An Analytical Descrptor of Three-Dimensional Geometry: Application to the Analysis of the Left Ventricle Shape and Contraction

A novel method to describe the instantaneous three-dimensional (3-D) geometry of the left ventricular (LV) endocardial surface by an analytical time-varying scalar function of Fourier spectrum coefficients is suggested. The method utilizes experimental echocardiographic data and uses a helical coordinate system to transform the 3-D data into a unidimensional numerical function. The instantaneous numerical function is then represented by its Fourier sine series which serves as an analytical shape descriptor from which the 3-D shape is reconstructed. The procedure can also be applied to data compression (spatial low-pass filtering), spectral analysis, and the evaluation of geometric similarity of 3-D shapes. When applied to the endocardial surface of the LV at end-diastole (ED) and end-systole (ES) this technique gives a quantitative analysis of the global LV contraction of the real heart.