Biomedical Engineering Reference
In-Depth Information
Table 12.1
Summary of IA inception studies. The spatial distributions of various hemodynamic
indices have been compared with known locations of aneurysm formation. It can be seen that
strong correlations are always observed in such studies. However, inconsistencies in conclusions
are present and the study sizes are always small
Study
CFD index
Positive correlation
Mantha et al. (
2006
)
Low WSS, AFI
3
/
3
Shimogonya et al. (
2009
)
GON
1
/
1
Ford et al. (
2009
)
GON
4
/
5
Baek et al. (
2009
)
High WSS, High Pressure
2
/
2
Singh et al. (
2010
)
High WSS, High OSI
2
/
2
et al.,
2009
); elevated WSS and pressure (Baek et al.,
2009
); elevated WSS and os-
cillatory shear index (OSI) (Singh et al.,
2010
); the interested reader is referred to
the relevant articles for specifics of how to calculate these hemodynamic indices.
Given the disparates in findings on CFD inception studies to date, there is clearly
the need for a more comprehensive study: we consider a selection of 22 sidewall
IAs, propose a novel method to reconstruct the hypothetical geometry of the artery
without IA and analyze spatial distributions of hemodynamic stimuli on the healthy
vasculature in the specific locations that the IAs are known, a priori, to develop.
12.2.1 Methodology
We have developed a novel approach to reconstruct the hypothetical geometry of
the healthy artery prior to IA formation. Here we briefly outline the methodol-
ogy (see Fig.
12.1
for graphical illustration). Clinical imaging data depicting an
IA is segmented with the software suite @neufuse (developed for the European
project @neurIST,
www.aneurist.org
'Integrated Biomedical Informatics for the
Management of Cerebral Aneurysms', see Villa-Uriol et al.,
2011
). A skeleton
of the vasculature is created and the segment containing the IA is removed (see
Fig.
12.1
(b)). Given the position vectors of the center points of the upstream and
downstream boundaries (neighboring the aneurysm section),
c
0
and
c
1
, respectively,
and unit normal vectors to the boundaries
n
0
and
n
1
(see Fig.
12.1
(c)), a cubic curve
c
(t)
=
(a
1
j
t
j
,a
2
j
t
j
,a
3
j
t
j
)
:
i
=
1
,
2
,
3;
j
=
0
,
1
,
2
,
3;
t
∈[
0
,
1
]
is constructed such
that
c
(t
c
(t
c
(t
ˆ
ˆ
=
0
)
=
c
0
,
c
(t
=
1
)
=
c
1
,
=
0
)
=
κ
n
0
,
=
1
)
=
κ
n
1
,
(12.1)
where
denotes differentiation with respect to
t
and
κ
=|
c
1
−
c
0
|
. The 12 unknown
coefficients
a
ij
∈ R
are uniquely determined by the 12 boundary conditions given
by Eq. (
12.1
). A Frenet-Frame is then defined along the curve
c
,i.e.
c
(t)
T
(t)
T
(t)
=
,
N
(t)
=
,
B
(t)
=
T
(t)
×
N
(t).
(12.2)
c
(t)
|
T
(t)
|
|
|
