3D modeling and parameterization of the left ventricle in echocardiographic images using deformable superquadrics

This paper proposes a new method for the quantitative analysis of the mobility of the left ventricle LV, based on a 3D dynamic model. One superquadric is used as the 3D global model. For data acquisition, an electromechanical device that allows acquiring the volume of images using 60 cross-sections in a rotational cylindrical 3D symmetry is adapted to an echograph. The images are filtered and later, they are segmented by a specialist. This processing provides images where the internal and external structures are already known. Finally, the 3D superquadrics model is used and we minimize the energy of the quadratic error using the method of descending gradient for several variables. We capture the geometrical and mathematical parameters when the model is adjusted to actual data. After, it is necessary to compute the medical parameters as: LVV, LV mass, stroke volume, ejection fraction, and cardiac output, etc. We propose new measures allowing the observation of the variations of the parameters in function of time. For example, in the calculation of the LVV, the results give a small error of 2% by respect on a manual segmentation made by the specialist. That demonstrates a good adjustment to the 3D volume images to the LV