An implementation of data assimilation techniques for transmural visualization of action potential propagation in cardiac tissue

Abstract

A number of models have been put forward which describe the motion and propagation of action potentials within cardiac muscle tissue. The information produced by these models can be unverifiable, as no techniques currently exist to accurately measure voltage within the walls of the cardiac tissue, especially in an in vivo environment. In most situations it is much simpler to measure the contractile motion of the cardiac muscle, which is one of the results of the propagation of these action potentials. Prior work has suggested that one can solve an inverse problem to derive the action potentials present in the cardiac tissue from measurements of the displacement caused by the contractile motion; nevertheless, the solutions to this inverse problem degrade quickly in the face of error in the measurements of these displacements. In our work, we show that one potential solution for reducing the effects of these errors is through the implementation of the Unscented Kalman Filter. This technique allows us to assimilate our error-prone measurements with knowledge of an electrophysiological model to improve our estimates and help refine our solutions to the inverse problem. Using this process, we are able to solve the one dimensional problem in a way that reduces the error present in our estimates significantly, which, in turn, allows us to more accurately resolve the electrical behavior in our system.