MEYER ET AL . : TRACKING THE MYOCARDIUM USING PHASE CONTRAST MR VELOCITIES 455 φ i deformation

| In this paper, we propose a new approach for tracking the deformation of the Left Ventricular (LV) my-ocardium from two-dimensional Magnetic Resonance (MR) phase contrast velocity elds. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others 1] and shown to be potentially useful for tracking discrete tissue elements, and therefore characterizing LV motion. However, we show here that these velocity data i.) are extremely noisy near the LV borders and ii.) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity elds. In this new approach, we use the natural spatial constraints of the endocardial and epicardial contours , detected semi-automatically in each image frame, to help remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a deforming mesh that is placed over the myocardium at one time frame and then tracked over the entire cardiac cycle. The deformation is guided by a Kalman lter that provides a compromise between a.) believing the dense eld velocity and the contour data when it is crisp and coherent in a local spatial and temporal sense and b.) employing a temporally smooth cyclic model of cardiac motion when contour and velocity data are not trustworthy. The Kalman lter is particularly well suited to this task as it produces an optimal estimate of the LV's kinematics (in the sense that the error is statistically minimized) given incomplete and noise corrupted data, and given a basic dynamical model of the LV. The method has been evaluated with simulated data ; the average error between tracked nodes and theoretical position was 1:8% of the total path length. The algorithm has also been evaluated with phantom data ; the average error was 4:4% of the total path length. We show that in our initial tests with phantoms that the new approach shows small, but concrete improvements over previous techniques that used primarily phase contrast velocity data alone. We feel that these improvements will be ampliied greatly as we move to direct comparisons in in vivo and three-dimensional datasets.