Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation

In the whole heart, millions of cardiac cells are involved in ventricular fibrillation (VF). Experimental studies indicate that VF is sustained by re-entrant activity, and that each re-entrant wave rotates around a filament of phase singularity. Filaments act as organising centres, and offer a way to simplify and quantify the complex spatio-temporal behaviour observed in VF. Where a filament touches the surface of fibrillating myocardium re-entrant activity can be observed, however the behaviour of filaments within bulk ventricular myocardium is difficult to observe directly using present experimental techniques. Large scale computational simulations of VF in three-dimensional (3D) tissue offer a tool to investigate the properties and behaviour of filaments, and the aim of this paper is to review recent advances in this area as well as to compare recent computational studies of fibrillation in whole ventricle geometries.     

Propagation of normal beats and re-entry in a computational model of ventricular cardiac tissue with regional differences in action potential shape and duration

There is substantial experimental evidence from studies using both intact tissue and isolated single cells to support the existence of different cell types within the ventricular wall of the heart, each possessing different electrical properties. However other studies have failed to find these differences, and instead support the idea that electrical coupling in vivo between regions with different cell types smoothes out differences in action potential shape and duration. In this study we have used a computational model of electrical activation in heterogenous 2D and 3D cardiac tissue to investigate the propagation of both normal beats and arrhythmias. We used the Luo–Rudy dynamic model for guinea pig ventricular cells, with simplified Ca²⁺ handling and transmural heterogeneity in I_Ks and I_to. With normal cell-to-cell coupling, a layer of M cells was not necessary for the formation of an upright T wave in the simulated electrocardiogram, and the amplitude and configuration of the T wave was not greatly affected by the thickness and configuration of the M cell layer. Transmural gradients in repolarisation pushed re-entrant waves with an intramural filament towards either the base or the apex of the ventricles, and caused transient break up of re-entry with a transmural filament.     

A finite element study relating to the rapid filling phase of the human ventricles

During the rapid diastolic filling phase at rest, the ventricles of the human heart double approximately in volume. In order to investigate whether the ventricular filling pressures measured under physiological conditions can give rise to such an extensive augmentation in ventricular volumes, a finite element model of the human right and left ventricles has been developed, taking into account the nonlinear mechanical behavior and effective compressibility of the myocardial tissue. The results were compared with the filling phase of the human left ventricle as extrapolated from measurements documented in the literature. We arrived at the conclusion that the ventricular pressures measured during the rapid filling phase cannot be the sole cause of the rise of the observed ventricular volumes. We rather advocate the assumption that further dilating mechanisms might be part of ventricular activity thus heralding a multiple function of the ventricular muscle body. A further result indicates that under normal conditions the influence of the viscoelasticity of the tissue should not be disregarded in ventricular mechanics.     

Modelling the cardiac transverse-axial tubular system

The transverse-axial tubular system (TATS) of cardiac ventricular myocytes is a complex network of tubules that arises as invaginations of the surface membrane; it appears to form a specialised region of cell membrane that is particularly important for excitation–contraction coupling. However, much remains unknown about the structure and role of the TATS. In this brief review we use experimental data and computer modelling to address the following key questions: (i) What fraction of the cell membrane is within the TATS? (ii) Is the composition of the TATS membrane the same as the surface membrane? (iii) How good is electrical coupling between the surface and TATS membranes? (iv) What fraction of each current is within the TATS? (v) How important is the complex structure of the TATS network? (vi) What is the effect of current inhomogeneity on lumenal ion concentrations? (vii) Does the TATS contribute to the functional changes observed in heart failure? Although there are many areas in which experimental evidence is lacking, computer models provide a method to assess and predict the possible function of the TATS; such models suggest that although the surface and TATS membranes are electrically well coupled, concentration of ion flux pathways within the TATS, coupled to restricted diffusion, may result in the ionic composition in the TATS lumen being different from that in the bulk extracellular space, and varying with activity and in pathological conditions.     

Atrial natriuretic factor in the impulse-conduction system of rat cardiac ventricles

Summary A complex network of atrial natriuretic factor-producing cells has been delineated by biochemical and morphological techniques in the rat ventricular myocardium. The chordae tendineae spuriae (CTS; false tendons) contain ANF mRNA and the ANF propeptide (Asn 1-Tyr 126) as assessed by Northern blot analysis, high-pressure liquid chromatography and immunohisto- and -cytochemistry, using three different affinity-purified antibodies: monoclonal and polyclonal antibodies against C-terminal ANF (Arg 101-Tyr 126) and polyclonal antibodies against N-terminal ANF (Asp 11-Ala 37). Two types of cells harboring ANF-containing secretory granules constitute the CTS: the majority (Purkinje type I) have ultrastructural similarities with both atrial and classical Purkinje fibers. Purkinje type-II fibers resemble working ventricular cardiocytes. Both cell types harbor a large paranuclear Golgi complex. The subendocardial Purkinje network is also made up of these two cell types. In this location, Purkinje type-I fibers form cable-like structures while Purkinje type-II fibers are either located beneath the former or abut directly on the endocardium. The latter are not separated from adjacent working ventricular cardiocytes by connective tissue septa. Coronary arteries and arterioles, as in birds, are surrounded by a cushion of Purkinje type-II fibers which blend with the surrounding myocardium. These results indicate that, in the rat, the entire intraventricular conduction system is constituted of endocrine cells producing ANF.Supported by a Medical Research Council of Canada Group Grant to the Multidisciplinary Research Group on Hypertension, by the National Research Council of Canada, the Pfizer Company (England), Bio-Méga Inc. and the Canadian Heart Foundation     

Realization of biophysical models of cardiac electrical activity

Considered are the principles of realization of biophysical models of heart ventricle electrical activity in the form of a double electric layer on the surface of the electrically active myocardium (epicardium and endocardium) and the boundary surfaces dividing the model compartments with different electrophysiological characteristics. The model parameters are the electrophysiological and anatomical characteristics of the heart such as the geometry of the ventricles and the specialized His-Purkinje conduction system, the velocity of depolarization spread over myocardium, the ratio of the velocities of excitation transmission through the Myocardium / His / Purkinje elements of the model, the shape of transmembrane action potentials on the boundary surfaces, the orientation of the intrinsic anatomical axes of the heart relative to the initial set of coordinates, and some other biophysical characteristics of the myocardium. This model is the main unit of a computer simulation system, which includes databases of real and simulated electrocardiosignals.     

Modulation of iNOS activity in age-related cardiac dysfunction

Based on the role of inducible nitric oxide synthase (iNOS) in heart failure, we hypothesized that the elevated expression of iNOS compared to young mice in the myocardium contributes to the age-related decline of left ventricular (LV) function. Cardiac iNOS mRNA and protein expression was singularly identified in old, wild type (WT) male mice (I6-month) and not in young WT male mice (6-month). Characterized with in vivo pressure-volume loops analysis, an age-related LV dysfunction was found in the old WT mice. The LV dysfunction of the aged mice was modified to that of the younger mice by the specific iNOS inhibitors, aminoguanidine (AMG, 10 mg/Kg, i.v. or infusion, n = 15) and S-methyl-isothiourea (MITU, 3 mg/Kg, i.v. n = 7), and declined with L-arginine (10 mg/Kg, i.v. n = 7). All three drugs had no effects on the LV function of young WT mice or old iNOS knockout (KO) mice. The NOx and cGMP levels were significantly higher only in the old WT mice (n = 6) and cGMP levels decreased to normal with AMG administration. In conclusion, these results suggested that the iNOS/NO/cGMP pathway may contribute to ventricular dysfunction during the aging process and that inhibition of iNOS activity significantly improved heart function in aged mice.     

A case of cardiac sarcoidosis mimicking Brugada syndrome

A 17-year-old boy was admitted for management of ventricular fibrillation (VF) with intermittent Brugada pattern on ECG. On evaluation, cardiac MRI revealed myocardial scar and mediastinal lymphadenopathy. 18-Fluorodeoxyglucose positron emission tomography scan showed inflammation in the heart, lungs, and lymph nodes. He was diagnosed as a case of cardiac sarcoidosis (CS) and treated with steroids. However, there was a reactivation of cardiac inflammation and the development of a second VF storm. Following catheter ablation, the patient's arrhythmia improved. This report highlights the inflammation due to CS mimicking channelopathic features.     

Mechanically induced electrical storm as a complication of cardiac resynchronization therapy: A case report

BackgroundCardiac resynchronization therapy (CRT) has been shown to improve both the functional status and mortality of heart failure patients with left bundle branch block. Multiple recent studies suggest several mechanisms for proarrhythmia associated with CRT device.Case summaryA 51-year-old male with symptomatic non-ischemic cardiomyopathy and no previous history of ventricular arrhythmias underwent placement of a biventricular cardioverter-defibrillator. The patient developed sustained monomorphic ventricular tachycardia (VT) soon after implantation. The VT recurred despite reprogramming to right ventricular only pacing. The electrical storm resolved only after a subsequent discharge from the defibrillator caused inadvertent dislodgement of the coronary sinus lead. No recurrent VT occurred throughout 10-years follow up after urgent coronary sinus lead revision.DiscussionWe describe the first reported case of mechanically induced electrical storm due to the physical presence of the CS lead in a patient with a new CRT-D device. It is important to recognize mechanical proarrhythmia as a potential mechanism of electrical storm, as it may be intractable to device reprogramming. Urgent coronary sinus lead revision should be considered. Further studies on this mechanism of proarrhythmia are needed.     

Genetic predisposition for sudden cardiac death in myocardial ischaemia: the Arrhythmia Genetics in the NEtherlandS study

Sudden cardiac death from ventricular fibrillation during myocardial infarction is a leading cause of total and cardiovascular mortality. This multifactorial, complex condition clusters in families, suggesting a substantial genetic cause. We carried out a genomewide association study (GWAS) for sudden cardiac death, in the AGNES (Arrhythmia Genetics in the Netherlands) population, consisting of patients with (cases) and without (controls) ventricular fibrillation during a first ST-elevation myocardial infarction. The most significant association was found at chromosome 21q21 (rs2824292; odds ratio = 1.78, 95% CI 1.47–2.13, P = 3.3 × 10⁻¹⁰), 98 kb proximal of the CXADR gene, encoding the Coxsackie and adenovirus receptor. This locus has not previously been implicated in arrhythmia susceptibility. Further research on the mechanism of this locus will ultimately provide novel insight into arrhythmia mechanisms in this condition.     

The effect of disease on human cardiac protein expression profiles in paired samples from right and left ventricles

Background

Cardiac diseases (e.g. coronary and valve) are associated with ventricular cellular remodeling. However, ventricular biopsies from left and right ventricles from patients with different pathologies are rare and thus little is known about disease-induced cellular remodeling in both sides of the heart and between different diseases. We hypothesized that the protein expression profiles between right and left ventricles of patients with aortic valve stenosis (AVS) and patients with coronary artery disease (CAD) are different and that the protein profile is different between the two diseases. Left and right ventricular biopsies were collected from patients with either CAD or AVS. The biopsies were processed for proteomic analysis using isobaric tandem mass tagging and analyzed by reverse phase nano-LC-MS/MS. Western blot for selected proteins showed strong correlation with proteomic analysis.

Results

Proteomic analysis between ventricles of the same disease (intra-disease) and between ventricles of different diseases (inter-disease) identified more than 500 proteins detected in all relevant ventricular biopsies. Comparison between ventricles and disease state was focused on proteins with relatively high fold (±1.2 fold difference) and significant (P < 0.05) differences. Intra-disease protein expression differences between left and right ventricles were largely structural for AVS patients and largely signaling/metabolism for CAD. Proteins commonly associated with hypertrophy were also different in the AVS group but with lower fold difference. Inter-disease differences between left ventricles of AVS and CAD were detected in 9 proteins. However, inter-disease differences between the right ventricles of CAD and AVS patients were associated with differences in 73 proteins. The majority of proteins which had a significant difference in one ventricle compared to the other pathology also had a similar trend in the adjacent ventricle.

Conclusions

This work demonstrates for the first time that left and right ventricles have a different proteome and that the difference is dependent on the type of disease. Inter-disease differential expression was more prominent for right ventricles. The finding that a protein change in one ventricle was often associated with a similar trend in the adjacent ventricle for a large number of proteins suggests cross-talk proteome remodeling between adjacent ventricles.     

Cytoskeletal modulation of electrical and mechanical activity in cardiac myocytes

The cardiac myocyte has an intracellular scaffold, the cytoskeleton, which has been implicated in several cardiac pathologies including hypertrophy and failure. In this review we describe the role that the cytoskeleton plays in modulating both the electrical activity (through ion channels and exchangers) and mechanical (or contractile) activity of the adult heart. We focus on the 3 components of the cytoskeleton, actin microfilaments, microtubules, and desmin filaments. The limited visual data available suggest that the subsarcolemmal actin cytoskeleton is sparse in the adult myocyte. Selective disruption of cytoskeletal actin by pharmacological tools has yet to be verified in the adult cell, yet evidence exists for modulation of several ionic currents, including I(CaL), I(Na), I(KATP), I(SAC) by actin microfilaments. Microtubules exist as a dense network throughout the adult cardiac cell, and their structure, architecture, kinetics and pharmacological manipulation are well described. Both polymerised and free tubulin are functionally significant. Microtubule proliferation reduces contraction by impeding sarcomeric motion; modulation of sarcoplasmic reticulum Ca(2+) release may also be involved in this effect. The lack of effect of microtubule disruption on cardiac contractility in adult myocytes, and the concentration-dependent modulation of the rate of contraction by the disruptor nocodazole in neonatal myocytes, support the existence of functionally distinct microtubule populations. We address the controversy regarding the stimulation of the beta-adrenergic signalling pathway by free tubulin. Work with mice lacking desmin has demonstrated the importance of intermediate filaments to normal cardiac function, but the precise role that desmin plays in the electrical and mechanical activity of cardiac muscle has yet to be determined.     

Focal extracellular potential: a means to monitor electrical activity in single cardiac myocytes

The focal extracellular potential (FEP) described in this study is an electrophysiological signal related to the transmembrane potential (V(m)) of cardiac myocytes that avoids the mechanical fragility, interference with contraction, and intracellular contact associated with conventional whole cell recording. One end of a frog ventricular myocyte was secured into a glass holding pipette. The FEP was measured differentially between this pipette and a bath pipette while the cell was voltage- or current-clamped by a third whole cell pipette. The FEP appeared as an amplitude-truncated action potential, while FEP duration accurately reflected the action potential duration (APD) at 90% repolarization (APD(90)). FEP magnitude increased as the holding pipette K(+) concentration ([K(+)]) was increased. The FEP-voltage relation was quasi-linear at negative V(m) with a slope that increased with elevated holding pipette [K(+)]. Increasing the membrane conductance inside the holding pipette by adding amphotericin B or cromakalim linearized the FEP-voltage relation across all V(m). The FEP accurately reported electrical activation and APD(90) during changes of stimulation frequency and episodes of cellular stretch.     

A continuum approach to modelling cell-cell adhesion

Cells adhere to each other through the binding of cell adhesion molecules at the cell surface. This process, known as cell-cell adhesion, is fundamental in many areas of biology, including early embryo development, tissue homeostasis and tumour growth. In this paper we develop a new continuous mathematical model of this phenomenon by considering the movement of cells in response to the adhesive forces generated through binding. We demonstrate that our model predicts the aggregation behaviour of a disassociated adhesive cell population. Further, when the model is extended to represent the interactions between multiple populations, we demonstrate that it is capable of replicating the different types of cell sorting behaviour observed experimentally. The resulting pattern formation is a direct consequence of the relative strengths of self-population and cross-population adhesive bonds in the model. While cell sorting behaviour has been captured previously with discrete approaches, it has not, until now, been observed with a fully continuous model.     

A working guide to boosted regression trees

1. Ecologists use statistical models for both explanation and prediction, and need techniques that are flexible enough to express typical features of their data, such as nonlinearities and interactions. 2. This study provides a working guide to boosted regression trees (BRT), an ensemble method for fitting statistical models that differs fundamentally from conventional techniques that aim to fit a single parsimonious model. Boosted regression trees combine the strengths of two algorithms: regression trees (models that relate a response to their predictors by recursive binary splits) and boosting (an adaptive method for combining many simple models to give improved predictive performance). The final BRT model can be understood as an additive regression model in which individual terms are simple trees, fitted in a forward, stagewise fashion. 3. Boosted regression trees incorporate important advantages of tree-based methods, handling different types of predictor variables and accommodating missing data. They have no need for prior data transformation or elimination of outliers, can fit complex nonlinear relationships, and automatically handle interaction effects between predictors. Fitting multiple trees in BRT overcomes the biggest drawback of single tree models: their relatively poor predictive performance. Although BRT models are complex, they can be summarized in ways that give powerful ecological insight, and their predictive performance is superior to most traditional modelling methods. 4. The unique features of BRT raise a number of practical issues in model fitting. We demonstrate the practicalities and advantages of using BRT through a distributional analysis of the short-finned eel (Anguilla australis Richardson), a native freshwater fish of New Zealand. We use a data set of over 13 000 sites to illustrate effects of several settings, and then fit and interpret a model using a subset of the data. We provide code and a tutorial to enable the wider use of BRT by ecologists.     

A critical interpretation of experiments of binding of peptide hormone to specific receptors by computer modelling

Many investigations dealing with the interaction of peptide hormones and specific cell membrane receptors imply the existence of two classes of independent binding sites. One class is characterized by high affinity and low capacity, the other one by low affinity and high capacity. This conclusion has been derived from the fact that the Scatchard plots of binding data show a significant upward curvature. Using a more precise and critical method of evaluation these findings probably must be revised in some cases. Other conclusions taken from linear plots concerning the regulation of hormone receptors should be discussed more carefully. Some sources of errors caused by an uncritical interpretation of Scatchard plots are demonstrated.     

A model model: a commentary on DiFrancesco and Noble (1985) ‘A model of cardiac electrical activity incorporating ionic pumps and concentration changes’

This paper summarizes the advances made by the DiFrancesco and Noble (DFN) model of cardiac cellular electrophysiology, which was published in Philosophical Transactions B in 1985. This model was developed at a time when the introduction of new techniques and provision of experimental data had resulted in an explosion of knowledge about the cellular and biophysical properties of the heart. It advanced the cardiac modelling field from a period when computer models considered only the voltage-dependent channels in the surface membrane. In particular, it included a consideration of changes of both intra- and extracellular ionic concentrations. In this paper, we summarize the most important contributions of the DiFrancesco and Noble paper. We also describe how computer modelling has developed subsequently with the extension from the single cell to the whole heart as well as its use in understanding disease and predicting the effects of pharmaceutical interventions. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.