Mathematical representation of the vascular structure and applications

Proceedings - SPM 2007: ACM Symposium on Solid and Physical Modeling

Volumn , Issue , 2007, Pages 373-378

  Li, Jie ^a   Regli, William C ^a   Sun, Wei ^a  

^a Drexel University   (United States)

Author keywords

Computational representation; Deformable model; NURBS; Swept volumes; Vascular modeling

Indexed keywords

BIOMIMETICS; MEDICAL APPLICATIONS;

COMPUTATIONAL REPRESENTATION; DEFORMABLE MODELS; SWEPT VOLUMES; VASCULAR MODELING;

CARDIOVASCULAR SYSTEM;

EID: 35348854983     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1236246.1236300     Document Type: Conference Paper

References (23)

1. ABDEL-MALEK, K., BLACKMORE, D., AND JOY, K. 2006. Swept volumes: foundations, perspectives, and applications. International Journal of Shape Modeling 12, 1, 87-127.
2. BEUTEL, J., KUNDEL, H. L., AND METTER, R. L. V. 2000. Handbook of Medical Imaging: Volume 1. Physics and Psychophysics. SPIE Press.
3. BLAZEK, J. 2001. Computational fluid dynamics: principles and applications. Elsevier, ch. 11.
4. BÜHLER, K., FELKEL, P., AND CRUZ, A. L. 2004. Geometric methods for vessel visualization and quantification - a survey. In Geometric Modelling for Scientific Visualization, 399-421.
5. CHEN, J., AND AMINI, A. A. 2004. Quantifying 3-d vascular structures in mra images using hybrid pde and geometric deformable models. IEEE Transactions on Medical Imaging 23, 10, 1251-1262.
6. COQUILLART, S. 1987. A control-point-based sweeping technique. IEEE Computer Graphics and Applications 7, 11, 36-44.
7. DE VOSSE, F. V. 2003. Mathematical modelling of the cardiovascular system. Journal of Engineering Mathematics 47, 3-4, 175-183.
8. FRANGI, A. F., NIESSEN, W. J., HOOGEVEEN, R. M., VAN WALSUM, T., AND VIERGEVER, M. A. 1999. Model-based quantitation of 3-d magnetic resonance angiographic images. IEEE Transactions on Medical Imaging 18, 10, 946-956.
9. HIDEAKI, H., AND NAGAAKI, O. 1990. 3-D blood vessel reconstruction by simulated annealing. In Proc. SPIE Vol. 1233, p. 97-102, Medical Imaging IV: Image Processing, Murray H. Loew; Ed., M. H. Loew, Ed., 97-102.
10. KIM, Y., AND HORII, S. C. 2000. Handbook of Medical Imaging: Volume 3. Display and PACS. SPIE Press.
11. KRETOWSKI, M., ROLLAND, Y., BEZY-WENDLING, J., AND COATRIEUX, J.-L. 2003. Physiologically based modeling of 3-d vascular networks and ct scan angiography. IEEE Transcations on Medical Imaging 22, 2, 248-257.
12. KU, D. N. 1997. Blood flow in arteries. Annual Review of Fluid Mechanics 29, 1, 399-434.
13. LONG, Q., XU, X. Y., BOURNE, M., AND GRIFFITH, T. M. 2000. Numerical study of blood flow in an anatomically realistic aortoiliac bifurcation generated from mri data. Magnetic Resonance in Medicine 43, 565-576.
14. MURRAY, C. D. 1926. The physiological principle of minimum work. i. the vascular system and the cost of blood volume. Physiology 12, 3, 207-214.
15. OELTZE, S., AND PREIM, B. 2005. Visualization of vasculature with convolution surfaces: method, validation and evaluation. IEEE Transactions on Medical Imaging 24, 4, 540-548.
16. PIEGL, L. A., AND TILLER, W. 1997. The NURBS book, 2 ed. Springer.
17. SETHIAN, J. A. 1996. Level set methods: evolving interfaces in geometry, fluid mechanics, computer vision, and materials science. Cambridge University Press.
18. SONKA, M., AND FITZPATRICK, J. M. 2000. Handbook of Medical Imaging: Volume 2. Medical Image Processing and Analysis. SPIE Press, ch. 14.
19. SZCZERBA, D., AND SZEKELY, G. 2005. A computational model of micro-vascular growth. International Conference on Computational Science, 17-24.
20. WANG, K. C.-Y. 2001. Level set methods for computational prototyping with application to hemodynamic modeling. PhD thesis, Department of Electrical Engineering of Stanford University.
21. WOMERSLEY, J. R. 1955. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. The Journal of Physiology 127, 3, 553-563.
22. YANG, J., AND ABDEL-MALEK, K. 2005. Approximate swept volumes of nurbs surfaces or solids. Computer-Aided Geometric Design 22, 1, 1-26.
23. YIM, P. J., CEBRAL, J. J., MULLICK, R., MARCOS, H. B., AND CHOYKE, P. L. 2001. Vessel surface reconstruction with a tubular deformable model. IEEE Transactions on Medical imaging 20, 12, 1411-1421.