Last updated: May 09 and 09:40pm

• Students: Mehmet Akif Gulsun
• Mentor(s): Gareth Funka-Lea

Detection of coronary arteries from medical image data and their statistical analysis are difficult tasks due to the large variation in their anatomy. The goal of this project is to investigate models for characterizing coronary arteries that can be used as prior models to support their detection in computed tomography angiography (CTA) scans and to allow for their statistical analysis. In the first part of this project, I look into statistics on territories by computing coronary average density map in a canonical coordinate system. In the second part, I build tree-shape models and compute geodesic deformation between them with two different metrics that can account for the variation in the tree-shape topology. Finally, I apply these tree-shape geodesic metrics for coronary tree matching and average tree computation. The methods are tested on 50 hand annotated coronary centerlines giving very promising results.

According to American Heart Association, coronary artery disease (CAD) is a leading cause of death among cardiovascular diseases in the United States. This fact puts emphasize on the necessity of its diagnosis, treatment and monitoring for which computed tomography angiography (CTA) is considered as the primary imaging modality because of its superior image resolution. In addition, recent advancements in CTA technology allows scans with significantly reduced radiation which encourages routine screenings. However, due to thin and longitudinal anatomy of coronary arteries, CTA data itself is difficult and time-consuming to be interpreted by the operators without additional post-processing. Therefore, detection of coronaries in CTA is needed for advanced visualization and quantification purposes.

In spite of the good image quality in CTA data, irregular topology of coronary anatomy, pathologies and imaging artifacts make coronary detection a challenge. Coronary prior models that are capable of capturing anatomical variations in the population can improve the detection by guiding commonly used local tracking methods or by supporting the prediction of global classification methods. Besides detection, statistical analysis of coronaries is also a challenge due to the large variation in their topology and branch geometry. Prior models can provide means to perform statistics on coronaries by either looking into their characteristics on territories or by building statistical shape models to compute their modes of variation. Furthermore, statistical coronary shape models can be used in various applications such as coronary branch labeling and correlation between coronary artery diseases and coronary anatomy.

Traditional statistical methods are well suited for shapes sharing a common topology which is not the case for coronaries. More advanced methods are needed to build shape models that can consider both coronary topology and branch shape. The specific aims of this project are

1. computing coronary distribution on territories
2. building tree-shape models and geodesic metrics that can account for topology and branch geometry

• Minimum: (Complete)
  1. alignment of coronary trees in the population
  2. computation of average coronary density map

• Expected: (Complete)
  1. computation of TED-based geodesic distance between two ordered depth-3 trees
  2. computation of QED-based geodesic distance between two ordered depth-3 trees

• Maximum: (Complete)
  1. coronary tree matching using TED
  2. computation of the average coronary tree in the population using QED
  3. membership score assignment to an unseen coronary tree using QED

In this project, 50 hand annotated CTA coronary datasets with corresponding left and right coronary trees, heart pericardium mesh and anatomical landmarks were received from Siemens. As a necessary task for statistical analysis, coronary centerlines in the training set are aligned. This is achieved by first defining a canonical coordinate system by fitting spherical model to the heart pericardium mesh where the axes of this coordinate system are determined from three key anatomical landmark points. Coronary centerlines are finally projected onto the canonical surface in order to find the correspondence between them.

In order to first investigate the distribution of aligned coronary centerlines on the canonical surface, average density map is computed from coronary vessel distance maps. This density map is displayed in 3D with color coded overlay on the canonical surface.

In the second part of the technical approach, two different tree-shape metrics, Tree Edit Distance (TED) and Quotient Euclidean Distance (QED) are implemented. TED metric is implemented using bidirectional Dijkstra and a topology matching algorithm. QED metric is implemented using unidirectional Dijkstra operating on Quotient Space with a new definition of identical tree-shapes for handling missing branches. In both metrics, branch labels are propagated for the application of them to tree matching. Computationally efficient implementations are provided.

In the last part, TED and QED metrics are applied to coronaries for average tree computation and coronary tree matching. Coronary centerlines are first preprocessed by recursively pruning small branches until a specific tree-depth is reached. Geodesic deformations are computed within left anterior descending (LAD) and circumflex (CX) subtrees of the left tree separately.

1. Coronary centerline annotations, heart pericardium models and key anatomical landmarks
   • Resolved: Provided by Siemens.
2. Ground truth trees for testing and validation
   • Resolved: Manual drawing tool is implemented. Example trees are generated for sanity check of the methods.
3. Development platform. Libraries for data loading / visualization / interactions and display of results
   • Resolved: Research prototype is available for live demo.
4. TED solver
   • Resolved: Implemented own algorithm.

1. Milestone name: Alignment of coronary centerlines
   • Planned Date: March 4
   • Expected Date: March 4
   • Status: ACHIEVED
2. Milestone name: Statistics on territories / Coronary Density Map
   • Planned Date: March 11
   • Expected Date: March 11
   • Status: ACHIEVED
3. Milestone name: Geodesic distance with TED algorithm
   • Planned Date: April 8
   • Expected Date: April 8
   • Status: ACHIEVED
4. Milestone name: Geodesic distance with QED algorithm
   • Planned Date: April 29 April 22
   • Expected Date: April 29 April 22
   • Status: ACHIEVED
5. Milestone name: Applications (Tree Matching, Average Tree, Membership Scores)
   • Planned Date: May 8
   • Expected Date: May 8
   • Status: ACHIEVED

QED Geodesic Deformation Movies

• Between sample trees
  • Side branches are flipped
  • Upper side branch is grown
  • Missing branches are grown
• Between coronary trees
  • Left coronary trees
  • Left coronary tree and left average tree
  • Left coronary tree and left average tree
  • Left coronary tree and left average tree
  • Right coronary tree and right average tree

• My experiments showed that the geodesic distance of an unseen coronary to the average tree is not sufficient for membership score assignment itself. This is due to the underlying high-dimensional geometric space which increases the likelihood of points being equidistant and also due to the variation in coronary tree size.

• Project Plan
  • Project plan presentation
  • Project plan proposal
• Project Background Reading
  • See Bibliography below for links.
• Project Checkpoint
  • Project checkpoint presentation
• Paper Seminar Presentations
  • An Airway Tree-shape Model for Geodesic Airway Branch Labeling, Feragen, et. al.
  • Paper Critical Review
  • Paper Review Presentation
• Project Final Presentation
  • Final Poster
  • Final Poster Teaser
• Project Final Report
  • Final Report

1. Donald Lloyd-Jones, Robert J Adams, Todd M Brown, Mercedes Carnethon, Shifan Dai, Giovanni De Simone, T Bruce Ferguson, Earl Ford, Karen Furie, Cathleen Gillespie, and et al. Executive summary: heart disease and stroke statistics{2010 update: a report from the american heart association. Circulation, 121(7):188-197, 2010
2. Philip Bille. A survey on tree edit distance and related problems. Theor. Comput. Sci., 337:217-239, June 2005
3. A. Feragen, F. Lauze, and M. Nielsen. Fundamental geodesic deformations in spaces of treelike shapes. In Pattern Recognition (ICPR), 2010 20th International Conference on, pages 2089-2093, aug. 2010
4. Aasa Feragen, Francois Lauze, Pechin Lo, Marleen de Bruijne, and Mads Nielsen. Geometries on spaces of treelike shapes. In Proceedings of the 10th Asian conference on Computer vision - Volume Part II, ACCV'10, pages 160-173, Berlin, Heidelberg, 2011. Springer-Verlag.
5. Stephen R. Aylward, Julien Jomier, Christelle Vivert, Vincent LeDigarcher, and Elizabeth Bullitt. Spatial graphs for intra-cranial vascular network characterization, generation, and discrimination. In MICCAI, pages 59-66, 2005
6. W H Tang and Albert C S Chung. Cerebral vascular tree matching of 3d-ra data based on tree edit distance. Medical Imaging and Augmented Reality, page 116123, 2006
7. Aasa Feragen, Sren Hauberg, Mads Nielsen, and Francois Lauze. Means in spaces of tree-like shapes. In ICCV, pages 736-746, 2011
8. Erik D. Demaine, Shay Mozes, Benjamin Rossman, and Oren Weimann. An optimal decomposition algorithm for tree edit distance. ACM Transactions on Algorithms, 6(1), 2009
9. A. Feragen, P. Lo, V. Gorbunova, M. Nielsen, A. Dirksen, F. Lauze, and M. de Bruijne. An airway tree-shape model for geodesic airway branch labeling. In Third MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 2011

I implemented the methods in my technical approach into a research prototype using Siemens' Extensible Imaging Platform (XIP). I used C++ for implementing processing and visualization components and HTML/Java for user interface. I did not publish the project sources here due to the issues with Siemens proprietary. However, I can show a live demo and explain my project code.