Publications (11)1.59 Total impact
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ABSTRACT: The problem of determining the point on the heart surface (projection) nearest to the arrhythmogenic focus, which is located inside the heart, is considered. Localization of this point is crucial for a successful cardiac ablation procedure. The sought projection is calculated on the basis of solving the inverse electrocardiography problem, which is a generalization of the Cauchy problem for the Laplace equation. The inverse electrocardiography problem is solved by the boundary integral equation and Tikhonov regularization methods. Examples of test computations are demonstrated, and the results of processing real electrophysiological data are presented and compared with the medical observation data.Mathematical Models and Computer Simulations 11/2012; 4(6).  [Show abstract] [Hide abstract]
ABSTRACT: Methods of assessing the electrophysiological state of the heart by solving the inverse problem of electrocardiography in potential form are actively used in clinical practice. Some results suggest, however, that on its own the electric potential of the heart may not be sufficient for diagnosing complex cases of cardiac arrhythmia. Studies have shown that the absolute value of the potential gradient is an important characteristic that produces a more precise assessment of the electrophysiological state of the heart. In this article we propose an algorithm for numerical reconstruction of the potential gradients from the solution of the inverse problem of electrocardiography.Computational Mathematics and Modeling 04/2012; 23(2).  [Show abstract] [Hide abstract]
ABSTRACT: The article presents a modification of the algorithm for the inverse problem of electrocardiography originally proposed in [6]. The modification is intended to improve the computation accuracy and to reduce the computing time.Computational Mathematics and Modeling 01/2011; 22(1):3034.  [Show abstract] [Hide abstract]
ABSTRACT: A numerical method is proposed for solving an inverse electrocardiography problem for a medium with a piecewise constant electrical conductivity. The method is based on the method of boundary integral equations and Tikhonov regularization.Computational Mathematics and Mathematical Physics 07/2010; 50(7):11721177. · 0.59 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A Dirichlet problem is considered in a threedimensional domain filled with a piecewise homogeneous medium. The uniqueness of its solution is proved. A system of Fredholm boundary integral equations of the second kind is constructed using the method of surface potentials, and a system of boundary integral equations of the first kind is derived directly from Green’s identity. A technique for the numerical solution of integral equations is proposed, and results of numerical experiments are presented.Computational Mathematics and Mathematical Physics 07/2009; 49(7):11411150. · 0.59 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider numerical methods for solving inverse problems that arise in heart electrophysiology. The first inverse problem is the Cauchy problem for the Laplace equation. Its solution algorithm is based on the Tikhonov regularization method and the method of boundary integral equations. The second inverse problem is the problem of finding the discontinuity surface of the coefficient of conductivity of a medium on the basis of the potential and its normal derivative given on the exterior surface. For its numerical solution, we suggest a method based on the method of boundary integral equations and the assumption on a special representation of the unknown surface.Differential Equations 07/2009; 45(7):10341043. · 0.42 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Boundary integral equation methods are considered for computing dc fields in threedimensional regions filled with a piecewisehomogeneous medium. The problem is formulated and a system of Fredholm boundary integral equations of first kind is constructed, following directly from Green’s formula. The numerical solution stages are considered in detail, including construction and triangulation of the numerical surfaces, evaluation of surface integrals, and solution of a system of blockmatrix equations.Computational Mathematics and Modeling 07/2009; 20(3):247257.  [Show abstract] [Hide abstract]
ABSTRACT: Cardiac arrhythmia is an important cause of decrease in life quality and duration. Cardiac arrhythmias are serious medical and social problems. Success in the treatment of cardiac arrhythmia depends on the quality of diagnosis. Electrophysiological mechanism of cardiac arrhythmia and localization of arrhythmogenic substrates are very important for intervention and surgical methods of treatment of cardiac arrhythmia [2]. Invasive electrophysiological examination (EPE) of the heart is the main method of topical and electro� physiological diagnosis of cardiac arrhythmia. EPE is based on direct detection of electrocardiograms at the endocardial or epicardial surface of the heart (endocar� dial or epicardial mapping). Endocardial or epicardial mapping requires detectors to be inserted into the heart chambers or pericardial cavity. Because of invasive char� acter of endocardial or epicardial mapping, this proce� dure should be performed immediately before incision antiarrhythmia treatment of myocardium within the framework of integral surgical or intervention treatment. Development of a noninvasive method for EPE of the heart is an urgent problem. The method should pro� vide electrophysiological information of the same diag� nostic quality as endocardial or epicardial mapping. This method would significantly increase safety and availabili� ty of accurate diagnosis of cardiac arrhythmia. Noninvasive EPE of the heart should be included into theBiomedical Engineering 10/2008; 42(6):273279.  [Show abstract] [Hide abstract]
ABSTRACT: The inverse electrocardiography problem related to medical diagnostics is considered in terms of potentials. Within the framework of the quasistationary model of the electric field of the heart, the solution of the problem is reduced to the solution of the Cauchy problem for the Laplace equation in R 3. A numerical algorithm based on the Tikhonov regularization method is proposed for the solution of this problem. The Cauchy problem for the Laplace equation is reduced to an operator equation of the first kind, which is solved via minimization of the Tikhonov functional with the regularization parameter chosen according to the discrepancy principle. In addition, an algorithm based on numerical solution of the corresponding Euler equation is proposed for minimization of the Tikhonov functional. The Euler equation is solved using an iteration method that involves solution of mixed boundary value problems for the Laplace equation. An individual mixed problem is solved by means of the method of boundary integral equations of the potential theory. In the study, the inverse electrocardiography problem is solved in region Ω close to the real geometry of the torso and heart.Moscow University Computational Mathematics and Cybernetics 06/2008; 32(2):6168.  [Show abstract] [Hide abstract]
ABSTRACT: If a source of seismic waves is situated a short distance from an interface there will be a considerable contribution to the field of the refracted wave from inhomogeneous waves excited by the source. This results information of a system of lowfrequency nonuniformly refracted and outflowing waves, constituting the subject of this article. Investigation of the system of nonuniformly refracted and outflowing waves for a case when the source is in a highvelocity medium revealed that the polarization of nonuniformly refracted waves and the homogeneous components of the outflowing waves is close to linear. With increasing distance between the source and interface the amplitudes of these waves decrease rapidly. The authors give an indepth analysis of the phenomenon for two cases: (1) plane interface of two fluid halfspaces, (2) plane interface of two elastic halfspaces. The article constitutes the first systematic analysis of the dynamic and kinematic characteristics of these types of waves. Comprehension of this phenomenon will prove useful in seismological and borehole investigations, particularly in seismic prospecting and especially when waveguides are present in the section.USSR Report Earth Sciences JPRS UES. 05/1984; 
Publication Stats
77  Citations  
1.59  Total Impact Points  
Top Journals
Institutions

2009–2012

Moscow State Textile University
Moskva, Moscow, Russia


2008–2009

Lomonosov Moscow State University
 • Faculty of Computational Mathematics and Cybernetics
 • Division of Mathematics
Moscow, Moscow, Russia
