S. Schuler, A. Wachter, and O. Dössel. Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials—Application to Atrial Ectopic Activity. In Frontiers in Physiology, vol. 9:1126, 2018
Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity.
Radiofrequency ablation (RFA) therapy is the gold standard in interventional treatment of many cardiac arrhythmias. A major obstacle are non transmural lesions, leading to recurrence of arrhythmias. Recent clinical studies have suggested intracardiac electrogram (EGM) criteria as a promising marker to evaluate lesion development. Seeking for a deeper understanding of underlying mechanisms, we established a simulation approach for acute RFA lesions. Ablation lesions were modeled by a passive necrotic core surrounded by a borderzone with properties of heated myocardium. Herein, conduction velocity and electrophysiological properties were altered. We simulated EGMs during RFA to study the relation between lesion formation and EGM changes using the bidomain model. Simulations were performed on a three dimensional setup including a geometrically detailed representation of the catheter with highly conductive electrodes. For validation, EGMs recorded during RFA procedures in five patients were analyzed and compared to simulation results. Clinical data showed major changes in the distal unipolar EGM. During RFA, the negative peak amplitude decreased up to 104% and maximum negative deflection was up to 88% smaller at the end of the ablation sequence. These changes mainly occurred in the first 10 s after ablation onset. Simulated unipolar EGM reproduced the clinical changes, reaching up to 83% negative peak amplitude reduction and 80% decrease in maximum negative deflection for transmural lesions. In future work, the established model may enable the development of further EGM criteria for transmural lesions even for complex geometries in order to support clinical therapy.
The boundary element method is widely used to solve the forward problem of electrocardiography, i.e. to calculate the body surface potentials (BSP) caused by the heart’s electrical activity. This requires discretization of boundary surfaces between compartments of a torso model. Often, the resolution of the surface bounding the heart is chosen above 1 mm, which can lead to spikes in resulting BSPs. We demonstrate that this artifact is caused by discontinuous propagation of the wavefront on coarse meshes and can be avoided by blurring cardiac sources before spatial downsampling. We evaluate different blurring methods and show that Laplacian blurring reduces the BSP error 5-fold for both transmembrane voltages and extracellular potentials downsampled to 3 different resolutions. We suggest a method to find the optimal blurring parameter without having to compute BSPs using a fine mesh.
S. Schuler, A. Loewe, and O. Dössel. Forcing Transmembrane Voltages to Decrease Slowly: A Temporal Regularization for ECG Imaging. In Computing in Cardiology, vol. 45, 2018
ECG imaging aims to reconstruct the cardiac electrical activity from non-invasive measurements of body surface potentials (BSP) by finding unique and physiologically meaningful solutions to the inverse problem of electrocardiography. This can be accomplished using regularization, which reduces the space of admissible solutions by demanding solution properties that are already known beforehand. Messnarz et. al. proposed a regularization scheme that requires transmembrane voltages (TMV) to not decrease over time. We suggest a generalization of this method that forces TMVs to decrease only slowly and as a result can also be applied to irregular cardiac activity. We first develop the method using a simplified spherical geometry and then show its benefit for imaging fibrillatory activity on a realistic geometry of the atria.
S. Schuler, L. Baron, A. Loewe, and O. Dössel. Developing and coupling a lumped element model of the closed loop human vascular system to a model of cardiac mechanics. In BMTMedPhys 2017, vol. 62(S1) , pp. S69, 2017
Modelling the interaction of the heart and the vascular system allows to study the pumping efficiency of the heart in a controlled environment under various cardiac and vascular conditions such as arrhythmias, dyssynchronies, regions of stiffened myocardium, valvular stenoses or decreased vascular compliances. To pose realistic hemodynamic boundary conditions to a four-chambered elastomechanical heart model, we developed a lumped element model of the closed loop human vascular system. Systemic and pulmonary circulations were each represented by a three-element Windkessel model emptying into a venous compliance. Both circulations were coupled by connecting the venous compliances to the corresponding atrium via venous resistances. Cardiac valves were represented by ideal diodes and resistances. Strong coupling between the heart and the vascular system model was accomplished by estimating the cardiac pressures that lead to continuous flows across the model interfaces. Active regulatory mechanisms were not considered. Pressures, flows and volumes throughout the circulatory system were simulated until a steady state was reached and the effects of model parameters on these hemodynamic parameters were evaluated in a sensitivity analysis. Increasing the systemic peripheral resistance by 50% caused an 8% decrease in stroke volume (SV) and a 33% increase in mean arterial pressure. Increased venous resistance descreased the E/A wave ratio of the atrioventricular flow and led to a reduced SV by impeding passive cardiac filling. Increasing the arterial compliance decreased mean cardiac pressures, while only slightly reducing the SV. Larger arterial resistances mainly caused higher peak systolic pressures. Furthermore, we show that embedding the heart model into surrounding elastic tissue by forcing permanent contact at the pericardial surface leads to more realistic time courses of atrial volumes and atrial pressure-volume curves composed of an A and a V loop as found in measurements. In conclusion, this work enables simulations of diseases that involve significant cardiovascular interaction.
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.
Intracardiac electrograms are essential for the diagnosis and treatment of various cardiac arrhythmias. To gain reliable information about structural alterations of underlying tissue, it is necessary to interpret these electrograms correctly. Therefore it has to be understood how other parameters influence the signal. Realistic 3D geometries were created and simulated using the bidomain model. Based on these simulations, the influences of catheter orientation, tissue thickness and conduction velocity on the amplitudes of intracardiac electrograms were evaluated.
Electrocardiographic Imaging (ECGI) requires robust ECG forward simulations to accurately calculate cardiac activity. However, many questions remain regarding ECG forward simulations, for instance: there are not common guidelines for the required cardiac source sampling. In this study we test equivalent double layer (EDL) forward simulations with differing cardiac source resolutions and different spatial interpolation techniques. The goal is to reduce error caused by undersampling of cardiac sources and provide guidelines to reduce said source undersampling in ECG forward simulations. Using a simulated dataset sampled at 5 spatial resolutions, we computed body surface potentials using an EDL forward simulation pipeline. We tested two spatial interpolation methods to reduce error due to undersampling triangle weighting and triangle splitting. This forward modeling pipeline showed high frequency artifacts in the predicted ECG time signals when the cardiac source resolution was too low. These low resolutions could also cause shifts in extrema location on the body surface maps. However, these errors in predicted potentials can be mitigated by using a spatial interpolation method. Using spatial interpolation can reduce the number of nodes required for accurate body surface potentials from 9,218 to 2,306. Spatial interpolation in this forward model could also help improve accuracy and reduce computational cost in subsequent ECGI applications.
The human heart is an organ of high complexity and hence, very challenging to simulate. To calculate the force developed by the human heart and therefore the tension of the muscle fibers, accurate models are necessary. The force generated by the cardiac muscle has physiologically imposed limits and depends on various characteristics such as the length, strain and the contraction velocity of the cardiomyocytes. Another characteristic is the activation time of each cardiomyocyte, which is a wave and not a static value for all cardiomyocytes. To simulate a physiologically correct excitation, the functionality of the cardiac simulation framework CardioMechanics was extended to incorporate inhomogeneous activation times. The functionality was then used to evaluate the effects of local activation times with two different tension models. The active stress generated by the cardiomyocytes was calculated by (i) an explicit function and (ii) an ode-based model. The results of the simulations showed that the maximum pressure in the left ventricle dropped by 2.3% for the DoubleHill model and by 5.3% for the Lumens model. In the right ventricle the simulations showed similar results. The maximum pressure in both the left and the right atrium increased using both models. Given that the simulation of the inhomogeneously activated cardiomyocytes increases the simulation time when used with the more precise Lumens model, the small drop in maximum pressure seems to be negligible in favor of a simpler simulation model.
Radiofrequency ablation (RFA) is a widely used clinical treatment for many types of cardiac arrhythmias. However, nontransmural lesions and gaps between linear lesions often lead to recurrence of the arrhythmia. Intrac- ardiac electrograms (IEGMs) provide real-time informa- tion regarding the state of the cardiac tissue surrounding the catheter tip. Nevertheless, the formation and inter- pretation of IEGMs during the RFA procedure is complex and yet not fully understood. In this in-silico study, we propose a computational model for acute ablation lesions. Our model consists of a necrotic scar core and a border zone, describing irreversible and reversible temperature induced electrophysiological phenomena. These phenom- ena are modeled by varying the intra- and extracellular conductivity of the tissue as well as a regulating zone factor. The computational model is evaluated regarding its feasibility and validity. Therefore, this model was com- pared to an existing one and to clinical measurements of ve patients undergoing RFA. The results show that the model can indeed be used to recreate IEGMs. We computed IEGMs arising from complex ablation scars, such as scars with gaps or two overlapping ellipsoid scars. For orthogo- nal catheter orientation, the presence of a second necrotic core in the near- eld of a punctiform acute ablation lesion had minor impact on the resulting signal morphology. The presented model can serve as a base for further research on the formation and interpretation of IEGMs.
Creating transmural ablation scars in a reliable way is a key issue in improvement of therapeutical pro- cedures for cardiac arrhythmias. About one third of the patients has to undergo several procedures till arrhythmic episodes are successfully treated. Morphological features of intracardiac electrograms might contribute to evaluate scar transmurality during the ablation procedure. We an- alyzed intracardiac signals before, during and after point- wise ablation in patients with atrial flutter. Unipolar elec- trograms of the distal electrode showed a relative decrease in amplitude of the second extremum of up to 99 % with a mean of 84±20.6 % after the endpoint of ablation.
Intracardiac electrograms are the key in under- standing, interpretation and treatment of cardiac arrhythmias. However, electrogram morphologies are strongly variable due to catheter position, orientation and contact. Simulations of intracardiac electrograms can improve comprehension and quantification of influencing parameters and therefore reduce misinterpretations. In this study simulated intracardiac electro- grams are analyzed regarding tilt angles of the catheter relative to the propagation direction, electrode tissue distances as well as clinical filter settings. Catheter signals are computed on a realistic 3D catheter geometry using bidomain simulations of cardiac electrophysiology. Thereby high conductivities of the catheter electrodes are taken into account. For validation, simulated electrograms are compared with in vivo electrograms recorded during an EP-study with direct annotation of catheter orientation and tissue contact. Good agreement was reached regarding timing and signal width of simulated and measured electrograms. Correlation was 0.92±0.07 for bipolar, 0.92±0.05 for unipolar distal and 0.80 ± 0.12 for unipolar proximal electrograms for different catheter orientations and locations.
Local activation time (LAT) maps help to understand the path of electrical excitation in cardiac arrhythmias. They can be generated automatically from intracardiac electrograms using various criteria provided by commercial electroanatomical mapping systems. This study compares existing criteria and a novel method based on the non-linear energy operator (NLEO) with respect to their precision and robustness.
S. Schuler. Developing and coupling a lumped parameter model of the closed loop human vascular system to a model of cardiac mechanics. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Masterarbeit. 2016
S. Schuler. Simulation von intrakardialen Elektrogrammen während der Katheterablation. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Bachelorarbeit. 2012