Title: Optimal Filtering Strategies for Simultaneous Recovery of Myocardial Kinematics and Elasticity

Pengcheng Shi
Biomedical Research Laboratory 
Department of Electrical and Electronic Engineering
Hong Kong University of Science and Technology
Clear Water Bay, Kowloon, Hong Kong

Email: eeship@ust.hk
Http://www.ee.ust.hk/~eeship/


ABSTRACT:
Accurate and robust estimation of the motion and material properties of the 
myocardium could help to better understand the pathophysiological processes 
associated with ischemic heart diseases. Given partial, noisy image-derived 
measurements on the cardiac kinematics, we present several integrated, 
simultaneous estimation schemes for the joint recovery of the cardiac 
kinematics and elasticity parameters. For a particular a priori constraining 
material model with uncertain subject-dependent parameters and a posteriori 
noisy imaging based observations, we combine the stochastic differential 
equations of the myocardial dynamics with the finite element method, and the 
material parameters and the imaging data are treated as random variables with 
known or unknown statistics. The system is then reformulated in state space 
representation to facilitate the estimation processes.

In the first efforts, under the Gaussian assumptions on the system and data 
inputs, the material parameters of the biomechanical model are treated as 
part of an augmented state vector, and with measurements taken over time, 
this state vector is adjusted by nonlinear filters so that they match the 
data in minimum-mean-square-errors (MMSE) manners through two H_2 filtering 
frameworks, the extended Kalman filter and the extended Kalman smoother.  
In practice, however, it is very unlikely that the system and data statistics 
are readily available, and one cannot always guarantee the validity of the 
Gaussian assumptions required by the H_2 estimators. Thus, a robust dual 
estimation framework based on H_infinity criteria has been developed. This 
dual min-max strategy is particularly powerful for real-world problems where 
the types and levels of model uncertainties and data disturbances are not 
available a priori. In our formulation, the dual estimation algorithm uses 
two separated iterative H_infinity filters: one for the kinematics estimation 
and another for the elasticity estimation. At each time step, we first 
generate the kinematics estimates with fixed sub-optimal material parameter 
estimates, and then recover the elasticity property given these sub-optimal 
kinematic state estimates. These two steps are repeated as necessary until 
convergence to optimal estimates. We demonstrate the power of these strategies
through experiments with both synthetic data and real magnetic resonance 
tagging and phase contrast image sequences.