Original Paper
Sum of the Curve Indices for Estimating the
Vascular Tortuousness of the
Internal Carotid Artery
Jae Kyun Kim, MD2, Jin Woo Choi, MD, Byung Se Choi, MD, Tae Il Kim, BS,
Sun Moon Whang, BS, Sang Joon Kim, MD, Dae Chul Suh, MD
Purpose: Most technical difficulties in intracranial stenting are derived from the vascular resistance
caused by the severe tortuousness of intracranial arteries. The purpose of this study was to develop
a practical method for measuring vascular tortuousness so that it would be possible to predict technical difficulties requiring further technical support.
Materials and Methods: We developed a best-fit circle metrics which made measurement of vascular tortuousness feasible, which was called “curve index (CI)”. We compared the curve index in 56 consecutive patients who underwent M1 stenting for symptomatic severe stenosis. The difference in the
CI between the successful and the aborted groups was statistically compared by using the MannWhitney U test. ROC curve analysis was performed to evaluate the diagnostic performance of the
best-fit circle metrics.
Results: There was no statistically significant difference between the successful and the aborted cases in
the CIs of each curve segment. However, the sum of all CIs of the aborted group was significantly
larger (3.49) than that of the successful group (2.53) (p = 0.013). On ROC curve analysis, the area
under the curve was 0.806. When we took the cut-off value to be 3, the sensitivity was 75% and the
specificity 85%.
Conclusion: We developed a practical method for measuring the CI of vessel curves in order to estimate
the tortuousness of the internal carotid artery. A CI less than 3, therefore, indicates a favorable vascular curvature for the intracranial stenting procedure. A vessel having a higher curve index was
more likely to be aborted.
Key Words : Vascular tortuousness; Internal carotid artery; Intracranial stent
Departments of Radiology and Research Institute of Radiology, Asan Medical Center, University of Ulsan, College of Medicine
Department of Radiology, Seoul Veterans Hospital
Received April 9, 2009;
accepted after revision July 16, 2009.
Correspondence to: Dae Chul Suh, MD, Department of Radiology, Asan Medical Center, University of Ulsan, College of Medicine, 388-1
Pungnap2-dong, Songpa-gu, Seoul, 138-736, Korea
Tel. 82-2-3010-4366 Fax. 82-2-476-0090
E-mail: [email protected]
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Jae Kyun Kim, et al.
Intracranial atherosclerosis is a major cause of an
ischemic stroke which accounts for 8-15% of strokes
caused by cerebral atherosclerosis, depending on the
population studied (1, 2). The rate of stroke ipsilateral
to the stenosis is 11% at one year and 14% at two years
despite the use of either warfarin or aspirin and
possible vascular risk factor modification (3-5). There
is an increasing tendency to use intracranial angioplasty
with/without stenting as an option to medical treatment
for revascularization of severe symptomatic intracranial stenosis (6-10).
Technical difficulties while performing intracranial
revascularization procedures are associated with
tortuousness of the cerebral vessels. Most difficulties
arise from vascular tortuousness, in other words, the
bending, kinking, twisting or looping of internal carotid
arteries. Therefore, it is crucial to measure and evaluate
vascular tortuousness before the revascularization
procedure in order to predict technical difficulties and
to be able to perform the procedure successfully using
other supportive methods (11). Although several
tortuousness metrics has been developed, they are too
complicated to use in routine clinical practice and also
require specialized software (12-14). In this study, we
propose a practical method for measuring vascular
tortuousness, which can be used in daily practice and
was tested in the patient group that underwent intracranial M1 stenting as the most distal and difficult
revascularization procedure; we also developed practical guidelines to predict the difficult tortuousness in
revascularization procedures.
MATERIALS AND METHODS
Measurement of Tortuousness
This study was approved by the institutional review
board. We adopted the idea of “the radius of
curvature”, i.e. a fluent curve has a larger radius of
Fig. 1. (A) Curve index (CI) means the
ratio between the radius of the best-fit
circle and diameter of the vessel.
Therefore, the sharper the curve is, the
larger the value of the corresponding
curve index is. If diameter of the vessel
is equal to the radius of curvature, CI is
equal to 1 (B). In case of CI being larger
than 1, diameter of the vessel is larger
than the radius of curve (C) and CI
being smaller than 1, diameter of the
vessel is smaller than the radius of
curve (D).
A
B
C
D
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Sum of the Curve Indices for Estimating the Vascular Tortuousness of the Internal Carotid Artery
curvature and a sharper curve has a smaller one. A
succession of circles that converge to kiss a curve are
said to be osculating circles (15). The word
“osculate”means “to kiss.”A minimum of three points
on the curve are needed to determine an osculating
circle. As the three points move closer together and
converge at a single point, the radius of the circle
becomes the normal to the tangent at that point. As
curves and circles have finite thickness in the real
world, it is impossible to draw an osculating circle
precisely in clinical practice.
Therefore, we used a best-fit circle that is a simplified
form of an osculating circle. Initially, a circle was
drawn at the concave aspect of a given curve. If the
circle’s edge was inside the curve’s edge, a larger circle
was drawn. This process was repeated until the circle’s
edge was outside the curve’s edge. Best-fit circles
could be drawn manually either on PACS (Picture
Archiving and Communication System) or using any
imaging software. Finally, the radius of the best-fit
circle was measured; the smaller the radius, the sharper
the curve and vice versa. As the magnification factor of
angiographs differed from patient-to-patient, the value
of the radius had to be standardized by dividing the
radius by the reference diameter of the vessel. As a
matter of convenience, we took an inverse of the
calculated value and called it the “curve index”or
simply Curve index (CI). If the value of the CI equals
0.5, it indicates that the diameter of the vessel is half
the radius of curvature (Fig .1).
When the guiding catheter is in the proximal cervical
segment of the internal carotid artery (ICA), the
number of curves between the guiding catheter tip and
the target vessel (M1) was determined to be five, i.e.
the cervical segment (in case there is a curve), cervico-
petrous junction, petro-cavernous junction, C4-5
(vertical-horizontal) junction, and the carotid genu. In
order to draw a best-fit curve, we chose a plane (anterioposterior view or lateral view) in which the vessel
curve angle was best demonstrated (Fig. 2). The anteroposterior view was suitable for assessing the cervicopetrous and petro-cavernous junctions. The lateral view
was suitable for assessing the cavernous siphon
consisting of C4-5 and carotid genu. When the
guiding catheter is in the petrous segment of the ICA,
there are three calculated curves as we assume that the
introducing devices inside the guiding catheter have
negligible resistance against the guiding catheter wall
(Fig. 3). Therefore, we considered the curves distal to
the tip of the guiding catheter as meaningful and the
curves proximal to the tip of the guiding catheter to
have zero CI. After all curve indices were obtained for
a given vessel, they were totaled.
Application in Patients Who Underwent M1
Stenting
We chose the M1 stenting procedure as the most
distal revascularization procedure which meets the
difficulties of the tortuous vessel angle of the cerebral
Table 1. Number of Internal Carotid Artery Curves Distal to the
Tip of the Guiding Catheter
No. of Curves
Succeeded (n=50)
Aborted (n=6)
1
2
3
4
5
01
03
18
21
07
0
0
1
3
2
Total
50
6
Fig. 2. There are four representative
curves in the carotid artery included in
the calculation of the curvature. (A)
Schematic and real drawings of two
curves of cervicopetrosal and petrocavernous segments are measured on
anteroposterior view. (B) Schematic and
realing drawings of two cavernous
segment curves are measured on the
lateral views. After all curve indexes for
a given vessel were obtained, they were
summed. In this case of success, sum
of all curve indices (CIs) is equal to CI1 +
CI 2 + CI 3 + CI 4 = 1.19 + 0.78 + 0.5 +
1.13 = 3.6. CI more than 3 means an
unfavorable vascular curvature for the
intracranial stenting procedure.
A
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B
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Jae Kyun Kim, et al.
vasculature. We compared the curve index in 56
consecutive patients who underwent M1 stenting for
symptomatic severe, i.e. greater than 70%, M1 stenosis
between October, 2003 and February, 2007. The
procedure was performed under the supervision of an
experienced interventional neuroradiologist (Suh, DC)
in a single large referral center. The stenting was
successful in 51 patients and was aborted in five
patients due to the vessel curve resistance. CI was
measured from the tip location of guiding catheter
which was retrospectively identified on the angiogram
at the time of the procedure. The patients’ age range
was 34 to 82 years (mean 57 years). The difference in
the CI between the successful and the aborted groups
was statistically compared using the Mann-Whitney U
test. Receiver characteristic operation curve analysis
Table 2. Curve Indices of the Internal Carotid Artery Curves
Curve Index
(CI)
Succeed
(n = 50)
Aborted
(n = 6)
CI1
CI2
CI3
CI4
CI5
*0.85
*0.61
*0.61
*0.81
0.80 (n = 9)
1.03
0.89
0.52
0.91
1.06 (n = 2)
0.145
0.041
0.130
0.329
0.727
Sum of All CIs
3.0
3.7
0.061
�
was performed to evaluate the diagnostic performance
of the best-fit circle metrics.
RESULTS
Table 1 shows the mean values of the CIs for each
curve of the ICA. There was no statistically significant
difference between the successful and the aborted cases
in the CIs of each curve segment (Table 2). However,
the sum of all CIs of the aborted group was significantly larger (3.49) than that of the successful group
(2.53) (p = 0.013).
Because the sum of the CI was calculated from the
curves from the guiding catheter tip to the target
vessels, advancement of the guiding catheter could
reduce the number of vessel curves. The number of
Table 3. Curve Indices of the Internal Carotid Artery Curves
Distal to the Tip of the Guiding Catheter
�
P-values
Note. - *Mean value of curve index. Mann-Whitney U test
Curve Index
(CI)
Succeed
(n = 50)
Aborted
(n = 6)
CI1
CI2
CI3
CI4
CI5
*0.85 (n = 50)
*0.60 (n = 49)
*0.61 (n = 46)
*0.78 (n = 28)
0.81 (n = 7)*
1.03 (n = 6)
0.89 (n = 6)
0.52 (n = 6)
0.84 (n = 5)
1.06 (n = 2)
0.145
0.034
0.121
0.478
0.667
Sum of All CIs
2.53
3.49
0.013
�
P-values
�
Note.- *Mean value of curve index. Mann-Whitney U test
A
B
C
Fig. 3. The right internal carotid angiogram shows a focal severe stenosis in the right M1 (A). Note guiding catheter tip in the petrous
segment to eliminate a considerable curve index from the almost 360 degree turning of the cervical ICA curvature (B). Because
curvature proximal to the guiding catheter can be ignored, sum of all curve indexes was much less than 3. (C) Final angiogram was
obtained after stenting procedure which was done without significant vessel resistance.
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Sum of the Curve Indices for Estimating the Vascular Tortuousness of the Internal Carotid Artery
counted vessel curve was greater in the aborted group
than in the successful group (Table 3). As this indicates
that further navigation and advancement of the guiding
catheter into the distal vessels would reduce the CI, it
raised the possibility of successful navigation (Fig. 3).
On receiver characteristic operation curve analysis, the
area under the curve was 0.806. When we took the cutoff value to be 3, which indicated the best diagnostic
performance, the sensitivity was 75% and the
specificity 85%.
DISCUSSION
The tortuousness of the ICA is an important factor in
the revascularization of intracranial stenosis. Excessive
tortuousness may cause difficulty in gaining access to
the target vessel, specifically the M1 segment. In this
study, we proposed a simple and useful method for
measuring and evaluating the vascular tortuousness of
the ICA based on the principle that the overall
tortuousness depends on the severity of each curve (CI)
as well as the number of curves. The sum of the curve
indices represents the overall difficulties in overcoming
the tortuousness of the carotid curves.
The simple way to minimize the curve index is to
introduce the guiding catheter beyond the cervical
segment of the ICA, thereby reducing the number of
curves. When we used a single-guiding catheter, the
most common reason the device could not pass the
cavernous segment was the pulling-back of the guiding
catheter caused by the resistance between the device
and the vessel wall of the cavernous ICA. To achieve a
higher position of the guiding catheter, stable guiding
catheter support is the key. Therefore, a double-guiding
catheter technique is another option for securing the
distal-guiding catheter tip in a stable position.
Limitation of our study is that AP view and lateral
view are not true tangential planes. However, angle
between coronal tangential plane and carotid canal is
relatively constant (25~35 degrees) in most patients,
AP view is an appropriate plane for assessment of
cervico-petrous junction and petro-cavernous junction.
There is no serious problem for measurement of the
angle between C4 and C5 (vertical-horizontal)
segments on lateral view because lateral view is not so
different with the true tangential plane in most patients.
It is appropriate to use lateral view for assessment of
the angle of carotid genu because there is no single
tangential plane for carotid genu.
Neurointervention 4, August 2009
CONCLUSION
We developed a practical method for measuring the
CI of vessel curves in order to estimate the tortuousness of the ICA. A CI less than 3, therefore, indicates a
favorable vascular curvature for the intracranial
stenting procedure. A possible way to improve the
technical success of the stenting procedure is to reduce
the CI by introducing a guiding catheter beyond the
proximal curves, i.e. the cervicopetrous junction, or by
supporting the guiding catheter by using a doubleguiding catheter technique. Our method may be practical for assessing and overcoming the technical difficulties of the revascularization procedure of the distal
cerebral vasculature.
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tortuous vessels. AJNR Am J Neuroradiol 2005;26:1375-1380
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신경중재치료의학 2009;4:101-106
1
울산대학교 의과대학 서울아산병원 영상의학과
2
서울보훈병원 영상의학과
두개내동맥의 스텐트삽입술에 있어서 대부분의 기술적인 어려움은 혈관의 심한 굽음에 의한 저항에서 비롯된
다. 본 연구에서는 혈관의 굽은 정도를 측정할 수 있는 실용적인 방법을 개발하여 기술적인 어려움을 예측하고자
하였다. 혈관의 굽은 부위에 최적원을 그리고 굽은 정도를 곡선지표 (Curve Index, 이하 CI)라 명명하였다. 유증
상의 심한 M1 분절협착으로 스텐트삽입술을 시행한 56명을 대상으로 곡선지표를 비교하였다. 스텐트삽입술을 성
공한 군과 실패한 군에서 각 분절의 곡선지표는 차이를 보이지 않았으나 곡선지표의 합은 성공한 군 (CI = 2.53)
보다 실패한 군 (CI = 3.49)에서 통계적으로 유의하게 더 높았다 (p = 0.013). ROC 분석에서 곡선내면적(AUC)
은 0.806이었으며 기준점을 3으로 할 때 민감도와 특이도는 각각 75%, 85% 이었다. 이상과 같이 곡선지표의 합
을 이용해서 혈관의 굽은 정도를 성공적으로 평가할 수 있으며 곡선지표의 합이 3이 넘을 때는 시술이 실패할 가
능성이 많으므로 기술적인 보완을 강구해야 할 것이다.
Key Words : Vascular tortuousness; Internal carotid artery; Intracranial stent
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