Reconstruction of 3-D Left Ventricular Motion from Planar Tagged Cardiac MR Images: An Estimation Theoretic Approach

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 3-D displacement field of the myocardium. The measurements are sparse, however, and interpolation is required to reconstruct a dense displacement field from which measures of local contractile performance such as strain can be computed. In this paper, we propose a method for estimating a dense displacement field from sparse displacement measurements. Our approach is based on a multidimensional stochastic model for the smoothness and divergence of the displacement field and the Fisher estimation framework. The main feature of this method is that both the displacement field model and the resulting estimate equation are defined only on the irregular domain of the myocardium. Our methods are validated on both simulated and in vivo heart data.