Epicardial Dispersion of Repolarization Promotes the Onset of Reentry in Brugada Syndrome: A Numerical Simulation Study.

The Brugada syndrome (BrS) is a cardiac arrhythmic disorder responsible for sudden cardiac death associated with the onset of ventricular arrhythmias, such as reentrant ventricular tachycardia and fibrillation. The mechanisms which lead to the onset of such electrical disorders in patients affected by BrS are not completely understood, yet. The aim of the present study is to investigate by means of numerical simulations the electrophysiological mechanisms at the basis of the morphology of electrocardiogram (ECG) and the onset of reentry associated with BrS. To this end, we consider the Bidomain equations coupled with the ten Tusscher-Panfilov membrane model, on an idealized wedge of human right ventricular tissue. The results have shown that: (1) epicardial dispersion of repolarization, generated by the coexistence of regions of early and late repolarization, due to different modulation of the [Formula: see text] current, produces ECG waveforms exhibiting qualitatively the typical BrS morphology, characterized by ST elevation and partially negative T-waves; (2) epicardial dispersion of repolarization promotes the onset of reentry during the implementation of the programmed stimulation protocol, because of the conduction block occurring when a premature beat reaches the border of late repolarizing regions; and (3) the modulation of the [Formula: see text] current affects the duration of reentry, which becomes sustained with a remarkable increase of [Formula: see text] in the subepicardial layers.

Cardiac electro-mechanical activity in a deforming human cardiac tissue: modeling, existence-uniqueness, finite element computation and application to multiple ischemic disease.

In this study, the cardiac electro-mechanical model in a deforming domain is taken with the addition of mechanical feedback and stretch-activated channel current coupled with the ten Tusscher human ventricular cell level model that results in a coupled PDE-ODE system. The existence and uniqueness of such a coupled system in a deforming domain is proved. At first, the existence of a solution is proved in the deformed domain. The local existence of the solution is proved using the regularization and the Faedo-Galerkin technique. Then, the global existence is proved using the energy estimates in appropriate Banach spaces, Gronwall lemma, and the compactness procedure. The existence of the solution in an undeformed domain is proved using the lower semi-continuity of the norms. Uniqueness is proved using Young's inequality, Gronwall lemma, and the Cauchy-Schwartz inequality. For the application purpose, this model is applied to understand the electro-mechanical activity in ischemic cardiac tissue. It also takes care of the development of active tension, conductive, convective, and ionic feedback. The Second Piola-Kirchoff stress tensor arising in Lagrangian mapping between reference and moving frames is taken as a combination of active, passive, and volumetric components. We investigated the effect of varying strength of hyperkalemia and hypoxia, in the ischemic subregions of human cardiac tissue with local multiple ischemic subregions, on the electro-mechanical activity of healthy and ischemic zones. This system is solved numerically using the [Formula: see text] finite element method in space and the implicit-explicit Euler method in time. Discontinuities arising with the modeled multiple ischemic regions are treated to the desired order of accuracy by a simple regularization technique using the interpolating polynomials. We examined the cardiac electro-mechanical activity for several cases in multiple hyperkalemic and hypoxic human cardiac tissue. We concluded that local multiple ischemic subregions severely affect the cardiac electro-mechanical activity more, in terms of action potential (v) and mechanical parameters, intracellular calcium ion concentration [Formula: see text], active tension ([Formula: see text]), stretch ([Formula: see text]) and stretch rate ([Formula: see text]), of a healthy cell in its vicinity, compared to a single Hyperkalemic or Hypoxic subregion. The four moderate hypoxically generated ischemic subregions affect the waveform of the stretch along the fiber and the stretch rate more than a single severe ischemic subregion.

Modeling and simulation of cardiac electric activity in a human cardiac tissue with multiple ischemic zones.

In this work, a human ventricular model (ten Tusscher and Panfilov model) coupled with the tissue level monodomain model is used to analyze the influence of multiple myocardial ischemia on the human cardiac tissue. The existence and uniqueness of the ischemic model comprising the monodomain model with a discontinuous ionic model for the human cardiac tissue is discussed. The coupled system of partial differential equation and ordinary differential equations are solved numerically using [Formula: see text] finite elements in space and Backward Euler finite difference scheme in time. The apriori finite element error estimate for the numerical scheme has been shown to be of [Formula: see text]. Essentially, we evaluate the impact of the increasing size of the ischemic region and the presence of the multiple ischemic regions having equal or different intensities on the neighboring healthy part of the cardiac tissue. We examine both the individual and the combined influence of two types of ischemia, Hyperkalemia (with the variation of the extracellular potassium ion concentration, [Formula: see text]) and Hypoxia (with the variation of intracellular Adenosine triphosphate (ATP) concentration via parameter [Formula: see text]) on the cardiac electrical activity of cardiac tissue. We observe that with the increase in the ischemic region size by a factor five times, there is an additional almost 10% drop in the action potential duration (APD) in the neighboring healthy regions. The combined effect of Hyperkalemia and Hypoxia brings an additional 12% drop in APD in the ischemic subregions and an additional 5% drop in APD in the neighboring healthy part of the cardic tissue in comparison to the only Hyperkalemic ischemia. When the Hyperkalemic and/or Hypoxic degeneracy of a ischemic zone is non-uniform then innercore degeneracy has greater influence on resting potential and APD of outercore of variable intensity ischemic zone than the other way. Also, increasing the number of ischemic subregions from 2 to 4 leads to a 4% drop in APD.

Effects of premature anodal stimulations on cardiac transmembrane potential and intracellular calcium distributions computed by anisotropic Bidomain models.

AIMS: Cardiac unipolar electrode stimulations induce a particular structure of the transmembrane potential distribution (Vm), called virtual electrode polarization (VEP), which plays an important role in the mechanisms of cardiac excitation, reentry induction, and ventricular defibrillation. Recent experimental studies, based on the optical mapping techniques, have shown that premature stimulations also induce significant changes in the intracellular calcium (Cai) spatial distribution. The aim of this work is to investigate and compare by means of numerical simulations the morphology of the Vm and Cai patterns, generated by applying an S1-S2 stimulation protocol with a premature S2 anodal pulse. METHODS AND RESULTS: We perform parallel finite element simulations of a three-dimensional orthotropic Bidomain model on a block of ventricular tissue by using four membrane models of two species (guinea pig and rabbit), that incorporate the phenomenological or more detailed mechanistic descriptions of the calcium dynamics. During the S2 anodal stimulus, the Cai spatial distribution, computed with all the considered models, presents a configuration similar to the typical VEP pattern of Vm, with a minimum inside the virtual anode and two maxima in the virtual cathodes. After the S2 stimulus turns off, the anode break excitation mechanism yields a Vm pattern exhibiting a clearly propagating wavefront. Differently, the Cai patterns do not show a clear separation between the resting and the activated regions, with the exception of one of the phenomenological models considered, but they show warped dog-bone shaped equi-level lines around an elevation in the virtual anode region. CONCLUSION: The VEP pattern of the Cai spatial distribution during the S2 stimulus is in agreement with the previous experimental studies. Moreover, the Cai minimum in the virtual anode can be mainly attributable to the outflow of calcium ions produced by the sodium-calcium (NCX) exchanger, without a significant contribution of the ICaL current.

Unexpected impairment of INa underpins reentrant arrhythmias in a knock-in swine model of Timothy syndrome.

Timothy syndrome 1 (TS1) is a multi-organ form of long QT syndrome associated with life-threatening cardiac arrhythmias, the organ-level dynamics of which remain unclear. In this study, we developed and characterized a novel porcine model of TS1 carrying the causative p.Gly406Arg mutation in CACNA1C, known to impair CaV1.2 channel inactivation. Our model fully recapitulated the human disease with prolonged QT interval and arrhythmic mortality. Electroanatomical mapping revealed the presence of a functional substrate vulnerable to reentry, stemming from an unforeseen constitutional slowing of cardiac activation. This signature substrate of TS1 was reliably identified using the reentry vulnerability index, which, we further demonstrate, can be used as a benchmark for assessing treatment efficacy, as shown by testing of multiple clinical and preclinical anti-arrhythmic compounds. Notably, in vitro experiments showed that TS1 cardiomyocytes display Ca2+ overload and decreased peak INa current, providing a rationale for the arrhythmogenic slowing of impulse propagation in vivo.

Role of Scar and Border Zone Geometry on the Genesis and Maintenance of Re-Entrant Ventricular Tachycardia in Patients With Previous Myocardial Infarction.

In patients with healed myocardial infarction, the left ventricular ejection fraction is characterized by low sensitivity and specificity in the prediction of future malignant arrhythmias. Thus, there is the need for new parameters in daily practice to perform arrhythmic risk stratification. The aim of this study is to identify some features of proarrhythmic geometric configurations of scars and border zones (BZ), by means of numerical simulations based on left ventricular models derived from post myocardial infarction patients. Two patients with similar clinical characteristics were included in this study. Both patients exhibited left ventricular scars characterized by subendo- and subepicardial BZ and a transmural BZ isthmus. The scar of patient #1 was significantly larger than that of patient #2, whereas the transmural BZ isthmus and the subdendo- and subepicardial BZs of patient #2 were thicker than those of patient #1. Patient #1 was positive at electrophysiologic testing, whereas patient #2 was negative. Based on the cardiac magnetic resonance (CMR) data, we developed a geometric model of the left ventricles of the two patients, taking into account the position, extent, and topological features of scars and BZ. The numerical simulations were based on the anisotropic monodomain model of electrocardiology. In the model of patient #1, sustained ventricular tachycardia (VT) was inducible by an S2 stimulus delivered at any of the six stimulation sites considered, while in the model of patient #2 we were not able to induce sustained VT. In the model of patient #1, making the subendo- and subepicardial BZs as thick as those of patient #2 did not affect the inducibility and maintenance of VT. On the other hand, in the model of patient #2, making the subendo- and subepicardial BZs as thin as those of patient #1 yielded sustained VT. In conclusion, the results show that the numerical simulations have an effective predictive capability in discriminating patients at high arrhythmic risk. The extent of the infarct scar and the presence of transmural BZ isthmuses and thin subendo- and subepicardial BZs promote sustained VT.

Numerical evaluation of cardiac mechanical markers as estimators of the electrical activation time.

Recent advances in the development of noninvasive cardiac imaging technologies have made it possible to measure longitudinal and circumferential strains at a high spatial resolution also at intramural level. Local mechanical activation times derived from these strains can be used as noninvasive estimates of electrical activation, in order to determine, eg, the origin of premature ectopic beats during focal arrhythmias or the pathway of reentrant circuits. The aim of this work is to assess the reliability of mechanical activation time markers derived from longitudinal and circumferential strains, denoted by ATell and ATecc , respectively, by means of three-dimensional cardiac electromechanical simulations. These markers are compared against the electrical activation time (ATv ), computed from the action potential waveform, and the reference mechanical activation markers derived from the active tension and fiber strain waveforms, denoted by ATta and ATeff , respectively. Our numerical simulations are based on a strongly coupled electromechanical model, including bidomain representation of the cardiac tissue, mechanoelectric (ie, stretch-activated channels) and geometric feedbacks, transversely isotropic strain energy function for the description of passive mechanics and detailed membrane and excitation-contraction coupling models. The results have shown that, during endocardial and epicardial ectopic stimulations, all the mechanical markers considered are highly correlated with ATv , exhibiting correlation coefficients larger than 0.8. However, during multiple endocardial stimulations, mimicking the ventricular sinus rhythm, the mechanical markers are less correlated with the electrical activation time, because of the more complex resulting excitation sequence. Moreover, the inspection of the endocardial and epicardial isochrones has shown that the ATell and ATecc mechanical activation sequences reproduce only some qualitative features of the electrical activation sequence, such as the areas of early and late activation, but in some cases, they might yield wrong excitation sources and significantly different isochrones patterns.

Machine Learning of Allosteric Effects: The Analysis of Ligand-Induced Dynamics to Predict Functional Effects in TRAP1.

Allosteric molecules provide a powerful means to modulate protein function. However, the effect of such ligands on distal orthosteric sites cannot be easily described by classical docking methods. Here, we applied machine learning (ML) approaches to expose the links between local dynamic patterns and different degrees of allosteric inhibition of the ATPase function in the molecular chaperone TRAP1. We focused on 11 novel allosteric modulators with similar affinities to the target but with inhibitory efficacy between the 26.3 and 76%. Using a set of experimentally related local descriptors, ML enabled us to connect the molecular dynamics (MD) accessible to ligand-bound (perturbed) and unbound (unperturbed) systems to the degree of ATPase allosteric inhibition. The ML analysis of the comparative perturbed ensembles revealed a redistribution of dynamic states in the inhibitor-bound versus inhibitor-free systems following allosteric binding. Linear regression models were built to quantify the percentage of experimental variance explained by the predicted inhibitor-bound TRAP1 states. Our strategy provides a comparative MD-ML framework to infer allosteric ligand functionality. Alleviating the time scale issues which prevent the routine use of MD, a combination of MD and ML represents a promising strategy to support in silico mechanistic studies and drug design.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures.

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics.

A model for the active deformation of cardiac tissue considering orthotropic constitutive laws is introduced and studied. In particular, the passive mechanical properties of the myocardium are described by the Holzapfel-Ogden relation, whereas the activation model is based on the concept of active strain. There, an incompatible intermediate configuration is considered, which entails a multiplicative decomposition between active and passive deformation gradients. The underlying Euler-Lagrange equations for minimizing the total energy are written in terms of these deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiomyocytes. The active strain formulation is compared with the classical active stress model from both numerical and modeling perspectives. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed, and different mechanical activation functions are considered. Taylor-Hood and MINI finite elements are used in the discretization of the overall mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main features of the phenomenon, while allowing savings in computational costs.

Intramural activation and repolarization sequences in canine ventricles. Experimental and simulation studies.

BACKGROUND: There are no published data showing the three-dimensional sequence of repolarization and the associated potential fields in the ventricles. Knowledge of the sequence of repolarization has medical relevance because high spatial dispersion of recovery times and action potential durations favors cardiac arrhythmias. In this study we describe measured and simulated 3-D excitation and recovery sequences and activation-recovery intervals (ARIs) (measured) or action potential durations (APDs) (simulated) in the ventricular walls. METHODS: We recorded from 600 to 1400 unipolar electrograms from canine ventricular walls during atrial and ventricular pacing at 350-450 ms cycle length. Measured excitation and recovery times and ARIs were displayed as 2-D maps in transmural planes or 3-D maps in the volume explored, using specially developed software. Excitation and recovery sequences and APD distributions were also simulated in parallelepipedal slabs using anisotropic monodomain or bidomain models based on the Lou-Rudy version 1 model with homogeneous membrane properties. RESULTS: Simulations showed that in the presence of homogeneous membrane properties, the sequence of repolarization was similar but not identical to the excitation sequence. In a transmural plane perpendicular to epicardial fiber direction, both activation and recovery pathways starting from an epicardial pacing site returned toward the epicardium at a few cm distance from the pacing site. However, APDs were not constant, but had a dispersion of approximately 14 ms in the simulated domain. The maximum APD value was near the pacing site and two minima appeared along a line perpendicular to fiber directions, passing through the pacing site. Electrical measurements in dog ventricles showed that, for short cycle lengths, both excitation and recovery pathways, starting from an epicardial pacing site, returned toward the epicardium. For slower pacing rates, pathways of recovery departed from the pathway of excitation. Highest ARI values were observed near the pacing site in part of the experiments. In addition, maps of activation-recovery intervals showed mid-myocardial clusters with activation-recovery intervals that were slightly longer than ARIs closer to the epi- or endocardium, suggesting the presence of M cells in those areas. Transmural dispersion of measured ARIs was on the order of 20-25 ms. Potential distributions during recovery were less affected by myocardial anisotropy than were excitation potentials.