J.M. Ferrero

Simulation of Action Potentials From Metabolically Impaired Cardiac Myocytes Role of ATP-Sensitive K+ Current

The role of the ATP-sensitive K+ current (IK-ATP) and its contribution to electrophysiological changes that occur during metabolic impairment in cardiac ventricular myocytes is still being discussed. The aim of this work was to quantitatively study this issue by using computer modeling. A model of IK-ATP is formulated and incorporated into the Luo-Rudy ionic model of the ventricular action potential. Action potentials under different degrees of activation of IK-ATP are simulated. Our results show that in normal ionic concentrations, only approximately 0.6% of the KATP channels, when open, should account for a 50% reduction in action potential duration. However, increased levels of intracellular Mg2+ counteract this shortening. Under conditions of high [K+]0, such as those found in early ischemia, the activation of only approximately 0.4% of the KATP channels could account for a 50% reduction in action potential duration. Thus, our results suggest that opening of IK-ATP channels should play a significant role in action potential shortening during hypoxic/ischemic episodes, with the fraction of open channels involved being very low ( < 1%). However, the results of the model suggest that activation of IK-ATP alone does not quantitatively account for the observed K+ efflux in metabolically impaired cardiac myocytes. Mechanisms other than KATP channel activation should be responsible for a significant part of the K+ efflux measured in hypoxic/ischemic situations.

Simulation and Mechanistic Investigation of the Arrhythmogenic Role of the Late Sodium Current in Human Heart Failure

Heart failure constitutes a major public health problem worldwide. The electrophysiological remodeling of failing hearts sets the stage for malignant arrhythmias, in which the role of the late Na+ current (INaL) is relevant and is currently under investigation. In this study we examined the role of INaL in the electrophysiological phenotype of ventricular myocytes, and its proarrhythmic effects in the failing heart. A model for cellular heart failure was proposed using a modified version of Grandi et al. model for human ventricular action potential that incorporates the formulation of INaL. A sensitivity analysis of the model was performed and simulations of the pathological electrical activity of the cell were conducted. The proposed model for the human INaL and the electrophysiological remodeling of myocytes from failing hearts accurately reproduce experimental observations. The sensitivity analysis of the modulation of electrophysiological parameters of myocytes from failing hearts due to ion channels remodeling, revealed a role for INaL in the prolongation of action potential duration (APD), triangulation of the shape of the AP, and changes in Ca2+ transient. A mechanistic investigation of intracellular Na+ accumulation and APD shortening with increasing frequency of stimulation of failing myocytes revealed a role for the Na+/K+ pump, the Na+/Ca2+ exchanger and INaL. The results of the simulations also showed that in failing myocytes, the enhancement of INaL increased the reverse rate-dependent APD prolongation and the probability of initiating early afterdepolarizations. The electrophysiological remodeling of failing hearts and especially the enhancement of the INaL prolong APD and alter Ca2+ transient facilitating the development of early afterdepolarizations. An enhanced INaL appears to be an important contributor to the electrophysiological phenotype and to the dysregulation of [Ca2+]i homeostasis of failing myocytes.

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.

Electrical activity and reentry during acute regional myocardial ischemia: insights from simulations

In this work, the authors use computer modeling to theoretically investigate the mechanisms involved in figure-of-eight reentry during acute regional myocardial ischemia, a pattern of excitation which may lead to ventricular fibrillation and sudden cardiac death. For this purpose, a modified version of the Luo–Rudy dynamic model for the action potential and ionic currents has been used, together with a two-dimensional model of the regionally ischemic ventricle. The virtual tissue comprises several realistically dimensioned and located transitional border zones for hyperkalemia, hypoxia and acidosis, simulating the substrate heterogeneity created by acute ischemia. Different types of patterns of excitation following the delivery of a premature stimulus were obtained, including figure-of-eight reentry. Action potentials and selected ionic currents which explain the reentry process are analyzed. The effect of the degree of ATP-sensitive current activation in the vulnerability to reentry is also studied. The results are in accordance with experimental observations, and demonstrate the ability of second-generation mathematical models to analyze and explain the mechanisms involved in ischemic reentry.

Influence of electrical coupling on early after depolarizations in ventricular myocytes

Computer modeling is used to study the effect of electrical coupling between a myocardial zone where early after-depolarizations (EADs) can develop and the normal neighboring tissue. The effects of such coupling on EAD development and on the likelihood of EAD propagation as an ectopic beat are studied. The influence on EAD formation is investigated by approximating two partially coupled myocardial zones modeled as two active elements coupled by a junctional resistance R. For R values lower than 800 /spl Omega/ cm/sup 2/, the action potentials are transmitted to the coupled element, and for R values higher than 850 /spl Omega/ cm/sup 2/ they are blocked. In both ranges of R, when the electrical coupling increases, the EADs appear at more negative takeoff potentials with higher amplitudes and upstrokes. The EADs are not elicited if the electrical coupling is too high. In a separate model of two one-dimensional cardiac fiber segments partially coupled by a resistance R, critical R values exist, between 42 and 54 /spl Omega/ cm/sup 2/ that facilitate EAD propagation. These results demonstrate that in myocardial zones favorable to the formation of EAD, the electrical coupling dramatically affects initiation of EAD and its spread to the neighboring tissue.

Systematic characterization of the ionic basis of rabbit cellular electrophysiology using two ventricular models.

Several mathematical models of rabbit ventricular action potential (AP) have been proposed to investigate mechanisms of arrhythmias and excitation-contraction coupling. Our study aims at systematically characterizing how ionic current properties modulate the main cellular biomarkers of arrhythmic risk using two widely-used rabbit ventricular models, and comparing simulation results using the two models with experimental data available for rabbit. A sensitivity analysis of AP properties, Ca²⁺ and Na⁺ dynamics, and their rate dependence to variations (±15% and ±30%) in the main transmembrane current conductances and kinetics was performed using the Shannon et al. (2004) and the Mahajan et al. (2008a,b) AP rabbit models. The effects of severe transmembrane current blocks (up to 100%) on steady-state AP and calcium transients, and AP duration (APD) restitution curves were also simulated using both models. Our simulations show that, in both virtual rabbit cardiomyocytes, APD is significantly modified by most repolarization currents, AP triangulation is regulated mostly by the inward rectifier K⁺ current (I(K1)) whereas APD rate adaptation as well as [Na⁺](i) rate dependence is influenced by the Na⁺/K⁺ pump current (I(NaK)). In addition, steady-state [Ca²⁺](i) levels, APD restitution properties and [Ca²⁺](i) rate dependence are strongly dependent on I(NaK), the L-Type Ca²⁺ current (I(CaL)) and the Na⁺/Ca²⁺ exchanger current (I(NaCa)), although the relative role of these currents is markedly model dependent. Furthermore, our results show that simulations using both models agree with many experimentally-reported electrophysiological characteristics. However, our study shows that the Shannon et al. model mimics rabbit electrophysiology more accurately at normal pacing rates, whereas Mahajan et al. model behaves more appropriately at faster rates. Our results reinforce the usefulness of sensitivity analysis for further understanding of cellular electrophysiology and validation of cardiac AP models.

Three-dimensional cardiac computational modelling: methods, features and applications.

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Electrophysiological and Structural Remodeling in Heart Failure Modulate Arrhythmogenesis. 1D Simulation Study

Background Heart failure is a final common pathway or descriptor for various cardiac pathologies. It is associated with sudden cardiac death, which is frequently caused by ventricular arrhythmias. Electrophysiological remodeling, intercellular uncoupling, fibrosis and autonomic imbalance have been identified as major arrhythmogenic factors in heart failure etiology and progression. Objective In this study we investigate in silico the role of electrophysiological and structural heart failure remodeling on the modulation of key elements of the arrhythmogenic substrate, i.e., electrophysiological gradients and abnormal impulse propagation. Methods Two different mathematical models of the human ventricular action potential were used to formulate models of the failing ventricular myocyte. This provided the basis for simulations of the electrical activity within a transmural ventricular strand. Our main goal was to elucidate the roles of electrophysiological and structural remodeling in setting the stage for malignant life-threatening arrhythmias. Results Simulation results illustrate how the presence of M cells and heterogeneous electrophysiological remodeling in the human failing ventricle modulate the dispersion of action potential duration and repolarization time. Specifically, selective heterogeneous remodeling of expression levels for the Na+/Ca2+ exchanger and SERCA pump decrease these heterogeneities. In contrast, fibroblast proliferation and cellular uncoupling both strongly increase repolarization heterogeneities. Conduction velocity and the safety factor for conduction are also reduced by the progressive structural remodeling during heart failure. Conclusion An extensive literature now establishes that in human ventricle, as heart failure progresses, gradients for repolarization are changed significantly by protein specific electrophysiological remodeling (either homogeneous or heterogeneous). Our simulations illustrate and provide new insights into this. Furthermore, enhanced fibrosis in failing hearts, as well as reduced intercellular coupling, combine to increase electrophysiological gradients and reduce electrical propagation. In combination these changes set the stage for arrhythmias.

Radio-frequency heating of the cornea: theoretical model and in vitro experiments

We present a theoretical model for the study of cornea heating with radio-frequency currents. This technique is used to reshape the cornea to correct refractive disorders. Our numerical model has allowed the study of the temperature distributions in the cornea and to estimate the dimensions of the lesion. The model incorporates a fragment of cornea, aqueous humor, and the active electrode placed on the cornea surface. The finite element method has been used to calculate the temperature distribution in the cornea by solving a coupled electric-thermal problem. We analyzed by means of computer simulations the effect of: a) temperature influence on the tissue electrical conductivity; b) the dispersion of the biological characteristics; c) the anisotropy of the cornea thermal conductivity; d) the presence of the tear film; and e) the insertion depth of the active electrode in the cornea, and the results suggest that these effects have a significant influence on the temperature distributions and thereby on the lesion dimensions. However, the cooling of the aqueous humor in the endothelium or the realistic value of the cornea curvature did not have a significant effect on the temperature distributions. An experimental model based on the lesions created in rabbit eyes has been used in order to compare the theoretical and experimental results. There is a tendency toward the agreement between experimental and theoretical results, although we have observed that the theoretical model overestimates the lesion dimension.

Effects of pinacidil on reentrant arrhythmias generated during acute regional ischemia: a simulation study

Many experimental studies have pointed out the controversy involving the arrhythmogenic effects of potassium channel openers (KCOs) in ischemia. KCOs activate the ATP-sensitive potassium current [IK(ATP)], resulting in action potential duration (APD) shortening, especially under pathological conditions such as ischemia. Acute myocardial ischemia leads to electrophysiological inhomogeneities in APD, conduction velocity, and refractoriness, which provide the substrate for reentry initiation and maintenance and may lead to malignant arrhythmias. The aim of this work is to analyze the effect of the KCO pinacidil on vulnerability to reentry during acute regional ischemia using computer simulations. We use a two-dimensional virtual heart tissue with implementation of acute regional ischemia conditions. Membrane kinetics are represented by a modified version of Luo–Rudy (phase II) action potential model that incorporates the effect of pinacidil on IK(ATP). The vulnerable window (VW) for reentry is quantified for different doses of pinacidil. Our results show that for doses below 3 μmol/l the VW widens with increasing pinacidil concentration, whereas for higher doses of pinacidil the VW decreases, becoming zero for concentrations above 10 μmol/l. The ionic mechanisms involved in this behavior are explored. This study demonstrates that the effect of pinacidil on arrhythmogenesis is strongly dose-dependent, and that high doses of pinacidil exert a strong antiarrhythmic effect.