Estimating Electrical Parameters of the Heart Using Diffusion Models and ECG/MCG Sensor Arrays

Abstract

<p> The estimation of physiological parameters that characterize electrical signal propagation in the heart is an important component of the inverse problem in electrocardiography. Recent studies show that some patterns in cardiac electrical signals (e.g. spiral waves) are associated with the re-entrance phenomenon seen in cardiac arrhythmia. Therefore, further research in this field will lead to improved detection and diagnosis of cardiac diseases and conditions. </p> <p> Electrical activity in the heart is initiated at the SA node and an electrical impulse propagates to the atria causing their mechanical contraction. Subsequent contraction of the ventricles (systole) followed by relaxation (diastole) completes the heart cycle. Evidence of electrical activity in cardiac cells is shown by a potential difference across the cell membrane that changes when ·ionic currents flow through the membrane's channels. This electrical activation of the heart can be modeled using a diffusion model in which the physiological parameters (e.g., conductivity) govern the resulting spatiatemporal process. </p> <p> In this thesis we derive an inverse model for the electrical activation of the heart using the Fitzhugh-N agumo diffusion equations which account for the dynamics of spiral waves in excitable media such as, in our case, cardiac cells. The electric potential is expressed through activator and inhibitor variables and we simulate the measurements of the electromagnetic field are on the torso surface. A signal processing model is derived where the physiological parameters are deterministic or stochastic, and the resulting physiological measurements are a function of space, time, and the parameters. </p> <p> We estimate these unknown parameters using an optimization algorithm that minimizes the cost function of the model. For our estimation we use Least Squares and we derive the Maximum Likelihood Estimator. We measure the performance using mean square error, and we compute the Cramer-Rao Lower Bound, which shows the minimum variance attainable. </p> <p> In our simulations we use a finite element mesh of a human torso to describe a realistic geometry to generate the potentials on the surface. Our results indicate that estimating the physiological parameters of a diffusion equation from the measurements taken outside the torso are feasible. This further suggests that ECG/MCG signals can be used to provide detailed information about the physiological properties of the electrical impulse generated in the heart and aid in diagnosis of various pathological conditions including arrhythmia. </p>