Constitutive Intracellular Na+ Excess in Purkinje Cells Promotes Arrhythmogenesis at Lower Levels of Stress Than Ventricular Myocytes From Mice With Catecholaminergic Polymorphic Ventricular Tachycardia.

BACKGROUND: In catecholaminergic polymorphic ventricular tachycardia (CPVT), cardiac Purkinje cells (PCs) appear more susceptible to Ca(2+) dysfunction than ventricular myocytes (VMs). The underlying mechanisms remain unknown. Using a CPVT mouse (RyR2(R4496C+/Cx40eGFP)), we tested whether PC intracellular Ca(2+) ([Ca(2+)]i) dysregulation results from a constitutive [Na(+)]i surplus relative to VMs. METHODS AND RESULTS: Simultaneous optical mapping of voltage and [Ca(2+)]i in CPVT hearts showed that spontaneous Ca(2+) release preceded pacing-induced triggered activity at subendocardial PCs. On simultaneous current-clamp and Ca(2+) imaging, early and delayed afterdepolarizations trailed spontaneous Ca(2+) release and were more frequent in CPVT PCs than CPVT VMs. As a result of increased activity of mutant ryanodine receptor type 2 channels, sarcoplasmic reticulum Ca(2+) load, measured by caffeine-induced Ca(2+) transients, was lower in CPVT VMs and PCs than respective controls, and sarcoplasmic reticulum fractional release was greater in both CPVT PCs and VMs than respective controls. [Na(+)]i was higher in both control and CPVT PCs than VMs, whereas the density of the Na(+)/Ca(2+) exchanger current was not different between PCs and VMs. Computer simulations using a PC model predicted that the elevated [Na(+)]i of PCs promoted delayed afterdepolarizations, which were always preceded by spontaneous Ca(2+) release events from hyperactive ryanodine receptor type 2 channels. Increasing [Na(+)]i monotonically increased delayed afterdepolarization frequency. Confocal imaging experiments showed that postpacing Ca(2+) spark frequency was highest in intact CPVT PCs, but such differences were reversed on saponin-induced membrane permeabilization, indicating that differences in [Na(+)]i played a central role. CONCLUSIONS: In CPVT mice, the constitutive [Na(+)]i excess of PCs promotes triggered activity and arrhythmogenesis at lower levels of stress than VMs.

KCNJ2 mutation in short QT syndrome 3 results in atrial fibrillation and ventricular proarrhythmia.

We describe a mutation (E299V) in KCNJ2, the gene that encodes the strong inward rectifier K(+) channel protein (Kir2.1), in an 11-y-old boy. The unique short QT syndrome type-3 phenotype is associated with an extremely abbreviated QT interval (200 ms) on ECG and paroxysmal atrial fibrillation. Genetic screening identified an A896T substitution in a highly conserved region of KCNJ2 that resulted in a de novo mutation E299V. Whole-cell patch-clamp experiments showed that E299V presents an abnormally large outward IK1 at potentials above -55 mV (P < 0.001 versus wild type) due to a lack of inward rectification. Coexpression of wild-type and mutant channels to mimic the heterozygous condition still resulted in a large outward current. Coimmunoprecipitation and kinetic analysis showed that E299V and wild-type isoforms may heteromerize and that their interaction impairs function. The homomeric assembly of E299V mutant proteins actually results in gain of function. Computer simulations of ventricular excitation and propagation using both the homozygous and heterozygous conditions at three different levels of integration (single cell, 2D, and 3D) accurately reproduced the electrocardiographic phenotype of the proband, including an exceedingly short QT interval with merging of the QRS and the T wave, absence of ST segment, and peaked T waves. Numerical experiments predict that, in addition to the short QT interval, absence of inward rectification in the E299V mutation should result in atrial fibrillation. In addition, as predicted by simulations using a geometrically accurate three-dimensional ventricular model that included the His-Purkinje network, a slight reduction in ventricular excitability via 20% reduction of the sodium current should increase vulnerability to life-threatening ventricular tachyarrhythmia.

Dominant frequency increase rate predicts transition from paroxysmal to long-term persistent atrial fibrillation.

BACKGROUND: Little is known about the mechanisms underlying the transition from paroxysmal to persistent atrial fibrillation (AF). In an ovine model of long-standing persistent AF we tested the hypothesis that the rate of electric and structural remodeling, assessed by dominant frequency (DF) changes, determines the time at which AF becomes persistent. METHODS AND RESULTS: Self-sustained AF was induced by atrial tachypacing. Seven sheep were euthanized 11.5±2.3 days after the transition to persistent AF and without reversal to sinus rhythm; 7 sheep were euthanized after 341.3±16.7 days of long-standing persistent AF. Seven sham-operated animals were in sinus rhythm for 1 year. DF was monitored continuously in each group. Real-time polymerase chain reaction, Western blotting, patch clamping, and histological analyses were used to determine the changes in functional ion channel expression and structural remodeling. Atrial dilatation, mitral valve regurgitation, myocyte hypertrophy, and atrial fibrosis occurred progressively and became statistically significant after the transition to persistent AF, with no evidence for left ventricular dysfunction. DF increased progressively during the paroxysmal-to-persistent AF transition and stabilized when AF became persistent. Importantly, the rate of DF increase correlated strongly with the time to persistent AF. Significant action potential duration abbreviation, secondary to functional ion channel protein expression changes (CaV1.2, NaV1.5, and KV4.2 decrease; Kir2.3 increase), was already present at the transition and persisted for 1 year of follow up. CONCLUSIONS: In the sheep model of long-standing persistent AF, the rate of DF increase predicts the time at which AF stabilizes and becomes persistent, reflecting changes in action potential duration and densities of sodium, L-type calcium, and inward rectifier currents.

Attraction of rotors to the pulmonary veins in paroxysmal atrial fibrillation: a modeling study.

Maintenance of paroxysmal atrial fibrillation (AF) by fast rotors in the left atrium (LA) or at the pulmonary veins (PVs) is not fully understood. To gain insight into this dynamic and complex process, we studied the role of the heterogeneous distribution of transmembrane currents in the PVs and LA junction (PV-LAJ) in the localization of rotors in the PVs. We also investigated whether simple pacing protocols could be used to predict rotor drift in the PV-LAJ. Experimentally observed heterogeneities in IK1, IKs, IKr, Ito, and ICaL in the PV-LAJ were incorporated into two- and pseudo three-dimensional models of Courtemanche-Ramirez-Nattel-Kneller human atrial kinetics to simulate various conditions and investigate rotor drifting mechanisms. Spatial gradients in the currents resulted in shorter action potential duration, minimum diastolic potential that was less negative, and slower upstroke and conduction velocity for rotors in the PV region than in the LA. Rotors under such conditions drifted toward the PV and stabilized at the shortest action potential duration and less-excitable region, consistent with drift direction under intercellular coupling heterogeneities and regardless of the geometrical constraint in the PVs. Simulations with various IK1 gradient conditions and current-voltage relationships substantiated its major role in the rotor drift. In our 1:1 pacing protocol, we found that among various action potential properties, only the minimum diastolic potential gradient was a rate-independent predictor of rotor drift direction. Consistent with experimental and clinical AF studies, simulations in an electrophysiologically heterogeneous model of the PV-LAJ showed rotor attraction toward the PV. Our simulations suggest that IK1 heterogeneity is dominant compared to other currents in determining the drift direction through its impact on the excitability gradient. These results provide a believed novel framework for understanding the complex dynamics of rotors in AF.

Reduced Na⁺ current density underlies impaired propagation in the diabetic rabbit ventricle.

Diabetes is associated with an increased risk of sudden cardiac death, but the underlying mechanisms remain unclear. Our goal was to investigate changes occurring in the action potential duration (APD) and conduction velocity (CV) in the diabetic rabbit ventricle, and delineate the principal ionic determinants. A rabbit model of alloxan-induced diabetes was utilized. Optical imaging was used to record electrical activity in isolated Langendorff-perfused hearts in normo-, hypo- and hyper-kalemia ([K(+)]o=4, 2, 12 mM respectively). Patch clamp experiments were conducted to record Na(+) current (I(Na)) in isolated ventricular myocytes. The mRNA/protein expression levels for Nav1.5 (the α-subunit of I(Na)) and connexin-43 (Cx43), as well as fibrosis levels were examined. Computer simulations were performed to interpret experimental data. We found that the APD was not different, but the CV was significantly reduced in diabetic hearts in normo-, hypo-, and, hyper-kalemic conditions (13%, 17% and 33% reduction in diabetic vs. control, respectively). The cell capacitance (Cm) was increased (by ~14%), and the density of INa was reduced by ~32% in diabetic compared to control hearts, but the other biophysical properties of I(Na) were unaltered. The mRNA/protein expression levels for Cx43 were unaltered. For Nav1.5, the mRNA expression was not changed, and though the protein level tended to be less in diabetic hearts, this reduction was not statistically significant. Staining showed no difference in fibrosis levels between the control and diabetic ventricles. Computer simulations showed that the reduced magnitude of I(Na) was a key determinant of impaired propagation in the diabetic ventricle, which may have important implications for arrhythmogenesis.

Identification and characterization of two novel KCNH2 mutations contributing to long QT syndrome.

We identified two different inherited mutations in KCNH2 gene, or human ether-a-go-go related gene (hERG), which are linked to Long QT Syndrome. The first mutation was in a 1-day-old infant, whereas the second was in a 14-year-old girl. The two KCNH2 mutations were transiently transfected into either human embryonic kidney (HEK) cells or human induced pluripotent stem-cell derived cardiomyocytes. We performed associated multiscale computer simulations to elucidate the arrhythmogenic potentials of the KCNH2 mutations. Genetic screening of the first and second index patients revealed a heterozygous missense mutation in KCNH2, resulting in an amino acid change (P632L) in the outer loop of the channel and substitution at position 428 from serine to proline (S428P), respectively. Heterologous expression of P632L and S428P into HEK cells produced no hERG current compared to the wild type (WT). Moreover, the co-transfection of WT and P632L yielded no hERG current; however, the co-transfection of WT and S428P yielded partial hERG current. Action potentials were prolonged in a complete or partial blockade of hERG current from computer simulations which was more severe in Purkinje than ventricular myocytes. Three dimensional simulations revealed a higher susceptibility to reentry in the presence of hERG current blockade. Our experimental findings suggest that both P632L and S428P mutations may impair the KCNH2 gene. The Purkinje cells exhibit a more severe phenotype than ventricular myocytes, and the hERG current blockade renders the ventricles an arrhythmogenic substrate from computer modeling.

A major role for HERG in determining frequency of reentry in neonatal rat ventricular myocyte monolayer.

RATIONALE: the rapid delayed rectifier potassium current, I(Kr), which flows through the human ether-a-go-go-related (hERG) channel, is a major determinant of the shape and duration of the human cardiac action potential (APD). However, it is unknown whether the time dependency of I(Kr) enables it to control APD, conduction velocity (CV), and wavelength (WL) at the exceedingly high activation frequencies that are relevant to cardiac reentry and fibrillation. OBJECTIVE: to test the hypothesis that upregulation of hERG increases functional reentry frequency and contributes to its stability. METHODS AND RESULTS: using optical mapping, we investigated the effects of I(Kr) upregulation on reentry frequency, APD, CV, and WL in neonatal rat ventricular myocyte (NRVM) monolayers infected with GFP (control), hERG (I(Kr)), or dominant negative mutant hERG G628S. Reentry frequency was higher in the I(Kr)-infected monolayers (21.12 ± 0.8 Hz; n=43 versus 9.21 ± 0.58 Hz; n=16; P<0.001) but slightly reduced in G628S-infected monolayers. APD(80) in the I(Kr)-infected monolayers was shorter (>50%) than control during pacing at 1 to 5 Hz. CV was similar in both groups at low frequency pacing. In contrast, during high-frequency reentry, the CV measured at varying distances from the center of rotation was significantly faster in I(Kr)-infected monolayers than controls. Simulations using a modified NRVM model predicted that rotor acceleration was attributable, in part, to a transient hyperpolarization immediately following the AP. The transient hyperpolarization was confirmed experimentally. CONCLUSIONS: hERG overexpression dramatically accelerates reentry frequency in NRVM monolayers. Both APD and WL shortening, together with transient hyperpolarization, underlies the increased rotor frequency and stability.

TIME- AND FREQUENCY-BASED INDEPENDENT EVALUATION OF QRST CANCELLATION TECHNIQUES FOR SINGLE-LEAD ELECTROCARDIOGRAMS DURING ATRIAL FIBRILLATION.

With the increased prevalence of atrial fibrillation (AF) - a rhythm disturbance in heart's top chambers - there is growing interest in accurate non-invasive diagnosis of atrial activity to improve its therapy. A key component in non-invasive analysis of atrial activity is a successful removal of the ventricular QRST complexes from electrocardiograms (ECGs). In this study, we have developed a new approach for an objective and physiologically-based evaluation of QRST cancellation methods based on comparisons with the power spectra of the AF. Three commonly used QRST cancellation methods were evaluated; namely, average beat subtraction, singular value cancellation, and principal component analysis. These methods were evaluated in time and frequency domains using a set of synthesized ECGs preserving the atrial-specific temporal and spectral properties. It was observed that the ABS method provided the best estimation when QRST morphological variability is low, while PCA produces an overall best estimate when a large QRST morphological variability is present.

Optical Deformation of Biological Cells using Dual-Beam Laser Tweezer.

Optical tweezer is a non-contact tool to trap and manipulate microparticles such as biological cells using coherent light beams. In this study, we utilized a dual-beam optical tweezer, created using two counterpropagating and slightly divergent laser beams to trap and deform biological cells. Human embryonic kidney 293 (HEK-293) and breast cancer (SKBR3) cells were used to characterize their membrane elasticity by optically stretching in the dual-beam optical tweezer. It was observed that the extent of deformation in both cell types increases with increasing optical trapping power. The SKBR3 cells exhibited greater percentage deformation than that of HEK-293 cells for a given trapping power. Our results demonstrate that the dual-beam optical tweezer provides measures of cell elasticity that can distinguish between various cell types. The non-contact optical cell stretching can be effectively utilized in disease diagnosis such as cancer based on the cell elasticity measures.

An in silico hiPSC-Derived Cardiomyocyte Model Built With Genetic Algorithm.

The formulation of in silico biophysical models generally requires optimization strategies for reproducing experimentally observed phenomena. In electrophysiological modeling, robust nonlinear regressive methods are often crucial for guaranteeing high fidelity models. Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), though nascent, have proven to be useful in cardiac safety pharmacology, regenerative medicine, and in the implementation of patient-specific test benches for investigating inherited cardiac disorders. This study demonstrates the potency of heuristic techniques at formulating biophysical models, with emphasis on a hiPSC-CM model using a novel genetic algorithm (GA) recipe we proposed. The proposed GA protocol was used to develop a hiPSC-CM biophysical computer model by fitting mathematical formulations to experimental data for five ionic currents recorded in hiPSC-CMs. The maximum conductances of the remaining ionic channels were scaled based on recommendations from literature to accurately reproduce the experimentally observed hiPSC-CM action potential (AP) metrics. Near-optimal parameter fitting was achieved for the GA-fitted ionic currents. The resulting model recapitulated experimental AP parameters such as AP durations (APD50, APD75, and APD90), maximum diastolic potential, and frequency of automaticity. The outcome of this work has implications for validating the biophysics of hiPSC-CMs in their use as viable substitutes for human cardiomyocytes, particularly in cardiac safety pharmacology and in the study of inherited cardiac disorders. This study presents a novel GA protocol useful for formulating robust numerical biophysical models. The proposed protocol is used to develop a hiPSC-CM model with implications for cardiac safety pharmacology.

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.

Convolutional Neural Network Based Breast Cancer Histopathology Image Classification.

Breast cancer is a global health concern, with approximately 30 million new cases projected to be reported by 2030. While efforts are being channeled into curative measures, preventive and diagnostic measures also need to be improved to curb the situation. Convolutional Neural Networks (CNNs) are a class of deep learning algorithms that have been widely adopted for the computerized classification of breast cancer histopathology images. In this work, we propose a set of training techniques to improve the performance of CNN-based classifiers for breast cancer identification. We combined transfer learning techniques with data augmentation and whole image training to improve the performance of the CNN classifier. Instead of conventional image patch extraction for training and testing, we employed a high-resolution whole-image training and testing on a modified network that was pre-trained on the Imagenet dataset. Despite the computational complexity, our proposed classifier achieved significant improvement over the previously reported studies on the open-source BreakHis dataset, with an average image level accuracy of about 91% and patient scores as high as 95%.Clinical Relevance- this work improves on the performance of CNN for breast cancer histopathology image classification. An improved Breast cancer image classification can be used for the preliminary examination of tissue slides in breast cancer diagnosis.

Accurate Estimation of Refractive Indices of Organic Microparticles in Dual-Beam Optical Trap.

The Refractive Index (RI) is an important parameter of characterizing optical properties of particles. In a dual-beam optical trap, two counter-propagating laser beams are used to trap micro-particles suspended in an aqueous medium. When a ray of light passes from one medium of lower RI (e.g. aqueous suspension medium) to another medium of higher RI (e.g. suspended particle), its momentum changes which exerts a proportional trapping force on the surface of the particle. Thus, accurate knowledge of RI of the particles and the surrounding medium is needed to determine the behavior of particles in an optical trap. The RI of micro-sized beads can be experimentally measured using traditional optical methods such as absorption microscopy. We developed an alternative theoretical method to estimate the RI of trapped particles based on non-contact optical trapping experimental outcomes. In our study, a theoretical model was formulated based on the experimentally measured minimum trapping powers for polystyrene and polyethylene beads using a dual-beam optical setup. The tendencies of trapping power-RI curves predicted by our model agreed very well with those measured experimentally. Our technique provides an alternative approach to determining the RI of a certain micro-size particle regardless of its size or density. Our method is especially advantageous over traditional methods to determine RI of biological particles which exhibit significant variations based on physiological and environmental conditions.

Genetic Algorithm For Fitting Cardiac Cell Biophysical Model Formulations.

Modeling cardiac cell electrophysiology relies on fitting model equations to experimental data obtained under voltage/current clamping conditions. The fitting procedure for these often-nonlinear ionic current equations are mostly executed by trial-and-error by hand or by gradient-based optimization approaches. These methods, though sometimes sufficient at converging at optimal solutions is based on the premise that the characteristic objective function is convex, which often does not apply to cardiac model equations. Meta-heuristic methods, such as evolutionary algorithms and particle swarm algorithms, have proven resilient against early convergence to local optima and saddle-point parameter solutions. This work presents a genetic algorithm-based approach for fitting the adult cardiomyocyte biophysical model formulations to the experimental data obtained in human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM). Specifically, whole-cell patch clamp ionic current data of rapid delayed rectifier potassium current, IKr, transient outward potassium current, Ito and hyperpolarization-activated current, If, was used for fitting. Using a two-point crossover scheme along with initial population and mutation constraints randomly selected from a uniformly distributed constrained parameter space, near-optimal fitting was achieved with R2 values (n = 5) of 0.9960±0.0007, 0.9995±0.0002, and 0.9974±0.0014 for IKr, Ito and If respectively.

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.

Delayed afterdepolarization-induced triggered activity in cardiac purkinje cells mediated through cytosolic calcium diffusion waves.

Cardiac Purkinje cells (PCs) are more susceptible to action potential abnormalities as compared to ventricular myocytes (VMs), which could be associated with their distinct intracellular calcium handling. We developed a detailed biophysical model of a mouse cardiac PC, which importantly reproduces the experimentally observed biphasic cytosolic calcium waves. The model includes a stochastic gating formulation for the opening and closing of ryanodine receptor (RyR) channels, simulated with a Monte Carlo method, to accurately reproduce cytosolic calcium wave propagation and the effects of spontaneous calcium release events. Simulations predict that during an action potential, smaller cytosolic calcium wavelets propagated from the sarcolemma towards the center of the cell and initiated larger magnitude cell-wide calcium waves via a calcium-induced-calcium release mechanism. In the presence of RyR mutations, frequent spontaneous calcium leaks from sarcoplasmic reticulum (SR) initiated calcium waves, which upon reaching the cell periphery produced delayed afterdepolarizations (DADs) via sodium-calcium exchanger (NCX) and T-type calcium (ICaT ) channel activation. In the presence of isoproterenol-mediated effects, DADs induced triggered activity by reactivation of fast sodium channels. Based on our model, we found that the activation of either L-type calcium channels (ICaL ), ICaT , sodium-potassium exchanger (INaK ) or NCX is sufficient for occurrence of triggered activity; however, a partial blockade of ICaT or INaK is essential for its successful termination. Our modeling study highlights valuable insights into the mechanisms of DAD-induced triggered activity mediated via cytosolic calcium waves in cardiac PCs and may elucidate the increased arrhythmogeneity in PCs.

Mechanisms by Which Ranolazine Terminates Paroxysmal but Not Persistent Atrial Fibrillation.

BACKGROUND: Ranolazine inhibits Na+ current (INa), but whether it can convert atrial fibrillation (AF) to sinus rhythm remains unclear. We investigated antiarrhythmic mechanisms of ranolazine in sheep models of paroxysmal (PxAF) and persistent AF (PsAF). METHODS: PxAF was maintained during acute stretch (N=8), and PsAF was induced by long-term atrial tachypacing (N=9). Isolated, Langendorff-perfused sheep hearts were optically mapped. RESULTS: In PxAF ranolazine (10 µmol/L) reduced dominant frequency from 8.3±0.4 to 6.2±0.5 Hz (P<0.01) before converting to sinus rhythm, decreased singularity point density from 0.070±0.007 to 0.039±0.005 cm-2 s-1 (P<0.001) in left atrial epicardium (LAepi), and prolonged AF cycle length (AFCL); rotor duration, tip trajectory, and variance of AFCL were unaltered. In PsAF, ranolazine reduced dominant frequency (8.3±0.5 to 6.5±0.4 Hz; P<0.01), prolonged AFCL, increased the variance of AFCL, had no effect on singularity point density (0.048±0.011 to 0.042±0.016 cm-2 s-1; P=ns) and failed to convert AF to sinus rhythm. Doubling the ranolazine concentration (20 µmol/L) or supplementing with dofetilide (1 µmol/L) failed to convert PsAF to sinus rhythm. In computer simulations of rotors, reducing INa decreased dominant frequency, increased tip meandering and produced vortex shedding on wave interaction with unexcitable regions. CONCLUSIONS: PxAF and PsAF respond differently to ranolazine. Cardioversion in the former can be attributed partly to decreased dominant frequency and singularity point density, and prolongation of AFCL. In the latter, increased dispersion of AFCL and likely vortex shedding contributes to rotor formation, compensating for any rotor loss, and may underlie the inefficacy of ranolazine to terminate PsAF.

Reduced-order preconditioning for bidomain simulations.

Simulations of the bidomain equations involve solving large, sparse, linear systems of the form Ax = b. Being an initial value problems, it is solved at every time step. Therefore, efficient solvers are essential to keep simulations tractable. Iterative solvers, especially the preconditioned conjugate gradient (PCG) method, are attractive since memory demands are minimized compared to direct methods, albeit at the cost of solution speed. However, a proper preconditioner can drastically speed up the solution process by reducing the number of iterations. In this paper, a novel preconditioner for the PCG method based on system order reduction using the Arnoldi method (A-PCG) is proposed. Large order systems, generated during cardiac bidomain simulations employing a finite element method formulation, are solved with the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner was suggested. The A-PCG was applied to quickly obtain an approximate solution, and subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than those of direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems.

Calcium Dynamics and Cardiac Arrhythmia.

This Special Collection will gather all studies highlighting recent advances in theoretical and experimental studies of arrhythmia, with a specific focus on research seeking to elucidate links between calcium homeostasis in cardiac cells and organ-scale disruption of heart rhythm.

Role of cytosolic calcium diffusion in cardiac purkinje cells.

The Cardiac Purkinje cells (PCs) exhibit distinct calcium (Ca2+) homeostasis than that in ventricular myocytes (VMs). Due to lack of t-tubules in PCs, the Ca2+ ions entering the cell have to diffuse through the cytoplasm to reach the sarcoplasmic reticulum (SR) before triggering Ca2+-induced-Ca2+-release (CICR). In recent experimental studies PCs have been shown to be more susceptible to action potential (AP) abnormalities than the VMs, however the exact mechanisms are poorly understood. In this study, we utilize morphologically realistic detailed biophysical mathematical model of a murine PC to systematically examine the role intracellular Ca2+ diffusion in the APs of PCs. A biphasic spatiotemporal Ca2+ diffusion process, as observed experimentally, was implemented in the model which includes radial Ca2+ wavelets and cell wide longitudinal Ca2+ diffusion wave (CWW). The AP morphology, specifically plateau, is affected due to changes in intracellular Ca2+ dynamics. When Ca2+ concentration in sarcolemmal region is elevated, it activated inward sodium Ca2+ exchanger (NCX) current resulting into prolongation of the plateau at faster diffusion rates. Our results demonstrate that the cytosolic Ca2+ diffusion waves play a significant role in shaping APs of PCs and could provide mechanistic insights into the increased arrhythmogeneity of PCs.