Eigenshape Analysis of Left Ventricular Outlines from Contrast Ventriculograms

  • Paul D. Sampson
  • Fred L. Bookstein
  • Florence H. Sheehan
  • Edward L. Bolson
Chapter
Part of the NATO ASI Series book series (NSSA, volume 284)

Abstract

The left ventricle of the heart functions by contraction. From digitized outlines we analyze its function by describing its shape, shape change, and size change (or “ejection fraction”) over the cardiac cycle, from end diastole (ED) to end systole (ES). For this purpose we introduce a new variant of eigenshape analysis for the morphometric analysis of outline data. The method begins with a mean outline defined by pointwise averages of a sample of outlines after they have been oriented in a Procrustes superposition by means of an “iterative closest point” algorithm. Individual outlines are then represented by vectors of deviations normal to the mean outline, and variation in shape is analyzed in terms of a singular value decomposition (SVD) of a sample matrix of such deviations. Principal modes of variation in shape are given by so-called “eigenshapes”—the left singular vectors of the SVD.

In application to the analysis of left ventricular outlines we compute an SVD for the joint representation of the outline shapes at both ED and ES. The results are discussed in terms of shape change. We use the scores on a subset of the principal eigenshapes to demonstrate a discriminant analysis distinguishing samples of “normals” from groups of clinical cases having either cardiomyopathy or infarcts associated with one of three types of coronary artery disease. We then discuss proposals for the morphometric analysis of two-dimensional outlines and three-dimensional surfaces that also include landmarks. These proposals integrate an eigenshape analysis with thin-plate spline based analyses of configurations of landmarks.

Keywords

Anisotropy Expense Cardiomyopathy Stein Archie 

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References

  1. Amini, A. A., R. Owen, P. Anandan, and J. Duncan. 1991. Non-rigid motion models for tracking the left ventricular wall. Pages 343–357 in A. Colchester, and D. Hawkes, (eds.), Information processing in medical imaging. Lecture Notes in Computer Science, No.5 1 1. Springer-Verlag: New York.CrossRefGoogle Scholar
  2. Barletta, G., M. Di Donato, M. Baroni, A. Fantini, F. Fantini. 1993. Left ventricular remodeling in chronic aortic regurgitation. International Journal of Cardiac Imaging 9: 185–194.PubMedCrossRefGoogle Scholar
  3. Bashein, G., F. H. Sheehan, M. L. Nessly, P. R. Detmer, and R. W. Martin. 1993. Three-dimensional transesophageal echocardigraphy for depiction of regional left ventricular performance: Initial results and future directions. International Journal of Cardiac Imaging 9: 121–131.PubMedCrossRefGoogle Scholar
  4. Besl, P. J., and N. D. McKay. 1992. A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and machine Intelligence 14: 239–256.CrossRefGoogle Scholar
  5. Bookstein, F. L. 1978. The measurement of biological shape and shape change. Lecture Notes in Biomathe-maties, Volume 24. Springer-Verlag: Berlin.CrossRefGoogle Scholar
  6. Bookstein, F. L. 1986. Size and shape spaces for landmark data in two dimensions (with discussion and rejoinder). Statistical Science 1: 181–242.CrossRefGoogle Scholar
  7. Bookstein, F. L. 1989. Principal warps: thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11: 567–85.CrossRefGoogle Scholar
  8. Bookstein, F. L. 1991a. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.Google Scholar
  9. Bookstein, F. L. 1991b. Four metrics for image variation. Pages 227–240 in D. Ortendahi, and J. Llacer (eds.), Proceedings of the XI International Conference on Information Processing in Medical Imaging. Progress in Clinical and Biological Research, Volume 363. Wiley-Liss: New York.Google Scholar
  10. Bookstein, F. L., and W. D. K. Green. 1993. A feature space for edgels in images with landmarks. Journal of Mathematical Imaging and Vision 3: 231–261.CrossRefGoogle Scholar
  11. Cutting, C. B., F. L. Bookstein, B. Haddad, D. Dean, and D. Kim. 1993. A spline-based approach for averaging three-dimensional curves and surfaces. Pages 29–44 in J. N. Wilson, and D. C. Wilson, (eds.), Mathematical methods in medical imaging II. S.P.I.E. Proceedings, Volume 2035.CrossRefGoogle Scholar
  12. Douglas, P. S., R. Morrow, A. Ioli, and N. Reichek. 1989. Left ventricular shape, afterload and survival in idiopathic dilated cardiomyopathy. Journal of the American College of Cardiology 13: 311–315.PubMedCrossRefGoogle Scholar
  13. Goodall, C. R. 1991. Procrustes methods in the statistical analysis of shape (with discussion and rejoinder). Journal of the Royal Statistical Society, Series B 53: 285–339.Google Scholar
  14. Gower, J. C. 1975. Generalized Procrustes analysis. Psychometrika 40: 33–51.CrossRefGoogle Scholar
  15. Kono, T., H. N. Sabbah, P. D. Stein, J. F. Brymer, and F. Khaja. 1991. Left ventricular shape as a determinant of functional mitral regurgitation in patients with severe heart failure secondary to either coronary artery disease or idiopathic dilated cardiomyopathy. American Journal of Cardiology 68: 355–359.PubMedCrossRefGoogle Scholar
  16. Kuhl, F. P., and C. R. Giardina. 1982. Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing 18: 236–258.CrossRefGoogle Scholar
  17. Lohmann, G. P. 1983. Eigenshape analysis of microfossils: A general morphometric procedure for describing changes in shape. Mathematical Geology 15: 659–672.CrossRefGoogle Scholar
  18. Marcus, L. F., E. Bello, and A. Garcia-Valdecasas (eds.) 1993. Contributions to morphometrics. Mongrafias del Museo Nacional de Ciencias Naturales 8, Madrid.Google Scholar
  19. Pfeffer, M. A., and E. Braunwald. 1990. Ventricular remodeling after myocardial infarction: Experimental observations and clinical implications. Circulation 81 (4): 1161–1172.PubMedCrossRefGoogle Scholar
  20. Reyment, R. A. 1991. Multidimensional Palaeobiology. Pergamon Press: New York.Google Scholar
  21. Rohlf, F. J. 1986. Relationships among eigenshape analysis, Fourier analysis, and analysis of coordinates. Mathematical Geology 18: 845–854.CrossRefGoogle Scholar
  22. Rohlf, F. J. 1990. Fitting curves to outlines. Pages 167–177 in F. J. Rohlf, and F. L. Bookstein, (eds.), Proceedings of the Michigan morphometrics workshop. University of Michigan Museums of Zoology Special Publication 2.Google Scholar
  23. Rohlf, F. J., and J. Archie. 1984. A comparison of Fourier methods for the description of wing shape in mosquitoes (Diptera: culicidae). Systematic Zoology 33: 302–317.CrossRefGoogle Scholar
  24. Rohlf, F. J., and F. L. Bookstein (eds.) 1990. Proceedings of the Michigan morphometrics workshop. University of Michigan Museum of Zoology Special Publication 2.Google Scholar
  25. Rohlf, F. J. and D. E. Slice. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology 39: 40–59.CrossRefGoogle Scholar
  26. Zahn, C. T., and R. Z. Roskies. 1972. Fourier descriptors for plane closed curves. IEEE Transactions on Computing 21: 269–281.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Paul D. Sampson
    • 1
  • Fred L. Bookstein
    • 2
  • Florence H. Sheehan
    • 3
  • Edward L. Bolson
    • 3
  1. 1.Department of StatisticsUniversity of WashingtonSeattleUSA
  2. 2.Institute of GerontologyUniversity of MichiganAnn ArborUSA
  3. 3.Division of CardiologySchool of Medicine University of WashingtonSeattleUSA

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