Computational framework for simulating the mechanisms and ECG of re-entrant ventricular fibrillation

Interactive Simulation of the ECG: Effects of Cell Types, Distributions, Shapes and Duration

The shape of the ECG depends on the lead positions but also on the distribution and dispersion of different cell types and their action potential (AP) durations and shapes. We present an interactive JavaScript program that allows fast simulations of the ECG by solving and displaying the dynamics of cardiac cells in tissue using a web browser. We use physiologically accurate ODE models of cardiac cells of different types including SA node, right and left atria, AV node, Purkinje, and right and left ventricular cells with dispersion that accounts for apex-to-base and epi-to-endo variations. The software allows for real-time variations for each cell type and their spatial range so as to identify how the shape of the ECG varies as a function of cell type, distribution, excitation duration and AP shape. The propagation of the wave is visualized in real time through all the regions as parameters are kept fixed or varied to modify ECG morphology. The code solves thousands of simulated cells in real time and is independent of operating system, so it can run on PCs, laptops, tablets and cellphones. This program can be used to teach students, fellows and the general public how and why lead positions and the different cell physiology in the heart affect the various features of the ECG.

Reaction-diffusion informed approach to determine myocardial ischemia using stochastic in-silico ECGs and CNNs

Every year, nine million people die globally from ischemic heart disease (IHD). There are many methods of early detection of IHD which can help prevent death, but few are able to determine the configuration and severity of this disease. Our study aims to determine the severity and configuration of ischemic zones by implementing the reaction-diffusion analysis of cardiac excitation in a model of the left ventricle of the human heart. Initially, this model is applied to compute twenty thousand in-silico ECG signals with stochastic distribution of ischemic parameters. Furthermore, generated data is effectively (r²=0.85) implemented for training a one-dimensional convolutional neural network to determine the severity and configuration of ischemia using only two lead surface ECG. Our results readily demonstrate that using a minimally configured portable ECG system can be instrumental for monitoring IHD and allowing early tracking of acute ischemic events.

Source-Sink Mismatch Causing Functional Conduction Block in Re-Entrant Ventricular Tachycardia

Ventricular tachycardia (VT) caused by a re-entrant circuit is a life-threatening arrhythmia that at present cannot always be treated adequately. A realistic model of re-entry would be helpful to accurately guide catheter ablation for interruption of the circuit. In this review, models of electrical activation wavefront propagation during onset and maintenance of re-entrant VT are discussed. In particular, the relationship between activation mapping and maps of transition in infarct border zone thickness, which results in source-sink mismatch, is considered in detail and supplemented with additional data. Based on source-sink mismatch, the re-entry isthmus can be modeled from its boundary properties. Isthmus boundary segments with large transitions in infarct border zone thickness have large source-sink mismatch, and functional block forms there during VT. These alternate with segments having lesser thickness change and therefore lesser source-sink mismatch, which act as gaps, or entrance and exit points, to the isthmus during VT. Besides post-infarction substrates, the source-sink model is likely applicable to other types of volumetric changes in the myocardial conducting medium, such as when there is presence of fibrosis or dissociation of muscle fibers.

Reprint of 'Model of unidirectional block formation leading to reentrant ventricular tachycardia in the infarct border zone of postinfarction canine hearts'

BACKGROUND

When the infarct border zone is stimulated prematurely, a unidirectional block line (UBL) can form and lead to double-loop (figure-of-eight) reentrant ventricular tachycardia (VT) with a central isthmus. The isthmus is composed of an entrance, center, and exit. It was hypothesized that for certain stimulus site locations and coupling intervals, the UBL would coincide with the isthmus entrance boundary, where infarct border zone thickness changes from thin-to-thick in the travel direction of the premature stimulus wavefront.

METHOD

A quantitative model was developed to describe how thin-to-thick changes in the border zone result in critically convex wavefront curvature leading to conduction block, which is dependent upon coupling interval. The model was tested in 12 retrospectively analyzed postinfarction canine experiments. Electrical activation was mapped for premature stimulation and for the first reentrant VT cycle. The relationship of functional conduction block forming during premature stimulation to functional block during reentrant VT was quantified.

RESULTS

For an appropriately placed stimulus, in accord with model predictions: 1. The UBL and reentrant VT isthmus lateral boundaries overlapped (error: 4.8±5.7mm). 2. The UBL leading edge coincided with the distal isthmus where the center-entrance boundary would be expected to occur. 3. The mean coupling interval was 164.6±11.0ms during premature stimulation and 190.7±20.4ms during the first reentrant VT cycle, in accord with model calculations, which resulted in critically convex wavefront curvature and functional conduction block, respectively, at the location of the isthmus entrance boundary and at the lateral isthmus edges.

DISCUSSION

Reentrant VT onset following premature stimulation can be explained by the presence of critically convex wavefront curvature and unidirectional block at the isthmus entrance boundary when the premature stimulation interval is sufficiently short. The double-loop reentrant circuit pattern is a consequence of wavefront bifurcation around this UBL followed by coalescence, and then impulse propagation through the isthmus. The wavefront is blocked from propagating laterally away from the isthmus by sharp increases in border zone thickness, which results in critically convex wavefront curvature at VT cycle lengths.

Model of unidirectional block formation leading to reentrant ventricular tachycardia in the infarct border zone of postinfarction canine hearts

BACKGROUND

When the infarct border zone is stimulated prematurely, a unidirectional block line (UBL) can form and lead to double-loop (figure-of-eight) reentrant ventricular tachycardia (VT) with a central isthmus. The isthmus is composed of an entrance, center, and exit. It was hypothesized that for certain stimulus site locations and coupling intervals, the UBL would coincide with the isthmus entrance boundary, where infarct border zone thickness changes from thin-to-thick in the travel direction of the premature stimulus wavefront.

METHOD

A quantitative model was developed to describe how thin-to-thick changes in the border zone result in critically convex wavefront curvature leading to conduction block, which is dependent upon coupling interval. The model was tested in 12 retrospectively analyzed postinfarction canine experiments. Electrical activation was mapped for premature stimulation and for the first reentrant VT cycle. The relationship of functional conduction block forming during premature stimulation to functional block during reentrant VT was quantified.

RESULTS

For an appropriately placed stimulus, in accord with model predictions: (1) The UBL and reentrant VT isthmus lateral boundaries overlapped (error: 4.8±5.7mm). (2) The UBL leading edge coincided with the distal isthmus where the center-entrance boundary would be expected to occur. (3) The mean coupling interval was 164.6±11.0ms during premature stimulation and 190.7±20.4ms during the first reentrant VT cycle, in accord with model calculations, which resulted in critically convex wavefront curvature with functional conduction block, respectively, at the location of the isthmus entrance boundary and at the lateral isthmus edges.

DISCUSSION

Reentrant VT onset following premature stimulation can be explained by the presence of critically convex wavefront curvature and unidirectional block at the isthmus entrance boundary when the premature stimulation interval is sufficiently short. The double-loop reentrant circuit pattern is a consequence of wavefront bifurcation around this UBL followed by coalescence, and then impulse propagation through the isthmus. The wavefront is blocked from propagating laterally away from the isthmus by sharp increases in border zone thickness, which results in critically convex wavefront curvature at VT cycle lengths.

Model of Bipolar Electrogram Fractionation and Conduction Block Associated With Activation Wavefront Direction at Infarct Border Zone Lateral Isthmus Boundaries

Background—

Improved understanding of the mechanisms underlying infarct border zone electrogram fractionation may be helpful to identify arrhythmogenic regions in the postinfarction heart. We describe the generation of electrogram fractionation from changes in activation wavefront curvature in experimental canine infarction.

Methods and Results—

A model was developed to estimate the extracellular signal shape that would be generated by wavefront propagation parallel to versus perpendicular to the lateral boundary (LB) of the reentrant ventricular tachycardia (VT) isthmus or diastolic pathway. LBs are defined as locations where functional block forms during VT, and elsewhere they have been shown to coincide with sharp thin-to-thick transitions in infarct border zone thickness. To test the model, bipolar electrograms were acquired from infarct border zone sites in 10 canine heart experiments 3 to 5 days after experimental infarction. Activation maps were constructed during sinus rhythm and during VT. The characteristics of model-generated versus actual electrograms were compared. Quantitatively expressed VT fractionation (7.6±1.2 deflections; 16.3±8.9-ms intervals) was similar to model-generated values with wavefront propagation perpendicular to the LB (9.4±2.4 deflections; 14.4±5.2-ms intervals). Fractionation during sinus rhythm (5.9±1.8 deflections; 9.2±4.4-ms intervals) was similar to model-generated fractionation with wavefront propagation parallel to the LB (6.7±3.1 deflections; 7.1±3.8-ms intervals). VT and sinus rhythm fractionation sites were adjacent to LBs ≈80% of the time.

Conclusions—

The results suggest that in a subacute canine infarct model, the LBs are a source of activation wavefront discontinuity and electrogram fractionation, with the degree of fractionation being dependent on activation rate and wavefront orientation with respect to the LB.

Effects of pacing site and stimulation history on alternans dynamics and the development of complex spatiotemporal patterns in cardiac tissue

Alternans of action potential duration has been associated with T wave alternans and the development of arrhythmias because it produces large gradients of repolarization. However, little is known about alternans dynamics in large mammalian hearts. Using optical mapping to record electrical activations simultaneously from the epicardium and endocardium of 9 canine right ventricles, we demonstrate novel arrhythmogenic complex spatiotemporal dynamics. (i) Alternans predominantly develops first on the endocardium. (ii) The postulated simple progression from normal rhythm to concordant to discordant alternans is not always observed; concordant alternans can develop from discordant alternans as the pacing period is decreased. (iii) In contrast to smaller tissue preparations, multiple stationary nodal lines may exist and need not be perpendicular to the pacing site or to each other. (iv) Alternans has fully three-dimensional dynamics and the epicardium and endocardium can show significantly different dynamics: multiple nodal surfaces can be transmural or intramural and can form concave/convex surfaces resulting in islands of discordant alternans. (v) The complex spatiotemporal patterns observed during alternans are very sensitive to both the site of stimulation and the stimulation history. Alternans in canine ventricles not only exhibit larger amplitudes and persist for longer cycle length regimes compared to those found in smaller mammalian hearts, but also show novel dynamics not previously described that enhance dispersion and show high sensitivity to initial conditions. This indicates some underlying predisposition to chaos and can help to guide the design of new drugs and devices controlling and preventing arrhythmic events.

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria--the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.

Correlation between P-wave morphology and origin of atrial focal tachycardia--insights from realistic models of the human atria and torso

Atrial arrhythmias resulting from abnormally rapid focal activity in the atria may be reflected in an altered P-wave morphology (PWM) in the ECG. Although clinically important, detailed relationships between PWM and origins of atrial focal excitations have not been established. To study such relationships, we developed computational models of the human atria and torso. The model simulation results were used to evaluate an extant clinical algorithm for locating the origin of atrial focal points from the ECG. The simulations showed that the algorithm was practical and could predict the atrial focal locations with 85% accuracy. We proposed a further refinement of the algorithm to distinguish between focal locations within the large atrial bundles.

Representing cardiac bidomain bath-loading effects by an augmented monodomain approach: application to complex ventricular models

Although the cardiac bidomain model has been widely used in the simulation of electrical activation, its relatively computationally expensive nature means that monodomain approaches are generally required for long-duration simulations (for example, investigations of arrhythmia mechanisms). However, the presence of a conducting bath surrounding the tissue is known to induce wavefront curvature (surface leading bulk), a phenomena absent in standard monodomain approaches. Here, we investigate the biophysical origin of the bidomain bath-loading induced wavefront curvature and present a novel augmented monodomain-equivalent bidomain approach faithfully replicating all aspects of bidomain wavefront morphology and conduction velocity, but with a fraction of the computational cost. Bath-loading effects are shown to be highly dependent upon specific conductivity parameters, but less dependent upon the thickness or conductivity of the surrounding bath, with even relatively thin surrounding fluid layers (~ 0.1 mm) producing significant wavefront curvature in bidomain simulations. We demonstrate that our augmented monodomain approach can be easily adapted for different conductivity sets and applied to anatomically complex models, thus facilitating fast and accurate simulation of cardiac wavefront dynamics during long-duration simulations, further aiding the faithful comparison of simulations with experiments.

Minimal model for human ventricular action potentials in tissue

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher-Noble-Noble-Panfilov (TNNP), and the Iyer-Mazhari-Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.

Effect of bundle branch block on cardiac output: a whole heart simulation study

The heart is an electrically controlled fluid pump which operates by mechanical contraction. Whole heart modelling is a computationally daunting task which must incorporate several subsystems: mechanical, electrical, and fluidic. Numerous feedback mechanisms on many levels, and operating at different scales, exist to finely control behaviour. Understanding these interactions is necessary to understand heart operation, as well as pathologies and therapies. A review of the components in such a model is given. The authors then present a framework for their electro-mechano-fluidic whole heart model based on cable methods. The model incorporates atria and ventricles, and has functioning valves with papillary muscles. The effect of altered propagation due to left and right bundle branch block on cardiac output is examined using the cable-based model. Results are compared to clinically observed phenomena. Good agreement was obtained, but tighter coupling of mechanical and electrical events is needed to fully account for behaviour. Cable-based models offer an alternative to continuum models.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.

Model of reentrant ventricular tachycardia based on infarct border zone geometry predicts reentrant circuit features as determined by activation mapping

BACKGROUND

Infarct border zone (IBZ) geometry likely affects inducibility and characteristics of postinfarction reentrant ventricular tachycardia, but the connection has not been established.

OBJECTIVE

The purpose of this study was to determine characteristics of postinfarction ventricular tachycardia in the IBZ.

METHODS

A geometric model describing the relationship between IBZ geometry and wavefront propagation in reentrant circuits was developed. Based on the formulation, slow conduction and block were expected to coincide with areas where IBZ thickness (T) is minimal and the local spatial gradient in thickness (DeltaT) is maximal, so that the degree of wavefront curvature rho proportional, variant DeltaT/T is maximal. Regions of fastest conduction velocity were predicted to coincide with areas of minimum DeltaT. In seven arrhythmogenic postinfarction canine heart experiments, tachycardia was induced by programmed stimulation, and activation maps were constructed from multichannel recordings. IBZ thickness was measured in excised hearts from histologic analysis or magnetic resonance imaging. Reentrant circuit properties were predicted from IBZ geometry and compared with ventricular activation maps after tachycardia induction.

RESULTS

Mean IBZ thickness was 231 +/- 140 microm at the reentry isthmus and 1440 +/- 770 microm in the outer pathway (P <0.001). Mean curvature rho was 1.63 +/- 0.45 mm(-1) at functional block line locations, 0.71 +/- 0.18 mm(-1) at isthmus entrance-exit points, and 0.33 +/- 0.13 mm(-1) in the outer reentrant circuit pathway. The mean conduction velocity about the circuit during reentrant tachycardia was 0.32 +/- 0.04 mm/ms at entrance-exit points, 0.42 +/- 0.13 mm/ms for the entire outer pathway, and 0.64 +/- 0.16 mm/ms at outer pathway regions with minimum DeltaT. Model sensitivity and specificity to detect isthmus location was 75.0% and 97.2%.

CONCLUSIONS

Reentrant circuit features as determined by activation mapping can be predicted on the basis of IBZ geometrical relationships.

Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia

The interpretation of normal and pathological electrocardiographic (ECG) patterns in terms of the underlying cellular and tissue electrophysiology is rudimentary, as the existing theories rely on geometrical aspects. We relate effects of sub-endocardial ischaemia on the ST-segment depression in ECG to patterns of transmural action potential propagation in a one-dimensional virtual ventricular wall. Our computational study exposes two electrophysiological mechanisms of ST depression: dynamic-predominantly positive spatial gradients in the membrane potential during abnormal repolarization of the wall, produced by action potential duration changes in the ischaemic region; and static-a negative spatial gradient of the resting membrane potential between the normal and ischaemic regions. Hyperkalaemia is the major contributor to both these mechanisms at the cellular level. These results complement simulations of the effects of cardiac geometry on the ECG, and dissect spatio-temporal and cellular electrophysiological mechanisms of ST depression seen in sub-endocardial ischaemia.

The sensitivity of the heart to static magnetic fields

Static magnetic fields induce flow potentials in arterial flows in and around the heart, that have been detected as distortions in the ECG. The resultant currents flowing through the myocardium could alter the rate or rhythm of the heart. No such changes have been seen in animal experiments, or with humans, in static fields up to 8 T. The possible effects of such currents induced by fields larger than 8 T on cardiac pacemaker rate, and arrhythmogenesis are reviewed, using virtual cardiac tissues-computational models of cardiac electrophysiology. Arrhythmogenesis can be by the initiation of ectopic beats, or by re-entry, whose probability of occurrence is increased by any increase in the electrical heterogeneity, in particular, the action potential duration heterogeneity of the ventricle. Focal ectopic activity would be readily detectable, but since re-entrant arrhythmias are very rare events, even a large increase in their probability of occurrence still leaves them unlikely to be observed. Both of these two arrhythmogenic mechanisms would show a steep sigmoidal, or threshold dependence on induced current intensity, with the threshold for increasing the vulnerability to re-entry less than the threshold for initiating activity. Failure to observe them at fields less than 8 T provides only a lower bound for any threshold for arrhythmogenesis.

Filament behavior in a computational model of ventricular fibrillation in the canine heart

The aim of this paper was to quantify the behavior of filaments in a computational model of re-entrant ventricular fibrillation. We simulated cardiac activation in an anisotropic monodomain with excitation described by the Fenton-Karma model with Beeler-Reuter restitution, and geometry by the Auckland canine ventricle. We initiated re-entry in the left and right ventricular free walls, as well as the septum. The number of filaments increased during the first 1.5 s before reaching a plateau with a mean value of about 36 in each simulation. Most re-entrant filaments were between 10 and 20 mm long. The proportion of filaments touching the epicardial surface was 65%, but most of these were visible for much less than one period of re-entry. This paper shows that useful information about filament dynamics can be gleaned from models of fibrillation in complex geometries, and suggests that the interplay of filament creation and destruction may offer a target for antifibrillatory therapy.