Effects of mechanical feedback on the stability of cardiac scroll waves: A bidomain electro-mechanical simulation study.

In this work, we investigate the influence of cardiac tissue deformation on re-entrant wave dynamics. We have developed a 3D strongly coupled electro-mechanical Bidomain model posed on an ideal monoventricular geometry, including fiber direction anisotropy and stretch-activated currents (SACs). The cardiac mechanical deformation influences the bioelectrical activity with two main mechanical feedback: (a) the geometric feedback (GEF) due to the presence of the deformation gradient in the diffusion coefficients and in a convective term depending on the deformation rate and (b) the mechano-electric feedback (MEF) due to SACs. Here, we investigate the relative contribution of these two factors with respect to scroll wave stability. We extend the previous works [Keldermann et al., Am. J. Physiol. Heart Circ. Physiol. 299, H134-H143 (2010) and Hu et al., PLoS One 8(4), e60287 (2013)] that were based on the Monodomain model and a simple non-selective linear SAC, while here we consider the full Bidomain model and both selective and non-selective components of SACs. Our simulation results show that the stability of cardiac scroll waves is influenced by MEF, which in case of low reversal potential of non-selective SACs might be responsible for the onset of ventricular fibrillation; GEF increases the scroll wave meandering but does not determine the scroll wave stability.

A clinical-in silico study on the effectiveness of multipoint bicathodic and cathodic-anodal pacing in cardiac resynchronization therapy.

Up to one-third of patients undergoing cardiac resynchronization therapy (CRT) are nonresponders. Multipoint bicathodic and cathodic-anodal left ventricle (LV) stimulations could overcome this clinical challenge, but their effectiveness remains controversial. Here we evaluate the performance of such stimulations through both in vivo and in silico experiments, the latter based on computer electromechanical modeling. Seven patients, all candidates for CRT, received a quadripolar LV lead. Four stimulations were tested: right ventricular (RVS); conventional single point biventricular (S-BS); multipoint biventricular bicathodic (CC-BS) and multipoint biventricular cathodic-anodal (CA-BS). The following parameters were processed: QRS duration; maximal time derivative of arterial pressure (dPdtmax); systolic arterial pressure (Psys); and stroke volume (SV). Echocardiographic data of each patient were then obtained to create an LV geometric model. Numerical simulations were based on a strongly coupled Bidomain electromechanical coupling model. Considering the in vivo parameters, when comparing S-BS to RVS, there was no significant decrease in SV (from 45 ± 11 to 44 ± 20 ml) and 6% and 4% increases of dPdtmax and Psys, respectively. Focusing on in silico parameters, with respect to RVS, S-BS exhibited a significant increase of SV, dPdtmax and Psys. Neither the in vivo nor in silico results showed any significant hemodynamic and electrical difference among S-BS, CC-BS and CA-BS configurations. These results show that CC-BS and CA-BS yield a comparable CRT performance, but they do not always yield improvement in terms of hemodynamic parameters with respect to S-BS. The computational results confirmed the in vivo observations, thus providing theoretical support to the clinical experiments.

Role of infarct scar dimensions, border zone repolarization properties and anisotropy in the origin and maintenance of cardiac reentry.

Cardiac ventricular tachycardia (VT) is a life-threatening arrhythmia consisting of a well organized structure of reentrant electrical excitation pathways. Understanding the generation and maintenance of the reentrant mechanisms, which lead to the onset of VT induced by premature beats in presence of infarct scar, is one of the most important issues in current electrocardiology. We investigate, by means of numerical simulations, the role of infarct scar dimension, repolarization properties and anisotropic fiber structure of scar tissue border zone (BZ) in the genesis of VT. The simulations are based on the Bidomain model, a reaction-diffusion system of Partial Differential Equations, discretized by finite elements in space and implicit-explicit finite differences in time. The computational domain adopted is an idealized left ventricle affected by an infarct scar extending transmurally. We consider two different scenarios: i) the scar region extends along the entire transmural wall thickness, from endocardium to epicardium, with the exception of a BZ region shaped as a central sub-epicardial channel (CBZ); ii) the scar region extends transmurally along the ventricular wall, from endocardium to a sub-epicardial surface, and is surrounded by a BZ region (EBZ). In CBZ simulations, the results have shown that: i) the scar extent is a crucial element for the genesis of reentry; ii) the repolarization properties of the CBZ, in particular the reduction of IKs and IKr currents, play an important role in the genesis of reentrant VT. In EBZ simulations, since the possible reentrant pathway is not assigned a-priori, we investigate in depth where the entry and exit sites of the cycle of reentry are located and how the functional channel of reentry develops. The results have shown that: i) the interplay between the epicardial anisotropic fiber structure and the EBZ shape strongly affects the propensity that an endocardial premature stimulus generates a cycle of reentry; ii) reentrant pathways always develop along the epicardial fiber direction; iii) very thin EBZs rather than thick EBZs facilitate the onset of cycles of reentry; iv) the sustainability of cycles of reentry depends on the endocardial stimulation site and on the interplay between the epicardial breakthrough site, local fiber direction and BZ rim.

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations.

Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.

Effects of transmural electrical heterogeneities and electrotonic interactions on the dispersion of cardiac repolarization and action potential duration: A simulation study.

It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution of the APDs in the entire wall. In this article, we implement a mathematical model to simulate the combined effect of (a) the non-homogeneous intrinsic membrane properties (in particular the non-homogeneous APDs) and (b) the electrotonic currents that modulate the APDs when the myocytes are embedded in the ventricular myocardium. In particular, we study the effect of (a) and (b) on the excitation and repolarization sequences and on the distribution of APDs in the ventricles. We implement a Monodomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous transmural intrinsic membrane properties, modeled according to the phase I Luo-Rudy membrane ionic model. Three-dimensional simulations are performed in a cartesian slab with a parallel finite element solver employing structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Simulations of excitation and repolarization sequences elicited by epicardial or endocardial pacing show that in a homogeneous slab the repolarization pathways approximately follow the activation sequence. Conversely, in the heterogeneous cases considered in this study, we observed two repolarization wavefronts that started from the epi and the endocardial faces respectively and collided in the thickness of the wall and in one case an additional repolarization wave starting from an intramural site. Introducing the heterogeneities along the transmural epi-endocardial direction affected both the repolarization sequence and the APD dispersion, but these effects were clearly discernible only in transmural planes. By contrast, in planes parallel to epi- and endocardium the APD distribution remained remarkably similar to that observed in the homogeneous model. Therefore, the patterns of the repolarization sequence and APD dispersion on the epicardial surface (or any other intramural surface parallel to it) do not reveal the uniform transmural heterogeneity.

Joint influence of transmural heterogeneities and wall deformation on cardiac bioelectrical activity: A simulation study.

The aim of this work is to investigate, by means of numerical simulations, the influence of myocardial deformation due to muscle contraction and relaxation on the cardiac repolarization process in presence of transmural intrinsic action potential duration (APD) heterogeneities. The three-dimensional electromechanical model considered consists of the following four coupled components: the quasi-static transversely isotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the anisotropic Bidomain model for the electrical current flow through the deforming cardiac tissue; the membrane model of ventricular myocytes, including stretch-activated channels. The numerical simulations are based on our finite element parallel solver, which employs Multilevel Additive Schwarz preconditioners for the solution of the discretized Bidomain equations and Newton-Krylov methods for the solution of the discretized non-linear finite elasticity equations. Our findings show that: (i) the presence of intrinsic transmural cellular APD heterogeneities is not fully masked by electrotonic current flow or by the presence of the mechanical deformation; (ii) despite the presence of transmural APD heterogeneities, the recovery process follows the activation sequence and there is no significant transmural repolarization gradient; (iii) with or without transmural APD heterogeneities, epicardial electrograms always display the same wave shape and discordance between the polarity of QRS complex and T-wave; (iv) the main effects of the mechanical deformation are an increase of the dispersion of repolarization time and APD, when computed over the total cardiac domain and over the endo- and epicardial surfaces, while there is a slight decrease along the transmural direction.

Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models.

Parallel numerical simulations of excitation and recovery in three-dimensional myocardial domains are presented. The simulations are based on the anisotropic Bidomain and Monodomain models, including intramural fiber rotation and orthotropic or axisymmetric anisotropy of the intra- and extra-cellular conductivity tensors. The Bidomain model consist of a system of two reaction-diffusion equations, while the Monodomain model consists of one reaction-diffusion equation. Both models are coupled with the phase I Luo-Rudy membrane model describing the ionic currents. Simulations of excitation and repolarization sequences on myocardial slabs of different sizes show how the distribution of the action potential durations (APD) is influenced by both the anisotropic electrical conduction and the fiber rotation. This influence occurs in spite of the homogeneous intrinsic properties of the cell membrane. The APD dispersion patterns are closely correlated to the anisotropic curvature of the excitation wavefront.

Cardiac excitation mechanisms, wavefront dynamics and strength-interval curves predicted by 3D orthotropic bidomain simulations.

The assessment and understanding of cardiac excitation mechanisms is very important for the development and improvement of implantable cardiac devices, pacing protocols, and arrhythmia treatments. Previous bidomain simulation studies have investigated cathodal and anodal make/break mechanisms of cardiac excitation and strength-interval (S-I) curves in two-dimensional sheets or cylindrical domains, that by symmetry reduce to the two-dimensional case. In this work, cathodal and anodal S-I curves are studied by means of detailed bidomain simulations which include: (i) three-dimensional cardiac slabs; (ii) transmural fiber rotation; (iii) unequal orthotropic anisotropy of the conducting media; (iv) incorporation of funny and electroporation currents in the ventricular membrane model. The predicted shape of cathodal and anodal S-I curves exhibit the same features of the S-I curves observed experimentally and the break/make transition coincides with the final descending phase of the S-I curves. Away from the break/make transition, only the break or make excitation mechanism is observed independently of the stimulus strength, whereas within an interval at the break/make transition, new paradoxical excitation behaviors are observed that depend on the stimulus strength.

Exploring anodal and cathodal make and break cardiac excitation mechanisms in a 3D anisotropic bidomain model.

Published studies have investigated the relevance of cardiac virtual electrode responses to unipolar cathodal and anodal stimulations for explaining the make and break excitation mechanisms. Most of these studies have considered 2D bidomain models or cylindrical domains that by symmetry reduce to the 2D case, so the triggering mechanisms and onset of excitation have not yet been fully elucidated in 3D anisotropic models. The goal of this work is to revisit these excitation mechanisms with 3D bidomain simulations considering two tissue types with unequal anisotropy ratio, including transmural fiber rotation and augmenting the Luo-Rudy I membrane model with the so-called funny and the electroporation currents. In addition to usual snapshots of transmembrane potential patterns, we compute from the action potential waveforms the activation time and associated isochrone sequences, yielding a detailed 3D description of the instant and location of excitation origin, shape and propagation of activation wavefronts. A specific aim of this work is to detect the location of the excitation onset and whether its trigger mechanism is (a) electrotonic, i.e. originating from discharge diffusion of currents flowing between virtual cathodes and anodes and/or (b) membrane-based, i.e. arising only from intrinsic depolarizing membrane currents. Our results show that the electrotonic mechanism is observed independently of the degree of unequal anisotropy in diastolic anode make and systolic cathode break. The membrane-based mechanism is observed in diastolic cathode make, diastolic anode break, only for a relative weak anisotropy, and systolic anode break. The excitation trigger mechanism, the location of the excitation origin and the pattern of the isochrone sequence are independent of the degree of anisotropy for diastolic cathode make, systolic cathode and anode break, while they might depend on the degree of anisotropy for diastolic anode make and break. Moreover, the tissue anisotropy has a strong influence on the threshold amplitude of the stimulation pulse triggering these mechanisms.

A reliability analysis of cardiac repolarization time markers.

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

Monophasic action potentials generated by bidomain modeling as a tool for detecting cardiac repolarization times.

Unipolar electrograms (EGs) and hybrid (or unorthodox or unipolar) monophasic action potentials (HMAPs) are currently the only proposed extracellular electrical recording techniques for obtaining cardiac recovery maps with high spatial resolution in exposed and isolated hearts. Estimates of the repolarization times from the HMAP downstroke phase have been the subject of recent controversies. The goal of this paper is to computationally address the controversies concerning the HMAP information content, in particular the reliability of estimating the repolarization time from the HMAP downstroke phase. Three-dimensional numerical simulations were performed by using the anisotropic bidomain model with a region of short action potential durations. EGs, transmembrane action potentials (TAPs), and HMAPs elicited by an epicardial stimulation close or away from a permanently depolarized site were computed. The repolarization time was computed as the moment of EG fastest upstroke (RT(eg)) during the T wave, of HMAP fastest downstroke (RT(HMAP)), and of TAP fastest downstroke (RT(tap)). The latter was taken as the gold standard for repolarization time. We also compared the times (RT90(HMAP), RT90(tap)) when the HMAP and TAP first reach 90% of their resting value during the downstroke. For all explored sites, the HMAP downstroke closely followed the TAP downstroke, which is the expression of local repolarization activity. Results show that HMAP and TAP markers are highly correlated, and both markers RT(HMAP) and RT(eg) (RT90(HMAP)) are reliable estimates of the TAP reference marker RT(tap) (RT90(tap)). Therefore, the downstroke phase of the HMAP contains valuable information for assessing repolarization times.