Denney and Prince : Reconstruction of 3 D Left Ventricular Motion

| Magnetic resonance (MR) tagging has shown great potential for noninvasive measurement of the motion of a beating heart. In MR tagged images, the heart appears with a spatially encoded pattern that moves with the tissue. The position of the tag pattern in each frame of the image sequence can be used to obtain a measurement of the 3D displacement eld of the myocardium. The measurements are sparse, however, and interpolation is required to reconstruct a dense displacement eld from which measures of local con-tractile performance such as strain can be computed. In this paper, we propose a method for estimating a dense displacement eld from sparse displacement measurements. Our approach is based on a multidimensional stochastic model for the smoothness and divergence of the displacement eld and the Fisher estimation framework. The main feature of this method is that both the displacement eld model and the resulting estimate equation are deened only on the irregular domain of the myocardium. Our methods are validated on both simulated and in vivo heart data.