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.

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.

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.

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.

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.

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.

Impact of the introduction of laparoscopic cholecystectomy on the population aged 70 and over.

BACKGROUND/AIMS: Laparoscopic cholecystectomy is reported to be better tolerated than open cholecystectomy by patients aged 70 and over. We evaluate its impact on patients aged 70 and over, from one single center. METHODOLOGY: We review 427 cholecystectomies performed in one single centre, from November 1992 through November 1999. We consider 23 patients, 70 years old or older at the time of surgery. The following objective parameters were considered and compared with the younger population: length of stay in the hospital; mean preoperative stay; mean postoperative stay; incidence of risk factors; postoperative complications. A questionnaire was also mailed to all individual 427 patients. RESULTS: Length of stay in the hospital declined in both population, during the time interval considered. The incidence of risk factors, both major and minor, increases consistently with age from less than 1% below the age of 30 to about 62% in the eighth decade and over. Major postoperative complications were 4.34% in patients > or = 70 vs. 2.8% in patients < 70 years of age. Mortality was nil in both groups. Ninety percent reported complete disappearance of preoperative symptoms. CONCLUSIONS: Laparoscopic cholecystectomy in geriatric patients is safe and risks are reasonably low. Selection of patients must be done on strict indications.

Spread of excitation in 3-D models of the anisotropic cardiac tissue. III. Effects of ventricular geometry and fiber structure on the potential distribution.

In a previous paper we studied the spread of excitation in a simplified model of the left ventricle, affected by fiber structure and obliqueness, curvature of the wall and Purkinje network. In the present paper we investigate the extracellular potential distribution u in the same ventricular model. Given the transmembrane potential v, associated with the spreading excitation, the extracellular potential u is obtained as solution of a linear elliptic equation with the source term related to v. The potential distributions were computed for point stimulations at different intramural depths. The results of the simulations enabled us to identify a number of common features which appears in all the potential patterns irrespective of pacing site. In addition, by splitting the sources into an axial and conormal component, we were able to evaluate the contribution of the classical uniform dipole layer to the total potential field and the role of the superimposed axial component.

Potential distributions generated by point stimulation in a myocardial volume: simulation studies in a model of anisotropic ventricular muscle.

INTRODUCTION: We present simulations of extracellular potential patterns elicited by delivering ectopic stimuli to a parallelepipedal slab of ventricular tissue represented as an anisotropic bidomain incorporating epi-endocardial fiber rotation. METHODS AND RESULTS: Simulations were based on an eikonal model that determines wavefront shapes throughout the slab at every time instant during the depolarization phase, coupled with an approximate model of the action potential profile. The endocardial face of the slab was in contact with blood and the composite volume was surrounded by an insulating medium. The effect of a simplified Purkinje network was also studied. RESULTS: (1) For all pacing depths, except endocardial pacing, a central negative area and two potential maxima were observed at QRS onset in all intramural planes parallel to the epicardium. In all planes, the axis joining the two maxima was approximately aligned with the direction of fibers in the plane of pacing. Endocardial pacing generated a different pattern, but only when blood was present; (2) During later stages of excitation, outflowing currents (from the wavefront toward the resting tissue) were always emitted, at all intramural depths, only from those portions of the wavefront that spread along fibers. At any given instant, the position of the two potential maxima in a series of planes parallel to the epicardium and intersecting the wavefront rotated as a function of depth, following the rotating direction of intramural fibers. Purkinje involvement modified the above patterns. CONCLUSION: Epicardial and endocardial potential maps provided information on pacing site and depth and on subsequent intramural propagation by reflecting the clockwise or counter-clockwise rotation of the deep positivity. Results may be applicable to epicardial and endocardial potential maps recorded at surgery or from endocavitary probes.

Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations.

In this paper we present a macroscopic model of the excitation process in the myocardium. The composite and anisotropic structure of the cardiac tissue is represented by a bidomain, i.e. a set of two coupled anisotropic media. The model is characterized by a non linear system of two partial differential equations of parabolic and elliptic type. A singular perturbation analysis is carried out to investigate the cardiac potential field and the structure of the moving excitation wavefront. As a consequence the cardiac current sources are approximated by an oblique dipole layer structure and the motion of the wavefront is described by eikonal equations. Finally numerical simulations are carried out in order to analyze some complex phenomena related to the spreading of the wavefront, like the front-front or front-wall collision. The results yielded by the excitation model and the eikonal equations are compared.

Oblique dipole layer potentials applied to electrocardiology.

We study the properties of the potential field generated by an oblique dipole layer. This field arises, for instance, in describing the potential elicited by a depolarization wavefront spreading in the myocardium when a dependence of the potential on the cardiac fiber orientation is introduced. The representation of cardiac bioelectric sources by means of an oblique dipole layer leads to a mathematical structure which generalizes the classical solid angle theory used in electrocardiology, which has been challenged by recent experimental evidence, and links models previously proposed with a view to adequately reproduce the potential observed in experiments. We investigate also the relationship between our model and an intracellular current model and we derive potential jump formulae for some models which account for the anisotropic structure of the myocardium. The potential generated by an oblique dipole layer is considered both for unbounded and bounded domains. In the latter case an integral boundary equation is derived and we study its solvability. A numerical procedure for solving this integral equation by means of the finite element method with collocation is outlined.

Potential fields generated by oblique dipole layers modeling excitation wavefronts in the anisotropic myocardium. Comparison with potential fields elicited by paced dog hearts in a volume conductor.

The potential distribution in a homogeneous, cylindrical volume conductor surrounding an isolated paced dog heart was first measured and then calculated by using a mathematical model that stimulates an anisotropic excitation wavefront spreading through the heart muscle. The study was performed with a view to establish to what extent the anisotropy of cardiac generators affects the potential field in the extra-cardiac conducting media at a great distance from the heart. The model considers an oblique dipole layer on the wavefront which, assuming axial symmetry of the electrical properties of the fibers, can be viewed as the superposition of an axial and transverse dipole layer. These layers are, respectively, parallel and perpendicular to the local fiber due to such an oblique distribution is also equivalent to the sum of the potentials generated, respectively, by a normal and an axial dipole layer. In this form, the model generalizes the classical, uniform double layer model, upon which the solid angle theory is based, by adding to it an axial component. The features of the measured potential fields, which could not be interpreted on the basis of the solid angle theory, were satisfactorily reproduced by the model, at least on a qualitative basis. The results clearly showed the dominant role played by the axial component of the potential field even at a considerable distance from the heart.

Numerical determination of intestinal membrane diffusing constants by a gradient method.

Optimisation problems arising in the identification of kinetic parameters of intestinal membranes are here considered. The dynamic behaviour of the membrane is described by means of a linear compartmental model. Using optimisation techniques of a gradient type, the intestinal kinetic parameters are identified, minimising a quadratic criterion between experimental data of D-histidine transport and model prediction. Numerical results are reported and their physiological implications discussed. The quantitative assessment of the asymmetry of diffusion constants with respect to diffusion direction seems to be an important result of this work.