Realistic Colon Simulation in CT Colonography Using Mesh Skinning Jianhua Yao, Ananda S. Chowdhury, and Ronald M. Summers Imaging Biomarkers and Computer-Aided Diagnosis Laboratory, Radiology and Imaging Sciences Department, Clinical Center, National Institutes of Health, Bethesda, Maryland 20892 USA [email protected]

ABSTRACT Realistic colon simulations do not exist but would be valuable for CT colonography (CTC) CAD development and validation of new colon image processing algorithms. The human colon is a convoluted tubular structure and very hard to model physically and electronically. In this investigation, we propose a novel approach to generate realistic colon simulation using mesh skinning. The method proceeds as follows. First, a digital phantom of a cylindrical tube is modeled to simulate a straightened colon. Second, haustral folds and teniae coli are added to the cylindrical tube. Third, a centerline equipped with rotation-minimizing frames (RMF) and distention values is computed. Fourth, mesh skinning is applied to warp the tube around the centerline and generate realistic colon simulation. Lastly, colonic polyps in the shape of ellipsoids are also modeled. Results show that the simulated colon highly resembles the real colon. This is the first colon simulation that incorporates most colon characteristics in one model, including curved centerline, variable distention, haustral folds, teniae coli and colonic polyps. Keyword: CT Colonography, Mesh Skinning, Colon Simulation

1. INTRODUCTION Colorectal cancer is the second leading cause of cancer death in the United States, estimated to claim over 53000 lives in 2006 alone 1. Screening is currently the most suitable method for early detection and removal of colonic polyps. CT colonography (CTC) is an emerging screening modality. CTC is a minimally invasive technique and can detect both precancerous polyps and colon cancers. The accuracy of CTC is reported by some investigators to be close to that of traditional optical colonoscopy (OC) 2. Since CTC is a diagnostic test, polyps found at CTC must be removed at a subsequent colonoscopic procedure. This separation of diagnostic and treatment phases presents an opportunity to reduce the number of unnecessary invasive OC procedures for screening purposes. Figure 1 shows one 2D slice, 3D surface rendering and 3D virtual fly-through of a CTC study. Many investigations had been conducted on CTC in the past decade. Major research fields include computer-aided detection (CAD) of colonic polyp 3-9, colon segmentation 10, polyp segmentation and measurement 11-14, colon flythrough navigation 15, 16, centerline extraction 17, 18, colon unfolding 19-22, and supine-prone registration 23. One important aspect of medical image processing research is the validation method and ground truth data. Most CTC investigation used records from OC 3 or manual tracing 12 on CTC as the reference standard or ground truth for validation. However, records from OC only have limited information such as distance along the colonoscope (with a resolution of about 5 cm) and estimated linear measurement of the polyp size. Manual polyp delineations on CTC are widely used in the validation of polyp detection and segmentation, but they suffer from intra- and inter-observer variability 11. For the investigations such as colon segmentation, navigation, unfolding and centerline extraction, the

Medical Imaging 2010: Visualization, Image-Guided Procedures, and Modeling, edited by Kenneth H. Wong, Michael I. Miga, Proc. of SPIE Vol. 7625, 76252J · © 2010 SPIE · CCC code: 1605-7422/10/$18 · doi: 10.1117/12.844224

Proc. of SPIE Vol. 7625 76252J-1

ground truth data is very difficult (if not impossible) to obtain since it involves a huge amount of 3D data and manual operation. To handle this problem, phantoms are widely used to validate the CTC techniques. One type of phantom is the physical phantom, where certain materials are used to fabricate a tubular colon structure. The first colon phantom was designed by Beaulieu et al. 24 using plastic tubes and spherical plastic beads to study the data acquisition implications for CTC. Zhang et al. 25 used a commercial phantom to evaluate their colon straightening algorithm. Ling et al. 26 used an air-filled acrylic tube placed within a water-filled box to evaluate the effect of scan orientation, polyp size, collimation and dose. Laghi et al. 27 used a colonic phantom with simulated polyps to optimize the CTC scanning protocol on a multidetector scanner. Johnson et al. 28 designed an air-filled colon phantom containing haustral folds, flexures and straight segments made out of borosilicate. They used this phantom to determine the thickest slice at the lowest radiation dose for CTC. Zalis et al. 29 designed a U-shape colon phantom made of soft tissue compatible material to evaluate the effect of bowel contrast material and subtraction software on the size measurements of polyps. Pickhardt et al. 30 used a polymethyl methacrylate cylinder and acrylic spheres to evaluate the linear measurement of polyps. Fletcher et al. 31 used a handblown glass colonic phantom filled with synthetic epoxy resin and powder polyps to evaluate the accuracy and precision of polyp measurement. Physical phantoms are hard to make and most investigations only use one physical phantom which is not sufficient to characterize all the diversities in human colon anatomy. Furthermore, physical phantoms are mostly used for evaluating the scanning protocol. Their use on image post-processing tasks such as colon segmentation and navigation is limited since ground truth is hard to obtain. Another type of phantom is the digital phantom, which uses mathematical and mechanical models to simulate colon and polyp structures. Summers et al. 32 applied mathematical models to study the curvature and shapes of polyps. Zhang et al. 33 used a curved tube model to demonstrate their elastic deformation model for colon straightening. Chowdhury et al. 34 used a cylindrical model equipped with haustral folds to evaluate their fold detection method. Digital phantoms have several advantages: they are easy to generate, can be modified to serve different applications and different phantoms can be generated using different parameters. However, one potential problem with the digital phantoms is that they do not appear to be very realistic. Until now, no digital phantom that resembles a real colon and incorporates all colon characteristics has been proposed in the literature. In this paper, we propose a realistic colon phantom based on mesh skinning. The rest of the paper is organized in the following manner. Section 2 describes the detailed method, including four stages to generate the phantom. Section 3 presents the results, and Section 4 provides the conclusion.

A) B) Figure 1. CT colonography A) 2D axial slice; B) 3D exterior surface rendering; C) 3D endoluminal fly-through.

Proc. of SPIE Vol. 7625 76252J-2

C)

2. METHODS 2.1 Method outline The flow chart of our method is summarized in Figure 2. The method proceeds as follows. First, a digital phantom of a cylindrical tube is modeled to simulate a straightened colon. Second, haustral folds and teniae coli are added to the cylindrical model. Third, a centerline equipped with rotation-minimizing frames (RMF) and distention values is computed. Fourth, mesh skinning is applied to warp the tube around the centerline and generate realistic colon simulation. Lastly, colonic polyps in the shape of ellipsoids are also modeled.

Cylindrical tube modeling

Haustral fold and teniae coli modeling

Centerline modeling

Mesh skinning

Polyp modeling

Figure 2. System flowchart

2.2 Straight colon modeling with haustral folds and teniae coli Since the colon is a tubular structure, we start with a cylinder to simulate a straightened colon. The cylindrical tube is created from a digital phantom in a 3D rectangular grid. The mathematical formula of the cylinder is,

⎧( x − x0 ) 2 + ( y − y 0 ) 2 ≤ R 2 ⎨ 0≤ z≤l ⎩

(1)

here the cylinder is parallel to the z axis, (x0, y0) is the location of its central axis, R is the radius and l is the length of the cylinder. x0, y0, R and l are controlled by a parameter file. The voxels inside the cylinder are set to a foreground value and those outside set to a background value. Haustral folds are then added in the form of indentations onto the tube. These folds are modeled as a series of trisected tori with elliptic cross-sections, and can be mathematically described by:

Proc. of SPIE Vol. 7625 76252J-3

⎧ x(u, v) − x0 ≤ ( R + h cos v) cos u ⎪ ⎨ y (u, v) − y 0 ≤ ( R + h cos v) sin u ⎪ z (u, v) − z 0 ≤ w sin v ⎩

(2)

In the above equation, (u, v) are in the interval of [0, 2π], (x0, y0, z0) is the location of center of the torus (essentially the centers are points on the axis of the cylinder), h is the height and w is the width of the torus, and R is same as in equation (1). Since the haustral fold consists of three sections partitioned by teniae coli, the torus is trisected into three parts. The trisections are partitioned equally in circumferential location at 0, 2π/3 and 4π/3, which is implemented by varying u in equation (2). Assuming the width of teniae coli to be Wt, u lies in the interval [0, 2π/3 - Wt] for fold 1, [2π/3, 4π/3 - Wt] for fold 2, and [4π/3, 2π - Wt] for fold 3. The location, thickness and height of the folds, and the width of teniae coli are all adjustable using a parameter file. By varying thickness, we generate thin and thick folds. In contrast, by changing height, we model shallow and deep folds. A volumetric image of a digital colon phantom is obtained in this process. Then a Gaussian kernel is applied to smooth the volumetric image. A marching cubes algorithm 35 is performed to compute the corresponding phantom surface. Example cross-sections and surface of the simulated straight colon are shown in Figure 3.

Haustral folds Teniae coli

A)

B)

C) Figure 3. Straight colon phantom with haustral folds and teniae coli A) Axial cross section, B) sagittal cross section, and C) 3D surface

2.3 Centerline modeling The next step is to warp the straight colon along a centerline just like in a real colon. To make the simulation realistic, we extract centerlines from clinical CTC studies and apply them in the simulation. We fit a B-spline curve for the centerline and discretize it at 0.5mm resolution. The Frenet-Serret frame (FSF) at the centerline point cj is defined by its r r r tangent t j , normal n j and binormal b j vectors. We then transform the FSF into a rotation-minimizing frame (RMF) 36

,M

j

{

}

r r r = t j , f 1 j , f 2 j , where

Proc. of SPIE Vol. 7625 76252J-4

r r r f 1 j = sin Ω j b j + cos Ω j n j r r r f 2 j = cos Ω j b j − sin Ω j n j

(3)

here Ω is the angle difference of two neighboring frames, u

Ω j = − ∫ τ (t ) c&(t ) dt

(4)

0

{r

r

r

}

here τ = det {c&, c&&, &c&&}/ c& × c&& is the torsion of the curve. The proof that the RMF M (u ) = t (u ), f 1 (u ), f 2 (u ) is rotation2

36

minimizing along the centerline can be found in . The RMF ensures a smooth transition along the centerline. Furthermore, distention values {dj} are also assigned to the centerline, which defines the diameter of the cross section at centerline location j. The distention values can be computed from a real colon using a progressive ring set technique or provided in a parameter file. The distention value is set to 0 to model collapsed colon segments. 2.4 Mesh skinning Mesh skinning 37 is a skeleton-driven deformation technique widely used in computer animation. We apply this technique to warp the cylindrical tube around the centerline. The mesh skinning is formulated as,

vi '.x = v~i .x × d j v '.y = v~ . y × d i

i

vi '.z = v~i .z

(5)

j

and

vi = c j + M j (vi '−c j ' )

(6)

~ is a vertex on the tube phantom surface, c ’ is the corresponding centerline point on the phantom, c is the here v j j i corresponding centerline point on the simulated colon, dj is the distention value at cj, Mj is the rotation-minimizing frame ~ on the simulated colon. The topological connectivity amongst vertices is at cj. vi is the transformed location of v i preserved in the simulation. 2.5 Colonic polyp modeling Lastly, colonic polyps, modeled as semi-ellipsoids, are added to the phantom. The formula is written as,

⎧( x − x p , y − y p , z − z p ) o O x ≤ rx ⎪ ⎨( x − x p , y − y p , z − z p ) o O y ≤ ry ⎪( x − x , y − y , z − z ) o O ≤ r p p p z z ⎩

(7)

Here (xp, yp, zp) is the location of the polyp, (Ox, Oy, Oz) is the orientation, and (rx, ry, rz) is the size. ◦ is the dot product between two 3D vectors. The size, location and orientation of the polyps are specified in a parameter file.

3

RESULTS

We have applied this technique to generate 20 different colon phantoms using centerline information from 20 different CTC studies. Figure 4 shows the exterior and interior colon surfaces of a CTC study and those of a simulated colon. The simulated colon highly resembles the real one when we examine the colon flexures, fold locations, and distensions. Noise, spiral artifact and fluid subtraction artifact are visible in the real colon. Those are currently not modeled in the phantom. We also added a 2.5cm polyp in the simulated colon, which is shown in Figure 5.

Proc. of SPIE Vol. 7625 76252J-5

4

CONCLUSION

This paper presents a novel approach to generate realistic colon simulations. This is the first colon simulation that incorporates most colon characteristics in one model, including a curved centerline, variable distention, haustral folds, teniae coli and colonic polyps. We employ a mesh skinning technique to generate realistic colon simulation. The simulation will be valuable in the validation of computer aided polyp detection, polyp measurement, colon unfolding, fold detection, teniae detection, supine and prone registration, and optical colonoscopy and CTC matching.

a) exterior surface of real colon

b) exterior surface of simulated colon

c) interior surface of real colon d) interior surface of simulated colon Figure 4. Surface of real and simulated colons The simulated colon in b) and d) uses the centerline from a) and c)

Proc. of SPIE Vol. 7625 76252J-6

Figure 5. Simulated 2.5 cm polyp (arrow) in a simulated colon

5. ACKNOWLEDGEMENTS The authors thank Perry J. Pickhardt, William R. Schindler and Richard Choi for providing computed tomographic colonography and supporting data. This research was supported by the Intramural Research Program of the National Institutes of Health, Clinical Center.

6. REFERENCES 1. 2.

A. Jemal, R. Siegel, E. Ward, Y. Hao, J. Xu, T. Murray, and M. J. Thun, "Cancer Statistics," CA Cancer J Clin 58, 71-96 (2008). P. J. Pickhardt, J. R. Choi, I. Hwang, J. A. Butler, M. L. Puckett, H. A. Hildebrandt, R. K. Wong, P. A. Nugent, P. A. Mysliwiec, and W. R. Schindler, "Computed Tomographic Virtual Colonoscopy to Screen for Colorectal Neoplasia in Asymptomatic Adults," the New England Journal of Medicine 349(23), 2191-2200 (2003). 3. R. M. Summers, J. Yao, P. J. Pickhardt, M. Franaszek, I. Bitter, D. Brickman, V. Krishna, and J. R. Choi, "Computed Tomographic Virtual Colonoscopy Computer-Aided Polyp Detection in a Screening Population," Gastroenterology 129, 18321844 (2005). 4. H. Yoshida and J. Nappi, "Three-dimensional computer-aided diagnosis scheme for detection of colonic polyps," IEEE Trans. Med. Imag. 20(12), 1261-1274 (2001). 5. S. B. Gokturk, C. Tomasi, B. Acar, C. F. Beaulieu, D. S. Paik, R. B. Jeffrey, J. Yee, and S. Napel, "A Statistical 3-D Pattern Processing Method for Computer-Aided Detection of Polyps in CT Colonography," IEEE Transactions on Medical Imaging 20(12), 1251-1260 (2001). 6. J. Li, R. Uitert, N. Petrick, J. Yao, M. Franaszek, A. Huang, and R. M. Summers, "Wavelet method for CT colonography computer-aided polyp detection," Medical Physics 35(8), 3527-3538 (2008). 7. W. Hong, F. Qiu, and A. Kaufman, "A Pipeline for Computer Aided Polyp Detection," IEEE Transactions on Visualization and Computer Graphics 12(5), 861-868 (2006). 8. D. S. Paik, C. F. Beaulieu, G. D. Rubin, B. Acar, R. B. Jeffrey, J. Yee, J. Dey, and S. Napel, "Surface normal overlap: A computer-aided detection algorithm, with application to colonic polyps and lung nodules in helical CT," IEEE Trans. Med. Imag. 23, 661-675 (2004). 9. J. Yao, J. Li, and R. M. Summers, "Colonic polyp detection and measurement using topographical height map," Pattern Recognition 42(6), 1029-1040 (2009). 10. M. Franaszek, R. M. Summers, P. J. Pickhardt, and J. R. Choi, "Hybrid segmentation of colon filled with air and opacified fluid for CT colonography," IEEE Trans. Med. Imag. 25(3), 358-368 (2006). 11. J. Yao, M. Miller, M. Franaszek, and R. M. Summers, "Colonic Polyp Segmentation in CT Colonography Based on Fuzzy Clustering and Deformable Models," IEEE Trans. Med. Imag. 23(11), 1344-1352 (2004).

Proc. of SPIE Vol. 7625 76252J-7

12. J. Yao and R. M. Summers, "Adaptive deformable model for colonic polyp segmentation and measurement on CT colonography," Medical Physics 34(5), 1655-1664 (2007). 13. J. J. Dijkers, C. van Wijk, F. M. Vos, J. Florie, Y. C. Nio, H. W. Venema, R. Truyen, and L. J. van Vliet, "Segmentation and Size Measurement of Polyps in CT Colonography," presented at the MICCAI, 2005. 14. E. Konukoglu, B. Acar, D. S. Paik, C. F. Beaulieu, J. Rosenberg, and S. Napel, " Polyp Enhancing Level Set Evolution of Colon Wall: Method and Pilot Study," IEEE Trans. Med. Imag. 26(12), 1649-1656 (2007). 15. F. M. Vos, I. Serlie, R. van Gelder, F. H. Post, R. Truyen, F. A. Gerritsen, J. Stoker, and A. Vossepoel, "A New Visualization Method for Virtual Colonoscopy," presented at the MICCAI, 2001. 16. A. Huang, D. Roy, and R. M. Summers, "Teniae coli guided navigation and registration for virtual colonoscopy," presented at the IEEE Visualization, Baltimore, MD, 2005. 17. R. L. Van Uitert and R. M. Summers, "Automatic correction of level set based subvoxel precise centerlines for virtual colonoscopy using the colon outer wall," IEEE Trans. Med. Imag. 26(8), 1069-1078 (2007). 18. G. Iodanescu and R. M. Summers, "Automated centerline for computed tomography colonography," Academic Radiology 10, 1291-1301 (2003). 19. S. Haker, S. Angenent, A. Tannenbaurn, and R. Kikinis, " Nondistorting flattening maps and the 3-D visualization of colon CT images," IEEE Trans. Med. Imag. 19(7), 665-670 (2000). 20. K. T. Johnson, C. D. Johnson, J. G. Fletcher, R. L. MacCarty, and R. M. Summers, "CT colonography using 360-degree virtual dissection: a feasibility study," AJR Am J Roentgen 186, 90-95 (2006). 21. D. S. Paik, C. Beaulieu, R. B. Jeffrey, C. Karadi, and S. Napel, "Visualization modes for CT colonography using Cylindrical and Planar Map Projections," Journal of Computer Assisted Tomography 24(2), 179-188 (2000). 22. S. Sudarsky, B. Geiger, C. Chefd'hotel, and L. Guendel, "Colon Unfolding Via Skeletal Subspace Deformation," presented at the MICCAI, New York, 2008. 23. P. Li, S. Napel, and B. Acar, "Registration of central paths and colonic polyps between supine and prone scans in computed tomography colonography: Pilot study," Medical Physics 31(10), 2912-2923 (2004). 24. C. Beaulieu, S. Napel, B. Daniel, I. Chen, G. D. Rubin, I. Johnstone, and R. B. Jeffrey, "Detection of colonic polyps in a phantom model: implications for virtual colonoscopy data acquisition," J Compu Assist Tomogr 22(4), 656-663 (1998). 25. Z. Zhang, G. Wang, B. P. Brown, E. G. McFarland, J. Haller, and M. W. Vannier, "Fast algorithm for soft straightening of the colon," Academic Radiology 7(3), 142-148 (2000). 26. S. Ling, R. M. Summers, M. Loew, C. H. Mccollough, and C. D. Johnson, "Computer-aided detection of polyps in a colon phantom: effect of scan orientation, polyp size, collimation, and dose," J Compu Assist Tomogr 26(6), 1013-1018 (2002). 27. A. Laghi, R. Iannaccone, F. Mangiapane, F. Piacentini, S. Iori, and R. Passariello, "Experimental colonic phantom for the evaluation of the optimal scanning technique for CT colonography using a multidetector spiral CT equipment " European Radiology 13(3), 459-466 (2003). 28. K. T. Johnson, C. D. Johnson, S. M. Anderson, M. R. Bruesewitz, and C. H. Mccollough, "CT colonography: determination of optimal CT technique using a novel colon phantom," Abdominal Imaging 29(2), 173-176 (2004). 29. M. E. Zalis, J. J. Perumpillichira, J. Y. Kim, C. Del Frate, C. Magee, and P. F. Hanh, "Polyp Size at CT Colonography after Electronic Subtraction Cleansing in an Anthropomorphic Colon Phantom," Radiology 236, 118-124 (2005). 30. P. J. Pickhardt, A. D. Lee, E. G. McFarland, and A. J. Taylor, "Linear Polyp Measurement at CT Colonography: In Vitro and in Vivo Comparison of Two-dimensional and Three-dimensional Displays," Radiology 236(3), 872-878 (2005). 31. J. G. Fletcher, F. Booya, Z. Melton, K. T. Johnson, L. Guendel, B. Schmidt, C. H. Mccollough, B. Young, J. L. Fidler, and W. S. Harmsen, "Automated Polyp Measurement with CT Colonography: Preliminary Observations in a Phantom Colon Model," AJR Am J Roentgen 188(945-952)(2007). 32. R. M. Summers, W. S. Selbie, J. D. Malley, L. M. Pusanik, A. Dwyer, N. Courcoutsakis, D. J. Shaw, D. E. Kleiner, M. C. Sneller, C. A. Langford, S. M. Holland, and J. Shelhamer, "Polypoid lesions of airways: early experience with computer-assisted detection by using virtual bronchoscopy and surface curvature," Radiology 208, 331-337 (1998). 33. Z. Zhang, J. X. Li, and M. J. Ackerman, "Colon straightening based on elastic mechanics model," presented at the IEEE International Symposium on Biomedical Imaging, 2004. 34. A. Chowdhury, S. Tan, J. Yao, M. Linguraru, M. Ward, and R. M. Summers, "Two Methods of Haustral Fold Detection from Computed Tomographic Virtual Colonoscopy Images," presented at the SPIE Medical Imaging, Florida, USA, 2009. 35. W. Lorensen and H. Cline, "Marching cubes: a high resolution 3d surface construction algorithm," Compute Graphics 21, 163169 (1987). 36. C. Maurer and B. Juttler, "Rational approximation of rotation minimizing frames using Pythagorean-hodograph cubics," Journal for Geometry and Graphics 3(2), 141-159 (1999). 37. J. P. Lewis, M. Cordner, and N. Fong, "Pose Space Deformation: A Unified Approach to Shape Interpolation and SkeletonDriven Deformation," proceeding of ACM SIGGRAPH, 165-172 (2000).

Proc. of SPIE Vol. 7625 76252J-8