Extracting motion parameters from the left ventricle angiography data

This paper presents a new approach for extracting surface motion parameters from the left ventricle (LV) data. The data are obtained using biplane (stereo) cineangiography and provided by Dr. David Smith [23]. The data set consists of 3-D coordinates of 30 bifurcation points on the surface of LV through several time frames. If an object undergoes rigid motion, the standard motion parameters are the translation vector and rotation matrix. The above parameters are not sufficient to describe the nonrigid motion, of which the LV motion is an example. Hence, we define the local surface stretching as an additional (with global rotation and translation) motion parameter. The process of recovering the stretching factor from the angiography data consists of three steps. At the first step, the surface of LV is reconstructed at each time instant. The reconstruction procedure involves converting data into polar coordinate system. Then the surface is reconstructed by applying the relaxation (iterative averaging) algorithm in polar coordinates. During the second step we calculate Gaussian curvature at each bifurcation point at each time instant. This achieved by least-squares surface fitting in the window around each point of interest. The third step is actual stretching factor recovery, which is based on comparison of Gaussian curvatures before and after the motion. This formula was first suggested in [11]. The final results of the algorithm are the reconstructed LV surface at each time instant together with cumulative stretching curves for each given bifurcation point.