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.

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.

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 AT_ell and AT_ecc , respectively, by means of three-dimensional cardiac electromechanical simulations. These markers are compared against the electrical activation time (AT_v ), computed from the action potential waveform, and the reference mechanical activation markers derived from the active tension and fiber strain waveforms, denoted by AT_ta and AT_eff , 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 AT_v , 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 AT_ell and AT_ecc 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.

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.

Cardiac kinematic parameters computed from video of in situ beating heart

Mechanical function of the heart during open-chest cardiac surgery is exclusively monitored by echocardiographic techniques. However, little is known about local kinematics, particularly for the reperfused regions after ischemic events. We report a novel imaging modality, which extracts local and global kinematic parameters from videos of in situ beating hearts, displaying live video cardiograms of the contraction events. A custom algorithm tracked the movement of a video marker positioned ad hoc onto a selected area and analyzed, during the entire recording, the contraction trajectory, displacement, velocity, acceleration, kinetic energy and force. Moreover, global epicardial velocity and vorticity were analyzed by means of Particle Image Velocimetry tool. We validated our new technique by i) computational modeling of cardiac ischemia, ii) video recordings of ischemic/reperfused rat hearts, iii) videos of beating human hearts before and after coronary artery bypass graft, and iv) local Frank-Starling effect. In rats, we observed a decrement of kinematic parameters during acute ischemia and a significant increment in the same region after reperfusion. We detected similar behavior in operated patients. This modality adds important functional values on cardiac outcomes and supports the intervention in a contact-free and non-invasive mode. Moreover, it does not require particular operator-dependent skills.

Cardiac kinematic parameters computed from video of in situ beating heart

Mechanical function of the heart during open-chest cardiac surgery is exclusively monitored by echocardiographic techniques. However, little is known about local kinematics, particularly for the reperfused regions after ischemic events. We report a novel imaging modality, which extracts local and global kinematic parameters from videos of in situ beating hearts, displaying live video cardiograms of the contraction events. A custom algorithm tracked the movement of a video marker positioned ad hoc onto a selected area and analyzed, during the entire recording, the contraction trajectory, displacement, velocity, acceleration, kinetic energy and force. Moreover, global epicardial velocity and vorticity were analyzed by means of Particle Image Velocimetry tool. We validated our new technique by i) computational modeling of cardiac ischemia, ii) video recordings of ischemic/reperfused rat hearts, iii) videos of beating human hearts before and after coronary artery bypass graft, and iv) local Frank-Starling effect. In rats, we observed a decrement of kinematic parameters during acute ischemia and a significant increment in the same region after reperfusion. We detected similar behavior in operated patients. This modality adds important functional values on cardiac outcomes and supports the intervention in a contact-free and non-invasive mode. Moreover, it does not require particular operator-dependent skills.

Simulating the effects of growth and fiber dispersion on the electromechanical response of a cardiac ventricular wedge affected from concentric hypertrophy

In this paper, we analyze the epicardial electromechanical response of an in silico cardiac ventricular wedge under both healthy and concentric hypertrophic conditions. This is achieved by taking into account the growth of the wedge thickness and the fiber dispersion that may follow. The electromechanical response is described in terms of some macroscopic measures, i.e. the action potential duration, the conduction velocity, the contractility and the contraction force. Our results suggest that growth reduces the action potential duration and conduction velocity, whilst it increases the contractility and contraction force, yielding an overall negative effect. In presence of fiber dispersion, the action potential duration and conduction velocity are not affected further, whilst the effect on the contractility and contraction force is enhanced.

Modelling the effect of thickness on the electromechanical properties of in vitro cardiac cultures: A simulation study

Nowadays, in vitro cardiac cultures offer a valid tool to study the bioelectrical activity and the biomechanics of the heart tissue. Modelling their properties could be helpful for researchers involved in this field. In this paper, we develop a three-dimensional electromechanical model to study how thickness affects the bioelectrical and biomechanical performances of an in vitro culture made of ventricular cells. In particular, by our in silico simulations we want to verify if thickness variations can be a key factor in modifying the response of the whole culture when this one is grown to become a cardiac patch. Therefore, for this parameter we choose three increasing values while keeping a fiber architecture among layers that is similar to the one of the in vivo heart but it is randomly stated at the beginning of each simulation. We prove that, independently from the selected architectures, the more thickness increases the more mechanical improvements are attained, but the more electrical problems may arise too.

In silico modelling and analysis of the electrical and mechanical properties of in vitro cardiac cultures with different fiber architectures

Today, in vitro cardiac cultures are widely exploited to investigate several aspects of the electromechanical behavior of the cardiac tissue. Thus, new forecasts may derive from modelling their properties. In particular, in this paper, we focus on the fiber architecture of cultures, i.e. on the way cellular sarcomeres are locally oriented, when they are designed to be cardiac patches. We employ a three-dimensional model to simulate the bioelectrical activity and the biomechanics of a multilayered culture made of ventricular cells and with four possible architectures consisting of: i) random fibers in all cells; ii) randomly rotating fibers among layers; iii) structurally rotating fibers from the bottom layer to the top one; iv) parallel fibers among layers. Our results suggest that the best configuration for a patch may be the architecture with structurally rotating fibers, which is the one that most approaches the anisotropic structure of the in vivo heart, thanks to its better electrical and mechanical performances.

An approach to inverse calculation of epicardial potentials from body surface maps

The inverse problem of evaluating epicardial potentials from a knowledge of heart and torso geometry as well as body surface potentials is here formulated as a problem in control theory. As is well known, such an inverse problem is ill-posed and a regularization technique has been devised to overrun this difficulty. The resulting regularized problem is well-posed and requires the minimization of a cost function including, besides the square distance of any predicted surface potential distribution from the experimental one, a regularization term involving the second derivatives of the identified epicardial potentials. The results here presented were obtained on a model problem for a plane geometry. Surface potentials generated by multipoles and perturbated with a noise level reflecting both instrumentation and electrode placement uncertainties were fitted by the proposed method and 'epicardial potentials' were determined with a maximum sum square relative error of 15%. The results suggest that by introducing suited regularity constraints, the a priori difficulties inherent to the problem of computing epicardial potentials from torso potentials, can be overcome.

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.

Anisotropic mechanisms for multiphasic unipolar electrograms: simulation studies and experimental recordings

The origin of the multiple, complex morphologies observed in unipolar epicardial electrograms, and their relationships with myocardial architecture, have not been fully elucidated. To clarify this problem we simulated electrograms (EGs) with a model representing the heart as an anisotropic bidomain with unequal anisotropy ratio, ellipsoidal ventricular geometry, transmural fiber rotation, epi-endocardial obliqueness of fiber direction and a simplified Purkinje network. The EGs were compared with those directly recorded from isolated dog hearts immersed in a conducting medium during ventricular excitation initiated by epicardial stimulation. The simulated EGs share the same multiphasic character of the recorded EGs. The origin of the multiple waves, especially those appearing in the EGs for sites reached by excitation wave fronts spreading across fibers, can be better understood after splitting the current sources, the potential distributions and the EGs into an axial and a conormal component and after taking also into account the effect of the reference or drift component. The split model provides an explanation of humps and spikes that appear in the QRS (the initial part of the ventricular EG) wave forms, in terms of the interaction between the geometry and direction of propagation of the wave front and the architecture of the fibers through which excitation is spreading.

Multiple components in the unipolar electrogram: a simulation study in a three-dimensional model of ventricular myocardium

INTRODUCTION

For many decades, the interpretation of unipolar electrograms (EGs) and ECGs was based on simple models of the heart as a current generator, e.g., the uniform dipole layer, and, more recently, the "oblique dipole layer." However, a number of recent and old experimental data are inconsistent with the predictions of these models. To address this problem, we implemented a numerical model simulating the spread of excitation through a parallelepipedal myocardial slab, with a view to identifying the factors that affect the shape, amplitude, and polarity of unipolar EGs generated by the spreading wavefront.

METHODS AND RESULTS

The numerical model represents a portion of the left ventricular wall as a parallelepipedal slab (6.5 x 6.5 x 1 cm); the myocardial tissue is represented as an anisotropic bidomain with epi-endocardial rotation of fiber direction and unequal anisotropy ratio. Following point stimulation, excitation times in the entire volume are computed by using an eikonal formulation. Potential distributions are computed by assigning a fixed shape to the action potential profile. EGs at multiple sites in the volume are computed from the time varying potential distributions. The simulations show that the unipolar QRS waveforms are the sum of a "field" component, representing the effect of an approaching or receding wavefront on the potential recorded by a unipolar electrode, and a previously unrecognized "reference" component, which reflects the drift, during the spread of excitation, of the reference potential, which moves from near the positive to near the negative extreme of the potential distribution during the spread of excitation.

CONCLUSION

The drift of the reference potential explains the inconsistencies between the predictions of the models and the actual shapes of the EGs. The drift modifies the slopes of EG waveforms during excitation and recovery and can be expected to affect the assessment of excitation and recovery times and QRS and ST-T areas. Removing the drift reestablishes consistency between potential distributions and electrographic waveforms.

Spread of excitation in 3-D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry

We investigate a three-dimensional macroscopic model of wave-front propagation related to the excitation process in the left ventricular wall represented by an anisotropic bidomain. The whole left ventricle is modeled, whereas, in a previous paper, only a flat slab of myocardial tissue was considered. The direction of cardiac fibers, which affects the anisotropic conductivity of the myocardium, rotates from the epi- to the endocardium. If the ventricular wall is conceived as a set of packed surfaces, the fibers may be tangent to them or more generally may cross them obliquely; the latter case is described by an "imbrication angle." The effect of a simplified Purkinje network also is investigated. The cardiac excitation process, more particularly the depolarization phase, is modeled by a nonlinear elliptic equation, called an eikonal equation, in the activation time. The numerical solution of this equation is obtained by means of the finite element method, which includes an upwind treatment of the Hamiltonian part of the equation. By means of numerical simulations in an idealized model of the left ventricle, we try to establish whether the eikonal approach contains the essential basic elements for predicting the features of the activation patterns experimentally observed. We discuss and compare these results with those obtained in our previous papers for a flat part of myocardium. The general rules governing the spread of excitation after local stimulations, previously delineated for the flat geometry, are extended to the present, more realistic monoventricular model.

Spread of excitation in a myocardial volume: simulation studies in a model of anisotropic ventricular muscle activated by point stimulation

INTRODUCTION

The purpose of this study was to present simulations of excitation wavefronts spreading through a parallelepipedal slab of ventricular tissue measuring 6.5 x 6.5 x 1.0 cm.

METHODS AND RESULTS

The slab incorporates the anisotropic properties of the myocardium including the transmural counterclockwise fiber rotation from epicardium to endocardium. Simulations were based on an eikonal model that determines excitation times throughout the ventricular wall, which is represented as an anisotropic bidomain. Excitation was initiated by delivering ectopic stimuli at various intramural depths. We also investigated the effect of a simplified Purkinje network on excitation patterns. Excitation wavefronts in the plane of pacing, parallel to epicardial-endocardial surfaces, were oblong with the major axis approximately oriented along the local fiber direction, with bulges and deformations due to attraction from rotating fibers in adjacent planes. The oblong intersections of the wavefront with planes at increasing distance from pacing plane rotated clockwise or counterclockwise, depending on pacing depth, but wavefront rotation was always less than fiber rotation in the same plane. For all pacing depths, excitation returned toward the plane of pacing. Return occurred in multiple, varying sectors of the slab depending on pacing depth, and was observed as close as 6 mm to the pacing site.

CONCLUSION

Curvature of wavefronts and collision with boundaries of slab markedly affected local velocities. Shape and separation of epicardial isochrones and spatial distribution of epicardial velocities varied as a function of site and depth of pacing. When the Purkinje network was added to the model, epicardial velocities revealed the subendocardial location of the Purkinje-myocardial junctions. Considerable insight into intramural events could be obtained from epicardial isochrones. If validated experimentally, results may be applicable to epicardial isochrones recorded at surgery.

Spreading of excitation in 3-D models of the anisotropic cardiac tissue. I. Validation of the eikonal model

In this work we investigate, by means of numerical simulations, the performance of two mathematical models describing the spread of excitation in a three dimensional block representing anisotropic cardiac tissue. The first model is characterized by a reaction-diffusion system in the transmembrane and extracellular potentials v and u. The second model is derived from the first by means of a perturbation technique. It is characterized by an eikonal equation, nonlinear and elliptic in the activation time psi(x). The level surfaces psi(x) = t represent the wave-front positions. The numerical procedures based on the two models were applied to test functions and to excitation processes elicited by local stimulations in a relatively small block. The results are in excellent agreement, and for the same problem the computation time required by the eikonal equation is a small fraction of that needed for the reaction-diffusion system. Thus we have strong evidence that the eikonal equation provides a reliable and numerically efficient model of the excitation process. Moreover, numerical simulations have been performed to validate an approximate model for the extracellular potential based on knowledge of the excitation sequence. The features of the extracellular potential distribution affected by the anisotropic conductivity of the medium were investigated.

Mathematical modeling of the excitation process in myocardial tissue: influence of fiber rotation on wavefront propagation and potential field

In our macroscopic model the heart tissue is represented as a bidomain coupling the intra- and extracellular media. Owing to the fiber structure of the myocardium, these media are anisotropic, and their conductivity tensors have a principal axis parallel to the local fiber direction. A reaction-diffusion system is derived that governs the distribution and evolution of the extracellular and transmembrane potentials during the depolarization phase of the heart beat. To investigate frontlike solutions, the system is rescaled and transformed into a system dependent on a small parameter. Subsequently a perturbation analysis is carried out that yields zero- and first-order approximations called eikonal equations. The effects of the transmural fiber rotation on wavefront propagation and the corresponding potential field, elicited by point stimulations, are investigated by means of numerical simulations.

A mathematical model of iron metabolism

A mathematical model of iron metabolism is presented. It comprises the following iron pools within the body: transferrin-bound iron in the plasma, iron in circulating red cells and their bone marrow precursors, iron in mucosal, parenchymal and reticuloendothelial cells. The control exerted by a hormone, called erythropoietin, on bone marrow utilization of iron for hemoglobin synthesis is taken into account. The model so obtained consists of a system of functional differential equations of retarded type. Most model parameters can be estimated from radiotracer experiments, others can be measured and numerical values can be assigned to the remaining ones making few reasonable assumptions according to the available physiological knowledge. Iron metabolism behavior under different therapeutical treatments was stimulated. Model predictions were compared to experimental data collected in clinical routine.