Analytic signal phase-based myocardial motion estimation in tagged MRI sequences by a bilinear model and motion compensation

Different mathematical tools, such as multidimensional analytic signals, allow for the calculation of 2D spatial phases of real-value images. The motion estimation method proposed in this paper is based on two spatial phases of the 2D analytic signal applied to cardiac sequences. By combining the information of these phases issued from analytic signals of two successive frames, we propose an analytical estimator for 2D local displacements. To improve the accuracy of the motion estimation, a local bilinear deformation model is used within an iterative estimation scheme. The main advantages of our method are: (1) The phase-based method allows the displacement to be estimated with subpixel accuracy and is robust to image intensity variation in time; (2) Preliminary filtering is not required due to the bilinear model. The proposed algorithm, integrating phase-based optical flow motion estimation and the combination of global motion compensation with local bilinear transform, allows spatio-temporal cardiac motion analysis, e.g. strain and dense trajectory estimation over the cardiac cycle. Results from 7 realistic simulated tagged magnetic resonance imaging (MRI) sequences show that our method is more accurate compared with state-of-the-art method for cardiac motion analysis and with another differential approach from the literature. The motion estimation errors (end point error) of the proposed method are reduced by about 33% compared with that of the two methods. In our work, the frame-to-frame displacements are further accumulated in time, to allow for the calculation of myocardial Lagrangian cardiac strains and point trajectories. Indeed, from the estimated trajectories in time on 11 in vivo data sets (9 patients and 2 healthy volunteers), the shape of myocardial point trajectories belonging to pathological regions are clearly reduced in magnitude compared with the ones from normal regions. Myocardial point trajectories, estimated from our phase-based analytic signal approach, seem therefore a good indicator of the local cardiac dynamics. Moreover, they are shown to be coherent with the estimated deformation of the myocardium.