Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5835_Библиотеки_им_академика_М_И_Перельмана.pdf
volume. A typical plaque having 10 to 30 slices requires approximately 15 minutes
of measuring time.
The vessel wall volume technique, which is commonly used for analyzing MR
images, is an alternative method for quantifying disease in the carotid arteries. In
this approach, the lumen (blood–intima boundary) and the vessel wall
(intima–adventia boundary) are segmented in each slice. The area inside the lumen
boundary is subtracted from the area inside the vessel wall boundary. Sequential
areas are averaged and multiplied by the ISD to give the incremental vessel wall vol-
ume. The summation of incremental volumes provides a measure of the total vessel
wall volume (Figure 3.6).
3.3.2 Studies of Plaque Volume
During the past few years, a number of investigators have explored the use of 3-D
US imaging in measurements of carotid plaque volume [15, 44–47]. These in vivo
and in vitro investigations have also reported on the variability of plaque volume
measurements for plaques ranging in size and geometry. Delcker et al. [45–49] have
measured carotid plaque volumes ranging from 2 to 200 mm
3
. The intraobserver
and interobserver variability for the full series of plaque sizes were found to be 2.8%
and 3.8%, respectively, demonstrating that 3-D US imaging can be used to obtain
reproducible measurements of carotid plaque volumes [36, 45, 49]. Delcker et al.
have further demonstrated that in vivo measurements of carotid plaques have bene
-
74 3-D US Imaging of the Carotid Arteries
Figure 3.4 Four views of the 3-D carotid ultrasound image shown in Figure 3.3. Each panel has
been volume rendered to display the appearance of the plaque in the common carotid artery. This
approach enhances the appearance of the plaque as image speckle is suppressed.
fitted from ECG-triggered data acquisition. The intraobserver variability, the
interobserver variability, and the follow-up variability were shown to decrease sig-
nificantly when compared to the non-ECG-triggered measurements [49]. Palombo
et al. [47] measured carotid plaque volume ranging from 7 to 450 mm
3
and
obtained reliability coefficients that were close to 1 for this in vivo intraobserver
and interobserver study.
The monitoring of carotid plaque progression and regression requires accurate
and reproducible techniques to measure and analyze carotid plaque volume and
morphology. Thus, reproducible segmentations of the vessel lumen, plaque surface,
and carotid wall borders are required. Although a number of studies have demon
-
strated the potential utility of 3-D US, few have attempted to quantify the accuracy
3.3 Measurement of Plaque Volume 75
(d)
(c)
(b)
(a)
(e)
Figure 3.5 Steps used in measurement of total plaque volume from 3-D US images. (a) First, the
3-D image is “sliced” to obtain a transverse view. (b, c) Using a mouse-driven cross-haired cursor,
the plaque is outline in successive image “slices” until all the plaques have been traversed. (d) The
vessel can be sliced to reveal a longitudinal view with the outlines of the plaques. (e) After outlin-
ing all of the plaques, the total volume can be calculated and a mesh fitted to provides a view of
the plaque surface together with the boundary of the vessel.
of these measurements by determining the actual volume of each plaque. In addi-
tion, the variability in the measurement of plaque volume has generally been
reported over a large range of plaque volumes. In the analysis of plaque progression,
it is important to understand the relationship between plaque volume and plaque
volume measurement variability so that plaque changes at different stages of plaque
progression can be interpreted appropriately. In the following sections we review
76 3-D US Imaging of the Carotid Arteries
(e)
(c)
(d)
(a) (b)
Figure 3.6 Steps used in measurement of vessel wall plus plaque volume from 3-D US images.
(a) First, the 3-D image is “sliced” to obtain a transverse view. (b, c) Using a mouse-driven
cross-haired cursor, the vessel boundary and the lumen boundary plaque are outlined separately in
successive image “slices” until all the slices have been traversed (typically 1.5 cm above and below
the carotid bifurcation). (d) The vessel can be sliced to reveal a longitudinal view with the outlines
and correct any errors. (e) After outlining has been completed, the vessel wall plus plaque volume
can be calculated and a mesh fitted to provide a view of the vessel and the lumen boundaries.
both the accuracy and the variability of plaque measurement as a function of plaque
volume.
3.3.3 The Effects of Interslice Distance
The value of the ISD between the slices of the acquired 3-D US images will affect the
measurement of the plaque volume. If the value of the ISD is chosen to be small (in
order to obtain results that are accurate), then the quantification of the volume pro-
cedure will be time consuming. If the value of ISD is chosen to be large (in order to
reduce the number of analyzed slices and to reduce the time of measurement), then
inaccurate and variable results may occur. Thus, we investigated the effects of the
ISD on the relative accuracy and variability of the plaque volume measurement by
measuring the volume of five plaques, which ranged in size from 42.2 to 604.1 mm
3
.
These plaques were measured five times using nine separate ISDs, which ranged
from 1.0 to 5.0 mm in increments of 0.5 mm. The results are shown in Figure 3.7.
These results show that the relative plaque volume (normalized to measurements
with an ISD of 1 mm) had remained unchanged for ISDs between 1.0 and 3.0 mm
and had decreased to 0.83 mm for larger ISDs. Thus, the plaque volume will be sys-
tematically underestimated for ISDs greater than 3.0 mm. The error bars in Figure
3.7 show that the variability of the plaque volume measurement increases as the ISD
increases. The coefficient of variation (i.e., the SD divided by the mean), which
increased as the ISD increased, was found to be approximately 10% for ISDs of 3
mm or less. Based on these results, we had chosen an ISD of 1 mm for quantifying
plaque volume.
3.3.4 The Accuracy of Plaque Volume Measurements
To ascertain the accuracy of the plaque volume measurements, the volume of the
measured plaque mustbe comparedto theactual volume of the plaque. Because 3-D
US-based measurements ofcarotid plaques in vivo cannot be compared to theactual
plaque volume obtained by any other method, an in vitro study using test phantoms
with known “plaque” volumes was conducted by Landry and Fenster [50]. In this in
3.3 Measurement of Plaque Volume 77
0.6
0.7
0.8
0.9
1
1
1.1
1.2
1.5
2
2.5
Inter-slice distance (mm)
Relative mean plaque volume
3 3.5
4
4.5 5
Figure 3.7 Relative mean plaque volume as a function of ISD for five plaque volumes measured
by a single observer five times using each ISD investigated. Relative volume is constant for ISDs of
1.0 to 3.0 mm, but then decreases to 0.83 mm for an ISD of 5.0 mm. Plaque volume measure
-
ment variability is shown by the error bars that represent ±1 SD. (From: [51]. © 2004 American
Heart Association. Reprinted with permission.)
vitro study, the vascular phantoms were made from blocks of colloidal agar that
contained Sigmacell to scatter the ultrasound beam and to produce the typical ultra-
sound image speckle; cylindrical channels were used to simulate the vessels. The
agar gel was sliced into “plaques” of varying height and length in order to produce
several simulated hypoechoic plaques. These “plaques” were then inserted into the
cylindrical channels, imaged with 3-D US, and measured.
The results from this study are shown in Figure 3.8. The measurement error of
the plaque volume is plotted as a function of plaque volume, which ranges from 68.2
to 285.5 mm
3
. The inserted image is a 3-D US sample of the simulated plaque in the
vascular phantom. The mean error for the measurement of the plaque volume was
found to be 3.1% ± 0.9%. The coefficient of variation (i.e., the SD divided by the
mean) in the measurement of the plaque volume was found to be 4.0% ± 1.0% and
5.1% ± 1.4% for intraobserver and interobserver measurements, respectively. Using
the manual planimetry method, Landry and Fenster have developed a theoretical
description for the variance in the measurement of plaque volume [50]. The
root-mean-square (RMS) difference between the experimentally and the theoreti-
cally determined values of the coefficient of variation for plaque volume
measurement was found to be 9%.
3.3.5 Variability of Plaque Volume Measurements
The variability of plaque volume measurements has been reported by a number of
investigators as an average that has been calculated over a wide range of plaque vol-
78 3-D US Imaging of the Carotid Arteries
0 50 100 150 200 250
300
0
1
2
3
4
5
6
|− |/VVV(%)
ama
V (mm )
a
3
(b)
(a)
Figure 3.8 (a) The error in the simulated plaque volume measurement plotted as the absolute
percent difference between the actual (V
a
) and measured (V
m
) plaque volumes as a function of the
average actual volume for each plaque. The error bars represent ±1 SD. (b) A longitudinal view
of the 3-D image of the simulated vessel and plaque sliced to reveal the simulated vessel (black)
and plaque. (From: [50]. © 2002 American Association of Physicists in Medicine. Reprinted with
permission.)
umes; however, it is also important to assess the effect of plaque volume on the vari-
ability in the measurement of plaque volume. To examine and determine this effect,
we conducted a multiple observer study, which determined the intraobserver and
interobserver variability in the measurement of plaque volume. Each of the five
observers measured the volume of 40 carotid plaques five times during five different
sessions using an ISD of 1.0 mm. Using a 3-D mechanical scanning approach, we
imaged the carotid plaques from a number of human subjects (23 males and 17
females with an average age of 73.8 ± 6.2 years) who were patients at the Premature
Atherosclerosis Clinic and the Stroke Prevention Clinic (London Health Science
Centre, University Campus, London, Ontario, Canada). The volume of the plaques
ranged from 37.4 to 604.1 mm
3
.
Table 3.1 and Figure 3.9 show a summary of the results obtained using Analysis
of Variance (ANOVA) [52, 53]. Table 3.1 lists the results for the entire set of data as
well as for the five subsets (a, b, c, d, e) consisting of seven to eight plaques, which
were grouped together by volume.
For the smallest volumes of plaques, which range from 37.4 to 89.5 mm
3
, Table
3.1 shows the interstandard and intrastandard error of measurement (SEM
i
)tobe
13.1% ± 1.8% and 12.5% ± 1.9%, respectively (subset a). For the largest volumes
of plaques, which range from 519.4 to 604.1 mm
3
(subset e), the SEM
inter
and
SEM
intra
were found to be 4.3% ± 1.0% and 3.9% ± 1.3%, respectively. Figure 3.9
not only shows this effect but also shows that the coefficient of variation in the
intraobserver measurement of the plaque volume decreases as the plaque volume
increases. For the entire range of plaque volumes measured in this study (37.4 to
604.1 mm
3
), we determined the intraobserver coefficient of variation to be 19.2%
and 1.9%, respectively. For the same range of plaque volumes, we determined the
range of the interobserver coefficient of variation to be from 24.1% to 2.2%.
3.3.6 Automated Segmentation of Plaques from 3-D US Images
The manual planimetry method for measuring plaque volume requires that an oper-
ator: (1) “cut” into a 3-D US image, (2) orient the revealed plane appropriately, and
(3) outline the plaque surface manually. To obtain the volume of the complete
plaque, the operator must “cut” further into the volume and repeat the process until
3.3 Measurement of Plaque Volume 79
Table 3.1 Summary of the ANOVA Results of Study in Which
the Volumes of 40 Plaques Were Repeatedly Measured by Five
Observers
Plaque Subset Mean V (mm
3
) SEM
inter
/V (%) SEM
intra
/V (%)
a 65.4 13.1 12.5
b 130.5 6.8 7.0
c 247.4 4.9 4.9
d 426.0 5.5 4.2
e 560.6 4.3 3.9
Global data 276.3 6.9 6.5
The plaques have been grouped in five subsets, and the mean of each subset tabu
-
lated. The interobserver and intraobserver coefficient of variation (standard error
of measurement divided by the mean) has been tabulated.
Source: [51].
the complete plaque is traversed. This approach for manually outlining the plaque is
not only arduous but also time consuming. Substantial experience is needed by an
operator in order to obtain reasonable results.
We have developed an efficient semiautomated segmentation algorithm that is
based on deformable models that require minimal user interaction and processing
time to segment the boundary of plaques [54–57]. Our approach is based on a
deformable model that defines a boundary as a series of vertices connected by a set
of vectors, which produces a 3-D mesh. This structure allows for the modeling of
forces between the nodes of the mesh and the external forces acting on the mesh,
which are based on the image properties (e.g., the image gradients found at the
lumen boundary). Using this model, we can calculate the forces at each vertex,
which is moved iteratively until the values of the forces acting on the vertices are
zero.
The algorithm contains three of the following major steps: (1) the placement of
the initial deformable balloon model (i.e., a 3-D mesh composed of triangles) inside
the lumen; (2) the inflation of the model toward the plaque and vessel surface; and
(3) the automatic localization of the plaque and vessel surface. When equilibrium is
reached (under the influence of inflation forces, internal forces, and image forces),
the model approximately represents the shape of the surface. Because the surface of
the plaque may not be smoothand uniform, wedeform themesh further byusing the
local image-based forces to localize the surface of the plaque. Equations (3.1) and
(3.2) describe the dynamics of the model and the forces acting on the model. Equa-
tion (3.1) defines the motion for the ith vertex of the mesh:
() ()
()
()
()
′+ =xt gxt fxt
ii i
(3.1)
80 3-D US Imaging of the Carotid Arteries
0
0 100
V (mm )
3
200
300
400 500 600 700
5
10
15
20
25
σ /(%)V
v
Figure 3.9 The results of the ANOVA analysis of the repeated measurements of 40 plaques made
by five observers. The results are plotted as the intraobserver coefficient of variation (standard devi-
ation divided by the mean plaque volume), σ
v
/V, as a function of mean plaque volume, V (dia-
monds). The five plaque volumes measured in the repeat 3-D US scan study are plotted as open
diamonds. The error bars represent ±1 SD. (From: [51]. © 2004 American Heart Association.
Reprinted with permission.)
The position and velocity of the vertex are given by x
i
(t) and
′
xt
i
()
, respectively.
The resultant surface tension at the vertex and the “driving” force are given by
g(x
i
(t)) and f(x
i
(t)), respectively. Equilibrium is reached when
′
xt
i
()
becomes zero.
The equilibrium position of each vertex, and hence the final shape of the model,
is obtained by iteratively updating the variable of time in (3.1) by Δt. Once the sur-
face of the plaque has been segmented, an image-based force replaces the inflation
force. The image force causes the mesh to fit the fine details of the plaque. A 3-D
potential function, P, is constructed from the image data, which attracts the model
to the 3-D gradients at the surface of the plaque:
()
()
[]
Px t G I
i
=∇ +1
σ
ε*
(3.2)
where G
σ
is a 3-D Gaussian smoothing kernel of width σ, and ε is a constant that
prevents the denominator of (3.2) from dividing by zero. The minima of the poten-
tial function coincide with the plaque surface. The potential function produces a
force field, which is used to deform the model as f(x
i
(t) =−k P(x
i
(t). The value of k,
which must be optimized so that the mesh will conform to the surface of the plaque,
is an adjustable term that controls the strength of the force. In addition, the surface
tension of the mesh must be also chosen appropriately. If the model is too stiff, then
it will not deform into small ulcerations, but if it is too compliant, then the model
may extend into echolucent regions.
Figure 3.10 shows the results of segmentation using a 3-D image of a patient’s
carotid arteries with plaque. The segmentation required only about 10 seconds to
generate the lumen surface of the arteries. The mean separation between manual
segmentation and semiautomated (algorithm) segmentation was 0.35 mm with a
standard deviation of 0.25 mm [56].
3.3 Measurement of Plaque Volume 81
0.61
0
σ(mm)
(b)
(a)
Figure 3.10 Analysis results of the 3-D carotid segmentation. (a) Image showing local agreement
between manual and algorithm segmentation. Agreement is shown in white and disagreement in
gray. (b) Local standard deviation (variability) in the 3-D algorithm segmented boundary, with the
scale on the right. (From: [56]. © 2000 American Association of Physicists in Medicine. Reprinted
with permission.)
3.3.7 Plaque Surface Morphology
The use of conventional 2-D US to identify characteristics of the plaque–lumen
boundary (i.e., surface irregularities, roughness, and ulcerations) remains difficult.
However, mounting evidence has not only been showing the importance of plaque
surface morphology [58–61] but also generating interest in the development of
improved ultrasound techniques for visualization and characterizing of plaque sur-
face features. Using 3-D US images, we have been developing improved quantitative
techniques for the analysis of plaque surface morphology. Our approach uses the
surface of an outlined plaque, which is obtained by either using manual planimetry
or using an automated approach. The outlines of a plaque are then converted to a
triangular surface mesh, which is smoothed to remove the variation in the surface
due to ultrasound speckle. We analyzed the mesh by calculating the local Gaussian
curvature at each node of the mesh. To reduce the variation in the measure of the
curvature, we determined the local mean Gaussian curvature value [62–64] by aver-
aging the curvature values of all surface points within a 1-mm radius of each point
on the mesh.
Figure 3.11 shows a result of the surface roughness metric measured by the
mean Gaussian curvature. The roughness metric has been coded in gray and mapped
onto the segmented surfaces of the vessels, showing an increase in the roughness for
some regions of the surface associated with the plaque. Although these types of
82 3-D US Imaging of the Carotid Arteries
Roughness
0.00267
0.161
0.318
0.476
0.634
Figure 3.11 Result of analysis of the surface morphology of a section of a common carotid artery.
The roughness index is coded in gray and is mapped onto the lumen wall–plaque boundary.
images have yet to be validated, they show the potential of using 3-D US images for
monitoring changes in the plaque surface morphology.
3.3.8 Local Distribution and Change of Carotid Wall and Plaque
A number of investigators have studied the spatial distribution of carotid plaque by
quantifying the degree of stenosis [20, 65]. Although stenosis profiles are useful in
describing the distribution of plaque along a vessel, they do not give the location of
the plaque burden within a given transverse slice of the vessel. The following sec-
tions describe a metric that can be used to compute the local distribution of carotid
disease on a point-by-point basis for each transverse carotid image slice. In addi-
tion, we have extended the quantification of plaque burden along the vessel to the
quantification of the change of the vessel wall plus plaque thickness of the carotid
vessel between two time points.
3.3.8.1 Reconstructing Surfaces from Polygonal Slices
Figures 3.12(a) and (c) show the carotid wall and lumen, which were segmented
manually five times by an expert observer, in 2-D transverse image slices that are 1
mm apart. The symmetric correspondence algorithm [66] was used to pair the verti-
ces on adjacent contours. With all of the correspondence vertices defined, the adja-
cent 2-D curves were connected to form polygonal surfaces. Figure 3.12(b) shows
the tessellated surface, which was constructed from the stack of 2-D contours of the
carotid wall. Figure 3.12(d) shows the surface constructed for the set of contours
representing the carotid lumen.
3.3.8.2 3-D Maps of Average and Standard Deviation Carotid Surfaces
For each of the 3-D carotid US images, an expert observer segmented the carotid
wall and lumen five times. After the five surfaces representing the wall and the
lumen had been reconstructed using the method described earlier, we obtained the
average and standard deviations of the wall and the lumen surfaces using the fol-
lowing steps:
1. For the segmentation of the vessel, the transverse plane was identified, and
the average of the normals of the five different transverse planes was
calculated. The five segmented surfaces were then resliced at 1-mm intervals
using the plane with the average normal, producing five 2-D contours at
1-mm intervals along the vessel.
2. Because the symmetric correspondence algorithm only established a
correspondence between a pair of curves, it was applied four times. The
smoothest curve (of the five curves obtained in step 1) was chosen, and
the symmetric correspondence mappings were established between the
smoothest curve and the remaining four curves.
3. Each of the vertices of the smoothest curve (defined in step 2) was linked
with correspondence points on four different curves, resulting in a group of
3.3 Measurement of Plaque Volume 83