Eigenshape Analysis of Left Ventricular Outlines from Contrast Ventriculograms

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.