Chest Modeling and Personalized Surgical Planning for Pectus Excavatum Qian Zhao1, Nabile Safdar1, Chunzhe Duan1, Anthony Sandler2, and Marius George Linguraru1,3 1 Sheikh Zayed Institute for Pediatric Surgical Innovation, Children’s National Medical Center, Washington DC, USA 2 Department of General and Thoracic Surgery, Children’s National Medical Center, Washington DC, USA 3 School of Medicine and Health Sciences, George Washington University, Washington DC, USA

Abstract. Pectus excavatum is among the most common major congenital anomalies of the chest wall whose correction can be performed via minimally invasive Nuss technique that places a pectus bar to elevate the sternum anteriorly. However, the size and bending of the pectus bar are manually modeled intraoperatively by trial-and-error. The procedure requires intense pain management in the months following surgery. In response, we are developing a novel distraction device for incremental and personalized PE correction with minimal risk and pain, akin to orthodontic treatment using dental braces. To design the device, we propose in this study a personalized surgical planning framework for PE correction from clinical noncontrast CT. First, we segment the ribs and sternum via kernel graph cuts. Then costal cartilages, which have very low contrast in noncontrast CT, are modeled as 3D anatomical curves using the cosine series representation and estimated using a statistical shape model. The size and shape of the correction device are estimated through model fitting. Finally, the corrected/post-surgical chest is simulated in relation to the estimated shape of correction device. The root mean square mesh distance between the estimated cartilages and ground truth on 30 noncontrast CT scans was 1.28±0.81 mm. Our method found that the average deformation of the sterna and cartilages with the simulation of PE correction was 49.71±10.11 mm. Keywords: Pectus excavatum, personalized surgical planning, costal cartilage estimation, statistical shape models, correction device.

1

Introduction

Pectus excavatum (PE), involving posterior depression of the sternum and adjacent costal cartilages and ribs, is among the most common major congenital anomalies of the chest wall [1]. Severe deformities can cause cardiopulmonary impairment and reduction in lung volume. Anatomic evaluation of PE can be clinically performed using noncontrast CT with an index of severity (Haller Index) calculated based on measurements, electrocardiogram and cardiopulmonary exercise testing [1]. P. Golland et al. (Eds.): MICCAI 2014, Part I, LNCS 8673, pp. 512–519, 2014. © Springer International Publishing Switzerland 2014

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Surgical repair of PE can be performed via either an open operation or the minimally invasive Nuss technique. The Nuss procedure involves the placement of a substernal concave bar (pectus bar), which is passed behind the sternum through the chest and “flipped” into a convex position to elevate the sternum outward. However, the size and bending of the pectus bar are manually modeled intra-operatively by trialand-error based on the patient’s thoracic morphology (curvature). The process is slow, labor intensive and requires a high degree of expertise and experience. Another major disadvantage of the Nuss technique is the intensely painful post-surgical recovery. To address the above challenges, we are developing a novel image-guided PE correction device that can be programmed to assume the desired chest shape and provide personalized treatment. The series of changes in the curvature and angulation that results in the final shape can be programmed to optimize the correction of the deformity. The device is intended to provide a personalized PE correction with minimal risk and pain, akin to orthodontic treatment using dental braces. The design of the device will be based on chest modeling (including the ribs, sternum and cartilages) from noncontrast CT data and simulation techniques. Prior works on PE surgical planning are scarce. Vilaça et al. simulated the postsurgical cosmetic outcome in PE patients [2, 3]. The method focused on the skin simulation using a mass-spring model. However, it has been shown that the conventional pectus bar modeling based on the patient’s skin profile is imprecise [4]. More recently, the same group evaluated a system simulating the pectus bar, but the design of the bar was not presented [5]. Wei et al. developed a biomechanical model of PE based on a finite element model using a single patient CT image [6], but the rib cage used to establish the model was manually segmented. Zhao et al. estimated the general cartilaginous region based on mesh contraction, but they did not estimate the results of surgical correction [7]. In this study, we propose an automatic method to personalize the surgical planning for PE correction by simulating the post-surgical results (which include for the first time the anatomy of the ribs, sternum and cartilages) and estimating the size and shape of the correction device. The severity analysis of PE is also assessed by comparing the preoperative and the estimated postoperative chest shape. We first automatically segment the ribs and sternum using kernel graph cuts, followed by skeletonization. Then the costal cartilages are estimated using a statistical shape model (SSM) based on cosine series representation of 3D anatomical curves, a key methodological contribution to allow the accurate analysis of cartilages which are otherwise difficult to visualize on noncontrast CT. To estimate the post-surgical or corrected chest, an ICA-based SSM of normal chests, built with healthy subjects, allows matching a patient's anatomy to its most similar normal subject. This allows precisely simulating the post-surgical results via registration and estimating the size and shape of the correction devices through model fitting. Finally, the severity of the deformations of the chest of PE patients is computed in relation to the estimated correction device. The technology is applicable to the design of both the Nuss/pectus bar and the novel incremental correction device.

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Method

The method was evaluated on 30 thoracic CT scans of slice thickness 0.62 mm including 15 healthy subjects and 15 PE patients. The dataset consists of 25 male and 5 female patients with severe PE requiring corrective surgery (Haller index: 2.5-5.7) and average age of 14 years (range: 9-21). 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 ribs, sterna, cartilages from CT scans were provided by a board certified radiologists as ground truth. The ribs and sternum are first segmented using kernel graph cuts via kernel mapping (radial basis function used in this study) of the image data in the piecewise constant model of graph cuts [8]. 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 generated [9] and smoothed using Humphrey’s Classes Laplacian smoothing [10].To model the rib cage, the skeletons of ribs and cartilages are extracted using a mesh contraction method [11] by using implicit Laplacian smoothing with global positional constraints. 2.1

Cartilage Estimation

The skeletons of ribs and cartilages are modeled as 3D curves and parameterized as coefficients of the cosine series expansion [12]. Unlike traditional splines, the cosine series representation does not have internal knots and explicitly models curves as a linear combination of the cosine basis. Modeling cartilages as 3D curves with cosine series representation does not require manually labeled landmarks or evenly-placed pseudo landmarks. Moreover, it allows different numbers of control points on 3D curves for different samples. We first map a 3D curve with ordered control points to the unit interval based on the geodesic distance of the curve . Then the curve is parameterized using the cosine basis of where is the degree of the cosine basis the form in the study). The curve reconstructed with degree cosine basis is ( , where is the cosine basis and the cosine represented as coefficients. As the cosine series expansion is a compact representation of 3D curves, parameters instead of for a degree cosine series expansion, there are only coordinates (usually ) for building the SSM. We build a SSM of under the assumption of a Gaussian prior and therefore using principal component analysis (PCA): , where represents the mean coefficients, the eigenvector matrix and the shape parameters. Thus the SSM for 3D curves is . Fig. 1 (a) shows the first principal mode for the skeletons of ribs 1 through 7 and the corresponding cartilages. For model fitting, we estimate each cartilage between the end point of the rib and the joint with the sternum (shown in Fig. 1 (b)) by minimizing the difference between the reconstructed rib skeleton and the real rib skeleton extracted from the ground truth in a least squares fashion:

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b* = arg min ΨPb P + ΨC − Yobs , subject to − 2 λ < b < 2 λ

(1)

b

keleton (observation) and where is the real rib sk to eigenvectors .

the eigenvalues correspondding

Fig. 1. The cartilages model, start s and end points for estimating cartilages and the skin surfface of a PE patient: (a) the first principal p modes of variation for ribs and cartilages via PCA;; the shape parameters are set to ; (b) the end points of ribs (red dots) and the joints withh the sternum (blue dots); and (c) the skin surface of a PE patient.

The final cartilages are generated g as tubes centered on the cartilage centerlines. For each point on the centerlinee, an ellipse is generated. The distances between the cennterlines and the surface mesh on o ribs and sterna estimate the major and minor axes off the end points of cartilages. Th he major and minor axes of the intermediate points are assumed to vary linearly betw ween the end points along the centerline of the cartilage. 2.2

Simulation of PE Correction C and Estimation of Correction Device

ICA-Based Rib Cage Mod del Building To create the multi-atlas of the normal chest (rib cage) shape, a SSM containing seven pairs of ribs (left and rightt) is built with data from 15 normal subjects. The moodel does not contain the cartilaages or sterna, which can be severely deformed in PE patients, to allow matching th he closest healthy chest shape to each PE case, as descriibed below. For each rib, ten lan ndmarks are uniformly sampled from the rib skeleton. T The SSM is built using indepen ndent component analysis (ICA), instead of PCA, to moodel the local shape variations: where are the training samples of the the mixing matrix and the independent coomrib skeleton with mean shaape , ponents (ICs) regarded herre as shape parameters. The ICs are ordered and seleccted using the method in [13] by using the entropy and the interquartile range to meassure the sample variation. The cosine series method is not applicable here as we model the whole chest instead of indiv vidual ribs. Correction Device Design and Rib Cage Correction t shape parameter of a PE patient’s ribs is first callcuWith the ICA-based SSM, the lated. Then the most similaar normal chest/ribs of a PE patient’s anatomy from the healthy multi-atlas databasee is found using the Mahalanobis distance

516

Q. Zhao et al.

s* = arg min (s − s′)T Σ −1 (s − s′),

(2)

s* ≠ s ′

where is the covariance matrix of the normal rib cage samples. The design (shape and size) of the correction device is estimated based on the costal surface fitted by the ribs and cartilages. For the pre-correction design (at the time of surgery), the device is fitted to the shape of the PE patient. For the post-correction design, the device is fitted to the shape of the corresponding most similar normal chest to that of the PE patient (aligned using the Procrustes analysis [14]). The centerline of the correction device is first estimated as a 3D curve through the most depressed points on the sternal posterior surface and lateral ribs between the anterior and midaxillary lines. Then the centerline is projected to the costal surface fitted by the ribs and cartilages using thin plate spline [15]. The correction device is estimated based on the projected centerline with the typical pectus bar size of 1.5cm width and 2 mm thickness [16]. The estimated correction device is personalized to PE patient’s costal curvature instead of their skin profile, which is more precise and accurate especially for female patients. Finally, the PE patient’s sternum, ribs and cartilages are deformed using a deformation field formed by the pre- and post-correction shape of the device based on B-spline registration [17] to simulate the corrected/post-surgical chest anatomy.

3

Experiments and Results

3.1

Cartilage Estimation

The Dice coefficient for the segmentation of ribs and sternum was 0.88±0.02 and (0.95±0.03 for sternum alone). One random normal case was selected as the template and its rib skeleton was registered to all other cases using non-rigid point registration to [18]. Before building the SSM of cartilages, all training samples were aligned using Procrustes analysis to remove the translation, rotation and scale [14]. One model was built for each skeleton. As mainly cartilages 4 through 7 are frequently affected in PE patients, we modeled ribs and cartilages 1 through 7 on both sides of the thorax (left and right) to a total of 14 models. The joints between cartilages and sternum were found by registering the testing sternum with the template. Note that for model training, the skeleton of both ribs and cartilages were extracted, while for model fitting, only the rib skeleton was used. Leave-one-out cross-validation was performed. Three metrics were adopted to evaluate the method. One is the root mean square centerline distance error (RMSE-C) between the estimated cartilage centerlines and its ground truth, which was on average 2.50±0.80 mm. The RMSE-C for normal and PE cases were 2.04±0.44 mm and 2.74±0.85 mm, respectively. Another metric is the root mean square mesh distance error (RMSE-M) between the estimated cartilage mesh and the ground truth that was 1.28±0.81 mm. The RMSE-M for normal and PE cases were 1.20±0.34 mm and 1.14±0.38 mm, respectively. No significant difference of RMSE-M was recorded using the Wilcoxon test between normal subjects and PE

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Table 1. The mean RMSE-C, RMSE-M and AMD errors for each pair of cartilages. Errors are larger on the inferior cartilages due to larger and complex shape variations. All values are in millimeters (mm). Rib pair

1

2

3

4

5

6

7

RMSE-C

1.94±1.17

0.72±0.34

0.80±0.36

1.12±0.56

1.83±0.91

2.95±1.33

4.69±1.86

RMSE-M

1.47±1.39

0.64±0.68

0.49±0.43

0.43±0.30

0.48±0.36

0.79±0.52

2.4±1.05

AMDE

0.60±0.16

0.33±0.05

0.29±0.07

0.26±0.05

0.27±0.04

0.35±0.06

0.57±0.17

patients (p=0.72). The third metric is the average mesh distance error (AMDE) between the estimated cartilages and the ground truth, which was 0.38±0.16 mm. The RMSE-C, RMSE-M and AMDE of each pair of cartilages with the corresponding standard deviation are shown in Table 1. Fig. 2 shows the estimated cartilages of a PE case with the RMSE-M representing by the colormap. It can be seen that the errors of the cartilages 6 and 7 were generally larger that may be caused by their large shape variations and complex structures. 3.2

Rib Cage Correction and Correction Device Estimation

For correction device estimation, we performed experiments on the 15 retrospective CT data of PE patients. The average Mahalanobis distances between the shape parameters of the pre- and post-corrected ribcage and that of the closest normal were 5.58±1.08 and 4.50±0.78, respectively. Our reasoning is that the rib cage of the PE patient should be similar to that of the closest normal. The root mean square (RMS) distance between the pre- and post-correction ribs and the most similar normal anatomy were 11.15±2.68 and 10.02±2.49mm, respectively. Thus our method correctly identifies that there is no significant change in the shape of the ribs with the correction as observed clinically. Distinctively, the average deformation with correction of the sterna and cartilages was 49.71±10.11mm. Since the conventional bar modeling and bending are based on the patient’s skin surface morphology, we evaluated our method using the distance between our automatically estimated device (Fig. 3.d) and the surface of the chest convex hull (Fig. 3.e), which was 16.50±4.60 mm. This result reconfirms that the skin surface morphology is not a precise approximation of the shape of the rib cage; this is particularly relevant for overweight patients and females. Instead, our method evaluates the shape of the sternum, ribs and cartilages, the anatomical areas involved in PE correction. An example of corrected rib cage (post-surgery simulation) from a PE patient is shown in Fig. 3, with the color indicating severity of the PE deformation as the difference between the pre- and post-surgical rib cage. For conventional Nuss surgery, the bar is fitted to the post-correction shape (Fig. 3.d), as the correction is done in a single but extremely painful step. For designing our new correction device, we require both the shape at the beginning of correction (Fig. 3.c) and at the end of correction (Fig. 3.d) to compute the incremental shape changes for PE correction. The intermediary steps are not addressed in this paper.

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Fig. 2. The estimated cartilagees of a PE patient: (a) the anatomy of the cartilages, ribs and ssternum; (b) the estimated cartilag ges using a colormap indicating RMSE-M; and (c) the side vview of (b). All values are in millim meters.

Fig. 3. The estimated corrected d rib cage and the shape of correction device: (a) the correctedd rib cage of the PE case shown in Fig.2 F and the color indicates the severity of the PE deformatioon as the difference between the pree- and post-surgical (simulated) rib cage; (b) the side view of (a); (c) the shape of the device beffore correction (note the lifting of the chest compared to Fig. 2.c, as shown by colormap); (d) th he shape of the device after correction using our method; andd (e) the shape of the device estimatted from the patient’s skin profile. All values are in millimeterrs.

4

Conclusion

We proposed a personalized d surgical planning method for PE correction using clinnical noncontrast CT scans, whicch allows the modeling of the chest anatomy, including the ribs, sternum and cartilages, and simulating precise post-surgical results for the ffirst time. As a methodological contribution, the skeletons of costal cartilages were m modeled as 3D curves using th he cosine series representation and estimated using a SSM built with the cosine coefficcients to allow the accurate analysis of cartilages which are difficult to visualize on non nconstrast CT. Then the ICA-based SSM of the normall rib cage allowed matching a PE E patient’s anatomy to its most similar normal subjects and estimating the severity of th he chest deformation. The average deformation of the ssterna and cartilages with the simulation of PE correction was 49.71±10.11 mm. T The technology is applicable to estimating the size and shape of both the Nuss/pectus bbar, as in current clinical practicce, and the design of the new correction device for optim mal and incremental correction of PE in a less painful and controlled setting.

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References 1. Jaroszewski, D., 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 23, 230–239 (2010) 2. Moreira, A.H.J., et al.: Pectus excavatum postsurgical outcome based on preoperative soft body dynamics simulation. In: Proc. SPIE, pp. 83160K–83160K (2012) 3. Vilaça, J.L., et al.: Virtual simulation of the postsurgical cosmetic outcome in patients with Pectus Excavatum. In: Proc. SPIE, pp. 79642L–79642L (2011) 4. Lai, J.-Y., et al.: The measurement and designation of the pectus bar by computed tomography. Journal of Pediatric Surgery 44, 2287–2290 (2009) 5. Vilaça, J.L., et al.: Automatic Prebent Customized Prosthesis for Pectus Excavatum Minimally Invasive Surgery Correction. Surgical Innovation (2013) 6. Wei, Y., et al.: Pectus Excavatum Nuss Orthopedic finite element simulation. In: Biomedical Engineering and Informatics (BMEI), pp. 1236–1239 (2010) 7. Zhao, Q., et al.: Estimation of Cartilaginous Region in Noncontrast CT of the Chest. In: Proc. SPIE (in press, 2014) 8. Salah, M.B., et al.: Multiregion Image Segmentation by Parametric Kernel Graph Cuts. IEEE Transactions on Image Processing 20, 545–557 (2011) 9. Fang, Q., Boas, D.A.: Tetrahedral mesh generation from volumetric binary and grayscale images. In: ISBI 2009, pp. 1142–1145 (2009) 10. Vollmer, J., et al.: Improved Laplacian Smoothing of Noisy Surface Meshes. Computer Graphics Forum 18, 131–138 (1999) 11. Au, O.K.-C., et al.: Skeleton extraction by mesh contraction. ACM Trans. Graph. 27, 1–10 (2008) 12. Chung, M.K., et al.: Cosine series representation of 3D curves and its application to white matter fiber bundles in diffusion tensor imaging. Statistics and Its Interface 3, 69–80 (2010) 13. Zhao, Q., Okada, K., Rosenbaum, K., Zand, D.J., Sze, R., Summar, M., Linguraru, M.G.: Hierarchical Constrained Local Model Using ICA and Its Application to Down Syndrome Detection. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part II. LNCS, vol. 8150, pp. 222–229. Springer, Heidelberg (2013) 14. Gower, J.C.: Generalized procrustes analysis. Psychometrika 40, 33–51 (1975) 15. Bookstein, F.L.: Principal warps: thin-plate splines and thes decomposition of deformations. PAMI 11, 567–585 (1989) 16. Puri, B., et al.: Nuss procedure for pectus excavatum - An early experience. Medical Journal Armed Forces India 59, 316–319 (2003) 17. Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. PAMI 14, 239–256 (1992) 18. Myronenko, A., Xubo, S.: Point Set Registration: Coherent Point Drift. PAMI 32, 2262– 2275 (2010)

Chest Modeling and Personalized Surgical Planning for Pectus ...

1 Sheikh Zayed Institute for Pediatric Surgical Innovation,. Children's National Medical Center, Washington DC, USA. 2 Department of General and Thoracic Surgery,. Children's National Medical Center, Washington DC, USA. 3 School of Medicine and Health Sciences,. George Washington University, Washington DC, USA.

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