Recovery of Myocardial Kinematic Function without the Time History of External Loads

A time-domain filtering algorithm is proposed to recover myocardial kinematic function using output-only measurements without the time history of external loads. The main contribution of this work is that the overall effect of all the external loads on the myocardium is treated as a random variable disturbed by the Gaussian white noise because the external loads of the myocardium are usually unknown in practical exercises. The kernel of our proposed algorithm is an iterative, multiframe, and sequential filtering procedure consisting of a Kalman filter and a least-squares filter. In our proposed implementation, the initial guess of myocardial kinematic function and residual innovation of all the state variables are first computed using a Kalman filter via state space equations only driven by the Gaussian white noise, and then the residual innovation is fed into a least-squares filter to estimate the total external loads of the myocardium. In the end, the initial guess of myocardial kinematic function is corrected using external loads provided by the least-squares filter. After the introduction of the whole structure of our algorithm, we demonstrate the ability of the framework on synthetic data and MR image sequences.