Citation
Adame Valero, I. M. (2007, April 4). Automated segmentation of atherosclerotic arteries in MR Images. ASCI dissertation series. ASCI graduate school|Laboratory for Clinical en Experimental Image processing, Faculty of Medicine / Leiden University Medical Center (LUMC), Leiden University. Retrieved from https://hdl.handle.net/1887/11467
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License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
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segmentation in 3D
follow up
studies
7
Automated 3D segmentation of MR images of the carotid artery in follow up studies and quantification of changes in the vessel wall over time
Adame IM, van der Geest RJ, Dehnavi RA, Tamsma JT, Doornbos J, Reiber JHC, Lelieveldt BPF.
Objective-- Accurate assessment of the arterial structure and the possible changes in plaque burden over time, are important to monitor the evolution of atherosclerosis disease, either naturally or under the effect of drug therapy. Our goal was the quantification of changes in the vessel wall over time (serial MR analysis), by automatically identifying the boundaries of the vessel wall in a segment of the carotid artery in MR images; and investigate factors that influence the accuracy and reproducibility of the measurements.
Materials and Methods-- Ten healthy adults were imaged twice using high resolution in vivo MRI, generating 2 serial scans (8 T1-weighted MR images/
patient). Those images were automatically segmented (one seed point is needed) using our method, which is based on a 3D geometrical model and dynamic programming. A 3D registration, based on gradient and intensity profile, was carried out to register the two scans of the same patient and evaluate changes in the vessel wall over time.
Results-- The accuracy of the segmentation was assessed by comparison with two independent standards (expert radiologists), yielding high correlation: r = 0.98 for lumen, r = 0.97 for outer wall, and r = 0.90 for vessel wall area.
Reproducibility regarding manual initialization (seed point) was 8.72% for intra- observer, and 10.83% for inter-observer. The algorithm was also validated on simulated long-term follow up atherosclerotic data, to assess its capabilities to detect changes in the vessel wall. The kappa statistic K = 0.71 showed substantial agreement between our method and the radiologists.
Conclusion— Though validation on real long-term follow up data is necessary, our method has proven capable of quantifying changes in the vessel wall in an accurate and reproducible manner.
Key words: Carotid artery, MRI, 3D segmentation, follow up study.
(submitted to MRM)
7 Automated 3D
segmentation of MR
images of the carotid
artery in follow up studies
and quantification of
changes in the vessel wall
over time
7.1 Introduction
n vivo noninvasive imaging of atherosclerotic plaque burden and composition, by modalities such as Magnetic Resonance Imaging (MRI), are promising methods which can be applied in the research setting to evaluate evolution of disease burden over time.
This in turn could influence clinical decision-making.
Magnetic Resonance Imaging (MRI) is ideal for serial studies of atherosclerotic lesions over time since it is a 3-dimensional (3D) noninvasive and non-ionizing imaging modality which can identify morphological and compositional features of atherosclerotic plaque in the carotid arteries1,2. MRI permits highly accurate in vivo measurement of arterial wall thickness in human atherosclerotic plaques3, with measurement errors similar to those reported by ultrasound, as has been shown by Saam et al.4.
Accurate and precise assessment of the possible changes in arterial vascular structure and the plaque composition over time is important in order to monitor and understand the progression or regression of the disease, either naturally or in response to drug therapy5-7. However, current imaging studies of atherosclerotic lesions often rely on a human observer’s interpretation of MR images, which is labor-intensive, subjective and time-consuming.
Automated analysis could yield an objective reproducible standardized method for the assessment of atherosclerosis and lead to an increased sensitivity to morphological changes
7
I
of the vessel wall. Currently, most automated methods focus on single time point MR, not on quantifying global or regional changes in serial MR.
Our goal in this study is twofold: on the one hand, development of an algorithm to perform a three-dimensional (3D) segmentation to automatically identify the boundaries of the vessel wall in a segment of the carotid artery in MR images; on the other hand, we pursue the automated quantification of changes in vessel wall over time, investigating different factors that influence the accuracy and reproducibility of the measurements, such as misregistration, or inter- and intra-observer variability.
7.2 Materials and Methods
This work reports a method based on a 3D geometrical model of an artery to automatically segment the lumen and outer wall in a segment of the carotid artery. Further, the model is employed to register and segment two serial scans of the same patient acquired at different time points (baseline (t1) and follow-up (t2)) and, thereby, study progression or regression of plaque burden in follow-up studies.
We use a model-based segmentation that includes a priori information, which helps improve the segmentation of poorly delineated structures, such as the outer boundary of the vessel wall. In this study, the a priori information comes from the fact that lumen and outer wall in cross-sections of vessels often present a circular or elliptical shape, which we have tried to mimic with our model.
This section is structured as follows: a) methods: model parameterization, model matching, local refinement, registration of both scans and finally, quantitative evaluation; and b) experimental setup: experiments and, validation and reproducibility.
7.2.1 Methods
7.2.1.1 Model Parameterization
Our model is based on a bi-elliptical frustum, which is a portion of a solid that lies between two parallel planes cutting the solid (see Figure 7.1). A bi-elliptical frustum resembles an elliptical frustum, except that its two ends are bi-ellipses. In geometry, an ellipse is a curve in a plane, defined by the set of points which have an equal total distance from two fixed points (foci). An ellipse can be considered as a circle (root circle) that has been compressed or elongated by a ratio of a /r or b /r, respectively, along the horizontal or vertical axis, as shown in Figure 7.2.
A bi-ellipse is composed of two semi-ellipses. Both of these segments have an identical root circle, but they have different ratios: a /r for the upper and b /r for the lower arc (see Figure 7.2).
Figure 7.1. Elliptical frustum
The parameters used to describe the frustum are the following (for each bi-ellipse):
- the coordinates of the center of the root circle O: (cx,cy) - the radius of the root circle r .
- the ratio between long and short axis ρh1 =r/a, ρh2 =r/b - the rotation angle θ
Figure 7.2. Bi-ellipse model and its root circle (thin line)
Using these parameters, each point (x,y) on the bottom and top bi-ellipses of the frustum can be represented as follows:
⎪⎪
⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪
⎪
⎩
⎪⎪⎪
⎨
⎧
⎟⎠
⎜ ⎞
⎝
⎛
≤
⎟ ≤
⎟⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
⎟⋅
⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅
⋅
⋅
− + ⋅
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
≤
⎟ ≤
⎟
⎠
⎞
⎜⎜
⎝
⋅⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅
⋅
⋅
− + ⋅
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
=
π α ρ π
α θ α θ
α θ α
θ
π ρ α
α θ α θ
α θ α
θ
2
; . 2 ) sin(
) sin(
) cos(
) cos(
) cos(
) sin(
) sin(
) cos(
0
; . 1 ) sin(
) sin(
) cos(
) cos(
) cos(
) sin(
) sin(
) cos(
r h r
cy cx
r h r cy
cx
y
x [1]
with θ =θ1;(cs,cy)=(cx1,cy1);r=r1;ρh1 =ρh1,1;ρh1 =ρh2,1 for the bottom bi-ellipse and θ =θ2;(cs,cy)=(cx2,cy2);r=r2;ρh1 =ρh1,2;ρh1 =ρh2,2 for the top bi-ellipse.
The rest of the points on the frustum are obtained by interpolation. For each point on the bottom bi-ellipse, its closest point on the top bi-ellipse is found and a linear interpolation is carried out.
7.2.1.2 Model matching
Our model, S, is described by a 12-dimensional parameter vector:
(
cx1,cy1,r1,ρh1,1,ρh2,1,θ1,cx2,cy2,r2,ρh1,2,ρh2,2,θ2)
, which are optimized for lumen and outer wall, by minimizing an energy measure, which is a function of the parameter vector.The minimum of the energy function is obtained by a constrained search (greedy sequential search) on the parameter space, and corresponds to the best fit of the model (frustum) to the vessel. This constrains the displacement of each point on the curve to the motion of all the other points. The energy function is described by the following expression:
( )
∑
∈∇
−
=
s
I E
x
x
s) | ( )|
( [2]
Where ∇I is the gradient of the image I, and x is a point on the curve s, which is an instance of the model S.
To speed up the process and avoid finding a local minimum, a multi-scale approach is employed in order to optimize the parameters of the model.
- In the first step the original image data (non-isotropic) is employed to drive the model to the vessel of interest.
- In the second step, the image data is interpolated in order to obtain an isotropic volume and the model parameters are further tuned to obtain the best fit.
The model matching is run twice: the first time for the lumen boundary and the second time for the outer wall boundary. Those two optimizations are linked by constraints of size and inclusion (the outer wall boundary must always contain the lumen).
7.2.1.3 Local refinement
Once the model is fitted to the image data, we have an initial segmentation for lumen and outer wall. To locally refine that segmentation, cross-sections are obtained (based on the image data) and the contours are further refined. This refinement is accomplished in two steps in a slice-by-slice manner. To compensate for small displacements, a rigid registration of the contours is carried out, using as best-fit criteria, the greatest gradient averaged along the contour. As mentioned above, the same model is employed to segment lumen and outer wall, except for some constraints, such as the fact that the lumen must be within the outer vessel wall. Another difference is the sign of the gradient. The gradient at a certain point on the contour is computed in the direction defined by the line passing through that contour point and the center of gravity of the contour (see Figure 7.3). For lumen,
) ( ) (A I P I
I = −
∇ , while for outer wall, ∇I =I(P)−I(B). In this way, we incorporate extra a priori information. For lumen contour: the lumen is darker than the vessel wall, while for outer wall contour, it is normally the opposite, the region inside the outer wall (vessel wall) is often brighter than the surrounding tissue.
Figure 7.3. O: center of gravity; P: contour point; A,B: points used to compute the gradient
Next, the contour is locally refined by means of a minimum cost approach based on dynamic programming8: at each point on the model a scan line perpendicular to the contour is constructed with the image intensity values on this line derived from the original image. The length of the scan lines is chosen such that only a small neighborhood around the model contour is included. Those values are annotated in a row of a scan matrix; each row corresponds to a point in the contour. In addition, a cost matrix is also computed, each element of which represents the cost that involves selecting the corresponding element in the scan matrix as the new point for the contour at that position. The values of the cost matrix are derived from the intensity changes in the scan matrix and are influenced by a few parameters. In our case, those parameters are: (a) side step size: maximum allowed displacement (perpendicular to the contour) for a point in the contour, with respect to its original position. (b) side step cost: cost associated to the displacement of a point in the contour.(c) stiffness: cost associated with the model. The higher this value, the less variation permitted from the original model contour. These parameters describe geometric properties of the vessel shape, which makes the parameter selection largely independent of the scanning protocol, therefore generalizing well toward other MR acquisition protocols.
7.2.1.4 Registration and Segmentation in Follow-up image data
In this step the model S, optimized for the baseline t1 (I1), is registered (rigid registration) to the anatomical region (carotid artery) on t2 (I2). The criteria employed for the registration are:
average gradient along the contour and, correlation of intensity profiles for each point on the contours. The registration is carried out for lumen and outer wall contours simultaneously.
Description of the method
Let S be the bi-ellipsoidal frustum (model) optimized for the baseline set of images I1. I2 is the set of images in time point 2 (follow up study). N xy cross-sections are obtained along the z direction. Let c be the center of gravity of cross-section j, and j v the ith point on the jth ij cross section of S. Our objective is to find a transformation T to fit S to the corresponding anatomical region on I2.
To compute the transformation T, we minimize an energy function based on gradient measurements ∇I2 and intensity profile, as proposed by Cootes et al.9 and Kelemen et al.10 Intensity profile of a point v on model surface S is defined as the intensities of a discrete set ij of sampling points on the baseline set of images I1 along direction u centered at ij v . ij
ij j ij j
i c v c v
uj =( − ) − [3]
Sampling points of the model profile are shifted along u and their intensities on Iij 2 are retrieved as subject profile and compared to model profile (I1). In our approach, similarity between two profiles is defined in terms of a correlation coefficient sij =C(vij,wij), where
w is the corresponding point found on Iij 2.
In order to speed up the registration process and avoid instabilities, multi-level transformations are employed11-13. In our approach, a rigid transformation is first computed to roughly fit S to I2. The result is used later to initialize a non-rigid transformation (see section Local Refinement in I2).
Let translation
(
tx,ty,tz)
and rotationρ be the unknown parameters of rigid transformation T.Our algorithm is outlined as follows:
1. In each iteration, compute sij =C(vij,wij) for each v by searching in direction ij u ij in a predefined region of I2 with step size δ (I2 is a sub-sampled version of the original data).
2. Compute the energy: ( | 2( ( ))| ij)
S v
ij s
v T I E
ij
∑
∈−
∇
−
= α β [4]
1 0
; 1
0≤α ≤ ≤β ≤ are weighting coefficients.
3. a. In the first iteration, initialize Emax =E; (Emax: maximum energy), TEmax =T ; b. In the following iterations, ifE≥Emax, assign Emax =E, TEmax =T;
4. Repeat steps 1 to 4 till the whole range of values defined for each parameter
(
tx,ty,tz,ρ)
is covered.5. Apply transformation TEmax corresponding toEmax, to model S.
7.2.1.5 Local Refinement in I2
Once the model is fitted to the image data I2 (rigid transformation), cross-sections are obtained (based on the image data) and the contours are further refined to get a more accurate segmentation, as it was done for the baseline images I1 by means of dynamic programming techniques (see section Local Refinement). This non-rigid step is needed because of changes between t1 and t2.
7.2.1.6 Quantitative Analysis
The vessel wall area (VWA) was calculated by substracting the luminal area from the outer contour area. Wall thickness measurements were obtained by automatically dividing the contours of the vessel wall into 6 segments using the centerline method as previously described14. An average thickness was automatically calculated per segment and the mean wall thickness value was used for the analysis.
7.2.2 Experimental Setup 7.2.2.1 Experiments
In our work we have set up two different validation experiments applying our segmentation algorithm to real short-term follow up data and simulated long-term atherosclerosis progression. The motivation behind them is twofold: firstly, assessment of the accuracy of the method to segment the vessel wall, and investigation of the factors influencing the accuracy of those measurements, such as intra- and inter-observer variability. Secondly, we also want to assess the reproducibility of the vessel wall measurements derived from the segmentation in two different scans, when no change in the vessel wall occurs (real data); and the capabilities of the algorithm to detect changes over time (simulated long-term data).
Actual Patient Data Images: short-term follow up data
Ten healthy adult subjects, seven males and three females, underwent MRI scans on two different occasions (t1 and t2). The second scan (t2) was performed at least four days after the first visit. The mean age in the group was 57 years, with a range of 25-79 years. The local medical ethical committee approved the study, and all volunteers gave informed consent.
MRI was performed using a 3T scanner (Philips, Achieva, Best, The Netherlands) using a standard phase array coil with two flexible elements of 14 x 17cm. A total of eight contiguous transverse slices with 2mm thickness were acquired starting from the flow-divider in the proximal (caudal) direction covering 1.6 cm of the carotid bulb and the common carotid artery. A dual inversion recovery (IR) (black-blood), fast gradient echo sequence with fat suppression was used to maximize contrast between the carotid wall and the lumen blood pool15. Images were acquired at each RR interval. The echo time was 3.6ms, TR 12ms, flip angle 45 degrees, and 2 signal averages were performed. ECG triggering was used for data acquisition at the end-diastole. A reinversion slice thickness of 3mm was used. The field of view was 140mm. With a matrix size of 306, a voxel size of 0.46mm x 0.46mm x 2mm was obtained. Each MR study took approximately 20-30 minutes depending on the cardiac frequency.
Macroscopic structural changes in the vascular structure are not expected within a timespan of one week. In order to test the capabilities of our algorithm to recognize and measure changes in the vessel wall, we modified the original image data to artificially generate atherosclerotic vessel walls, with and without lumen shrinkage.
Simulated atherosclerosis progression
The enlarged vessel wall was generated by means of a mathematical model to simulate outward remodeling in the vessel wall. Expert contours –manually traced by radiologists-(C) were used as starting point to generate the deformation to be carried upon the image data.
Those contours were modified as follows to obtain the deformed contours (C’):
C z y
x ∈
∀( , , ) , (x ,'y ,'z')∈ C' z’= z;
) ; tan (
)1 (
) (
; '
2 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
+ ≠
− ∆ +
==
=
c c
c
x x if x
x sign x
x x if x
x
α
γ [5]
) ; (
tan ) ' (
) (
);
) ' (
⎭⎬
⎫
⎩⎨
⎧
≠
− +
==
∆
−
= +
c c c
x x if x
x y
x x if y
y sign y y
α γ
⎟⎟⎠
⎜⎜ ⎞
⎝
⎛
−
= −
c c
x x
y a tan y
α ;
) , ,
(xc yc z : center of gravity of contour C at cross-section z.
See Figure 7.4 for a summary of the different deformations generated, depending on the length of the lesion in z, and the values of the parametersγ and ∆ .
Original contours (C) and modified contours (C’) were used to modify the image data. The contours were used to define a thin-plate spline transformation16, which is applied to warp the intensities from the original images to the artificially deformed images. Examples can be seen in Figure 7.5.
7.2.2.2 Validation & Reproducibility
Accuracy
The accuracy of the algorithm was assessed by comparison with an independent standard (contours manually drawn by expert radiologists). Histological data was not available for the subjects involved in this study. However, the good correlation between vessel wall MR and histology has been demonstrated elsewhere17.
Figure 7.4. Different simulated atherosclerosis types
Reproducibility
For all subjects, the method was tested twice: firstly, taking scan t1 as baseline and t2 as follow up; and secondly taking scan t2 as baseline and t1 as follow up, in order to measure the sensitivity of the method to the initial scan.
A B
C D
Inter- and intra-observer Reproducibility
Reproducibility was expressed as standard deviations and coefficients of variation (COV).
For intra-observer reproducibility, the sensitivity to the initial positioning of the seed points was measured by running four independent analyses. Prior to each analysis the seed points were repositioned. To assess inter-observer reproducibility three observers conducted the analysis for all subjects.
Agreement with Radiologists
To assess the accuracy of the automated measurements, interclass correlations (ICCs) were calculated to quantify the agreement between the measurements obtained by our algorithm and two experts blinded to the results of the algorithm. The ICC was calculated for the automated results (auto) and expert 1 (exp1), auto and expert 2 (exp2) and, exp1 and exp2.
Accuracy in measuring changes in vessel wall over time. Precision: agreement between experts
and automated measurements
In order to assess the capabilities of the automated method to detect changes in the vessel wall over time, we tested our method on the modified image data, and used the kappa statistic18 to assess agreement between expert 1 and our method. We considered that there were significant changes in the vessel wall when (VWA−∆VWA) VWA≥10%, where VWA is the vessel wall area in the baseline image (healthy vessel) and VWA+∆VWA is the vessel wall area in the follow up image (deformed vessel).
7.3 Results
Accuracy of the algorithm: agreement with Radiologists
The algorithm was validated on black-blood MR transversal slices from 10 subjects (two datasets: baseline and follow up). Table 7.1 provides descriptive statistics for the measurements by expert and automatic results. From these statistics and the interclass correlations from Table 7.2, we can observe that there is a high agreement between the measurements derived from our automated method and the independent standard (expert contours traced by radiologists). Table 7.3 presents the average paired difference between the automatic and manual measurement pairs.
Mean Vessel Wall
thickness (mm) Lumen Area (mm2) Outer Wall Area (mm2) Vessel Wall Area (mm2)
Expert 1 Expert 2 Automated
0.87±0.24 0.92±0.23 0.95±0.20
38.32±11.54 37.84±12.00 36.82±10.53
61.00±19.35 61.61±20.05 59.05±18.32
22.68±8.69 23.76±8.89 21.86±8.93 Table 7.1 Descriptive statistics for lumen, outer wall and vessel wall areas (per slice) for each independent observer and the automated algorithm
Auto contours vs. exp1 Auto contours vs. exp2 exp1 vs. exp2 Vessel wall area
Lumen Area Outer wall area
0.896 0.977 0.966
0.912 0.975 0.969
0.912 0.996 0.992
Table 7.2 Correlations between the quantitative measurements obtained from the automatically detected contours (auto: output of our algorithm) and those manually traced by two expert radiologists (exp1, exp2).
Auto vs. exp1 Auto vs. exp2 exp1vs. exp2
Vessel wall thickness
Vessel wall area
Lumen Area
Outer wall area
0.08±0.17 mm (0.09±0.18 %) (p<0.05)
-1.50±3.01 mm2 (-7.63±14.75 %) (p=NS)
-1.50±1.53 mm2 (-3.91±3.55 %) (p=NS)
-3.01±3.98 mm2 (-5.15±6.32 %) (p=NS)
0.04±0.17 mm (0.04±0.18 %) (p=NS)
-2.58±2.97 mm2 (-12.84±15.14 %) (p=NS)
-1.02±1.75 mm2 (-2.33±3.95 %) (p=NS)
-3.61±3.88 mm2 (-6.04±6.27 %) (p=NS)
-0.05±0.07 mm (-0.05±0.08 %) (p<0.05)
-1.08±1.56 mm2 (-5.21±7.41 %) (p=NS)
-0.48±0.64 mm2 (-1.58±1.50 %) (p=NS)
-0.60±1.72 mm2 (-0.89±2.88 %) (p=NS) Table 7.3. Average paired differences between measurements derived from the automated processing (auto) and those obtained from the two
independent standards (exp1 and exp2), for vessel wall thickness (mean), and area measurements.
Reproducibility
We ran the method taking scan t1 as baseline and t2 as follow up; then taking scan t2 as baseline and t1 as follow up. The paired differences in the vessel wall area measurements/per slice are: -0.63 ± 2.38 mm2 (-5.21 ± 17.22%) p = NS. Table 7.4 shows inter and intra- observer reproducibility.
Standard deviation COV (%) Intra-observer
Inter-observer
1.81 mm2 1.97 mm2
8.72 10.83
Table 7.4. .Inter- and intra-observer reproducibility, regarding manual initialization (seed point), for vessel wall area measurements
Accuracy in measuring changes in vessel wall over time: agreement between experts and
automated measurements
Figure 7.6 presents vessel wall thickness measurements as measured in the baseline (t1) and in the follow up datasets (t2) for four representative examples. In Figures 7.6a and 7.6b, almost no change in vessel wall thickness was detected between t1 and t2, as expected, since the images were acquired within one week time. This also shows the good reproducibility of the method. In Figures 7.6c and 6d, however, the differences in vessel wall thickness for the simulated follow up data can be observed. Furthermore, the length of the lesion is clearly visible from these graphs.
Figure 7.6. Vessel wall thickness as measured in scan 1 (t1) and scan 2 (t2) for a subject . The x-axis shows cross-sections of the vessel segment from top to bottom. A-B) Short-term follow up data (no changes in vessel wall) C-D) Simulated long-term follow up data (progression of
atherosclerosis: vessel wall enlargement).
Table 7.5 presents statistics on the agreement between expert 1 and our automated method applied to the modified follow up data (enlarged vessel wall):
- the observed agreement waspo =
(
0.625+0.25)
=0.875,- the expected agreement: pe =
(
0.75*0.625+0.25*0.375)
=0.5625,- and kappa K =(0.875−0.5625) (1−0.5625)=0.7143, 0.6≤ K ≤0.8 means substantial agreement18.
Expert measurements Significant change in vessel wall detected?
?
% 10 )
(VWA−∆VWA VWA≥
YES NO TOTAL
YES NO
0.625 0.125
0 0.25
0.625 0.375 Automated method
measurements
TOTAL 0.75 0.25 1
Table 7.5. Variation expert's measurements - automated method's measurements. : vessel wall area in baseline image; : vessel wall area in follow up image (enlarged vessel wall); : relative enlargement of the vessel wall.
Figure 7.7. Examples of segmentation results for different deformation steps. A, B, C, D) automated segmentation; E, F, G, H) independent standard
Figure 7.8. Automatically detected contours of the outer wall, for two time points: ‘dark gray’: baseline (scan t1) and, ‘light gray with grid’:
simulated atherosclerotic data (scan t2).
7.4 Discussion
The methods presented in this work can be divided in three parts: 1) segmentation of the vessel wall in MR images of the carotid artery by means of a geometric model (elliptical frustrum) and dynamic programming; 2) registration of the carotid segment of interest between two scans of the same patient at different time points (baseline and follow up); and 3) measurement of the changes in vessel wall between the two time points.
Two different validation scenarios were set up to assess the accuracy of the reported method.
Firstly, it was validated on actual MR data: two datasets (baseline and follow up) were available for each subject participating in the study. Nevertheless, those results did not prove that the algorithm had the capabilities to detect changes in the vessel wall over time. Since no follow up data was available for severe atherosclerotic patients, we modified the follow up datasets from our healthy subjects to artificially deform the vessel wall, thereby simulating atherosclerosis progression (Figure 7.5). The algorithm was applied to these data and its capabilities to detect changes in the vessel wall were assessed by using the kappa statistic (see Table 7.5). A value of K = 0.71 was obtained, which means substantial agreement between our automated method and the expert (independent standard)18. This agreement between automated and manual contours can also be observed in Figure 7.7.
The maximum processing time for the registration and segmentation of both datasets (baseline and follow up) is about 5 min.
Regarding other works reported in the literature, different methods have been described to segment the vessel wall in 2D cross-sections in in vitro MR images: Yang et al.19 used 2D splines, and Adams et al.20 developed a method based on snakes. 2D snakes have also been applied by Yuan et al.21 to segment in vivo MR images of the carotid artery. We also presented a method to detect the boundaries of the vessel wall in in vivo MR images of the carotid artery, based on a 2D geometrical model and dynamic programming22.
Image artifacts, spatial inhomogeneity of coil sensitivity and other factors, often result in degraded image quality, which makes accurate segmentation a challenging task. Therefore, the use of all the available information is crucial in order to gain accuracy and remove subjectivity from the segmentation process.
Many segmentation methods have been proposed for generating 3D surface models of the blood pool in MR images of the main arteries23,24. Recently Rinck et al.25 reported a method based on tubular structures to segment lumen and outer wall in CT images of the carotid artery. However, to our knowledge, not much has been done to include the outer wall boundary in the 3D segmentation for MR images. Steinman et al.26 presented a method to generate 3D models of the lumen and wall boundaries, which required the operator to place 6 points in each cross-section to initialize a 2D discrete dynamic contour, from which the 3D model was generated.
Our method uses a priori information on vessel wall morphology, combined with image information in order to perform a 3D segmentation of the carotid artery in in vivo MR images.
Unlike Steinman et al., minimal interaction is required (only one seed point in a cross- section), which removes subjectivity from the segmentation process. Furthermore, this work
also presents automated 3D registration of a segment of the carotid artery in a baseline dataset with a follow up dataset, allowing for measurements of changes in the vessel wall overtime. Currently, measurements of changes in follow up studies are mainly derived from manual analysis27, which is time consuming and labor-intensive.
Our algorithm performed well in the analyzed data. However, it should be validated against data from patients with atherosclerosis who have been followed up over longer periods of time, in order to have a more realistic scenario.
Another limitation of the method is the fact that one single tubular segment is modeled, meaning that it can not be applied to bifurcations. Nevertheless, the model could be modified to cover the bifurcation, by defining a composed model, consisting of different segments (each one described by an elliptical frustum as presented in this work), in such manner that the ends of segments would intersect at the branching point.
7.5 Conclusions and Future work
We have developed a method to carry out 3D registration and segmentation of the vessel wall in a segment of the carotid artery in in vivo MR images. When compared to reference standards, it has proven to be reproducible and accurate. Nevertheless it needs validation on a larger cohort of patients presenting more severe atherosclerosis; and long-term follow up data. Future work will focus on that validation and on the development of a model that includes the bifurcation. Therefore, a composed model, as described above could be implemented. In addition, a model based on B-splines28 could also be generated and the performance of both approaches compared.
Another issue is the low spatial resolution of MR data and the presence of acquisition artifacts. Better image quality is expected to improve image segmentation.
Acknowledgements
This work is supported by the Dutch Science Foundation (NWO), under an innovational research incentive grant nr. 016.026.017.
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