Estimating Current Density in the Heart Using Structured and Unstructured Covariance Analysis

The inverse problem of electrocardiography can be defined as the determination of the electrical activity of the heart from measurements of the body-surface electromagnetic field. The solution to this inverse problem may ultimately improve the ability to detect and treat cardiac diseases early. We present an algorithm for estimating the current density of the heart using ECG and magnetocardiography (MCG) sensor arrays. We model the electrical activity of the heart using current density represented by a set of deterministic and stochastic spatio-temporal basis functions. In order to solve the corresponding Fredholm equation we apply the element-free Galerkin method and compute the measurements as a function of the torso geometry and cardiac source. Then, we maximize the likelihood function to estimate the unknown parameters assuming a presence of spatially correlated Gaussian noise with unknown covariance matrix. Numerical examples illustrate the applicability of our results.