Effect of heterogeneous APD restitution on VF organization in a model of the human ventricles

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.

Activation of PKC affects the ventricular restitution properties and arrhythmogenesis through L-type Ca+ current

OBJECTIVE

To investigate the role of protein kinase C (PKC) in action potential duration (APD) restitution and ventricular tachyarrhythmias (VAs).

METHODS AND RESULTS

Rabbits hearts were isolated and prepared for Langendorff perfusion technique. The stimuli-extra-stimulus (S1-S2) method and dynamic S1 pacing protocol were performed to construct APD restitution and to induce APD alternans or VA, respectively, at 10 sites throughout the ventricular chamber. Administration of phorbol-12-myristate-13-acetate (PMA) (100 nM) (n = 15) greatly steepened the restitution curves (Smax > 1) (p < .01) at each site compared to the control group (n = 15). Furthermore, treatment with PMA also induced larger spatial dispersions of Smax (p < .05) and decreased the thresholds of the VA and APD alternans (p < .01). However, perfused with the PKC inhibitor, bisindolylmaleimide (BIM) (500 nM) (n = 10), reversibly flattened the APD restitution curves at each site (Smax < 1), decreased the spatial dispersions of Smax, and increased the thresholds of APD alternans and VA. According to the results of patch-clamp, peak amplitude of L-type Ca2+ current was significantly increased by addition of PMA compared with control (CTL) group (p < .05). Antagonize this current with verapamil (n = 10) can fully inhibited the PMA induced increasing of Smax and inducibility of VA and alternans.

CONCLUSION

PKC activation increased the dispersion of APD restitution and thus led to occurrence of VA, which possibly related to the increased Ca2+ influx.

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.

Effect of strain-dependent conduction slowing on the re-entry formation and maintenance in cardiac muscle: 2D computer simulation

The effect of mechano-electrical feedback on re-entry formation and maintenance was studied using a model of myocardial electromechanics that accounts for two components of myocardial conductivity and delayed strain-dependent changes in membrane capacitance that causes a conduction slowing. Two scenarios were simulated in 2D numerical experiments: (i) propagation of an excitation-contraction wave beyond the edge of a nonconductive nonexcitable obstacle; (ii) circulation of a re-entry wave around a nonconductive nonexcitable obstacle. The simulations demonstrated that the delayed strain-dependent deceleration of the conduction waves promotes the detachment of the excitation-contraction waves from the sharp edge of an elongated obstacle and modulates the re-entry waves rotating around a compact obstacle. The data show that the mechano-electrical feedback, together with an increase in the stimulation frequency and an increase in the excitation threshold, is an arrhythmogenic factor that must be taken into account when analyzing the possibility of the re-entry formation.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Scroll wave with negative filament tension in a model of the left ventricle of the human heart and its overdrive pacing

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev-Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10-20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10 s.

Characterization of the Electrophysiologic Remodeling of Patients With Ischemic Cardiomyopathy by Clinical Measurements and Computer Simulations Coupled With Machine Learning

Rationale

Patients with ischemic cardiomyopathy (ICMP) are at high risk for malignant arrhythmias, largely due to electrophysiological remodeling of the non-infarcted myocardium. The electrophysiological properties of the non-infarcted myocardium of patients with ICMP remain largely unknown.

Objectives

To assess the pro-arrhythmic behavior of non-infarcted myocardium in ICMP patients and couple computational simulations with machine learning to establish a methodology for the development of disease-specific action potential models based on clinically measured action potential duration restitution (APDR) data.

Methods and Results

We enrolled 22 patients undergoing left-sided ablation (10 ICMP) and compared APDRs between ICMP and structurally normal left ventricles (SNLVs). APDRs were clinically assessed with a decremental pacing protocol. Using genetic algorithms (GAs), we constructed populations of action potential models that incorporate the cohort-specific APDRs. The variability in the populations of ICMP and SNLV models was captured by clustering models based on their similarity using unsupervised machine learning. The pro-arrhythmic potential of ICMP and SNLV models was assessed in cell- and tissue-level simulations. Clinical measurements established that ICMP patients have a steeper APDR slope compared to SNLV (by 38%, p < 0.01). In cell-level simulations, APD alternans were induced in ICMP models at a longer cycle length compared to SNLV models (385–400 vs 355 ms). In tissue-level simulations, ICMP models were more susceptible for sustained functional re-entry compared to SNLV models.

Conclusion

Myocardial remodeling in ICMP patients is manifested as a steeper APDR compared to SNLV, which underlies the greater arrhythmogenic propensity in these patients, as demonstrated by cell- and tissue-level simulations using action potential models developed by GAs from clinical measurements. The methodology presented here captures the uncertainty inherent to GAs model development and provides a blueprint for use in future studies aimed at evaluating electrophysiological remodeling resulting from other cardiac diseases.

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.

High-frequency pacing of scroll waves in a three-dimensional slab model of cardiac tissue

Vortices in excitable media underlie dangerous cardiac arrhythmias. One way to eliminate them is by stimulating the excitable medium with a period smaller than the period of the vortex. So far, this phenomenon has been studied mostly for two-dimensional vortices known as spiral waves. Here we present a first study of this phenomenon for three-dimensional vortices, or scroll waves, in a slab. We consider two main types of scroll waves dynamics: with positive filament tension and with negative filament tension and show that such elimination is possible for some values of the period in all cases. However, in the case of negative filament tension for relatively long stimulation periods, three-dimensional instabilities occur and make elimination impossible. We derive equations of motion for the drift of paced filaments and identify a bifurcation parameter that determines whether the filaments orient themselves perpendicular to the impeding wave train or not.

Overdrive pacing of spiral waves in a model of human ventricular tissue

High-voltage electrical defibrillation remains the only reliable method of quickly controlling life-threatening cardiac arrhythmias. This paper is devoted to studying an alternative approach, low-voltage cardioversion (LVC), which is based on ideas from non-linear dynamics and aims to remove sources of cardiac arrhythmias by applying high-frequency stimulation to cardiac tissue. We perform a detailed in-silico study of the elimination of arrhythmias caused by rotating spiral waves in a TP06 model of human cardiac tissue. We consider three parameter sets with slopes of the APD restitution curve of 0.7, 1.1 and 1.4, and we study LVC at the baseline and under the blocking of INa and ICaL and under the application of the drugs verapamil and amiodarone. We show that pacing can remove spiral waves; however, its efficiency can be substantially reduced by dynamic instabilities. We classify these instabilities and show that the blocking of INa and the application of amiodarone increase the efficiency of the method, while the blocking of ICaL and the application of verapamil decrease the efficiency. We discuss the mechanisms and the possible clinical applications resulting from our study.

Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

Non-linear electrical waves propagate through the heart and control cardiac contraction. Abnormal wave propagation causes various forms of the heart disease and can be lethal. One of the main causes of abnormality is a condition of cardiac fibrosis, which, from mathematical point of view, is the presence of multiple non-conducting obstacles for wave propagation. The fibrosis can have different texture which varies from diffuse (e.g., small randomly distributed obstacles), patchy (e.g., elongated interstitional stria), and focal (e.g., post-infarct scars) forms. Recently, Nezlobinsky et al. (2020) used 2D biophysical models to quantify the effects of elongation of obstacles (fibrosis texture) and showed that longitudinal and transversal propagation differently depends on the obstacle length resulting in anisotropy for wave propagation. In this paper, we extend these studies to 3D tissue models. We show that 3D consideration brings essential new effects; for the same obstacle length in 3D systems, anisotropy is about two times smaller compared to 2D, however, wave propagation is more stable with percolation threshold of about 60% (compared to 35% in 2D). The percolation threshold increases with the obstacle length for the longitudinal propagation, while it decreases for the transversal propagation. Further, in 3D, the dependency of velocity on the obstacle length for the transversal propagation disappears.

Drift of Scroll Waves in a Mathematical Model of a Heterogeneous Human Heart Left Ventricle

Rotating spiral waves of electrical excitation underlie many dangerous cardiac arrhythmias. The heterogeneity of myocardium is one of the factors that affects the dynamics of such waves. In this paper, we present results of our simulations for scroll wave dynamics in a heterogeneous model of the human left ventricle with analytical anatomically based representation of the geometry and anisotropy. We used a set of 18 coupled differential equations developed by ten Tusscher and Panfilov (TP06 model) which describes human ventricular cells based on their measured biophysical properties. We found that apicobasal heterogeneity dramatically changes the scroll wave dynamics. In the homogeneous model, the scroll wave annihilates at the base, but the moderate heterogeneity causes the wave to move to the apex and then continuously rotates around it. The rotation speed increased with the degree of the heterogeneity. However, for large heterogeneity, we observed formation of additional wavebreaks and the onset of complex spatio-temporal patterns. Transmural heterogeneity did not change the dynamics and decreased the lifetime of the scroll wave with an increase in heterogeneity. Results of our numerical experiments show that the apex may be a preferable location of the scroll wave, which may be important for development of clinical interventions.

Anisotropic conduction in the myocardium due to fibrosis: the effect of texture on wave propagation

Cardiac fibrosis occurs in many forms of heart disease. It is well established that the spatial pattern of fibrosis, its texture, substantially affects the onset of arrhythmia. However, in most modelling studies fibrosis is represented by multiple randomly distributed short obstacles that mimic only one possible texture, diffuse fibrosis. An important characteristic feature of other fibrosis textures, such as interstitial and patchy textures, is that fibrotic inclusions have substantial length, which is suggested to have a pronounced effect on wave propagation. In this paper, we study the effect of the elongation of inexcitable inclusions (obstacles) on wave propagation in a 2D model of cardiac tissue described by the TP06 model for human ventricular cells. We study in detail how the elongation of obstacles affects various characteristics of the waves. We quantify the anisotropy induced by the textures, its dependency on the obstacle length and the effects of the texture on the shape of the propagating wave. Because such anisotropy is a result of zig-zag propagation we show, for the first time, quantification of the effects of geometry and source-sink relationship, on the zig-zag nature of the pathway of electrical conduction. We also study the effect of fibrosis in the case of pre-existing anisotropy and introduce a procedure for scaling of the fibrosis texture. We show that fibrosis can decrease or increase the preexisting anisotropy depending on its scaled texture.

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.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.

Pathophysiology, incidence, management, and consequences of cardiac arrhythmia in pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension

Arrhythmias are increasingly recognized as serious, end-stage complications of pre-capillary pulmonary hypertension, including pulmonary arterial hypertension (PAH) and chronic thromboembolic pulmonary hypertension (CTEPH). Although arrhythmias contribute to symptoms, morbidity, in-hospital mortality, and possibly sudden death in PAH/CTEPH, there remains a paucity of epidemiologic, pathophysiologic, and outcome data to guide management of these patients. This review summarizes the most current evidence on the topic: from the molecular mechanisms driving arrhythmia in the hypertrophied or failing right heart, to the clinical aspects of epidemiology, diagnosis, and management.

Investigation of the relationship between two novel electrocardiogram-based sudden cardiac death risk markers and autonomic function

BACKGROUND

Regional Restitution Instability Index (R2I2) and Peak ECG Restitution Slope (PERS) are promising sudden cardiac death (SCD) risk markers. R2I2 and PERS use the standard 12‑lead ECG to measure properties of electrical restitution implicated in ventricular arrhythmogenesis. We investigated the relationship between R2I2, PERS and autonomic function to inform future application of these risk markers.

METHODS

Blinded, prospective, observational study of 44 patients with ischaemic cardiomyopathy undergoing risk stratification for an ICD. Patients underwent an electrophysiological study for determination of R2I2 and PERS. 24-hour ambulatory ECG monitoring was carried out for determination of time-domain heart rate variability (HRV).

RESULTS

During median follow up of 22 months, 11 patients experienced ventricular arrhythmia (VA)/SCD. Weak inverse correlation was seen between R2I2 and HRV-i (rho: -0.36, p = 0.02). R2I2 and PERS were significantly higher in patients experiencing VA/SCD than those not (mean ± SEM:1.14 ± 0.11 vs 0.84 ± 0.05, p = 0.01) and (1.73 ± 0.27 vs 1.07 ± 0.08, p = 0.002) respectively. Patients with low HRV-i and high PERS had an incidence rate ratio for VA/SCD 14.5 times that of patients with high HRV-i and low PERS (p = 0.02).

CONCLUSION

This small study suggests that there is minimal correlation between R2I2, PERS and autonomic function as measured by HRV. Combining PERS with HRV identified patients at particularly high risk of ventricular arrhythmia/SCD. A combined PERS+HRV risk marker may improve SCD risk stratification in patients with ischaemic cardiomyopathy.

Dynamic Action Potential Restitution Contributes to Mechanical Restitution in Right Ventricular Myocytes From Pulmonary Hypertensive Rats

We investigated the steepened dynamic action potential duration (APD) restitution of rats with pulmonary artery hypertension (PAH) and right ventricular (RV) failure and tested whether the observed APD restitution properties were responsible for negative mechanical restitution in these myocytes. PAH and RV failure were provoked in male Wistar rats by a single injection of monocrotaline (MCT) and compared with saline-injected animals (CON). Action potentials were recorded from isolated RV myocytes at stimulation frequencies between 1 and 9 Hz. Action potential waveforms recorded at 1 Hz were used as voltage clamp profiles (action potential clamp) at stimulation frequencies between 1 and 7 Hz to evoke rate-dependent currents. Voltage clamp profiles mimicking typical CON and MCT APD restitution were applied and cell shortening simultaneously monitored. Compared with CON myocytes, MCT myocytes were hypertrophied; had less polarized diastolic membrane potentials; had action potentials that were triggered by decreased positive current density and shortened by decreased negative current density; APD was longer and APD restitution steeper. APD90 restitution was unchanged by exposure to the late Na⁺-channel blocker (5 μM) ranolazine or the intracellular Ca²⁺ buffer BAPTA. Under AP clamp, stimulation frequency-dependent inward currents were smaller in MCT myocytes and were abolished by BAPTA. In MCT myocytes, increasing stimulation frequency decreased contraction amplitude when depolarization duration was shortened, to mimic APD restitution, but not when depolarization duration was maintained. We present new evidence that the membrane potential of PAH myocytes is less stable than normal myocytes, being more easily perturbed by external currents. These observations can explain increased susceptibility to arrhythmias. We also present novel evidence that negative APD restitution is at least in part responsible for the negative mechanical restitution in PAH myocytes. Thus, our study links electrical restitution remodeling to a defining mechanical characteristic of heart failure, the reduced ability to respond to an increase in demand.

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.

Slow Adaptation of Ventricular Repolarization as a Cause of Arrhythmia?

Introduction: This article is part of the Focus Theme of Methods of Information in Medicine on “Biosignal Interpretation: Advanced Methods for Studying Cardiovascular and Respiratory Systems”.

Background: Adaptation of the QT-interval to changes in heart rate reflects on the body-surface electrocardiogram the adaptation of action potential duration (APD) at the cellular level. The initial fast phase of APD adaptation has been shown to modulate the arrhythmia substrate. Whether the slow phase is potentially proarrhythmic remains unclear.

Objectives: To analyze in-vivo human data and use computer simulations to examine effects of the slow APD adaptation phase on dispersion of repolarization and reentry in the human ventricle.

Methods: Electrograms were acquired from 10 left and 10 right ventricle (LV/RV) endocardial sites in 15 patients with normal ventricles during RV pacing. Activation-recovery intervals, as a surrogate for APD, were measured during a sustained increase in heart rate. Observed dynamics were studied using computer simulations of human tissue electrophysiology.

Results: Spatial heterogeneity of rate adaptation was observed in all patients. Inhomogeneity in slow APD adaptation time constants (ΔTs) was greater in LV than RV (ΔTs LV = 31.8 ± 13.2, ΔTs RV = 19.0 ± 12.8 s, P < 0.01). Simulations showed that altering local slow time constants of adaptation was sufficient to convert partial wavefront block to block with successful reentry.

Conclusions: Using electrophysiological data acquired in-vivo in human and computer simulations, we identify heterogeneity in the slow phase of APD adaptation as an important component of arrhythmogenesis.

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.

Spatial Patterns of Excitation at Tissue and Whole Organ Level Due to Early Afterdepolarizations

Early after depolarizations (EAD) occur in many pathological conditions, such as congenital or acquired channelopathies, drug induced arrhythmias, and several other situations that are associated with increased arrhythmogenicity. In this paper we present an overview of the relevant computational studies on spatial EAD dynamics in 1D, 2D, and in 3D anatomical models and discuss the relation of EADs to cardiac arrhythmias. We also discuss unsolved problems and highlight new lines of research in this area.

Murine Electrophysiological Models of Cardiac Arrhythmogenesis

Cardiac arrhythmias can follow disruption of the normal cellular electrophysiological processes underlying excitable activity and their tissue propagation as coherent wavefronts from the primary sinoatrial node pacemaker, through the atria, conducting structures and ventricular myocardium. These physiological events are driven by interacting, voltage-dependent, processes of activation, inactivation, and recovery in the ion channels present in cardiomyocyte membranes. Generation and conduction of these events are further modulated by intracellular Ca2+ homeostasis, and metabolic and structural change. This review describes experimental studies on murine models for known clinical arrhythmic conditions in which these mechanisms were modified by genetic, physiological, or pharmacological manipulation. These exemplars yielded molecular, physiological, and structural phenotypes often directly translatable to their corresponding clinical conditions, which could be investigated at the molecular, cellular, tissue, organ, and whole animal levels. Arrhythmogenesis could be explored during normal pacing activity, regular stimulation, following imposed extra-stimuli, or during progressively incremented steady pacing frequencies. Arrhythmic substrate was identified with temporal and spatial functional heterogeneities predisposing to reentrant excitation phenomena. These could arise from abnormalities in cardiac pacing function, tissue electrical connectivity, and cellular excitation and recovery. Triggering events during or following recovery from action potential excitation could thereby lead to sustained arrhythmia. These surface membrane processes were modified by alterations in cellular Ca2+ homeostasis and energetics, as well as cellular and tissue structural change. Study of murine systems thus offers major insights into both our understanding of normal cardiac activity and its propagation, and their relationship to mechanisms generating clinical arrhythmias.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart

Acute regional ischemia in the heart can lead to cardiac arrhythmias such as ventricular fibrillation (VF), which in turn compromise cardiac output and result in secondary global cardiac ischemia. The secondary ischemia may influence the underlying arrhythmia mechanism. A recent clinical study documents the effect of global cardiac ischaemia on the mechanisms of VF. During 150 seconds of global ischemia the dominant frequency of activation decreased, while after reperfusion it increased rapidly. At the same time the complexity of epicardial excitation, measured as the number of epicardical phase singularity points, remained approximately constant during ischemia. Here we perform numerical studies based on these clinical data and propose explanations for the observed dynamics of the period and complexity of activation patterns. In particular, we study the effects on ischemia in pseudo-1D and 2D cardiac tissue models as well as in an anatomically accurate model of human heart ventricles. We demonstrate that the fall of dominant frequency in VF during secondary ischemia can be explained by an increase in extracellular potassium, while the increase during reperfusion is consistent with washout of potassium and continued activation of the ATP-dependent potassium channels. We also suggest that memory effects are responsible for the observed complexity dynamics. In addition, we present unpublished clinical results of individual patient recordings and propose a way of estimating extracellular potassium and activation of ATP-dependent potassium channels from these measurements.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Initiation and dynamics of a spiral wave around an ionic heterogeneity in a model for human cardiac tissue

In relation to cardiac arrhythmias, heterogeneity of cardiac tissue is one of the most important factors underlying the onset of spiral waves and determining their type. In this paper, we numerically model heterogeneity of realistic size and value and study formation and dynamics of spiral waves around such heterogeneity. We find that the only sustained pattern obtained is a single spiral wave anchored around the heterogeneity. Dynamics of an anchored spiral wave depend on the extent of heterogeneity, and for certain heterogeneity size, we find abrupt regional increase in the period of excitation occurring as a bifurcation. We study factors determining spatial distribution of excitation periods of anchored spiral waves and discuss consequences of such dynamics for cardiac arrhythmias and possibilities for experimental testings of our predictions.

The role of action potential alternans in the initiation of atrial fibrillation in humans: a review and future directions

This review highlights the role of atrial monophasic action potential duration (APD) in understanding atrial electrical properties in paroxysmal, persistent, and permanent atrial fibrillation (AF) states. Alternans of APD and rate maladaptation in a spatially divergent way appear mechanistically involved in AF initiation, development, and persistence. The underlying pathophysiology warrants further investigation.

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.

Computational cardiology: the heart of the matter

This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Cardiac arrhythmia mechanisms in rats with heart failure induced by pulmonary hypertension

Pulmonary hypertension provokes right heart failure and arrhythmias. Better understanding of the mechanisms underlying these arrhythmias is needed to facilitate new therapeutic approaches for the hypertensive, failing right ventricle (RV). The aim of our study was to identify the mechanisms generating arrhythmias in a model of RV failure induced by pulmonary hypertension. Rats were injected with monocrotaline to induce either RV hypertrophy or failure or with saline (control). ECGs were measured in conscious, unrestrained animals by telemetry. In isolated hearts, electrical activity was measured by optical mapping and myofiber orientation by diffusion tensor-MRI. Sarcoplasmic reticular Ca(2+) handling was studied in single myocytes. Compared with control animals, the T-wave of the ECG was prolonged and in three of seven heart failure animals, prominent T-wave alternans occurred. Discordant action potential (AP) alternans occurred in isolated failing hearts and Ca(2+) transient alternans in failing myocytes. In failing hearts, AP duration and dispersion were increased; conduction velocity and AP restitution were steeper. The latter was intrinsic to failing single myocytes. Failing hearts had greater fiber angle disarray; this correlated with AP duration. Failing myocytes had reduced sarco(endo)plasmic reticular Ca(2+)-ATPase activity, increased sarcoplasmic reticular Ca(2+)-release fraction, and increased Ca(2+) spark leak. In hypertrophied hearts and myocytes, dysfunctional adaptation had begun, but alternans did not develop. We conclude that increased electrical and structural heterogeneity and dysfunctional sarcoplasmic reticular Ca(2+) handling increased the probability of alternans, a proarrhythmic predictor of sudden cardiac death. These mechanisms are potential therapeutic targets for the correction of arrhythmias in hypertensive, failing RVs.

Reduced Na(+) and higher K(+) channel expression and function contribute to right ventricular origin of arrhythmias in Scn5a+/- mice

Brugada syndrome (BrS) is associated with ventricular tachycardia originating particularly in the right ventricle (RV). We explore electrophysiological features predisposing to such arrhythmic tendency and their possible RV localization in a heterozygotic Scn5a+/- murine model. Na(v)1.5 mRNA and protein expression were lower in Scn5a+/- than wild-type (WT), with a further reduction in the RV compared with the left ventricle (LV). RVs showed higher expression levels of K(v)4.2, K(v)4.3 and KChIP2 in both Scn5a+/- and WT. Action potential upstroke velocity and maximum Na(+) current (I(Na)) density were correspondingly decreased in Scn5a+/-, with a further reduction in the RV. The voltage dependence of inactivation was shifted to more negative values in Scn5a+/-. These findings are predictive of a localized depolarization abnormality leading to slowed conduction. Persistent Na(+) current (I(pNa)) density was decreased in a similar pattern to I(Na). RV transient outward current (I(to)) density was greater than LV in both WT and Scn5a+/-, and had larger time constants of inactivation. These findings were also consistent with the observation that AP durations were smallest in the RV of Scn5a+/-, fulfilling predictions of an increased heterogeneity of repolarization as an additional possible electrophysiological mechanism for arrhythmogenesis in BrS.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²⁺ current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

Coupled personalization of cardiac electrophysiology models for prediction of ischaemic ventricular tachycardia

In order to translate the important progress in cardiac electrophysiology modelling of the last decades into clinical applications, there is a requirement to make macroscopic models that can be used for the planning and performance of the clinical procedures. This requires model personalization, i.e. estimation of patient-specific model parameters and computations compatible with clinical constraints. Simplified macroscopic models can allow a rapid estimation of the tissue conductivity, but are often unreliable to predict arrhythmias. Conversely, complex biophysical models are more complete and have mechanisms of arrhythmogenesis and arrhythmia sustainibility, but are computationally expensive and their predictions at the organ scale still have to be validated. We present a coupled personalization framework that combines the power of the two kinds of models while keeping the computational complexity tractable. A simple eikonal model is used to estimate the conductivity parameters, which are then used to set the parameters of a biophysical model, the Mitchell-Schaeffer (MS) model. Additional parameters related to action potential duration restitution curves for the tissue are further estimated for the MS model. This framework is applied to a clinical dataset derived from a hybrid X-ray/magnetic resonance imaging and non-contact mapping procedure on a patient with heart failure. This personalized MS model is then used to perform an in silico simulation of a ventricular tachycardia (VT) stimulation protocol to predict the induction of VT. This proof of concept opens up possibilities of using VT induction modelling in order to both assess the risk of VT for a given patient and also to plan a potential subsequent radio-frequency ablation strategy to treat VT.

Arrhythmogenic substrate in hearts of rats with monocrotaline-induced pulmonary hypertension and right ventricular hypertrophy

Mechanisms associated with right ventricular (RV) hypertension and arrhythmias are less understood than those in the left ventricle (LV). The aim of our study was to investigate whether and by what mechanisms a proarrhythmic substrate exists in a rat model of RV hypertension and hypertrophy. Rats were injected with monocrotaline (MCT; 60 mg/kg) to induce pulmonary artery hypertension or with saline (CON). Myocardial levels of mRNA for genes expressing ion channels were measured by real-time RT-PCR. Monophasic action potential duration (MAPD) was recorded in isolated Langendorff-perfused hearts. MAPD restitution was measured, and arrhythmias were induced by burst stimulation. Twenty-two to twenty-six days after treatment, MCT animals had RV hypertension, hypertrophy, and decreased ejection fractions compared with CON. A greater proportion of MCT hearts developed sustained ventricular tachycardias/fibrillation (0.83 MCT vs. 0.14 CON). MAPD was prolonged in RV and less so in the LV of MCT hearts. There were decreased levels of mRNA for K(+) channels. Restitution curves of MCT RV were steeper than CON RV or either LV. Dispersion of MAPD was greater in MCT hearts and was dependent on stimulation frequency. Computer simulations based on ion channel gene expression closely predicted experimental changes in MAPD and restitution. We have identified a proarrhythmic substrate in the hearts of MCT-treated rats. We conclude that steeper RV electrical restitution and rate-dependant RV-LV action potential duration dispersion may be contributing mechanisms and be implicated in the generation of arrhythmias associated with in RV hypertension and hypertrophy.

Whole-heart modeling: applications to cardiac electrophysiology and electromechanics

Recent developments in cardiac simulation have rendered the heart the most highly integrated example of a virtual organ. We are on the brink of a revolution in cardiac research, one in which computational modeling of proteins, cells, tissues, and the organ permit linking genomic and proteomic information to the integrated organ behavior, in the quest for a quantitative understanding of the functioning of the heart in health and disease. The goal of this review is to assess the existing state-of-the-art in whole-heart modeling and the plethora of its applications in cardiac research. General whole-heart modeling approaches are presented, and the applications of whole-heart models in cardiac electrophysiology and electromechanics research are reviewed. The article showcases the contributions that whole-heart modeling and simulation have made to our understanding of the functioning of the heart. A summary of the future developments envisioned for the field of cardiac simulation and modeling is also presented. Biophysically based computational modeling of the heart, applied to human heart physiology and the diagnosis and treatment of cardiac disease, has the potential to dramatically change 21st century cardiac research and the field of cardiology.

Personalization of a cardiac electrophysiology model using optical mapping and MRI for prediction of changes with pacing

Computer models of cardiac electrophysiology (EP) can be a very efficient tool to better understand the mechanisms of arrhythmias. Quantitative adjustment of such models to experimental data (personalization) is needed in order to test their realism and predictive power, but it remains challenging at the organ scale. In this paper, we propose a framework for the personalization of a 3-D cardiac EP model, the Mitchell-Schaeffer (MS) model, and evaluate its volumetric predictive power under various pacing scenarios. The personalization was performed on ex vivo large porcine healthy hearts using diffusion tensor MRI (DT-MRI) and optical mapping data. The MS model was simulated on a 3-D mesh incorporating local fiber orientations, built from DT-MRI. The 3-D model parameters were optimized using features such as 2-D epicardial depolarization and repolarization maps, extracted from the optical mapping. We also evaluated the sensitivity of our personalization framework to different pacing locations and showed results on its robustness. Further, we evaluated volumetric model predictions for various epi- and endocardial pacing scenarios. We demonstrated promising results with a mean personalization error around 5 ms and a mean prediction error around 10 ms (5% of the total depolarization time). Finally, we discussed the potential translation of such work to clinical data and pathological hearts.

Image-based models of cardiac structure in health and disease

Computational approaches to investigating the electromechanics of healthy and diseased hearts are becoming essential for the comprehensive understanding of cardiac function. In this article, we first present a brief review of existing image-based computational models of cardiac structure. We then provide a detailed explanation of a processing pipeline which we have recently developed for constructing realistic computational models of the heart from high resolution structural and diffusion tensor (DT) magnetic resonance (MR) images acquired ex vivo. The presentation of the pipeline incorporates a review of the methodologies that can be used to reconstruct models of cardiac structure. In this pipeline, the structural image is segmented to reconstruct the ventricles, normal myocardium, and infarct. A finite element mesh is generated from the segmented structural image, and fiber orientations are assigned to the elements based on DTMR data. The methods were applied to construct seven different models of healthy and diseased hearts. These models contain millions of elements, with spatial resolutions in the order of hundreds of microns, providing unprecedented detail in the representation of cardiac structure for simulation studies.

Influences of sites and protocols on inducing ventricular fibrillation: A computer simulation study

In cardiac electrophysiological study, several electrical stimulation protocols have been employed to induce ventricular fibrillations (VF). In addition, sites of inducing may have different impacts on inducing results as well as different inducing protocols. To study whether VF inducing method is determinant of induced outcome, we simulated VFs induced with different protocols at different sites based on the Wei-Harumi whole heart model. Simulations showed that only certain combinations of pacing protocols and sites could induce sustainable VFs, which had similar frequency distributions. This result suggested that the interactions between protocols and sites determine the odds of successful inducing but once the VF was induced, the pattern was solely determined by inner cardiac properties.

Heterogeneous memory in restitution of action potential duration in pig ventricles

BACKGROUND

Restitution of action potential duration and memory importantly affect electrical stability in ventricles. Studies have reported heterogeneous restitution among different regions of the ventricles. However, existence of heterogeneity in memory is not as well investigated.

METHODS

Transmembrane potentials were recorded in endocardial and epicardial tissues from both ventricles of farm pigs. Pacing protocols with sinusoidally changing diastolic intervals were used to reveal hysteresis in restitution, from which quantitative measures of memory were calculated.

RESULTS

Larger measures of hysteresis were observed in the endocardium than the epicardium (P < .05): loop thickness (in milliseconds), 26.9 vs 16.2; overall tilt, 0.376 vs 0.249; and loop area (in square milliseconds), 7288 vs 4146. Except for overall tilt, no significant differences in these measures were observed between ventricles.

CONCLUSION

Heterogeneity in memory exists in pig ventricles. Because regions with the steepest restitution may also have the largest memory, our results suggest that heterogeneity in memory should also be factored in when predicting electrical stability.

Integrative computational models of cardiac arrhythmias -- simulating the structurally realistic heart

Simulation of cardiac electrical function, and specifically, simulation aimed at understanding the mechanisms of cardiac rhythm disorders, represents an example of a successful integrative multiscale modeling approach, uncovering emergent behavior at the successive scales in the hierarchy of structural complexity. The goal of this article is to present a review of the integrative multiscale models of realistic ventricular structure used in the quest to understand and treat ventricular arrhythmias. It concludes with the new advances in image-based modeling of the heart and the promise it holds for the development of individualized models of ventricular function in health and disease.

Origin of complex behaviour of spatially discordant alternans in a transgenic rabbit model of type 2 long QT syndrome

Enhanced dispersion of repolarization has been proposed as an important mechanism in long QT related arrhythmias. Dispersion can be dynamic and can be augmented with the occurrence of spatially out-of-phase action potential duration (APD) alternans (discordant alternans; DA). We investigated the role of tissue heterogeneity in generating DA using a novel transgenic rabbit model of type 2 long QT syndrome (LQT2). Littermate control (LMC) and LQT2 rabbit hearts (n = 5 for each) were retrogradely perfused and action potentials were mapped from the epicardial surface using di-4-ANEPPS and a high speed CMOS camera. Spatial dispersion (Delta APD and Delta slope of APD restitution) were both increased in LQT2 compared to LMC (Delta APD: 34 +/- 7 ms vs. 23 +/- 6 ms; Delta slope: 1.14 +/- 0.23 vs. 0.59 +/- 0.19). Onset of DA under a ramp stimulation protocol was seen at longer pacing cycle length (CL) in LQT2 compared to LMC hearts (206 +/- 24 ms vs. 156 +/- 5 ms). Nodal lines between regions with APD alternans out of phase from each other were correlated with conduction velocity (CV) alternation in LMC but not in LQT2 hearts. In LQT2 hearts, larger APD dispersion was associated with onset of DA at longer pacing CL. At shorter CLs, closer to ventricular fibrillation induction (VF), nodal lines in LQT2 (n = 2 out of 5) showed persistent complex beat-to-beat changes in nodal line formation of DA associated with competing contribution from CV restitution and tissue spatial heterogeneity, increasing vulnerability to conduction block. In conclusion, tissue heterogeneity plays a significant role in providing substrate for ventricular arrhythmia in LQT2 rabbits by facilitating DA onset and contributing to unstable nodal lines prone to reentry formation.

Interaction of Activation–Repolarization Coupling and Restitution Properties in Humans

Background— Dynamic modulation of repolarization is important in arrhythmogenesis. An inverse relation exists in myocardium between activation time (AT) and action potential duration (APD). We hypothesized that resulting gradients of APD and diastolic interval (DI) interact with restitution properties and modulate the timing of repolarization.

Methods and Results— Activation-recovery intervals (ARI) were acquired from reconstructed noncontact unipolar electrograms from the left ventricular endocardium in 9 patients (7 male) with normal ventricles. At a basic paced cycle length (median, 450 ms), ARIs shortened along the path of activation, with a mandatory reciprocal increase of DIs. In the median patient, this range of DIs started at 230 ms at the site of earliest activation and increased to 279 ms at the site of latest activation at a basic cycle length of 450 ms. Four consecutive standard S1 to S2 restitution curves were performed. At sites with a longer ARI (and therefore shorter DI) close to the site of stimulation, premature stimulation produced more shortening of ARIs; therefore, the time course of restitution was steeper than at more distal sites. At normal heart rate, the decrease in ARIs along the conduction pathway compensated for later activation. Thus, dispersion in repolarization time (RT) is smaller than dispersion in ARI in a heart with a steep negative AT–ARI relationship. This protective effect is lost in hearts without such a relationship. In the patients with a steep AT–ARI relationship at basic cycle length, this relation is lost after premature stimulation and is a function of prematurity. Thus, dispersion in RT is larger after shortly coupled extra stimuli in patients with a steep AT–ARI relationship.

Conclusions— A complex interplay exists between activation–repolarization coupling and restitution properties, largely driven by ARI and DI gradients. This plays a significant role in the dynamics of repolarization in humans.

A computational study of mother rotor VF in the human ventricles

Sudden cardiac death is one of the major causes of death in the industrialized world. It is most often caused by a cardiac arrhythmia called ventricular fibrillation (VF). Despite its large social and economical impact, the mechanisms for VF in the human heart yet remain to be identified. Two of the most frequently discussed mechanisms observed in experiments with animal hearts are the multiple wavelet and mother rotor hypotheses. Most recordings of VF in animal hearts are consistent with the multiple wavelet mechanism. However, in animal hearts, mother rotor fibrillation has also been observed. For both multiple wavelet and mother rotor VF, cardiac heterogeneity plays an important role. Clinical data of action potential restitution measured from the surface of human hearts have been recently published. These in vivo data show a substantial degree of spatial heterogeneity. Using these clinical restitution data, we studied the dynamics of VF in the human heart using a heterogeneous computational model of human ventricles. We hypothesized that this observed heterogeneity can serve as a substrate for mother rotor fibrillation. We found that, based on these data, mother rotor VF can occur in the human heart and that ablation of the mother rotor terminates VF. Furthermore, we found that both mother rotor and multiple wavelet VF can occur in the same heart depending on the initial conditions at the onset of VF. We studied the organization of these two types of VF in terms of filament numbers, excitation periods, and frequency domains. We conclude that mother rotor fibrillation is a possible mechanism in the human heart.

A meta-analysis of cardiac electrophysiology computational models

Computational models of cardiac electrophysiology are exemplar demonstrations of the integration of multiple data sets into a consistent biophysical framework. These models encapsulate physiological understanding to provide quantitative predictions of function. The combination or extension of existing models within a common framework allows integrative phenomena in larger systems to be investigated. This methodology is now routinely applied, as demonstrated by the increasing number of studies which use or extend previously developed models. In this study, we present a meta-analysis of this model re-use for two leading models of cardiac electrophysiology in the form of parameter inheritance trees, a sensitivity analysis and a comparison of the functional significance of the sodium potassium pump for defining restitution curves. These results indicate that even though the models aim to represent the same physiological system, both the sources of parameter values and the function of equivalent components are significantly different.