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.

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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12938-015-0033-5) contains supplementary material, which is available to authorized users.

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.

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.

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.