Abstract:

Approximating the fast dynamics of depolarization waves in the human heart described by the monodomain model is numerically challenging. Splitting methods for the PDE-ODE coupling enable the computation with very fine space and time discretizations. Here, we compare different splitting approaches regarding convergence, accuracy, and efficiency. Simulations were performed for a benchmark problem with the Beeler-Reuter cell model on a truncated ellipsoid approximating the left ventricle including a localized stimulation. For this configuration, we provide a reference solution for the transmembrane potential. We found a semi-implicit approach with state variable interpolation to be the most efficient scheme. The results are transferred to a more physiological setup using a bi-ventricular domain with a complex external stimulation pattern to evaluate the accuracy of the activation time for different resolutions in space and time.

Abstract:

Sinus node (SN) pacemaking is based on a coupling between surface membrane ion-channels and intracellular Ca2+-handling. The fundamental role of the inward Na+/Ca2+ exchanger (NCX) is firmly established. However, little is known about the reverse mode exchange. A simulation study attributed important role to reverse NCX activity, however experimental evidence is still missing. Whole-cell and perforated patch-clamp experiments were performed on rabbit SN cells supplemented with fluorescent Ca2+-tracking. We established 2 and 8 mM pipette NaCl groups to suppress and enable reverse NCX. NCX was assessed by specific block with 1 μM ORM-10962. Mechanistic simulations were performed by Maltsev–Lakatta minimal computational SN model. Active reverse NCX resulted in larger Ca2+-transient amplitude with larger SR Ca2+-content. Spontaneous action potential (AP) frequency increased with 8 mM NaCl. When reverse NCX was facilitated by 1 μM strophantin the Ca2+i and spontaneous rate increased. ORM-10962 applied prior to strophantin prevented Ca2+i and AP cycle change. Computational simulations indicated gradually increasing reverse NCX current, Ca2+i and heart rate with increasing Na+i. Our results provide further evidence for the role of reverse NCX in SN pacemaking. The reverse NCX activity may provide additional Ca2+-influx that could increase SR Ca2+-content, which consequently leads to enhanced pacemaking activity.

Abstract:

The sinoatrial node (SAN) is a complex structure that spontaneously depolarizes rhythmically ("pacing") and excites the surrounding non-automatic cardiac cells ("drive") to initiate each heart beat. However, the mechanisms by which the SAN cells can activate the large and hyperpolarized surrounding cardiac tissue are incompletely understood. Experimental studies demonstrated the presence of an insulating border that separates the SAN from the hyperpolarizing influence of the surrounding myocardium, except at a discrete number of sinoatrial exit pathways (SEPs). We propose a highly detailed 3D model of the human SAN, including 3D SEPs to study the requirements for successful electrical activation of the primary pacemaking structure of the human heart. A total of 788 simulations investigate the ability of the SAN to pace and drive with different heterogeneous characteristics of the nodal tissue (gradient and mosaic models) and myocyte orientation. A sigmoidal distribution of the tissue conductivity combined with a mosaic model of SAN and atrial cells in the SEP was able to drive the right atrium (RA) at varying rates induced by gradual If block. Additionally, we investigated the influence of the SEPs by varying their number, length, and width. SEPs created a transition zone of transmembrane voltage and ionic currents to enable successful pace and drive. Unsuccessful simulations showed a hyperpolarized transmembrane voltage (-66 mV), which blocked the L-type channels and attenuated the sodium-calcium exchanger. The fiber direction influenced the SEPs that preferentially activated the crista terminalis (CT). The location of the leading pacemaker site (LPS) shifted toward the SEP-free areas. LPSs were located closer to the SEP-free areas (3.46 ± 1.42 mm), where the hyperpolarizing influence of the CT was reduced, compared with a larger distance from the LPS to the areas where SEPs were located (7.17± 0.98 mm). This study identified the geometrical and electrophysiological aspects of the 3D SAN-SEP-CT structure required for successful pace and drive in silico.

Abstract:

Interatrial conduction block refers to a disturbance in the propagation of electrical impulses in the conduction pathways between the right and the left atrium. It is a risk factor for atrial fibrillation, stroke, and premature death. Clin- ical diagnostic criteria comprise an increased P wave dura- tion and biphasic P waves in lead II, III and aVF due to ret- rograde activation of the left atrium. Machine learning algo- rithms could improve the diagnosis but require a large-scale, well-controlled and balanced dataset. In silico electrocardio- gram (ECG) signals, optimally obtained from a statistical shape model to cover anatomical variability, carry the poten- tial to produce an extensive database meeting the requirements for successful machine learning application. We generated the first in silico dataset including interatrial conduction block of 9,800simulated ECG signals based on a bi-atrial statistical shape model. Automated feature analysis was performed to evaluate P wave morphology, duration and P wave terminal force in lead V1. Increased P wave duration and P wave ter- minal force in lead V1 were found for models with interatrial conduction block compared to healthy models. A wide vari- ability of P wave morphology was detected for models with in- teratrial conduction block. Contrary to previous assumptions, our results suggest that a biphasic P wave morphology seems to be neither necessary nor sufficient for the diagnosis of in- teratrial conduction block. The presented dataset is ready for a classification with machine learning algorithms and can be easily extended.

Abstract:

Atrial fibrillation is responsible for a significant and steadily rising burden. Simultaneously, the treatment options for atrial fibrillation are far from optimal. Personalized simulations of cardiac electrophysiology could assist clinicians in the risk stratification and therapy planning for atrial fibrillation. However, the use of personalized simulations in clinics is currently not possible due to either too high computational costs or non-sufficient accuracy. Eikonal simulations come with low computational costs but cannot replicate the influence of cardiac tissue geometry on the conduction velocity of the wave propagation. Consequently, they currently lack the required accuracy to be applied in clinics. Biophysically detailed simulations on the other hand are accurate but associated with too high computational costs. To tackle this issue, a regression model is created based on biophysically detailed bidomain simulation data. This regression formula calculates the conduction velocity dependent on the thickness and curvature of the heart wall. Afterwards the formula was implemented into the eikonal model with the goal to increase the accuracy of the eikonal model without losing its advantage of computational efficiency. The results of the modified eikonal simulations demonstrate that (i) the local activation times become significantly closer to those of the biophysically detailed bidomain simulations, (ii) the advantage of the eikonal model of a low sensitivity to the resolution of the mesh was reduced further, and (iii) the unrealistic occurrence of endo-epicardial dissociation in simulations was remedied. The results suggest that the accuracy of the eikonal model was significantly increased. At the same time, the additional computational costs caused by the implementation of the regression formula are neglectable. In conclusion, a successful step towards a more accurate and fast computational model of cardiac electrophysiology was achieved.

Abstract:

Aims Atrial flutter (AFlut) is a common re-entrant atrial tachycardia driven by self-sustainable mechanisms that cause excitations to propagate along pathways different from sinus rhythm. Intra-cardiac electrophysiological mapping and catheter ablation are often performed without detailed prior knowledge of the mechanism perpetuating AFlut, likely prolonging the procedure time of these invasive interventions. We sought to discriminate the AFlut location [cavotricuspid isthmus-dependent (CTI), peri-mitral, and other left atrium (LA) AFlut classes] with a machine learning-based algorithm using only the non-invasive signals from the 12-lead electrocardiogram (ECG). Methods and results Hybrid 12-lead ECG dataset of 1769 signals was used (1424 in silico ECGs, and 345 clinical ECGs from 115 patients—three different ECG segments over time were extracted from each patient corresponding to single AFlut cycles). Seventy-seven features were extracted. A decision tree classifier with a hold-out classification approach was trained, validated, and tested on the dataset randomly split after selecting the most informative features. The clinical test set comprised 38 patients (114 clinical ECGs). The classifier yielded 76.3% accuracy on the clinical test set with a sensitivity of 89.7%, 75.0%, and 64.1% and a positive predictive value of 71.4%, 75.0%, and 86.2% for CTI, peri-mitral, and other LA class, respectively. Considering majority vote of the three segments taken from each patient, the CTI class was correctly classified at 92%. Conclusion Our results show that a machine learning classifier relying only on non-invasive signals can potentially identify the location of AFlut mechanisms. This method could aid in planning and tailoring patient-specific AFlut treatments.

Abstract:

Objective: To investigate cardiac activation maps estimated using electrocardiographic imaging and to find methods reducing line-of-block (LoB) artifacts, while preserving real LoBs. Methods: Body surface potentials were computed for 137 simulated ventricular excitations. Subsequently, the inverse problem was solved to obtain extracellular potentials (EP) and transmembrane voltages (TMV). From these, activation times (AT) were estimated using four methods and compared to the ground truth. This process was evaluated with two cardiac mesh resolutions. Factors contributing to LoB artifacts were identified by analyzing the impact of spatial and temporal smoothing on the morphology of source signals. Results: AT estimation using a spatiotemporal derivative performed better than using a temporal derivative. Compared to deflection-based AT estimation, correlation-based methods were less prone to LoB artifacts but performed worse in identifying real LoBs. Temporal smoothing could eliminate artifacts for TMVs but not for EPs, which could be linked to their temporal morphology. TMVs led to more accurate ATs on the septum than EPs. Mesh resolution had a negligible effect on inverse reconstructions, but small distances were important for cross-correlation-based estimation of AT delays. Conclusion: LoB artifacts are mainly caused by the inherent spatial smoothing effect of the inverse reconstruction. Among the configurations evaluated, only deflection-based AT estimation in combination with TMVs and strong temporal smoothing can prevent LoB artifacts, while preserving real LoBs. Significance: Regions of slow conduction are of considerable clinical interest and LoB artifacts observed in non-invasive ATs can lead to misinterpretations. We addressed this problem by identifying factors causing such artifacts and methods to reduce them.

Abstract:

Computational simulations of cardiac electrophysiology provide detailed information on the depolarization phenomena at different spatial and temporal scales. With the development of new hardware and software, in silico experiments have gained more importance in cardiac electrophysiology research. For plane waves in healthy tissue, in vivo and in silico electrograms at the surface of the tissue demonstrate symmetric morphology and high peak-to-peak amplitude. Simulations provided insight into the factors that alter the morphology and amplitude of the electrograms. The situation is more complex in remodeled tissue with fibrotic infiltrations. Clinically, different changes including fractionation of the signal, extended duration and reduced amplitude have been described. In silico, numerous approaches have been proposed to represent the pathological changes on different spatial and functional scales. Different modeling approaches can reproduce distinct subsets of the clinically observed electrogram phenomena. This review provides an overview of how different modeling approaches to incorporate fibrotic and structural remodeling affect the electrogram and highlights open challenges to be addressed in future research.

Abstract:

Cardiac resynchronization therapy is a valuable tool to restore left ventricular function in patients experiencing dyssynchronous ventricular activation. However, the non-responder rate is still as high as 40%. Recent studies suggest that left ventricular torsion or specifically the lack thereof might be a good predictor for the response of cardiac resynchronization therapy. Since left ventricular torsion is governed by the muscle fiber orientation and the heterogeneous electromechanical activation of the myocardium, understanding the relation between these components and the ability to measure them is vital. To analyze if locally altered electromechanical activation in heart failure patients affects left ventricular torsion, we conducted a simulation study on 27 personalized left ventricular models. Electroanatomical maps and late gadolinium enhanced magnetic resonance imaging data informed our in-silico model cohort. The angle of rotation was evaluated in every material point of the model and averaged values were used to classify the rotation as clockwise or counterclockwise in each segment and sector of the left ventricle. 88% of the patient models (n = 24) were classified as a wringing rotation and 12% (n = 3) as a rigid-body-type rotation. Comparison to classification based on in vivo rotational NOGA XP maps showed no correlation. Thus, isolated changes of the electromechanical activation sequence in the left ventricle are not sufficient to reproduce the rotation pattern changes observed in vivo and suggest that further patho-mechanisms are involved.

Abstract:

Left atrial enlargement (LAE) is one of the risk factors for atrial fibrillation (AF). A non-invasive and automated detection of LAE with the 12-lead electrocardiogram (ECG) could therefore contribute to an improved AF risk stratification and an early detection of new-onset AF incidents. However, one major challenge when applying machine learning techniques to identify and classify cardiac diseases usually lies in the lack of large, reliably labeled and balanced clinical datasets. We therefore examined if the extension of clinical training data by simulated ECGs derived from a novel bi-atrial shape model could improve the automated detection of LAE based on P waves of the 12-lead ECG. We derived 95 volumetric geometries from the bi-atrial statistical shape model with continuously increasing left atrial volumes in the range of 30 ml to 65 ml. Electrophysiological simulations with 10 different conduction velocity settings and 2 different torso models were conducted. Extracting the P waves of the 12-lead ECG thus yielded a synthetic dataset of 1,900 signals. Besides the simulated data, 7,168 healthy and 309 LAE ECGs from a public clinical ECG database were available for training and testing of an LSTM network to identify LAE. The class imbalance of the training data could be reduced from 1:23 to 1:6 when adding simulated data to the training set. The accuracy evaluated on the test dataset comprising a subset of the clinical ECG recordings improved from 0.91 to 0.95 if simulated ECGs were included as an additional input for the training of the classifier. Our results suggest that using a bi-atrial statistical shape model as a basis for ECG simulations can help to overcome the drawbacks of clinical ECG recordings and can thus lead to an improved performance of machine learning classifiers to detect LAE based on the 12-lead ECG.

Abstract:

Computational models of the fluid dynamics in the human heart are a powerful tool to investigate disease mechanisms and their impact on the blood flow patterns. These models can for example be used to assess alterations occurring in hypertrophic cardiomyopathy, which is a genetic disease that increases the risk of sudden cardiac death. To overcome the challenges of a moving mesh approach, we modeled the movement of the endocardial surface based on an immersed boundary method. The verification on a simple moving 2D geometry proved plausible results. The application to the dis- eased, hypertrophic heart geometry confirmed that the computation of the mesh movement is made possible with this approach.