# 3-D reconstruction of the coronary artery tree from multiple views of a rotational X-ray angiography

## Abstract

To present an efficient and robust method for 3-D reconstruction of the coronary artery tree from multiple ECG-gated views of an X-ray angiography. 2-D coronary artery centerlines are extracted automatically from X-ray projection images using an enhanced multi-scale analysis. For the difficult data with low vessel contrast, a semi-automatic tool based on fast marching method is implemented to allow manual correction of automatically-extracted 2-D centerlines. First, we formulate the 3-D symbolic reconstruction of coronary arteries from multiple views as an energy minimization problem incorporating a soft epipolar line constraint and a smoothness term evaluated in 3-D. The proposed formulation results in the robustness of the reconstruction to the imperfectness in 2-D centerline extraction, as well as the reconstructed coronary artery tree being inherently smooth in 3-D. We further propose to solve the energy minimization problem using α-expansion moves of Graph Cuts, a powerful optimization technique that yields a local minimum in a strong sense at a relatively low computational complexity. We show experimental results on a synthetic coronary phantom, a porcine data set and 11 patient data sets. For the coronary phantom, results obtained using different number of views are presented. 3-D reconstruction error evaluated by the mean plus one standard deviation is below one millimeter when 4 or more views are used. For real data, reconstruction using 4 to 5 views and 256 depth labels averaged around 12 s on a computer with 2.13 GHz Intel Pentium M and achieves a mean 2-D back-projection error of 1.18 mm (ranging from 0.84 to 1.71 mm) in 12 cases. The accuracy for multi-view reconstruction of the coronary artery tree as reported from the phantom and patient studies is promising, and the efficiency is significantly improved compared to other approaches reported in the literature, which range from a few to tens of minutes. Visually good and smooth reconstruction is demonstrated.

## Keywords

X-ray angiography 3-D reconstruction Coronary arteries Cardio-vascular disease Energy minimization Graph-cuts optimization## Notes

### Acknowledgments

The authors are thankful to Dr. Chenyang Xu, Dr. Guenter Lauritsch and Dr. Jan Boese for their generous support and enlightening discussions on this project, and are thankful to Prof. Patrick Serruys and Prof. Johannes Brachmann for providing the data in this study.

## References

- 1.Heart disease and stroke statistics—2007 update. A report from the American Heart Association Statistics Committee and Stroke Statistics Subcommittee, Circulation 2006Google Scholar
- 2.Green N, Chen S, Hansgen A, Messenger J, Groves B, Carroll J (2005) Angiographic views used for percutaneous coronary interventions: a three-dimensional analysis of physician-determined vs. computer-generated views. Catheterization and Cardiovascular Interventions 64:451–459CrossRefPubMedGoogle Scholar
- 3.Wellnhofer E, Wahle A, Mugaragu I, Gross J, Oswald H, Fleck E (1999) Validation of an accurate method for three-dimensional reconstruction and quantitative assessment of volumes, lengths and diameters of coronary vascular branches and segments from biplane angiographic projections. Int J Card Imaging 15:339–353CrossRefPubMedGoogle Scholar
- 4.Messenger J, Chen S, Carroll J, Burchenal J, Kioussopoulos K, Groves B (2000) 3-D coronary reconstruction from routine single-plane coronary angiograms: clinical validation and quantitative analysis of the right coronary artery in 100 patients. Int J Card Imaging 16:413–427CrossRefPubMedGoogle Scholar
- 5.Gollapudi R, Valencia R, Lee S, Wong G, Teirstein P, Price M (2006) Utility of three-dimensional reconstruction of coronary angiography to guide percutaneous coronary intervention. Catheterization and Cardiovascular Interventions 69:479–482CrossRefGoogle Scholar
- 6.Schlundt C, Kreft J, Fuchs F, Achenbach S, Daniel W, Ludwig J (2006) Three-dimensional on-line reconstruction of coronary bifurcated lesions to optimize side-branch stenting. Catheterization and Cardiovascular Interventions 69:249–253CrossRefGoogle Scholar
- 7.Nguyen T, Sklansky J (1994) Reconstructing the 3-D medial axes of coronary arteries in single-view cineangiograms. IEEE Trans Med Imaging 13(1):61–73CrossRefPubMedGoogle Scholar
- 8.Merle A et al (1998) 3D reconstruction of the deformable coronary tree skeleton from two X-ray angiographic views. Computers in Cardiology 25:757–760Google Scholar
- 9.Chen S, Carroll J (2000) 3-D reconstruction of coronary arterial tree to optimize angiographic visualization. IEEE Trans Med Imaging 19(4):318–336CrossRefPubMedGoogle Scholar
- 10.Sprague K (2006) Coronary X-ray angiographic reconstruction and image orientation. Med Phys 3(3):707–718CrossRefGoogle Scholar
- 11.Andriotis A et al (2008) A new method of three-dimensional coronary artery reconstruction from X-ray angiography: validation against a virtual phantom and multislice computed tomography. Catheterization and Cardiovascular Interventions 71:28–43CrossRefPubMedGoogle Scholar
- 12.Chen S et al (2003) Kinematic and deformation analysis of 4-D coronary arterial trees reconstructed from cine angiograms. IEEE Trans Med Imaging 22:710–721CrossRefPubMedGoogle Scholar
- 13.Jandt U, Schafer D, Grass M, Rasche V (2009) Automatic generation of time resolved motion vector fields of coronary arteries and 4D surface extraction using rotational X-ray angiography. Phys Med Biol 54:45–64CrossRefPubMedGoogle Scholar
- 14.Shechter G, Devernay F, Coste-Maniere E, Quyyumi A, McVeigh E (2003) Three-dimensional motion tracking of coronary arteries in biplane cineangiograms. IEEE Trans. Med. Imaging 22:493–503CrossRefPubMedGoogle Scholar
- 15.Blondel C, Vaillant R, Malandain G, Ayache N (2004) 3D tomographic reconstruction of coronary arteries using a precomputed 4D motion field. Phys Med Biol 49:2197–2208CrossRefPubMedGoogle Scholar
- 16.Blondel C et al (2006) Reconstruction of coronary arteries from a single rotational X-ray projection sequence. IEEE Trans Med Imaging 25(5):653–663CrossRefPubMedGoogle Scholar
- 17.Hansis E, Schafer D, Dossel O, Grass M (2008) Projection-based motion compensation for gated coronary artery reconstruction from rotational X-ray angiograms. Phys Med Biol 53:3807–3820CrossRefPubMedGoogle Scholar
- 18.Young S, Movassaghi B, Weese J, Rasche V (2003) 3D vessel axis extraction using 2D calibrated X-ray projections for coronary modeling. Proc. SPIE 5032:1491–1498CrossRefGoogle Scholar
- 19.Mourgues F, Devernay F (2001) 3D + t modeling of coronary artery tree from standard non simultaneous angiograms. LNCS 2208: 1320–1322 (MICCAI 2001)Google Scholar
- 20.Movassaghi B, Rasche V, Grass M, Viergever M, Niessen W (2004) A quantitative analysis of 3D coronary modeling from two or more projection images. IEEE Trans. Med. Imaging 23:1517–1531CrossRefPubMedGoogle Scholar
- 21.Boykov Y, Veksler O, Zabih R (2001) Fast approximate energy minimization via graph cuts. IEEE Trans PAMI 23(11):1222–1239Google Scholar
- 22.Kim J, Kolmogorov V, Zabih R (2003) Visual correspondence using energy minimization and mutual information. Proc Int Conf Comp Vis 1033–1040Google Scholar
- 23.Kolmogorov V, Zabih R (2002) Multi-camera scene reconstruction via graph cuts. Proc. European Conf. Computer Vision 3:82–96Google Scholar
- 24.Kwatra V, Schodl A, Essa I, Turk G, Bobick A (2003) Graphcut textures: image and video synthesis using graph cuts. ACM Trans Graphics Proc SIGGRAPH 22(3):277–286Google Scholar
- 25.Lombaert H, Sun Y, Grady L, Xu C (2005) A multilevel banded graph cuts method for fast image segmentation. Proc Int Conf Comp Vis 259–265Google Scholar
- 26.Funka-Lea G, Boykov Y, Florin C, Jolly M, Moreau-Gobard R, Ramaraj R, Rinck D (2006) Automatic heart isolation for CT coronary visualization using graph-cuts. Proc Int Symp Biomed Imaging 614–617Google Scholar
- 27.Weickert J (1999) Coherence-enhancing diffusion filtering. Int. Journal of Computer Vision 31:111–127CrossRefGoogle Scholar
- 28.Frangi A, Niessen W, Vincken K, Viergever M (1998) Multiscale vessel enhancement filtering. Lect Notes Comput Sci 1496:130–137CrossRefGoogle Scholar
- 29.Palagyi K, Sorantin E, Balogh E, Kuba A, Halmai C, Erdohelyi B, Hausegger K (2001) A sequential 3D thinning algorithm and its medical applications. IPMI 409–415Google Scholar
- 30.Mortensen E, Barrett W (1995) Intelligent scissors for image composition. ACMGoogle Scholar
- 31.Sethian J (1998) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision and material sciences. CambridgeGoogle Scholar
- 32.Friedman J, Bentley J, Finkel R (1977) An algorithm for finding best matches in logarithmic expected time. ACM Trans Math Softw 3(3):209–226CrossRefGoogle Scholar
- 33.For L, Fulkerson D (1962) Flows in networks. Princeton, Princeton Univ. PressGoogle Scholar
- 34.Grigoriev D, Karpinski M, Heide F, Smolensky R (1996) A lower bound for randomized algebraic decision trees. Proc ACM Symp Theory of Comput 612–619Google Scholar
- 35.Kitamura K, Tobis J, Sklansky J (1988) Estimating the 3-D skeletons and transverse areas of coronary arteries from biplane angiograms. IEEE Trans. Med. Imaging 7:173–187CrossRefPubMedGoogle Scholar
- 36.Van Tran L, Bahn R, Sklansky J (1992) Reconstructing the cross sections of coronary arteries from biplane angiograms. IEEE Trans. Med. Imaging 11:517–529CrossRefPubMedGoogle Scholar
- 37.O’Donnell T, Funka-Lea G, Tek H, Jolly MP, Rasch M, Setser R (2006) Comprehensive cardiovascular image analysis using MR and CT at siemens corporate research. Int J Comput Vision 70(2):165–178CrossRefGoogle Scholar
- 38.Keating T, Wolf P, Scarpace F (1975) An improved method of digital image correlation. Photogrammetric Eng. Remote Sensing 41:993–1002Google Scholar
- 39.Klein J, Hoff J, Peifer J (1998) A quantitative evaluation of the three dimensional reconstruction of patients coronary arteries. Int J Card Imaging 14:75–87CrossRefPubMedGoogle Scholar
- 40.Shechter G, Ozturk C, Resar J, Mcveigh E (2004) Respiratory motion of the heart from free breathing coronary angiograms. IEEE Trans Med Imaging 23(8):1046–1056CrossRefPubMedGoogle Scholar
- 41.McLeish K, Hill D, Atkinson D, Blackall J, Razavi R (2002) A study of the motion and deformation of the heart due to respiration. IEEE Trans Med Imaging 21:1142–1150CrossRefPubMedGoogle Scholar
- 42.Prummer M, Wigstrom L, Hornegger J, Boese J, Lauritsch G, Strobel N, Fahrig R (2006) Cardiac C-arm CT: efficient motion correction for 4D-FBP. IEEE Nuclear Sci Symp Conf Record pp 2620–2628Google Scholar
- 43.Seifarth H, Wienbeck S, Püsken M, Juergens KU, Maintz D, Vahlhaus C, Heindel W, Fischbach R (2007) Optimal systolic and diastolic reconstruction windows for coronary CT angiography using dual-source CT. American Journal of Roentgenology; 189:1317–1323CrossRefPubMedGoogle Scholar
- 44.Hansis E, Schaefer D, Doessel O, Grass M (2008) Automatic optimum phase point selection based on centerline consistency for 3D rotational coronary angiography. Int J Comp Assisted Radiol Surg 355–361Google Scholar