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.

Whole-heart computational modelling provides further mechanistic insights into ST-elevation in Brugada syndrome

Background

Brugada syndrome (BrS) is characterized by dynamic ST-elevations in right precordial leads and increased risk of ventricular fibrillation and sudden cardiac death. As the mechanism underlying ST-elevation and malignant arrhythmias is controversial computational modeling can aid in exploring the disease mechanism. Thus we aim to test the main competing hypotheses ('delayed depolarization' vs. 'early repolarization') of BrS in a whole-heart computational model.

Methods

In a 3D whole-heart computational model, delayed epicardial RVOT activation with local conduction delay was simulated by reducing conductivity in the epicardial RVOT. Early repolarization was simulated by instead increasing the transient outward potassium current (Ito) in the same region. Additionally, a reduction in the fast sodium current (INa) was incorporated in both models.

Results

Delayed depolarization with local conduction delay in the computational model resulted in coved-type ST-elevation with negative T-waves in the precordial surface ECG leads. 'Saddleback'-shaped ST-elevation was obtained with reduced substrate extent or thickness. Increased Ito simulations showed early repolarization in the RVOT with a descending but not coved-type ST-elevation. Reduced INa did not show a significant effect on ECG morphology.

Conclusions

In this whole-heart BrS computational model of both major hypotheses, realistic coved-type ECG resulted only from delayed epicardial RVOT depolarization with local conduction delay but not early repolarizing ion channel modifications. These simulations provide further support for the depolarization hypothesis as electrophysiological mechanism underlying BrS.

MedalCare-XL: 16,900 healthy and pathological synthetic 12 lead ECGs from electrophysiological simulations

Mechanistic cardiac electrophysiology models allow for personalized simulations of the electrical activity in the heart and the ensuing electrocardiogram (ECG) on the body surface. As such, synthetic signals possess known ground truth labels of the underlying disease and can be employed for validation of machine learning ECG analysis tools in addition to clinical signals. Recently, synthetic ECGs were used to enrich sparse clinical data or even replace them completely during training leading to improved performance on real-world clinical test data. We thus generated a novel synthetic database comprising a total of 16,900 12 lead ECGs based on electrophysiological simulations equally distributed into healthy control and 7 pathology classes. The pathological case of myocardial infraction had 6 sub-classes. A comparison of extracted features between the virtual cohort and a publicly available clinical ECG database demonstrated that the synthetic signals represent clinical ECGs for healthy and pathological subpopulations with high fidelity. The ECG database is split into training, validation, and test folds for development and objective assessment of novel machine learning algorithms.

Functional Characterization of a Spectrum of Novel Romano-Ward Syndrome KCNQ1 Variants

The KCNQ1 gene encodes the α-subunit of the cardiac voltage-gated potassium (Kv) channel KCNQ1, also denoted as Kv7.1 or KvLQT1. The channel assembles with the ß-subunit KCNE1, also known as minK, to generate the slowly activating cardiac delayed rectifier current I_Ks, a key regulator of the heart rate dependent adaptation of the cardiac action potential duration (APD). Loss-of-function variants in KCNQ1 cause the congenital Long QT1 (LQT1) syndrome, characterized by delayed cardiac repolarization and a QT interval prolongation in the surface electrocardiogram (ECG). Autosomal dominant loss-of-function variants in KCNQ1 result in the LQT syndrome called Romano-Ward syndrome (RWS), while autosomal recessive variants affecting function, lead to Jervell and Lange-Nielsen syndrome (JLNS), associated with deafness. The aim of this study was the characterization of novel KCNQ1 variants identified in patients with RWS to widen the spectrum of known LQT1 variants, and improve the interpretation of the clinical relevance of variants in the KCNQ1 gene. We functionally characterized nine human KCNQ1 variants using the voltage-clamp technique in Xenopus laevis oocytes, from which we report seven novel variants. The functional data was taken as input to model surface ECGs, to subsequently compare the functional changes with the clinically observed QTc times, allowing a further interpretation of the severity of the different LQTS variants. We found that the electrophysiological properties of the variants correlate with the severity of the clinically diagnosed phenotype in most cases, however, not in all. Electrophysiological studies combined with in silico modelling approaches are valuable components for the interpretation of the pathogenicity of KCNQ1 variants, but assessing the clinical severity demands the consideration of other factors that are included, for example in the Schwartz score.

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.

A Fully-Coupled Electro-Mechanical Whole-Heart Computational Model: Influence of Cardiac Contraction on the ECG

The ECG is one of the most commonly used non-invasive tools to gain insights into the electrical functioning of the heart. It has been crucial as a foundation in the creation and validation of in silico models describing the underlying electrophysiological processes. However, so far, the contraction of the heart and its influences on the ECG have mainly been overlooked in in silico models. As the heart contracts and moves, so do the electrical sources within the heart responsible for the signal on the body surface, thus potentially altering the ECG. To illuminate these aspects, we developed a human 4-chamber electro-mechanically coupled whole heart in silico model and embedded it within a torso model. Our model faithfully reproduces measured 12-lead ECG traces, circulatory characteristics, as well as physiological ventricular rotation and atrioventricular valve plane displacement. We compare our dynamic model to three non-deforming ones in terms of standard clinically used ECG leads (Einthoven and Wilson) and body surface potential maps (BSPM). The non-deforming models consider the heart at its ventricular end-diastatic, end-diastolic and end-systolic states. The standard leads show negligible differences during P-Wave and QRS-Complex, yet during T-Wave the leads closest to the heart show prominent differences in amplitude. When looking at the BSPM, there are no notable differences during the P-Wave, but effects of cardiac motion can be observed already during the QRS-Complex, increasing further during the T-Wave. We conclude that for the modeling of activation (P-Wave/QRS-Complex), the associated effort of simulating a complete electro-mechanical approach is not worth the computational cost. But when looking at ventricular repolarization (T-Wave) in standard leads as well as BSPM, there are areas where the signal can be influenced by cardiac motion of the heart to an extent that should not be ignored.

Analyzing the Role of Repolarization Gradients in Post-infarct Ventricular Tachycardia Dynamics Using Patient-Specific Computational Heart Models

Aims: Disease-induced repolarization heterogeneity in infarcted myocardium contributes to VT arrhythmogenesis but how apicobasal and transmural (AB-TM) repolarization gradients additionally affect post-infarct VT dynamics is unknown. The goal of this study is to assess how AB-TM repolarization gradients impact post-infarct VT dynamics using patient-specific heart models.

Method: 3D late gadolinium-enhanced cardiac magnetic resonance images were acquired from seven post-infarct patients. Models representing the patient-specific scar and infarct border zone distributions were reconstructed without (baseline) and with repolarization gradients along both the AB-TM axes. AB only and TM only models were created to assess the effects of each ventricular gradient on VT dynamics. VTs were induced in all models via rapid pacing.

Results: Ten baseline VTs were induced. VT inducibility in AB-TM models was not significantly different from baseline (p>0.05). Reentry pathways in AB-TM models were different than baseline pathways due to alterations in the location of conduction block (p<0.05). VT exit sites in AB-TM models were different than baseline VT exit sites (p<0.05). VT inducibility of AB only and TM only models were not significantly different than that of baseline (p>0.05) or AB-TM models (p>0.05). Reentry pathways and VT exit sites in AB only and TM only models were different than in baseline (p<0.05). Lastly, repolarization gradients uncovered multiple VT morphologies with different reentrant pathways and exit sites within the same structural, conducting channels.

Conclusion: VT inducibility was not impacted by the addition of AB-TM repolarization gradients, but the VT reentrant pathway and exit sites were greatly affected due to modulation of conduction block. Thus, during ablation procedures, physiological and pharmacological factors that impact the ventricular repolarization gradient might need to be considered when targeting the VTs.

The openCARP simulation environment for cardiac electrophysiology

BACKGROUND AND OBJECTIVE

Cardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present the openCARP simulation environment as one solution that could foster the needs of large parts of this community.

METHODS AND RESULTS

openCARP and the Python-based carputils framework allow developing and sharing simulation pipelines which automate in silico experiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expanding openCARP user community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes how openCARP fulfills them. We introduce the openCARP modeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.

CONCLUSION

As an open simulator, openCARP can advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with the carputils framework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility of in silico experiments.

Computer Modeling of the Heart for ECG Interpretation—A Review

Computer modeling of the electrophysiology of the heart has undergone significant progress. A healthy heart can be modeled starting from the ion channels via the spread of a depolarization wave on a realistic geometry of the human heart up to the potentials on the body surface and the ECG. Research is advancing regarding modeling diseases of the heart. This article reviews progress in calculating and analyzing the corresponding electrocardiogram (ECG) from simulated depolarization and repolarization waves. First, we describe modeling of the P-wave, the QRS complex and the T-wave of a healthy heart. Then, both the modeling and the corresponding ECGs of several important diseases and arrhythmias are delineated: ischemia and infarction, ectopic beats and extrasystoles, ventricular tachycardia, bundle branch blocks, atrial tachycardia, flutter and fibrillation, genetic diseases and channelopathies, imbalance of electrolytes and drug-induced changes. Finally, we outline the potential impact of computer modeling on ECG interpretation. Computer modeling can contribute to a better comprehension of the relation between features in the ECG and the underlying cardiac condition and disease. It can pave the way for a quantitative analysis of the ECG and can support the cardiologist in identifying events or non-invasively localizing diseased areas. Finally, it can deliver very large databases of reliably labeled ECGs as training data for machine learning.

Model Systems for Addressing Mechanism of Arrhythmogenesis in Cardiac Repair

PURPOSE OF REVIEW

Cardiac cell-based therapy represents a promising approach for cardiac repair. However, one of the main challenges is cardiac arrhythmias associated with stem cell transplantation. The current review summarizes the recent progress in model systems for addressing mechanisms of arrhythmogenesis in cardiac repair.

RECENT FINDINGS

Animal models have been extensively developed for mechanistic studies of cardiac arrhythmogenesis. Advances in human induced pluripotent stem cells (hiPSCs), patient-specific disease models, tissue engineering, and gene editing have greatly enhanced our ability to probe the mechanistic bases of cardiac arrhythmias. Additionally, recent development in multiscale computational studies and machine learning provides yet another powerful tool to quantitatively decipher the mechanisms of cardiac arrhythmias. Advancing efforts towards the integrations of experimental and computational studies are critical to gain insights into novel mitigation strategies for cardiac arrhythmias in cell-based therapy.

Parameter variations in personalized electrophysiological models of human heart ventricles

The objectives of this study were to evaluate the accuracy of personalized numerical simulations of the electrical activity in human ventricles by comparing simulated electrocardiograms (ECGs) with real patients’ ECGs and analyzing the sensitivity of the model output to variations in the model parameters. We used standard 12-lead ECGs and up to 224 unipolar body-surface ECGs to record three patients with cardiac resynchronization therapy devices and three patients with focal ventricular tachycardia. Patient-tailored geometrical models of the ventricles, atria, large vessels, liver, and spine were created using computed tomography data. Ten cases of focal ventricular activation were simulated using the bidomain model and the TNNP 2006 cellular model. The population-based values of electrical conductivities and other model parameters were used for accuracy analysis, and their variations were used for sensitivity analysis. The mean correlation coefficient between the simulated and real ECGs varied significantly (from r = 0.29 to r = 0.86) among the simulated cases. A strong mean correlation (r > 0.7) was found in eight of the ten model cases. The accuracy of the ECG simulation varied widely in the same patient depending on the localization of the excitation origin. The sensitivity analysis revealed that variations in the anisotropy ratio, blood conductivity, and cellular apicobasal heterogeneity had the strongest influence on transmembrane potential, while variation in lung conductivity had the greatest influence on body-surface ECGs. Futhermore, the anisotropy ratio predominantly affected the latest activation time and repolarization time dispersion, while the cellular apicobasal heterogeneity mainly affected the dispersion of action potential duration, and variation in lung conductivity mainly led to changes in the amplitudes of ECGs and cardiac electrograms. We also found that the effects of certain parameter variations had specific regional patterns on the cardiac and body surfaces. These observations are useful for further developing personalized cardiac models.

A Framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs

Cardiac digital twins (Cardiac Digital Twin (CDT)s) of human electrophysiology (Electrophysiology (EP)) are digital replicas of patient hearts derived from clinical data that match like-for-like all available clinical observations. Due to their inherent predictive potential, CDTs show high promise as a complementary modality aiding in clinical decision making and also in the cost-effective, safe and ethical testing of novel EP device therapies. However, current workflows for both the anatomical and functional twinning phases within CDT generation, referring to the inference of model anatomy and parameters from clinical data, are not sufficiently efficient, robust and accurate for advanced clinical and industrial applications. Our study addresses three primary limitations impeding the routine generation of high-fidelity CDTs by introducing; a comprehensive parameter vector encapsulating all factors relating to the ventricular EP; an abstract reference frame within the model allowing the unattended manipulation of model parameter fields; a novel fast-forward electrocardiogram (Electrocardiogram (ECG)) model for efficient and bio-physically-detailed simulation required for parameter inference. A novel workflow for the generation of CDTs is then introduced as an initial proof of concept. Anatomical twinning was performed within a reasonable time compatible with clinical workflows (<4h) for 12 subjects from clinically-attained magnetic resonance images. After assessment of the underlying fast forward ECG model against a gold standard bidomain ECG model, functional twinning of optimal parameters according to a clinically-attained 12 lead ECG was then performed using a forward Saltelli sampling approach for a single subject. The achieved results in terms of efficiency and fidelity demonstrate that our workflow is well-suited and viable for generating biophysically-detailed CDTs at scale.

Quantification and classification of potassium and calcium disorders with the electrocardiogram: What do clinical studies, modeling, and reconstruction tell us?

Diseases caused by alterations of ionic concentrations are frequently observed challenges and play an important role in clinical practice. The clinically established method for the diagnosis of electrolyte concentration imbalance is blood tests. A rapid and non-invasive point-of-care method is yet needed. The electrocardiogram (ECG) could meet this need and becomes an established diagnostic tool allowing home monitoring of the electrolyte concentration also by wearable devices. In this review, we present the current state of potassium and calcium concentration monitoring using the ECG and summarize results from previous work. Selected clinical studies are presented, supporting or questioning the use of the ECG for the monitoring of electrolyte concentration imbalances. Differences in the findings from automatic monitoring studies are discussed, and current studies utilizing machine learning are presented demonstrating the potential of the deep learning approach. Furthermore, we demonstrate the potential of computational modeling approaches to gain insight into the mechanisms of relevant clinical findings and as a tool to obtain synthetic data for methodical improvements in monitoring approaches.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Solving the Inverse Problem of Electrocardiography on the Endocardium Using a Single Layer Source

The inverse problem of electrocardiography consists in reconstructing cardiac electrical activity from given body surface electrocardiographic measurements. Despite tremendous progress in the field over the last decades, the solution of this problem in terms of electrical potentials on both epi- and the endocardial heart surfaces with acceptable accuracy remains challenging. This paper presents a novel numerical approach aimed at improving the solution quality on the endocardium. Our method exploits the solution representation in the form of electrical single layer densities on the myocardial surface. We demonstrate that this representation brings twofold benefits: first, the inverse problem can be solved for the physiologically meaningful single layer densities. Secondly, a conventional transfer matrix for electrical potentials can be split into two parts, one of which turned out to posess regularizing properties leading to improved endocardial reconstructions. The method was tested in-silico for ventricular pacings utilizing realistic CT-based heart and torso geometries. The proposed approach provided more accurate solution on the ventricular endocardium compared to the conventional potential-based solutions with Tikhonov regularization of the 0th, 1st, and 2nd orders. Furthermore, we show a uniform spatio-temporal behavior of the single layer densities over the heart surface, which could be conveniently employed in the regularization procedure.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

Cardiac ischemia-insights from computational models

BACKGROUND

Complementary to clinical and experimental studies, computational cardiac modeling serves to obtain a comprehensive understanding of the cardiovascular system in order to analyze dysfunction, evaluate existing, and develop novel treatment strategies.

OBJECTIVES

We describe the basics of multiscale computational modeling of cardiac electrophysiology from the molecular ion channel to the whole body scale. By modeling cardiac ischemia, we illustrate how in silico experiments can contribute to our understanding of how the pathophysiological mechanisms translate into changes observed in diagnostic tools such as the electrocardiogram (ECG).

MATERIALS AND METHODS

Quantitative in silico modeling spans a wide range of scales from ion channel biophysics to ECG signals. For each of the scales, a set of mathematical equations describes electrophysiology in relation to the other scales. Integration of ischemia-induced changes is performed on the ion channel, single-cell, and tissue level. This approach allows us to study how effects simulated at molecular scales translate to changes in the ECG.

RESULTS

Ischemia induces action potential shortening and conduction slowing. Hence, ischemic myocardium has distinct and significant effects on propagation and repolarization of excitation, depending on the intramural extent of the ischemic region. For transmural and subendocardial ischemic regions, ST segment elevation and depression, respectively, were observed, whereas intermediate ischemic regions were found to be electrically silent (NSTEMI).

CONCLUSIONS

In silico modeling contributes quantitative and mechanistic insight into fundamental ischemia-related arrhythmogenic mechanisms. In addition, computational modeling can help to translate experimental findings at the (sub-)cellular level to the organ and body context (e. g., ECG), thereby providing a thorough understanding of this routinely used diagnostic tool that may translate into optimized applications.

Universal ventricular coordinates: A generic framework for describing position within the heart and transferring data

Being able to map a particular set of cardiac ventricles to a generic topologically equivalent representation has many applications, including facilitating comparison of different hearts, as well as mapping quantities and structures of interest between them. In this paper we describe Universal Ventricular Coordinates (UVC), which can be used to describe position within any biventricular heart. UVC comprise four unique coordinates that we have chosen to be intuitive, well defined, and relevant for physiological descriptions. We describe how to determine these coordinates for any volumetric mesh by illustrating how to properly assign boundary conditions and utilize solutions to Laplace's equation. Using UVC, we transferred scalar, vector, and tensor data between four unstructured ventricular meshes from three different species. Performing the mappings was very fast, on the order of a few minutes, since mesh nodes were searched in a KD tree. Distance errors in mapping mesh nodes back and forth between meshes were less than the size of an element. Analytically derived fiber directions were also mapped across meshes and compared, showing  < 5° difference over most of the ventricles. The ability to transfer gradients was also demonstrated. Topologically variable structures, like papillary muscles, required further definition outside of the UVC framework. In conclusion, UVC can aid in transferring many types of data between different biventricular geometries.

Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles

Early Afterdepolarizations, EADs, are defined as the reversal of the action potential before completion of the repolarization phase, which can result in ectopic beats. However, the series of mechanisms of EADs leading to these ectopic beats and related cardiac arrhythmias are not well understood. Therefore, we aimed to investigate the influence of this single cell behavior on the whole heart level. For this study we used a modified version of the Ten Tusscher-Panfilov model of human ventricular cells (TP06) which we implemented in a 3D ventricle model including realistic fiber orientations. To increase the likelihood of EAD formation at the single cell level, we reduced the repolarization reserve (RR) by reducing the rapid delayed rectifier Potassium current and raising the L-type Calcium current. Varying these parameters defined a 2D parametric space where different excitation patterns could be classified. Depending on the initial conditions, by either exciting the ventricles with a spiral formation or burst pacing protocol, we found multiple different spatio-temporal excitation patterns. The spiral formation protocol resulted in the categorization of a stable spiral (S), a meandering spiral (MS), a spiral break-up regime (SB), spiral fibrillation type B (B), spiral fibrillation type A (A) and an oscillatory excitation type (O). The last three patterns are a 3D generalization of previously found patterns in 2D. First, the spiral fibrillation type B showed waves determined by a chaotic bi-excitable regime, i.e. mediated by both Sodium and Calcium waves at the same time and in same tissue settings. In the parameter region governed by the B pattern, single cells were able to repolarize completely and different (spiral) waves chaotically burst into each other without finishing a 360 degree rotation. Second, spiral fibrillation type A patterns consisted of multiple small rotating spirals. Single cells failed to repolarize to the resting membrane potential hence prohibiting the Sodium channel gates to recover. Accordingly, we found that Calcium waves mediated these patterns. Third, a further reduction of the RR resulted in a more exotic parameter regime whereby the individual cells behaved independently as oscillators. The patterns arose due to a phase-shift of different oscillators as disconnection of the cells resulted in continuation of the patterns. For all patterns, we computed realistic 9 lead ECGs by including a torso model. The B and A type pattern exposed the behavior of Ventricular Tachycardia (VT). We conclude that EADs at the single cell level can result in different types of cardiac fibrillation at the tissue and 3D ventricle level.

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.

Patient-specific modeling of left ventricular electromechanics as a driver for haemodynamic analysis

Aims

Models of blood flow in the left ventricle (LV) and aorta are an important tool for analysing the interplay between LV deformation and flow patterns. Typically, image-based kinematic models describing endocardial motion are used as an input to blood flow simulations. While such models are suitable for analysing the hemodynamic status quo, they are limited in predicting the response to interventions that alter afterload conditions. Mechano-fluidic models using biophysically detailed electromechanical (EM) models have the potential to overcome this limitation, but are more costly to build and compute. We report our recent advancements in developing an automated workflow for the creation of such CFD ready kinematic models to serve as drivers of blood flow simulations.

Methods and results

EM models of the LV and aortic root were created for four pediatric patients treated for either aortic coarctation or aortic valve disease. Using MRI, ECG and invasive pressure recordings, anatomy as well as electrophysiological, mechanical and circulatory model components were personalized.

Results

The implemented modeling pipeline was highly automated and allowed model construction and execution of simulations of a patient’s heartbeat within 1 day. All models reproduced clinical data with acceptable accuracy.

Conclusion

Using the developed modeling workflow, the use of EM LV models as driver of fluid flow simulations is becoming feasible. While EM models are costly to construct, they constitute an important and nontrivial step towards fully coupled electro-mechano-fluidic (EMF) models and show promise as a tool for predicting the response to interventions which affect afterload conditions.

Electrocardiographic features for the measurement of drivers' mental workload

This study examines the effect of mental workload on the electrocardiogram (ECG) of participants driving the Lane Change Task (LCT). Different levels of mental workload were induced by a secondary task (n-back task) with three levels of difficulty. Subjective data showed a significant increase of the experienced workload over all three levels. An exploratory approach was chosen to extract a large number of rhythmical and morphological features from the ECG signal thereby identifying those which differentiated best between the levels of mental workload. No single rhythmical or morphological feature was able to differentiate between all three levels. A group of parameters were extracted which were at least able to discriminate between two levels. For future research, a combination of features is recommended to achieve best diagnosticity for different levels of mental workload.

Comparison of Baseline Wander Removal Techniques considering the Preservation of ST Changes in the Ischemic ECG: A Simulation Study

The most important ECG marker for the diagnosis of ischemia or infarction is a change in the ST segment. Baseline wander is a typical artifact that corrupts the recorded ECG and can hinder the correct diagnosis of such diseases. For the purpose of finding the best suited filter for the removal of baseline wander, the ground truth about the ST change prior to the corrupting artifact and the subsequent filtering process is needed. In order to create the desired reference, we used a large simulation study that allowed us to represent the ischemic heart at a multiscale level from the cardiac myocyte to the surface ECG. We also created a realistic model of baseline wander to evaluate five filtering techniques commonly used in literature. In the simulation study, we included a total of 5.5 million signals coming from 765 electrophysiological setups. We found that the best performing method was the wavelet-based baseline cancellation. However, for medical applications, the Butterworth high-pass filter is the better choice because it is computationally cheap and almost as accurate. Even though all methods modify the ST segment up to some extent, they were all proved to be better than leaving baseline wander unfiltered.

Simple T-Wave Metrics May Better Predict Early Ischemia as Compared to ST Segment

There is pressing clinical need to identify developing heart attack (infarction) in patients as early as possible. However, current state-of-the-art tools in clinical practice, underpinned by the evaluation of elevation of the ST segment of the 12-lead electrocardiogram (ECG), do not identify all patients suffering from lack of blood flow to the heart muscle (cardiac ischemia), worsening the risk for further adverse events and patient outcome overall. In this study, we aimed to explore and compare the portions of cardiac repolarization in the ECG that best capture the electrophysiological changes associated with ischemia. We developed three-dimensional electrophysiological models of the human ventricles and torso, incorporating biophysically-based membrane kinetics and realistic activation sequence, to compute simulated ECGs and their alteration with the application of simulated ischemia of differing severity in diverse regions of the heart. Results suggest that metrics based on the T-wave in addition to the ST segment may be more sensitive to detecting ischemia than those using the ST segment alone. Further research into how such simulation-aided risk assessment methods may aid workflows in extant clinical practice, with the ultimate goal of multimodality clinical support, is warranted.

Comparison of Electric- and Magnetic-Cardiograms Produced by Myocardial Ischemia in Models of the Human Ventricle and Torso

Myocardial ventricular ischemia arises from a lack of blood supply to the heart, which may cause abnormal repolarization and excitation wave conduction patterns in the tissue, leading to cardiac arrhythmias and even sudden death. Current diagnosis of cardiac ischemia by the 12-lead electrocardiogram (ECG) has limitations as they are insensitive in many cases and may show unnoticeable differences to normal patterns. As the magnetic field provides extra information on cardiac excitation and is more sensitive to tangential currents to the surface of the chest, whereas the electric field is more sensitive to flux currents, it has been hypothesized that the magnetocardiogram (MCG) may provide a complementary method to the ECG in ischemic diagnosis. However, it is unclear yet about the differences in sensitivity regions of body surface ECG and MCG signals to ischemic conditions. The aim of this study was to investigate such differences by using 12-, 36- ECG and 36-MCG computed from multi-scale biophysically detailed computational models of the human ventricles and torso in both control and ischemic conditions. It was shown that ischemia produced changes in the ECG and MCG signals in the QRS complex, T-wave and ST-segment, with greater relative differences seen in the 36-lead ECG and MCG as compared to the 12-leads ECG (34% and 37% vs 26%, respectively). The 36-lead ECG showed more averaged sensitivity than the MCG in the change of T-wave due to ischemia (37% vs 32%, respectively), whereas the MCG showed greater sensitivity than the ECG in the change of the ST-segment (50% vs 40%, respectively). In addition, both MCG and ECG showed regional-dependent changes to ischemia, but with MCG showing a stronger correlation between ischemic region in the heart. In conclusion, MCG shows more sensitivity than ECG in response to ischemia, which may provide an alternative method for the diagnosis of ischemia.

Joint influence of transmural heterogeneities and wall deformation on cardiac bioelectrical activity: A simulation study

The aim of this work is to investigate, by means of numerical simulations, the influence of myocardial deformation due to muscle contraction and relaxation on the cardiac repolarization process in presence of transmural intrinsic action potential duration (APD) heterogeneities. The three-dimensional electromechanical model considered consists of the following four coupled components: the quasi-static transversely isotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the anisotropic Bidomain model for the electrical current flow through the deforming cardiac tissue; the membrane model of ventricular myocytes, including stretch-activated channels. The numerical simulations are based on our finite element parallel solver, which employs Multilevel Additive Schwarz preconditioners for the solution of the discretized Bidomain equations and Newton-Krylov methods for the solution of the discretized non-linear finite elasticity equations. Our findings show that: (i) the presence of intrinsic transmural cellular APD heterogeneities is not fully masked by electrotonic current flow or by the presence of the mechanical deformation; (ii) despite the presence of transmural APD heterogeneities, the recovery process follows the activation sequence and there is no significant transmural repolarization gradient; (iii) with or without transmural APD heterogeneities, epicardial electrograms always display the same wave shape and discordance between the polarity of QRS complex and T-wave; (iv) the main effects of the mechanical deformation are an increase of the dispersion of repolarization time and APD, when computed over the total cardiac domain and over the endo- and epicardial surfaces, while there is a slight decrease along the transmural direction.

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.

Transmural, interventricular, apicobasal and anteroposterior action potential duration gradients are all essential to the genesis of the concordant and realistic T wave: A whole-heart model study

BACKGROUND

It has been reported that ventricular repolarization dispersion resulting from transmural, apicobasal and interventricular action potential duration (APD) gradients makes the T wave concordant with the QRS complex.

METHOD AND RESULTS

A whole-heart model integrating transmural, apicobasal, interventricular and anteroposterior APD gradients was used, and the corresponding electrocardiograms were simulated to study the influence of these APD gradients on the T-wave amplitudes. The simulation results showed that changing a single APD gradient (e.g., interventricular APD gradient alone) only made substantial changes to the T-wave amplitudes in a limited number of leads and was not able to generate T waves with amplitudes comparable with clinical findings in all leads. A combination of transmural, apicobasal and interventricular APD gradients could simulate T waves with amplitudes similar to clinical values in the limb leads only. Adding the anteroposterior APD gradient into the model greatly improved the consistency between the simulated T-wave amplitudes and the clinical values.

CONCLUSION

The simulation results support that the transmural, apicobasal, interventricular and the anteroposterior APD gradient are all essential to the genesis of the clinical T wave.

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.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Uncertainty and variability in models of the cardiac action potential: Can we build trustworthy models?

Cardiac electrophysiology models have been developed for over 50 years, and now include detailed descriptions of individual ion currents and sub-cellular calcium handling. It is commonly accepted that there are many uncertainties in these systems, with quantities such as ion channel kinetics or expression levels being difficult to measure or variable between samples. Until recently, the original approach of describing model parameters using single values has been retained, and consequently the majority of mathematical models in use today provide point predictions, with no associated uncertainty.

In recent years, statistical techniques have been developed and applied in many scientific areas to capture uncertainties in the quantities that determine model behaviour, and to provide a distribution of predictions which accounts for this uncertainty. In this paper we discuss this concept, which is termed uncertainty quantification, and consider how it might be applied to cardiac electrophysiology models.

We present two case studies in which probability distributions, instead of individual numbers, are inferred from data to describe quantities such as maximal current densities. Then we show how these probabilistic representations of model parameters enable probabilities to be placed on predicted behaviours. We demonstrate how changes in these probability distributions across data sets offer insight into which currents cause beat-to-beat variability in canine APs. We conclude with a discussion of the challenges that this approach entails, and how it provides opportunities to improve our understanding of electrophysiology.

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Uncertainty and variability in action potential models can be quantified.

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A probabilistic method for inferring maximal current densities is developed and applied.

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We use this to infer the currents responsible for canine beat-to-beat variability.

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Emulation of mathematical models provides rich information at low computational cost.

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The importance of considering uncertainty and variability in future is discussed.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

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.

Action potential duration gradients in the heart ventricles and the cardiac electric field during ventricular repolarization (a model study)

BACKGROUND

We simulated contributions of transmural, apicobasal, anteroposterior and interventricular action potential duration (APD) gradients to the body surface potential distribution (BSPD) with constant or varied magnitudes of the transmural and apicobasal gradients.

METHODS

Simulations were done in the framework of the discrete computer model of the rabbit heart ventricles on the basis of realistic activation sequence and APDs. The APD gradients were set constant at 20 ms or varied in the range of ±80 ms.

RESULTS

The apicobasal, transmural and interventricular APD gradients of 20 ms produced similar BSPDs, whereas the BSPD inversion was caused by the inverted apicobasal or transmural 80 ms gradients. The transmural APD gradient produced transversal and mainly apicobasal T-wave vectors due to wall curvature and cancellation effects. The "normal" transversal and apicobasal repolarization gradients were decreased and increased by activation sequence, respectively.

CONCLUSION

The different APD gradients contributed consistently to the development of BSPD.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

In Silico Organ Modelling in Predicting Efficacy and Safety of New Medicines

The development of new medicines faces important challenges due to difficulties in the assessment of their efficacy and their safety in the targeted human population. In silico approaches through the use of mathematical modelling and computer simulations are increasingly being used to overcome some of the limitations of current experimental methods used in the development of new medicines. This chapter describes state-of-the-art in silico approaches for the evaluation of the safety and efficacy of medicines targeting important causes of mortality such as cardiovascular disease. Firstly, we describe the in silico multi-scale mathematical models and simulation techniques required to describe drug-induced effects on physiological systems such as the heart from the subcellular to the whole organ level. Then we illustrate the power of in silico approaches used to augment experimental and clinical investigations, by providing the framework to unravel multi-scale mechanisms underlying variability in the response to medicines and to focus on effects in human rather than animal models. We devote the last part of the chapter to discussing the process of validation of in silico models and simulations, which is key in building up their credibility.

Computational generation of the Purkinje network driven by clinical measurements: the case of pathological propagations

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models.

Application of stochastic phenomenological modelling to cell-to-cell and beat-to-beat electrophysiological variability in cardiac tissue

Variability in the action potential of isolated myocytes and tissue samples is observed in experimental studies. Variability is manifested as both differences in the action potential (AP) morphology between cells (extrinsic variability), and also ‘intrinsic’ or beat-to-beat variability of repolarization (BVR) in the AP duration of each cell. We studied the relative contributions of experimentally recorded intrinsic and extrinsic variability to dispersion of repolarization in tissue. We developed four cell-specific parameterizations of a phenomenological stochastic differential equation AP model exhibiting intrinsic variability using APs recorded from isolated guinea pig ventricular myocytes exhibiting BVR. We performed simulations in tissue using the four different model parameterizations in the presence and the absence of both intrinsic and extrinsic variability. We altered the coupling of the tissue to determine how inter-cellular coupling affected the dispersion of the AP duration in tissue. Both intrinsic and extrinsic variability were gradually revealed by reduction of tissue coupling. However, the recorded extrinsic variability between individual myocytes produced a greater degree of dispersion in repolarization in tissue than the intrinsic variability of each myocyte.

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We modelled inter-cell and beat-to-beat repolarization variability in cardiomyocytes.

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We coupled the cells together into cardiac tissue.

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Reducing tissue coupling increased repolarization dispersion in tissue.

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Inter-cell variability had a greater effect on repolarization dispersion.

Computational assessment of drug-induced effects on the electrocardiogram: from ion channel to body surface potentials

Background and Purpose

Understanding drug effects on the heart is key to safety pharmacology assessment and anti-arrhythmic therapy development. Here our goal is to demonstrate the ability of computational models to simulate the effect of drug action on the electrical activity of the heart, at the level of the ion-channel, cell, heart and ECG body surface potential.

Experimental Approach

We use the state-of-the-art mathematical models governing the electrical activity of the heart. A drug model is introduced using an ion channel conductance block for the hERG and fast sodium channels, depending on the IC₅₀ value and the drug dose. We simulate the ECG measurements at the body surface and compare biomarkers under different drug actions.

Key Results

Introducing a 50% hERG-channel current block results in 8% prolongation of the APD₉₀ and 6% QT interval prolongation, hERG block does not affect the QRS interval. Introducing 50% fast sodium current block prolongs the QRS and the QT intervals by 12% and 5% respectively, and delays activation times, whereas APD₉₀ is not affected.

Conclusions and Implications

Both potassium and sodium blocks prolong the QT interval, but the underlying mechanism is different: for potassium it is due to APD prolongation; while for sodium it is due to a reduction of electrical wave velocity. This study shows the applicability of in silico models for the investigation of drug effects on the heart, from the ion channel to the ECG-based biomarkers.

The functional role of electrophysiological heterogeneity in the rabbit ventricle during rapid pacing and arrhythmias

Electrophysiological heterogeneity in action potential recordings from healthy intact hearts remains highly variable and, where present, is almost entirely abolished at fast pacing rates. Consequently, the functional importance of intrinsic action potential duration (APD) heterogeneity in healthy ventricles, and particularly its role during rapidly activating reentrant arrhythmias, remain poorly understood. By incorporating both transmural and apicobasal APD heterogeneity within a biventricular rabbit computational model and comparing with an equivalent homogeneous model, we directly investigated the functional importance of intrinsic APD heterogeneity under fast pacing and arrhythmogenic protocols. Although differences in APD were significantly modulated at the tissue level during pacing and further reduced as pacing frequency increased, small differences were still noticeable. Such differences were further marginally accentuated/attenuated via electrotonic effects relative to wavefront propagation directions. The remaining small levels of APD heterogeneity under the fastest pacing frequencies resulted in arrhythmia initiation via heterogeneous conduction block, in contrast to complete block in the homogeneous model. Such induction mechanisms were more evident during premature stimuli at slower paced rhythms where intrinsic heterogeneity remained to a greater degree. During sustained arrhythmias, however, intrinsic heterogeneity made little difference to overall reentrant behavior, either visually, or in terms of duration, metrics quantifying filament/phase singularity dynamics, and global electrocardiogram characteristics. These findings suggest that, despite being important during arrhythmia initiation, intrinsic electrophysiological heterogeneity plays little functional role during rapid pacing and sustained arrhythmia dynamics in the healthy ventricle and thus questions the need to incorporate such detail in computational models when simulating rapid arrhythmias.

A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models

Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace-Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.

Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability; 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations; 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations; 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.