Application of robust Generalised Cross-Validation to the inverse problem of electrocardiology

Generalization and Regularization for Inverse Cardiac Estimators

Electrocardiographic Imaging (ECGI) aims to estimate the intracardiac potentials noninvasively, hence allowing the clinicians to better visualize and understand many arrhythmia mechanisms. Most of the estimators of epicardial potentials use a signal model based on an estimated spatial transfer matrix together with Tikhonov regularization techniques, which works well specially in simulations, but it can give limited accuracy in some real data. Based on the quasielectrostatic potential superposition principle, we propose a simple signal model that supports the implementation of principled out-of-sample algorithms for several of the most widely used regularization criteria in ECGI problems, hence improving the generalization capabilities of several of the current estimation methods. Experiments on simple cases (cylindrical and Gaussian shapes scrutinizing fast and slow changes, respectively) and on real data (examples of torso tank measurements available from Utah University, and an animal torso and epicardium measurements available from Maastricht University, both in the EDGAR public repository) show that the superposition-based out-of-sample tuning of regularization parameters promotes stabilized estimation errors of the unknown source potentials, while slightly increasing the re-estimation error on the measured data, as natural in non-overfitted solutions. The superposition signal model can be used for designing adequate out-of-sample tuning of Tikhonov regularization techniques, and it can be taken into account when using other regularization techniques in current commercial systems and research toolboxes on ECGI.

Electrocardiogram Signal Classification in the Diagnosis of Heart Disease Based on RBF Neural Network

Heart disease is a common disease affecting human health. Electrocardiogram (ECG) classification is the most effective and direct method to detect heart disease, which is helpful to the diagnosis of most heart disease symptoms. At present, most ECG diagnosis depends on the personal judgment of medical staff, which leads to heavy burden and low efficiency of medical staff. Automatic ECG analysis technology will help the work of relevant medical staff. In this paper, we use the MIT-BIH ECG database to extract the QRS features of ECG signals by using the Pan-Tompkins algorithm. After extraction of the samples, $K$ -means clustering is used to screen the samples, and then, RBF neural network is used to analyze the ECG information. The classifier trains the electrical signal features, and the classification accuracy of the final classification model can reach 98.9%. Our experiments show that this method can effectively detect the abnormality of ECG signal and implement it for the diagnosis of heart disease.

The Impact of Torso Signal Processing on Noninvasive Electrocardiographic Imaging Reconstructions

Goal:

To evaluate state-of-the-art signal processing methods for epicardial potential-based noninvasive electrocardiographic imaging reconstructions of single-site pacing data.

Methods:

Experimental data were obtained from two torso-tank setups in which Langendorff-perfused hearts (n = 4) were suspended and potentials recorded simultaneously from torso and epicardial surfaces. 49 different signal processing methods were applied to torso potentials, grouped as i) high-frequency noise removal (HFR) methods ii) baseline drift removal (BDR) methods and iii) combined HFR+BDR. The inverse problem was solved and reconstructed electrograms and activation maps compared to those directly recorded.

Results:

HFR showed no difference compared to not filtering in terms of absolute differences in reconstructed electrogram amplitudes nor median correlation in QRS waveforms (p > 0.05). However, correlation and mean absolute error of activation times and pacing site localization were improved with all methods except a notch filter. HFR applied post-reconstruction produced no differences compared to pre-reconstruction. BDR and BDR+HFR significantly improved absolute and relative difference, and correlation in electrograms (p < 0.05). While BDR+HFR combined improved activation time and pacing site detection, BDR alone produced significantly lower correlation and higher localization errors (p < 0.05).

Conclusion:

BDR improves reconstructed electrogram morphologies and amplitudes due to a reduction in lambda value selected for the inverse problem. The simplest method (resetting the isoelectric point) is sufficient to see these improvements. HFR does not impact electrogram accuracy, but does impact post-processing to extract features such as activation times. Removal of line noise is insufficient to see these changes. HFR should be applied post-reconstruction to ensure over-filtering does not occur.

A Robust Algorithm for Selecting Optimal Regularization Parameter Based on Bilateral Accumulative Area

The choice of regularization parameters is very important for the reconstruction result in the inverse problem of electrocardiology. In this study, the bilateral accumulative area detector is introduced to estimate the optimal parameter points of the L-curve and Generalized Cross-Validation method to Tikhonov regularization and truncated singular value decomposition. The experimental results suggest that this method can achieve high validity and high robustness for the estimation of regularization parameters compared to conventional methods.

Advantages and pitfalls of noninvasive electrocardiographic imaging

BACKGROUND

With increasing clinical use of Electrocardiographic Imaging (ECGI), it is imperative to understand the limits of this technique. The objective of this study is to evaluate a potential-based ECGI approach for activation and repolarization mapping in sinus rhythm.

METHOD

Langendorff-perfused pig hearts were suspended in a human-shaped torso tank. Electrograms were recorded with a 108-electrode sock and ECGs with 256 electrodes embedded in the tank surface. Left bundle branch block (LBBB) was developed in 4 hearts through ablation, and repolarization abnormalities in another 4 hearts through regional perfusion of dofetilide and pinacidil. Electrograms were noninvasively reconstructed and reconstructed activation and repolarization features were compared to those recorded.

RESULTS

Visual consistency between ECGI and recorded activation and repolarization maps was high. While reconstructed repolarization times showed significantly more error than activation times quantitatively, patterns were reconstructed with a similar level of accuracy. The number of epicardial breakthrough sites was underestimated by ECGI and these were misplaced (>20 mm) in location. Likewise, ECGI reconstructed activation maps demonstrated artificial lines of block resulting from a W-shaped QRS waveform that were not present in recorded maps. Nevertheless, ECGI allowed identification of regions of abnormal repolarization reasonably accurately in terms of size, location and timing.

CONCLUSIONS

This study validates a potential-based ECGI approach to noninvasively image activation and recovery in sinus rhythm. Despite inaccuracies in epicardial breakthroughs and lines of conduction block, other important clinical features such as regions of abnormal repolarization can be accurately derived making ECGI a valuable clinical tool.

ECG Imaging to Detect the Site of Ventricular Ischemia Using Torso Electrodes: A Computational Study

Electrocardiography provides some information useful for ischemic diagnosis. However, more recently there has been substantial growth in the area of ECG imaging, which by solving the inverse problem of electrocardiography aims to produce high-resolution mapping of the electrical and magnetic dynamics of the heart. Most inverse studies use the full resolution of the body surface potential (BSP) to reconstruct the epicardial potentials, however using a limited number of torso electrodes to interpolate the BSP is more clinically relevant and has an important effect on the reconstruction which must be quantified. A circular ischemic lesion on the right ventricle lateral wall 27 mm in radius is reconstructed using three Tikhonov methods along with 6 different electrode configurations ranging from 32 leads to 1,024 leads. The 2nd order Tikhonov solution performed the most accurately (~80% lesion identified) followed by the 1st (~50% lesion identified) and then the 0 order Tikhonov solution performed the worst with a maximum of ~30% lesion identified regardless of how many leads were used. With an increasing number of leads the solution produces less error, and the error becomes more localised around the lesion for all three regularisation methods. In noisy conditions, the relative performance gap of the 1st and 2nd order Tikhonov solutions was reduced, and determining an accurate regularisation parameter became relatively more difficult. Lesions located on the left ventricle walls were also able to be identified but comparatively to the right ventricle lateral wall performed marginally worse with lesions located on the interventricular septum being able to be indicated by the reconstructions but not successfully identified against the error. The quality of reconstruction was found to decrease as the lesion radius decreased, with a lesion radius of <20 mm becoming difficult to correctly identify against the error even when using >512 torso electrodes.

Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data

The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.

Accuracy of electrocardiographic imaging using the method of fundamental solutions

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.

Study on Temperature and Synthetic Compensation of Piezo-Resistive Differential Pressure Sensors by Coupled Simulated Annealing and Simplex Optimized Kernel Extreme Learning Machine

As a high performance-cost ratio solution for differential pressure measurement, piezo-resistive differential pressure sensors are widely used in engineering processes. However, their performance is severely affected by the environmental temperature and the static pressure applied to them. In order to modify the non-linear measuring characteristics of the piezo-resistive differential pressure sensor, compensation actions should synthetically consider these two aspects. Advantages such as nonlinear approximation capability, highly desirable generalization ability and computational efficiency make the kernel extreme learning machine (KELM) a practical approach for this critical task. Since the KELM model is intrinsically sensitive to the regularization parameter and the kernel parameter, a searching scheme combining the coupled simulated annealing (CSA) algorithm and the Nelder-Mead simplex algorithm is adopted to find an optimal KLEM parameter set. A calibration experiment at different working pressure levels was conducted within the temperature range to assess the proposed method. In comparison with other compensation models such as the back-propagation neural network (BP), radius basis neural network (RBF), particle swarm optimization optimized support vector machine (PSO-SVM), particle swarm optimization optimized least squares support vector machine (PSO-LSSVM) and extreme learning machine (ELM), the compensation results show that the presented compensation algorithm exhibits a more satisfactory performance with respect to temperature compensation and synthetic compensation problems.