A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart

Construction of 3D MR image-based computer models of pathologic hearts, augmented with histology and optical fluorescence imaging to characterize action potential propagation

Cardiac computer models can help us understand and predict the propagation of excitation waves (i.e., action potential, AP) in healthy and pathologic hearts. Our broad aim is to develop accurate 3D MR image-based computer models of electrophysiology in large hearts (translatable to clinical applications) and to validate them experimentally. The specific goals of this paper were to match models with maps of the propagation of optical AP on the epicardial surface using large porcine hearts with scars, estimating several parameters relevant to macroscopic reaction-diffusion electrophysiological models. We used voltage-sensitive dyes to image AP in large porcine hearts with scars (three specimens had chronic myocardial infarct, and three had radiofrequency RF acute scars). We first analyzed the main AP waves' characteristics: duration (APD) and propagation under controlled pacing locations and frequencies as recorded from 2D optical images. We further built 3D MR image-based computer models that have information derived from the optical measures, as well as morphologic MRI data (i.e., myocardial anatomy, fiber directions and scar definition). The scar morphology from MR images was validated against corresponding whole-mount histology. We also compared the measured 3D isochronal maps of depolarization to simulated isochrones (the latter replicating precisely the experimental conditions), performing model customization and 3D volumetric adjustments of the local conductivity. Our results demonstrated that mean APD in the border zone (BZ) of the infarct scars was reduced by ~13% (compared to ~318 ms measured in normal zone, NZ), but APD did not change significantly in the thin BZ of the ablation scars. A generic value for velocity ratio (1:2.7) in healthy myocardial tissue was derived from measured values of transverse and longitudinal conduction velocities relative to fibers direction (22 cm/s and 60 cm/s, respectively). The model customization and 3D volumetric adjustment reduced the differences between measurements and simulations; for example, from one pacing location, the adjustment reduced the absolute error in local depolarization times by a factor of 5 (i.e., from 58 ms to 11 ms) in the infarcted heart, and by a factor of 6 (i.e., from 60 ms to 9 ms) in the heart with the RF scar. Moreover, the sensitivity of adjusted conductivity maps to different pacing locations was tested, and the errors in activation times were found to be of approximately 10-12 ms independent of pacing location used to adjust model parameters, suggesting that any location can be used for model predictions.

Noninvasive detection of epicardial and endocardial activity of the heart

Determining electrical activation of the heart in a noninvasive way is one of the challenges in cardiac electrophysiology. The ECG provides some, but limited information about the electrical status of the heart. This article describes a method to determine both endocardial and epicardial activation of the heart of an individual patient from 64 electrograms recorded from the body surface. Information obtained in this way might be helpful for the treatment of arrhythmias, to assess the effect of drugs on conduction in the heart and to assess electrical stability of the heart.

Bidomain ECG simulations using an augmented monodomain model for the cardiac source

The electrocardiogram (ECG) is an essential clinical tool for the non-invasive assessment of cardiac function. Computational simulations of ECGs using bidomain models are considered the biophysically most detailed approach, but computational costs are significant. Alternatively, pseudo-bidomain formulations can be used, combining a monodomain model with an infrequent bidomain solve to obtain full extracellular potential (φ(e)) distributions and traces. However, previous attempts at such approaches did not see the expected significant decrease in compute time and did not include important effects of bath-loading on activation wavefront morphology (present in full bidomain models), representing a less accurate source term for φ(e) solution. ECG traces can also be derived from computationally cheaper φ(e) recovery techniques, whereby the time-course of φ(e) is approximated at a particular point using the monodomain transmembrane potential as source term. However, φ(e) recovery methods also assume tissue to be immersed in an unbounded conductive medium; not the case in most practical scenarios. We recently demonstrated how bath-loading effects in bidomain simulations could be replicated using an augmented monodomain model, faithfully reproducing bidomain wavefront shapes and activation patterns. Here, a computationally-efficient pseudobidomain formulation is suggested which combines the advantages of an augmented monodomain method with an infrequent bidomain solve, providing activation sequences, ECG traces and φ(e) distributions in a bounded medium surrounding the heart which closely match those of the full bidomain, but at ≈ 10% the computational cost. We demonstrate the important impact of both bath-loading and a finite surrounding bath on spatiotemporal φ(e) distributions, thus demonstrating the utility of our novel pseudo-bidomain model in ECG computation with respect to previous pseudo-bidomain and φ(e) recovery approaches.

Performance of hybrid programming models for multiscale cardiac simulations: preparing for petascale computation

Future multiscale and multiphysics models that support research into human disease, translational medical science, and treatment can utilize the power of high-performance computing (HPC) systems. We anticipate that computationally efficient multiscale models will require the use of sophisticated hybrid programming models, mixing distributed message-passing processes [e.g., the message-passing interface (MPI)] with multithreading (e.g., OpenMP, Pthreads). The objective of this study is to compare the performance of such hybrid programming models when applied to the simulation of a realistic physiological multiscale model of the heart. Our results show that the hybrid models perform favorably when compared to an implementation using only the MPI and, furthermore, that OpenMP in combination with the MPI provides a satisfactory compromise between performance and code complexity. Having the ability to use threads within MPI processes enables the sophisticated use of all processor cores for both computation and communication phases. Considering that HPC systems in 2012 will have two orders of magnitude more cores than what was used in this study, we believe that faster than real-time multiscale cardiac simulations can be achieved on these systems.

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.

In silico investigation of electrically silent acute cardiac ischemia in the human ventricles

Acute cardiac ischemia, which is caused by the occlusion of a coronary artery, often leads to lethal ventricular arrhythmias or heart failure. The early diagnosis of this pathology is based on changes of the electrocardiogram (ECG), i.e., mainly shifts of the ST segment. However, the underlying mechanisms responsible for these shifts are not completely understood. Furthermore, clinical observations indicate that some acute ischemia cases can hardly be detected using standard 12-lead ECG only. Therefore, multiscale computer simulations of cardiac ischemia using realistic models of human ventricles were carried out in this work. For this purpose, the transmembrane voltage distributions in the heart and the corresponding body surface potentials were computed with varying transmural extent of the ischemic region at different ischemia stages. Some of the simulated ischemia cases were " electrically silent," i.e., they could hardly be identified in the 12-lead ECG.

Orthogonal recursive bisection as data decomposition strategy for massively parallel cardiac simulations

We present the orthogonal recursive bisection algorithm that hierarchically segments the anatomical model structure into subvolumes that are distributed to cores. The anatomy is derived from the Visible Human Project, with electrophysiology based on the FitzHugh-Nagumo (FHN) and ten Tusscher (TT04) models with monodomain diffusion. Benchmark simulations with up to 16,384 and 32,768 cores on IBM Blue Gene/P and L supercomputers for both FHN and TT04 results show good load balancing with almost perfect speedup factors that are close to linear with the number of cores. Hence, strong scaling is demonstrated. With 32,768 cores, a 1000 ms simulation of full heart beat requires about 6.5 min of wall clock time for a simulation of the FHN model. For the largest machine partitions, the simulations execute at a rate of 0.548 s (BG/P) and 0.394 s (BG/L) of wall clock time per 1 ms of simulation time. To our knowledge, these simulations show strong scaling to substantially higher numbers of cores than reported previously for organ-level simulation of the heart, thus significantly reducing run times. The ability to reduce runtimes could play a critical role in enabling wider use of cardiac models in research and clinical applications.

Simulating human cardiac electrophysiology on clinical time-scales

In this study, the feasibility of conducting in silico experiments in near-realtime with anatomically realistic, biophysically detailed models of human cardiac electrophysiology is demonstrated using a current national high-performance computing facility. The required performance is achieved by integrating and optimizing load balancing and parallel I/O, which lead to strongly scalable simulations up to 16,384 compute cores. This degree of parallelization enables computer simulations of human cardiac electrophysiology at 240 times slower than real time and activation times can be simulated in approximately 1 min. This unprecedented speed suffices requirements for introducing in silico experimentation into a clinical workflow.

Scroll-wave dynamics in human cardiac tissue: lessons from a mathematical model with inhomogeneities and fiber architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.

Transmural and apicobasal gradients in repolarization contribute to T-wave genesis in human surface ECG

The cellular basis of the T-wave morphology of surface ECG remains controversial in clinical cardiology. We examined the effect of action potential duration (APD) distribution on T-wave morphology using a realistic model of the human ventricle and torso. We developed a finite-element model of the ventricle consisting of ∼26 million elements, including the conduction system, each implemented with the ion current model of cardiomyocytes. This model was embedded in a torso model with distinct organ structures to obtain the standard ECG leads. The APD distribution was changed in the transmural direction by locating the M cells in either the endocardial or epicardial region. We also introduced apicobasal gradients by modifying the ion channel parameters. Both the transmural gradient (with M cells on the endocardial side) and the apicobasal gradient produced positive T waves, although a very large gradient was required for the apicobasal gradient. By contrast, T waves obtained with the transmural gradient were highly symmetric and, therefore, did not represent the true physiological state. Only combination of the transmural and the moderate apicobasal gradients produced physiological T waves in surface ECG. Positive T waves in surface ECG mainly originated from the transmural distribution of APD with M cells on the endocardial side, although the apicobasal gradient was also required to attain the physiological waveform.

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.

Petascale computation performance of lightweight multiscale cardiac models using hybrid programming models

Future multiscale and multiphysics models must use the power of high performance computing (HPC) systems to enable research into human disease, translational medical science, and treatment. Previously we showed that computationally efficient multiscale models will require the use of sophisticated hybrid programming models, mixing distributed message passing processes (e.g. the message passing interface (MPI)) with multithreading (e.g. OpenMP, POSIX pthreads). The objective of this work is to compare the performance of such hybrid programming models when applied to the simulation of a lightweight multiscale cardiac model. Our results show that the hybrid models do not perform favourably when compared to an implementation using only MPI which is in contrast to our results using complex physiological models. Thus, with regards to lightweight multiscale cardiac models, the user may not need to increase programming complexity by using a hybrid programming approach. However, considering that model complexity will increase as well as the HPC system size in both node count and number of cores per node, it is still foreseeable that we will achieve faster than real time multiscale cardiac simulations on these systems using hybrid programming models.

Image-based models of cardiac structure in health and disease

Computational approaches to investigating the electromechanics of healthy and diseased hearts are becoming essential for the comprehensive understanding of cardiac function. In this article, we first present a brief review of existing image-based computational models of cardiac structure. We then provide a detailed explanation of a processing pipeline which we have recently developed for constructing realistic computational models of the heart from high resolution structural and diffusion tensor (DT) magnetic resonance (MR) images acquired ex vivo. The presentation of the pipeline incorporates a review of the methodologies that can be used to reconstruct models of cardiac structure. In this pipeline, the structural image is segmented to reconstruct the ventricles, normal myocardium, and infarct. A finite element mesh is generated from the segmented structural image, and fiber orientations are assigned to the elements based on DTMR data. The methods were applied to construct seven different models of healthy and diseased hearts. These models contain millions of elements, with spatial resolutions in the order of hundreds of microns, providing unprecedented detail in the representation of cardiac structure for simulation studies.

ST segment elevation by current-to-load mismatch: an experimental and computational study

BACKGROUND

Recently, we demonstrated that ajmaline caused ST segment elevation in the heart of an SCN5A mutation carrier by excitation failure in structurally discontinuous myocardium. In patients with Brugada syndrome, ST segment elevation is modulated by cardiac sodium (I(Na)), transient outward (I(to)), and L-type calcium currents (I(CaL)).

OBJECTIVE

To establish experimentally whether excitation failure by current-to-load mismatch causes ST segment elevation and is modulated by I(to) and I(CaL).

METHODS

In porcine epicardial shavings, isthmuses of 0.9, 1.1, or 1.3 mm in width were created parallel to the fiber orientation. Local activation was recorded electrically or optically (di-4-ANEPPS) simultaneously with a pseudo-electrocardiogram (ECG) before and after ajmaline application. Intra- and extracellular potentials and ECGs were simulated in a computer model of the heart and thorax before and after introduction of right ventricular structural discontinuities and during varying levels of I(Na), I(to), and I(CaL).

RESULTS

In epicardial shavings, conduction blocked after ajmaline in a frequency-dependent manner in all preparations with isthmuses ≤ 1.1 mm width. Total conduction block occurred in three of four preparations with isthmuses of 0.9 mm versus one of seven with isthmuses ≥ 1.1 mm (P<.05). Excitation failure resulted in ST segment elevation on the pseudo-ECG. In computer simulations, subepicardial structural discontinuities caused local activation delay and made the success of conduction sensitive to I(Na), I(to), and I(CaL). Reduction of I(to) and increase of I(CaL) resulted in a higher excitatory current, overcame subepicardial excitation failure, and reduced the ST segment elevation.

CONCLUSIONS

Excitation failure by current-to-load mismatch causes ST segment elevation and, like ST segment elevation in Brugada patients, is modulated by I(to) and I(CaL).

Modeling the role of the coronary vasculature during external field stimulation

The exact mechanisms by which defibrillation shocks excite cardiac tissue far from both the electrodes and heart surfaces require elucidation. Bidomain theory explains this phenomena through the existence of intramural virtual electrodes (VEs), caused by discontinuities in myocardial tissue structure. In this study, we assess the modeling components essential in constructing a finite-element cardiac tissue model including blood vessels from high-resolution magnetic resonance data and investigate the specific role played by coronary vasculature in VE formation, which currently remains largely unknown. We use a novel method for assigning histologically based fiber architecture around intramural structures and include an experimentally derived vessel lumen wall conductance within the model. Shock-tissue interaction in the presence of vessels is assessed through comparison with a simplified model lacking intramural structures. Results indicate that VEs form around blood vessels for shocks > 8 V/cm. The magnitude of induced polarizations is attenuated by realistic representation of fiber negotiation around vessel cavities, as well as the insulating effects of the vessel lumen wall. Furthermore, VEs formed around large subepicardial vessels reduce epicardial polarization levels. In conclusion, we have found that coronary vasculature acts as an important substrate for VE formation, which may help interpretation of optical mapping data.

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

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

A macro finite-element formulation for cardiac electrophysiology simulations using hybrid unstructured grids

Electrical activity in cardiac tissue can be described by the bidomain equations whose solution for large-scale simulations still remains a computational challenge. Therefore, improvements in the discrete formulation of the problem, which decrease computational and/or memory demands are highly desirable. In this study, we propose a novel technique for computing shape functions of finite elements (FEs). The technique generates macro FEs (MFEs) based on the local decomposition of elements into tetrahedral subelements with linear shape functions. Such an approach necessitates the direct use of hybrid meshes (HMs) composed of different types of elements. MFEs are compared to classic standard FEs with respect to accuracy and RAM memory usage under different scenarios of cardiac modeling, including bidomain and monodomain simulations in 2-D and 3-D for simple and complex tissue geometries. In problems with analytical solutions, MFEs displayed the same numerical accuracy of standard linear triangular and tetrahedral elements. In propagation simulations, conduction velocity and activation times agreed very well with those computed with standard FEs. However, MFEs offer a significant decrease in memory requirements. We conclude that HMs composed of MFEs are well suited for solving problems in cardiac computational electrophysiology.

Arrhythmic risk biomarkers for the assessment of drug cardiotoxicity: from experiments to computer simulations

In this paper, we illustrate how advanced computational modelling and simulation can be used to investigate drug-induced effects on cardiac electrophysiology and on specific biomarkers of pro-arrhythmic risk. To do so, we first perform a thorough literature review of proposed arrhythmic risk biomarkers from the ionic to the electrocardiogram levels. The review highlights the variety of proposed biomarkers, the complexity of the mechanisms of drug-induced pro-arrhythmia and the existence of significant animal species differences in drug-induced effects on cardiac electrophysiology. Predicting drug-induced pro-arrhythmic risk solely using experiments is challenging both preclinically and clinically, as attested by the rise in the cost of releasing new compounds to the market. Computational modelling and simulation has significantly contributed to the understanding of cardiac electrophysiology and arrhythmias over the last 40 years. In the second part of this paper, we illustrate how state-of-the-art open source computational modelling and simulation tools can be used to simulate multi-scale effects of drug-induced ion channel block in ventricular electrophysiology at the cellular, tissue and whole ventricular levels for different animal species. We believe that the use of computational modelling and simulation in combination with experimental techniques could be a powerful tool for the assessment of drug safety pharmacology.

Models of cardiac tissue electrophysiology: progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

[Multiscale modeling of cardiac electrical activity]

Models of cardiac electrical activity cover a wide range of spatial scales, from the genesis of the ionic currents in individual cardiomyocytes to the generation of electrocardiograms on the torso. The level of detail that is appropriate and practicable depends on the problem investigated and the scope of the computations that are required. We briefly present three examples of modelling: the dynamics of the entrainment of a single cell, the impact of fibrosis on electrical propagation in a piece of tissue and the generation of ECG in human. In each case, the methods, results and limitations are discussed.

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.

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.

Mechanism of right precordial ST-segment elevation in structural heart disease: excitation failure by current-to-load mismatch

BACKGROUND

The Brugada sign has been associated with mutations in SCN5A and with right ventricular structural abnormalities. Their role in the Brugada sign and the associated ventricular arrhythmias is unknown.

OBJECTIVE

The purpose of this study was to delineate the role of structural abnormalities and sodium channel dysfunction in the Brugada sign.

METHODS

Activation and repolarization characteristics of the explanted heart of a patient with a loss-of-function mutation in SCN5A (G752R) and dilated cardiomyopathy were determined after induction of right-sided ST-segment elevation by ajmaline. In addition, right ventricular structural discontinuities and sodium channel dysfunction were simulated in a computer model encompassing the heart and thorax.

RESULTS

In the explanted heart, disappearance of local activation in unipolar electrograms at the basal right ventricular epicardium was followed by monophasic ST-segment elevation. The local origin of this phenomenon was confirmed by coaxial electrograms. Neither early repolarization nor late activation correlated with ST-segment elevation. At sites of local ST-segment elevation, the subepicardium was interspersed with adipose tissue and contained more fibrous tissue than either the left ventricle or control hearts. In computer simulations entailing right ventricular structural discontinuities, reduction of sodium channel conductance or size of the gaps between introduced barriers resulted in subepicardial excitation failure or delayed activation by current-to-load mismatch and in the Brugada sign on the ECG.

CONCLUSION

Right ventricular excitation failure and activation delay by current-to-load mismatch in the subepicardium can cause the Brugada sign. Therefore, current-to-load mismatch may underlie the ventricular arrhythmias in patients with the Brugada sign.

Non-invasive imaging of cardiac activation and recovery

The sequences of activation and recovery of the heart have physiological and clinical relevance. We report on progress made over the last years in the method that images these timings based on an equivalent double layer on the myocardial surface serving as the equivalent source of cardiac activity, with local transmembrane potentials (TMP) acting as their strength. The TMP wave forms were described analytically by timing parameters, found by minimizing the difference between observed body surface potentials and those based on the source description. The parameter estimation procedure involved is non-linear, and consequently requires the specification of initial estimates of its solution. Those of the timing of depolarization were based on the fastest route algorithm, taking into account properties of anisotropic propagation inside the myocardium. Those of recovery were based on electrotonic effects. Body surface potentials and individual geometry were recorded on: a healthy subject, a WPW patient and a Brugada patient during an Ajmaline provocation test. In all three cases, the inversely estimated timing agreed entirely with available physiological knowledge. The improvements to the inverse procedure made are attributed to our use of initial estimates based on the general electrophysiology of propagation. The quality of the results and the required computation time permit the application of this inverse procedure in a clinical setting.

Non-invasive imaging of cardiac activation and recovery

The sequences of activation and recovery of the heart have physiological and clinical relevance. We report on progress made over the last years in the method that images these timings based on an equivalent double layer on the myocardial surface serving as the equivalent source of cardiac activity, with local transmembrane potentials (TMP) acting as their strength. The TMP wave forms were described analytically by timing parameters, found by minimizing the difference between observed body surface potentials and those based on the source description. The parameter estimation procedure involved is non-linear, and consequently requires the specification of initial estimates of its solution. Those of the timing of depolarization were based on the fastest route algorithm, taking into account properties of anisotropic propagation inside the myocardium. Those of recovery were based on electrotonic effects. Body surface potentials and individual geometry were recorded on: a healthy subject, a WPW patient and a Brugada patient during an Ajmaline provocation test. In all three cases, the inversely estimated timing agreed entirely with available physiological knowledge. The improvements to the inverse procedure made are attributed to our use of initial estimates based on the general electrophysiology of propagation. The quality of the results and the required computation time permit the application of this inverse procedure in a clinical setting.

Validation of a simple model for the morphology of the T wave in unipolar electrograms

Local unipolar electrograms (UEGs) permit assessment of local activation and repolarization times at multiple sites simultaneously. However, UEG-based indexes of local repolarization are still debated, in particular for positive T waves. Previous experimental and computer modeling studies have not been able to terminate the debate. In this study we validate a simple theoretical model of the UEG and use it to explain how repolarization statistics in the UEG relate to those in the action potential. The model reconstructs the UEG by taking the difference between an inverted local action potential and a position-independent remote signal. In normal tissue, this extremely simple model predicts T-wave morphology with surprising accuracy while explaining in a readily understandable way why the instant of repolarization is always related to the steepest upstroke of the UEG, both in positive and negative T waves, and why positive T waves are related to early repolarizing sites, whereas negative T waves are related to late repolarizing sites.

Concurrent optimization of timing delays and electrode positioning in biventricular pacing based on a computer heart model assuming 17 left ventricular segments

BACKGROUND

The efficacy of cardiac resynchronization therapy through biventricular pacing (BVP) has been demonstrated by numerous studies in patients suffering from congestive heart failure. In order to achieve a guideline for optimal treatment with BVP devices, an automated non-invasive strategy based on a computer model of the heart is presented.

MATERIALS AND METHODS

The presented research investigates an off-line optimization algorithm regarding electrode positioning and timing delays. The efficacy of the algorithm is demonstrated in four patients suffering from left bundle branch block (LBBB) and myocardial infarction (MI). The computer model of the heart was used to simulate the LBBB in addition to several MI allocations according to the different left ventricular subdivisions introduced by the American Heart Association. Furthermore, simulations with reduced interventricular conduction velocity were performed in order to model interventricular excitation conduction delay. More than 800,000 simulations were carried out by adjusting a variety of 121 pairs of atrioventricular and interventricular delays and 36 different electrode positioning set-ups. Additionally, three different conduction velocities were examined. The optimization measures included the minimum root mean square error (E(RMS)) between physiological, pathological and therapeutic excitation, and also the difference of QRS-complex duration. Both of these measures were computed automatically.

RESULTS

Depending on the patient's pathology and conduction velocity, a reduction of E(RMS) between physiological and therapeutic excitation could be reached. For each patient and pathology, an optimal pacing electrode pair was determined. The results demonstrated the importance of an individual adjustment of BVP parameters to the patient's anatomy and pathology.

CONCLUSION

This work proposes a novel non-invasive optimization algorithm to find the best electrode positioning sites and timing delays for BVP in patients with LBBB and MI. This algorithm can be used to plan an optimal therapy for an individual patient.

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.

Simulation of cardiac electrophysiology on next-generation high-performance computers

Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) coupled with a system of ordinary differential equations representing cell membrane dynamics. Current software to solve such models does not provide the required computational speed for practical applications. One reason for this is that little use is made of recent developments in adaptive numerical algorithms for solving systems of PDEs. Studies have suggested that a speedup of up to two orders of magnitude is possible by using adaptive methods. The challenge lies in the efficient implementation of adaptive algorithms on massively parallel computers. The finite-element (FE) method is often used in heart simulators as it can encapsulate the complex geometry and small-scale details of the human heart. An alternative is the spectral element (SE) method, a high-order technique that provides the flexibility and accuracy of FE, but with a reduced number of degrees of freedom. The feasibility of implementing a parallel SE algorithm based on fully unstructured all-hexahedra meshes is discussed. A major computational task is solution of the large algebraic system resulting from FE or SE discretization. Choice of linear solver and preconditioner has a substantial effect on efficiency. A fully parallel implementation based on dynamic partitioning that accounts for load balance, communication and data movement costs is required. Each of these methods must be implemented on next-generation supercomputers in order to realize the necessary speedup. The problems that this may cause, and some of the techniques that are beginning to be developed to overcome these issues, are described.

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.

A reliability analysis of cardiac repolarization time markers

Only a limited number of studies have addressed the reliability of extracellular markers of cardiac repolarization time, such as the classical marker RT(eg) defined as the time of maximum upslope of the electrogram T wave. This work presents an extensive three-dimensional simulation study of cardiac repolarization time, extending the previous one-dimensional simulation study of a myocardial strand by Steinhaus [B.M. Steinhaus, Estimating cardiac transmembrane activation and recovery times from unipolar and bipolar extracellular electrograms: a simulation study, Circ. Res. 64 (3) (1989) 449]. The simulations are based on the bidomain - Luo-Rudy phase I system with rotational fiber anisotropy and homogeneous or heterogeneous transmural intrinsic membrane properties. The classical extracellular marker RT(eg) is compared with the gold standard of fastest repolarization time RT(tap), defined as the time of minimum derivative during the downstroke of the transmembrane action potential (TAP). Additionally, a new extracellular marker RT90(eg) is compared with the gold standard of late repolarization time RT90(tap), defined as the time when the TAP reaches 90% of its resting value. The results show a good global match between the extracellular and transmembrane repolarization markers, with small relative mean discrepancy (<or=1.6%) and high correlation coefficients (>or=0.92), ensuring a reasonably good global match between the associated repolarization sequences. However, large local discrepancies of the extracellular versus transmembrane markers may ensue in regions where the curvature of the repolarization front changes abruptly (e.g. near front collisions) or is negligible (e.g. where repolarization proceeds almost uniformly across fiber). As a consequence, the spatial distribution of activation-recovery intervals (ARI) may provide an inaccurate estimate of (and weakly correlated with) the spatial distribution of action potential durations (APD).

Low energy defibrillation in human cardiac tissue: a simulation study

We aim to assess the effectiveness of feedback-controlled resonant drift pacing as a method for low energy defibrillation. Antitachycardia pacing is the only low energy defibrillation approach to have gained clinical significance, but it is still suboptimal. Low energy defibrillation would avoid adverse side effects associated with high voltage shocks and allow the application of implantable cardioverter defibrillator (ICD) therapy, in cases where such therapy is not tolerated today. We present results of computer simulations of a bidomain model of cardiac tissue with human atrial ionic kinetics. Reentry was initiated and low energy shocks were applied with the same period as the reentry, using feedback to maintain resonance. We demonstrate that such stimulation can move the core of reentrant patterns, in the direction that depends on the location of the electrodes and the time delay in the feedback. Termination of reentry is achieved with shock strength one-order-of-magnitude weaker than in conventional single-shock defibrillation. We conclude that resonant drift pacing can terminate reentry at a fraction of the shock strength currently used for defibrillation and can potentially work where antitachycardia pacing fails, due to the feedback mechanisms. Success depends on a number of details that these numerical simulations have uncovered.

Cardiac anisotropy in boundary-element models for the electrocardiogram

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies.

Estimating atrial action potential duration from electrograms

Electrogram analysis is important in clinical and experimental settings. Activation recovery interval (ARI) has been used to measure ventricular action potential duration (APD) but its suitability for the atria has not been addressed. Mapping of atrial repolarization may be especially important during nerve stimulation since large heterogenous APD changes may manifest. This study assessed the utility of estimating APD in the atria using electrograms. A computer model of the atria was used to compute electrograms. Two different atrial waveforms were used, as well as two ventricular. APD was modulated with an acetylcholine- (ACh) dependent potassium channel and varying the spatial ACh distribution. ARI was computed, as well as the area under the repolarization wave (ATa). APD was measured by four methods. Atrial electrograms were also compared to monophasic action potentials recorded from a dog. ARI computed from atrial action potentials was not very precise, with errors ranging over 30 ms. Determining changes in APD induced by changing [ACh] yielded larger errors. Conversely, ventricular action potentials produced ARIs that very closely correlated with APD, and changes in APD . Positive ATa indicated regions of shortened APD, and islands of ACh release were clearly demarcated by ATa polarity. Experimentally, ARI was able to detect changes in APD, but did not measure APD well. The faster rate of ventricular repolarization produces larger currents that are less susceptible to electrotonic coupling effects, improving correlation with APD. ARI most closely correlated with APD measured as a fixed threshold above rest. Atrial APs produce electrograms that can be used to detect changes in APD. This may be improved by decreasing coupling. The ATa is a robust measure for precisely identifying spatial APD heterogeneities.

Orthogonal recursive bisection data decomposition for high performance computing in cardiac model simulations: dependence on anatomical geometry

Orthogonal recursive bisection (ORB) algorithm can be used as data decomposition strategy to distribute a large data set of a cardiac model to a distributed memory supercomputer. It has been shown previously that good scaling results can be achieved using the ORB algorithm for data decomposition. However, the ORB algorithm depends on the distribution of computational load of each element in the data set. In this work we investigated the dependence of data decomposition and load balancing on different rotations of the anatomical data set to achieve optimization in load balancing. The anatomical data set was given by both ventricles of the Visible Female data set in a 0.2 mm resolution. Fiber orientation was included. The data set was rotated by 90 degrees around x, y and z axis, respectively. By either translating or by simply taking the magnitude of the resulting negative coordinates we were able to create 14 data set of the same anatomy with different orientation and position in the overall volume. Computation load ratios for non - tissue vs. tissue elements used in the data decomposition were 1:1, 1:2, 1:5, 1:10, 1:25, 1:38.85, 1:50 and 1:100 to investigate the effect of different load ratios on the data decomposition. The ten Tusscher et al. (2004) electrophysiological cell model was used in monodomain simulations of 1 ms simulation time to compare performance using the different data sets and orientations. The simulations were carried out for load ratio 1:10, 1:25 and 1:38.85 on a 512 processor partition of the IBM Blue Gene/L supercomputer. Th results show that the data decomposition does depend on the orientation and position of the anatomy in the global volume. The difference in total run time between the data sets is 10 s for a simulation time of 1 ms. This yields a difference of about 28 h for a simulation of 10 s simulation time. However, given larger processor partitions, the difference in run time decreases and becomes less significant. Depending on the processor partition size, future work will have to consider the orientation of the anatomy in the global volume for longer simulation runs.

Strong scaling and speedup to 16,384 processors in cardiac electro-mechanical simulations

High performance computing is required to make feasible simulations of whole organ models of the heart with biophysically detailed cellular models in a clinical setting. Increasing model detail by simulating electrophysiology and mechanical models increases computation demands. We present scaling results of an electro - mechanical cardiac model of two ventricles and compare them to our previously published results using an electrophysiological model only. The anatomical data-set was given by both ventricles of the Visible Female data-set in a 0.2 mm resolution. Fiber orientation was included. Data decomposition for the distribution onto the distributed memory system was carried out by orthogonal recursive bisection. Load weight ratios for non-tissue vs. tissue elements used in the data decomposition were 1:1, 1:2, 1:5, 1:10, 1:25, 1:38.85, 1:50 and 1:100. The ten Tusscher et al. (2004) electrophysiological cell model was used and the Rice et al. (1999) model for the computation of the calcium transient dependent force. Scaling results for 512, 1024, 2048, 4096, 8192 and 16,384 processors were obtained for 1 ms simulation time. The simulations were carried out on an IBM Blue Gene/L supercomputer. The results show linear scaling from 512 to 16,384 processors with speedup factors between 1.82 and 2.14 between partitions. The most optimal load ratio was 1:25 for on all partitions. However, a shift towards load ratios with higher weight for the tissue elements can be recognized as can be expected when adding computational complexity to the model while keeping the same communication setup. This work demonstrates that it is potentially possible to run simulations of 0.5 s using the presented electro-mechanical cardiac model within 1.5 hours.

Computational modeling of cardiac disease: potential for personalized medicine

Cardiovascular diseases are leading causes of death, reduce life quality and consume almost half a trillion dollars in healthcare expenses in the USA alone. Cardiac modeling and simulation technologies hold promise as important tools to improve cardiac care and are already in use to elucidate the fundamental mechanisms of cardiac physiology and pathophysiology. However, the emphasis has been on simulating average or exemplar cases. This report describes two classes of cardiac modeling efforts. First, electrophysiological models of channelopathies simulate the altered electrical activity that is thought to promote arrhythmias. Second, electromechanical models attempt to capture both the electrophysiological and mechanical aspects of heart function. One goal of the community is to develop models with sufficient patient customization to assist in personalized treatment planning. Some model aspects can be customized with existing data collection techniques to more closely represent individual patients while other model aspects will likely remain based on generic data. Despite important challenges, cardiac models hold promise to be important enablers of personalized medicine.

Spatial-temporal filter effect in a computer model study of ventricular fibrillation

Prediction of countershock success from ventricular fibrillation (VF) ECG is a major challenge in critical care medicine. Recent findings indicate that stable, high frequency mother rotors are one possible mechanism maintaining VF. A computer model study was performed to investigate how epicardiac sources are reflected in the ECG. In the cardiac tissues of two computer models - a model with cubic geometry and a simplified torso model with a left ventricle - a mother rotor was induced by increasing the potassium rectifier current. On the epicardium, the dominant frequency (DF) map revealed a constant DF of 23 Hz (cubic model) and 24.4 Hz (torso model) in the region of the mother rotor, respectively. A sharp drop of frequency (3-18 Hz in the cubic model and 12.4-18 Hz in the torso model) occurred in the surrounding epicardial tissue of chaotic fibrillatory conduction. While no organized pattern was observable on the body surface of the cubic model, the mother rotor frequency can be identified in the anterior surface of the torso model because of the chosen position of the mother rotor in the ventricle (shortest distance to the body surface). Nevertheless, the DFs were damped on the body surfaces of both models (4.6-8.5 Hz in the cubic model and 14.4-16.4 Hz in the torso model). Thus, it was shown in this computer model study that wave propagation transforms the spatial low pass filtering of the thorax into a temporal low pass. In contrast to the resistive-capacitive low pass filter formed by the tissue, this spatial-temporal low pass filter becomes effective at low frequencies (tens of Hertz). This effect damps the high frequency components arising from the heart and it hampers a direct observation of rapid, organized sources of VF in the ECGs, when in an emergency case an artifact-free recording is not possible.

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.