Modeling and tracking of the cardiac left ventricular motion by a state space harmonic model in MRI sequence

We present a new method for modeling the left ventricular motion of the heart from a magnetic resonance imaging (MRI) sequence. We propose to model the 3D time-space trajectory of the points of the endocardial regions of the left ventricle (LV) using an harmonic model of movement, which is linear and describes the dynamics of the left ventricle throughout the cardiac cycle. This new state space model is based on the assumption of quasi-periodicity of the cardiac cycle. We describe our method to obtain the state canonical vector and the corresponding state equations of the harmonic state model (HSM). A Kalman filter is used on this harmonic state model as an estimation tool of the filtered trajectory of the LV. It allows to obtain a robust estimation of the state vector which contains the measured parameter and its derivatives. Thus, a robust estimation of the instantaneous velocity of the LV region is computed using the whole information of the sequence included in the harmonic model. The model is validated on real cardiac sequences. We detail how to get the 3D time-space trajectories of the LV edge points. The results obtained are particularly interesting because they demonstrate the capability of our method to understand and discriminate normal cases from pathological cases.