D. Potyagaylo, O. Dossel, and P. van Dam. Influence of Modeling Errors on the Initial Estimate for Nonlinear Myocardial Activation Times Imaging Calculated With Fastest Route Algorithm. In IEEE Transactions on Biomedical Engineering, vol. 63(12) , pp. 2576-2584, 2016
Noninvasive reconstruction of cardiac electrical activity has a great potential to support clinical decision making, planning and treatment. Recently, significant progress has been made in the estimation of the cardiac activation from body surface potential maps (BSPMs) using boundary element method (BEM) with the equivalent double layer (EDL) as source model. In this formulation, noninvasive assessment of activation times results in a nonlinear optimization problem with an initial estimate calculated with the fastest route algorithm (FRA). Each FRAsimulated activation sequence is converted into the ECG. The best initialization is determined by the sequence providing the highest correlation between predicted and measured potentials.We quantitatively assess the effects of the forward modeling errors on the FRA-based initialization. We present three simulation setups to investigate the effects of volume conductor model simplifications, neglecting the cardiac anisotropy and geometrical errors on the localization of ectopic beats starting on the ventricular surface. For the analysis, 12-lead ECG and 99 electrodes BSPM system were used. The areas in the heart exposing the largest localization errors were volume conductor model and electrode configuration specific with an average error <10 mm. The results show the robustness of the FRA-based initialization with respect to the considered modeling errors.
One promising application of electrocardiographic (ECG) imaging is noninvasive reconstruction of atrial activities. However, despite numerous clinical studies, which are mostly concerned with complex irregular excitation patterns, there are relatively few in silico investigations on the imaging of ectopic activation. In the present work, we explore the localization accuracy of ECG imaging regarding atrial focal sites. For the forward calculations, we used four realistic geometrical models with complex anatomical structure and a rule-based fiber orientation embedded into the atrial model. Excitation propagation was simulated with the monodomain model. For each geometrical model, 20 activation sequences originating from the posterior wall of the left atrium were simulated. Based on the bidomain theory, the body surface potential maps resulting from these focal events were computed. For the inverse reconstructions, we employed a full-search procedure based on the fastest route algorithm assuming uniform excitation propagation. Localization errors were revealed to be dependent on the model-specific atrial geometry. We also performed similarity analysis for the first halves of the P wave duration, which improved the results in three models.
Over the last decades, the information content derived from cardiac electric and magnetic field measurements has been debated. Our co-workers Wilhelms et al. inves- tigated electrically silent acute ischemia in human ven- tricles caused by occlusion of a coronary artery. In the present work, we extend the previous study by calculating associated magnetic fields produced by early stage acute ischemia with varying transmural extent. Multiscale com- putational simulations were performed for calculations of body surface potential maps (BSPM) and magnetocardio- grams (MCG) on a magnetometer sensor matrix situated above the anterior chest wall. Depending on the ischemia size, the ST-segments of the simulated electrocardiograms (ECG) experienced depression for subendocardial cases and elevation for transmural ischemia. One intermedi- ate extent resulted in a zero ST-segment which makes it diagnostically indistinguishable from the healthy case. Magnetic field calculations for this electrically silent is- chemia also revealed no difference compared to the control case. Otherwise, both ECG and MCG signals during ST- segments showed either depression or elevation from zero line. In this simulation study, MCG did not deliver addi- tional information to uncover electrically silent ischemia. For a general conclusion, further in-silico investigations with different ischemia shapes, sizes and positions should be performed and clinical studies with recordings of both ECG and MCG signals have to be conducted.
The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance.
Ventricular tachycardia (VT) can be one cause of sudden cardiac death affecting 4.25 million persons per year worldwide. A curative treatment is catheter ablation in order to inactivate the abnormally triggering regions. To facilitate and expedite the localization during the ablation procedure, we present two novel localization techniques based on convolutional neural networks (CNNs). In contrast to existing methods, e.g. using ECG imaging, our approaches were designed to be independent of the patient-specific geometries and directly applicable to surface ECG signals, while also delivering a binary transmural position. One method outputs ranked alternative solutions. Results can be visualized either on a generic or patient geometry. The CNNs were trained on a data set containing only simulated data and evaluated both on simulated and clinical test data. On simulated data, the median test error was below 3mm. The median localization error on the clinical data was as low as 32mm. The transmural position was correctly detected in up to 82% of all clinical cases. Using the ranked alternative solutions, the top-3 median error dropped to 20mm on clinical data. These results demonstrate a proof of principle to utilize CNNs to localize the activation source without the intrinsic need of patient-specific geometrical information. Furthermore, delivering multiple solutions can help the physician to find the real activation source amongst more than one possible locations. With further optimization, these methods have a high potential to speed up clinical interventions. Consequently they could decrease procedural risk and improve VT patients' outcomes.
S. Schuler, N. Pilia, D. Potyagaylo, and A. Loewe. Cobiveco: Consistent biventricular coordinates for precise and intuitive description of position in the heart – with MATLAB implementation. In Medical Image Analysis, vol. 74, pp. 102247, 2021
Ventricular coordinates are widely used as a versatile tool for various applications that benefit from a description of local position within the heart. However, the practical usefulness of ventricular coordinates is determined by their ability to meet application-specific requirements. For regression-based estimation of biventricular position, for example, a symmetric definition of coordinate directions in both ventricles is important. For the transfer of data between different hearts as another use case, the consistency of coordinate values across different geometries is particularly relevant. To meet these requirements, we compare different approaches to compute coordinates and present Cobiveco, a symmetric, consistent and intuitive biventricular coordinate system that builds upon existing coordinate systems, but overcomes some of their limitations. A novel one-way transfer error is introduced to assess the consistency of the coordinates. Normalized distances along bijective trajectories between two boundaries were found to be superior to solutions of Laplace’s equation for defining coordinate values, as they show better linearity in space. Evaluation of transfer and linearity errors on 36 patient geometries revealed a more than 4-fold improvement compared to a state-of-the-art method. Finally, we show two application examples underlining the relevance for cardiac data processing. Cobiveco MATLAB code is available under a permissive open-source license.
A. M. Janssen, D. Potyagaylo, O. Dössel, and T. F. Oostendorp. Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart.. In Medical & biological engineering & computing, vol. 56(6) , pp. 1013-1025, 2018
Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.
The Purkinje system is part of the fast-conducting ventricular excitation system. The anatomy of the Purkinje system varies from person to person and imposes a unique excitation pattern on the ventricular myocardium, which defines the morphology of the QRS complex of the ECG to a large degree. While it cannot be imaged in-vivo, it plays an important role for personalizing computer simulations of cardiac electrophysiology. Here, we present a new method to automatically model and customize the Purkinje system based on the measured electrocardiogram (ECG) of a patient. A graphbased algorithm was developed to generate Purkinje systems based on the parameters fibre density, minimal distance from the atrium, conduction velocity, and position and timing of excitation sources mimicking the bundle branches. Based on the resulting stimulation profile, the activation times of the ventricles were calculated using the fast marching approach. Predescribed action potentials and a finite element lead field matrix were employed to obtain surface ECG signals. The root mean square error (RMSE) between the simulated and measured QRS complexes of the ECGs was used as cost function to perform optimization of the Purkinje parameters. One complete evaluation from Purkinje tree generation to the simulated ECG could be computed in about 10 seconds on a standard desktop computer. The measured ECG of the patient used to build the anatomical model was matched via parallel simplex optimization with a remaining RMSE of 4.05 mV in about 16 hours. The approach presented here allows to tailor the structure of the Purkinje system through the measured ECG in a patient-specific way. The computationally efficient implementation facilitates global optimization.
Electrocardiographic imaging (ECGI) has recently gained attention as a viable diagnostic tool for reconstructing cardiac electrical activity in normal hearts as well as in cardiac arrhythmias. However, progress has been limited by the lack of both standards and unbiased comparisons of approaches and techniques across the community, as well as the consequent difficulty of effective collaboration across research groups.. To address these limitations, we created the Consortium for Electrocardiographic Imaging (CEI), with the objective of facilitating collaboration across the research community in ECGI and creating standards for comparisons and reproducibility. Here we introduce CEI and describe its two main efforts, the creation of EDGAR, a public data repository, and the organization of three collaborative workgroups that address key components and applications in ECGI. Both EDGAR and the workgroups will facilitate the sharing of ideas, data and methods across the ECGI community and thus address the current lack of reproducibility, broad collaboration, and unbiased comparisons.
ECG imaging is an emerging technology for the reconstruction of cardiac electric activity from non-invasively measured body surface potential maps. In this case report, we present the first evaluation of transmurally imaged activation times against endocardially reconstructed isochrones for a case of sustained monomorphic ventricular tachycardia (VT). Computer models of the thorax and whole heart were produced from MR images. A recently published approach was applied to facilitate electrode localization in the catheter laboratory, which allows for the acquisition of body surface potential maps while performing non-contact mapping for the reconstruction of local activation times. ECG imaging was then realized using Tikhonov regularization with spatio-temporal smoothing as proposed by Huiskamp and Greensite and further with the spline-based approach by Erem et al. Activation times were computed from transmurally reconstructed transmembrane voltages. The results showed good qualitative agreement between the non-invasively and invasively reconstructed activation times. Also, low amplitudes in the imaged transmembrane voltages were found to correlate with volumes of scar and grey zone in delayed gadolinium enhancement cardiac MR. The study underlines the ability of ECG imaging to produce activation times of ventricular electric activity-and to represent effects of scar tissue in the imaged transmembrane voltages.
INTRODUCTION: The "Experimental Data and Geometric Analysis Repository", or EDGAR is an Internet-based archive of curated data that are freely distributed to the international research community for the application and validation of electrocardiographic imaging (ECGI) techniques. The EDGAR project is a collaborative effort by the Consortium for ECG Imaging (CEI, ecg-imaging.org), and focused on two specific aims. One aim is to host an online repository that provides access to a wide spectrum of data, and the second aim is to provide a standard information format for the exchange of these diverse datasets. METHODS: The EDGAR system is composed of two interrelated components: 1) a metadata model, which includes a set of descriptive parameters and information, time signals from both the cardiac source and body-surface, and extensive geometric information, including images, geometric models, and measure locations used during the data acquisition/generation; and 2) a web interface. This web interface provides efficient, search, browsing, and retrieval of data from the repository. RESULTS: An aggregation of experimental, clinical and simulation data from various centers is being made available through the EDGAR project including experimental data from animal studies provided by the University of Utah (USA), clinical data from multiple human subjects provided by the Charles University Hospital (Czech Republic), and computer simulation data provided by the Karlsruhe Institute of Technology (Germany). CONCLUSIONS: It is our hope that EDGAR will serve as a communal forum for sharing and distribution of cardiac electrophysiology data and geometric models for use in ECGI research.
Electrocardiographic imaging (ECG imaging) is a method to depict electrophysiological processes in the heart. It is an emerging technology with the potential of making the therapy of cardiac arrhythmia less invasive, less expensive, and more precise. A major challenge for integrating the method into clinical workflow is the seamless and correct identification and localization of electrodes on the thorax and their assignment to recorded channels. This work proposes a camera-based system, which can localize all electrode positions at once and to an accuracy of approximately 1+/-1 mm. A system for automatic identification of individual electrodes is implemented that overcomes the need of manual annotation. For this purpose, a system of markers is suggested, which facilitates a precise localization to subpixel accuracy and robust identification using an error-correcting code. The accuracy of the presented system in identifying and localizing electrodes is validated in a phantom study. Its overall capability is demonstrated in a clinical scenario.
Electrocardiographic imaging (ECGI) is a non-invasive diagnostical tool solving the inverse problem of ECG, which means the reconstruction of electrical potentials in the heart from the ECG data. The ill-posednees of this problem makes necessary addition of a-priori information. A typical approach is the Tikhonov regularization looking for the best balance between minimizing the data misfit and the regularization term which characterizes desired properties of the solution. However, the quality of an obtained solution, and as a result its clinical relevance, could be significantly improved by application of methods for non-smooth regularization. In this work we introduced a possible dictionary definition for the electrical sources in the heart: we subdivided the heart into 100 pieces and considered them to constitute the columns of our dictionary. We also provided a short discussion on differences between synthesis and analysis models, tested the analysis algorithm with a penalty matrix which is not related to the defined dictionary (discrete gradient operator for all heart points) and compared the performance of these three algorithms for two simulated ventricular ectopic foci. The analysis method with the gradient operator showed a slightly superior performance although all methods correctly identified the regions of interest.
D. Potyagaylo, W. H. W. Schulze, and O. Dössel. Local regularization of endocardial and epicardial surfaces for better localization of ectopic beats in the inverse problem of ECG. In Computing in Cardiology Conference, vol. 41, pp. 837-840, 2014
The problem of non-invasively finding cardiac electri- cal sources from body surface potential maps (BSPM) is ill-posed. A standard Tikhonov regularization approach to the problem produces a solution biased toward the elec- trodes and thus to the left ventricular epicardium, which limits its potential to reconstruct endocardial sources. In this work we consider a transmembrane voltages based in- verse problem of ECG for the identification of extrasys- tole origins from simulated BSPM. With use of a pair of heart wall epicardial/endocardial extrasystoles and a pair of septal ectopic foci we demonstrate the performance of the inverse procedures while firstly solving the problem for all nodes, then for epicardium and endocardium sep- arately. Based on the observations and the logic behind the gradient of sources we define simple rules on how to classify an extrasystole under consideration according to these 3 reconstructions. Furthermore, when the amount of noise is known, we propose a new method with two regu- larization parameters which assign different weightings to endocardial and epicardial components of the solution.
The inverse problem of ECG is the task of cardiac source reconstruction from the measured body surface potential maps (BSPM). It is ill posed and therefore requires regularization, which is usually applied uniformly to the whole heart geometry. In order to improve the solution quality and localize potentials extrema we propose a local regularization method: the weighting is done iteratively according to the solution spatial content. The performed test showed the ability of the new method to overcome over smoothing and to better reconstruct strong solution gradients.
D. Potyagaylo, M. Segel, W. H. W. Schulze, and O. Dössel. Noninvasive Localization of Ectopic Foci: a New Optimization Approach for Simultaneous Reconstruction of Transmembrane Voltages and Epicardial Potentials. In FIMH, LNCS 7945, pp. 166-173, 2013
The goal of ECG imaging is the reconstruction of cardiac electrical activities from the potentials measured on the thorax sur- face. The tool can gain prominent clinical value for diagnosis and pre- interventional planning. The problem is however ill-posed, i.e. it is highly sensitive to modelling and measurement errors. In order to overcome this obstacle a regularization technique must be applied. In this paper we pro- pose a new optimization based method for simultaneous reconstruction of transmembrane voltages and epicardial potentials for localizing the origin of ventricular ectopic beats.Compared to second-order Tikhonov regularization, the new approach showed superior performance in marking activated regions and provided meaningful results where Tikhonov method failed.
D. Potyagaylo, W. H. W. Schulze, and O. Dössel. Solving the transmembrane potential based inverse problem of ECG under physiological constraints on the solution range. In Biomedizinische Technik / Biomedical Engineering, vol. 57(s1) , pp. 170, 2012
In this paper we propose an iteratively regularized Gauss-Newton method to solve the inverse ECG problem and efficiently choose the parameter of regularization. The classical stopping criterium for this regularization technique Morozov discrepancy principle, cannot be used in our application because the noise level estimate and problem model error are typically not available. We formulate the stopping rule based on the statistical formulation of the parameter and the physiological nature of the sought solution. With Laplace operator as a regularization matrix, the regularization parameter can be seen as an indirect measure of deviation in the solution: smaller parameters lead to a broader solution range. From our knowledge about electrophysiology of the heart we can assume values of −85 mV and +25 mV as a lower and an upper estimates for transmembrane potentials. Under this assumption we stop Gaus-Newton iteration as soon as the difference between solution smallest and largest values achieves 110 mV. Three simulation protocols confirm our ansatz: the proposed method was compared with the commonly used in the feld L-curve based Tikhonov method, showing superior performance during an initial phase of an ectopic heart activation sequence.
We suggest a new regularization method for reconstruction of cardiac transmembrane voltages (TMV) from body surface potentials that is based on imposing similarity between time-aligned TMVs. An iterative scheme is proposed to update the delays needed for time-alignment. Evaluation of the method using simulated ventricular pacings showed a clear improvement over second order Tikhonov.
S. Schuler, D. Potyagaylo, and O. Dössel. Using a Spatio-Temporal Basis for ECG Imaging of Ventricular Pacings: Insights From Simulations and First Application to Clinical Data. In 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 1559-1562, 2019
ECG imaging estimates the cardiac electrical activity from body surface potentials. As this involves solving a severly ill-posed problem, additional information is required to get a unique and stable solution. Recent progress is based on introducing more problem-specific information by exploiting the structure of cardiac excitation. However, added information must be either certain or general enough to not impair the solution. We have recently developed a method that uses a spatio-temporal basis to restrict the solution space. In the present work, we analyzed this method with respect to one of the most fundamental assumptions made during basis creation: cardiac (an)isotropy. We tested the reconstruction using simulations of ventricular pacings and then applied it to clinical data. In simulations, the overall median localization error was smallest with a basis including fiber orientation. For the clinical data, however, the overall error was smallest with an isotropic basis. This observation suggests that modeling priors should be introduced with care, whereby further work is needed.
A common treatment of focal ventricular tachycardia is the catheter ablation of triggering sites. They have to be found manually by the physician during an intervention in a catheter lab. Thus, a method for determining the position of the focus automatically is desired. The inverse problem of electrocardiography addresses this problem by reconstructing the source of the ectopic beats using the surface ECG. This problem is ill-posed and therefore needs specific methods for solving it. We propose a machine learning approach for localisation of the ectopic foci in the heart to assist cardiologists with their therapy planning.We simulated 600 120-lead ECGs with different known excitation origins in the heart using a cellular automaton followed by a forward calculation. Features from the ECGs were used as input for a support vector regression (SVR). We assumed a functional relation between features from the ECG and the excitation origin. To benchmark SVR, we also used the well-known Tikhonov 0th order regularisation to reconstruct the transmembrane potentials in the heart and detect the location of the ectopic foci. Parameters for SVR and regularisation were chosen using a grid search minimising the error between estimated and true excitation origin. Compared to the Tikhonov regularisation method, SVR achieved a smaller deviation between estimated and real excitation origin evaluated with 6-fold cross validation. Future work could investigate on the behaviour on data from simulations with other torso and electrophysiological models, the influence of other methods for feature extraction and finally the evaluation with clinical data.
S. Schuler, D. Potyagaylo, and O. Dössel. ECG Imaging of Simulated Atrial Fibrillation: Imposing Epi-Endocardial Similarity Facilitates the Reconstruction of Transmembrane Voltages. In Computing in Cardiology, vol. 44, 2017
Electrocardiographic imaging (ECGI) could help in diagnosis and treatment of atrial fibrillation (AF), the most common life-threatening arrhythmia. Based on a previous work by Figuera et al. on the reconstruction of epicardial potentials (EP) during AF, we explore the performance of a Tikhonov regularization with two spatial constraints for transmembrane voltage (TMV) based ECGI. We develop a new method to impose epi-endocardial similarity and show its benefit for ECGI of atrial activity. Apart from TMVs, local activation times and dominant frequency are evaluated as target parameters. In the AF models studied, joint reconstruction of epi- and endocardial TMVs showed performance comparable to the previously reported EPs imaging.
This work investigates the impact of time constant offset in the body surface potential map (BSPM) on the recon- struction quality in electrocardiographic imaging (ECGI). For this purpose, a study comparing four different approaches for the reconstruction of the transmembrane voltage distribution (TMV) was carried out. From this four methods two of them were newly designed to estimate and remove the offset from the BSPM. The first approach uses a new formulation of the Tikhonov-Greensite method as augmented regularization to estimate and remove the time constant offset during the reconstruction. The second algorithm is related to classical signal processing. It applies a mode filter to remove the time constant offset in the BSPM and afterwards reconstructs the ventricular ectopic beat (VEB) using the Tikhonov-Greensite regularization. It can be shown that the time constant offset has a significant influence on the reconstruction quality and should be removed. The preferred method to remove time constant offset is the mode filter.
ECG imaging as noninvasive method is aiming to reconstruct the distribution of the transmembrane voltage amplitudes (TMVs) from the body surface potential map (BSPM). Due to the ill-posedness, standard approaches like the Tikhonov regularization method cause blurring and artefacts in the solution. To suppress blurring and artefacts, this work investigated a model based approach, the unscented Kalman filter (UKF). The intention of this paper is to show the potential of an UKF approach by using an idealized parametrization.
This handout describes the simulation dataset KIT-20-PVC_Simulation-1906-10-30, which was contributed by the Karlsruhe Institute of Technology (KIT) to the Experimental Data and Geometric Analysis Repository (EDGAR) database.
Solving the inverse problem of electrocardiography could help to diagnose and to plan the treatment of heart diseases. The conductivity distribution within the body is important to solve the inverse problem. In this work the influence of neglecting an organ as an inhomogeneity on the forward and inverse problem was investigated. For different simplified body models optimal conductivities were determined by minimizing the error between the BSPMs produced by this model and reference BSPMs calculated with a complex model containing eight segmented organs. The BSPMs from simulated catheter stimulations were used for the optimization. With the obtained optimal conductivities lead-field matrices were calculated and compared to the lead-field matrix of the complex model. Besides the heart, the lungs and the intracardial blood, we found that the liver also plays an important role to describe the relationship between the activation in the heart and the body surface potential map correctly.
Electrocardiographic imaging (ECGI) facilitates the non-invasive reconstruction of electrical activity in the entire heart at once. ECGI requires both recordings of multi-channel ECG signals as well as an MRI-based model of the thorax. The model is used to solve the underlying Poissons problem, which relates the gradient of transmembrane voltages in the heart to the ECG and is a spatial differential equation. In ECGI, this relationship has to be established before starting inverse calculations, i.e. the forward problem has to be solved. It solution depends strongly on the spatial discretization of the model, as its resolution affects the representation of the source gradients. To study the convergence of resolution-related effects in the forward problem, we use a simplified thorax model which allows for very high resolutions. An ECG is produced for the excitation origin of a premature ventricular contraction in the apex. The study reveals that the greatest resolution-related effects vanish below a resolution of 5 mm of the cardiac tissue. At below 1 mm, resolution effects stabilize and only marginal effects from the spatial structure of the mesh persist down to a resolution of 0.25 mm.
A new method to predict changes in a lead-field matrix induced by conductivity variations of a single body tissue is proposed. The approach is based on the princi- ple component analysis (PCA) with three initial lead-field matrices transformed to vectors as input. For each tissue blood, lungs, muscles and fat a PCA was carried out. Further, for each tissue the default conductivity value and the conductivity varied by ±50 % were used to calculate the sample lead-field matrices. The results of the PCAs in- dicate that for every tissue the first principle component suffices to predict the conductivity-induced changes in the samples. With an interpolation of the scores we addition- ally show that the prediction is not bound to the sample ma- trices but moreover every matrix within each conductivity range is possibly estimated and conclusively predicted.
ECG imaging is a non-invasive technique of characterizing the electrical activity and the corresponding excitation conduction of the heart using body surface ECG. The method may provide great opportunities in the planning of cardiac interventions and in the diagnosis of cardiac diseases. This work introduces an algorithm for the imaging of transmembrane voltages that is based on a Kalman filter with an augmented measurement model. In the latter, a regularization term is integrated as additional measurement. The filter is trained using a-priori-knowledge from a simulation model. Two effects are investigated: the influence of the training data on the reconstruction quality and the representation of a-priori knowledge in the trained covariance matrices. The proposed algorithm shows a promising quality of reconstruction and may be used in the future to introduce generic physiological knowledge in solutions of cardiac source imaging.
With ECG imaging it is possible to reconstruct cardiac electrical activity noninvasively from measurements of the electrocardiogram (ECG). To facilitate the recon- struction, an MRI- or CT- based model of the body is re- quired, which is represented as a volume conductor. A mathematically ill-posed problem is solved to reconstruct the cardiac sources from potentials collected on the body surface. To obtain a body surface potential map (BSPM) electrodes are ideally placed allover the entire thorax. In practical applications, however, the number of electrodes is limited and the placing is subject to constraints. We in- vestigate the effect of different electrode setups on the ill- posedness of the inverse problem. In particular, electrode setups are chosen to comply with constraints for female pa- tients in the catheter lab.
W. H. W. Schulze, D. Potyagaylo, and O. Dössel. Activation time imaging in the presence of myocardial ischemia: Choice of initial estimates for iterative solvers. In Computing in Cardiology, 2011, vol. 39, pp. 961-964, 2012
In this work, a simulation study is performed that demonstrates how activation times of cardiac action potentials can be reconstructed from body surface potential maps (BSPMs). An extrasystole is simulated in the ventricles, which are affected by myocardial ischemia or necrosis, and the related BSPM is calculated. Initial estimates are required for iterative algorithms that solve the related non-linear reconstruction problem. As a good initial estimate is essential for a proper reconstruction, the robustness of two methods is tested against the influence of pathological conditions: the critical times method and a linear timeintegral based method. While the first method extrapolates activation times into inactive tissue in this study, the latter carves out ischemic or necrotic tissue as homogeneous regions. In an outlook, a concept for the combination of both methods is proposed.