A Kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem

In this article, we aimed to reduce the effects of geometric errors and measurement noise on the inverse problem of Electrocardiography (ECG) solutions. We used the Kalman filter to solve the inverse problem in terms of epicardial potential distributions. The geometric errors were introduced into the problem via wrong determination of the size and location of the heart in simulations. An error model, which is called the enhanced error model (EEM), was modified to be used in inverse problem of ECG to compensate for the geometric errors. In this model, the geometric errors are modeled as additive Gaussian noise and their noise variance is added to the measurement noise variance. The Kalman filter method includes a process noise component, whose variance should also be estimated along with the measurement noise. To estimate these two noise variances, two different algorithms were used: (1) an algorithm based on residuals, (2) expectation maximization algorithm. The results showed that it is important to use the correct noise variances to obtain accurate results. The geometric errors, if ignored in the inverse solution procedure, yielded incorrect epicardial potential distributions. However, even with a noise model as simple as the EEM, the solutions could be significantly improved.


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Onak, Onder Nazim; Serinağaoğlu Doğrusöz, Yeşim; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2019-05-01)
In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart's electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of...
A fully implicit finite element method for bidomain models of cardiac electrophysiology
Dal, Hüsnü; Göktepe, Serdar (Informa UK Limited, 2012-01-01)
This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential phi(i) - phi(e) and the extracellular potential phi(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method result...
ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging
Erenler, T; Serinağaoğlu Doğrusöz, Yeşim (Springer Science and Business Media LLC, 2019-10-01)
In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represe...
Parallel implementation of the accelerated BEM approach for EMSI of the human brain
ATASEVEN, YOLDAŞ; Akalin-Acar, Z.; Acar, C. E.; Gençer, Nevzat Güneri (Springer Science and Business Media LLC, 2008-07-01)
Boundary element method (BEM) is one of the numerical methods which is commonly used to solve the forward problem (FP) of electro-magnetic source imaging with realistic head geometries. Application of BEM generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming. This study presents a relatively cheap and effective solution for parallel implementation of the BEM to reduce the processing times to clinically acceptable valu...
A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes
Ferhatoglu, Erhan; Ciğeroğlu, Ender; Özgüven, Hasan Nevzat (Elsevier BV, 2018-07-01)
In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the n...
Citation Formats
U. Aydin and Y. Serinağaoğlu Doğrusöz, “A Kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem,” MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING, pp. 1003–1013, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42778.