Quantitative characterization and sorting of three-dimensional geometries: application to left ventricles in vivo

A procedure for automatic sorting of three-dimensional (3-D) shapes is proposed. The procedure is applied to sort into normal and abnormal categories, human left ventricles (LV) using in vivo data from 19 subjects (ten normal and nine abnormal LV's) studied by ultrafast tomography (Cine-CT). The procedure starts by utilizing a vector in a helical coordinate system to describe the spatial geometry of each individual LV cavity. This individual vector is then anatomically aligned and normalized to eliminate effects due to size, yielding a dimensionless vector, denoted as 'geometrical cardiogram' (GCG). The GCG characterizes the instantaneous 3-D geometrical information of the individual LV. For the group of healthy subjects, the Karhunen-Loeve Transform (KLT) is then applied to compress the geometric information contained in their individual's GCG vectors, at end diastole (ED) and end systole (ES), and yield a unique set of basis vectors. The 'normal shape domain' is next defined as a truncated set of the KLT basis vectors from which a normal GCG can be reconstructed with a mean squared error (MSE) smaller than a defined threshold. The calculated MSE of any individual GCG reconstructed in this domain is then used as a criterion for sorting the 3-D shapes. Hearts which yield MSE greater than the threshold are considered abnormal. When applied to the study group of 19 subjects a significant difference (p <0.0001) between the MSE values obtained for the normal LV's, and those obtained for the abnormal LV's was detected, thus leading to a successful sorting of all the studied LV's. Finally, the KLT is applied to yield a compact representation of the 3-D geometry of any LV (normal or abnormal0.