From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Studying the Influence of Finite Element Mesh Size on the Accuracy of Ventricular Tachycardia Simulation

Background

Ventricular tachycardia (VT) is a life-threatening heart condition commonly seen in patients with myocardial infarction (MI). Although personalized computational modeling has been used to understand VT and its treatment noninvasively, this approach can be computationally intensive and time consuming. Therefore, finding a balance between mesh size and computational efficiency is important. This study aimed to find an optimal mesh resolution that minimizes the need for computational resources while maintaining numerical accuracy and to investigate the effect of mesh resolution variation on the simulation results.

Methods

We constructed ventricular models from contrast-enhanced magnetic resonance imaging data from six patients with MI. We created seven different models for each patient, with average edge lengths ranging from 315 to 645 µm using commercial software, Mimics. Programmed electrical stimulation was used to assess VT inducibility from 19 sites in each heart model.

Results

The simulation results in the slab model with adaptive tetrahedral mesh (same as in the patient-specific model) showed that the absolute and relative differences in conduction velocity (CV) were 6.1 cm/s and 7.8% between average mesh sizes of 142 and 600 µm, respectively. However, the simulation results in the six patient-specific models showed that average mesh sizes with 350 µm yielded over 85% accuracy for clinically relevant VT. Although average mesh sizes of 417 and 478 µm could also achieve approximately 80% accuracy for clinically relevant VT, the percentage of incorrectly predicted VTs increases. When conductivity was modified to match the CV in the model with the finest mesh size, the overall ratio of positively predicted VT increased.

Conclusions

The proposed personalized heart model could achieve an optimal balance between simulation time and VT prediction accuracy when discretized with adaptive tetrahedral meshes with an average edge length about 350 µm.

Tipping the scales of understanding: An engineering approach to design and implement whole-body cardiac electrophysiology experimental models

The study of cardiac electrophysiology is built on experimental models that span all scales, from ion channels to whole-body preparations. Novel discoveries made at each scale have contributed to our fundamental understanding of human cardiac electrophysiology, which informs clinicians as they detect, diagnose, and treat complex cardiac pathologies. This expert review describes an engineering approach to developing experimental models that is applicable across scales. The review also outlines how we applied the approach to create a set of multiscale whole-body experimental models of cardiac electrophysiology, models that are driving new insights into the response of the myocardium to acute ischemia. Specifically, we propose that researchers must address three critical requirements to develop an effective experimental model: 1) how the experimental model replicates and maintains human physiological conditions, 2) how the interventions possible with the experimental model capture human pathophysiology, and 3) what signals need to be measured, at which levels of resolution and fidelity, and what are the resulting requirements of the measurement system and the access to the organs of interest. We will discuss these requirements in the context of two examples of whole-body experimental models, a closed chest in situ model of cardiac ischemia and an isolated-heart, torso-tank preparation, both of which we have developed over decades and used to gather valuable insights from hundreds of experiments.

Thermal ablation effects on rotors that characterize functional re-entry cardiac arrhythmia

Thermal ablation is a well-established successful treatment for cardiac arrhythmia, but it still presents limitations that require further studies and developments. In the rotor-driven functional re-entry arrhythmia, tissue heterogeneity results on the generation of spiral/scroll waves and wave break dynamics that may cause dangerous sustainable fibrillation. The selection of the target region to perform thermal ablation to mitigate this type of arrhythmia is challenging, since it considerably affects the local electrophysiology dynamics. This work deals with the numerical simulation of the thermal ablation of a cardiac muscle tissue and its effects on the dynamics of rotor-driven functional re-entry arrhythmia. A non-homogeneous two-dimensional rectangular region is used in the present numerical analysis, where radiofrequency ablation is performed. The electrophysiology problem for the propagation of the action potential in the cardiac tissue is simulated with the Fenton-Karma model. Thermal damage caused to the tissue by the radiofrequency heating is modeled by the Arrhenius equation. The effects of size and position of a heterogeneous region in the original muscle tissue were first analyzed, in order to verify the possible existence of the functional re-entry arrhythmia during the time period considered in the simulations. For each case that exhibited re-entry arrhythmia, six different ablation procedures were analyzed, depending on the position of the radiofrequency electrode and heating time. The obtained results revealed the effects of different model parameters on the existence and possible mitigation of the functional re-entry arrhythmia.

Personalized computational heart models with T1-mapped fibrotic remodeling predict sudden death risk in patients with hypertrophic cardiomyopathy

Hypertrophic cardiomyopathy (HCM) is associated with risk of sudden cardiac death (SCD) due to ventricular arrhythmias (VAs) arising from the proliferation of fibrosis in the heart. Current clinical risk stratification criteria inadequately identify at-risk patients in need of primary prevention of VA. Here, we use mechanistic computational modeling of the heart to analyze how HCM-specific remodeling promotes arrhythmogenesis and to develop a personalized strategy to forecast risk of VAs in these patients. We combine contrast-enhanced cardiac magnetic resonance imaging and T1 mapping data to construct digital replicas of HCM patient hearts that represent the patient-specific distribution of focal and diffuse fibrosis and evaluate the substrate propensity to VA. Our analysis indicates that the presence of diffuse fibrosis, which is rarely assessed in these patients, increases arrhythmogenic propensity. In forecasting future VA events in HCM patients, the imaging-based computational heart approach achieved 84.6%, 76.9%, and 80.1% sensitivity, specificity, and accuracy, respectively, and significantly outperformed current clinical risk predictors. This novel VA risk assessment may have the potential to prevent SCD and help deploy primary prevention appropriately in HCM patients.

Multiscale Modeling of the Mitochondrial Origin of Cardiac Reentrant and Fibrillatory Arrhythmias

While mitochondrial dysfunction has been implicated in the pathogenesis of cardiac arrhythmias, how the abnormality occurring at the organelle level escalates to influence the rhythm of the heart remains incompletely understood. This is due, in part, to the complexity of the interactions formed by cardiac electrical, mechanical, and metabolic subsystems at various spatiotemporal scales that is difficult to fully comprehend solely with experiments. Computational models have emerged as a powerful tool to explore complicated and highly dynamic biological systems such as the heart, alone or in combination with experimental measurements. Here, we describe a strategy of integrating computer simulations with optical mapping of cardiomyocyte monolayers to examine how regional mitochondrial dysfunction elicits abnormal electrical activity, such as rebound and spiral waves, leading to reentry and fibrillation in cardiac tissue. We anticipate that this advanced modeling technology will enable new insights into the mechanisms by which changes in subcellular organelles can impact organ function.

Preliminary Study: Learning the Impact of Simulation Time on Reentry Location and Morphology Induced by Personalized Cardiac Modeling

Personalized cardiac modeling is widely used for studying the mechanisms of cardiac arrythmias. Due to the high demanding of computational resource of modeling, the arrhythmias induced in the models are usually simulated for just a few seconds. In clinic, it is common that arrhythmias last for more than several minutes and the morphologies of reentries are not always stable, so it is not clear that whether the simulation of arrythmias for just a few seconds is long enough to match the arrhythmias detected in patients. This study aimed to observe how long simulation of the induced arrhythmias in the personalized cardiac models is sufficient to match the arrhythmias detected in patients. A total of 5 contrast enhanced MRI datasets of patient hearts with myocardial infarction were used in this study. Then, a classification method based on Gaussian mixture model was used to detect the infarct tissue. For each reentry, 3 s and 10 s were simulated. The characteristics of each reentry simulated for different duration were studied. Reentries were induced in all 5 ventricular models and sustained reentries were induced at 39 stimulation sites in the model. By analyzing the simulation results, we found that 41% of the sustained reentries in the 3 s simulation group terminated in the longer simulation groups (10 s). The second finding in our simulation was that only 23.1% of the sustained reentries in the 3 s simulation did not change location and morphology in the extended 10 s simulation. The third finding was that 35.9% reentries were stable in the 3 s simulation and should be extended for the simulation time. The fourth finding was that the simulation results in 10 s simulation matched better with the clinical measurements than the 3 s simulation. It was shown that 10 s simulation was sufficient to make simulation results stable. The findings of this study not only improve the simulation accuracy, but also reduce the unnecessary simulation time to achieve the optimal use of computer resources to improve the simulation efficiency and shorten the simulation time to meet the time node requirements of clinical operation on patients.

Optogenetic Stimulation Using Anion Channelrhodopsin (GtACR1) Facilitates Termination of Reentrant Arrhythmias With Low Light Energy Requirements: A Computational Study

Optogenetic defibrillation of hearts expressing light-sensitive cation channels (e.g., ChR2) has been proposed as an alternative to conventional electrotherapy. Past modeling work has shown that ChR2 stimulation can depolarize enough myocardium to interrupt arrhythmia, but its efficacy is limited by light attenuation and high energy needs. These shortcomings may be mitigated by using new optogenetic proteins like Guillardia theta Anion Channelrhodopsin (GtACR1), which produces a repolarizing outward current upon illumination. Accordingly, we designed a study to assess the feasibility of GtACR1-based optogenetic arrhythmia termination in human hearts. We conducted electrophysiological simulations in MRI-based atrial or ventricular models (n = 3 each), with pathological remodeling from atrial fibrillation or ischemic cardiomyopathy, respectively. We simulated light sensitization via viral gene delivery of three different opsins (ChR2, red-shifted ChR2, GtACR1) and uniform endocardial illumination at the appropriate wavelengths (blue, red, or green light, respectively). To analyze consistency of arrhythmia termination, we varied pulse timing (three evenly spaced intervals spanning the reentrant cycle) and intensity (atrial: 0.001–1 mW/mm²; ventricular: 0.001–10 mW/mm²). In atrial models, GtACR1 stimulation with 0.005 mW/mm² green light consistently terminated reentry; this was 10–100x weaker than the threshold levels for ChR2-mediated defibrillation. In ventricular models, defibrillation was observed in 2/3 models for GtACR1 stimulation at 0.005 mW/mm² (100–200x weaker than ChR2 cases). In the third ventricular model, defibrillation failed in nearly all cases, suggesting that attenuation issues and patient-specific organ/scar geometry may thwart termination in some cases. Across all models, the mechanism of GtACR1-mediated defibrillation was voltage forcing of illuminated tissue toward the modeled channel reversal potential of −40 mV, which made propagation through affected regions impossible. Thus, our findings suggest GtACR1-based optogenetic defibrillation of the human heart may be feasible with ≈2–3 orders of magnitude less energy than ChR2.

Sex Differences in Drug-Induced Arrhythmogenesis

The electrical activity in the heart varies significantly between men and women and results in a sex-specific response to drugs. Recent evidence suggests that women are more than twice as likely as men to develop drug-induced arrhythmia with potentially fatal consequences. Yet, the sex-specific differences in drug-induced arrhythmogenesis remain poorly understood. Here we integrate multiscale modeling and machine learning to gain mechanistic insight into the sex-specific origin of drug-induced cardiac arrhythmia at differing drug concentrations. To quantify critical drug concentrations in male and female hearts, we identify the most important ion channels that trigger male and female arrhythmogenesis, and create and train a sex-specific multi-fidelity arrhythmogenic risk classifier. Our study reveals that sex differences in ion channel activity, tissue conductivity, and heart dimensions trigger longer QT-intervals in women than in men. We quantify the critical drug concentration for dofetilide, a high risk drug, to be seven times lower for women than for men. Our results emphasize the importance of including sex as an independent biological variable in risk assessment during drug development. Acknowledging and understanding sex differences in drug safety evaluation is critical when developing novel therapeutic treatments on a personalized basis. The general trends of this study have significant implications on the development of safe and efficacious new drugs and the prescription of existing drugs in combination with other drugs.

Data integration for the numerical simulation of cardiac electrophysiology

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient-specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported.

An effective heterogeneous whole-heart mathematical model of cardiac induction system with heart rate variability

The main objective of this research work is to develop an effective mathematical model of cardiac conduction system using a heterogeneous whole-heart model. The model is in the form of a system of modified Van der Pol and FitzHugh-Nagumo differential equations capable of describing the heart dynamics. The proposed model extends the range of normal and pathological electrocardiogram (ECG) waveforms that can be generated by the model. The effects of the respiratory sinus arrhythmia (RSA) and the Mayer waves (MW) are both incorporated to modulate the intrinsic frequency of the main oscillator that represents the sinoatrial node. Also, three pathological conditions are incorporated into the model. The heart rate variability (HRV) phenomenon is incorporated into the synthetic ECGs produced which yields valuable information about the cardiovascular health and the performance of the autonomic nervous system. The spectral analysis of the generated RR tachogram delivers power spectrums that resemble those obtained from real recordings. Also, the proposed model generates synthetic ECGs that characteristic the three considered pathological conditions, namely, the tall T wave, the ECG with U wave, and the Wolff-Parkinson-White syndrome. In general, the significance of this research work is in developing a mathematical model that represents the interactions between different pacemakers and allows analysis of cardiac rhythms. To show the effectiveness and the accuracy of the presented model, the results are compared to published results. The proposed model can be a useful tool to study the influences of different physiological conditions on the profile of the ECG. The synthetic ECG signals produced can be used as signal sources for the assessment of diagnostic ECG signal processing devices.

Deep learning-based reduced order models in cardiac electrophysiology

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms—such as deep feedforward neural networks and convolutional autoencoders—to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.

Arrhythmogenic propensity of the fibrotic substrate after atrial fibrillation ablation: a longitudinal study using magnetic resonance imaging-based atrial models

AIMS

Inadequate modification of the atrial fibrotic substrate necessary to sustain re-entrant drivers (RDs) may explain atrial fibrillation (AF) recurrence following failed pulmonary vein isolation (PVI). Personalized computational models of the fibrotic atrial substrate derived from late gadolinium enhanced (LGE)-magnetic resonance imaging (MRI) can be used to non-invasively determine the presence of RDs. The objective of this study is to assess the changes of the arrhythmogenic propensity of the fibrotic substrate after PVI.

METHODS AND RESULTS

Pre- and post-ablation individualized left atrial models were constructed from 12 AF patients who underwent pre- and post-PVI LGE-MRI, in six of whom PVI failed. Pre-ablation AF sustained by RDs was induced in 10 models. RDs in the post-ablation models were classified as either preserved or emergent. Pre-ablation models derived from patients for whom the procedure failed exhibited a higher number of RDs and larger areas defined as promoting RD formation when compared with atrial models from patients who had successful ablation, 2.6 ± 0.9 vs. 1.8 ± 0.2 and 18.9 ± 1.6% vs. 13.8 ± 1.5%, respectively. In cases of successful ablation, PVI eliminated completely the RDs sustaining AF. Preserved RDs unaffected by ablation were documented only in post-ablation models of patients who experienced recurrent AF (2/5 models); all of these models had also one or more emergent RDs at locations distinct from those of pre-ablation RDs. Emergent RDs occurred in regions that had the same characteristics of the fibrosis spatial distribution (entropy and density) as regions that harboured RDs in pre-ablation models.

CONCLUSION

Recurrent AF after PVI in the fibrotic atria may be attributable to both preserved RDs that sustain AF pre- and post-ablation, and the emergence of new RDs following ablation. The same levels of fibrosis entropy and density underlie the pro-RD propensity in both pre- and post-ablation substrates.

Preprocedure Application of Machine Learning and Mechanistic Simulations Predicts Likelihood of Paroxysmal Atrial Fibrillation Recurrence Following Pulmonary Vein Isolation

BACKGROUND

Pulmonary vein isolation (PVI) is an effective treatment strategy for patients with atrial fibrillation (AF), but many experience AF recurrence and require repeat ablation procedures. The goal of this study was to develop and evaluate a methodology that combines machine learning (ML) and personalized computational modeling to predict, before PVI, which patients are most likely to experience AF recurrence after PVI.

METHODS

This single-center retrospective proof-of-concept study included 32 patients with documented paroxysmal AF who underwent PVI and had preprocedural late gadolinium enhanced magnetic resonance imaging. For each patient, a personalized computational model of the left atrium simulated AF induction via rapid pacing. Features were derived from pre-PVI late gadolinium enhanced magnetic resonance images and from results of simulations of AF induction. The most predictive features were used as input to a quadratic discriminant analysis ML classifier, which was trained, optimized, and evaluated with 10-fold nested cross-validation to predict the probability of AF recurrence post-PVI.

RESULTS

In our cohort, the ML classifier predicted probability of AF recurrence with an average validation sensitivity and specificity of 82% and 89%, respectively, and a validation area under the curve of 0.82. Dissecting the relative contributions of simulations of AF induction and raw images to the predictive capability of the ML classifier, we found that when only features from simulations of AF induction were used to train the ML classifier, its performance remained similar (validation area under the curve, 0.81). However, when only features extracted from raw images were used for training, the validation area under the curve significantly decreased (0.47).

CONCLUSIONS

ML and personalized computational modeling can be used together to accurately predict, using only pre-PVI late gadolinium enhanced magnetic resonance imaging scans as input, whether a patient is likely to experience AF recurrence following PVI, even when the patient cohort is small.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

Computationally guided personalized targeted ablation of persistent atrial fibrillation

Atrial fibrillation (AF) — the most common arrhythmia — significantly increases the risk of stroke and heart failure. Although catheter ablation can restore normal heart rhythms, patients with persistent AF who develop atrial fibrosis often undergo multiple failed ablations and thus increased procedural risks. Here, we present personalized computational modelling for the reliable predetermination of ablation targets, which are then used to guide the ablation procedure in patients with persistent AF and atrial fibrosis. We first show that a computational model of the atria of patients identifies fibrotic tissue that if ablated will not sustain AF. We then integrated the target-ablation sites in a clinical-mapping system, and tested its feasibility in 10 patients with persistent AF. The computational prediction of ablation targets avoids lengthy electrical mapping and could improve the accuracy and efficacy of targeted AF ablation in patients whilst eliminating the need for repeat procedures.

Role of 3-Dimensional Architecture of Scar and Surviving Tissue in Ventricular Tachycardia: Insights From High-Resolution Ex Vivo Porcine Models

BACKGROUND

An improved knowledge of the spatial organization of infarct structure and its contribution to ventricular tachycardia (VT) is important for designing optimal treatments. This study explores the relationship between the 3-dimensional structure of the healed infarct and the VT reentrant pathways in high-resolution models of infarcted porcine hearts.

METHODS

Structurally detailed models of infarcted ventricles were reconstructed from ex vivo late gadolinium enhancement and diffusion tensor magnetic resonance imaging data of 8 chronically infarcted porcine hearts at submillimeter resolution (0.25×0.25×0.5 mm³). To characterize the 3-dimensional structure of surviving tissue in the zone of infarct, a novel scar-mapped thickness metric was introduced. Further, using the ventricular models, electrophysiological simulations were conducted to determine and analyze the 3-dimensional VT pathways that were established in each of the complex infarct morphologies.

RESULTS

The scar-mapped thickness metric revealed the heterogeneous organization of infarct and enabled us to systematically characterize the distribution of surviving tissue thickness in 8 hearts. Simulation results demonstrated the involvement of a subendocardial tissue layer of varying thickness in the majority of VT pathways. Importantly, they revealed that VT pathways are most frequently established within thin surviving tissue structures of thickness ≤2.2 mm (90th percentile) surrounding the scar.

CONCLUSIONS

The combination of high-resolution imaging data and ventricular simulations revealed the 3-dimensional distribution of surviving tissue surrounding the scar and demonstrated its involvement in VT pathways. The new knowledge obtained in this study contributes toward a better understanding of infarct-related VT.

Sensitivity of Ablation Targets Prediction to Electrophysiological Parameter Variability in Image-Based Computational Models of Ventricular Tachycardia in Post-infarction Patients

Ventricular tachycardia (VT), which could lead to sudden cardiac death, occurs frequently in patients with myocardial infarction. Computational modeling has emerged as a powerful platform for the non-invasive investigation of lethal heart rhythm disorders in post-infarction patients and for guiding patient VT ablation. However, it remains unclear how VT dynamics and predicted ablation targets are influenced by inter-patient variability in action potential duration (APD) and conduction velocity (CV). The goal of this study was to systematically assess the effect of changes in the electrophysiological parameters on the induced VTs and predicted ablation targets in personalized models of post-infarction hearts. Simulations were conducted in 5 patient-specific left ventricular models reconstructed from late gadolinium-enhanced magnetic resonance imaging scans. We comprehensively characterized all possible pre-ablation and post-ablation VTs in simulations conducted with either an “average human VT”-based electrophysiological representation (i.e., EP_avg) or with ±10% APD or CV (i.e., EP_var); additional simulations were also executed in some models for an extended range of these parameters. The results showed that: (1) a subset of reentries (76.2–100%, depending on EP parameter set) conducted with ±10% APD/CV was observed in approximately the same locations as reentries observed in EP_avg cases; (2) emergent VTs could be induced sometimes after ablation in EP_avg models, and these emergent VTs often corresponded to the pre-ablation reentries in simulations with EP_var parameter sets. These findings demonstrate that the VT ablation target uncertainty in patient-specific ventricular models with an average representation of VT-remodeled electrophysiology is relatively low and the ablation targets stable, as the localization of the induced VTs was primarily driven by the remodeled structural substrate. Thus, personalized ventricular modeling with an average representation of infarct-remodeled electrophysiology may uncover most targets for VT ablation.

Convolutional neural network-based approach for segmentation of left ventricle myocardial scar from 3D late gadolinium enhancement MR images

PURPOSE

Accurate three-dimensional (3D) segmentation of myocardial replacement fibrosis (i.e., scar) is emerging as a potentially valuable tool for risk stratification and procedural planning in patients with ischemic cardiomyopathy. The main purpose of this study was to develop a semiautomated method using a 3D convolutional neural network (CNN)-based for the segmentation of left ventricle (LV) myocardial scar from 3D late gadolinium enhancement magnetic resonance (LGE-MR) images.

METHODS

Our proposed CNN is built upon several convolutional and pooling layers aimed at choosing appropriate features from LGE-MR images to distinguish between myocardial scar and healthy tissues of the left ventricle. In contrast to previous methods that consider image intensity as the sole feature, CNN-based algorithms have the potential to improve the accuracy of scar segmentation through the creation of unconventional features that separate scar from normal myocardium in the feature space. The first step of our pipeline was to manually delineate the left ventricular myocardium, which was used as the region of interest for scar segmentation. Our developed algorithm was trained using 265,220 volume patches extracted from ten 3D LGE-MR images, then was validated on 450,454 patches from a testing dataset of 24 3D LGE-MR images, all obtained from patients with chronic myocardial infarction. We evaluated our method in the context of several alternative methods by comparing algorithm-generated segmentations to manual delineations performed by experts.

RESULTS

Our CNN-based method reported an average Dice similarity coefficient (DSC) and Jaccard Index (JI) of 93.63% ± 2.6% and 88.13% ± 4.70%. In comparison to several previous methods, including K-nearest neighbor (KNN), hierarchical max flow (HMF), full width at half maximum (FWHM), and signal threshold to reference mean (STRM), the developed algorithm reported significantly higher accuracy for DSC with a P-value less than 0.0001.

CONCLUSIONS

Our experimental results demonstrated that our CNN-based proposed method yielded the highest accuracy of all contemporary LV myocardial scar segmentation methodologies, inclusive of the most widely used signal intensity-based methods, such as FWHM and STRM. To our knowledge, this is the first description of LV myocardial scar tissue segmentation from 3D LGE-MR images using a CNN-based method.

Virtual electrophysiological study as a tool for evaluating efficacy of MRI techniques in predicting adverse arrhythmic events in ischemic patients

Myocardial infarct (MI) related indices determined by late gadolinium enhancement (LGE) MRI have been widely investigated in determining patients suitable for implantable cardiovascular-defibrillator (ICD) therapy to complement left ventricular ejection fraction (LV EF). In comparison to LGE-MRI using inversion-recovery fast-gradient-echo (IR-FGRE), T1 mapping techniques, such as multi contrast late enhancement (MCLE), have been shown to provide more quantitative and reproducible estimates of infarct regions. The objective of this study is to use individualized heart computer models in determining the efficacy of IR-FGRE and MCLE techniques in predicting the occurrence of post-MI ventricular tachycardia (VT). Twenty-seven patients with MI underwent LGE-MRI using IR-FGRE and MCLE prior to ICD implantation and were followed up for 6-46 months. Individualized image-based computational models were built separately for each imaging technique; simulations of propensity to VT were conducted with each model. The imaging methods were evaluated by comparing simulated inducibility of VT to clinical outcome (appropriate ICD therapy) in patients. Twelve patients had at least one appropriate ICD therapy for VT at follow-up. For both MCLE and IR-FGRE, the outcomes of the simulations of VT were significantly associated with the events of appropriate ICD therapy. This indicates that, as compared to conventional measurements such as LV EF, the simulations of VT corresponding to both MCLE and IR-FGRE were more sensitive in predicting appropriate ICD therapy in post-MI patients.

GEMS: A Fully Integrated PETSc-Based Solver for Coupled Cardiac Electromechanics and Bidomain Simulations

Cardiac contraction is coordinated by a wave of electrical excitation which propagates through the heart. Combined modeling of electrical and mechanical function of the heart provides the most comprehensive description of cardiac function and is one of the latest trends in cardiac research. The effective numerical modeling of cardiac electromechanics remains a challenge, due to the stiffness of the electrical equations and the global coupling in the mechanical problem. Here we present a short review of the inherent assumptions made when deriving the electromechanical equations, including a general representation for deformation-dependent conduction tensors obeying orthotropic symmetry, and then present an implicit-explicit time-stepping approach that is tailored to solving the cardiac mono- or bidomain equations coupled to electromechanics of the cardiac wall. Our approach allows to find numerical solutions of the electromechanics equations using stable and higher order time integration. Our methods are implemented in a monolithic finite element code GEMS (Ghent Electromechanics Solver) using the PETSc library that is inherently parallelized for use on high-performance computing infrastructure. We tested GEMS on standard benchmark computations and discuss further development of our software.

Personalized virtual-heart technology for guiding the ablation of infarct-related ventricular tachycardia

Ventricular tachycardia (VT), which can lead to sudden cardiac death, occurs frequently in patients with myocardial infarction. Catheter-based radiofrequency ablation of cardiac tissue has achieved only modest efficacy, owing to the inaccurate identification of ablation targets by current electrical mapping techniques, which can lead to extensive lesions and to a prolonged, poorly tolerated procedure. Here we show that personalized virtual-heart technology based on cardiac imaging and computational modelling can identify optimal infarct-related VT ablation targets in retrospective animal (5 swine) and human studies (21 patients) and in a prospective feasibility study (5 patients). We first assessed in retrospective studies (one of which included a proportion of clinical images with artifacts) the capability of the technology to determine the minimum-size ablation targets for eradicating all VTs. In the prospective study, VT sites predicted by the technology were targeted directly, without relying on prior electrical mapping. The approach could improve infarct-related VT ablation guidance, where accurate identification of patient-specific optimal targets could be achieved on a personalized virtual heart prior to the clinical procedure.

Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model

Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

Fast-slow asymptotics for a Markov chain model of fast sodium current

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

A feasibility study of arrhythmia risk prediction in patients with myocardial infarction and preserved ejection fraction

AIM

To predict arrhythmia susceptibility in myocardial infarction (MI) patients with left ventricular ejection fraction (LVEF)  >35% using a personalized virtual heart simulation approach.

METHODS AND RESULTS

A total of four contrast enhanced magnetic resonance imaging (MRI) datasets of patient hearts with MI and average LVEF of 44.0 ± 2.6% were used in this study. Because of the preserved LVEF, the patients were not indicated for implantable cardioverter defibrillator (ICD) insertion. One patient had spontaneous ventricular tachycardia (VT) prior to the MRI scan; the others had no arrhythmic events. Simulations of arrhythmia susceptibility were blind to clinical outcome. Models were constructed from patient MRI images segmented to identify myocardium, grey zone, and scar based on pixel intensity. Grey zone was modelled as having altered electrophysiology. Programmed electrical stimulation (PES) was performed to assess VT inducibility from 19 bi-ventricular sites in each heart model. Simulations successfully predicted arrhythmia risk in all four patients. For the patient with arrhythmic event, in-silico PES resulted in VT induction. Simulations correctly predicted that VT was non-inducible for the three patients with no recorded VT events.

CONCLUSIONS

Results demonstrate that the personalized virtual heart simulation approach may provide a novel risk stratification modality to non-invasively and effectively identify patients with LVEF  >35% who could benefit from ICD implantation.

Decomposition of fractionated local electrograms using an analytic signal model based on sigmoid functions

Microstructural heterogeneities in cardiac tissue, such as embedded connective tissue secondary to fibrosis, may lead to complex patterns of electrical activation that are reflected in the fractionation of extracellularly recorded electrograms. The decomposition of such electrograms into non-fractionated components is expected to provide additional information to allow a more precise classification of the microstructural properties adjacent to a given recording site. For the sake of this, an analytic signal model is introduced in this study that is capable of reliably identifying extracellular waveforms associated with sites of initiating, free-running, and terminating or colliding activation wavefronts. Using this signal model as a template, a procedure is developed for the automatic decomposition of complex fractionated electrograms into non-fractionated components. The decomposition method has been validated using electrograms obtained from one- and two-dimensional computer simulations in which all relevant intracellular and extracellular quantities are accessible at a very high spatiotemporal resolution and can be manipulated in a controlled manner. Fractionated electrograms were generated in these models by incorporating microstructural obstacles that mimicked inlays of connective tissue. Using this signal model, fractionated electrograms emerging from microstructural heterogeneities in the submillimeter range with latencies between components down to 0.6 ms can be decomposed.

Coupling calcium dynamics and mitochondrial bioenergetic: an in silico study to simulate cardiomyocyte dysfunction

The coupling of intracellular Ca(2+) dynamics with mitochondrial bioenergetic is crucial for the functioning of cardiomyocytes both in healthy and disease conditions. The pathophysiological signature of the Cardiomyocyte Dysfunction (CD) is commonly related to decreased ATP production due to mitochondrial functional impairment and to an increased mitochondrial calcium content ([Ca(2+)]m). These features advanced the therapeutic approaches which aim to reduce [Ca(2+)]m. But whether [Ca(2+)]m overload is the pathological trigger for CD or a physiological consequence, remained controversial. We addressed this issue in silico and showed that [Ca(2+)]m might not directly cause CD. Through model parameter recalibration, we demonstrated how mitochondria cope up with functionally impaired processes and consequently accumulate calcium. A strong coupling of the [Ca(2+)]m oscillations with the ATP synthesis rate ensures robust calcium cycling and avoids CD. We suggested a cardioprotective role of the mitochondrial calcium uniporter and predicted that a mitochondrial sodium calcium exchanger could be a potential therapeutic target to restore the normal functioning of the cardiomyocyte.

Opsin spectral sensitivity determines the effectiveness of optogenetic termination of ventricular fibrillation in the human heart: a simulation study

KEY POINTS

Optogenetics-based defibrillation, a theoretical alternative to electrotherapy, involves expression of light-sensitive ion channels in the heart (via gene or cell therapy) and illumination of the cardiac surfaces (via implanted LED arrays) to elicit light-induced activations. We used a biophysically detailed human ventricular model to determine whether such a therapy could terminate fibrillation (VF) and identify which combinations of light-sensitive ion channel properties and illumination configurations would be effective. Defibrillation was successful when a large proportion (> 16.6%) of ventricular tissue was directly stimulated by light that was bright enough to induce an action potential in an uncoupled cell. While illumination with blue light never successfully terminated VF, illumination of red light-sensitive ion channels with dense arrays of implanted red light sources resulted in successful defibrillation. Our results suggest that cardiac expression of red light-sensitive ion channels is necessary for the development of effective optogenetics-based defibrillation therapy using LED arrays.

ABSTRACT

Optogenetics-based defibrillation has been proposed as a novel and potentially pain-free approach to enable cardiomyocyte-selective defibrillation in humans, but the feasibility of such a therapy remains unknown. This study aimed to (1) assess the feasibility of terminating sustained ventricular fibrillation (VF) via light-induced excitation of opsins expressed throughout the myocardium and (2) identify the ideal (theoretically possible) opsin properties and light source configurations that would maximise therapeutic efficacy. We conducted electrophysiological simulations in an MRI-based human ventricular model with VF induced by rapid pacing; light sensitisation via systemic, cardiac-specific gene transfer of channelrhodopsin-2 (ChR2) was simulated. In addition to the widely used blue light-sensitive ChR2-H134R, we also modelled theoretical ChR2 variants with augmented light sensitivity (ChR2+), red-shifted spectral sensitivity (ChR2-RED) or both (ChR2-RED+). Light sources were modelled as synchronously activating LED arrays (LED radius: 1 mm; optical power: 10 mW mm-2 ; array density: 1.15-4.61 cm-2 ). For each unique optogenetic configuration, defibrillation was attempted with two different optical pulse durations (25 and 500 ms). VF termination was only successful for configurations involving ChR2-RED and ChR2-RED+ (for LED arrays with density ≥ 2.30 cm-2 ), suggesting that opsin spectral sensitivity was the most important determinant of optogenetic defibrillation efficacy. This was due to the deeper penetration of red light in cardiac tissue compared with blue light, which resulted in more widespread light-induced propagating wavefronts. Longer pulse duration and higher LED array density were associated with increased optogenetic defibrillation efficacy. In all cases observed, the defibrillation mechanism was light-induced depolarisation of the excitable gap, which led to block of reentrant wavefronts.

Mechanisms of arrhythmogenesis related to calcium-driven alternans in a model of human atrial fibrillation

The occurrence of atrial fibrillation (AF) is associated with progressive changes in the calcium handling system of atrial myocytes. Calcium cycling instability has been implicated as an underlying mechanism of electrical alternans observed in patients who experience AF. However, the extent to which calcium-induced alternation of electrical activity in the atria contributes to arrhythmogenesis is unknown. In this study, we investigated the effects of calcium-driven alternans (CDA) on arrhythmia susceptibility in a biophysically detailed, 3D computer model of the human atria representing electrical and structural remodeling secondary to chronic AF. We found that elevated propensity to CDA rendered the atria vulnerable to ectopy-induced arrhythmia. It also increased the complexity and persistence of arrhythmias induced by fast pacing, with unstable scroll waves meandering and frequently breaking up to produce multiple wavelets. Our results suggest that calcium-induced electrical instability may increase arrhythmia vulnerability and promote increasing disorganization of arrhythmias in the chronic AF-remodeled atria, thus playing an important role in the progression of the disease.

Early somatic mosaicism is a rare cause of long-QT syndrome

Somatic mosaicism, the occurrence and propagation of genetic variation in cell lineages after fertilization, is increasingly recognized to play a causal role in a variety of human diseases. We investigated the case of life-threatening arrhythmia in a 10-day-old infant with long QT syndrome (LQTS). Rapid genome sequencing suggested a variant in the sodium channel Na_V1.5 encoded by SCN5A, NM_000335:c.5284G > T predicting p.(V1762L), but read depth was insufficient to be diagnostic. Exome sequencing of the trio confirmed read ratios inconsistent with Mendelian inheritance only in the proband. Genotyping of single circulating leukocytes demonstrated the mutation in the genomes of 8% of patient cells, and RNA sequencing of cardiac tissue from the infant confirmed the expression of the mutant allele at mosaic ratios. Heterologous expression of the mutant channel revealed significantly delayed sodium current with a dominant negative effect. To investigate the mechanism by which mosaicism might cause arrhythmia, we built a finite element simulation model incorporating Purkinje fiber activation. This model confirmed the pathogenic consequences of cardiac cellular mosaicism and, under the presenting conditions of this case, recapitulated 2:1 AV block and arrhythmia. To investigate the extent to which mosaicism might explain undiagnosed arrhythmia, we studied 7,500 affected probands undergoing commercial gene-panel testing. Four individuals with pathogenic variants arising from early somatic mutation events were found. Here we establish cardiac mosaicism as a causal mechanism for LQTS and present methods by which the general phenomenon, likely to be relevant for all genetic diseases, can be detected through single-cell analysis and next-generation sequencing.

Myocardial Infarct Segmentation From Magnetic Resonance Images for Personalized Modeling of Cardiac Electrophysiology

Accurate representation of myocardial infarct geometry is crucial to patient-specific computational modeling of the heart in ischemic cardiomyopathy. We have developed a methodology for segmentation of left ventricular (LV) infarct from clinically acquired, two-dimensional (2D), late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) images, for personalized modeling of ventricular electrophysiology. The infarct segmentation was expressed as a continuous min-cut optimization problem, which was solved using its dual formulation, the continuous max-flow (CMF). The optimization objective comprised of a smoothness term, and a data term that quantified the similarity between image intensity histograms of segmented regions and those of a set of training images. A manual segmentation of the LV myocardium was used to initialize and constrain the developed method. The three-dimensional geometry of infarct was reconstructed from its segmentation using an implicit, shape-based interpolation method. The proposed methodology was extensively evaluated using metrics based on geometry, and outcomes of individualized electrophysiological simulations of cardiac dys(function). Several existing LV infarct segmentation approaches were implemented, and compared with the proposed method. Our results demonstrated that the CMF method was more accurate than the existing approaches in reproducing expert manual LV infarct segmentations, and in electrophysiological simulations. The infarct segmentation method we have developed and comprehensively evaluated in this study constitutes an important step in advancing clinical applications of personalized simulations of cardiac electrophysiology.

Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models

Sudden cardiac death (SCD) from arrhythmias is a leading cause of mortality. For patients at high SCD risk, prophylactic insertion of implantable cardioverter defibrillators (ICDs) reduces mortality. Current approaches to identify patients at risk for arrhythmia are, however, of low sensitivity and specificity, which results in a low rate of appropriate ICD therapy. Here, we develop a personalized approach to assess SCD risk in post-infarction patients based on cardiac imaging and computational modelling. We construct personalized three-dimensional computer models of post-infarction hearts from patients' clinical magnetic resonance imaging data and assess the propensity of each model to develop arrhythmia. In a proof-of-concept retrospective study, the virtual heart test significantly outperformed several existing clinical metrics in predicting future arrhythmic events. The robust and non-invasive personalized virtual heart risk assessment may have the potential to prevent SCD and avoid unnecessary ICD implantations.

Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models

Sudden cardiac death (SCD) from arrhythmias is a leading cause of mortality. For patients at high SCD risk, prophylactic insertion of implantable cardioverter defibrillators (ICDs) reduces mortality. Current approaches to identify patients at risk for arrhythmia are, however, of low sensitivity and specificity, which results in a low rate of appropriate ICD therapy. Here, we develop a personalized approach to assess SCD risk in post-infarction patients based on cardiac imaging and computational modelling. We construct personalized three-dimensional computer models of post-infarction hearts from patients' clinical magnetic resonance imaging data and assess the propensity of each model to develop arrhythmia. In a proof-of-concept retrospective study, the virtual heart test significantly outperformed several existing clinical metrics in predicting future arrhythmic events. The robust and non-invasive personalized virtual heart risk assessment may have the potential to prevent SCD and avoid unnecessary ICD implantations.

Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology

PURPOSE

Accurate three-dimensional (3D) reconstruction of myocardial infarct geometry is crucial to patient-specific modeling of the heart aimed at providing therapeutic guidance in ischemic cardiomyopathy. However, myocardial infarct imaging is clinically performed using two-dimensional (2D) late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) techniques, and a method to build accurate 3D infarct reconstructions from the 2D LGE-CMR images has been lacking. The purpose of this study was to address this need.

METHODS

The authors developed a novel methodology to reconstruct 3D infarct geometry from segmented low-resolution (Lo-res) clinical LGE-CMR images. Their methodology employed the so-called logarithm of odds (LogOdds) function to implicitly represent the shape of the infarct in segmented image slices as LogOdds maps. These 2D maps were then interpolated into a 3D image, and the result transformed via the inverse of LogOdds to a binary image representing the 3D infarct geometry. To assess the efficacy of this method, the authors utilized 39 high-resolution (Hi-res) LGE-CMR images, including 36 in vivo acquisitions of human subjects with prior myocardial infarction and 3 ex vivo scans of canine hearts following coronary ligation to induce infarction. The infarct was manually segmented by trained experts in each slice of the Hi-res images, and the segmented data were downsampled to typical clinical resolution. The proposed method was then used to reconstruct 3D infarct geometry from the downsampled images, and the resulting reconstructions were compared with the manually segmented data. The method was extensively evaluated using metrics based on geometry as well as results of electrophysiological simulations of cardiac sinus rhythm and ventricular tachycardia in individual hearts. Several alternative reconstruction techniques were also implemented and compared with the proposed method.

RESULTS

The accuracy of the LogOdds method in reconstructing 3D infarct geometry, as measured by the Dice similarity coefficient, was 82.10% ± 6.58%, a significantly higher value than those of the alternative reconstruction methods. Among outcomes of electrophysiological simulations with infarct reconstructions generated by various methods, the simulation results corresponding to the LogOdds method showed the smallest deviation from those corresponding to the manual reconstructions, as measured by metrics based on both activation maps and pseudo-ECGs.

CONCLUSIONS

The authors have developed a novel method for reconstructing 3D infarct geometry from segmented slices of Lo-res clinical 2D LGE-CMR images. This method outperformed alternative approaches in reproducing expert manual 3D reconstructions and in electrophysiological simulations.

Precisely parameterized experimental and computational models of tissue organization

Patterns of cellular organization in diverse tissues frequently display a complex geometry and topology tightly related to the tissue function. Progressive disorganization of tissue morphology can lead to pathologic remodeling, necessitating the development of experimental and theoretical methods of analysis of the tolerance of normal tissue function to structural alterations. A systematic way to investigate the relationship of diverse cell organization to tissue function is to engineer two-dimensional cell monolayers replicating key aspects of the in vivo tissue architecture. However, it is still not clear how this can be accomplished on a tissue level scale in a parameterized fashion, allowing for a mathematically precise definition of the model tissue organization and properties down to a cellular scale with a parameter dependent gradual change in model tissue organization. Here, we describe and use a method of designing precisely parameterized, geometrically complex patterns that are then used to control cell alignment and communication of model tissues. We demonstrate direct application of this method to guiding the growth of cardiac cell cultures and developing mathematical models of cell function that correspond to the underlying experimental patterns. Several anisotropic patterned cultures spanning a broad range of multicellular organization, mimicking the cardiac tissue organization of different regions of the heart, were found to be similar to each other and to isotropic cell monolayers in terms of local cell-cell interactions, reflected in similar confluency, morphology and connexin-43 expression. However, in agreement with the model predictions, different anisotropic patterns of cell organization, paralleling in vivo alterations of cardiac tissue morphology, resulted in variable and novel functional responses with important implications for the initiation and maintenance of cardiac arrhythmias. We conclude that variations of tissue geometry and topology can dramatically affect cardiac tissue function even if the constituent cells are themselves similar, and that the proposed method can provide a general strategy to experimentally and computationally investigate when such variation can lead to impaired tissue function.

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Integrating Multiscale Modeling with Drug Effects for Cancer Treatment

In this paper, we review multiscale modeling for cancer treatment with the incorporation of drug effects from an applied system's pharmacology perspective. Both the classical pharmacology and systems biology are inherently quantitative; however, systems biology focuses more on networks and multi factorial controls over biological processes rather than on drugs and targets in isolation, whereas systems pharmacology has a strong focus on studying drugs with regard to the pharmacokinetic (PK) and pharmacodynamic (PD) relations accompanying drug interactions with multiscale physiology as well as the prediction of dosage-exposure responses and economic potentials of drugs. Thus, it requires multiscale methods to address the need for integrating models from the molecular levels to the cellular, tissue, and organism levels. It is a common belief that tumorigenesis and tumor growth can be best understood and tackled by employing and integrating a multifaceted approach that includes in vivo and in vitro experiments, in silico models, multiscale tumor modeling, continuous/discrete modeling, agent-based modeling, and multiscale modeling with PK/PD drug effect inputs. We provide an example application of multiscale modeling employing stochastic hybrid system for a colon cancer cell line HCT-116 with the application of Lapatinib drug. It is observed that the simulation results are similar to those observed from the setup of the wet-lab experiments at the Translational Genomics Research Institute.

Ion Channels and Oxidative Stress as a Potential Link for the Diagnosis or Treatment of Liver Diseases

Oxidative stress results from a disturbed balance between oxidation and antioxidant systems. Reactive oxygen species (ROS) and reactive nitrogen species (RNS) may be either harmful or beneficial to the cells. Ion channels are transmembrane proteins that participate in a large variety of cellular functions and have been implicated in the development of a variety of diseases. A significant amount of the available drugs in the market targets ion channels. These proteins have sulfhydryl groups of cysteine and methionine residues in their structure that can be targeted by ROS and RNS altering channel function including gating and conducting properties, as well as the corresponding signaling pathways associated. The regulation of ion channels by ROS has been suggested to be associated with some pathological conditions including liver diseases. This review focuses on understanding the role and the potential association of ion channels and oxidative stress in liver diseases including fibrosis, alcoholic liver disease, and cancer. The potential association between ion channels and oxidative stress conditions could be used to develop new treatments for major liver diseases.

Lessons learned from multi-scale modeling of the failing heart

Heart failure constitutes a major public health problem worldwide. Affected patients experience a number of changes in the electrical function of the heart that predispose to potentially lethal cardiac arrhythmias. Due to the multitude of electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes ambiguous, perhaps because these findings are highly dependent on the etiology, the stage of heart failure, and the experimental model used to study these changes. Nevertheless, a number of common features of failing hearts have been documented. Prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. Intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. Multi-scale computational simulations are a powerful tool that complements experimental and clinical research. The development of biophysically detailed computer models of single myocytes and cardiac tissues has contributed greatly to our understanding of processes underlying excitation and repolarization in the heart. The electrical, structural, and metabolic remodeling that arises in cardiac tissues during heart failure has been addressed from different computational perspectives to further understand the arrhythmogenic substrate. This review summarizes the contributions from computational modeling and simulation to predict the underlying mechanisms of heart failure phenotypes and their implications for arrhythmogenesis, ranging from the cellular level to whole-heart simulations. The main aspects of heart failure are presented in several related sections. An overview of the main electrophysiological and structural changes that have been observed experimentally in failing hearts is followed by the description and discussion of the simulation work in this field at the cellular level, and then in 2D and 3D cardiac structures. The implications for arrhythmogenesis in heart failure are also discussed including therapeutic measures, such as drug effects and cardiac resynchronization therapy. Finally, the future challenges in heart failure modeling and simulation will be discussed.

Accuracy of prediction of infarct-related arrhythmic circuits from image-based models reconstructed from low and high resolution MRI

Identification of optimal ablation sites in hearts with infarct-related ventricular tachycardia (VT) remains difficult to achieve with the current catheter-based mapping techniques. Limitations arise from the ambiguities in determining the reentrant pathways location(s). The goal of this study was to develop experimentally validated, individualized computer models of infarcted swine hearts, reconstructed from high-resolution ex-vivo MRI and to examine the accuracy of the reentrant circuit location prediction when models of the same hearts are instead reconstructed from low clinical-resolution MRI scans. To achieve this goal, we utilized retrospective data obtained from four pigs ~10 weeks post infarction that underwent VT induction via programmed stimulation and epicardial activation mapping via a multielectrode epicardial sock. After the experiment, high-resolution ex-vivo MRI with late gadolinium enhancement was acquired. The Hi-res images were downsampled into two lower resolutions (Med-res and Low-res) in order to replicate image quality obtainable in the clinic. The images were segmented and models were reconstructed from the three image stacks for each pig heart. VT induction similar to what was performed in the experiment was simulated. Results of the reconstructions showed that the geometry of the ventricles including the infarct could be accurately obtained from Med-res and Low-res images. Simulation results demonstrated that induced VTs in the Med-res and Low-res models were located close to those in Hi-res models. Importantly, all models, regardless of image resolution, accurately predicted the VT morphology and circuit location induced in the experiment. These results demonstrate that MRI-based computer models of hearts with ischemic cardiomyopathy could provide a unique opportunity to predict and analyze VT resulting for from specific infarct architecture, and thus may assist in clinical decisions to identify and ablate the reentrant circuit(s).

A New MRI-Based Model of Heart Function with Coupled Hemodynamics and Application to Normal and Diseased Canine Left Ventricles

A methodology for the simulation of heart function that combines an MRI-based model of cardiac electromechanics (CE) with a Navier–Stokes-based hemodynamics model is presented. The CE model consists of two coupled components that simulate the electrical and the mechanical functions of the heart. Accurate representations of ventricular geometry and fiber orientations are constructed from the structural magnetic resonance and the diffusion tensor MR images, respectively. The deformation of the ventricle obtained from the electromechanical model serves as input to the hemodynamics model in this one-way coupled approach via imposed kinematic wall velocity boundary conditions and at the same time, governs the blood flow into and out of the ventricular volume. The time-dependent endocardial surfaces are registered using a diffeomorphic mapping algorithm, while the intraventricular blood flow patterns are simulated using a sharp-interface immersed boundary method-based flow solver. The utility of the combined heart-function model is demonstrated by comparing the hemodynamic characteristics of a normal canine heart beating in sinus rhythm against that of the dyssynchronously beating failing heart. We also discuss the potential of coupled CE and hemodynamics models for various clinical applications.

Three-dimensional histology: tools and application to quantitative assessment of cell-type distribution in rabbit heart

Aims

Cardiac histo-anatomical organization is a major determinant of function. Changes in tissue structure are a relevant factor in normal and disease development, and form targets of therapeutic interventions. The purpose of this study was to test tools aimed to allow quantitative assessment of cell-type distribution from large histology and magnetic resonance imaging- (MRI) based datasets.

Methods and results

Rabbit heart fixation during cardioplegic arrest and MRI were followed by serial sectioning of the whole heart and light-microscopic imaging of trichrome-stained tissue. Segmentation techniques developed specifically for this project were applied to segment myocardial tissue in the MRI and histology datasets. In addition, histology slices were segmented into myocytes, connective tissue, and undefined. A bounding surface, containing the whole heart, was established for both MRI and histology. Volumes contained in the bounding surface (called ‘anatomical volume’), as well as that identified as containing any of the above tissue categories (called ‘morphological volume’), were calculated. The anatomical volume was 7.8 cm³ in MRI, and this reduced to 4.9 cm³ after histological processing, representing an ‘anatomical’ shrinkage by 37.2%. The morphological volume decreased by 48% between MRI and histology, highlighting the presence of additional tissue-level shrinkage (e.g. an increase in interstitial cleft space). The ratio of pixels classified as containing myocytes to pixels identified as non-myocytes was roughly 6:1 (61.6 vs. 9.8%; the remaining fraction of 28.6% was ‘undefined’).

Conclusion

Qualitative and quantitative differentiation between myocytes and connective tissue, using state-of-the-art high-resolution serial histology techniques, allows identification of cell-type distribution in whole-heart datasets. Comparison with MRI illustrates a pronounced reduction in anatomical and morphological volumes during histology processing.

Modelling the heart as a communication system

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in two-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.

Image-based Reconstruction of 3D Myocardial Infarct Geometry for Patient Specific Applications

Accurate reconstruction of the three-dimensional (3D) geometry of a myocardial infarct from two-dimensional (2D) multi-slice image sequences has important applications in the clinical evaluation and treatment of patients with ischemic cardiomyopathy. However, this reconstruction is challenging because the resolution of common clinical scans used to acquire infarct structure, such as short-axis, late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) images, is low, especially in the out-of-plane direction. In this study, we propose a novel technique to reconstruct the 3D infarct geometry from low resolution clinical images. Our methodology is based on a function called logarithm of odds (LogOdds), which allows the broader class of linear combinations in the LogOdds vector space as opposed to being limited to only a convex combination in the binary label space. To assess the efficacy of the method, we used high-resolution LGE-CMR images of 36 human hearts in vivo, and 3 canine hearts ex vivo. The infarct was manually segmented in each slice of the acquired images, and the manually segmented data were downsampled to clinical resolution. The developed method was then applied to the downsampled image slices, and the resulting reconstructions were compared with the manually segmented data. Several existing reconstruction techniques were also implemented, and compared with the proposed method. The results show that the LogOdds method significantly outperforms all the other tested methods in terms of region overlap.

Virtual electrophysiological study of atrial fibrillation in fibrotic remodeling

Research has indicated that atrial fibrillation (AF) ablation failure is related to the presence of atrial fibrosis. However it remains unclear whether this information can be successfully used in predicting the optimal ablation targets for AF termination. We aimed to provide a proof-of-concept that patient-specific virtual electrophysiological study that combines i) atrial structure and fibrosis distribution from clinical MRI and ii) modeling of atrial electrophysiology, could be used to predict: (1) how fibrosis distribution determines the locations from which paced beats degrade into AF; (2) the dynamic behavior of persistent AF rotors; and (3) the optimal ablation targets in each patient. Four MRI-based patient-specific models of fibrotic left atria were generated, ranging in fibrosis amount. Virtual electrophysiological studies were performed in these models, and where AF was inducible, the dynamics of AF were used to determine the ablation locations that render AF non-inducible. In 2 of the 4 models patient-specific models AF was induced; in these models the distance between a given pacing location and the closest fibrotic region determined whether AF was inducible from that particular location, with only the mid-range distances resulting in arrhythmia. Phase singularities of persistent rotors were found to move within restricted regions of tissue, which were independent of the pacing location from which AF was induced. Electrophysiological sensitivity analysis demonstrated that these regions changed little with variations in electrophysiological parameters. Patient-specific distribution of fibrosis was thus found to be a critical component of AF initiation and maintenance. When the restricted regions encompassing the meander of the persistent phase singularities were modeled as ablation lesions, AF could no longer be induced. The study demonstrates that a patient-specific modeling approach to identify non-invasively AF ablation targets prior to the clinical procedure is feasible.

Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.

Atrial fibrillation is an irregular heart rhythm affecting millions of people worldwide. Effective treatment of this cardiac disorder relies upon our detailed knowledge and understanding of the mechanisms that lead to arrhythmia. Recent clinical observations have suggested that alternans, a phenomenon where the shape of the electrical signal in the heart alternates from beat to beat, may play an important role in this process, but the underlying mechanisms remain unknown. In this study, we use computational models to conduct a detailed examination of the causes and contributors to alternans associated with human atrial fibrillation. We find that in atria remodeled by atrial fibrillation, alternans appears near resting heart rates because several aspects of calcium cycling are disrupted in the atrial cells. In particular, the release and uptake of calcium from the cellular storage compartment, the sarcoplasmic reticulum, becomes imbalanced, leading to alternation in calcium signals from beat to beat. These findings provide important insights into the mechanisms of proarrhythmic alternans in human atrial fibrillation which may be used to develop novel therapeutic targets and treatment strategies in the future.

Measurement bias in activation-recovery intervals from unipolar electrograms

The activation-recovery interval (ARI) calculated from unipolar electrograms is regularly used as a convenient surrogate measure of local cardiac action potential durations (APD). This method enables important research bridging between computational studies and in vitro and in vivo human studies. The Wyatt method is well established as a theoretically sound method for calculating ARIs; however, some studies have observed that it is prone to a bias error in measurement when applied to positive T waves. This article demonstrates that recent theoretical and computational studies supporting the use of the Wyatt method are likely to have underestimated the extent of this bias in many practical experimental recording scenarios. This work addresses these situations and explains the measurement bias by adapting existing theoretical expressions of the electrogram to represent practical experimental recording configurations. A new analytic expression for the electrogram's local component is derived, which identifies the source of measurement bias for positive T waves. A computer implementation of the new analytic model confirms our hypothesis that the bias is systematically dependent on the electrode configuration. These results provide an aid to electrogram interpretation in general, and this work's outcomes are used to make recommendations on how to minimize measurement error.