Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

The relative role of patient physiology and device optimisation in cardiac resynchronisation therapy: A computational modelling study

Cardiac resynchronisation therapy (CRT) is an established treatment for heart failure, however the effective selection of patients and optimisation of therapy remain controversial. While extensive research is ongoing, it remains unclear whether improvements in patient selection or therapy planning offers a greater opportunity for the improvement of clinical outcomes. This computational study investigates the impact of both physiological conditions that guide patient selection and the optimisation of pacing lead placement on CRT outcomes. A multi-scale biophysical model of cardiac electromechanics was developed and personalised to patient data in three patients. These models were separated into components representing cardiac anatomy, pacing lead location, myocardial conductivity and stiffness, afterload, active contraction and conduction block for each individual, and recombined to generate a cohort of 648 virtual patients. The effect of these components on the change in total activation time of the ventricles (ΔTAT) and acute haemodynamic response (AHR) was analysed. The pacing site location was found to have the largest effect on ΔTAT and AHR. Secondary effects on ΔTAT and AHR were found for functional conduction block and cardiac anatomy. The simulation results highlight a need for a greater emphasis on therapy optimisation in order to achieve the best outcomes for patients.

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Ventricular conduction block indicates patient response to CRT.

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Placement of CRT pacing leads strongly affects response to therapy.

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Improved treatment planning should be prioritised in order to maximise CRT outcomes.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

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

Local Gradients in Electrotonic Loading Modulate the Local Effective Refractory Period: Implications for Arrhythmogenesis in the Infarct Border Zone

Ectopic electrical activity that originates in the peri-infarct region can give rise to potentially lethal re-entrant arrhythmias. The spatial variation in electrotonic loading that results from structural remodelling in the infarct border zone may increase the probability that focal activity will trigger electrical capture, but this has not previously been investigated systematically. This study uses in-silico experiments to examine the structural modulation of effective refractory period on ectopic beat capture. Informed by 3-D reconstructions of myocyte organization in the infarct border zone, a region of rapid tissue expansion is abstracted to an idealized representation. A novel metric is introduced that defines the local electrotonic loading as a function of passive tissue properties and boundary conditions. The effective refractory period correlates closely with local electrotonic loading, while the action potential duration, conduction, and upstroke velocity reduce in regions of increasing electrotonic load. In the presence of focal ectopic stimuli, spatial variation in effective refractory period can cause unidirectional conduction block providing a substrate for reentrant arrhythmias. Consequently, based on the observed results, a possible novel mechanism for arrhythmogenesis in the infarct border zone is proposed.

Beneficial Effect on Cardiac Resynchronization From Left Ventricular Endocardial Pacing Is Mediated by Early Access to High Conduction Velocity Tissue: Electrophysiological Simulation Study

BACKGROUND

Cardiac resynchronization therapy (CRT) delivered via left ventricular (LV) endocardial pacing (ENDO-CRT) is associated with improved acute hemodynamic response compared with LV epicardial pacing (EPI-CRT). The role of cardiac anatomy and physiology in this improved response remains controversial. We used computational electrophysiological models to quantify the role of cardiac geometry, tissue anisotropy, and the presence of fast endocardial conduction on myocardial activation during ENDO-CRT and EPI-CRT.

METHODS AND RESULTS

Cardiac activation was simulated using the monodomain tissue excitation model in 2-dimensional (2D) canine and human and 3D canine biventricular models. The latest activation times (LATs) for LV endocardial and biventricular epicardial tissue were calculated (LVLAT and TLAT), as well the percentage decrease in LATs for endocardial (en) versus epicardial (ep) LV pacing (defined as %dLV=100×(LVLATep-LVLATen)/LVLATep and %dT=100×(TLATep-TLATen)/TLATep, respectively). Normal canine cardiac anatomy is responsible for %dLV and %dT values of 7.4% and 5.5%, respectively. Concentric and eccentric remodeled anatomies resulted in %dT values of 15.6% and 1.3%, respectively. The 3D biventricular-paced canine model resulted in %dLV and %dT values of -7.1% and 1.5%, in contrast to the experimental observations of 16% and 11%, respectively. Adding fast endocardial conduction to this model altered %dLV and %dT to 13.1% and 10.1%, respectively.

CONCLUSIONS

Our results provide a physiological explanation for improved response to ENDO-CRT. We predict that patients with viable fast-conducting endocardial tissue or distal Purkinje network or both, as well as concentric remodeling, are more likely to benefit from reduced ATs and increased synchrony arising from endocardial pacing.

Stochastic spontaneous calcium release events trigger premature ventricular complexes by overcoming electrotonic load

AIMS

Premature ventricular complexes (PVCs) due to spontaneous calcium (Ca) release (SCR) events at the cell level can precipitate ventricular arrhythmias. However, the mechanistic link between SCRs and PVC formation remains incompletely understood. The aim of this study was to investigate the conditions under which delayed afterdepolarizations resulting from stochastic subcellular SCR events can overcome electrotonic source-sink mismatch, leading to PVC initiation.

METHODS AND RESULTS

A stochastic subcellular-scale mathematical model of SCR was incorporated in a realistic model of the rabbit ventricles and Purkinje system (PS). Elevated levels of diastolic sarcoplasmic reticulum Ca(2+) (CaSR) were imposed until triggered activity was observed, allowing us to compile statistics on probability, timing, and location of PVCs. At CaSR≥ 1500 µmol/L PVCs originated in the PS. When SCR was incapacitated in the PS, PVCs also emerged in the ventricles, but at a higher CaSR (≥1550 µmol/L) and with longer waiting times. For each model configuration tested, the probability of PVC occurrence increased from 0 to 100% within a well-defined critical CaSR range; this transition was much more abrupt in organ-scale models (∼50 µmol/L CaSR range) than in the tissue strand (∼100 µmol/L) or single-cell (∼450 µmol/L) models. Among PVCs originating in the PS, ∼68% were located near Purkinje-ventricular junctions (<1 mm).

CONCLUSION

SCR events overcome source-sink mismatch to trigger PVCs at a critical CaSR threshold. Above this threshold, PVCs emerge due to increased probability and reduced variability in timing of SCR events, leading to significant diastolic depolarization. Sites of lower electronic load, such as the PS, are preferential locations for triggering.

Three-dimensional atrial wall thickness maps to inform catheter ablation procedures for atrial fibrillation

AIMS

Transmural lesion formation is critical to success in atrial fibrillation ablation and is dependent on left atrial wall thickness (LAWT). Pre- and peri-procedural planning may benefit from LAWT measurements.

METHODS AND RESULTS

To calculate the LAWT, the Laplace equation was solved over a finite element mesh of the left atrium derived from the segmented computed tomographic angiography (CTA) dataset. Local LAWT was then calculated from the length of field lines derived from the Laplace solution that spanned the wall from the endocardium or epicardium. The method was validated on an atrium phantom and retrospectively applied to 10 patients who underwent routine coronary CTA for standard clinical indications at our institute. The Laplace wall thickness algorithm was validated on the left atrium phantom. Wall thickness measurements had errors of <0.2 mm for thicknesses of 0.5-5.0 mm that are attributed to image resolution and segmentation artefacts. Left atrial wall thickness measurements were performed on 10 patients. Successful comprehensive LAWT maps were generated in all patients from the coronary CTA images. Mean LAWT measurements ranged from 0.6 to 1.0 mm and showed significant inter and intra patient variability.

CONCLUSIONS

Left atrial wall thickness can be measured robustly and efficiently across the whole left atrium using a solution of the Laplace equation over a finite element mesh of the left atrium. Further studies are indicated to determine whether the integration of LAWT maps into pre-existing 3D anatomical mapping systems may provide important anatomical information for guiding radiofrequency ablation.

Structural heterogeneity modulates effective refractory period: a mechanism of focal arrhythmia initiation

Reductions in electrotonic loading around regions of structural and electrophysiological heterogeneity may facilitate capture of focal triggered activity, initiating reentrant arrhythmias. How electrotonic loading, refractoriness and capture of focal ectopics depend upon the intricate nature of physiological structural anatomy, as well as pathological tissue remodelling, however, is not well understood. In this study, we performed computational bidomain simulations with anatomically-detailed models representing the rabbit left ventricle. We used these models to quantify the relationship between local structural anatomy and spatial heterogeneity in action potential (AP) characteristics, electrotonic currents and effective refractory periods (ERPs) under pacing and restitution protocols. Regions surrounding vessel cavities, in addition to tissue surfaces, had significantly lower peak downstream electrotonic currents than well coupled myocardium ( vs A/cm²), with faster maximum AP upstroke velocities ( vs mV/ms), although noticeably very similar APDs ( vs ms) and AP restitution properties. Despite similarities in APDs, ERPs in regions of low electrotonic load in the vicinity of surfaces, intramural vessel cavities and endocardial structures were up to ms shorter compared to neighbouring well-coupled tissue, leading to regions of sharp ERP gradients. Consequently, focal extra-stimuli timed within this window of ERP heterogeneity between neighbouring regions readily induced uni-directional block, inducing reentry. Most effective induction sites were within channels of low ERPs between large vessels and epicardium. Significant differences in ERP driven by reductions in electrotonic loading due to fine-scale physiological structural heterogeneity provides an important mechanism of capture of focal activity and reentry induction. Application to pathological ventricles, particularly myocardial infarction, will have important implications in anti-arrhythmia therapy.

Simulating photon scattering effects in structurally detailed ventricular models using a Monte Carlo approach

Light scattering during optical imaging of electrical activation within the heart is known to significantly distort the optically-recorded action potential (AP) upstroke, as well as affecting the magnitude of the measured response of ventricular tissue to strong electric shocks. Modeling approaches based on the photon diffusion equation have recently been instrumental in quantifying and helping to understand the origin of the resulting distortion. However, they are unable to faithfully represent regions of non-scattering media, such as small cavities within the myocardium which are filled with perfusate during experiments. Stochastic Monte Carlo (MC) approaches allow simulation and tracking of individual photon “packets” as they propagate through tissue with differing scattering properties. Here, we present a novel application of the MC method of photon scattering simulation, applied for the first time to the simulation of cardiac optical mapping signals within unstructured, tetrahedral, finite element computational ventricular models. The method faithfully allows simulation of optical signals over highly-detailed, anatomically-complex MR-based models, including representations of fine-scale anatomy and intramural cavities. We show that optical action potential upstroke is prolonged close to large subepicardial vessels than further away from vessels, at times having a distinct “humped” morphology. Furthermore, we uncover a novel mechanism by which photon scattering effects around vessels cavities interact with “virtual-electrode” regions of strong de-/hyper-polarized tissue surrounding cavities during shocks, significantly reducing the apparent optically-measured epicardial polarization. We therefore demonstrate the importance of this novel optical mapping simulation approach along with highly anatomically-detailed models to fully investigate electrophysiological phenomena driven by fine-scale structural heterogeneity.

An efficient finite element approach for modeling fibrotic clefts in the heart

Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.

Influence of the Purkinje-muscle junction on transmural repolarization heterogeneity

AIMS

To elucidate the properties of the PMJ and myocardium underlying these effects. Transmural heterogeneity of action potential duration (APD) is known to play an important role in arrhythmogenesis. Regions of non-uniformities of APD gradients often overlap considerably with the location of Purkinje-muscle junctions (PMJs). We therefore hypothesized that such junctions are novel sources of local endocardial and transmural heterogeneity of repolarization, and that remodelling due to heart failure modulates this response.

METHODS AND RESULTS

Spatial gradients of endocardial APD in left ventricular wedge preparations from healthy sheep (n = 5) were correlated with locations of PMJs identified through Purkinje stimulation under optical mapping. APD prolongation was dependent on proximity of the PMJ to the imaged surface, whereby shallow PMJs significantly modulated local APD when stimulating either Purkinje (P = 0.0116) or endocardium (P = 0.0123). In addition, we model a PMJ in 5 × 5× 10 mm transmural tissue wedges using healthy and novel failing human ventricular and Purkinje ionic models. Short distances of the PMJ to cut surfaces (<0.875 mm) revealed that APD maxima were localized to the PMJ in healthy myocardium, whereas APD minima were observed in failing myocardium. Amplitudes and spatial gradients of APD were prominent at functional PMJs and quiescent PMJs. Furthermore, increasing the extent of Purkinje fibre branching or decreasing tissue conductivity augmented local APD prolongation in both failing and non-failing models.

CONCLUSIONS

The Purkinje network has the potential to influence myocardial AP morphology and rate-dependent behaviour, and furthermore to underlie enhanced transmural APD heterogeneities and spatial gradients of APD in non-failing and failing myocardium.

Sensitivity and specificity of substrate mapping: an in silico framework for the evaluation of electroanatomical substrate mapping strategies

BACKGROUND

Voltage mapping is an important tool for characterizing proarrhythmic electrophysiological substrate, yet it is subject to geometric factors that influence bipolar amplitudes and thus compromise performance. The aim of this study was to characterize the impact of catheter orientation on the ability of bipolar amplitudes to accurately discriminate between healthy and diseased tissues.

METHODS AND RESULTS

We constructed a 3-dimensional, in silico, bidomain model of cardiac tissue containing transmural lesions of varying diameter. A planar excitation wave was stimulated and electrograms were sampled with a realistic catheter model at multiple positions and orientations. We carried out validation studies in animal experiments of acute ablation lesions mapped with a clinical mapping system. Bipolar electrograms sampled at higher inclination angles of the catheter with respect to the tissue demonstrated improvements in both sensitivity and specificity of lesion detection. Removing low-voltage electrograms with concurrent activation of both electrodes, suggesting false attenuation of the bipolar electrogram due to alignment with the excitation wavefront, had little effect on the accuracy of voltage mapping.

CONCLUSIONS

Our results demonstrate possible mechanisms for the impact of catheter orientation on voltage mapping accuracy. Moreover, results from our simulations suggest that mapping accuracy may be improved by selectively controlling the inclination of the catheter to record at higher angles with respect to the tissue.

Mechanism of reentry induction by a 9-V battery in rabbit ventricles

Although the application of a 9-V battery to the epicardial surface is a simple method of ventricular fibrillation induction, the fundamental mechanisms underlying this process remain unstudied. We used a combined experimental and modelling approach to understand how the interaction of direct current (DC) from a battery may induce reentrant activity within rabbit ventricles and its dependence on battery application timing and duration. A rabbit ventricular computational model was used to simulate 9-V battery stimulation for different durations at varying onset times during sinus rhythm. Corresponding high-resolution optical mapping measurements were conducted on rabbit hearts with DC stimuli applied via a relay system. DC application to diastolic tissue induced anodal and cathodal make excitations in both simulations and experiments. Subsequently, similar static epicardial virtual electrode patterns were formed that interacted with sinus beats but did not induce reentry. Upon battery release during diastole, break excitations caused single ectopics, similar to application, before sinus rhythm resumed. Reentry induction was possible for short battery applications when break excitations were slowed and forced to take convoluted pathways upon interaction with refractory tissue from prior make excitations or sinus beats. Short-lived reentrant activity could be induced for battery release shortly after a sinus beat for longer battery applications. In conclusion, the application of a 9-V battery to the epicardial surface induces reentry through a complex interaction of break excitations after battery release with prior induced make excitations or sinus beats.

Mechanistic inquiry into the role of tissue remodeling in fibrotic lesions in human atrial fibrillation

Atrial fibrillation (AF), the most common arrhythmia in humans, is initiated when triggered activity from the pulmonary veins propagates into atrial tissue and degrades into reentrant activity. Although experimental and clinical findings show a correlation between atrial fibrosis and AF, the causal relationship between the two remains elusive. This study used an array of 3D computational models with different representations of fibrosis based on a patient-specific atrial geometry with accurate fibrotic distribution to determine the mechanisms by which fibrosis underlies the degradation of a pulmonary vein ectopic beat into AF. Fibrotic lesions in models were represented with combinations of: gap junction remodeling; collagen deposition; and myofibroblast proliferation with electrotonic or paracrine effects on neighboring myocytes. The study found that the occurrence of gap junction remodeling and the subsequent conduction slowing in the fibrotic lesions was a necessary but not sufficient condition for AF development, whereas myofibroblast proliferation and the subsequent electrophysiological effect on neighboring myocytes within the fibrotic lesions was the sufficient condition necessary for reentry formation. Collagen did not alter the arrhythmogenic outcome resulting from the other fibrosis components. Reentrant circuits formed throughout the noncontiguous fibrotic lesions, without anchoring to a specific fibrotic lesion.

Effects of regional mitochondrial depolarization on electrical propagation: implications for arrhythmogenesis

BACKGROUND

Sudden cardiac death often involves arrhythmias triggered by metabolic stress. Loss of mitochondrial function is thought to contribute to the arrhythmogenic substrate, but how mitochondria contribute to uncoordinated electrical activity is poorly understood. It has been proposed that the formation of metabolic current sinks, caused by the nonuniform collapse of mitochondrial inner membrane potential (ΔΨm), contributes to re-entrant arrhythmias because ΔΨm depolarization is tightly coupled to the activation of sarcolemmal ATP-sensitive K(+) channels, hastening action potential repolarization and shortening the refractory period.

METHODS AND RESULTS

Here, we use computational and experimental methods to investigate how ΔΨm instability can induce re-entrant arrhythmias. We develop the first tissue-level model of cardiac electrical propagation incorporating cellular electrophysiology, excitation-contraction coupling, mitochondrial energetics, and reactive oxygen species balance. Simulations show that re-entry and fibrillation can be initiated by regional ΔΨm loss because of the disparity of refractory periods inside and outside the metabolic sink. Computational results are compared with the effects of a metabolic sink generated experimentally by local perfusion of a mitochondrial uncoupler in a monolayer of cardiac myocytes.

CONCLUSIONS

The results demonstrate that regional mitochondrial depolarization triggered by oxidative stress activates sarcolemmal ATP-sensitive K(+) currents to form a metabolic sink. Consequent shortening of the action potential inside, but not outside, the sink increases the propensity for re-entry. ΔΨm recovery during pacing can lead to novel mechanisms of ectopic activation. The findings highlight the importance of mitochondria as potential therapeutic targets for sudden death associated with cardiovascular disease.

Modeling the dispersion in electromechanically coupled myocardium

We present an approach to model the dispersion of fiber and sheet orientations in the myocardium. By utilizing structure parameters, an existing orthotropic and invariant-based constitutive model developed to describe the passive behavior of the myocardium is augmented. Two dispersion parameters are fitted to experimentally observed angular dispersion data of the myocardial tissue. Computations are performed on a unit myocardium tissue cube and on a slice of the left ventricle indicating that the dispersion parameter has an effect on the myocardial deformation and stress development. The use of fiber dispersions relating to a pathological myocardium had a rather big effect. The final example represents an ellipsoidal model of the left ventricle indicating the influence of fiber and sheet dispersions upon contraction over a cardiac cycle. Although only a minor shift in the pressure-volume (PV) loops between the cases with no dispersions and with fiber and sheet dispersions for a healthy myocardium was observed, a remarkably different behavior is obtained with a fiber dispersion relating to a diseased myocardium. In future simulations, this dispersion model for myocardial tissue may advantageously be used together with models of, for example, growth and remodeling of various cardiac diseases.

Automatic Parameterization Strategy for Cardiac Electrophysiology Simulations

Driven by recent advances in medical imaging, image segmentation and numerical techniques, computer models of ventricular electrophysiology account for increasingly finer levels of anatomical and biophysical detail. However, considering the large number of model parameters involved parameterization poses a major challenge. A minimum requirement in combined experimental and modeling studies is to achieve good agreement in activation and repolarization sequences between model and experiment or patient data. In this study, we propose basic techniques which aid in determining bidomain parameters to match activation sequences. An iterative parameterization algorithm is implemented which determines appropriate bulk conductivities which yield prescribed velocities. In addition, a method is proposed for splitting the computed bulk conductivities into individual bidomain conductivities by prescribing anisotropy ratios.

Simulating the Mechanics of Myocardial Tissue Using Strongly Scalable Parallel Algorithms

Due to preferential orientations of fibers, such as collagen or myocytes, the modeling of the mechanics of myocardial tissue leads to anisotropic and highly nonlinear material models. For micro-anatomically realistic geometries the computational effort to handle these sophisticated models is very challenging and demands the usage of strongly scalable parallel algorithms. In this context we mention two possible approaches and show numerical examples.

On boundary stimulation and optimal boundary control of the bidomain equations

The bidomain equations with Neumann boundary stimulation and optimal control of these stimuli are investigated. First an analytical framework for boundary control is provided. Then a parallel finite element based algorithm is devised and its efficiency is demonstrated not only for the direct problem but also for the optimal control problem. The computations realize a model configuration corresponding to optimal boundary defibrillation of a reentry phenomenon by applying current density stimuli.

Tachycardia in post-infarction hearts: insights from 3D image-based ventricular models

Ventricular tachycardia, a life-threatening regular and repetitive fast heart rhythm, frequently occurs in the setting of myocardial infarction. Recently, the peri-infarct zones surrounding the necrotic scar (termed gray zones) have been shown to correlate with ventricular tachycardia inducibility. However, it remains unknown how the latter is determined by gray zone distribution and size. The goal of this study is to examine how tachycardia circuits are maintained in the infarcted heart and to explore the relationship between the tachycardia organizing centers and the infarct gray zone size and degree of heterogeneity. To achieve the goals of the study, we employ a sophisticated high-resolution electrophysiological model of the infarcted canine ventricles reconstructed from imaging data, representing both scar and gray zone. The baseline canine ventricular model was also used to generate additional ventricular models with different gray zone sizes, as well as models in which the gray zone was represented as different heterogeneous combinations of viable tissue and necrotic scar. The results of the tachycardia induction simulations with a number of high-resolution canine ventricular models (22 altogether) demonstrated that the gray zone was the critical factor resulting in arrhythmia induction and maintenance. In all models with inducible arrhythmia, the scroll-wave filaments were contained entirely within the gray zone, regardless of its size or the level of heterogeneity of its composition. The gray zone was thus found to be the arrhythmogenic substrate that promoted wavebreak and reentry formation. We found that the scroll-wave filament locations were insensitive to the structural composition of the gray zone and were determined predominantly by the gray zone morphology and size. The findings of this study have important implications for the advancement of improved criteria for stratifying arrhythmia risk in post-infarction patients and for the development of new approaches for determining the ablation targets of infarct-related tachycardia.