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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
Bookstein, F. L. 1978. The measurement of biological shape and shape change. Lecture Notes in Biomathe-maties, Volume 24. Springer-Verlag: Berlin.
Bookstein, F. L. 1986. Size and shape spaces for landmark data in two dimensions (with discussion and rejoinder). Statistical Science 1: 181–242.
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.
Bookstein, F. L. 1991a. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.
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.
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.
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.
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.
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.
Gower, J. C. 1975. Generalized Procrustes analysis. Psychometrika 40: 33–51.
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.
Kuhl, F. P., and C. R. Giardina. 1982. Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing 18: 236–258.
Lohmann, G. P. 1983. Eigenshape analysis of microfossils: A general morphometric procedure for describing changes in shape. Mathematical Geology 15: 659–672.
Marcus, L. F., E. Bello, and A. Garcia-Valdecasas (eds.) 1993. Contributions to morphometrics. Mongrafias del Museo Nacional de Ciencias Naturales 8, Madrid.
Pfeffer, M. A., and E. Braunwald. 1990. Ventricular remodeling after myocardial infarction: Experimental observations and clinical implications. Circulation 81 (4): 1161–1172.
Reyment, R. A. 1991. Multidimensional Palaeobiology. Pergamon Press: New York.
Rohlf, F. J. 1986. Relationships among eigenshape analysis, Fourier analysis, and analysis of coordinates. Mathematical Geology 18: 845–854.
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.
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.
Rohlf, F. J., and F. L. Bookstein (eds.) 1990. Proceedings of the Michigan morphometrics workshop. University of Michigan Museum of Zoology Special Publication 2.
Rohlf, F. J. and D. E. Slice. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology 39: 40–59.
Zahn, C. T., and R. Z. Roskies. 1972. Fourier descriptors for plane closed curves. IEEE Transactions on Computing 21: 269–281.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Sampson, P.D., Bookstein, F.L., Sheehan, F.H., Bolson, E.L. (1996). Eigenshape Analysis of Left Ventricular Outlines from Contrast Ventriculograms. In: Marcus, L.F., Corti, M., Loy, A., Naylor, G.J.P., Slice, D.E. (eds) Advances in Morphometrics. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9083-2_18
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9083-2_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9085-6
Online ISBN: 978-1-4757-9083-2
eBook Packages: Springer Book Archive