CARTILAGE ESTIMATION IN NONCONTRAST THORACIC CT Qian Zhao1, Nabile Safdar1, Glenna Yu2, Emmarie Myers1, Antony Koroulakis3, Chunzhe Duan1, Anthony Sandler4, Marius George Linguraru1 1

Sheikh Zayed Institute for Pediatric Surgical Innovation, Children’s National Medical Center, Washington DC, USA 2 Computer Science Department, Princeton University, NJ, USA 3 School of Medicine, George Washington University, Washington DC, USA 4 Department of General and Thoracic Surgery, Children’s National Medical Center, Washington DC, USA

ABSTRACT

Surgical repair of PE can be performed via either open operation (Ravitch technique) or minimally invasive procedure (Nuss technique) that involves sternum relocation with or without resection of cartilages. The advantages of the Nuss approach include no incision of anterior chest wall, no resection of rib cartilages, and no sternal osteotomy. Cartilage plays an important role in PE correction, particularly in minimally invasive procedures where current surgical planning is ad-hoc and based on the experience of the surgeon. The complex anatomy of 3D cartilages is an important factor for the design of surgical devices for PE correction. Moreover, the accurate analysis of the cartilaginous structures is essential for severity analysis of PE. In our study, estimating the costal cartilages will allow for modeling the entire rib cage, providing critical information for surgical planning. However, cartilage estimation in noncontrast CT scans is an unexplored topic and a challenging task, due to the poor contrast between cartilage and muscle in the chest (shown in Fig.1). The segmentation of costal cartilages was only addressed in contrast CT [3] and MRI images [4]. Specific to PE correction, Vilaça et al simulated the postsurgical cosmetic outcome in patients with PE [5, 6]. The method focuses on the skin simulation using a mass-spring model. The cartilages were simply estimated using B-spline interpolation mainly for visualization without quantitative evaluation. In this study, we propose a novel method to estimate cartilages in the rib cage using a statistical shape model based on cosine series representation of 3D anatomical curves and skin contraction. The ribs and sternum are first segmented by using interactive region growing, followed by the mesh extraction. The skeletons of the ribs, extracted using surface contraction method, are 3D curves and modeled with cosine series expansion. Then, a statistical shape model is built on the cosine coefficients using skeletons of both ribs and cartilages. During model fitting, the cartilages are estimated by minimizing the difference between the reconstructed rib centerlines and their corresponding ground truth. Finally, the cartilage surface is approximated by the contracted surface of the thoracic skin.

Pectus excavatum (PE) is the most common major congenital deformity that involves the lower sternum and cartilages. Noncontrast CT is useful to assess the deformity of the bones and guide minimally invasive surgery. However, it has very poor visibility of cartilages even for the experienced clinicians who need to assess the 3D geometry of cartilages. In this study, we propose a novel method to estimate cartilages in noncontrast CT scans. The ribs and sternum are first segmented using region growing. The skeleton of the ribs is extracted and modeled by cosine series expansion. Then a statistical shape model is built with the cosine coefficients to estimate the cartilages as curves that connect the ribs and sternum. The results are refined by the cartilage surface that is approximated by contracting the skin surface to the bones. Leave-one-out validation was performed on 12 CT scans from healthy and PE subjects. The average distance between the estimated cartilages and ground truth is 1.53 mm. The promising results indicate that our method could estimate the costal cartilages in noncontrast CT effectively and assist to develop an imagebased surgical planning system for PE correction. Index Terms— Pectus excavatum, cartilage estimation, statistical shape model, cosine series representation 1. INTRODUCTION Pectus excavatum (PE) is a posterior depression of the sternum and adjacent costal cartilages and is the most common major congenital deformity of the chest wall found in patients in the United States [1]. It occurs in approximately 1 of every 300 to 400 white male births [2]. PE is more than a cosmetic deformity. Severe deformities can cause cardiopulmonary impairment and reduction in lung volume resulting in easy fatigability, decreased stamina and diminished exercise tolerance. The PE depression most frequently involves the lower end of sternum and cartilages 4 through 7 with varying degrees of rotation and asymmetry. Anatomic evaluation of PE can be performed using noncontrast CT and an index of severity can be calculated based on the physical measurements [1].

978-1-4673-1961-4/14/$31.00 ©2014 IEEE

409

expansion [11]. Unlike traditional splines, the cosine series representation does not have internal knots and explicitly models curves as a linear combination of cosine basis. We denote a 3D curve with n ordered control points p1 , , pn

as X = [ x1 , y1 , z1 ;  xn , yn , zn ] and map it to the unit interval [ 0,1] based on the geodesic distance of the curve

Fig. 1 Noncontrast thoracic CT scans: (a) axial view (b) coronal view and (c) sagittal view. The ribs and sternum are clearly shown, while the cartilages are hardly visible in noncontrast CT.

∑ ∑

pj → tj =

2. METHODS

j i =1 n i =1

pi − pi −1 pi − pi −1

,

(2)

where we assume t1 = 0 . Then the curve is parameterized using the cosine basis of the form (3) = ψ 0 ( t ) 1,= ψ k (t ) 2 cos ( kπ t ) ,

The method was evaluated on 12 thoracic CT scans of slice thickness 0.62 mm including six healthy subjects and six PE patients. Each volumetric image consisted of axial images of size 512 ×512 pixels with in-plane resolution ranging from 0.59 to 0.82 mm. The manually segmented cartilages from CT scans by our radiologists were provided as the ground truth. The method includes model training and fitting that will be introduced in detail.

where k is the degree of cosine basis. The curve reconstructed with k degree cosine basis is represented as (4) Yn×3 = Ψ n×k Ck ×3 , where Y is the reconstructed curve, Ψ the cosine basis and C the cosine coefficients that are estimated as

C = ( ΨT Ψ ) ΨT Y . −1

2.1. Segmentation and Skeleton Extraction The ribs and sternum are segmented using interactive region growing and smoothed via morphological operations [7]. The whole chest is also segmented and smoothed using the aforementioned method to estimate the skin surface. However, this type of segmentation is not applicable to the cartilage, which is poorly, if at all, visible in noncontrast CT. After segmentation, the surface meshes are extracted from both the osseous (ribs and sternum) and whole chest (skin) segmentations [8] and smoothed using HC (Humphrey’s Classes) Laplacian smoothing [9]. To model the rib cage, the skeleton of ribs and cartilages are extracted using a mesh contraction method [10]. The geometric contraction removes details and noise from the mesh surface by applying a Laplacian smoothing that moves the vertices V to V ′ along their normal directions by solving the discrete Laplacian equation: LV ′ = 0 , where L is the curvature-flow Laplace operator. To ensure that the contracted mesh abstracts the original shape well, all the vertices are attracted to their current positions using soft constraints with different weights. The skeleton is obtained by solving the following equations for the vertex positions WL L   0  (1)  W  V ′ = W V  ,  H   H  where WL and WH are the diagonal weighting matrices that balance the contraction and attraction constraints.

(5)

The cosine series expansion is a compact representation of 3D curves. For a k degree cosine series expansion, there are only 3 ( k + 1) parameters instead of 3n coordinates (usually n  k ) for building the statistical shape model. After curve parameterization, we build a statistical model of the cosine coefficients C using PCA (6) C = C + P ⋅ b, where C represents the mean coefficients, P the eigenvector matrix and b the shape parameters. Substituting (7) to (5), we obtain the statistical shape model for 3D curves (7) Y = ΨC + ΨPb. Fig. 2 shows the first three principal modes for skeleton of ribs 1 through 8 and the corresponding cartilages.

Fig.2 The first three principal modes of PCA: (a) the first principal mode; (b) the second principal modes and (c) the third principal mode. The shape parameters are set to ±2 λ .

For model fitting, we estimate each cartilage between the end point of the rib and the joint with the sternum by minimizing the difference between the reconstructed rib skeleton using (8) and the real rib skeleton extracted from the ground truth in a least squares fashion

2.2. Statistical Shape Model based on Cosine Series Representation

= b*

The skeletons of ribs and cartilages are modeled as 3D curves and parameterized as coefficients of the cosine series

arg min ΨPb + ΨC − Yobs , b

410

(8)

subject to − 2 λ < b < 2 λ where Yobs is the real rib skeleton (observation) and λ the eigenvalues corresponding to eigenvectors P . The estimated skeletons of ribs and cartilages are reconstructed using (8). 2.3. Cartilage Refinement by Skin Surface Contraction The cartilages 6 through 8 have longer length and larger variations compared to the first five pairs, so they are prone to errors and refined by using the cartilage surface contracted from the skin surface. To estimate the anterior surface of the cartilage, we contract the skin surface to the anterior surface of the ribs and sternum. As the skin and bone structures are different types of objects, typical registration methods fail to register one to the other directly. In this study, we proposed to register the skin surface and rib cage using surface contraction. The vertices of the skin surface are first projected to the bone mesh to create correspondences. Then the deformation field is computed using B-spline registration with these correspondences [12]. Finally, the vertices of the skin surface are contracted along their normal directions with the amount indicated by the deformation filed. The contracted skin surface, touching the anterior surface of the bone mesh, simulates the cartilage surface  c (9) v= vis − di ni , i where vis is the ith vertex on the skin surface, di the distortion  value of the ith vertex, ni its normal direction and vic the projected vertex on the cartilage surface. The cartilage skeleton and the cartilage surface are not parallel and the distance between them is fitted as a Gaussian function using the training samples. For cartilage centerline refinement, the estimated cartilages are first projected to the cartilage surface and then projected back with the distance trained as a Gaussian function  (10) v → u → v ′ = u + g ⋅ nF , where v is the estimated cartilage centerline, u the projection of v on the cartilage surface, v ′ the refined cartilage centerline, g the distance values generated by the fitted  Gaussian function and nF the normal of the face that contains u on the cartilage surface. The cartilage surface with the projection of ribs and cartilages is shown in Fig. 3. The final cartilages are generated as tubes from the refined cartilage centerlines. For each point on the centerline, an ellipse is generated. The major and minor axes of the end points of cartilages are estimated by the distance between the centerlines and the surface mesh. The major and minor axes of the intermediate points are assumed to vary linearly between the end points of the cartilage along the centerline.

411

Fig. 3 The cartilage surface with the projections of the centerlines of ribs and cartilages: (a) a normal case; (b) a PE case and (c) a CT scan of axial view of the PE case. The deformed region in the PE case has been highlighted with a red circle compared with the healthy case.

3. EXPERIMENTS One random normal case is selected as the template and its rib skeleton is registered to all other cases using non-rigid point registration to obtain the correspondences [13]. Before building the statistical shape model, all training samples are aligned using Procrustes analysis [14]. The skeletons of ribs and cartilages are parameterized using the cosine series representation of 19 degrees. One model is built for each skeleton. As only cartilages 4 through 7 are frequently affected in PE patients, we model cartilages 1 through 8 on both sides of the thorax (left and right) to a total of 16 models. The joints between cartilages and sternum are found by registering the testing sternum with the template. Leaveone-out validation was performed and each cartilage was estimated between the end point of the rib and the joint with the sternum. Please note that for model training, the skeletons of both ribs and cartilages were extracted, while for model fitting, only the rib skeleton was used. We evaluated the method in two ways. One metric D1 is the average distance between the estimated cartilage centerlines and the real centerlines extracted from ground truth, which was 2.09±1.26 mm (mean±std) in our study. The D1 distance for PE and normal cases were 2.45±1.41 and 1.75±1.10 mm, respectively. The other metric D2 is the average surface distance between the estimated cartilages and the ground truth mesh, which was 1.53±1.0 mm. The D2 distance for PE and normal cases were 1.61±0.58 mm and 1.46±0.51 mm, respectively. No significant difference was recorded using the Wilcoxon test (p=0.11). The average centerline distance and point to mesh distance of each pair of cartilage with the corresponding standard deviation is shown in Table I. Fig. 4 shows the estimated rib cage and Fig. 5 shows the estimated cartilages for both healthy and PE cases. It can be seen that the errors of the cartilages 6 through 8 are generally larger due to their large variation and deformation in PE patients. Fig. 6 shows the rib cage deformation in PE patients compared with a healthy case. The deformity is computed as the distance along y-axis (posterior to anterior) between the rib cage and its mass

center. It can be seen that the deformities mainly involve the cartilages and lower sternum.

as 3D curves using the cosine series representation. A statistical shape model was built with the cosine coefficients. During model fitting, the cartilages were estimated by minimizing the difference between the reconstructed rib centerlines and the rib ground truth. The final results were refined by the cartilage surface that was approximated by contracting the skin surface. The average distance between the estimated cartilages and the ground truth mesh was 1.53 mm. The estimated cartilages depicted the cartilage deformation of pectus excavatum patients, indicating the severity of the disease. Data collection is ongoing. We will also investigate the fully automatic segmentation of ribs and sternum in future work.

Table I The average centerline distance and point to mesh distance with the corresponding standard deviation for each pair of cartilages. Rib Pair

1

2

3

4

5

6

7

8

D1 (mm)

1.45

1.47

1.18

1.73

1.90

2.95

3.28

3.69

Std (mm)

0.85

0.72

0.76

1.17

1.07

1.08

1.30

1.32

D2 (mm)

1.52

1.22

1.10

1.31

1.44

1.93

2.04

1.93

Std (mm)

0.41

0.39

0.24

0.42

0.44

0.50

0.65

0.48

5. ACKNOWLEDGMENT This project was supported by a philanthropic gift from the government of Abu Dhabi to Children’s National Medical Center. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the donor. 6. REFERENCES

Fig.4 The estimated anatomy of the rib cage: (a) a healthy case; (b) a PE case.

[1]

[2] [3] [4] Fig.5 The estimated cartilages: (a) a healthy case; (b) a PE case. All values are in millimeters.

[5] [6] [7]

[8]

[9]

Fig. 6 The comparison of the rib cage deformation between (a) a healthy case and (b) a PE case. The color indicates the distance along y-axis between the rib cage and its mass center. All values are in millimeters.

[10] [11]

4. CONCLUSION

[12]

We presented a method to estimate the costal cartilages from noncontrast CT scans. The ribs, sternum and the whole chest wall were first segmented using region growing method, followed by surface mesh extraction. Then the skeletons of ribs and cartilages were extracted and modeled

[13] [14]

412

D. Jaroszewski, et al., "Current Management of Pectus Excavatum: A Review and Update of Therapy and Treatment Recommendations," The Journal of the American Board of Family Medicine, vol. 23, pp. 230-239, March 1, 2010 2010. M. Gonzalez, et al., "Management of pectus excavatum," Revue medicale suisse, vol. 9, pp. 1312-1316, 2013. A. B. Holbrook and K. B. Pauly, "Segmentation of Costal Cartilage in Abdominal CT Data using Watershed Markers," AIP Conference Proceedings, vol. 911, pp. 226-231, 2007. Y. Noorda, et al., "Segmentation of the Cartilage in the Rib Cage in 3D MRI," in Abdominal Imaging. Computational and Clinical Applications. vol. 7601, H. Yoshida, et al., Eds.: Springer Berlin Heidelberg, 2012, pp. 229-237. J. L. Vilaça, et al., "Virtual simulation of the postsurgical cosmetic outcome in patients with Pectus Excavatum," pp. 79642-79642, 2011. A. H. J. Moreira, et al., "Pectus excavatum postsurgical outcome based on preoperative soft body dynamics simulation," pp. 83160K83160K, 2012. Z. Ma, et al., "A review of algorithms for medical image segmentation and their applications to the female pelvic cavity," Computer Methods in Biomechanics and Biomedical Engineering, vol. 13, pp. 235-246, 2010/04/01 2009. Q. Fang and D. A. Boas, "Tetrahedral mesh generation from volumetric binary and grayscale images," in Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on, 2009, pp. 1142-1145. J. Vollmer, et al., "Improved Laplacian Smoothing of Noisy Surface Meshes," Computer Graphics Forum, vol. 18, pp. 131-138, 1999. O. K.-C. Au, et al., "Skeleton extraction by mesh contraction," ACM Trans. Graph., vol. 27, pp. 1-10, 2008. M. K. Chung, et al., "Cosine series representation of 3D curves and its application to white matter fiber bundles in diffusion tensor imaging," Statistics and Its Interface, vol. 3, pp. 69-80, 2010. P. J. Besl and N. D. McKay, "Method for registration of 3-D shapes," 1992, pp. 586-606. A. Myronenko and S. Xubo, "Point Set Registration: Coherent Point Drift," Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 32, pp. 2262-2275, 2010. J. C. Gower, "Generalized procrustes analysis," Psychometrika, vol. 40, pp. 33-51, 1975/03/01 1975.

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