Definition of a 4 D continuous planispheric transformation for the tracking and the analysis of LV motion

Cardiologists assume that analysis of the motion of the heart (especially the left ventricle) can give some information about the health of the myocardium. A 4D polar transformation is defined to describe the left ventricle (LV) motion and a method is presented to estimate it from sequences of 3D images. The transformation is defined in 3Dplanispheric coordinates (3PC) by a small number of parameters involved in a set of simple linear equations. It is continuous and regular in time and space, periodicity in time can be imposed. The local motion can be easily decomposed intoa few canonical motions (radial motion, rotation around the long-axis, elevation). To recover the motion from original data, the 4D polar transformation is calculated using an adaptation of the Iterative Closest Point algorithm. We present the mathematical framework and a demonstration of its feasability on a series of gated SPECT sequences.

[1]  Laurent D. Cohen,et al.  Tracking medical 3D data with a parametric deformable model , 1995, Proceedings of International Symposium on Computer Vision - ISCV.

[2]  Alok Gupta,et al.  A periodic generalized cylinder model with local deformations for tracking closed contours exhibiting repeating motion , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[3]  Chahab Nastar,et al.  Vibration Modes for Nonrigid Motion Analysis in 3D Images , 1994, ECCV.

[4]  J C Gore,et al.  Development and evaluation of tracking algorithms for cardiac wall motion analysis using phase velocity MR imaging , 1994, Magnetic resonance in medicine.

[5]  Jinah Park,et al.  Deformable models with parameter functions: application to heart-wall modeling , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[6]  Alistair A. Young,et al.  Tracking and finite element analysis of stripe deformation in magnetic resonance tagging , 1995, IEEE Trans. Medical Imaging.

[7]  François G. Meyer,et al.  TRACKING MYOCARDIAL DEFORMATION USING SPATIALLY-CONSTRAINED VELOCITIES , 1995 .

[8]  Dana H. Ballard,et al.  COMPUTER MODEL FOR EXTRACTING MOVING HEART SURFACES FROM FOUR-DIMENSIONAL CARDIAC ULTRASOUND DATA. , 1979 .

[9]  James S. Duncan,et al.  A Unified Framework to Assess Myocardial Function from 4D Images , 1995, CVRMed.

[10]  Demetri Terzopoulos,et al.  A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis. , 1995, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[11]  P. Radeva,et al.  Deformable B-solids and implicit snakes for localization and tracking of SPAMM MRI-data , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[12]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[13]  Jean-Jacques Risler,et al.  Méthodes mathématiques pour la CAO , 1991 .

[14]  Rachid Deriche,et al.  3D edge detection using recursive filtering: Application to scanner images , 1991, CVGIP Image Underst..

[15]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[16]  Patrick Clarysse,et al.  3D boundary extraction of the left ventricle by a deformable model with a priori information , 1995, Proceedings., International Conference on Image Processing.

[17]  J. Duncan,et al.  A recursive filter for temporal analysis of cardiac motion , 1994, Proceedings of IEEE Workshop on Biomedical Image Analysis.

[18]  Dmitry B. Goldgof,et al.  The Use of Three- and Four-Dimensional Surface Harmonics for Rigid and Nonrigid Shape Recovery and Representation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Jinah Park,et al.  Analysis of left ventricular wall motion based on volumetric deformable models and MRI-SPAMM , 1996, Medical Image Anal..

[20]  E. McVeigh.  MRI of myocardial function: motion tracking techniques. , 1996, Magnetic resonance imaging.

[21]  A. Douglas,et al.  Description of the deformation of the left ventricle by a kinematic model. , 1992, Journal of biomechanics.

[22]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[23]  P. Hunter,et al.  The analysis of cardiac function: a continuum approach. , 1988, Progress in biophysics and molecular biology.

[24]  Jerry L Prince,et al.  3D displacement field reconstruction from planar tagged cardiac MR images , 1994, Proceedings of IEEE Workshop on Biomedical Image Analysis.

[25]  Laurent D. Cohen,et al.  Tracking and motion analysis of the left ventricle with deformable superquadrics , 1996, Medical Image Anal..

[26]  Alistair A. Young,et al.  Semi-automatic tracking of myocardial motion in MR tagged images , 1995, IEEE Trans. Medical Imaging.

[27]  John S. Duncan,et al.  Shape-based 4D left ventricular myocardial function analysis , 1994, Proceedings of IEEE Workshop on Biomedical Image Analysis.

[28]  Nicholas Ayache,et al.  Dense Non-Rigid Motion Estimation in Sequences of 3D Images Using Differential Constraints , 1995, CVRMed.

[29]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Jean-Philippe Thirion,et al.  Fast Non-Rigid Matching of 3D Medical Images , 1995 .

[31]  Nicholas Ayache,et al.  Randomness and geometric features in computer vision , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[32]  J. Declerck.  Étude de la dynamique cardiaque par analyse d'images tridimensionnelles , 1997 .

[33]  Jerry L Prince,et al.  Cardiac motion simulator for tagged MRI , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[34]  J. Murcia.  Reconstruction d'images cardiaques en tomographie d'émission monophotonique à l'aide de modèles spatio-temporels , 1996 .

[35]  A. Young,et al.  Three‐Dimensional Left Ventricular Deformation in Hypertrophic Cardiomyopathy , 1994, Circulation.

[36]  J. Declerck,et al.  Automatic registration and alignment on a template of cardiac stress and rest SPECT images , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[37]  Dmitry B. Goldgof,et al.  Motion analysis of nonrigid surfaces , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[38]  Nicholas Ayache,et al.  Definition of a 4D continuous polar transformation for the tracking and the analysis of LV motion , 1997, CVRMed.

[39]  James S. Duncan,et al.  Bending and stretching models for LV wall motion analysis from curves and surfaces , 1992, Image Vis. Comput..

[40]  Richard M. Leahy,et al.  Determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast CT cardiac images , 1994, IEEE Trans. Medical Imaging.