Aorta segmentation in non-contrast cardiac CT Images using an entropy-based cost function

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1 Aorta segmentation in non-contrast cardiac CT Images using an entropy-based cost function Olga C. Avila-Montes, Uday Kurkure, Ioannis A. Kakadiaris Computational Biomedicine Lab, Dept. of Computer Science, University of Houston, Houston TX, USA ABSTRACT Studies have shown that aortic calcification is associated with increased risk of cardiovascular disease. Furthermore, aortic calcium assessment can be performed on standard cardiac calcium scoring Computed Tomography scans, which may help to avoid additional imaging studies. In this paper, we present an entropy-based, narrow band restricted, iterative method for segmentation of the ascending aorta in non-contrast CT images, as a step towards aortic calcification detection and pericardial fat quantitation. First, an estimate of the aorta center and radius is obtained by applying dynamic programming in Hough space. In the second step, these estimates serve to reduce the aorta boundary search area to within a narrow band, and the contour is updated iteratively using dynamic programming methods. Our algorithm is able to overcome the limitations of previous approaches in characterizing (i) the boundary edge features and (ii) non-circular shape at aortic root. The results from the proposed method compare favorably with the manually traced aorta boundaries and outperform other approaches in terms of boundary distance and volume overlap. Keywords: aorta segmentation, dynamic programming, entropy, non-contrast computed tomography 1. INTRODUCTION Coronary heart disease (CHD) is the primary cause of morbidity and mortality in the United States and around the globe. According to the National Heart Lung and Blood Institute, cardiovascular diseases, including atherosclerosis and its complications, were responsible for about one million deaths in 2004 in the United States. 1 Studies have found that coronary artery calcium is a distinct marker for atherosclerosis. 2 Such calcifications can also occur in extra-coronary structures including the ascending aorta, the aortic arch, the descending aorta, and the abdominal aorta. Several studies have shown that the calcification of the thoracic aorta, aortic arch, and aortic valve is associated with increased risk of cardiovascular disease. 3 6 Recent research has also shown close association between thoracic aorta calcium, aortic valve calcium and advanced coronary artery calcium 7 10 hinting at the presence of systematic atherosclerosis. Prior to including aortic calcium measurements in cardiovascular risk assessment, longitudinal studies need to be conducted to assess the incremental value of thoracic aorta calcium in addition to coronary artery calcium. The aorta and coronary artery calcifications can be quantified by non-contrast Computed Tomography (CT) imaging. 8, 11 Moreover, the thoracic aorta calcifications can be measured from standard cardiac calcium scoring CT scans without requiring any additional scanning, which is especially advantageous for retrospective studies. Currently, aortic calcium scoring is not routinely performed in clinical practice because the available calcium scoring tools require manual annotation of the calcifications, which is a labor-intensive and time-consuming process. One way to automate the process of aortic calcium scoring is to determine the aortic boundaries and extract calcifications within these boundaries automatically or with minimal user interaction. Moreover, for the problem of pericardial fat detection, one would like to exclude the aorta from the region of interest. 12 Considerable research has been conducted towards thoracic aorta segmentation in magnetic resonance (MR) images, magnetic resonance angiography (MRA) images, 16, 17 and Computed Tomography angiography (CTA) images. 18 All of these methods rely on the presence of high contrast between lumen and its surroundings to obtain sufficiently large intensity gradients at the vessel boundary only. However, the lack of contrast between Corresponding Author: Ioannis A. Kakadiaris (ioannisk@uh.edu)

2 blood pool regions, muscle walls and fat in the non-contrast CT imaging renders aorta segmentation as a challenging task. Recently, Isgum et al. 19 proposed an atlas-based aorta segmentation method for non-contrast CT data. Their method was evaluated on high resolution CT scans acquired as part of a lung cancer screening trial. Thus, its applicability to low resolution, highly anisotropic calcium scoring CT scans is questionable. In our previous work, 20 we proposed a method for aorta localization and segmentation. The aorta localization step estimated the approximate location and size of the aorta through dynamic programming-based Hough circle selection. Aorta segmentation was accomplished by using dynamic programming-based boundary detection in the polar coordinate system. However, the previous method exhibited significant errors in boundary detection for the ascending aorta when there was lack of edge information and when the aorta s shape did not conform to the circular shape assumption (especially near the aortic root). In this paper, we present an entropy-based cost function for aortic boundary detection to overcome the effect of noise and lack of edge features. The local entropy provides a measure of dispersion of image intensity and, hence, it can be used as an indicator of the edge characteristics. Furthermore, we present an iterative, narrowband method to compute a locally optimal boundary using dynamic programming. The narrow-band approach restricts the search region locally to avoid unexpected contour deformations, whereas the iterative nature of the method allows the deforming contour to reach the real boundary of the aorta, irrespective of its shape. The rest of the paper is organized as follows: Section 2 provides a detailed description of the proposed algorithms for automated segmentation of the aorta. In Section 3, we present validation results on clinical data when compared to manual annotations. 2. METHODS Our approach is broadly divided into two main steps: (i) aorta localization, and (ii) aorta segmentation. In the first step, the approximate position and size of the aorta are estimated by exploiting the circular shape of the aorta in axial images. In the second step, we use the estimated position and size of the aorta to detect refined aortic boundary contours using dynamic programming methods. 2.1 Localization of the Aorta In spite of heart dynamics, the aorta maintains its global tubular shape with only minor local deformations. Since the thoracic aorta runs mainly vertically, its appearance in axial slices approximates a circular shape which can be extracted using the Hough transform. The Hough space is computed by performing a convolution operation using a circular kernel of radius r, H = E K, where H is the Hough space, E is the edge response obtained with the Canny edge detector, and K is the circular kernel. The Hough space is treated as a medialness feature space, where the coordinates of the circle s center and radius are the dimensions of the space. A dynamic programming-based optimal path search is performed on the Hough spaces of subsequent axial slices to obtain a series of optimal best-fit circles for the aorta. To select an appropriate Hough circle corresponding to the aorta, we assume that there is little deviation in cross-sectional size and horizontal positioning of the aorta in subsequent axial slices. Therefore, the optimal path is defined to be a path connecting the Hough spaces from consecutive slices that has minimum cost with respect to the change in radius, translation, and accumulator votes. Further details about this step can be found in our earlier work Segmentation of the Aorta The problem of detecting a closed, circular boundary contour can be formulated as an optimal path detection problem in a polar coordinate system. In this formulation, the optimal path is detected in the two-dimensional space in which one dimension is the distance from the center point (radius) and the other dimension is the angle from a fixed direction. This formulation can be extended to detect a closed contour that deviates away from the circular shape by modifying the coordinate system of the search space if an initial contour is available. One of the dimensions of this modified coordinate system corresponds to the parametric representation of the initial contour and the other to the normals of the contour. The search space can be restricted by controlling the length of the normals on either side of the contour. However, if the boundary has high curvature, the normals may cross each other, leading (depending on the length of the normals) to the folding of the search space.

3 To overcome the above-mentioned limitations, we propose a method to compute the narrow band search space and the coordinate system. The narrow band is obtained by limiting the space at a certain distance from the contour through a distance transform. The inner and outer boundaries of the narrow band are parameterized with an equal number of points forming one of the dimensions of the search space. A correspondence is sought between the boundaries to obtain the connecting line segments which are also parameterized with an equal number of points forming the other dimension of the search space. This formulation allows the contour to deviate from a circular shape and does not cause folding of the search space. The contour can be refined further following an iterative procedure Construction of an entropy-based cost function The optimal path detection problem can be solved using dynamic programming, however, its success depends largely on the cost function used. We define the cost of a path as the sum of local energies along the path, given by: N C(p 1, p 2,, p N ) = c F (p 1 ) + (c F (p i ) + c G (p i 1, p i )), (1) where {p 1,, p i,, p N } are the N points of the path B N. The desired boundary ˆB N is the optimal polyline B N that has the global minimum cost C(B N ). The cost term c F (p i ) exploits features that characterize the boundary and c G (p i 1, p i ) imposes the spatial continuity yielding a smooth boundary. These two terms are expressed as: Q c F (p i ) = w j fj (p i ) (i = 1,, N), (2) j=1 i=2 c G (p i 1, p i ) = w Q+1 g(p i 1, p i ) (i = 2,, N), (3) where the local cost terms f j (p i ) (j = 1,, Q) are transformations of image features f j (p i ), Q represents to the number of features used and g(p i 1, p i ) is the distance between two consecutive points of the path. Note that these local cost terms are application-specific and should be carefully selected in order to reflect the characteristics of the boundary formation that we wish to describe. We use the following features for the feature-based cost function: Intensity ( f 1 (p i )): This term forces the boundary to follow the homogeneous path through the pixels with higher blood intensity values. Gradient ( f 2 (p i )): The gradient cost component term is responsible for moving the boundary towards the points having strong gradient value in a direction perpendicular to the boundary. Local Entropy ( f 3 (p i )): Local entropy measures the randomness or the degree of disorder of an image. It is defined as E = p log(p), where p is the probability of occurrence of a gray level within a local neighborhood. From the previous equation we can observe that the local entropy within a certain region will diminish as the region becomes more homogeneous, because the changes in grey levels are small for homogenous regions. On the other hand, the local entropy will have high values in regions with grey level transitions, showing that such regions are not texturally uniform. The object of interest, such as an organ boundary, exhibits a certain amount of disorder because it describes the transition between different homogenous regions. Since the local entropy feature is able to highlight such regions of interest, the entropy-based cost component term forces the optimal path to follow the aorta boundaries. The use of the entropy term allows a better representation of the spatial structural information contained in the image because it provides additional information regarding the region boundaries and gives an idea about the transition of intensities between adjacent pixels Contour initialization First, a non-linear gray-scale modification is performed to enhance blood and suppress other types of tissue. Then, a polar coordinate system is constructed using the pair of (ˆx, ŷ) coordinates and radius ˆr as center and radius estimates, respectively. Figure 1(a) depicts the rays from the center estimate, and the obtained polar image is depicted in Fig. 1(b). When processing the first slice, the estimates (ˆx, ŷ) and ˆr are obtained from the

4 (b) (a) (c) (d) Figure 1. (a) CT image overlaid with the selected Hough circle (black) and radial rays (white) from its center to transform into a polar coordinate system. (b) Polar transformed image. (c) Optimal path (white) obtained by the dynamic programming method overlaid on the cost image. (d) Depiction of the detected boundary contour (white) transformed back into the Euclidean coordinate system. center coordinates (x L, y L ) and radius r L of the circle resulting from the localization step described in Sec However, the estimates (ˆx, ŷ, ˆr) are updated when the aorta boundary contour is available from the previous slice, such that its center coordinates (x S, y S ) and average radius r S contribute as follows: (ˆx k, ŷ k, ˆr k) = β ( x k L, y k L, r k L) + (1 β) ( x k 1 S where N corresponds to the number of slices., y k 1 S, r k 1 S ) (k = 2,, N), (4) Finally, an optimal path is detected using the cost function described in Sec through dynamic programming in the constructed polar coordinate system. In order to incorporate a 3D surface continuity factor, a new cost term f 4 (p i ) is added to Eq. (2) based on the distance from the previous contour. This term guides the initialization of the following slices, and benefits low contrast slices by using information from their neighboring slices. The detected path (Fig. 1(c)) is transformed back into Euclidean coordinates, providing the aortic boundaries, as depicted in Fig. 1(d) Aorta boundary detection In this step, the initial contour obtained from the previous step is iteratively refined by recomputing the optimal path within a narrow band in a new coordinate system. The essential idea in this refinement stage is to consider a narrow band around the current estimation of the aorta contour in both directions (inwards and outwards) as a local search space. Thus, the contour is updated within only this band through dynamic programming, and the narrow band is also updated in each iteration as the contour changes. The narrow band is bounded on either side by two curves (C 1 and C 2 ), which are at a Euclidean distance δ from the contour. The distance δ determines the capture range of the contour. If it is too large, the contour may get attracted to undesired features. If it is too small, the contour may not be able to capture the real aorta boundary. The inner and outer boundaries of the narrow band are defined as circular linked lists of vertices by sampling them into N points. To determine the correspondence between the points of inner and outer contours, both contours lists are rotated such that the start positions of both lists have the shortest possible distance. Each line segment connecting the corresponding pair of points from the curves C 1 and C 2 is discretized into M points (Fig. 2(a)). The new coordinate system is formed by rearranging the N boundary points from the inner and the outer contours and the M points from each line segment connecting the N points, yielding an image grid of size N M, as depicted in Fig. 2(b). Using dynamic programming and the cost function described in Sec , an optimal path representing the aorta boundary is detected in the new search space (Fig. 2(c)) and transformed back to the original space (Fig. 2(d)). The boundary estimation is refined by applying this step iteratively until there are no significant changes between the segmentation result of two consecutive iterations or until a maximum number of iterations T has been reached.

5 (b) (a) (c) (d) Figure 2. (a) CT image overlaid with aorta boundary contour (black) obtained in t 1 iterations and the line segments connecting the inner and outer contours of the narrow band (white) to be transformed into the new coordinate system. (b) Depiction of the transformed image. (c) Optimal path (white) obtained at the current t iteration by the dynamic programming method overlaid on the cost image. (d) Detected boundary contour (white) transformed back into the Euclidean coordinates. 3. RESULTS AND DISCUSSION We applied our entropy-based segmentation method on 30 randomly selected non-contrast cardiac CT scans. The images were acquired on an electron-beam CT (EBCT) scanner (GE Imatron). For each scan, a stack of contiguous slices were acquired with slice thickness of 3 mm each. Each image was reconstructed to pixels with 16-bit gray value resolution. The pixels sizes ranged from mm to mm. The axial slices were processed in order from inferior to superior starting at the aortic root. We empirically determined the weights to be w j=1,,5 = { 1, 2, 0.7, 0.7, 0.6}. The constant β was set to be 0.5 for the given problem. In Fig. 3 the importance of the addition of the local entropy term in the dynamic programming cost function is depicted on a representative axial CT slice (Fig. 3(a)) located near the aortic root. The aorta boundary resulting from the previous approach, 20 the proposed method without using the entropy-based cost term, and the proposed method using the entropy-based cost term are depicted in Figs. 3(b)-(d), respectively. The positive impact that the local entropy term has in the final aorta segmentation for this slice can be clearly observed. The advantage of using the entropy as an additional cost term lies in its ability to highlight regions of interest such as the edges, moving the optimal path towards the real aorta boundary. The accuracy of the proposed method was assessed using the boundary distance error. The convexity of the aorta allows us to use the root mean squared radial distance (R) between the boundaries as a boundary error metric. The boundary contours are parameterized over θ with the centroid c µ of the manual contour being the center of rotation. The error metric R is computed as a root mean square distance between corresponding points on the manual and automated boundary contours obtained from the intersections of the radial lines drawn outward from the centroid to the boundary contours. Figure 4 depicts the cumulative radial distance errors between automatic and manual contours for ascending aorta for the proposed segmentation method (Fig. 4, solid line). We compare the segmentation results against the Hough circles extracted in the localization step (Fig. 4, dotted line) and the results from the Kurkure et al. 20 method (Fig. 4, dashed line). It can be observed that the refined contours follow the aortic boundary more closely than either the Hough circles or the previous method in all the cases. The volume overlap is estimated in terms of a well-known overlap measure, the Dice similarity coefficient (DSC), defined as: DSC(S µ, S α ) = 2 S µ Sα S µ + S α, (5) where S µ and S α represent the manual and the proposed segmentation methods, and V denotes the number of voxels labeled by V. Table 1 provides descriptive statistics of the DSC measures obtained for the ascending aorta by the Kurkure et al. 20 method and the proposed method. In summary, the volume overlap measures

6 (a) (b) (c) (d) Figure 3. (a) Original CT image and aorta boundary detected by (b) the method proposed by Kurkure et al., 20 (c) the proposed method without the entropy-based cost term, and (d) the proposed method with the entropy-based cost term. Figure 4. Cumulative radial distance error, R, of the localization method (dotted line), the method proposed by Kurkure et al. 20 (dashed line) and the proposed method (solid line). of the aorta segmentation with the manual annotations were 88.7% and 94.5% for the method by Kurkure et al. 20 and the proposed method, respectively. Figure 5 depicts a 3D isosurface visualization of the ascending and descending aorta segmentation results obtained using our method in two non-contrast cardiac CT scans of randomly selected patients. 4. CONCLUSION An entropy-based method for the segmentation of the ascending aorta is presented in this paper. The use of the local entropy in the cost function enabled the dynamic programming method to find the aorta boundary where the edge features failed, improving the segmentation results of the aorta significantly. Moreover, the iterative, narrow band-based approach allowed the contour to deviate from the circular shape assumption to capture the aortic boundary near the root of the aorta. The results from the proposed method compare well with the manually traced aorta boundaries and outperforms the previous approach. ACKNOWLEDGMENTS This work was supported in part by NIH 1R21EB A2 and UH Eckhard Pfeiffer Endowment Fund. Any opinions, findings, conclusions or recommendations expressed in this material are of the authors and may not reflect the views of the NIH. REFERENCES [1] National Institutes of Health, Disease statistics, tech. rep., National Heart Lung and Blood Institute (2007).

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