# PhD. Topics

## Institute of Measurement Science

Topic
Probabilistic and statistical methods for the inverse problem in electrocardiography solution
PhD. program
Applied mathematics
Name of the supervisor
Ing. Jana Švehlíková, PhD.
Contact:
Receiving school
Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Department of Applied Mathematics and Statistics
Annotation
The inverse problem of electrocardiography has been developed during the last decades, mainly thanks to technological progress and the design of new specialized equipment in medicine. They allow us to record many signals simultaneously on one side and to obtain information about the position and condition of internal organs noninvasively by imaging methods (CT, MR, USG) on the other side. Every mechanical contraction of the myocardium is provoked by the origin and propagation of an electrical signal that can be recorded on the body surface as an ECG signal. An impairment of the myocardium causes a change of this electrical signal; other diagnoses result from the origin of the undesired electric signal, which decreases the heart output. The inverse problem of electrocardiography is called also “electrocardiographic imaging” because it aims to obtain noninvasively specific information about the heart from a multiple-lead ECG signals measurement on the torso (so-called ECG mapping) and from the information about the torso geometry and position of the heart and other internal organs from a CT/MR scan. A relationship between the electrical signals on the heart and on the torso is described by integral equations, which lead after discretization to a system of linear equations. However, the system is, in general, ill-posed, i.e., it does not have a unique solution. Various regularization methods (constraints), based on apriori medical knowledge about possible heart signal propagation, which should be mathematically described are used to obtain a proper solution. The next problem in inverse solution results from so-called intraindividual variability, i.e., even the periodical signals measured from the same subject (person) do not repeat exactly but with some uncertainty. The other approach to inverse problem solutions is the use of probabilistic and statistical methods. The dissertation aims to learn/study the existing statistical methods of the inverse problem solution and apply them to available clinical data—next, a specification of the parameters for optimization leading to the best solution. The problem is handled within an international bilateral project with METU (Middle East Technical University), Ankara, Turkey.