On the optimality of magnetic resonance tag patterns for heart wall motion estimation

Tracking of cardiac motion using magnetic resonance tagging has attracted increasing attention in recent years. Several methods for tagging the cardiac tissue and tracking the motion of the tags have been developed. However, the choice of tag pattern that minimizes tracking error has received less attention. In this paper, we are concerned with the optimal tagging and acquisition of MR tagged images for cardiac motion analysis. We formulate the measurement of tissue deformation as a multidimensional parametric estimation problem which can be solved using the nonlinear least squares estimator. Along with this, we derive the Cramer-Rao lower bound (CRLB) on the average estimation error variance. We then show that under certain conditions a complex sinusoidal tag shape minimizes the CRLB. We validate our results with computer simulations. Finally, based on the previous findings, we make recommendations concerning the most desirable imaging strategy for images tagged with a complex sinusoidal tag pattern.