Reconstructing Cardiac Wave Dynamics From Myocardial Motion Data

Various models exist to predict the active stresses and membrane potentials within cardiac muscle tissue. However, there exist no methods to reliably measure active stresses, nor do there exist ways to measure transmural membrane potentials that are suitable for in vivo usage. Prior work has devised a linear model to map from the active stresses within the tissue to displacements [1]. In situations where measurements of tissue displacements are entirely precise, we are able to naively solve for the active stresses from the measurements with ease. However, real measurement processes always carry some associated random error and, in the presence of this error, our naive solution to this inverse problem fails. In this work we propose the use of the Ensemble Transform Kalman Filter to more reliably solve this inverse problem. This technique is faster than other related Kalman Filter techniques while still generating high quality estimates which improve on our naive solution. We demonstrate, using in silico simulations, that the Ensemble Transform Kalman Filter produces errors whose standard deviation is an order of magnitude smaller than the least-squares solution.