Photon scattering effects in optical mapping of propagation and arrhythmogenesis in the heart

A comprehensive framework for evaluation of high pacing frequency and arrhythmic optical mapping signals

Introduction: High pacing frequency or irregular activity due to arrhythmia produces complex optical mapping signals and challenges for processing. The objective is to establish an automated activation time-based analytical framework applicable to optical mapping images of complex electrical behavior. Methods: Optical mapping signals with varying complexity from sheep (N = 7) ventricular preparations were examined. Windows of activation centered on each action potential upstroke were derived using Hilbert transform phase. Upstroke morphology was evaluated for potential multiple activation components and peaks of upstroke signal derivatives defined activation time. Spatially and temporally clustered activation time points were grouped in to wave fronts for individual processing. Each activation time point was evaluated for corresponding repolarization times. Each wave front was subsequently classified based on repetitive or non-repetitive events. Wave fronts were evaluated for activation time minima defining sites of wave front origin. A visualization tool was further developed to probe dynamically the ensemble activation sequence. Results: Our framework facilitated activation time mapping during complex dynamic events including transitions to rotor-like reentry and ventricular fibrillation. We showed that using fixed AT windows to extract AT maps can impair interpretation of the activation sequence. However, the phase windowing of action potential upstrokes enabled accurate recapitulation of repetitive behavior, providing spatially coherent activation patterns. We further demonstrate that grouping the spatio-temporal distribution of AT points in to coherent wave fronts, facilitated interpretation of isolated conduction events, such as conduction slowing, and to derive dynamic changes in repolarization properties. Focal origins precisely detected sites of stimulation origin and breakthrough for individual wave fronts. Furthermore, a visualization tool to dynamically probe activation time windows during reentry revealed a critical single static line of conduction slowing associated with the rotation core. Conclusion: This comprehensive analytical framework enables detailed quantitative assessment and visualization of complex electrical behavior.

High resolution optical mapping of cardiac electrophysiology in pre-clinical models

Optical mapping of animal models is a widely used technique in pre-clinical cardiac research. It has several advantages over other methods, including higher spatial resolution, contactless recording and direct visualisation of action potentials and calcium transients. Optical mapping enables simultaneous study of action potential and calcium transient morphology, conduction dynamics, regional heterogeneity, restitution and arrhythmogenesis. In this dataset, we have optically mapped Langendorff perfused isolated whole hearts (mouse and guinea pig) and superfused isolated atria (mouse). Raw datasets (consisting of over 400 files) can be combined with open-source software for processing and analysis. We have generated a comprehensive post-processed dataset characterising the baseline cardiac electrophysiology in these widely used pre-clinical models. This dataset also provides reference information detailing the effect of heart rate, clinically used anti-arrhythmic drugs, ischaemia-reperfusion and sympathetic nervous stimulation on cardiac electrophysiology. The effects of these interventions can be studied in a global or regional manner, enabling new insights into the prevention and initiation of arrhythmia.

Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior

Cardiac arrhythmias are among the leading causes of mortality. They often arise from alterations in the electrophysiological properties of cardiac cells and their underlying ionic mechanisms. It is therefore critical to further unravel the pathophysiology of the ionic basis of human cardiac electrophysiology in health and disease. In the first part of this review, current knowledge on the differences in ion channel expression and properties of the ionic processes that determine the morphology and properties of cardiac action potentials and calcium dynamics from cardiomyocytes in different regions of the heart are described. Then the cellular mechanisms promoting arrhythmias in congenital or acquired conditions of ion channel function (electrical remodeling) are discussed. The focus is on human-relevant findings obtained with clinical, experimental, and computational studies, given that interspecies differences make the extrapolation from animal experiments to human clinical settings difficult. Deepening the understanding of the diverse pathophysiology of human cellular electrophysiology will help in developing novel and effective antiarrhythmic strategies for specific subpopulations and disease conditions.

Examination of the Effects of Conduction Slowing on the Upstroke of Optically Recorded Action Potentials

Introduction

The upstroke of optical action potentials (APs) recorded from intact hearts are generally recognized to be slower than those recorded with microelectrodes. This is thought to reflect spatial signal averaging within the volume of tissue that makes up the optical signal. However, to date, there has been no direct experimental study on the relationship between conduction velocity (CV) and optical AP upstroke morphology in the intact heart. Notably, it is known that sodium channel block and gap junction inhibition, which both slow CV, exert differential effects on the upstroke velocity of microelectrode-recorded APs. Whether such differences are evident in optical APs is not known. The present study sought to determine the relationship between tissue CV and optical AP upstroke velocity in intact mouse hearts.

Materials and Methods

Isolated, perfused mouse hearts were stained with the potentiometric dye Rh-237. Fluorescent signals were recorded from across the anterior surface of the left and right ventricles during constant pacing. Maximum rate of change in fluorescence (dF/dt_max) and tissue CV were assessed in control conditions, during an acute period of low-flow ischemia, and following perfusion of flecainide (1–3 μmol/L), a sodium channel blocker, or carbenoxolone (10–50 μmol/L), a gap junction inhibitor.

Results

During epicardial pacing, an anisotropic pattern was observed in both activation and dF/dt_max maps, with more rapid optical AP upstroke velocities orientated along the fastest conduction paths (and vice versa). Low-flow ischemia resulted in a time-dependent slowing of ventricular CV, which was accompanied by a concomitant reduction in optical AP upstroke velocity. All values returned to baseline on tissue reperfusion. Both flecainide and carbenoxolone were associated with a concentration-dependent reduction in CV and decrease in optical AP upstroke velocity, despite distinct mechanisms of action. Similar responses to carbenoxolone were observed for low- (156 μm pixel with) and high- (20 μm pixel width) magnification recordings. Comparison of data from all interventions revealed a linear relationship between CV and upstroke dF/dt.

Conclusion

In intact mouse hearts, slowing of optical AP upstroke velocity is directly proportional to the change in CV associated with low-flow ischemia, sodium channel block, and gap junction inhibition.

Tissue-Specific Optical Mapping Models of Swine Atria Informed by Optical Coherence Tomography

Computational models and experimental optical mapping of cardiac electrophysiology serve as powerful tools to investigate the underlying mechanisms of arrhythmias. Modeling can also aid the interpretation of optical mapping signals, which may have different characteristics with respect to the underlying electrophysiological signals they represent. However, despite the prevalence of atrial arrhythmias such as atrial fibrillation, models of optical electrical mapping incorporating realistic structure of the atria are lacking. Therefore, we developed image-based models of atrial tissue using structural information extracted from optical coherence tomography (OCT), which can provide volumetric tissue characteristics in high resolution. OCT volumetric data of four swine atrial tissue samples were used to develop models incorporating tissue geometry, tissue-specific myofiber orientation, and ablation lesion regions. We demonstrated the use of these models through electrophysiology and photon scattering simulations. Changes in transmural electrical conduction were observed with the inclusion of OCT-derived, depth-resolved fiber orientation. Additionally, the amplitude of optical mapping signals were not found to correspond with lesion transmurality because of lesion geometry and electrical propagation occurring beyond excitation light penetration. This work established a framework for the development of tissue-specific models of atrial tissue derived from OCT imaging data, which can be useful in future investigations of electrophysiology and optical mapping signals with respect to realistic atrial tissue structure.

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

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

Early afterdepolarizations promote transmural reentry in ischemic human ventricles with reduced repolarization reserve

AIMS

Acute ischemia is a major cause of sudden arrhythmic death, further promoted by potassium current blockers. Macro-reentry around the ischemic region and early afterdepolarizations (EADs) caused by electrotonic current have been suggested as potential mechanisms in animal and isolated cell studies. However, ventricular and human-specific arrhythmia mechanisms and their modulation by repolarization reserve remain unclear. The goal of this paper is to unravel multiscale mechanisms underlying the modulation of arrhythmic risk by potassium current (IKr) block in human ventricles with acute regional ischemia.

METHODS AND RESULTS

A human ventricular biophysically-detailed model, with acute regional ischemia is constructed by integrating experimental knowledge on the electrophysiological ionic alterations caused by coronary occlusion. Arrhythmic risk is evaluated by determining the vulnerable window (VW) for reentry following ectopy at the ischemic border zone. Macro-reentry around the ischemic region is the main reentrant mechanism in the ischemic human ventricle with increased repolarization reserve due to the ATP-sensitive potassium current (IK(ATP)) activation. Prolongation of refractoriness by 4% caused by 30% IKr reduction counteracts the establishment of macro-reentry and reduces the VW for reentry (by 23.5%). However, a further decrease in repolarization reserve (50% IKr reduction) is less anti-arrhythmic despite further prolongation of refractoriness. This is due to the establishment of transmural reentry enabled by electrotonically-triggered EADs in the ischemic border zone. EADs are produced by L-type calcium current (ICaL) reactivation due to prolonged low amplitude electrotonic current injected during the repolarization phase.

CONCLUSIONS

Electrotonically-triggered EADs are identified as a potential mechanism facilitating intramural reentry in a regionally-ischemic human ventricles model with reduced repolarization reserve.

Variability of Action Potentials Within and Among Cardiac Cell Clusters Derived from Human Embryonic Stem Cells

Electrophysiological variability in cardiomyocytes derived from pluripotent stem cells continues to be an impediment for their scientific and translational applications. We studied the variability of action potentials (APs) recorded from clusters of human embryonic stem cell-derived cardiomyocytes (hESC-CMs) using high-resolution optical mapping. Over 23,000 APs were analyzed through four parameters: APD₃₀, APD₈₀, triangulation and fractional repolarization. Although measures were taken to reduce variability due to cell culture conditions and rate-dependency of APs, we still observed significant variability in APs among and within the clusters. However, similar APs were found in spatial locations with close proximity, and in some clusters formed distinct regions having different AP characteristics that were reflected as separate peaks in the AP parameter distributions, suggesting multiple electrophysiological phenotypes. Using a recently developed automated method to group cells based on their entire AP shape, we identified distinct regions of different phenotypes within single clusters and common phenotypes across different clusters when separating APs into 2 or 3 subpopulations. The systematic analysis of the heterogeneity and potential phenotypes of large populations of hESC-CMs can be used to evaluate strategies to improve the quality of pluripotent stem cell-derived cardiomyocytes for use in diagnostic and therapeutic applications and in drug screening.

Imaging of Ventricular Fibrillation and Defibrillation: The Virtual Electrode Hypothesis

Ventricular fibrillation is the major underlying cause of sudden cardiac death. Understanding the complex activation patterns that give rise to ventricular fibrillation requires high resolution mapping of localized activation. The use of multi-electrode mapping unraveled re-entrant activation patterns that underlie ventricular fibrillation. However, optical mapping contributed critically to understanding the mechanism of defibrillation, where multi-electrode recordings could not measure activation patterns during and immediately after a shock. In addition, optical mapping visualizes the virtual electrodes that are generated during stimulation and defibrillation pulses, which contributed to the formulation of the virtual electrode hypothesis. The generation of virtual electrode induced phase singularities during defibrillation is arrhythmogenic and may lead to the induction of fibrillation subsequent to defibrillation. Defibrillating with low energy may circumvent this problem. Therefore, the current challenge is to use the knowledge provided by optical mapping to develop a low energy approach of defibrillation, which may lead to more successful defibrillation.

Fibroblast-myocyte electrotonic coupling: does it occur in native cardiac tissue?

Heterocellular electrotonic coupling between cardiac myocytes and non-excitable connective tissue cells has been a long-established and well-researched fact in vitro. Whether or not such coupling exists in vivo has been a matter of considerable debate. This paper reviews the development of experimental insight and conceptual views on this topic, describes evidence in favour of and against the presence of such coupling in native myocardium, and identifies directions for further study needed to resolve the riddle, perhaps less so in terms of principal presence which has been demonstrated, but undoubtedly in terms of extent, regulation, patho-physiological context, and actual relevance of cardiac myocyte–non-myocyte coupling in vivo. This article is part of a Special Issue entitled "Myocyte-Fibroblast Signalling in Myocardium."

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Electrical coupling of cardiomyocytes and fibroblasts is well-established in vitro

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Whether such hetero-cellular coupling exists in vivo has been a matter of debate

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We review the development of experimental and conceptual insight into the topic

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Conclusion 1: hetero-cellular coupling in heart tissue has been shown in principle

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Conclusion 2: extent, regulation, context, and relevance remain to be established

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.

A novel approach for deriving global activation maps from non-averaged cardiac optical signals

Cardiac arrhythmias are often characterized by non-repetitive complex activation sequences. The properties of electrical activity in cardiac tissue, such as activation time (AT), can be accurately determined using optical imaging of electrical signals using voltage-sensitive dyes. The electrical AT of optical action potentials is known to accurately correlate with the time of the maximal derivative (dF/dt(max)) of the upstroke of ensemble averaged optical signals. The sensitivity of dF/dt(max) to noise is therefore problematic for mapping AT from nonrepetitive activity. Here we experimentally evaluated a novel method to determine activation times (AT) from non-averaged epicardial optical signals. The method depends upon the time delays of activation between adjacent pixels developing a global AT map, as opposed to measuring local AT from each pixel independently based on dF/dt(max). ATs from dF/dt(max) and global AT maps of non-ensemble averaged signals were correlated with averaged signals. Global ATs improved linear correlation coefficients and accuracy of AT patterns. Furthermore, global AT maps were significantly more robust at reproducing AT maps between consecutive stable beats. The proposed method of global AT mapping will potentially enable accurate mapping of non-repetitive propagation during arrhythmias.

Combining wet and dry research: experience with model development for cardiac mechano-electric structure-function studies

Since the development of the first mathematical cardiac cell model 50 years ago, computational modelling has become an increasingly powerful tool for the analysis of data and for the integration of information related to complex cardiac behaviour. Current models build on decades of iteration between experiment and theory, representing a collective understanding of cardiac function. All models, whether computational, experimental, or conceptual, are simplified representations of reality and, like tools in a toolbox, suitable for specific applications. Their range of applicability can be explored (and expanded) by iterative combination of 'wet' and 'dry' investigation, where experimental or clinical data are used to first build and then validate computational models (allowing integration of previous findings, quantitative assessment of conceptual models, and projection across relevant spatial and temporal scales), while computational simulations are utilized for plausibility assessment, hypotheses-generation, and prediction (thereby defining further experimental research targets). When implemented effectively, this combined wet/dry research approach can support the development of a more complete and cohesive understanding of integrated biological function. This review illustrates the utility of such an approach, based on recent examples of multi-scale studies of cardiac structure and mechano-electric function.

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

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

Extracting surface activation time from the optically recorded action potential in three-dimensional myocardium

Optical mapping has become an indispensible tool for studying cardiac electrical activity. However, due to the three-dimensional nature of the optical signal, the optical upstroke is significantly longer than the electrical upstroke. This raises the issue of how to accurately determine the activation time on the epicardial surface. The purpose of this study was to establish a link between the optical upstroke and exact surface activation time using computer simulations, with subsequent validation by a combination of microelectrode recordings and optical mapping experiments. To simulate wave propagation and associated optical signals, we used a hybrid electro-optical model. We found that the time of the surface electrical activation (t(E)) within the accuracy of our simulations coincided with the maximal slope of the optical upstroke (t(F)*) for a broad range of optical attenuation lengths. This was not the case when the activation time was determined at 50% amplitude (t(F50)) of the optical upstroke. The validation experiments were conducted in isolated Langendorff-perfused rat hearts and coronary-perfused pig left ventricles stained with either di-4-ANEPPS or the near-infrared dye di-4-ANBDQBS. We found that t(F)* was a more accurate measure of t(E) than was t(F50) in all experimental settings tested (P = 0.0002). Using t(F)* instead of t(F50) produced the most significant improvement in measurements of the conduction anisotropy and the transmural conduction time in pig ventricles.

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.

Effect of activation sequence on transmural patterns of repolarization and action potential duration in rabbit ventricular myocardium

Although transmural heterogeneity of action potential duration (APD) is established in single cells isolated from different tissue layers, the extent to which it produces transmural gradients of repolarization in electrotonically coupled ventricular myocardium remains controversial. The purpose of this study was to examine the relative contribution of intrinsic cellular gradients of APD and electrotonic influences to transmural repolarization in rabbit ventricular myocardium. Transmural optical mapping was performed in left ventricular wedge preparations from eight rabbits. Transmural patterns of activation, repolarization, and APD were recorded during endocardial and epicardial stimulation. Experimental results were compared with modeled data during variations in electrotonic coupling. A transmural gradient of APD was evident during endocardial stimulation, which reflected differences previously seen in isolated cells, with the longest APD at the endocardium and the shortest at the epicardium (endo: 165 ± 5 vs. epi: 147 ± 4 ms; P < 0.05). During epicardial stimulation, this gradient reversed (epi: 162 ± 4 vs. endo: 148 ± 6 ms; P < 0.05). In both activation sequences, transmural repolarization followed activation and APD shortened along the activation path such that significant transmural gradients of repolarization did not occur. This correlation between transmural activation time and APD was recapitulated in simulations and varied with changes in intercellular coupling, confirming that it is mediated by electrotonic current flow between cells. These data suggest that electrotonic influences are important in determining the transmural repolarization sequence in rabbit ventricular myocardium and that they are sufficient to overcome intrinsic differences in the electrophysiological properties of the cells across the ventricular wall.

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.

Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.