Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

The electrical restitution of the non-propagated cardiac ventricular action potential

Sudden changes in pacing cycle length are frequently associated with repolarization abnormalities initiating cardiac arrhythmias, and physiologists have long been interested in measuring the likelihood of these events before their manifestation. A marker of repolarization stability has been found in the electrical restitution (ER), the response of the ventricular action potential duration to a pre- or post-mature stimulation, graphically represented by the so-called ER curve. According to the restitution hypothesis (ERH), the slope of this curve provides a quantitative discrimination between stable repolarization and proneness to arrhythmias. ER has been studied at the body surface, whole organ, and tissue level, and ERH has soon become a key reference point in theoretical, clinical, and pharmacological studies concerning arrhythmia development, and, despite criticisms, it is still widely adopted. The ionic mechanism of ER and cellular applications of ERH are covered in the present review. The main criticism on ERH concerns its dependence from the way ER is measured. Over the years, in fact, several different experimental protocols have been established to measure ER, which are also described in this article. In reviewing the state-of-the art on cardiac cellular ER, I have introduced a notation specifying protocols and graphical representations, with the aim of unifying a sometime confusing nomenclature, and providing a physiological tool, better defined in its scope and limitations, to meet the growing expectations of clinical and pharmacological research.

Enhanced optimization-based method for the generation of patient-specific models of Purkinje networks

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions.

An inner-outer subcycling algorithm for parallel cardiac electrophysiology simulations

This paper explores cardiac electrophysiological simulations of the monodomain equations and introduces a novel subcycling time integration algorithm to exploit the structure of the ionic model. The aim of this work is to improve upon the efficiency of parallel cardiac monodomain simulations by using our subcycling algorithm in the computation of the ionic model to handle the local sharp changes of the solution. This will reduce the turnaround time for the simulation of basic cardiac electrical function on both idealized and patient-specific geometry. Numerical experiments show that the proposed approach is accurate and also has close to linear parallel scalability on a computer with more than 1000 processor cores. Ultimately, the reduction in simulation time can be beneficial in clinical applications, where multiple simulations are often required to tune a model to match clinical measurements.

A simple and efficient adaptive time stepping technique for low-order operator splitting schemes applied to cardiac electrophysiology

We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude-found in a previous one-dimensional analytical study by Spiteri and Ziaratgahi-to construct the new time step controller for three-dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step. This conforms with observations in numerical experiments supporting the need for a significantly smaller time step length during depolarization than during repolarization. The proposed scheme is compared with classical proportional-integral-differential controllers using state-of-the-art error estimators, which are also presented in details as they have not been previously applied in the context of cardiac EP with operator splitting techniques. Benchmarks show that choosing the time step as a sigmoidal function of the reaction magnitude is highly efficient and full cardiac cycles can be computed with precision even in a realistic biventricular setup. The proposed scheme outperforms common adaptive time stepping techniques, while depending on fewer tuning parameters.

A computational model of rabbit geometry and ECG: Optimizing ventricular activation sequence and APD distribution

Computational modeling of electrophysiological properties of the rabbit heart is a commonly used way to enhance and/or complement findings from classic lab work on single cell or tissue levels. Yet, thus far, there was no possibility to extend the scope to include the resulting body surface potentials as a way of validation or to investigate the effect of certain pathologies. Based on CT imaging, we developed the first openly available computational geometrical model not only of the whole heart but also the complete torso of the rabbit. Additionally, we fabricated a 32-lead ECG-vest to record body surface potential signals of the aforementioned rabbit. Based on the developed geometrical model and the measured signals, we then optimized the activation sequence of the ventricles, recreating the functionality of the Purkinje network, and we investigated different apico-basal and transmural gradients in action potential duration. Optimization of the activation sequence resulted in an average root mean square error between measured and simulated signal of 0.074 mV/ms for all leads. The best-fit T-Wave, compared to measured data (0.038 mV/ms), resulted from incorporating an action potential duration gradient from base to apex with a respective shortening of 20 ms and a transmural gradient with a shortening of 15 ms from endocardium to epicardium. By making our model and measured data openly available, we hope to give other researchers the opportunity to verify their research, as well as to create the possibility to investigate the impact of electrophysiological alterations on body surface signals for translational research.

Wearables in the home-based assessment of abnormal movements in Parkinson's disease: a systematic review of the literature

At present, the standard practices for home-based assessments of abnormal movements in Parkinson's disease (PD) are based either on subjective tools or on objective measures that often fail to capture day-to-day fluctuations and long-term information in real-life conditions in a way that patient's compliance and privacy are secured. The employment of wearable technologies in PD represents a great paradigm shift in healthcare remote diagnostics and therapeutics monitoring. However, their applicability in everyday clinical practice seems to be still limited. We carried out a systematic search across the Medline Database. In total, 246 publications, published until 1 June 2020, were identified. Among them, 26 reports met the inclusion criteria and were included in the present review. We focused more on clinically relevant aspects of wearables' application including feasibility and efficacy of the assessment, the number, type and body position of the wearable devices, type of PD motor symptom, environment and duration of assessments and validation methodology. The aim of this review is to provide a systematic overview of the current knowledge and state-of-the-art of the home-based assessment of motor symptoms and fluctuations in PD patients using wearable technology, highlighting current problems and laying foundations for future works.

Effect of Shock Vector Orientation in Modulating and Terminating Rotors - a Simulation Study

The main treatment option for Ventricular Fibrillation (VF), especially in out-of-hospital cardiac arrests (OHCA) is defibrillation. Typically, the survival-to-discharge rates are very poor for OHCA. Existing studies have shown that rotors may be the sources of arrhythmia and ablating them could modulate or terminate VF. However, tracking rotors and ablating them is not a feasible solution in a OHCA scenario. Hence, if the sources (or rotors) can be regionally localized non-invasively and this information can be used to direct the orientation of the shock vectors, it may aid the termination of rotors and defibrillation success. In this work, using computational modeling, we present our initial results on testing the effect of shock vector orientation on modulating (or) terminating rotors. A combination of Sovilj's and Aliev Panfilov's monodomain cardiac models were used in inducing rotors and testing the effect of shock vector magnitude and direction. Based on our simulation results on an average with four experimental trials, a shock vector directed in the perpendicular direction along the axis of the rotor terminated the rotor with 16% lesser magnitude than parallel direction and 38% lesser magnitude than in oblique direction.Clinical Relevance- A rotor localization dependent defibrillation strategy may aid the defibrillation protocol procedures to improve the survival rates. Based on the four experimental trials, the results indicate shock vectors oriented perpendicular to the axis of the rotors were efficient in modulating or terminating rotors with lower magnitude than other directions.

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.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

Gap Junctional Communication via Connexin43 between Purkinje Fibers and Working Myocytes Explains the Epicardial Activation Pattern in the Postnatal Mouse Left Ventricle

The mammalian ventricular myocardium forms a functional syncytium due to flow of electrical current mediated in part by gap junctions localized within intercalated disks. The connexin (Cx) subunit of gap junctions have direct and indirect roles in conduction of electrical impulse from the cardiac pacemaker via the cardiac conduction system (CCS) to working myocytes. Cx43 is the dominant isoform in these channels. We have studied the distribution of Cx43 junctions between the CCS and working myocytes in a transgenic mouse model, which had the His-Purkinje portion of the CCS labeled with green fluorescence protein. The highest number of such connections was found in a region about one-third of ventricular length above the apex, and it correlated with the peak proportion of Purkinje fibers (PFs) to the ventricular myocardium. At this location, on the septal surface of the left ventricle, the insulated left bundle branch split into the uninsulated network of PFs that continued to the free wall anteriorly and posteriorly. The second peak of PF abundance was present in the ventricular apex. Epicardial activation maps correspondingly placed the site of the first activation in the apical region, while some hearts presented more highly located breakthrough sites. Taken together, these results increase our understanding of the physiological pattern of ventricular activation and its morphological underpinning through detailed CCS anatomy and distribution of its gap junctional coupling to the working myocardium.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Granulocyte colony-stimulating factor attenuates myocardial remodeling and ventricular arrhythmia susceptibility via the JAK2-STAT3 pathway in a rabbit model of coronary microembolization

Background

Coronary microembolization (CME) has a poor prognosis, with ventricular arrhythmia being the most serious consequence. Understanding the underlying mechanisms could improve its management. We investigated the effects of granulocyte colony-stimulating factor (G-CSF) on connexin-43 (Cx43) expression and ventricular arrhythmia susceptibility after CME.

Methods

Forty male rabbits were randomized into four groups (n = 10 each): Sham, CME, G-CSF, and AG490 (a JAK2 selective inhibitor). Rabbits in the CME, G-CSF, and AG490 groups underwent left anterior descending (LAD) artery catheterization and CME. Animals in the G-CSF and AG490 groups received intraperitoneal injection of G-CSF and G-CSF + AG490, respectively. The ventricular structure was assessed by echocardiography. Ventricular electrical properties were analyzed using cardiac electrophysiology. The myocardial interstitial collagen content and morphologic characteristics were evaluated using Masson and hematoxylin-eosin staining, respectively.

Results

Western blot and immunohistochemistry were employed to analyze the expressions of Cx43, G-CSF receptor (G-CSFR), JAK2, and STAT3. The ventricular effective refractory period (VERP), VERP dispersion, and inducibility and lethality of ventricular tachycardia/fibrillation were lower in the G-CSF than in the CME group (P < 0.01), indicating less severe myocardial damage and arrhythmias. The G-CSF group showed higher phosphorylated-Cx43 expression (P < 0.01 vs. CME). Those G-CSF-induced changes were reversed by A490, indicating the involvement of JAK2. G-CSFR, phosphorylated-JAK2, and phosphorylated-STAT3 protein levels were higher in the G-CSF group than in the AG490 (P < 0.01) and Sham (P < 0.05) groups.

Conclusion

G-CSF might attenuate myocardial remodeling via JAK2-STAT3 signaling and thereby reduce ventricular arrhythmia susceptibility after CME.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

Comprehensive Uncertainty Quantification and Sensitivity Analysis for Cardiac Action Potential Models

Recent efforts to ensure the reliability of computational model-based predictions in healthcare, such as the ASME V&V40 Standard, emphasize the importance of uncertainty quantification (UQ) and sensitivity analysis (SA) when evaluating computational models. UQ involves empirically determining the uncertainty in model inputs-typically resulting from natural variability or measurement error-and then calculating the resultant uncertainty in model outputs. SA involves calculating how uncertainty in model outputs can be apportioned to input uncertainty. Rigorous comprehensive UQ/SA provides confidence that model-based decisions are robust to underlying uncertainties. However, comprehensive UQ/SA is not currently feasible for whole heart models, due to numerous factors including model complexity and difficulty in measuring variability in the many parameters. Here, we present a significant step to developing a framework to overcome these limitations. We: (i) developed a novel action potential (AP) model of moderate complexity (six currents, seven variables, 36 parameters); (ii) prescribed input variability for all parameters (not empirically derived); (iii) used a single "hyper-parameter" to study increasing levels of parameter uncertainty; (iv) performed UQ and SA for a range of model-derived quantities with physiological relevance; and (v) present quantitative and qualitative ways to analyze different behaviors that occur under parameter uncertainty, including "model failure". This is the first time uncertainty in every parameter (including conductances, steady-state parameters, and time constant parameters) of every ionic current in a cardiac model has been studied. This approach allowed us to demonstrate that, for this model, the simulated AP is fully robust to low levels of parameter uncertainty - to our knowledge the first time this has been shown of any cardiac model. A range of dynamics was observed at larger parameter uncertainty (e.g., oscillatory dynamics); analysis revealed that five parameters were highly influential in these dynamics. Overall, we demonstrate feasibility of performing comprehensive UQ/SA for cardiac cell models and demonstrate how to assess robustness and overcome model failure when performing cardiac UQ analyses. The approach presented here represents an important and significant step toward the development of model-based clinical tools which are demonstrably robust to all underlying uncertainties and therefore more reliable in safety-critical decision-making.

Model of Left Ventricular Contraction: Validation Criteria and Boundary Conditions

Computational models of cardiac contraction can provide critical insight into cardiac function and dysfunction. A necessary step before employing these computational models is their validation. Here we propose a series of validation criteria based on left ventricular (LV) global (ejection fraction and twist) and local (strains in a cylindrical coordinate system, aggregate cardiomyocyte shortening, and low myocardial compressibility) MRI measures to characterize LV motion and deformation during contraction. These validation criteria are used to evaluate an LV finite element model built from subject-specific anatomy and aggregate cardiomyocyte orientations reconstructed from diffusion tensor MRI. We emphasize the key role of the simulation boundary conditions in approaching the physiologically correct motion and strains during contraction. We conclude by comparing the global and local validation criteria measures obtained using two different boundary conditions: the first constraining the LV base and the second taking into account the presence of the pericardium, which leads to greatly improved motion and deformation.

Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification

Prolonged QT intervals are a major risk factor for ventricular arrhythmias and a leading cause of sudden cardiac death. Various drugs are known to trigger QT interval prolongation and increase the proarrhythmic potential. Yet, how precisely the action of drugs on the cellular level translates into QT interval prolongation on the whole organ level remains insufficiently understood. Here we use machine learning techniques to systematically characterize the effect of 30 common drugs on the QT interval. We combine information from high fidelity three-dimensional human heart simulations with low fidelity one-dimensional cable simulations to build a surrogate model for the QT interval using multi-fidelity Gaussian process regression. Once trained and cross-validated, we apply our surrogate model to perform sensitivity analysis and uncertainty quantification. Our sensitivity analysis suggests that compounds that block the rapid delayed rectifier potassium current I Kr have the greatest prolonging effect of the QT interval, and that blocking the L-type calcium current I CaL and late sodium current I NaL shortens the QT interval. Our uncertainty quantification allows us to propagate the experimental variability from individual block-concentration measurements into the QT interval and reveals that QT interval uncertainty is mainly driven by the variability in I Kr block. In a final validation study, we demonstrate an excellent agreement between our predicted QT interval changes and the changes observed in a randomized clinical trial for the drugs dofetilide, quinidine, ranolazine, and verapamil. We anticipate that both the machine learning methods and the results of this study will have great potential in the efficient development of safer drugs.

A demonstration of modularity, reuse, reproducibility, portability and scalability for modeling and simulation of cardiac electrophysiology using Kepler Workflows

Multi-scale computational modeling is a major branch of computational biology as evidenced by the US federal interagency Multi-Scale Modeling Consortium and major international projects. It invariably involves specific and detailed sequences of data analysis and simulation, often with multiple tools and datasets, and the community recognizes improved modularity, reuse, reproducibility, portability and scalability as critical unmet needs in this area. Scientific workflows are a well-recognized strategy for addressing these needs in scientific computing. While there are good examples if the use of scientific workflows in bioinformatics, medical informatics, biomedical imaging and data analysis, there are fewer examples in multi-scale computational modeling in general and cardiac electrophysiology in particular. Cardiac electrophysiology simulation is a mature area of multi-scale computational biology that serves as an excellent use case for developing and testing new scientific workflows. In this article, we develop, describe and test a computational workflow that serves as a proof of concept of a platform for the robust integration and implementation of a reusable and reproducible multi-scale cardiac cell and tissue model that is expandable, modular and portable. The workflow described leverages Python and Kepler-Python actor for plotting and pre/post-processing. During all stages of the workflow design, we rely on freely available open-source tools, to make our workflow freely usable by scientists.

We present a computational workflow as a proof of concept for integration and implementation of a reusable and reproducible cardiac multi-scale electrophysiology model that is expandable, modular and portable. This framework enables scientists to create intuitive, user-friendly and flexible end-to-end automated scientific workflows using a graphical user interface. Kepler is an advanced open-source platform that supports multiple models of computation. The underlying workflow engine handles scalability, provenance, reproducibility aspects of the code, performs orchestration of data flow, and automates execution on heterogeneous computing resources. One of the main advantages of workflow utilization is the integration of code written in multiple languages Standardization occurs at the interfaces of the workflow elements and allows for general applications and easy comparison and integration of code from different research groups or even multiple programmers coding in different languages for various purposes from the same group. A workflow driven problem-solving approach enables domain scientists to focus on resolving the core science questions, and delegates the computational and process management burden to the underlying Workflow. The workflow driven approach allows scaling the computational experiment with distributed data-parallel execution on multiple computing platforms, such as, HPC resources, GPU clusters, Cloud etc. The workflow framework tracks software version information along with hardware information to allow users an opportunity to trace any variation in workflow outcome to the system configurations.

Microstructural Infarct Border Zone Remodeling in the Post-infarct Swine Heart Measured by Diffusion Tensor MRI

Introduction: Computational models of the heart increasingly require detailed microstructural information to capture the impact of tissue remodeling on cardiac electromechanics in, for example, hearts with myocardial infarctions. Myocardial infarctions are surrounded by the infarct border zone (BZ), which is a site of electromechanical property transition. Magnetic resonance imaging (MRI) is an emerging method for characterizing microstructural remodeling and focal myocardial infarcts and the BZ can be identified with late gadolinium enhanced (LGE) MRI. Microstructural remodeling within the BZ, however, remains poorly characterized by MRI due, in part, to the fact that LGE and DT-MRI are not always available for the same heart. Diffusion tensor MRI (DT-MRI) can evaluate microstructural remodeling by quantifying the DT apparent diffusion coefficient (ADC, increased with decreased cellularity), fractional anisotropy (FA, decreased with increased fibrosis), and tissue mode (decreased with increased fiber disarray). The purpose of this work was to use LGE MRI in post-infarct porcine hearts (N = 7) to segment remote, BZ, and infarcted myocardium, thereby providing a basis to quantify microstructural remodeling in the BZ and infarcted regions using co-registered DT-MRI. Methods: Chronic porcine infarcts were created by balloon occlusion of the LCx. 6-8 weeks post-infarction, MRI contrast was administered, and the heart was potassium arrested, excised, and imaged with LGE MRI (0.33 × 0.33 × 0.33 mm) and co-registered DT-MRI (1 × 1 × 3 mm). Myocardium was segmented as remote, BZ, or infarct by LGE signal intensity thresholds. DT invariants were used to evaluate microstructural remodeling by quantifying ADC, FA, and tissue mode. Results: The BZ significantly remodeled compared to both infarct and remote myocardium. BZ demonstrated a significant decrease in cellularity (increased ADC), significant decrease in tissue organization (decreased FA), and a significant increase in fiber disarray (decreased tissue mode) relative to remote myocardium (all p < 0.05). Microstructural remodeling in the infarct was similar, but significantly larger in magnitude (all p < 0.05). Conclusion: DT-MRI can identify regions of significant microstructural remodeling in the BZ that are distinct from both remote and infarcted myocardium.

Predicting drug-induced arrhythmias by multiscale modeling

Drugs often have undesired side effects. In the heart, they can induce lethal arrhythmias such as torsades de pointes. The risk evaluation of a new compound is costly and can take a long time, which often hinders the development of new drugs. Here, we establish a high-resolution, multiscale computational model to quickly assess the cardiac toxicity of new and existing drugs. The input of the model is the drug-specific current block from single cell electrophysiology; the output is the spatio-temporal activation profile and the associated electrocardiogram. We demonstrate the potential of our model for a low-risk drug, ranolazine, and a high-risk drug, quinidine: For ranolazine, our model predicts a prolonged QT interval of 19.4% compared with baseline and a regular sinus rhythm at 60.15 beats per minute. For quinidine, our model predicts a prolonged QT interval of 78.4% and a spontaneous development of torsades de pointes both in the activation profile and in the electrocardiogram. Our model reveals the mechanisms by which electrophysiological abnormalities propagate across the spatio-temporal scales, from specific channel blockage, via altered single cell action potentials and prolonged QT intervals, to the spontaneous emergence of ventricular tachycardia in the form of torsades de pointes. Our model could have important implications for researchers, regulatory agencies, and pharmaceutical companies on rationalizing safe drug development and reducing the time-to-market of new drugs.

Validation and Trustworthiness of Multiscale Models of Cardiac Electrophysiology

Computational models of cardiac electrophysiology have a long history in basic science applications and device design and evaluation, but have significant potential for clinical applications in all areas of cardiovascular medicine, including functional imaging and mapping, drug safety evaluation, disease diagnosis, patient selection, and therapy optimisation or personalisation. For all stakeholders to be confident in model-based clinical decisions, cardiac electrophysiological (CEP) models must be demonstrated to be trustworthy and reliable. Credibility, that is, the belief in the predictive capability, of a computational model is primarily established by performing validation, in which model predictions are compared to experimental or clinical data. However, there are numerous challenges to performing validation for highly complex multi-scale physiological models such as CEP models. As a result, credibility of CEP model predictions is usually founded upon a wide range of distinct factors, including various types of validation results, underlying theory, evidence supporting model assumptions, evidence from model calibration, all at a variety of scales from ion channel to cell to organ. Consequently, it is often unclear, or a matter for debate, the extent to which a CEP model can be trusted for a given application. The aim of this article is to clarify potential rationale for the trustworthiness of CEP models by reviewing evidence that has been (or could be) presented to support their credibility. We specifically address the complexity and multi-scale nature of CEP models which makes traditional model evaluation difficult. In addition, we make explicit some of the credibility justification that we believe is implicitly embedded in the CEP modeling literature. Overall, we provide a fresh perspective to CEP model credibility, and build a depiction and categorisation of the wide-ranging body of credibility evidence for CEP models. This paper also represents a step toward the extension of model evaluation methodologies that are currently being developed by the medical device community, to physiological models.

Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

Stochastic spontaneous calcium release events and sodium channelopathies promote ventricular arrhythmias

Premature ventricular complexes (PVCs), the first initiating beats of a variety of cardiac arrhythmias, have been associated with spontaneous calcium release (SCR) events at the cell level. However, the mechanisms underlying the degeneration of such PVCs into arrhythmias are not fully understood. The objective of this study was to investigate the conditions under which SCR-mediated PVCs can lead to ventricular arrhythmias. In particular, we sought to determine whether sodium (Na⁺) current loss-of-function in the structurally normal ventricles provides a substrate for unidirectional conduction block and reentry initiated by SCR-mediated PVCs. To achieve this goal, a stochastic model of SCR was incorporated into an anatomically accurate compute model of the rabbit ventricles with the His-Purkinje system (HPS). Simulations with reduced Na⁺ current due to a negative-shift in the steady-state channel inactivation showed that SCR-mediated delayed afterdepolarizations led to PVC formation in the HPS, where the electrotonic load was lower, conduction block, and reentry in the 3D myocardium. Moreover, arrhythmia initiation was only possible when intrinsic electrophysiological heterogeneity in action potential within the ventricles was present. In conclusion, while benign in healthy individuals SCR-mediated PVCs can lead to life-threatening ventricular arrhythmias when combined with Na⁺ channelopathies.

Incorporating inductances in tissue-scale models of cardiac electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

The importance of mechano-electrical feedback and inertia in cardiac electromechanics

In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Cardiac Purkinje fibers provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is on the basis of operator splitting and is provided with 3 different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all 3 implementations produce equivalent convergence rates, and shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all 3 implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure GPU implementations outperform the pure CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.

A viscoactive constitutive modeling framework with variational updates for the myocardium

We present a constitutive modeling framework for contractile cardiac mechanics by formulating a single variational principle from which incremental stress-strain relations and kinetic rate equations for active contraction and relaxation can all be derived. The variational framework seamlessly incorporates the hyperelastic behavior of the relaxed and contracted tissue along with the rate - and length - dependent generation of contractile force. We describe a three-element, Hill-type model that unifies the active tension and active deformation approaches. As in the latter approach, we multiplicatively decompose the total deformation gradient into active and elastic parts, with the active deformation parametrizing the contractile Hill element. We adopt as internal variables the fiber, cross-fiber, and sheet normal stretch ratios. The kinetics of these internal variables are modeled via definition of a kinetic potential function derived from experimental force-velocity relations. Additionally, we account for dissipation during tissue deformation by adding a Newtonian viscous potential. To model the force activation, the kinetic equations are coupled with the calcium transient obtained from a cardiomyocyte electrophysiology model. We first analyze our model at the material point level using stress and strain versus time curves for different viscosity values. Subsequently, we couple our constitutive framework with the finite element method (FEM) and study the deformation of three-dimensional tissue slabs with varying cardiac myocyte orientation. Finally, we simulate the contraction and relaxation of an ellipsoidal left ventricular model and record common kinematic measures, such as ejection fraction, and myocardial tissue volume changes.

Generating Purkinje networks in the human heart

The Purkinje network is an integral part of the excitation system in the human heart. Yet, to date, there is no in vivo imaging technique to accurately reconstruct its geometry and structure. Computational modeling of the Purkinje network is increasingly recognized as an alternative strategy to visualize, simulate, and understand the role of the Purkinje system. However, most computational models either have to be generated manually, or fail to smoothly cover the irregular surfaces inside the left and right ventricles. Here we present a new algorithm to reliably create robust Purkinje networks within the human heart. We made the source code of this algorithm freely available online. Using Monte Carlo simulations, we demonstrate that the fractal tree algorithm with our new projection method generates denser and more compact Purkinje networks than previous approaches on irregular surfaces. Under similar conditions, our algorithm generates a network with 1219±61 branches, three times more than a conventional algorithm with 419±107 branches. With a coverage of 11±3mm, the surface density of our new Purkije network is twice as dense as the conventional network with 22±7mm. To demonstrate the importance of a dense Purkinje network in cardiac electrophysiology, we simulated three cases of excitation: with our new Purkinje network, with left-sided Purkinje network, and without Purkinje network. Simulations with our new Purkinje network predicted more realistic activation sequences and activation times than simulations without. Six-lead electrocardiograms of the three case studies agreed with the clinical electrocardiograms under physiological conditions, under pathological conditions of right bundle branch block, and under pathological conditions of trifascicular block. Taken together, our results underpin the importance of the Purkinje network in realistic human heart simulations. Human heart modeling has the potential to support the design of personalized strategies for single- or bi-ventricular pacing, radiofrequency ablation, and cardiac defibrillation with the common goal to restore a normal heart rhythm.

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart’s susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.

Ventricular fibrillation (VF) is one of the leading causes of sudden death. During VF, the electrical wave of activation in the heart breaks up chaotically. Consequently, the heart is unable to contract synchronously and pump blood to the rest of the body. In our work we formulate and validate a model of heart failure (HF) that allows us to evaluate the arrhythmogenic potential of individual and combined electrophysiological changes. In diagnostic cardiology, the electrocardiogram (ECG) is one of the most commonly used tools for detecting abnormalities in the heart electrophysiology. One of our goals is to use our numerical model to link changes at the cellular and tissue level in a failing heart to a numerically computed ECG. This allows us to characterize the precursor to and the risk of VF. In order to understand the mechanisms underlying VF in HF, we design a test that simulates a HF patient performing physical exercise. We show that under fast heart rates with changes in pacing, HF patients are more prone to VF due to a new conduction blocking mechanism. In the long term, our mathematical model is suitable for investigating the effect of drug therapies in HF.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria and the 'minimal model for human ventricular action potentials' by Bueno-Orovio, Cherry, and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor-capacitor transmission condition. Various electrocardiograms (ECGs) are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, and Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article. Copyright © 2015 John Wiley & Sons, Ltd.

Protective Role of False Tendon in Subjects with Left Bundle Branch Block: A Virtual Population Study

False tendons (FTs) are fibrous or fibromuscular bands that can be found in both the normal and abnormal human heart in various anatomical forms depending on their attachment points, tissue types, and geometrical properties. While FTs are widely considered to affect the function of the heart, their specific roles remain largely unclear and unexplored. In this paper, we present an in silico study of the ventricular activation time of the human heart in the presence of FTs. This study presents the first computational model of the human heart that includes a FT, Purkinje network, and papillary muscles. Based on this model, we perform simulations to investigate the effect of different types of FTs on hearts with the electrical conduction abnormality of a left bundle branch block (LBBB). We employ a virtual population of 70 human hearts derived from a statistical atlas, and run a total of 560 simulations to assess ventricular activation time with different FT configurations. The obtained results indicate that, in the presence of a LBBB, the FT reduces the total activation time that is abnormally augmented due to a branch block, to such an extent that surgical implant of cardiac resynchronisation devices might not be recommended by international guidelines. Specifically, the simulation results show that FTs reduce the QRS duration at least 10 ms in 80% of hearts, and up to 45 ms for FTs connecting to the ventricular free wall, suggesting a significant reduction of cardiovascular mortality risk. In further simulation studies we show the reduction in the QRS duration is more sensitive to the shape of the heart then the size of the heart or the exact location of the FT. Finally, the model suggests that FTs may contribute to reducing the activation time difference between the left and right ventricles from 12 ms to 4 ms. We conclude that FTs may provide an alternative conduction pathway that compensates for the propagation delay caused by the LBBB. Further investigation is needed to quantify the clinical impact of FTs on cardiovascular mortality risk.

Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model

Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias.

Regional segmentation of ventricular models to achieve repolarization dispersion in cardiac electrophysiology modeling

The electrocardiogram (ECG) is one of the most significant outputs of a computational model of cardiac electrophysiology because it relates the numerical results to clinical data and is a universal tool for diagnosing heart diseases. One key features of the ECG is the T-wave, which is caused by longitudinal and transmural heterogeneity of the action potential duration (APD). Thus, in order to model a correct wave of repolarization, different cell properties resulting in different APDs must be assigned across the ventricular wall and longitudinally from apex to base. To achieve this requirement, a regional parametrization of the heart is necessary. We propose a robust approach to obtain the transmural and longitudinal segmentation in a general heart geometry without relying on ad hoc procedures. Our approach is based on auxiliary harmonic lifting analyses, already used in the literature to generate myocardial fiber orientations. Specifically, the solution of a sequence of Laplace boundary value problems allows parametrically controlled segmentation of both heart ventricles. The flexibility and simplicity of the proposed method is demonstrated through several representative examples, varying the locations and extents of the epicardial, midwall, and endocardial layers. Effects of the control parameters on the T-wave morphology are illustrated via computed ECGs.

Low-energy defibrillation with multi-electrodes stimulation: A simulation study

The objective of this study is to explore the possible ways to reduce defibrillation energy and further reveal the mechanism of electric defibrillation. A bidomain simulation study was performed on a rabbit whole-ventricle electrophysiological model and the feasibility of the defibrillation strategy with multi-electrodes stimulation was verified. Simulation results indicate that the new approach is effective in low-energy defibrillation.