Elvio Heidenreich

A Three-Dimensional Human Atrial Model with Fiber Orientation. Electrograms and Arrhythmic Activation Patterns Relationship

The most common sustained cardiac arrhythmias in humans are atrial tachyarrhythmias, mainly atrial fibrillation. Areas of complex fractionated atrial electrograms and high dominant frequency have been proposed as critical regions for maintaining atrial fibrillation; however, there is a paucity of data on the relationship between the characteristics of electrograms and the propagation pattern underlying them. In this study, a realistic 3D computer model of the human atria has been developed to investigate this relationship. The model includes a realistic geometry with fiber orientation, anisotropic conductivity and electrophysiological heterogeneity. We simulated different tachyarrhythmic episodes applying both transient and continuous ectopic activity. Electrograms and their dominant frequency and organization index values were calculated over the entire atrial surface. Our simulations show electrograms with simple potentials, with little or no cycle length variations, narrow frequency peaks and high organization index values during stable and regular activity as the observed in atrial flutter, atrial tachycardia (except in areas of conduction block) and in areas closer to ectopic activity during focal atrial fibrillation. By contrast, cycle length variations and polymorphic electrograms with single, double and fragmented potentials were observed in areas of irregular and unstable activity during atrial fibrillation episodes. Our results also show: 1) electrograms with potentials without negative deflection related to spiral or curved wavefronts that pass over the recording point and move away, 2) potentials with a much greater proportion of positive deflection than negative in areas of wave collisions, 3) double potentials related with wave fragmentations or blocking lines and 4) fragmented electrograms associated with pivot points. Our model is the first human atrial model with realistic fiber orientation used to investigate the relationship between different atrial arrhythmic propagation patterns and the electrograms observed at more than 43000 points on the atrial surface.

Adaptive Macro Finite Elements for the Numerical Solution of Monodomain Equations in Cardiac Electrophysiology

Many problems in Biology and Engineering are governed by anisotropic reaction–diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction–diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Modeling the Human Heart Under Acute Ischemia

Ventricular tachycardia and ventricular fibrillation are known to be two types of cardiac arrhythmias that usually take place during acute ischemia and frequently lead to sudden death. In this work, a methodology for the in-silico study of the regionally acute ischemic heart is presented. The chapter describes the mathematical formulation of the electrophysiology of the heart. A numerical scheme for the efficient numerical solution of the mathematical problem is also given. Along with the mathematical basis for the solution of the electrophysiology problem, the highly electrophysiological detailed action potential model for human proposed by ten Tusscher (Am J Physiol Heart Circ Physiol 291:1088–1100, 2006) has been adapted to make it suitable for modeling ischemic conditions (hyperkalemia, hipoxia, and acidic conditions). At this step, a formulation of the ATP-sensitive K+ current has been introduced into the existing model and the resulting model has been subjected to ischemic conditions. The results show that the three components of ischemia decrease the action potential duration (APD) as well as the conduction velocity, while effective refractory period (ERP) depicts a non-monotonic behavior. The modified action potential model was implemented on a 3-D geometrically and anatomically accurate regionally ischemic human heart. The ischemic region was located in the anterior side of the left ventricle mimicking the occlusion of the circumflex artery. Realistic heterogeneity and fiber anisotropy were considered in the model. The model predicts the generation of figure-of-eight re-entries which cross the central ischemic zone formed in the epicardial surface due to the longer refractory period of the midmyocardial layers. Also, focal activity experimentally observed in the epicardium caused by re-entrant wavefronts propagating in the mid-myocardium that re-emerge in the heart surface was found in the simulations.

Reentrant mechanisms triggered by ectopic activity in a three-dimensional realistic model of human atrium. a computer simulation study

Atrial fibrillation (AF) is the most common tachiarrhythmia. The pulmonary veins (PVs) have the predominant source of ectopic activity involved in the initiation of AF. Atrial remodelling, due to rapid and irregular activation during AF, leaves the tissue vulnerable to reentries. In this work the effects of electrical remodelling were incorporated in a 3D anisotropic model of human atrium. An ectopic focus was applied near to PVs. Electrograms were computed in simulated-electrodes in back wall of left atrial. The ectopic focus induced a figure-of-eight reentry that degenerated to mother rotor, after collisions and wave breaks were observed. Electrograms were more irregular during figure-of-eight reentry and collisions than during rotor activity. Spectral analysis shows multiple frequency peaks, as a consequence of changes of reentrant patterns. Dominant frequency was similar in all measuring points.

Post-repolarization refractoriness in human ventricular cardiac cells

Computer simulations have been used to study the mechanisms of postrepolarization refractoriness in cardiac cells under ischemic conditions at the cellular level. The ten Tusscher model of the cardiac action potential has been used with the formulation of the ATP-sensitive K+ current by Ferrero et al being adopted. Cells were subjected to hyperkalemia, hypoxic and acidic conditions. The results show that the three components of ischemia decrease the action potential duration (APD) as well as the conduction velocity, while effective refractory period (ERP) depicts a non-monotonic behavior. Under hyperkalemic conditions, no supernormal conduction is observed near physiologic values, and conduction relies on ICa(L) for [K+]o > 11 mmol/L. Under hypoxic conditions the trend observed in hyperkalemia are maintained but conduction blocking is obtained at a [K+]o concentration of 10 mmol/L. This condition minimally affects the conduction velocity of the hyperkalemic tissue. Acidosis gradually increases the difference between ERP and APD for reductions above the 60%, with conduction blocking occuring at 90%.

Modeling drug effects on personalized 3D models of the heart: a simulation study

The use of anti-arrhythmic drugs is common to treat heart rhythm disorders. Computational modeling and simulation are powerful tools that can be used to investigate the effects of specific drugs on cardiac electrophysiology. In this work a patient-specific anatomical heart model is built to study the effects of dofetilide, a drug that affects IKr current in cardiac cells. We study the multi-scale effects of the drug, from cellular to organ level, by simulating electrical propagation on tissue coupled cellular ion kinetics for several heart beats. Different cell populations configurations namely endocardial, midmyocardial and epicardial are used to test the effect of tissue heterogeneity. Results confirmed the expected effects of dofetilide at cellular level, increasing the action potential duration. Pseudo-ECGs obtained for each heart beat correlated well with cellular results showing prolongation of QT segment. These techniques can be applied over the development of more complex drugs that affect multiple cellular currents.

Vulnerability to reentry in a 3D regionally ischemic ventricular slab preparation: A simulation study

Ventricular tachycardia and ventricular fibrillation are known to be two types of cardiac arrhythmias that usually take place during acute ischemia and frequently lead to sudden death. In this work, we have studied the different patterns of activation displayed in a virtual ventricular slab preparation after premature stimulation during acute ischemia. Furthermore, we also have analyzed the vulnerable window (VW) under such conditions. Influence of the tissue structure and morphology of the ischemic zone have also been considered. For a centered ischemic zone, eight shaped reentry was originated at the mid plane of the slab and the VW was found to be almost the same as for the 2D simulations. Eight shaped reentry were formed in the epicardial surface as the morphology of the ischemic zone changed (the centre of the ischemic zone was moved toward the epicardial surface). These changes also caused a reduction in the VW of a 24% as compared with the centered ischemic zone.

Ectopic Foci Study on the Crest Terminalis in 3D Computer Model of Human Atrial

Atrial fibrillation (AF) is the most common arrhythmia in clinical practice. Epidemiological studies show that AF tends to persist over time, creating electrophysiological and anatomical changes called remodeled atrial. It has been shown that these changes result in variations in conduction velocity (CV) in the atrial tissue. The changes caused by electrical remodeling in a model of action potential (AP) of atrial myocytes have been incorpotated in this study, coupled with an anatomically realistic three-dimensional model of human dilated atrium. Simulations of the spread of AP in terms of anatomical and electrical remodeling and remodeling of gap junctions were measured vulnerable windows of reentry generation on the crest terminalis of the atrium. The results obtained indicate that vulnerable window in the remodeling of gap junctions shifted 38 ms with respect to the model dilated, which shows the impact of structural remodeling Several types of permanent reentry of figures in form of eight and in form of rotor, favored by the underlying anatomy of the atrium were obtained.