen fibre orientation was measured in a configuration (stretch
state) with little fibre crimp. The orientation distribution of fictitious uncrimped fi-
bres in
κ
(
t
)
through an affine transformation
was obtained using a pull back operation. Consistent with previously reported re-
sults, we found the distribution of projected fibre orientations in the media to be
approximately symmetrically distributed about the circumferential direction.
Therefore, as in [35], a single mean reference direction
a
0
was used, aligned with
the circumferential direction. In this way, material constants
κ
0
that are related to the actual fibres in
,
ρ
(
Θ
)
λ
a
0
,and
were
a
obtained from images of the collagen fibres. The parameters
H
0
and
could then be
calculated from these values using (6.40).
C
0
was calculated from the applied tissue
stretch and used to obtain
κ
λ
t
from (6.40). The material constants
η
,
η
,
γ
aniso
were determined using nonlinear regression analysis of the fit of (6.40) to the mea-
sured data, Fig. 6.5. Data fit the conic splay model well for the illustrative sample
(Fig. 6.5), with
R
2
iso
ansio
=
0
.
96. Material parameters were obtained as
η
iso
= 196 kPa,
η
