Exploring Possible Choices of the Tikhonov Regularization Parameter for the Method of Fundamental Solution in Electrocardiography

Chamorro-Servent, Judit; Dubois, Rémi; Coudière, Yves

doi:10.22489/cinc.2017.056-347

Cited by 2 publications

(4 citation statements)

References 12 publications

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“…From Figures 6 and 7, it can be seen that there is a reduction in RE (as defined here) of between 2.3% and 24.8% compared to the CRESO solution. This is a similar or better improvement than suggested in [29,30]. Finally, Bouyssier et al [22] present simulations over a heartbeat cycle with average CC of about 0.7 and average RE of about 0.85, which is also in keeping with the data presented here.…”

Section: Discussionsupporting

confidence: 88%

“…The studies presented in [29,30] also use the CRESO method as the gold standard and measure the improvements in their new methods by comparison with the CRESO solutions.…”

Section: Discussionmentioning

confidence: 99%

“…The MFS approach has been applied to various inverse problems previously [26,27] and, as mentioned above, in particular to the inverse problem of electrocardiology [24]. Recent applications of the MFS to ECGI include studies of the locations of the heart and torso boundaries [28], application of the U-curve and the discrete Picard condition [29,30].…”

Section: Introductionmentioning

confidence: 99%

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Accuracy of electrocardiographic imaging using the method of fundamental solutions

Johnston

2018

Computers in Biology and Medicine

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Solving the inverse problem of electrocardiology via the Method of Fundamental Solutions has been proposed previously. The advantage of this approach is that it is a meshless method, so it is far easier to implement numerically than many other approaches. However, determining the heart surface potential distribution is still an ill-posed problem and thus requires some form of Tikhonov regularisation to obtain the required distributions. In this study, several methods for determining an "optimal" regularisation parameter are compared in the context of solving the inverse problem of electrocardiology via the Method of Fundamental Solutions. It is found that the Robust Generalised Cross-Validation method most often yields epicardial potential distributions with the least relative error when compared to the input distribution. The study also compares the inverse solutions obtained with the Method of Fundamental Solutions with those obtained in a previous study using the boundary element method. It is found that choosing the best solution methodology and regularisation parameter determination method depends on the particular scenario being considered.

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Section: Discussionsupporting

confidence: 88%

“…The studies presented in [29,30] also use the CRESO method as the gold standard and measure the improvements in their new methods by comparison with the CRESO solutions.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accuracy of electrocardiographic imaging using the method of fundamental solutions

Johnston

2018

Computers in Biology and Medicine

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“…In current practice, one often only experiences such effects while observing the reconstruction results, without a prior understanding of the potential effect of certain regularization parameter values on the solution of the inverse problem. At the same time, some regularization parameter estimation methods may display a lack of robustness, convergence, or efficacy in specific circumstances [ 16 ]. By turning the attention to the regularization parameter itself, it may be easier to observe the influence of different choices of parameter values on the reconstructed solutions, and consequently to assess the values provided by different regularization parameter estimation methods.…”

Section: Introductionmentioning

confidence: 99%

Influence of the Tikhonov Regularization Parameter on the Accuracy of the Inverse Problem in Electrocardiography

Wang

Karel

Bonizzi

et al. 2023

Sensors

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The electrocardiogram (ECG) is the standard method in clinical practice to non-invasively analyze the electrical activity of the heart, from electrodes placed on the body’s surface. The ECG can provide a cardiologist with relevant information to assess the condition of the heart and the possible presence of cardiac pathology. Nonetheless, the global view of the heart’s electrical activity given by the ECG cannot provide fully detailed and localized information about abnormal electrical propagation patterns and corresponding substrates on the surface of the heart. Electrocardiographic imaging, also known as the inverse problem in electrocardiography, tries to overcome these limitations by non-invasively reconstructing the heart surface potentials, starting from the corresponding body surface potentials, and the geometry of the torso and the heart. This problem is ill-posed, and regularization techniques are needed to achieve a stable and accurate solution. The standard approach is to use zero-order Tikhonov regularization and the L-curve approach to choose the optimal value for the regularization parameter. However, different methods have been proposed for computing the optimal value of the regularization parameter. Moreover, regardless of the estimation method used, this may still lead to over-regularization or under-regularization. In order to gain a better understanding of the effects of the choice of regularization parameter value, in this study, we first focused on the regularization parameter itself, and investigated its influence on the accuracy of the reconstruction of heart surface potentials, by assessing the reconstruction accuracy with high-precision simultaneous heart and torso recordings from four dogs. For this, we analyzed a sufficiently large range of parameter values. Secondly, we evaluated the performance of five different methods for the estimation of the regularization parameter, also in view of the results of the first analysis. Thirdly, we investigated the effect of using a fixed value of the regularization parameter across all reconstructed beats. Accuracy was measured in terms of the quality of reconstruction of the heart surface potentials and estimation of the activation and recovery times, when compared with ground truth recordings from the experimental dog data. Results show that values of the regularization parameter in the range (0.01–0.03) provide the best accuracy, and that the three best-performing estimation methods (L-Curve, Zero-Crossing, and CRESO) give values in this range. Moreover, a fixed value of the regularization parameter could achieve very similar performance to the beat-specific parameter values calculated by the different estimation methods. These findings are relevant as they suggest that regularization parameter estimation methods may provide the accurate reconstruction of heart surface potentials only for specific ranges of regularization parameter values, and that using a fixed value of the regularization parameter may represent a valid alternative, especially when computational efficiency or consistency across time is required.

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Exploring Possible Choices of the Tikhonov Regularization Parameter for the Method of Fundamental Solution in Electrocardiography

Cited by 2 publications

References 12 publications

Accuracy of electrocardiographic imaging using the method of fundamental solutions

Accuracy of electrocardiographic imaging using the method of fundamental solutions

Influence of the Tikhonov Regularization Parameter on the Accuracy of the Inverse Problem in Electrocardiography

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