Definition of a four-dimensional continuous planispheric transformation for the tracking and the analysis of left-ventricle motion

Cardiologists assume that analysis of the motion of the heart (especially the left ventricle) can provide useful information about the health of the myocardium. A 4-D polar transformation is defined to describe the left-ventricle (LV) motion and a method is presented to estimate it from sequences of 3-D images. The transformation is defined in 3-D planispheric 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, and periodicity in time can be imposed. The local motion can be easily decomposed into a few canonical motions (radial motion, rotation around the long-axis, elevation). To recover the motion from original data, the 4-D 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.