Construction of a computer model to investigate sawtooth effects in the Purkinje system

A His bundle pacing protocol for suppressing ventricular arrhythmia maintenance and improving defibrillation efficacy

BACKGROUND

The excitable gap (EG), defined as the excitable tissue between two subsequent wavefronts of depolarization, is critical for maintaining reentry that underlies deadly ventricular arrhythmias. EG in the His-Purkinje Network (HPN) plays an important role in the maintenance of electrical wave reentry that underlies these arrhythmias.

OBJECTIVE

To determine if rapid His bundle pacing (HBP) during reentry reduces the amount of EG in the HPN and ventricular myocardium to suppress reentry maintenance and/or improve defibrillation efficacy.

METHODS

In a virtual human biventricular model, reentry was initiated with rapid line pacing followed by HBP delivered for 3, 6, or 9 s at pacing cycle lengths (PCLs) ranging from 10 to 300 ms (n=30). EG was calculated independently for the HPN and myocardium over each PCL. Defibrillation efficacy was assessed for each PCL by stimulating myocardial surface EG with delays ranging from 0.25 to 9 s (increments of 0.25 s, n=36) after the start of HBP. Defibrillation was successful if reentry terminated within 1 s after EG stimulation. This defibrillation protocol was repeated without HBP. To test the approach under different pathological conditions, all protocols were repeated in the model with right (RBBB) or left (LBBB) bundle branch block.

RESULTS

Compared to without pacing, HBP for >3 seconds reduced average EG in the HPN and myocardium across a broad range of PCLs for the default, RBBB, and LBBB models. HBP >6 seconds terminated reentrant arrhythmia by converting HPN activation to a sinus rhythm behavior in the default (6/30 PCLs) and RBBB (7/30 PCLs) models. Myocardial EG stimulation during HBP increased the number of successful defibrillation attempts by 3%-19% for 30/30 PCLs in the default model, 3%-6% for 14/30 PCLs in the RBBB model, and 3%-11% for 27/30 PCLs in the LBBB model.

CONCLUSION

HBP can reduce the amount of excitable gap and suppress reentry maintenance in the HPN and myocardium. HBP can also improve the efficacy of low-energy defibrillation approaches targeting excitable myocardium. HBP during reentrant arrhythmias is a promising anti-arrhythmic and defibrillation strategy.

The Purkinje network plays a major role in low-energy ventricular defibrillation

BACKGROUND

During ventricular fibrillation (VF), targeting the excitable gap (EG) of reentry throughout the myocardium with low-energy surface stimulation shows promise for painless defibrillation. However, the Purkinje network may provide alternative pathways for reentry to evade termination. This study investigates the role of the Purkinje network in painless defibrillation.

METHODS

In a computational human biventricular model featuring a Purkinje network, VF was initiated with 4 Hz epicardial pacing. Defibrillation was attempted by stimulating myocardial surface EG with a low-energy 2 ms duration pulse at 2x stimulus capture, which was administered at coupling intervals incremented by 0.25 s between 0.25 and 5 s after VF initiation. Defibrillation was accomplished if reentry ceased ≤ 1 s after the defibrillation pulse. The protocol was repeated with the Purkinje network and myocardial surface EG stimulated simultaneously, and again after uncoupling the Purkinje network from the myocardium.

RESULTS

VF with the Purkinje network coupled and uncoupled had comparable dominant frequency in the left (3.81 ± 0.44 versus 3.77 ± 0.53 Hz) and right (3.80 ± 0.37 versus 3.76 ± 0.48 Hz) ventricles. When uncoupling the Purkinje network, myocardial surface EG stimulation terminated VF for all defibrillation pulses. When coupled, myocardial EG surface stimulation terminated VF for only 55% of the defibrillation pulses, but improved to 100% when stimulated simultaneously with Purkinje network EG. Defibrillation failures were attributed to EG evading stimulation in the Purkinje network.

CONCLUSIONS

Defibrillation that exclusively targets myocardium can fail due to accessory pathways in the Purkinje network that allow for reentrant activity to evade termination and maintain VF. Painless defibrillation strategies should be adapted to include the Purkinje network.

Whole-heart ventricular arrhythmia modeling moving forward: Mechanistic insights and translational applications

Ventricular arrhythmias are the primary cause of sudden cardiac death and one of the leading causes of mortality worldwide. Whole-heart computational modeling offers a unique approach for studying ventricular arrhythmias, offering vast potential for developing both a mechanistic understanding of ventricular arrhythmias and clinical applications for treatment. In this review, the fundamentals of whole-heart ventricular modeling and current methods of personalizing models using clinical data are presented. From this foundation, the authors summarize recent advances in whole-heart ventricular arrhythmia modeling. Efforts in gaining mechanistic insights into ventricular arrhythmias are discussed, in addition to other applications of models such as the assessment of novel therapeutics. The review emphasizes the unique benefits of computational modeling that allow for insights that are not obtainable by contemporary experimental or clinical means. Additionally, the clinical impact of modeling is explored, demonstrating how patient care is influenced by the information gained from ventricular arrhythmia models. The authors conclude with future perspectives about the direction of whole-heart ventricular arrhythmia modeling, outlining how advances in neural network methodologies hold the potential to reduce computational expense and permit for efficient whole-heart modeling.

On the nature of delays allowing anatomical re-entry involving the Purkinje network: a simulation study

AIMS

Clinical observations suggest that the Purkinje network can be part of anatomical re-entry circuits in monomorphic or polymorphic ventricular arrhythmias. However, significant conduction delay is needed to support anatomical re-entry given the high conduction velocity within the Purkinje network.

METHODS AND RESULTS

We investigated, in computer models, whether damage rendering the Purkinje network as either an active lesion with slow conduction or a passive lesion with no excitable ionic channel, could explain clinical observations. Active lesions had compromised sodium current and a severe reduction in gap junction coupling, while passive lesions remained coupled by gap junctions, but modelled the membrane as a fixed resistance. Both types of tissue could provide significant delays of over 100 ms. Electrograms consistent with those obtained clinically were reproduced. However, passive tissue could not support re-entry as electrotonic coupling across the delay effectively increased the proximal refractory period to an extremely long interval. Active tissue, conversely, could robustly maintain re-entry.

CONCLUSION

Formation of anatomical re-entry using the Purkinje network is possible through highly reduced gap junctional coupling leading to slowed conduction.

Estimation of Personalized Minimal Purkinje Systems From Human Electro-Anatomical Maps

The Purkinje system is a heart structure responsible for transmitting electrical impulses through the ventricles in a fast and coordinated way to trigger mechanical contraction. Estimating a patient-specific compatible Purkinje Network from an electro-anatomical map is a challenging task, that could help to improve models for electrophysiology simulations or provide aid in therapy planning, such as radiofrequency ablation. In this study, we present a methodology to inversely estimate a Purkinje network from a patient's electro-anatomical map. First, we carry out a simulation study to assess the accuracy of the method for different synthetic Purkinje network morphologies and myocardial junction densities. Second, we estimate the Purkinje network from a set of 28 electro-anatomical maps from patients, obtaining an optimal conduction velocity in the Purkinje network of 1.95 ± 0.25 m/s, together with the location of their Purkinje-myocardial junctions, and Purkinje network structure. Our results showed an average local activation time error of 6.8±2.2 ms in the endocardium. Finally, using the personalized Purkinje network, we obtained correlations higher than 0.85 between simulated and clinical 12-lead ECGs.

How Electrode Position Affects Selective His Bundle Capture: A Modelling Study

In certain cardiac conduction system pathologies, like bundle branch block, block may be proximal, allowing for electrical stimulation of the more distal His bundle to most effectively restore activation. While selective stimulation of the His bundle is sought, surrounding myocardium may also be excited, resulting in nonselective pacing. The myocardium and His bundle have distinct capture thresholds, but the factors affecting whether His bundle pacing is selective or nonselective remain unelucidated.

OBJECTIVE

We investigated the properties which affect the capture thresholds in order to improve selective pacing.

METHODS

We performed biophysically detailed, computer simulations of a His fibre running through a septal wedge preparation to compute capture thresholds under various configurations of electrode polarity and orientation.

RESULTS

The myocardial capture threshold was close to that of the His bundle. The His fibre needed to intersect with the electrode tip to favor its activation. Inserting the electrode fully within the septum increased the myocardial capture threshold. Reversing polarity, to rely on anode break excitation, also increased the ease of selective pacing.

CONCLUSION

Model results were consistent with clinical observations. For selective pacing, the tip needs to be in contact with the His fibre and anodal stimulation is preferable.

SIGNIFICANCE

This study provides insight into helping establish electrode and stimulation parameters for selective His bundle pacing in patients.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Compartmentalized Structure of the Moderator Band Provides a Unique Substrate for Macroreentrant Ventricular Tachycardia

Supplemental Digital Content is available in the text.

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases.

Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model

Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

Stochastic spontaneous calcium release events and sodium channelopathies promote ventricular arrhythmias

Premature ventricular complexes (PVCs), the first initiating beats of a variety of cardiac arrhythmias, have been associated with spontaneous calcium release (SCR) events at the cell level. However, the mechanisms underlying the degeneration of such PVCs into arrhythmias are not fully understood. The objective of this study was to investigate the conditions under which SCR-mediated PVCs can lead to ventricular arrhythmias. In particular, we sought to determine whether sodium (Na⁺) current loss-of-function in the structurally normal ventricles provides a substrate for unidirectional conduction block and reentry initiated by SCR-mediated PVCs. To achieve this goal, a stochastic model of SCR was incorporated into an anatomically accurate compute model of the rabbit ventricles with the His-Purkinje system (HPS). Simulations with reduced Na⁺ current due to a negative-shift in the steady-state channel inactivation showed that SCR-mediated delayed afterdepolarizations led to PVC formation in the HPS, where the electrotonic load was lower, conduction block, and reentry in the 3D myocardium. Moreover, arrhythmia initiation was only possible when intrinsic electrophysiological heterogeneity in action potential within the ventricles was present. In conclusion, while benign in healthy individuals SCR-mediated PVCs can lead to life-threatening ventricular arrhythmias when combined with Na⁺ channelopathies.

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Cardiac Purkinje fibers provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is on the basis of operator splitting and is provided with 3 different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all 3 implementations produce equivalent convergence rates, and shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all 3 implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure GPU implementations outperform the pure CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.

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.

Protective Role of False Tendon in Subjects with Left Bundle Branch Block: A Virtual Population Study

False tendons (FTs) are fibrous or fibromuscular bands that can be found in both the normal and abnormal human heart in various anatomical forms depending on their attachment points, tissue types, and geometrical properties. While FTs are widely considered to affect the function of the heart, their specific roles remain largely unclear and unexplored. In this paper, we present an in silico study of the ventricular activation time of the human heart in the presence of FTs. This study presents the first computational model of the human heart that includes a FT, Purkinje network, and papillary muscles. Based on this model, we perform simulations to investigate the effect of different types of FTs on hearts with the electrical conduction abnormality of a left bundle branch block (LBBB). We employ a virtual population of 70 human hearts derived from a statistical atlas, and run a total of 560 simulations to assess ventricular activation time with different FT configurations. The obtained results indicate that, in the presence of a LBBB, the FT reduces the total activation time that is abnormally augmented due to a branch block, to such an extent that surgical implant of cardiac resynchronisation devices might not be recommended by international guidelines. Specifically, the simulation results show that FTs reduce the QRS duration at least 10 ms in 80% of hearts, and up to 45 ms for FTs connecting to the ventricular free wall, suggesting a significant reduction of cardiovascular mortality risk. In further simulation studies we show the reduction in the QRS duration is more sensitive to the shape of the heart then the size of the heart or the exact location of the FT. Finally, the model suggests that FTs may contribute to reducing the activation time difference between the left and right ventricles from 12 ms to 4 ms. We conclude that FTs may provide an alternative conduction pathway that compensates for the propagation delay caused by the LBBB. Further investigation is needed to quantify the clinical impact of FTs on cardiovascular mortality risk.

Modeling our understanding of the His-Purkinje system

The His-Purkinje System (HPS) is responsible for the rapid electric conduction in the ventricles. It relays electrical impulses from the atrioventricular node to the muscle cells and, thus, coordinates the contraction of ventricles in order to ensure proper cardiac pump function. The HPS has been implicated in the genesis of ventricular tachycardia and fibrillation as a source of ectopic beats, as well as forming distinct portions of reentry circuitry. Despite its importance, it remains much less well characterized, structurally and functionally, than the myocardium. Notably, important differences exist with regard to cell structure and electrophysiology, including ion channels, intracellular calcium handling, and gap junctions. Very few computational models address the HPS, and the majority of organ level modeling studies omit it. This review will provide an overview of our current knowledge of structure and function (including electrophysiology) of the HPS. We will review the most recent advances in modeling of the system from the single cell to the organ level, with considerations for relevant interspecies distinctions.

Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System

A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

Image-Based Structural Modeling of the Cardiac Purkinje Network

The Purkinje network is a specialized conduction system within the heart that ensures the proper activation of the ventricles to produce effective contraction. Its role during ventricular arrhythmias is less clear, but some experimental studies have suggested that the Purkinje network may significantly affect the genesis and maintenance of ventricular arrhythmias. Despite its importance, few structural models of the Purkinje network have been developed, primarily because current physical limitations prevent examination of the intact Purkinje network. In previous modeling efforts Purkinje-like structures have been developed through either automated or hand-drawn procedures, but these networks have been created according to general principles rather than based on real networks. To allow for greater realism in Purkinje structural models, we present a method for creating three-dimensional Purkinje networks based directly on imaging data. Our approach uses Purkinje network structures extracted from photographs of dissected ventricles and projects these flat networks onto realistic endocardial surfaces. Using this method, we create models for the combined ventricle-Purkinje system that can fully activate the ventricles through a stimulus delivered to the Purkinje network and can produce simulated activation sequences that match experimental observations. The combined models have the potential to help elucidate Purkinje network contributions during ventricular arrhythmias.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

A comprehensive multiscale framework for simulating optogenetics in the heart

Optogenetics has emerged as an alternative method for electrical control of the heart, where illumination is used to elicit a bioelectric response in tissue modified to express photosensitive proteins (opsins). This technology promises to enable evocation of spatiotemporally precise responses in targeted cells or tissues, thus creating new possibilities for safe and effective therapeutic approaches to ameliorate cardiac function. Here, we present a comprehensive framework for multi-scale modelling of cardiac optogenetics, allowing both mechanistic examination of optical control and exploration of potential therapeutic applications. The framework incorporates accurate representations of opsin channel kinetics and delivery modes, spatial distribution of photosensitive cells, and tissue illumination constraints, making possible the prediction of emergent behaviour resulting from interactions at sub-organ scales. We apply this framework to explore how optogenetic delivery characteristics determine energy requirements for optical stimulation and to identify cardiac structures that are potential pacemaking targets with low optical excitation threshold.

The role of Purkinje-myocardial coupling during ventricular arrhythmia: a modeling study

The Purkinje system is the fast conduction network of the heart which couples to the myocardium at discrete sites called Purkinje-Myocyte Junctions (PMJs). However, the distribution and number of PMJs remains elusive, as does whether a particular PMJ is functional. We hypothesized that the Purkinje system plays a role during reentry and that the number of functional PMJs affect reentry dynamics. We used a computer finite element model of rabbit ventricles in which we varied the number of PMJs. Sustained, complex reentry was induced by applying an electric shock and the role of the Purkinje system in maintaining the arrhythmia was assessed by analyzing phase singularities, frequency of activation, and bidirectional propagation at PMJs. For larger junctional resistances, increasing PMJ density increased the mean firing rate in the Purkinje system, the percentage of successful retrograde conduction at PMJs, and the incidence of wave break on the epicardium. However, the mean firing of the ventricles was not affected. Furthermore, increasing PMJ density above 13/ did not alter reentry dynamics. For lower junctional resistances, the trend was not as clear. We conclude that Purkinje system topology affects reentry dynamics and conditions which alter PMJ density can alter reentry dynamics.

Transmural IK(ATP) heterogeneity as a determinant of activation rate gradient during early ventricular fibrillation: mechanistic insights from rabbit ventricular models

BACKGROUND

Activation rate (AR) gradients develop during ventricular fibrillation (VF), with the highest AR on the surface near Purkinje system (PS) terminals (endocardium in humans and rabbits and epicardium in pigs). The application of glibenclamide to block adenosine triphosphate (ATP)-sensitive potassium current (IK(ATP)) before VF induction eliminates transmural AR gradients and prevents the induction of sustained arrhythmia. It remains unclear whether the PS, which is resistant to ischemia, is also a factor in AR heterogeneity.

OBJECTIVE

To dissect IK(ATP) and PS contributions to AR gradients during VF by using detailed computer simulations.

METHODS

We constructed rabbit ventricular models with either subendocardial or subepicardial PS terminals. Physiologically relevant IK(ATP) gradients were implemented, and early VF was induced and observed.

RESULTS

Prominent AR gradients were observed only in models with large IK(ATP) gradients. The critical underlying factor of AR gradient maintenance was refractoriness in low-IK(ATP) regions, which blocked the propagation of action potentials from high-IK(ATP) regions. The PS played no role in transmural AR gradient maintenance, but did cause local spatial heterogeneity of AR on the surface adjacent to terminals. Simulated glibenclamide application during VF led to spontaneous arrhythmia termination within a few seconds in most cases, which builds on previous experimental findings of anti-VF properties of glibenclamide pretreatment.

CONCLUSION

Differential IK(ATP) across the ventricular wall is an important factor underlying AR gradients during VF; thus, higher epicardial AR in pigs is most likely due to an abundance of epicardial IK(ATP). For terminating early VF, our results suggest that IK(ATP) modulation is a stronger target than Purkinje ablation.

Fusion during entrainment of orthodromic reciprocating tachycardia is enhanced for basal pacing sites but diminished when pacing near Purkinje system end points

BACKGROUND

In the electrophysiological laboratory, orthodromic atrioventricular reciprocating tachycardia (ORT) can be distinguished from atrial tachycardia and atrioventricular node reentry tachycardia by identifying orthodromic and antidromic wavefront fusion during ventricular overdrive pacing (VOP). Previous work has shown that basal VOP near the accessory pathway (AP) increases the likelihood of observing fusion; however, in a third of cases, fusion is not appreciable regardless of VOP location.

OBJECTIVE

To explore the hypothesis that pacing near His-Purkinje system (PS) end points reduces fusion quality, which may explain patients with nonresponsive ORT.

METHODS

In a novel computer model of ORT, simulations were performed with a variety of AP locations and pacing sites; results were analyzed to assess factors influencing fusion quality in pseudo-electrocardiogram signals.

RESULTS

Entrainment by basal VOP near the AP was more likely to produce fusion visible on simulated electrocardiograms compared to entrainment by apical VOP, but this advantage was dramatically diminished when the pacing site was also near PS end points. Prediction of fusion quality based on AP proximity alone was dramatically improved when corrected to penalize for PS proximity.

CONCLUSIONS

These results suggest that basal VOP near the AP and far from the PS is optimal; this could be tested in patients. A denser basal ramification of PS fibers is known to exist in a minority of human hearts; our findings indicate that this unusual PS configuration is a plausible explanation for ORT cases where fusion is never observed in spite of entrainment by basal VOP near the AP.

An image-based model of the whole human heart with detailed anatomical structure and fiber orientation

Many heart anatomy models have been developed to study the electrophysiological properties of the human heart. However, none of them includes the geometry of the whole human heart. In this study, an anatomically detailed mathematical model of the human heart was firstly reconstructed from the computed tomography images. In the reconstructed model, the atria consisted of atrial muscles, sinoatrial node, crista terminalis, pectinate muscles, Bachmann's bundle, intercaval bundles, and limbus of the fossa ovalis. The atrioventricular junction included the atrioventricular node and atrioventricular ring, and the ventricles had ventricular muscles, His bundle, bundle branches, and Purkinje network. The epicardial and endocardial myofiber orientations of the ventricles and one layer of atrial myofiber orientation were then measured. They were calculated using linear interpolation technique and minimum distance algorithm, respectively. To the best of our knowledge, this is the first anatomically-detailed human heart model with corresponding experimentally measured fibers orientation. In addition, the whole heart excitation propagation was simulated using a monodomain model. The simulated normal activation sequence agreed well with the published experimental findings.

Modeling atrial arrhythmias: impact on clinical diagnosis and therapies

Atrial arrhythmias are the most frequent sustained rhythm disorders in humans and often lead to severe complications such as heart failure and stroke. Despite the important insights provided by animal models into the mechanisms of atrial arrhythmias, direct translation of experimental findings to new therapies in patients has not been straightforward. With the advances in computer technology, large-scale electroanatomical computer models of the atria that integrate information from the molecular to organ scale have reached a level of sophistication that they can be used to interpret the outcome of experimental and clinical studies and aid in the rational design of therapies. This paper reviews the state-of-the-art of computer models of the electrical dynamics of the atria and discusses the evolving role of simulation in assisting the clinical diagnosis and treatment of atrial arrhythmias.

BOUBAKER POLYNOMIALS EXPRESSION TO THE MAGNETIC PHASE-SHIFT INDUCED IN LEON–VIGMOND 3D-MODEL OF THE HUMAN HEART

The heart is simulated as an electrically controlled fluid pump which operates by mechanical contraction. Human heart modeling is undoubtedly a computationally daunting task which must incorporate magnetic, plastic, mechanic and electric patterns. In this paper, a polynomial mathematical formulation for the magnetic field phase shift in a particular heart 3D-model is proposed. The developed model can give an insight into the local and global complex dynamics of the heart magnetic field under controlled excitation as guides to monitoring i.e., the transition from normal to abnormal myocardial activity or collateral dysfunctions. The used protocol allowed handling the boundary conditions in a smooth way.

Construction of 3D Realistic Purkinje System: A Locally Linear Embedding-Based Method

The geometry of canine ventricle with purkinje system provides the data basis for the simulation and analysis of the mechanisms of ventricular pathophysiology. The acquisition of the geometry of the purkinje system, however, is very challenging, and traditional construction approaches are mainly based on modeling using fractal geometry. In this paper, we propose a novel locally linear embedding (LLE)-based method to construct 3D anatomical purkinje system of the canine left ventricle (LV). First, we collect the 2D purkinje system data in a canine ventricle and extract the endocardial surface of the canine left ventricle from 3D canine ventricle. Then, LLE is used to map the 3D geometry of the endocardial surface to a 2D subspace, and the 2D purkinje system data is further embedded into this 2D subspace. Finally, LLE is adopted to map both the 3D geometry of the endocardial surface and the 2D purkinje system data back to the 3D space. An experiment is designed to verify the effectiveness of the LLE-based construction method. The proposed method approaches is promising in restoring realistic purkinje system of the left canine ventricle.

A mathematical model of the Purkinje-muscle junctions

This paper is devoted to the construction of a mathematical model of the His-Purkinje tree and the Purkinje-Muscle Junctions (PMJ). A simple numerical scheme is proposed in order to perform some simple numerical experiments.

Rabbit-specific ventricular model of cardiac electrophysiological function including specialized conduction system

The function of the ventricular specialized conduction system in the heart is to ensure the coordinated electrical activation of the ventricles. It is therefore critical to the overall function of the heart, and has also been implicated as an important player in various diseases, including lethal ventricular arrhythmias such as ventricular fibrillation and drug-induced torsades de pointes. However, current ventricular models of electrophysiology usually ignore, or include highly simplified representations of the specialized conduction system. Here, we describe the development of an image-based, species-consistent, anatomically-detailed model of rabbit ventricular electrophysiology that incorporates a detailed description of the free-running part of the specialized conduction system. Techniques used for the construction of the geometrical model of the specialized conduction system from a magnetic resonance dataset and integration of the system model into a ventricular anatomical model, developed from the same dataset, are described. Computer simulations of rabbit ventricular electrophysiology are conducted using the novel anatomical model and rabbit-specific membrane kinetics to investigate the importance of the components and properties of the conduction system in determining ventricular function under physiological conditions. Simulation results are compared to panoramic optical mapping experiments for model validation and results interpretation. Full access is provided to the anatomical models developed in this study.

Integrated approach for the study of anatomical variability in the cardiac Purkinje system: from high resolution MRI to electrophysiology simulation

The ordered electrical stimulation of the ventricles is achieved by a specialized network of fibres known as the Purkinje system. The gross anatomy and basic functional role of the Purkinje system is well understood. However, very little is known about the detailed anatomy of the Purkinje system, its inter-individual variability and the implications of the variability in ventricular function, in part due to limitations in experimental techniques. In this study, we aim to provide new insight into the inter-individual variability of the free running Purkinje system anatomy and its impact on ventricular electrophysiological function. As a first step towards achieving this aim, high resolution magnetic resonance imaging (MRI) datasets of rat and the rabbit ventricles are obtained and analysed using a novel semi-automatic image processing algorithm for segmentation of the free-running Purkinje system. Segmented geometry from the MRI datasets is used to construct a computational model of the Purkinje system, which is incorporated in to an anatomically-based ventricular geometry to simulate ventricular electrophysiological activity.

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.

Arrhythmogenesis by single ectopic beats originating in the Purkinje system

Cells in the Purkinje system (PS) are known to be more vulnerable than ventricular myocytes to secondary excitations during the action potential (AP) plateau or repolarization phases, known as early afterdepolarizations (EADs). Since myocytes have a lower intrinsic AP duration than the PS cells to which they are coupled, EADs occurring in distal branches of the PS are more likely to result in propagating ectopic beats. In this study, we use a computer model of the rabbit ventricles and PS to investigate the consequences of EADs occurring at different times and places in the cardiac conduction system. We quantify the role of tissue conductivity and excitability, as well as interaction with sinus excitation, in determining whether an EAD-induced ectopic beat will establish reentrant activity. We demonstrate how a single ectopic beat arising from an EAD in the distal PS can give rise to reentrant arrhythmia; in contrast, EADs in the proximal PS were unable to initiate reentry. Clinical studies have established the PS as a potential substrate for reentry, but the underlying mechanisms of these types of disorder are not well understood, nor are conditions leading to their development clearly defined; this work provides new insights into the role of the PS in such circumstances. Our findings indicate that simulated EADs in the distal PS can induce premature beats, which can lead to the tachycardias involving the conduction system due to interactions with sinus activity or impaired myocardial conduction velocity.

Effects of the purkinje system and cardiac geometry on biventricular pacing: a model study

Heart failure leads to gross cardiac structural changes. While cardiac resynchronization therapy (CRT) is a recognized treatment for restoring synchronous activation, it is not clear how changes in cardiac shape and size affect the electrical pacing therapy. This study used a human heart computer model which incorporated anatomical structures such as myofiber orientation and a Purkinje system (PS) to study how pacing affected failing hearts. The PS was modeled as a tree structure that reproduced its retrograde activation feature. In addition to a normal geometry, two cardiomyopathies were modeled: dilatation and hypertrophy. A biventricular pacing protocol was tested in the context of atrio-ventricular block. The contribution of the PS was examined by removing it, as well as by increasing endocardial conductivity. Results showed that retrograde conduction into the PS was a determining factor for achieving intraventricular synchrony. Omission of the PS led to an overestimate of the degree of electrical dyssynchrony while assessing CRT. The activation patterns for the three geometries showed local changes in the order of activation of the lateral wall in response to the same pacing strategy. These factors should be carefully considered when determining lead placement and optimizing device parameters in clinical practice.

Mathematical modeling of electrocardiograms: a numerical study

This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated.

Simulations of reduced conduction reserve in the diabetic rat heart: response to uncoupling and reduced excitability

Experimental results have shown that action potential (AP) conduction in ventricular tissue from streptozotocin-diabetic (STZ) rats is compromised. This was manifest as increased sensitivity of conduction velocity (CV) to the gap junction uncoupler heptanol, as well as increased sensitivity of CV to reduced cellular excitability due to elevated extracellular K(+) concentration, in the STZ hearts. This "reduced conduction reserve" has been suggested to be due to lateralization of connexin43 (Cx43) proteins, rendering them nonfunctional, resulting in compromised intercellular electrical coupling. In this study, we have used computer simulations of one-dimensional AP conduction in a model of rat ventricular myocytes to verify this interpretation. Our results show that compromised intercellular coupling indeed reduces conduction reserve and predict a response to gap junction uncoupling with heptanol that is consistent with experiments. However, our simulations also show that compromised intercellular coupling is insufficient to explain the increased sensitivity to reduced cellular excitability. A thorough investigation of possible underlying mechanisms, suggests that subtle alterations in the voltage-dependence of steady-state gating for the Na(+) current (I (Na)), combined with compromised intercellular coupling, is a likely mechanism for these observations.

Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function

Recent advances in magnetic resonance (MR) imaging technology have unveiled a wealth of information regarding cardiac histoanatomical complexity. However, methods to faithfully translate this level of fine-scale structural detail into computational whole ventricular models are still in their infancy, and, thus, the relevance of this additional complexity for simulations of cardiac function has yet to be elucidated. Here, we describe the development of a highly detailed finite-element computational model (resolution: approximately 125 microm) of rabbit ventricles constructed from high-resolution MR data (raw data resolution: 43 x 43 x 36 microm), including the processes of segmentation (using a combination of level-set approaches), identification of relevant anatomical features, mesh generation, and myocyte orientation representation (using a rule-based approach). Full access is provided to the completed model and MR data. Simulation results were compared with those from a simplified model built from the same images but excluding finer anatomical features (vessels/endocardial structures). Initial simulations showed that the presence of trabeculations can provide shortcut paths for excitation, causing regional differences in activation after pacing between models. Endocardial structures gave rise to small-scale virtual electrodes upon the application of external field stimulation, which appeared to protect parts of the endocardium in the complex model from strong polarizations, whereas intramural virtual electrodes caused by blood vessels and extracellular cleft spaces appeared to reduce polarization of the epicardium. Postshock, these differences resulted in the genesis of new excitation wavefronts that were not observed in more simplified models. Furthermore, global differences in the stimulus recovery rates of apex/base regions were observed, causing differences in the ensuing arrhythmogenic episodes. In conclusion, structurally simplified models are well suited for a large range of cardiac modeling applications. However, important differences are seen when behavior at microscales is relevant, particularly when examining the effects of external electrical stimulation on tissue electrophysiology and arrhythmia induction. This highlights the utility of histoanatomically detailed models for investigations of cardiac function, in particular for future patient-specific modeling.

Purkinje-mediated effects in the response of quiescent ventricles to defibrillation shocks

In normal cardiac function, orderly activation of the heart is facilitated by the Purkinje system (PS), a specialized network of fast-conducting fibers that lines the ventricles. Its role during ventricular defibrillation remains unelucidated. Physical characteristics of the PS make it a poor candidate for direct electrical observation using contemporary experimental techniques. This study uses a computer modeling approach to assess contributions by the PS to the response to electrical stimulation. Normal sinus rhythm was simulated and epicardial breakthrough sites were distributed in a manner consistent with experimental results. Defibrillation shocks of several strengths and orientations were applied to quiescent ventricles, with and without PS, and electrical activation was analyzed. All shocks induced local polarizations in PS branches parallel to the field, which led to the rapid spread of excitation through the network. This produced early activations at myocardial sites where tissue was unexcited by the shock and coupled to the PS. Shocks along the apico-basal axis of the heart resulted in a significant abbreviation of activation time when the PS was present; these shocks are of particular interest because the fields generated by internal cardioverter defibrillators tend to have a strong component in the same direction. The extent of PS-induced changes, both temporal and spatial, was constrained by the amount of shock-activated myocardium. Increasing field strength decreased the transmission delay between PS and ventricular tissue at Purkinje-myocardial junctions (PMJs), but this did not have a major effect on the organ-level response. Weaker shocks directly affect a smaller volume of myocardial tissue but easily excite the PS, which makes the PS contribution to far field excitation more substantial than for stronger shocks.

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.

Arrhythmogenic mechanisms of the Purkinje system during electric shocks: a modeling study

BACKGROUND

The function of the Purkinje system (PS) is to ensure fast and uniform activation of the heart. Although this vital role during sinus rhythm is well understood, this is not the case when shocks are applied to the heart, especially in the case of failed defibrillation. The PS activates differently from the myocardium, has different electrophysiological properties, and provides alternate propagation pathways; thus, there are many ways in which it can contribute to postshock behavior.

OBJECTIVE

The purpose of this study was to elucidate the role of the PS in the initiation and maintenance of postshock arrhythmias.

METHODS

A computer model of the ventricles including the PS was subjected to different reentry induction protocols.

RESULTS

The PS facilitated reentry induction at relatively weaker shocks. Disconnecting the PS from the ventricles during the postshock interval revealed that the PS helps stabilize early-stage reentry by providing focal breakthroughs. During later stages, the PS contributed to reentry by leading to higher frequency rotors. The PS also promoted wave front splitting during reentry due to electrotonic coupling, which prolongs action potential durations at PS-myocyte junctions. The presence of a PS results in the anchoring of reentrant activations that propagate through the pathways provided by the PS.

CONCLUSIONS

The PS is proarrhythmic in that it provides pathways that prolong activity, and it plays a supplementary role in maintaining the later stages of reentry (>800 ms).

Generation of histo-anatomically representative models of the individual heart: tools and application

This paper presents methods to build histo-anatomically detailed individualized cardiac models. The models are based on high-resolution three-dimensional anatomical and/or diffusion tensor magnetic resonance images, combined with serial histological sectioning data, and are used to investigate individualized cardiac function. The current state of the art is reviewed, and its limitations are discussed. We assess the challenges associated with the generation of histo-anatomically representative individualized in silico models of the heart. The entire processing pipeline including image acquisition, image processing, mesh generation, model set-up and execution of computer simulations, and the underlying methods are described. The multifaceted challenges associated with these goals are highlighted, suitable solutions are proposed, and an important application of developed high-resolution structure-function models in elucidating the effect of individual structural heterogeneity upon wavefront dynamics is demonstrated.

CHASTE: incorporating a novel multi-scale spatial and temporal algorithm into a large-scale open source library

Recent work has described the software engineering and computational infrastructure that has been set up as part of the Cancer, Heart and Soft Tissue Environment (CHASTE) project. CHASTE is an open source software package that currently has heart and cancer modelling functionality. This software has been written using a programming paradigm imported from the commercial sector and has resulted in a code that has been subject to a far more rigorous testing procedure than that is usual in this field. In this paper, we explain how new functionality may be incorporated into CHASTE. Whiteley has developed a numerical algorithm for solving the bidomain equations that uses the multi-scale (MS) nature of the physiology modelled to enhance computational efficiency. Using a simple geometry in two dimensions and a purpose-built code, this algorithm was reported to give an increase in computational efficiency of more than two orders of magnitude. In this paper, we begin by reviewing numerical methods currently in use for solving the bidomain equations, explaining how these methods may be developed to use the MS algorithm discussed above. We then demonstrate the use of this algorithm within the CHASTE framework for solving the monodomain and bidomain equations in a three-dimensional realistic heart geometry. Finally, we discuss how CHASTE may be developed to include new physiological functionality--such as modelling a beating heart and fluid flow in the heart--and how new algorithms aimed at increasing the efficiency of the code may be incorporated.

Numerical solution of the bidomain equations

Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.

Reduced conduction reserve of the propagating cardiac impulse in the diabetic rat heart: a model study

Conduction velocity is dependent on two main factors: intercellular electrical coupling and cellular electrical excitability. There is significant redundancy, 'conduction reserve', in these parameters such that significant reduction in the conduction velocity of the action potential requires either a severe change in one of these parameters or a combined change in both parameters. Studies in diabetic rat hearts have shown a significant reduction in the conduction reserve and it was hypothesized that this is mainly due to the lateralization of the gap junction protein connexin 43 (Cx43). To gain a better understanding of the effect of reduced intercellular coupling, a rat ventricle myocyte model was used to simulate propagation along a strand of cells. Simulations were performed to assess the effect of reduction of intercellular conductance on the conduction velocity. As the conductance of the gap junction decreased a significant reduction in the conduction velocity was observed. The relationship between conduction velocity and intercellular coupling became steeper with decreasing coupling, such that conduction velocity became increasingly sensitive to further uncoupling. This is consistent with experimental results, in which application of the gap junction uncoupler heptanol caused a larger conduction slowing in diabetic hearts than in controls.

Role of Purkinje system in cardiac arrhythmias

The mechanisms responsible for postshock behavior of the heart are poorly understood. Below threshold shocks may induce arrhythmias that are difficult to contain. Cardiac vulnerability to shocks and defibrillation efficacy are largely determined by the postshock activity during the occurrence of a brief electrically quiescent period, known as the isoelectric window (IW) and activations following the IW period. This paper presents a detailed computer simulation study that underlines the role of the Purkinje system (PS) in postshock arrhythmogenesis. Reentry was induced in an anatomically realistic rabbit heart model using three different shocking protocols. Regions of vulnerability were determined for each protocol with and without PS. The role of PS during reentry was studied by isolating the PS from myocardium at various instances. The earliest post-shock activations were observed originating from the PS which initiated the reentry. The PS was shown to facilitate the reentry induction at weaker shocks. The PS also helped to stabilize the reentry in the early stages but did not play any significant role in the later stages. This research provides valuable insights into the postshock arrhythmogenesis and maintenance, and extends the discussion on the occurrence of IW as observed during clinical and experimental studies.

Towards predictive modelling of the electrophysiology of the heart

The simulation of cardiac electrical function is an example of a successful integrative multiscale modelling approach that is directly relevant to human disease. Today we stand at the threshold of a new era, in which anatomically detailed, tomographically reconstructed models are being developed that integrate from the ion channel to the electromechanical interactions in the intact heart. Such models hold high promise for interpretation of clinical and physiological measurements, for improving the basic understanding of the mechanisms of dysfunction in disease, such as arrhythmias, myocardial ischaemia and heart failure, and for the development and performance optimization of medical devices. The goal of this article is to present an overview of current state-of-art advances towards predictive computational modelling of the heart as developed recently by the authors of this article. We first outline the methodology for constructing electrophysiological models of the heart. We then provide three examples that demonstrate the use of these models, focusing specifically on the mechanisms for arrhythmogenesis and defibrillation in the heart. These include: (1) uncovering the role of ventricular structure in defibrillation; (2) examining the contribution of Purkinje fibres to the failure of the shock; and (3) using magnetic resonance imaging reconstructed heart models to investigate the re-entrant circuits formed in the presence of an infarct scar.

Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems

Significant advancements in imaging technology and the dramatic increase in computer power over the last few years broke the ground for the construction of anatomically realistic models of the heart at an unprecedented level of detail. To effectively make use of high-resolution imaging datasets for modeling purposes, the imaged objects have to be discretized. This procedure is trivial for structured grids. However, to develop generally applicable heart models, unstructured grids are much preferable. In this study, a novel image-based unstructured mesh generation technique is proposed. It uses the dual mesh of an octree applied directly to segmented 3-D image stacks. The method produces conformal, boundary-fitted, and hexahedra-dominant meshes. The algorithm operates fully automatically with no requirements for interactivity and generates accurate volume-preserving representations of arbitrarily complex geometries with smooth surfaces. The method is very well suited for cardiac electrophysiological simulations. In the myocardium, the algorithm minimizes variations in element size, whereas in the surrounding medium, the element size is grown larger with the distance to the myocardial surfaces to reduce the computational burden. The numerical feasibility of the approach is demonstrated by discretizing and solving the monodomain and bidomain equations on the generated grids for two preparations of high experimental relevance, a left ventricular wedge preparation, and a papillary muscle.

Simulation of the QRS complex using papillary muscle positions as the site of early activation in human subjects

BACKGROUND

Simulation of the electrical activation of the heart and its comparison with real in vivo activation is a promising method in testing potential determinants of excitation. Simulation of the electrical activity of the human heart is now emerging as a step forward for understanding and predicting electrophysiologic patterns in humans. Initial points of excitation and the manner in which the activation spreads from these points are important variables determining QRS complex characteristics. It has been suggested that in humans, the initial excitation of the left ventricle is a primary determinant of QRS complex characteristics, and that excitation begins at the papillary muscles and septum, where the fascicles of the left bundle branch insert. The aim of this study is to test the hypothesis that QRS duration and direction of QRS axis in the frontal plane have excellent agreement between real QRS and simulated QRS using papillary muscle position to indicate the border of the origin of early ventricular activation.

METHODS

Fourteen healthy adult volunteers were included in the study. Magnetic resonance imaging data were obtained to assess the papillary muscle positions. Twelve-lead electrocardiographic (ECG) recordings were used to obtain real ECG data for assessment of QRS duration and QRS axis in each subject. Simulation software developed by ECG-TECH Corp (Huntington, NY) was used to simulate the ECG of each subject to determine simulated QRS duration and QRS frontal plane axis. QRS duration and QRS axis data were compared between simulated and real ECG and agreement between these variables was calculated.

RESULTS

Seventy-nine percent of subjects had a difference of the QRS duration between real and simulated ECG of less than 10 milliseconds. The calculated strength of agreement between simulated and real QRS duration was 71% and considered as "good" (kappa statistics). In 70% of subjects, the difference in the QRS axis was less than 10 degrees . The calculated strength of agreement between simulated and real QRS axis was 80% and considered as "excellent" (kappa statistics).

CONCLUSIONS

The results of this study suggest that the sites of the initiation of electrical activity in the left ventricle, as assessed by the positions of papillary muscles, may be considered as primary determinants of the QRS duration and QRS axis in humans. This knowledge may help in predicting normal QRS characteristic on a patient-specific basis. In this study, simulation of the QRS complex was based on papillary muscles from human hearts.

From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales

Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation-contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from sub-microseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications.