Probabilistic and statistical methods for the inverse problem in electrocardiography solution

PhD study program: Applied Mathematics
Akademic year: 2023-2024
Advisor: Ing. Jana Švehlíková, PhD. (umersveh@savba.sk)
External educational institution: Institute of Measurement Science SAS
Accepting university: 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 design of new specialized equipment in medicine. They allow to record many signals simultaneously on one side and to obtain the information about the position and condition of internal organs noninvasively by imaging methods (CT, MR, USG) on the other side. Every mechanical contraction of myocardium is proceeded by an 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 an origin of undesired electric signal which decreases the heart output. The inverse problem of electrocardiography is called also an “electrocardiographic imaging”, because it aims to obtain noninvasively a 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 has not a unique solution. Various reguralization methods (constrains) which imply from mathematically described apriori medical knowledge about a possible heart signals propagation 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 uncertainity. The other approach to inverse problem solutions is the use of probabilistic and statistical methods. The aim of the dissertation is to learn/study the existing statistical methods of the inverse problem solution and to apply them on 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.

The aim of the dissertation is the development of methods for solving the inverse problem of electrocardiography and their application to the measured clinical data.