Vulnerability to reentry in a regionally ischemic tissue: a simulation study

The mechanisms of potassium loss in acute myocardial ischemia: New insights from computational simulations

Acute myocardial ischemia induces hyperkalemia (accumulation of extracellular potassium), a major perpetrator of lethal reentrant ventricular arrhythmias. Despite considerable experimental efforts to explain this pathology in the last decades, the intimate mechanisms behind hyperkalemia remain partially unknown. In order to investigate these mechanisms, we developed a novel computational model of acute myocardial ischemia which couples a) an electrophysiologically detailed human cardiomyocyte model that incorporates modifications to account for ischemia-induced changes in transmembrane currents, with b) a model of cardiac tissue and extracellular K ⁺ transport. The resulting model is able to reproduce and explain the triphasic time course of extracellular K ⁺ concentration within the ischemic zone, with values of [ K + ] o close to 14 mmol/L in the central ischemic zone after 30 min. In addition, the formation of a [ K + ] o border zone of approximately 1.2 cm 15 min after the onset of ischemia is predicted by the model. Our results indicate that the primary rising phase of [ K + ] o is mainly due to the imbalance between K ⁺ efflux, that increases slightly, and K ⁺ influx, that follows a reduction of the NaK pump activity by more than 50%. The onset of the plateau phase is caused by the appearance of electrical alternans (a novel mechanism identified by the model), which cause an abrupt reduction in the K ⁺ efflux. After the plateau, the secondary rising phase of [ K + ] o is caused by a subsequent imbalance between the K ⁺ influx, which continues to decrease slowly, and the K ⁺ efflux, which remains almost constant. Further, the study shows that the modulation of these mechanisms by the electrotonic coupling is the main responsible for the formation of the ischemic border zone in tissue, with K ⁺ transport playing only a minor role. Finally, the results of the model indicate that the injury current established between the healthy and the altered tissue is not sufficient to depolarize non-ischemic cells within the healthy tissue.

Mechanisms of ventricular arrhythmias elicited by coexistence of multiple electrophysiological remodeling in ischemia: A simulation study

Myocardial ischemia, injury and infarction (MI) are the three stages of acute coronary syndrome (ACS). In the past two decades, a great number of studies focused on myocardial ischemia and MI individually, and showed that the occurrence of reentrant arrhythmias is often associated with myocardial ischemia or MI. However, arrhythmogenic mechanisms in the tissue with various degrees of remodeling in the ischemic heart have not been fully understood. In this study, biophysical detailed single-cell models of ischemia 1a, 1b, and MI were developed to mimic the electrophysiological remodeling at different stages of ACS. 2D tissue models with different distributions of ischemia and MI areas were constructed to investigate the mechanisms of the initiation of reentrant waves during the progression of ischemia. Simulation results in 2D tissues showed that the vulnerable windows (VWs) in simultaneous presence of multiple ischemic conditions were associated with the dynamics of wave propagation in the tissues with each single pathological condition. In the tissue with multiple pathological conditions, reentrant waves were mainly induced by two different mechanisms: one is the heterogeneity along the excitation wavefront, especially the abrupt variation in conduction velocity (CV) across the border of ischemia 1b and MI, and the other is the decreased safe factor (SF) for conduction at the edge of the tissue in MI region which is attributed to the increased excitation threshold of MI region. Finally, the reentrant wave was observed in a 3D model with a scar reconstructed from MRI images of a MI patient. These comprehensive findings provide novel insights for understanding the arrhythmic risk during the progression of myocardial ischemia and highlight the importance of the multiple pathological stages in designing medical therapies for arrhythmias in ischemia.

Analysis of vulnerability to reentry in acute myocardial ischemia using a realistic human heart model

Electrophysiological alterations of the myocardium caused by acute ischemia constitute a pro-arrhythmic substrate for the generation of potentially lethal arrhythmias. Experimental evidence has shown that the main components of acute ischemia that induce these electrophysiological alterations are hyperkalemia, hypoxia (or anoxia in complete artery occlusion), and acidosis. However, the influence of each ischemic component on the likelihood of reentry is not completely established. Moreover, the role of the His-Purkinje system (HPS) in the initiation and maintenance of arrhythmias is not completely understood. In the present work, we investigate how the three components of ischemia affect the vulnerable window (VW) for reentry using computational simulations. In addition, we analyze the role of the HPS on arrhythmogenesis. A 3D biventricular/torso human model that includes a realistic geometry of the central and border ischemic zones with one of the most electrophysiologically detailed model of ischemia to date, as well as a realistic cardiac conduction system, were used to assess the VW for reentry. Four scenarios of ischemic severity corresponding to different minutes after coronary artery occlusion were simulated. Our results suggest that ischemic severity plays an important role in the generation of reentries. Indeed, this is the first 3D simulation study to show that ventricular arrhythmias could be generated under moderate ischemic conditions, but not in mild and severe ischemia. Moreover, our results show that anoxia is the ischemic component with the most significant effect on the width of the VW. Thus, a change in the level of anoxia from moderate to severe leads to a greater increment in the VW (40 ms), in comparison with the increment of 20 ms and 35 ms produced by the individual change in the level of hyperkalemia and acidosis, respectively. Finally, the HPS was a necessary element for the generation of approximately 17% of reentries obtained. The retrograde conduction from the myocardium to HPS in the ischemic region, conduction blocks in discrete sections of the HPS, and the degree of ischemia affecting Purkinje cells, are suggested as mechanisms that favor the generation of ventricular arrhythmias.

Pro-arrhythmic Effects of Hydrogen Sulfide in Healthy and Ischemic Cardiac Tissues: Insight From a Simulation Study

Hydrogen sulfide (H₂S), an ambient air pollutant, has been reported to increase cardiac events in patients with cardiovascular diseases, but the underlying mechanisms remain not elucidated. This study investigated the pro-arrhythmic effects of H₂S in healthy and ischemic conditions. Experimental data of H₂S effects on ionic channels (including the L-type Ca²⁺ channel and ATP-sensitive K⁺ channel) were incorporated into a virtual heart model to evaluate their integral action on cardiac arrhythmogenesis. It was shown that H₂S depressed cellular excitability, abbreviated action potential duration, and augmented tissue’s transmural dispersion of repolarization, resulting in an increase in tissue susceptibility to initiation and maintenance of reentry. The observed effects of H₂S on cardiac excitation are more remarkable in the ischemic condition than in the healthy condition. This study provides mechanistic insights into the pro-arrhythmic effects of air pollution (H₂S), especially in the case with extant ischemic conditions.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia

Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.

Post-repolarization refractoriness increases vulnerability to block and initiation of reentrant impulses in heterogeneous infarcted myocardium

Myocardial infarction causes remodeling of the tissue structure and the density and kinetics of several ion channels in the cell membrane. Heterogeneities in refractory period (ERP) have been shown to occur in the infarct border zone and have been proposed to lead to initiation of arrhythmias. The purpose of this study is to quantify the window of vulnerability (WV) to block and initiation of reentrant impulses in myocardium with ERP heterogeneities using computer simulations. We found that ERP transitions at the border between normal ventricular cells (NZ) with different ERPs are smooth, whereas ERP transitions between NZ and infarct border zone cells (IZ) are abrupt. The profile of the ERP transitions is a combination of electrotonic interaction between NZ and IZ cells and the characteristic post-repolarization refractoriness (PRR) of IZ cells. ERP heterogeneities between NZ and IZ cells are more vulnerable to block and initiation of reentrant impulses than ERP heterogeneities between NZ cells. The relationship between coupling intervals of premature impulses (V1V2) and coupling intervals between premature and first reentrant impulses (V2T1) at NZ/NZ and NZ/IZ borders is inverse (i.e. the longer the coupling intervals of premature impulses the shorter the coupling interval between the premature and first reentrant impulses); this is in contrast with the reported V1V2/V2T1 relationship measured during initiation of reentrant impulses in canine infarcted hearts which is direct.

IN CONCLUSION

(1) ERP transitions at the NZ-IZ border are abrupt as a consequence of PRR; (2) PRR increases the vulnerability to block and initiation of reentrant impulses in heterogeneous myocardium; (3) V1V2/V2T1 relationships measured at ERP heterogeneities in the computer model and in experimental canine infarcts are not consistent. Therefore, it is likely that other mechanisms like micro and/or macro structural heterogeneities also contribute to initiation of reentrant impulses in infarcted hearts.

EFFECTS OF ACUTE GLOBAL ISCHEMIA ON RE-ENTRANT ARRHYTHMOGENESIS: A SIMULATION STUDY

Sudden cardiac death is mainly caused by arrhythmogenesis. For a functional abnormal heart, such as an ischemic heart, the probability of arrhythmia occurring is greatly increased. During myocardial ischemia, re-entry is prone to degenerate into ventricular fibrillation (VF). Therefore it has important meaning to investigate the intricate mechanisms underlying VF under an ischemic condition in order to better facilitate therapeutic interventions. In this paper, to analyze the functional influence of acute global ischemia on cardiac electrical activity and subsequently on re-entrant arrhythmogenesis, we take into account three main pathophysiological consequences of ischemia: hyperkalaemia, acidosis, and anoxia, and develop a 3D human ventricular ischemic model that combines a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue which incorporates fiber direction anisotropy and the stimulation activation sequence. The results show that under acute global ischemia, the tissue excitability and the slope of ventricular cellular action potential duration restitution (APDR) are greatly decreased. As a result, the complexity of VF activation patterns is reduced. For the three components of ischemia, hyperkalaemia is the dominant contributor to the stability of re-entry under acute global ischemia. Increasing [K+]o acts to prolong the cell refractory period, reduce the tissue excitability and slow the conduction velocity. Our results also show that VF can be eliminated by decreasing cellular excitability, primarily by elevating the concentration value of extracellular K+.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Multiscale computational analysis of the bioelectric consequences of myocardial ischaemia and infarction

Ischaemic heart disease is considered as the single most frequent cause of death, provoking more than 7 000 000 deaths every year worldwide. A high percentage of patients experience sudden cardiac death, caused in most cases by tachyarrhythmic mechanisms associated to myocardial ischaemia and infarction. These diseases are difficult to study using solely experimental means due to their complex dynamics and unstable nature. In the past decades, integrative computational simulation techniques have become a powerful tool to complement experimental and clinical research when trying to elucidate the intimate mechanisms of ischaemic electrophysiological processes and to aid the clinician in the improvement and optimization of therapeutic procedures. The purpose of this paper is to briefly review some of the multiscale computational models of myocardial ischaemia and infarction developed in the past 20 years, ranging from the cellular level to whole-heart simulations.

In silico ischaemia-induced reentry at the Purkinje-ventricle interface

AIMS

This computational modelling work illustrates the influence of hyperkalaemia and electrical uncoupling induced by defined ischaemia on action potential (AP) propagation and the incidence of reentry at the Purkinje-ventricle interface in mammalian hearts.

METHODS AND RESULTS

Unidimensional and bidimensional models of the Purkinje-ventricle subsystem, including ischaemic conditions (defined as phase 1B) in the ventricle and an ischaemic border zone, were developed by altering several important electrophysiological parameters of the Luo-Rudy AP model of the ventricular myocyte. Purkinje electrical activity was modelled using the equations of DiFrancesco and Noble. Our study suggests that an extracellular potassium concentration [K(+)]o >14 mM and a slight decrease in intercellular coupling induced by ischaemia in ventricle can cause conduction block from Purkinje to ventricle. Under these conditions, propagation from ventricle to Purkinje is possible. Thus, unidirectional block (UDB) and reentry can result. When conditions of UDB are met, retrograde propagation with a long delay (320 ms) may re-excite Purkinje cells, and give rise to a reentrant pathway. This induced reentry may be the origin of arrhythmias observed in phase 1B ischaemia.

CONCLUSION

In a defined setting of ischaemia (phase 1B), a small amount of uncoupling between ventricular cells, as well as between Purkinje and ventricular tissue, may induce UDBs and reentry. Hyperkalaemia is also confirmed to be an important factor in the genesis of reentrant rhythms, since it regulates the range of coupling in which UDBs may be induced.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

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.

Automaticity in acute ischemia: bifurcation analysis of a human ventricular model

Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([K(o)(+)]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an "injury current" (I(S)) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels (I(Katp)). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model [K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 291, H1088 (2006)] as a function of three ischemia-relevant parameters [K(o)(+)], I(S), and I(Katp). In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [K(o)(+)] and I(Katp) significantly altered the bifurcation structure of I(S), including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart.

Exploring the role of pH in modulating the effects of lidocaine in virtual ischemic tissue

Lidocaine is a class I antiarrhytmic drug that blocks Na(+) channels and exists in both neutral and charged forms at a physiological pH. In this work, a mathematical model of pH and the frequency-modulated effects of lidocaine has been developed and incorporated into the Luo-Rudy model of the ventricular action potential. We studied the effects of lidocaine on Na(+) current, maximum upstroke velocity, and conduction velocity and demonstrated that a decrease of these parameters was dependent on pH, frequency, and concentration. We also tested the action of lidocaine under pathological conditions. Specifically, we investigated its effects on conduction block under acute regional ischemia. Our results in one-dimensional fiber simulations showed a reduction of the window of block in the presence of lidocaine, thereby highlighting the role of reduced conduction velocity and safe conduction. This reduction may be related to the antifibrillatory effects of the drug by hampering wavefront fragmentation. In bidimensional acute ischemic tissue, lidocaine increased the vulnerable window for reentry and exerted proarrhythmic effects. In conclusion, the present simulation study used a newly formulated model of lidocaine, which considers pH and frequency modulation, and revealed the mechanisms by which lidocaine facilitates the onset of reentries. The results of this study also help to increase our understanding of the potential antifibrillatory effects of the drug.

Mechanisms for initiation of reentry in acute regional ischemia phase 1B

BACKGROUND

During phase 1B of acute regional ischemia, the subepicardial and subendocardial layers coupled to the inexcitable midmyocardium remain viable.

OBJECTIVE

The purpose of this study was to examine how the degree of hyperkalemia in the surviving layers, the lateral width of border zone between the normal tissue and the central ischemic zone, and the degree of cellular uncoupling between the surviving layers and the midmyocardium contribute to initiation of reentry.

METHODS

Simulations were conducted on the state-of-the-art model of rabbit ventricles with realistic representation of the spatial distribution of the ischemic insult.

RESULTS

Hyperkalemia in the surviving layers led to induction of reentry by increasing refractoriness and slowing conduction in the layers. Such reentries were formed solely in the subepicardium. A minimal level of hyperkalemia was required for induction of reentry. Progress increase in hyperkalemia led to a biphasic change in vulnerability to reentry. For each level of hyperkalemia, increased cellular uncoupling between subepicardium and midmyocardium increased inducibility of reentry by restoring subepicardial tissue excitability via blocking midmyocardial electrotonic effect. In addition, increased lateral width of the border zone prevented inducibility of reentry as conduction block occurred in the central ischemic zone when the wave propagated across the border zone from the normal zone.

CONCLUSION

The degree of hyperkalemia in the surviving subepicardium, the lateral width of border zone, and cellular uncoupling between the subepicardium and midmyocardium determine dispersion of refractoriness, conduction velocity, excitability, and, therefore, inducibility of reentry during phase 1B.

Modeling of cardiac ischemia in human myocytes and tissue including spatiotemporal electrophysiological variations

Cardiac tissue exhibits spatially heterogeneous electrophysiological properties. In cardiac diseases, these properties also change in time. This study introduces a framework to investigate their role in cardiac ischemia using mathematical modeling and computational simulations at cellular and tissue level. Ischemia was incorporated by reproducing effects of hyperkalemia, acidosis, and hypoxia with a human electrophysiological model. In tissue, spatial heterogeneous ischemia was described by central ischemic (CIZ) and border zone. Anisotropic conduction was simulated with a bidomain approach in an anatomical ventricle model including realistic fiber orientation and transmural, apico-basal, and interventricular electrophysiological heterogeneities. A model of electrical conductivity in a human torso served for ECG calculations. Ischemia increased resting but reduced peak voltage, action potential duration, and upstroke velocity. These effects were strongest in subepicardial cells. In tissue, conduction velocity decreased towards CIZ but effective refractory period increased. At 10 min of ischemia 19% of subepi- and 100% of subendocardial CIZ cells activated with a delay of 34.6+/-7.8 ms and 55.9+/-18.8 ms, respectively, compared to normal. Significant ST elevation and premature T wave end appeared only with the subepicardial CIZ. The model reproduced effects of ischemia at cellular and tissue level. The results suggest that the presented in silico approach can complement experimental studies, e.g., in understanding the role of ischemia or the onset of arrhythmia.

The relative role of refractoriness and source-sink relationship in reentry generation during simulated acute ischemia

During acute myocardial ischemia, reentrant episodes may lead to ventricular fibrillation (VF), giving rise to potentially mortal arrhythmias. VF has been traditionally related to dispersion of refractoriness and more recently to the source-sink relationship. Our goal is to theoretically investigate the relative role of dispersion of refractoriness and source-sink mismatch in vulnerability to reentry in the specific situation of regional myocardial acute ischemia. The electrical activity of a regionally ischemic tissue was simulated using a modified version of the Luo-Rudy dynamic model. Ischemic conditions were varied to simulate the time-course of acute ischemia. Our results showed that dispersion of refractoriness increased with the severity of ischemia. However, no correlation between dispersion of refractoriness and the width of the vulnerable window was found. Additionally, in approximately 50% of the reentries, unidirectional block (UDB) took place in cells completely recovered from refractoriness. We examined patterns of activation after premature stimulation and they were intimately related to the source-sink relationship, quantified by the safety factor (SF). Moreover, the isoline where the SF dropped below unity matched the area where propagation failed. It was concluded that the mismatch of the source-sink relationship, rather than solely refractoriness, was the ultimate cause of the UDB leading to reentry. The SF represents a very powerful tool to study the mechanisms responsible for reentry.