0-7803-6465-1/00/$ 10.00 ©2000 IEEE 1639 Quantitative analysis of Left Ventricle Shape and Motion, Using a 3D Dynamic Model: Deformable Superquadrics. Víctor Torrealba 1,2,3 , Antonio Bosnjak 1,2 , Manuel Acuña 2 , Basel Solaiman 1 , Guillermo Montilla 2 , Christian Roux 1 . Abstract - This paper presents a method for the quantitative analysis of the left ventricle mobility, based on the development of a 3D deformable dynamic model. The model is a superquadric-one with different parametric deformations. The data input for the adjustment of this model is a sequence of volumes of the left ventricle obtained in an echocardiography test. An electromechanical device controlled by the computer is adapted. This allows the acquisition of 60 slices in a rotational 3D symmetry. A specialist cardiologist segments the volumes. An objective function is defined to the adjustment of model parameters. The energy of the error is minimized when the parameters are adjusted using a similar focus to the training of the Back Propagation neural network. The dynamics of the position, orientation, size, torsion and its shape have been recovered from the model. This focus permits the obtaining of results clinically useful. If we compare quantitatively the volume of the left ventricle and the volume of the developed superquadrics, in function of time, a small error around 1% is observed in the volume calculation. Therefore, we can conclude that deformable superquadric captures the global parameters of the left ventricle. Key words - 3D Cardiac Dynamic. Deformable Models. Deformable Superquadrics. Echocardiography. 1. Introduction. The movement estimation of walls of the left ventricle is clinically useful and very important at the present time since it has been demonstrated that different heart pathologies have direct repercussion on the ventricle dynamics, and for such reason, there are many research works in this area from the last years. Different authors [1,2,3,4] have reported that during the cardiac cycle, there are global movements of the Left Ventricle, and they can be break down in a series of independent movements: The Global movements of the Left Ventricle are: Translation, Rotation, Contraction, Radial Expansion, Torsion, and Longitudinal Deformation. The objective of this work is the development of a deformable model, which allows the analysis the 3D movement of the left ventricle with a clinical utility. The quantitative parameters of movement of the ventricular walls are captured by the developed model from a dynamic sequence of 3D echocardiography. 2. Deformable model: Superquadric. The superquadrics (figure 1) are a family of parametric curves, which were used for the first time by Gardiner [5] like an extension of the ellipsoids. A superquadric surface is the spherical product of two superquadric curves and can be defined in a 3D vector form as follows: ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ) ( sin * c ) ( )sin ( cos * b ) ( )cos ( cos * a ) , S( e1 e2 e1 e2 e1 θ φ θ φ θ φ θ z y x (1) Where the parameters ‘θ’ y ‘φ’ are between: 2 2 π π θ ≤ ≤ − and . π φ π ≤ ≤ − ‘θ’ y ‘φ’ correspond to latitude and longitude angles, respectively, expressed in a spherical coordinate system. The values a, b and c define the size of the superquadric in the coordinate x, y and z respectively. The exponent’s e 1 and e 2 are the square ness parameters along the z-axis, and the x- y plane, respectively. Figure 1. Superquadric, (ellipsoidal).