¹Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
²Lomonosov Moscow State University, Moscow, Russia

Abstract. The main approaches to studying the human heart using non-invasive measurements are discussed. Methods such as echocardiography, computed tomography, and magnetic resonance imaging are used to study the heart's structure. Cardiac function is studied primarily using electrocardiography and magnetic cardiography. Data sets available for use in mathematical modeling of the heart to study its function and for diagnostic purposes are described. A method of functional tomography is proposed that transforms a set of time series into a spatial distribution of electrical or magnetic sources. Experimental magnetic cardiography data obtained at the Center for Neuromagnetism, New York University, at the Kurchatov Institute National Research Center and the Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, were used to reconstruct the three-dimensional functional structure of the heart and time series of electrical activity of the heart. The current dipole found from the magnetic cardiogram was successfully localized in the space of the reconstructed heart structure, and its amplitude and direction changed in accordance with the phase of the cardiac cycle. The method can be used for a detailed study of the spatial distribution of elementary sources of electrical activity of the human heart based on multichannel non-invasive measurements. 

Key words: cardiovascular system, computed tomography, magnetic resonance imaging, electrocardiography, magnetic cardiography, ballistocardiography, open datasets, Fourier transform, inverse problem solution, functional tomography from cardiography data