En el primer vídeo se nos explica lo que fue el primer paso para el comercio: el trueque se conoc... more En el primer vídeo se nos explica lo que fue el primer paso para el comercio: el trueque se conoce como trueque al intercambio de bienes y servicios por otros bienes y servicios sin que se utilice dinero para completar la transacción. En la antigüedad ésta era la forma de moneda por así decirlo, las necesidades de la población eran suplidas mediante cambios rudimentarios; huevos por tomates como hace referencia el Sr del vídeo.
The bidomain and monodomain equations are well established as the standard set of equations for t... more The bidomain and monodomain equations are well established as the standard set of equations for the simulation of cardiac electrophysiological behaviour. However, the computational cost of detailed bidomain/monodomain simulations limits their applicability ...
American journal of physiology. Heart and circulatory physiology, 2004
Effect of acute global ischemia on the upper limit of vulnerability: a simulation study. The goal... more Effect of acute global ischemia on the upper limit of vulnerability: a simulation study. The goal of this modeling research is to provide mechanistic insight into the effect of altered membrane kinetics associated with 5-12 min of acute global ischemia on the upper limit of cardiac vulnerability (ULV) to electric shocks. We simulate electrical activity in a finiteelement bidomain model of a 4-mm-thick slice through the canine ventricles that incorporates realistic geometry and fiber architecture. Global acute ischemia is represented by changes in membrane dynamics due to hyperkalemia, acidosis, and hypoxia. Two stages of acute ischemia are simulated corresponding to 5-7 min (stage 1) and 10 -12 min (stage 2) after the onset of ischemia. Monophasic shocks are delivered in normoxia and ischemia over a range of coupling intervals, and their outcomes are examined to determine the highest shock strength that resulted in induction of reentrant arrhythmia. Our results demonstrate that acute ischemia stage 1 results in ULV reduction to 0.8A from its normoxic value of 1.4A. In contrast, no arrhythmia is induced regardless of shock strength in acute ischemia stage 2. An investigation of mechanisms underlying this behavior revealed that decreased postshock refractoriness resulting mainly from 1) ischemic electrophysiological substrate and 2) decrease in the extent of areas positively-polarized by the shock is responsible for the change in ULV during stage 1. In contrast, conduction failure is the main cause for the lack of vulnerability in acute ischemia stage 2. The insight provided by this study furthers our understanding of mechanisms by which acute ischemia-induced changes at the ionic level modulate cardiac vulnerability to electric shocks.
American journal of physiology. Heart and circulatory physiology, 2009
Abnormalities in repolarization and its rate dependence are known to be related to increased proa... more Abnormalities in repolarization and its rate dependence are known to be related to increased proarrhythmic risk. A number of repolarization-related electrophysiological properties are commonly used as preclinical biomarkers of arrhythmic risk. However, the variability and complexity of repolarization mechanisms make the use of cellular biomarkers to predict arrhythmic risk preclinically challenging. Our goal is to investigate the role of ionic current properties and their variability in modulating cellular biomarkers of arrhythmic risk to improve risk stratification and identification in humans. A systematic investigation into the sensitivity of the main preclinical biomarkers of arrhythmic risk to changes in ionic current conductances and kinetics was performed using computer simulations. Four stimulation protocols were applied to the ten Tusscher and Panfilov human ventricular model to quantify the impact of +/-15 and +/-30% variations in key model parameters on action potential (AP) properties, Ca(2+) and Na(+) dynamics, and their rate dependence. Simulations show that, in humans, AP duration is moderately sensitive to changes in all repolarization current conductances and in L-type Ca(2+) current (I(CaL)) and slow component of the delayed rectifier current (I(Ks)) inactivation kinetics. AP triangulation, however, is strongly dependent only on inward rectifier K(+) current (I(K1)) and delayed rectifier current (I(Kr)) conductances. Furthermore, AP rate dependence (i.e., AP duration rate adaptation and restitution properties) and intracellular Ca(2+) and Na(+) levels are highly sensitive to both I(CaL) and Na(+)/K(+) pump current (I(NaK)) properties. This study provides quantitative insights into the sensitivity of preclinical biomarkers of arrhythmic risk to variations in ionic current properties in humans. The results show the importance of sensitivity analysis as a powerful method for the in-depth validation of mathematical models in cardiac electrophysiology.
Enhanced temporal and spatial variability in cardiac repolarization has been related to increased... more Enhanced temporal and spatial variability in cardiac repolarization has been related to increased arrhythmic risk both clinically and experimentally. Causes and modulators of variability in repolarization and their implications in arrhythmogenesis are however not well understood. At the ionic level, the slow component of the delayed rectifier potassium current (I Ks ) is an important determinant of ventricular repolarization. In this study, a combination of experimental and computational multiscale studies is used to investigate the role of intrinsic and extrinsic noise in I Ks in modulating temporal and spatial variability in ventricular repolarization in human and guinea pig. Results show that under physiological conditions: i), stochastic fluctuations in I Ks gating properties (i.e., intrinsic noise) cause significant beat-to-beat variability in action potential duration (APD) in isolated cells, whereas cell-to-cell differences in channel numbers (i.e., extrinsic noise) also contribute to cell-to-cell APD differences; ii), in tissue, electrotonic interactions mask the effect of I Ks noise, resulting in a significant decrease in APD temporal and spatial variability compared to isolated cells. Pathological conditions resulting in gap junctional uncoupling or a decrease in repolarization reserve uncover the manifestation of I Ks noise at cellular and tissue level, resulting in enhanced ventricular variability and abnormalities in repolarization such as afterdepolarizations and alternans.
Many drugs fail in the clinical trials and therefore do not reach the market due to adverse effec... more Many drugs fail in the clinical trials and therefore do not reach the market due to adverse effects on cardiac electrical function. This represents a growing concern for both regulatory and pharmaceutical agencies as it translates into important socio-economic costs. Drugs affecting cardiac activity come from diverse pharmacological groups and their interaction with cardiac electrophysiology can result in increased risk of potentially life threatening arrhythmias, such as Torsade de Pointes. The mechanisms of drug interaction with the heart are very complex and the effects span from the ion channel to the whole organ level. This makes their investigation using solely experimental in vitro and in vivo techniques very difficult. Computational modelling of cardiac electrophysiological behaviour has provided insight into the mechanisms of cardiac arrhythmogenesis, with high spatio-temporal resolution, from the ion channel to the whole organ level. It therefore represents a powerful tool in investigating mechanisms of drug-induced changes in cardiac behaviour and in their pro-arrhythmic potential. This article presents a comprehensive review of the recent advances in detailed models of drug action on cardiac electrophysiological activity.
Despite the fact that elucidating the mechanisms of cardiac vulnerability to electric shocks is c... more Despite the fact that elucidating the mechanisms of cardiac vulnerability to electric shocks is crucial to understanding why defibrillation shocks fail, important aspects of cardiac vulnerability remain unknown. This research utilizes a novel anatomically based bidomain finite-element model of the rabbit ventricles to investigate the effect of shock polarity reversal on the reentrant activity induced by an external defibrillation-strength shock in the paced ventricles. The specific goal of the study is to examine how differences between left and right ventricular chamber anatomy result in differences in the types of reentrant circuits established by the shock. Truncated exponential monophasic shocks of duration 8 ms were delivered via two external electrodes at various timings. Vulnerability grids were constructed for shocks of reversed polarity (referred to as RV− or LV− when either the RV or the LV electrode is a cathode). Our results demonstrate that reversing electrode polarity from RV− to LV− changes the dominant type of post-shock reentry: it is figure-of-eight for RV− and quatrefoil for LV− shocks. Differences in secondary types of post-shock arrhythmia also occur following shock polarity reversal. These effects of polarity reversal are primarily due to the fact that the LV wall is thicker than the RV, resulting in a post-shock excitable gap that is predominantly within the LV wall for RV− shocks and in the septum for LV− shocks.
Transmural electrophysiological heterogeneities have been shown to contribute to arrhythmia induc... more Transmural electrophysiological heterogeneities have been shown to contribute to arrhythmia induction in the heart; however, their role in defibrillation failure has never been examined. The goal of this study is to investigate how transmural heterogeneities in ionic currents and gap-junctional coupling contribute to arrhythmia generation following defibrillation strength shocks. This study used a 3D anatomically realistic bidomain model of the rabbit ventricles. Transmural heterogeneity in ionic currents and reduced sub-epicardial intercellular coupling were incorporated based on experimental data. The ventricles were paced apically, and truncated-exponential monophasic shocks of varying strength and timing were applied via large external electrodes. Simulations demonstrate that inclusion of transmural heterogeneity in ionic currents results in an increase in vulnerability to shocks, reflected in the increased upper limit of vulnerability, ULV, and the enlarged vulnerable window, VW. These changes in vulnerability stem from increased post-shock dispersion in repolarisation as it increases the likelihood of establishment of re-entrant circuits. In contrast, reduced sub-epicardial coupling results in decrease in both ULV and VW. This decrease is caused by altered virtual electrode polarisation around the region of sub-epicardal uncoupling, and specifically, by the increase in (1) the amount of positively polarised myocardium at shock-end and (2) the spatial extent of post-shock wavefronts.
Many experimental studies have pointed out the controversy involving the arrhythmogenic effects o... more 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 [I K(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 I K(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.
Understanding how electric current delivered to the heart in order to terminate lethal arrhythmia... more Understanding how electric current delivered to the heart in order to terminate lethal arrhythmias traverses myocardial structures and interacts with wavefronts of fibrillation has been challenging researchers for many years. Of particular importance is insight into the mechanisms by which the shock fails. Reinitiation of fibrillation is related not only to the effect of the shock on the electrical state of the myocardium but also to the intrinsic properties of the tissue that lead to destabilization of postshock activations and their degradation into electric turbulence. The complexity of the relationships and dependencies to be teased out and dissected in this quest have been staggering. Historically, overwhelming electrical artifacts prevented researchers from recording during, as well as shortly after, the shock. A breakthrough in mapping cardiac activity associated with defibrillation occurred during the last decade of the 20th century with the introduction of potentiometric dyes, which allowed continuous recording of activity before, during, and after the shock.
Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have ... more Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have been extensively documented, the contribution of ventricular anatomy to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been quantified; this is caused by lack of experimental methodology capable of mapping 3-D electrical activity. The goal of this study was to use optical imaging experiments and 3-D bidomain simulations to investigate the role of structural differences between left and right ventricles in vulnerability to electric shocks in rabbit hearts. The ventricles were paced apically, and uniform-field, truncated-exponential, monophasic shocks of reversed polarity were applied over a range of coupling intervals (CIs) in experiment and model. Experiments and simulations revealed that reversing the direction of externally-applied field (RVϪ or LVϪ shocks) alters the shape of the vulnerability area (VA), the 2-D grid encompassing episodes of arrhythmia induction. For RVϪ shocks, VA was nearly rectangular indicating little dependence of postshock arrhythmogenesis on CI. For LVϪ shocks, the probability of arrhythmia induction was higher for longer than for shorter CIs. The 3-D simulations demonstrated that these effects stem from the fact that reversal of field direction results in relocation of the main postshock excitable area from LV wall (RVϪ shocks) to septum (LVϪ shocks). Furthermore, the effect of septal (but not LV) excitable area in postshock propagation was found to strongly depend on preshock state. Knowledge regarding the location of the main postshock excitable area within the 3-D ventricular volume could be important for improving defibrillation efficacy. (Circ Res. 2005;97:168-175.)
Ionic (I i ) and gating currents (I g ) from noninactivating Shaker H4 K ϩ channels were recorded... more Ionic (I i ) and gating currents (I g ) from noninactivating Shaker H4 K ϩ channels were recorded with the cut-open oocyte voltage clamp and macropatch techniques. Steady state and kinetic properties were studied in the temperature range 2-22 Њ C. The time course of I i elicited by large depolarizations consists of an initial delay followed by an exponential rise with two kinetic components. The main I i component is highly temperature dependent (Q 10 Ͼ 4) and mildly voltage dependent, having a valence times the fraction of electric field ( z ) of 0.2-0.3 e o . The I g On response obtained between Ϫ 60 and 20 mV consists of a rising phase followed by a decay with fast and slow kinetic components. The main I g component of decay is highly temperature dependent (Q 10 Ͼ 4) and has a z between 1.6 and 2.8 e o in the voltage range from Ϫ 60 to Ϫ 10 mV, and ف 0.45 e o at more depolarized potentials. After a pulse to 0 mV, a variable recovery period at Ϫ 50 mV reactivates the gating charge with a high temperature dependence (Q 10 Ͼ 4). In contrast, the reactivation occurring between Ϫ 90 and Ϫ 50 mV has a Q 10 ϭ 1.2. Fluctuation analysis of ionic currents reveals that the open probability decreases 20% between 18 and 8 Њ C and the unitary conductance has a low temperature dependence with a Q 10 of 1.44. Plots of conductance and gating charge displacement are displaced to the left along the voltage axis when the temperature is decreased. The temperature data suggests that activation consists of a series of early steps with low enthalpic and negative entropic changes, followed by at least one step with high enthalpic and positive entropic changes, leading to final transition to the open state, which has a negative entropic change. key words: Shaker K ϩ channel • gating and ionic current kinetics • charge movement • voltage-activation process • enthalpic and entropic changes Portions of this work were previously published in abstract form (Rodríguez, B.M., D. Sigg, and F. 1 Abbreviations used in this paper: G-V curve, conductance versus voltage curve; MES, methanosulphonate; NMG, N-methyl-glucamine; P or -V curve, relative open probability versus voltage curve; Q-V curve, charge versus voltage curve.
The purpose of this study is to characterize the changes in vulnerability to electric shocks duri... more The purpose of this study is to characterize the changes in vulnerability to electric shocks during phase 1A of global ischemia in the rabbit ventricles and to determine the mechanisms responsible for these changes. Mechanisms responsible for the changes in cardiac vulnerability over the course of ischemia phase 1A remain poorly understood. The lack of understanding results from the rapid ischemic change in cardiac electrophysiologic properties, which renders experimental evaluation of vulnerability difficult. To examine dynamic changes in vulnerability to electric shocks over the course of acute global ischemia phase 1A, this study used a three-dimensional anatomically accurate bidomain model of ischemic rabbit ventricles. Monophasic shocks are applied at various coupling intervals to construct vulnerability grids in normoxia and at various stages of ischemia phase 1A. Our simulations demonstrate that 2 to 3 minutes after the onset of ischemia, the upper limit of vulnerability remains at its normoxic value (12.75 V/cm); however, arrhythmias are induced at shorter coupling intervals. As ischemia progresses, the upper limit of vulnerability decreases, reaching 6.4 V/cm in the advanced stage of ischemia phase 1A, and the vulnerable window shifts towards longer coupling intervals. Changes in the upper limit of vulnerability result from an increase in the spatial extent of the shock-end excitation wavefronts and the slower recovery from shock-induced positive polarization. Shifts in the vulnerable window stem from decreases in local repolarization times and the occurrence of postshock conduction failure caused by prolonged postrepolarization refractoriness.
2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, 2010
QT prolongation is the only clinically proven, yet insufficient, electrocardiogram (ECG) biomarke... more QT prolongation is the only clinically proven, yet insufficient, electrocardiogram (ECG) biomarker for drug-induced cardiac toxicity. The goal of this study is to evaluate whether JT area, i.e., total area of the T-wave, can serve as an ECG biomarker for drug-induced cardiac toxicity using both signal processing and computational modeling approaches. An ECG dataset that contained recordings from patients under control and sotalol condition was analyzed. In order to relate sotalol-induced ECG changes to its effect on ion channel level, i.e., blockade of the rapid component of the delayed rectifier potassium channel (I(Kr)), varied degrees of I(Kr) blockade were simulated in a slab of ventricular tissue. The mean JT area increased by 36.5% following the administration of sotalol in patients. Simulations in the slab tissue showed that sotalol increased action potential duration preferentially in the midmyocardium, which led to increased transmural dispersion of repolarization and JT area. In conclusion, JT area reflects the transmural dispersion of repolarization and may be a potentially useful surrogate/supplemental ECG biomarker to assess drug safety.
Pflügers Archiv - European Journal of Physiology, 2014
The sodium-potassium pump is widely recognized as the principal mechanism for active ion transpor... more The sodium-potassium pump is widely recognized as the principal mechanism for active ion transport across the cellular membrane of cardiac tissue, being responsible for the creation and maintenance of the transarcolemmal sodium and potassium gradients, crucial for cardiac cell electrophysiology. Importantly, sodiumpotassium pump activity is impaired in a number of major diseased conditions, including ischemia and heart failure. However, its subtle ways of action on cardiac electrophysiology, both directly through its electrogenic nature and indirectly via the regulation of cell homeostasis, make it hard to predict the electrophysiological consequences of reduced sodium-potassium pump activity in cardiac repolarization. In this review, we discuss how recent studies adopting the systems biology approach, through the integration of experimental and modeling methodologies, have identified the sodium-potassium pump as one of the most important ionic mechanisms in regulating key properties of cardiac repolarization and its rate dependence, from subcellular to whole organ levels. These include the role of the pump in the biphasic modulation of cellular repolarization and refractoriness, the rate control of intracellular sodium and calcium dynamics and therefore of the adaptation of repolarization to changes in heart rate, as well as its importance in regulating pro-arrhythmic substrates through modulation of dispersion of repolarization and restitution. Theoretical findings are consistent across a variety of cell types and species including human, and widely in agreement with experimental findings. The novel insights and hypotheses on the role of the pump in cardiac electrophysiology obtained through this integrative approach could eventually lead to novel therapeutic and diagnostic strategies.
Fluorescent photon scattering is known to distort optical recordings of cardiac transmembrane pot... more Fluorescent photon scattering is known to distort optical recordings of cardiac transmembrane potentials; however, this process is not well quantified, hampering interpretation of experimental data. This study presents a novel model, which accurately synthesizes fluorescent recordings over the irregular geometry of the rabbit ventricles. Using the model, the study aims to provide quantification of fluorescent signal distortion for different optical characteristics of the preparation and of the surrounding medium. A bi-domain representation of electrical activity is combined with finite element solutions to the photon diffusion equation simulating both the excitation and emission processes, along with physically realistic boundary conditions at the epicardium, which allow simulation of different experimental setups. We demonstrate that distortion in the optical signal as a result of fluorescent photon scattering is truly a three-dimensional phenomenon and depends critically upon the geometry of the preparation, the scattering properties of the tissue, the direction of wavefront propagation, and the specifics of the experimental setup. Importantly, we show that in an anatomically accurate model of ventricular geometry and fiber orientation, the morphology of the optical signal does not provide reliable information regarding the intramural direction of wavefront propagation. These findings underscore the potential of the new model in interpreting experimental data.
Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitat... more Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitation of the technique is signal distortion due to photon scattering. The goal of this experimental/simulation study is to investigate the role of three-dimensional photon scattering in optical signal distortion during ventricular tachycardia (VT) and defibrillation. A three-dimensional realistic bidomain rabbit ventricular model was combined with a model of photon transport. Shocks were applied via external electrodes to induce sustained VT, and transmembrane potentials (Vm) were compared with synthesized optical signals (Vopt). Fluorescent recordings were conducted in isolated rabbit hearts to validate simulation results. Results demonstrate that shock-induced membrane polarization magnitude is smaller in Vopt and in experimental signals as compared to Vm. This is due to transduction of potentials from weakly polarized midmyocardium to the epicardium. During shock-induced reentry and in sustained VT, photon scattering, combined with complex wavefront dynamics, results in optical action potentials near a filament exhibiting i), elevated resting potential, ii), reduced amplitude relative to pacing, and iii), dual-humped morphologies. A shift of up to 4 mm in the phase singularity location was observed in Vopt maps when compared to Vm. This combined experimental/simulation study provides an interpretation of optical recordings during VT and defibrillation.
Philosophical Transactions of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
has described the software engineering and computational infrastructure that has been set up as p... more has described the software engineering and computational infrastructure that has been set up as part of the Chaste project. Chaste-Cancer Heart And Soft Tissue Environment-is an open source software package that currently has heart and cancer modelling functionality. This software has been written using a programming paradigm imported from the commercial sector, and has resulted in code that has been subject to a far more rigorous testing procedure than is usual in this field. The exceptionally large number of tests written for each small, individual subroutine of this code allows software development to be carried out with confidence that new developments do not inadvertently degrade earlier functionality. This software may be developed for two main purposes-either to add new physiological functionality, or to incorporate a different numerical algorithm for solving the governing equations which allows a given level of accuracy to be attained more efficiently. In this paper, we will focus on the second of these purposes for the field of cardiac electrophysiological modelling. Whiteley (Annals of Biomedical Engineering, vol. 36, pp. 1398-1408) has developed a numerical algorithm for solving the bidomain equations that utilizes the multi-scale nature of the physiology modelled to enhance computational efficiency. When using this algorithm, only quantities that vary on short time-scales or short length-scales are computed to a fine resolution. Other more slowly varying quantities are computed at a lower resolution. Interpolation is then used to transfer information between different resolutions. Using a simple geometry in two dimensions and a purpose-built code, this algorithm was reported to give an increase in computational efficiency of over two orders of magnitude. In this paper, we begin by reviewing numerical methods currently in use for solving the bidomain equations, explaining how these methods may be developed to utilize the multi-scale algorithm discussed above. We then demonstrate the use of this algorithm within the Chaste framework for solving the monodomain and bido- † Author for correspondence (jonathan.whiteley@comlab.ox.ac.uk) main equations in a three-dimensional realistic heart geometry. Finally, we discuss how Chaste may be developed to include new physiological functionality-such as modelling a beating heart and fluid flow in the heart-and how new algorithms aimed at increasing the efficiency of the code may be incorporated.
En el primer vídeo se nos explica lo que fue el primer paso para el comercio: el trueque se conoc... more En el primer vídeo se nos explica lo que fue el primer paso para el comercio: el trueque se conoce como trueque al intercambio de bienes y servicios por otros bienes y servicios sin que se utilice dinero para completar la transacción. En la antigüedad ésta era la forma de moneda por así decirlo, las necesidades de la población eran suplidas mediante cambios rudimentarios; huevos por tomates como hace referencia el Sr del vídeo.
The bidomain and monodomain equations are well established as the standard set of equations for t... more The bidomain and monodomain equations are well established as the standard set of equations for the simulation of cardiac electrophysiological behaviour. However, the computational cost of detailed bidomain/monodomain simulations limits their applicability ...
American journal of physiology. Heart and circulatory physiology, 2004
Effect of acute global ischemia on the upper limit of vulnerability: a simulation study. The goal... more Effect of acute global ischemia on the upper limit of vulnerability: a simulation study. The goal of this modeling research is to provide mechanistic insight into the effect of altered membrane kinetics associated with 5-12 min of acute global ischemia on the upper limit of cardiac vulnerability (ULV) to electric shocks. We simulate electrical activity in a finiteelement bidomain model of a 4-mm-thick slice through the canine ventricles that incorporates realistic geometry and fiber architecture. Global acute ischemia is represented by changes in membrane dynamics due to hyperkalemia, acidosis, and hypoxia. Two stages of acute ischemia are simulated corresponding to 5-7 min (stage 1) and 10 -12 min (stage 2) after the onset of ischemia. Monophasic shocks are delivered in normoxia and ischemia over a range of coupling intervals, and their outcomes are examined to determine the highest shock strength that resulted in induction of reentrant arrhythmia. Our results demonstrate that acute ischemia stage 1 results in ULV reduction to 0.8A from its normoxic value of 1.4A. In contrast, no arrhythmia is induced regardless of shock strength in acute ischemia stage 2. An investigation of mechanisms underlying this behavior revealed that decreased postshock refractoriness resulting mainly from 1) ischemic electrophysiological substrate and 2) decrease in the extent of areas positively-polarized by the shock is responsible for the change in ULV during stage 1. In contrast, conduction failure is the main cause for the lack of vulnerability in acute ischemia stage 2. The insight provided by this study furthers our understanding of mechanisms by which acute ischemia-induced changes at the ionic level modulate cardiac vulnerability to electric shocks.
American journal of physiology. Heart and circulatory physiology, 2009
Abnormalities in repolarization and its rate dependence are known to be related to increased proa... more Abnormalities in repolarization and its rate dependence are known to be related to increased proarrhythmic risk. A number of repolarization-related electrophysiological properties are commonly used as preclinical biomarkers of arrhythmic risk. However, the variability and complexity of repolarization mechanisms make the use of cellular biomarkers to predict arrhythmic risk preclinically challenging. Our goal is to investigate the role of ionic current properties and their variability in modulating cellular biomarkers of arrhythmic risk to improve risk stratification and identification in humans. A systematic investigation into the sensitivity of the main preclinical biomarkers of arrhythmic risk to changes in ionic current conductances and kinetics was performed using computer simulations. Four stimulation protocols were applied to the ten Tusscher and Panfilov human ventricular model to quantify the impact of +/-15 and +/-30% variations in key model parameters on action potential (AP) properties, Ca(2+) and Na(+) dynamics, and their rate dependence. Simulations show that, in humans, AP duration is moderately sensitive to changes in all repolarization current conductances and in L-type Ca(2+) current (I(CaL)) and slow component of the delayed rectifier current (I(Ks)) inactivation kinetics. AP triangulation, however, is strongly dependent only on inward rectifier K(+) current (I(K1)) and delayed rectifier current (I(Kr)) conductances. Furthermore, AP rate dependence (i.e., AP duration rate adaptation and restitution properties) and intracellular Ca(2+) and Na(+) levels are highly sensitive to both I(CaL) and Na(+)/K(+) pump current (I(NaK)) properties. This study provides quantitative insights into the sensitivity of preclinical biomarkers of arrhythmic risk to variations in ionic current properties in humans. The results show the importance of sensitivity analysis as a powerful method for the in-depth validation of mathematical models in cardiac electrophysiology.
Enhanced temporal and spatial variability in cardiac repolarization has been related to increased... more Enhanced temporal and spatial variability in cardiac repolarization has been related to increased arrhythmic risk both clinically and experimentally. Causes and modulators of variability in repolarization and their implications in arrhythmogenesis are however not well understood. At the ionic level, the slow component of the delayed rectifier potassium current (I Ks ) is an important determinant of ventricular repolarization. In this study, a combination of experimental and computational multiscale studies is used to investigate the role of intrinsic and extrinsic noise in I Ks in modulating temporal and spatial variability in ventricular repolarization in human and guinea pig. Results show that under physiological conditions: i), stochastic fluctuations in I Ks gating properties (i.e., intrinsic noise) cause significant beat-to-beat variability in action potential duration (APD) in isolated cells, whereas cell-to-cell differences in channel numbers (i.e., extrinsic noise) also contribute to cell-to-cell APD differences; ii), in tissue, electrotonic interactions mask the effect of I Ks noise, resulting in a significant decrease in APD temporal and spatial variability compared to isolated cells. Pathological conditions resulting in gap junctional uncoupling or a decrease in repolarization reserve uncover the manifestation of I Ks noise at cellular and tissue level, resulting in enhanced ventricular variability and abnormalities in repolarization such as afterdepolarizations and alternans.
Many drugs fail in the clinical trials and therefore do not reach the market due to adverse effec... more Many drugs fail in the clinical trials and therefore do not reach the market due to adverse effects on cardiac electrical function. This represents a growing concern for both regulatory and pharmaceutical agencies as it translates into important socio-economic costs. Drugs affecting cardiac activity come from diverse pharmacological groups and their interaction with cardiac electrophysiology can result in increased risk of potentially life threatening arrhythmias, such as Torsade de Pointes. The mechanisms of drug interaction with the heart are very complex and the effects span from the ion channel to the whole organ level. This makes their investigation using solely experimental in vitro and in vivo techniques very difficult. Computational modelling of cardiac electrophysiological behaviour has provided insight into the mechanisms of cardiac arrhythmogenesis, with high spatio-temporal resolution, from the ion channel to the whole organ level. It therefore represents a powerful tool in investigating mechanisms of drug-induced changes in cardiac behaviour and in their pro-arrhythmic potential. This article presents a comprehensive review of the recent advances in detailed models of drug action on cardiac electrophysiological activity.
Despite the fact that elucidating the mechanisms of cardiac vulnerability to electric shocks is c... more Despite the fact that elucidating the mechanisms of cardiac vulnerability to electric shocks is crucial to understanding why defibrillation shocks fail, important aspects of cardiac vulnerability remain unknown. This research utilizes a novel anatomically based bidomain finite-element model of the rabbit ventricles to investigate the effect of shock polarity reversal on the reentrant activity induced by an external defibrillation-strength shock in the paced ventricles. The specific goal of the study is to examine how differences between left and right ventricular chamber anatomy result in differences in the types of reentrant circuits established by the shock. Truncated exponential monophasic shocks of duration 8 ms were delivered via two external electrodes at various timings. Vulnerability grids were constructed for shocks of reversed polarity (referred to as RV− or LV− when either the RV or the LV electrode is a cathode). Our results demonstrate that reversing electrode polarity from RV− to LV− changes the dominant type of post-shock reentry: it is figure-of-eight for RV− and quatrefoil for LV− shocks. Differences in secondary types of post-shock arrhythmia also occur following shock polarity reversal. These effects of polarity reversal are primarily due to the fact that the LV wall is thicker than the RV, resulting in a post-shock excitable gap that is predominantly within the LV wall for RV− shocks and in the septum for LV− shocks.
Transmural electrophysiological heterogeneities have been shown to contribute to arrhythmia induc... more Transmural electrophysiological heterogeneities have been shown to contribute to arrhythmia induction in the heart; however, their role in defibrillation failure has never been examined. The goal of this study is to investigate how transmural heterogeneities in ionic currents and gap-junctional coupling contribute to arrhythmia generation following defibrillation strength shocks. This study used a 3D anatomically realistic bidomain model of the rabbit ventricles. Transmural heterogeneity in ionic currents and reduced sub-epicardial intercellular coupling were incorporated based on experimental data. The ventricles were paced apically, and truncated-exponential monophasic shocks of varying strength and timing were applied via large external electrodes. Simulations demonstrate that inclusion of transmural heterogeneity in ionic currents results in an increase in vulnerability to shocks, reflected in the increased upper limit of vulnerability, ULV, and the enlarged vulnerable window, VW. These changes in vulnerability stem from increased post-shock dispersion in repolarisation as it increases the likelihood of establishment of re-entrant circuits. In contrast, reduced sub-epicardial coupling results in decrease in both ULV and VW. This decrease is caused by altered virtual electrode polarisation around the region of sub-epicardal uncoupling, and specifically, by the increase in (1) the amount of positively polarised myocardium at shock-end and (2) the spatial extent of post-shock wavefronts.
Many experimental studies have pointed out the controversy involving the arrhythmogenic effects o... more 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 [I K(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 I K(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.
Understanding how electric current delivered to the heart in order to terminate lethal arrhythmia... more Understanding how electric current delivered to the heart in order to terminate lethal arrhythmias traverses myocardial structures and interacts with wavefronts of fibrillation has been challenging researchers for many years. Of particular importance is insight into the mechanisms by which the shock fails. Reinitiation of fibrillation is related not only to the effect of the shock on the electrical state of the myocardium but also to the intrinsic properties of the tissue that lead to destabilization of postshock activations and their degradation into electric turbulence. The complexity of the relationships and dependencies to be teased out and dissected in this quest have been staggering. Historically, overwhelming electrical artifacts prevented researchers from recording during, as well as shortly after, the shock. A breakthrough in mapping cardiac activity associated with defibrillation occurred during the last decade of the 20th century with the introduction of potentiometric dyes, which allowed continuous recording of activity before, during, and after the shock.
Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have ... more Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have been extensively documented, the contribution of ventricular anatomy to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been quantified; this is caused by lack of experimental methodology capable of mapping 3-D electrical activity. The goal of this study was to use optical imaging experiments and 3-D bidomain simulations to investigate the role of structural differences between left and right ventricles in vulnerability to electric shocks in rabbit hearts. The ventricles were paced apically, and uniform-field, truncated-exponential, monophasic shocks of reversed polarity were applied over a range of coupling intervals (CIs) in experiment and model. Experiments and simulations revealed that reversing the direction of externally-applied field (RVϪ or LVϪ shocks) alters the shape of the vulnerability area (VA), the 2-D grid encompassing episodes of arrhythmia induction. For RVϪ shocks, VA was nearly rectangular indicating little dependence of postshock arrhythmogenesis on CI. For LVϪ shocks, the probability of arrhythmia induction was higher for longer than for shorter CIs. The 3-D simulations demonstrated that these effects stem from the fact that reversal of field direction results in relocation of the main postshock excitable area from LV wall (RVϪ shocks) to septum (LVϪ shocks). Furthermore, the effect of septal (but not LV) excitable area in postshock propagation was found to strongly depend on preshock state. Knowledge regarding the location of the main postshock excitable area within the 3-D ventricular volume could be important for improving defibrillation efficacy. (Circ Res. 2005;97:168-175.)
Ionic (I i ) and gating currents (I g ) from noninactivating Shaker H4 K ϩ channels were recorded... more Ionic (I i ) and gating currents (I g ) from noninactivating Shaker H4 K ϩ channels were recorded with the cut-open oocyte voltage clamp and macropatch techniques. Steady state and kinetic properties were studied in the temperature range 2-22 Њ C. The time course of I i elicited by large depolarizations consists of an initial delay followed by an exponential rise with two kinetic components. The main I i component is highly temperature dependent (Q 10 Ͼ 4) and mildly voltage dependent, having a valence times the fraction of electric field ( z ) of 0.2-0.3 e o . The I g On response obtained between Ϫ 60 and 20 mV consists of a rising phase followed by a decay with fast and slow kinetic components. The main I g component of decay is highly temperature dependent (Q 10 Ͼ 4) and has a z between 1.6 and 2.8 e o in the voltage range from Ϫ 60 to Ϫ 10 mV, and ف 0.45 e o at more depolarized potentials. After a pulse to 0 mV, a variable recovery period at Ϫ 50 mV reactivates the gating charge with a high temperature dependence (Q 10 Ͼ 4). In contrast, the reactivation occurring between Ϫ 90 and Ϫ 50 mV has a Q 10 ϭ 1.2. Fluctuation analysis of ionic currents reveals that the open probability decreases 20% between 18 and 8 Њ C and the unitary conductance has a low temperature dependence with a Q 10 of 1.44. Plots of conductance and gating charge displacement are displaced to the left along the voltage axis when the temperature is decreased. The temperature data suggests that activation consists of a series of early steps with low enthalpic and negative entropic changes, followed by at least one step with high enthalpic and positive entropic changes, leading to final transition to the open state, which has a negative entropic change. key words: Shaker K ϩ channel • gating and ionic current kinetics • charge movement • voltage-activation process • enthalpic and entropic changes Portions of this work were previously published in abstract form (Rodríguez, B.M., D. Sigg, and F. 1 Abbreviations used in this paper: G-V curve, conductance versus voltage curve; MES, methanosulphonate; NMG, N-methyl-glucamine; P or -V curve, relative open probability versus voltage curve; Q-V curve, charge versus voltage curve.
The purpose of this study is to characterize the changes in vulnerability to electric shocks duri... more The purpose of this study is to characterize the changes in vulnerability to electric shocks during phase 1A of global ischemia in the rabbit ventricles and to determine the mechanisms responsible for these changes. Mechanisms responsible for the changes in cardiac vulnerability over the course of ischemia phase 1A remain poorly understood. The lack of understanding results from the rapid ischemic change in cardiac electrophysiologic properties, which renders experimental evaluation of vulnerability difficult. To examine dynamic changes in vulnerability to electric shocks over the course of acute global ischemia phase 1A, this study used a three-dimensional anatomically accurate bidomain model of ischemic rabbit ventricles. Monophasic shocks are applied at various coupling intervals to construct vulnerability grids in normoxia and at various stages of ischemia phase 1A. Our simulations demonstrate that 2 to 3 minutes after the onset of ischemia, the upper limit of vulnerability remains at its normoxic value (12.75 V/cm); however, arrhythmias are induced at shorter coupling intervals. As ischemia progresses, the upper limit of vulnerability decreases, reaching 6.4 V/cm in the advanced stage of ischemia phase 1A, and the vulnerable window shifts towards longer coupling intervals. Changes in the upper limit of vulnerability result from an increase in the spatial extent of the shock-end excitation wavefronts and the slower recovery from shock-induced positive polarization. Shifts in the vulnerable window stem from decreases in local repolarization times and the occurrence of postshock conduction failure caused by prolonged postrepolarization refractoriness.
2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, 2010
QT prolongation is the only clinically proven, yet insufficient, electrocardiogram (ECG) biomarke... more QT prolongation is the only clinically proven, yet insufficient, electrocardiogram (ECG) biomarker for drug-induced cardiac toxicity. The goal of this study is to evaluate whether JT area, i.e., total area of the T-wave, can serve as an ECG biomarker for drug-induced cardiac toxicity using both signal processing and computational modeling approaches. An ECG dataset that contained recordings from patients under control and sotalol condition was analyzed. In order to relate sotalol-induced ECG changes to its effect on ion channel level, i.e., blockade of the rapid component of the delayed rectifier potassium channel (I(Kr)), varied degrees of I(Kr) blockade were simulated in a slab of ventricular tissue. The mean JT area increased by 36.5% following the administration of sotalol in patients. Simulations in the slab tissue showed that sotalol increased action potential duration preferentially in the midmyocardium, which led to increased transmural dispersion of repolarization and JT area. In conclusion, JT area reflects the transmural dispersion of repolarization and may be a potentially useful surrogate/supplemental ECG biomarker to assess drug safety.
Pflügers Archiv - European Journal of Physiology, 2014
The sodium-potassium pump is widely recognized as the principal mechanism for active ion transpor... more The sodium-potassium pump is widely recognized as the principal mechanism for active ion transport across the cellular membrane of cardiac tissue, being responsible for the creation and maintenance of the transarcolemmal sodium and potassium gradients, crucial for cardiac cell electrophysiology. Importantly, sodiumpotassium pump activity is impaired in a number of major diseased conditions, including ischemia and heart failure. However, its subtle ways of action on cardiac electrophysiology, both directly through its electrogenic nature and indirectly via the regulation of cell homeostasis, make it hard to predict the electrophysiological consequences of reduced sodium-potassium pump activity in cardiac repolarization. In this review, we discuss how recent studies adopting the systems biology approach, through the integration of experimental and modeling methodologies, have identified the sodium-potassium pump as one of the most important ionic mechanisms in regulating key properties of cardiac repolarization and its rate dependence, from subcellular to whole organ levels. These include the role of the pump in the biphasic modulation of cellular repolarization and refractoriness, the rate control of intracellular sodium and calcium dynamics and therefore of the adaptation of repolarization to changes in heart rate, as well as its importance in regulating pro-arrhythmic substrates through modulation of dispersion of repolarization and restitution. Theoretical findings are consistent across a variety of cell types and species including human, and widely in agreement with experimental findings. The novel insights and hypotheses on the role of the pump in cardiac electrophysiology obtained through this integrative approach could eventually lead to novel therapeutic and diagnostic strategies.
Fluorescent photon scattering is known to distort optical recordings of cardiac transmembrane pot... more Fluorescent photon scattering is known to distort optical recordings of cardiac transmembrane potentials; however, this process is not well quantified, hampering interpretation of experimental data. This study presents a novel model, which accurately synthesizes fluorescent recordings over the irregular geometry of the rabbit ventricles. Using the model, the study aims to provide quantification of fluorescent signal distortion for different optical characteristics of the preparation and of the surrounding medium. A bi-domain representation of electrical activity is combined with finite element solutions to the photon diffusion equation simulating both the excitation and emission processes, along with physically realistic boundary conditions at the epicardium, which allow simulation of different experimental setups. We demonstrate that distortion in the optical signal as a result of fluorescent photon scattering is truly a three-dimensional phenomenon and depends critically upon the geometry of the preparation, the scattering properties of the tissue, the direction of wavefront propagation, and the specifics of the experimental setup. Importantly, we show that in an anatomically accurate model of ventricular geometry and fiber orientation, the morphology of the optical signal does not provide reliable information regarding the intramural direction of wavefront propagation. These findings underscore the potential of the new model in interpreting experimental data.
Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitat... more Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitation of the technique is signal distortion due to photon scattering. The goal of this experimental/simulation study is to investigate the role of three-dimensional photon scattering in optical signal distortion during ventricular tachycardia (VT) and defibrillation. A three-dimensional realistic bidomain rabbit ventricular model was combined with a model of photon transport. Shocks were applied via external electrodes to induce sustained VT, and transmembrane potentials (Vm) were compared with synthesized optical signals (Vopt). Fluorescent recordings were conducted in isolated rabbit hearts to validate simulation results. Results demonstrate that shock-induced membrane polarization magnitude is smaller in Vopt and in experimental signals as compared to Vm. This is due to transduction of potentials from weakly polarized midmyocardium to the epicardium. During shock-induced reentry and in sustained VT, photon scattering, combined with complex wavefront dynamics, results in optical action potentials near a filament exhibiting i), elevated resting potential, ii), reduced amplitude relative to pacing, and iii), dual-humped morphologies. A shift of up to 4 mm in the phase singularity location was observed in Vopt maps when compared to Vm. This combined experimental/simulation study provides an interpretation of optical recordings during VT and defibrillation.
Philosophical Transactions of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
has described the software engineering and computational infrastructure that has been set up as p... more has described the software engineering and computational infrastructure that has been set up as part of the Chaste project. Chaste-Cancer Heart And Soft Tissue Environment-is an open source software package that currently has heart and cancer modelling functionality. This software has been written using a programming paradigm imported from the commercial sector, and has resulted in code that has been subject to a far more rigorous testing procedure than is usual in this field. The exceptionally large number of tests written for each small, individual subroutine of this code allows software development to be carried out with confidence that new developments do not inadvertently degrade earlier functionality. This software may be developed for two main purposes-either to add new physiological functionality, or to incorporate a different numerical algorithm for solving the governing equations which allows a given level of accuracy to be attained more efficiently. In this paper, we will focus on the second of these purposes for the field of cardiac electrophysiological modelling. Whiteley (Annals of Biomedical Engineering, vol. 36, pp. 1398-1408) has developed a numerical algorithm for solving the bidomain equations that utilizes the multi-scale nature of the physiology modelled to enhance computational efficiency. When using this algorithm, only quantities that vary on short time-scales or short length-scales are computed to a fine resolution. Other more slowly varying quantities are computed at a lower resolution. Interpolation is then used to transfer information between different resolutions. Using a simple geometry in two dimensions and a purpose-built code, this algorithm was reported to give an increase in computational efficiency of over two orders of magnitude. In this paper, we begin by reviewing numerical methods currently in use for solving the bidomain equations, explaining how these methods may be developed to utilize the multi-scale algorithm discussed above. We then demonstrate the use of this algorithm within the Chaste framework for solving the monodomain and bido- † Author for correspondence (jonathan.whiteley@comlab.ox.ac.uk) main equations in a three-dimensional realistic heart geometry. Finally, we discuss how Chaste may be developed to include new physiological functionality-such as modelling a beating heart and fluid flow in the heart-and how new algorithms aimed at increasing the efficiency of the code may be incorporated.
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Papers by Blanca Rodríguez