One-Dimensional Mathematical Model of the Atrioventricular Node Including Atrio-Nodal, Nodal, and Nodal-His Cells

Mathematical models are a repository of knowledge as well as research and teaching tools. Although action potential models have been developed for most regions of the heart, there is no model for the atrioventricular node (AVN). We have developed action potential models for single atrio-nodal, nodal, and nodal-His cells. The models have the same action potential shapes and refractoriness as observed in experiments. Using these models, together with models for the sinoatrial node (SAN) and atrial muscle, we have developed a one-dimensional (1D) multicellular model including the SAN and AVN. The multicellular model has slow and fast pathways into the AVN and using it we have analyzed the rich behavior of the AVN. Under normal conditions, action potentials were initiated in the SAN center and then propagated through the atrium and AVN. The relationship between the AVN conduction time and the timing of a premature stimulus (conduction curve) is consistent with experimental data. After premature stimulation, atrioventricular nodal reentry could occur. After slow pathway ablation or block of the L-type Ca²⁺ current, atrioventricular nodal reentry was abolished. During atrial fibrillation, the AVN limited the number of action potentials transmitted to the ventricle. In the absence of SAN pacemaking, the inferior nodal extension acted as the pacemaker. In conclusion, we have developed what we believe is the first detailed mathematical model of the AVN and it shows the typical physiological and pathophysiological characteristics of the tissue. The model can be used as a tool to analyze the complex structure and behavior of the AVN.     

The ultrastructure of the sinu-atrial node of the bat

The sinu-atrial node (SAN) of the bat, Pipistrellus subflavus, is capable of generating a wide range of spontaneous activity varying from 20 bpm when hibernating to bursts of 800 bpm during active flight. Electrophysiological studies have shown an absence of arrhythmias even below 4 degrees C body temperature. In order to determine whether these physiological capabilities are based upon unique ultrastructural features of the bat SAN, the present study was conducted. We found that the structure of the SAN of the bat is typically mammalian. Diameters of all three cell types in the SAN (nodal, transitional, and atrial) are smaller than those observed in any other mammalian species. A morphometric analysis of cell junctions reveals that nodal-nodal and transitional-transitional cell contacts are primarily undifferentiated with few nexuses. Atrial-atrial cell contacts have a dominance of fasciae adherentes-type junctions with a small area left undifferentiated. Nexuses are much more prevalent in atrial-atrial cell contacts.     

Telocytes in the human sinoatrial node

The sinoatrial node (SAN) is composed mostly of pacemaker, transitional and Purkinje‐like cells. Pacemaker cells, especially in the centre of the SAN, are surrounded by dense fibrous tissue and do not have any contact with transitional cells. We hypothesize that the SAN contains telocytes that have contacts with pacemaker cells and contractile myocardium. Immunohistochemistry using antibodies against HCN4 and antibody combinations against CD34 and HCN4 was carried out on 12 specimens. Confocal laser scanning microscopy (CLSM) with two mixtures of primary antibodies, namely CD34/S100 and vimentin/S100, was performed in three cases. In two cases, CLSM was carried out with CD117 antibody. Specimens for electron microscopy and immunocytochemistry with HCN4 immunogold labelling were taken from another three patients. In our study, we found cells with the immunophenotype of telocytes in the SAN. There were twice as many of these cells in the centre of the SAN as in the periphery (20.3 ± 4.8 versus 10.8 ± 4.4 per high‐power field). They had close contact with pacemaker cells and contractile cardiomyocytes and expressed HCN4. The ultrastructural characteristics of these cells are identical to those of telocytes observed earlier in other organs. Our study provides evidence that telocytes are present in the SAN.     

Isolation of a novel family of genes related to 2-oxoglutarate-dependent dioxygenases from soybean and analysis of their expression during root nodule senescence

A screen for genes involved in root nodule senescence has led to the isolation of the senescence-associated nodulin 1 (SAN1) multigene family from Glycine max (soybean). The three, tandemly repeated SAN1 genes each have three exons and two introns and are highly conserved. SAN1A and SAN1B code for conceptual proteins of 352 and 353 amino acids, respectively, and share over 83% sequence identity, while SAN1C encodes a truncated protein of 126 amino acids and is likely to be a pseudogene. The SAN1-encoded proteins share sequence similarity and highly conserved motifs with plant 2-oxoglutarate-dependent dioxygenases (2-ODDs), suggesting that they encode 2-ODDs. Analyses of the steady-state mRNA levels of SAN1A and SAN1B during senescence induced by treatment with fixed nitrogen or darkness demonstrate that SAN1A is downregulated during induced senescence. In contrast, SAN1B is upregulated by both treatments. The expression of the SAN1 genes is not restricted to nodules, suggesting that in addition to their function(s) in these organs, they play a more general role in plant metabolism.     

Determinants of heterogeneity, excitation and conduction in the sinoatrial node: a model study

The sinoatrial node (SAN) is a complex structure that exhibits anatomical and functional heterogeneity which may depend on: 1) The existence of distinct cell populations, 2) electrotonic influences of the surrounding atrium, 3) the presence of a high density of fibroblasts, and 4) atrial cells intermingled within the SAN. Our goal was to utilize a computer model to predict critical determinants and modulators of excitation and conduction in the SAN. We built a theoretical "non-uniform" model composed of distinct central and peripheral SAN cells and a "uniform" model containing only central cells connected to the atrium. We tested the effects of coupling strength between SAN cells in the models, as well as the effects of fibroblasts and interspersed atrial cells. Although we could simulate single cell experimental data supporting the "multiple cell type" hypothesis, 2D "non-uniform" models did not simulate expected tissue behavior, such as central pacemaking. When we considered the atrial effects alone in a simple homogeneous "uniform" model, central pacemaking initiation and impulse propagation in simulations were consistent with experiments. Introduction of fibroblasts in our simulated tissue resulted in various effects depending on the density, distribution, and fibroblast-myocyte coupling strength. Incorporation of atrial cells in our simulated SAN tissue had little effect on SAN electrophysiology. Our tissue model simulations suggest atrial electrotonic effects as plausible to account for SAN heterogeneity, sequence, and rate of propagation. Fibroblasts can act as obstacles, current sinks or shunts to conduction in the SAN depending on their orientation, density, and coupling.     

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the "pinwheel experiment" emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.     

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.     

A rapidly activating delayed rectifier K+ current regulates pacemaker activity in adult mouse sinoatrial node cells

We have investigated the physiological role of the "rapidly activating" delayed rectifier K+ current (IKr) in pacemaker activity in isolated sinoatrial node (SAN) myocytes and the expression of mouse ether-a-go-go (mERG) genes in the adult mouse SAN. In isolated, voltage-clamped SAN cells, outward currents evoked by depolarizing steps (greater than -40 mV) were strongly inhibited by the class III methanesulfonanilide compound E-4031 (1-2.5 microM), and the deactivation "tail" currents that occurred during repolarization to a membrane potential of -45 mV were completely blocked. E-4031-sensitive currents (IKr) reached a maximum at a membrane potential of -10 mV and showed pronounced inward rectification at more-positive membrane potentials. Activation of IKr occurred at -40 to 0 mV, with half-activation at about -24 mV. The contribution of IKr to action potential repolarization and diastolic depolarization was estimated by determining the E-4031-sensitive current evoked during voltage clamp with a simulated mouse SAN action potential. IKr reached its peak value (approximately 0.6 pA/pF) near -25 mV, close to the midpoint of the repolarization phase of the simulated action potential, and deactivated almost completely during the diastolic interval. E-4031 (1 microM) slowed the spontaneous pacing rate of Langendorff-perfused, isolated adult mouse hearts by an average of 36.5% (n = 5). Expression of mRNA corresponding to three isoforms coded by the mouse ERG1 gene (mERG1), mERG1a, mERG1a', and mERG1b, was consistently found in the SAN. Our data provide the first detailed characterization of IKr in adult mouse SAN cells, demonstrate that this current plays an important role in pacemaker activity, and indicate that multiple isoforms of mERG1 can contribute to native SAN IKr.     

Anatomy of the sinoatrial node and the supply of its vascularization in man

Seventy heart preparations of persons belonging to different sex and age have been investigated, using a complex of anatomical and histological techniques. The dimensions of the sinoatrial node (SAN) vary with age and depend on various size and form of the heart. The large atrial branch of the right and left coronary arteries supplies mainly the SAN with blood. More seldom the atrial branches of both cardiac arteries, having anastomoses, realize the SAN blood supply. The character of the SAN vascularization depends on branching variations of the atrial vessels. At the right coronary variant the sources of the SAN blood supply are the SAN branch, the right intermediate or right posterior atrial branches, and at the left coronary variant--the anterior left, the posterior left and the intermediate left atrial branches. At the even variant the SAN blood supply sources are the right intermediate and the anterior left atrial or the right posterior and the left posterior atrial branches. The data obtained can be used for comparison with the results of coronography to make a skilled analysis of clinical-roentgenological observations.     

Role of dual pacemaker mechanisms in sinoatrial node discharge

We investigated whether in the sinoatrial node (SAN) there are two different pacemaker mechanisms and whether either one can maintain spontaneous discharge. These questions were studied by means of an electrophysiological technique and of blockers of different diastolic currents in rabbit and guinea pig isolated SAN. In SAN subsidiary pacemakers of both species, Cs(+) (5-10 mM) or high [K(+)](o) (10-12 mM) decreased the maximum diastolic potential, abolished diastolic depolarization (DD) at polarized levels (subsidiary DD), unmasked a U-shaped dominant DD at depolarized levels, but did not stop the SAN. In rabbit SAN, E4031 (1 microM) and d-sotalol (100 microM) did not stop discharge, but did so after block of subsidiary DD by high [K(+)](o) or Cs(+). In guinea pig SAN, in Tyrode solution E4031, d-sotalol or indapamide (100 microM) did not stop SAN discharge. In the presence of Cs(+) or high [K(+)](o) indapamide (but not E4031 or d-sotalol) stopped the SAN. Ba(2+) (1-5 mM) led to stoppage of discharge both in Tyrode solution and in high [K(+)](o) or Cs(+). Depolarization by blockers of DD unmasked sinusoidal fluctuations, which during recovery were responsible for resumption of discharge. We conclude that in rabbit and guinea pig SAN, two different pacemaker mechanisms (Cs(+)- and K(+)-sensitive subsidiary DD, and Cs(+)- and K(+)-insensitive dominant DD) can independently sustain discharge, but block of both mechanisms leads to quiescence. Abolition of dominant DD by blockers of I(K) is consistent with a decay of I(K) as the dominant pacemaking mechanism, I(Kr) being more important in rabbit and I(Ks) in guinea pig. Sinusoidal fluctuations appear to be an essential component of the pacemaking process.     

Ectopic expression of Nkx2.5 suppresses the formation of the sinoatrial node in mice

The sinoatrial node (SAN), functionally known as the pacemaker, regulates the cardiac rhythm or heartbeat. Several genes are expressed in the developing SAN and form a genetic network regulating the fate of the SAN cells. The short stature homeobox gene Shox2 is an important player in the SAN genetic network by regulating the expression of different cardiac conduction molecular markers including the early cardiac differentiation marker Nkx2.5. Here we report that the expression patterns of Shox2 and Nkx2.5 are mutually exclusive from the earliest stages of the venous pole and the SAN formation. We show that tissue specific ectopic expression of Shox2 in the developing mouse heart downregulates the expression of Nkx2.5 and causes cardiac malformations; however, it is not sufficient to induce a SAN cell fate switch in the working myocardium. On the other hand, tissue specific overexpression of Nkx2.5 in the heart leads to severe hypoplasia of the SAN and the venous valves, dis-regulation of the SAN genetic network, and change of the SAN cell fate into working myocardium, and causes embryonic lethality, recapitulating the phenotypes including bradycardia observed in Shox2^−/− mutants. These results indicate that Nkx2.5 activity is detrimental to the normal formation of the SAN. Taken together, our results demonstrate that Shox2 downregulation of Nkx2.5 is essential for the proper development of the SAN and that Shox2 functions to shield the SAN from becoming working myocardium by acting upstream of Nkx2.5.     

The Functions of Atrial Strands Interdigitating with and Penetrating into Sinoatrial Node: A Theoretical Study of the Problem

The sinoatrial node (SAN)-atrium system is closely involved with the activity of heart beating. The impulse propagation and phase-locking behaviors of this system are of theoretical interest. Some experiments have revealed that atrial strands (ASs) interdigitate with and penetrate into the SAN, whereby the SAN-atrium system works as a complex network. In this study, the functions of ASs are numerically investigated using realistic cardiac models. The results indicate that the ASs penetrating into the central region of the SAN play a major role in propagating excitation into the atrium. This is because the threshold SAN-AS coupling for an AS to function as an alternative path for propagation is lower at the center than at the periphery. However, ASs penetrating into the peripheral region have a great effect in terms of enlarging the 1:1 entrainment range of the SAN because the automaticity of the SAN is evidently reduced by ASs. Moreover, an analytical formula for approximating the enlargement of the 1:1 range is derived.     

Transmural reentry during acute global ischemia and reperfusion in canine ventricular muscle

Coronary occlusion and reperfusion produce tachyarrhythmias. We tested the hypothesis that variations in transmural activation after global ischemia and reperfusion were responsible for arrhythmias. We arterially perfused 36 isolated transmural wedges from canine left ventricular free walls. After > or =100 min of stabilization, the artery was occluded for 25 min, followed by reperfusion at various flow rates. We recorded 256 channels of fluorescent action potentials on transmural surfaces from preocclusion to >15 min after reperfusion. During endocardial pacing at 300 ms, ischemia of > or =570 +/- 165 s (n = 34) produced 1:1 endocardial conduction and then 2:1 and 4:1 block as the wave fronts conducted toward epicardium. Transmural reentry appeared after 535 +/- 146 s of ischemia (n = 31). Further ischemia caused epicardial inactivation and eliminated reentry (n = 24). During reperfusion, tissues progressed through sequences of epicardial inactivation and reappearance of activation with 1:1, 2:1, and 4:1 conduction; both sustained and nonsustained reentry occurred. We conclude that heterogeneous activation responses to endocardial pacing during acute ischemia provide the substrate for initiating reentry, suppressed reentry during further ischemia, and caused reentry during reperfusion.     

Effects of Na(+) channel and cell coupling abnormalities on vulnerability to reentry: a simulation study

The role of dynamic instabilities in the initiation of reentry in diseased (remodeled) hearts remains poorly explored. Using computer simulations, we studied the effects of altered Na(+) channel and cell coupling properties on the vulnerable window (VW) for reentry in simulated two-dimensional cardiac tissue with and without dynamic instabilities. We related the VW for reentry to effects on conduction velocity, action potential duration (APD), effective refractory period dispersion and restitution, and concordant and discordant APD alternans. We found the following: 1). reduced Na(+) current density and slowed recovery promoted postrepolarization refractoriness and enhanced concordant and discordant APD alternans, which increased the VW for reentry; 2). uniformly reduced cell coupling had little effect on cellular electrophysiological properties and the VW for reentry. However, randomly reduced cell coupling combined with decoupling promoted APD dispersion and alternans, which also increased the VW for reentry; 3). the combination of decreased Na(+) channel conductance, slowed Na(+) channel recovery, and cellular uncoupling synergistically increased the VW for reentry; and 4) the VW for reentry was greater when APD restitution slope was steep than when it was flat. In summary, altered Na(+) channel and cellular coupling properties increase vulnerability to reentrant arrhythmias. In remodeled hearts with altered Na(+) channel properties and cellular uncoupling, dynamic instabilities arising from electrical restitution exert important influences on the VW for reentry.     

Characterization of the effects of ryanodine, TTX, E-4031 and 4-AP on the sinoatrial and atrioventricular nodes

AIMS: To characterize the effects of inhibition of Ryanodine receptor (RyR), TTX-sensitive neuronal Na+ current (iNa), "rapidly activating" delayed rectifier K+ current (iKr) and ultrarapid delayed rectifier potassium current (IKur) on the pacemaker activity of the sinoatrial node (SAN) and the atrioventricular node (AVN) in the mouse. METHODS: The structure of mouse AVN was studied by histology and immunolabelling of Cx43 and hyperpolarization-activated, cyclic nucleotide-binding channels (HCN). The effects of Ryanodine, TTX, E-4031 and 4-AP on pacemaker activities recorded from mouse intact SAN and AVN preparations have been investigated. RESULTS: Immuno-histological characterization delineated the structure of the AVN showing the similar molecular phenotype of the SAN. The effects of these inhibitors on the cycle length (CL) of the spontaneous pacemaker activity of the SAN and the AVN were characterized. Inhibition of RyR by 0.2 and 2 microM Ryanodine prolonged CL by 42+/-12.3% and 64+/-18.1% in SAN preparations by 163+/-72.3% and 241+/-91.2% in AVN preparations. Inhibition of TTX-sensitive iNa by 100 nM TTX prolonged CL by 22+/-6.0% in SAN preparations and 53+/-13.6% in the AVN preparations. Block of iKr by E-4031 prolonged CL by 68+/-12.5% in SAN preparations and 28+/-3.4% in AVN preparations. Inhibition of iKur by 50 microM 4-AP prolonged CL by 20+/-3.4% in SAN preparations and 18+/-3.0% in AVN preparations. CONCLUSION: Mouse SAN and AVN showed distinct different response to the inhibition of RyR, TTX-sensitive INa, IKr and iKur, which reflects the variation in contribution of these currents to the pacemaker function of the cardiac nodes in the mouse. Our data provide valuable information for developing virtual tissue models of mouse SAN and AVN.     

The G-protein–gated K+ channel,IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation

Parasympathetic regulation of sinoatrial node (SAN) pacemaker activity modulates multiple ion channels to temper heart rate. The functional role of the G-protein–activated K⁺ current (I_KACh) in the control of SAN pacemaking and heart rate is not completely understood. We have investigated the functional consequences of loss of I_KACh in cholinergic regulation of pacemaker activity of SAN cells and in heart rate control under physiological situations mimicking the fight or flight response. We used knockout mice with loss of function of the Girk4 (Kir3.4) gene (Girk4^−/− mice), which codes for an integral subunit of the cardiac I_KACh channel. SAN pacemaker cells from Girk4^−/− mice completely lacked I_KACh. Loss of I_KACh strongly reduced cholinergic regulation of pacemaker activity of SAN cells and isolated intact hearts. Telemetric recordings of electrocardiograms of freely moving mice showed that heart rate measured over a 24-h recording period was moderately increased (10%) in Girk4^−/− animals. Although the relative extent of heart rate regulation of Girk4^−/− mice was similar to that of wild-type animals, recovery of resting heart rate after stress, physical exercise, or pharmacological β-adrenergic stimulation of SAN pacemaking was significantly delayed in Girk4^−/− animals. We conclude that I_KACh plays a critical role in the kinetics of heart rate recovery to resting levels after sympathetic stimulation or after direct β-adrenergic stimulation of pacemaker activity. Our study thus uncovers a novel role for I_KACh in SAN physiology and heart rate regulation.     

Sanguinarine impedes metastasis and causes inversion of epithelial to mesenchymal transition in breast cancer

BackgroundA large number of breast cancer patients perishes due to metastasis instead of primary tumor, but molecular mechanisms contributing towards cancer metastasis remain poorly understood. Therefore, prompting development of novel treatment is inevitable. A vast variety of plant derived natural substance possesses several therapeutically active constituents, e.g. alkaloids, flavonoids, tannins, resins, terpenoids etc. that exhibit various pharmacological properties e.g. anti-inflammatory, anti-microbial and anti-cancer properties. Sanguinarine (SAN) alkaloid found its place among such naturally occurring substances that exerts several pharmacological activities, including anti-cancer effects.PurposeUntil now, role of SAN not only against epithelial-mesenchymal transition (EMT) but also against metastasis progression in breast cancer remains indistinct. Thus, aim of the present study was to investigate effects of SAN on EMT process and cancer metastasis in animal model.MethodsMTT assay was performed to assess SAN effects on proliferation in breast cancer. Scratch assay was performed to evaluate effects of SAN on migration in breast cancer. Colony formation assay was performed to determine effects of SAN on colonization characteristics of breast cancer. Western blotting was performed to measure EMT regulating protein expression as well as major pathway protein expression induced against TGF-β treatment in breast cancer. Tail vein method of injecting breast cancer cells in bulb/c mice was conducted to study metastasis progression and thereafter assessing effects of SAN against metastasis in mice.ResultsIn vivo results: MTT assay performed, demonstrated dose dependent inhibition of cell proliferation in breast cancer. Scratch assay results showed, SAN played a major role as migration inhibitor in estrogen receptor positive (ER+) breast cancer. Colony forming assay results demonstrated that SAN constrains ability of breast cancer to develop into well-defined colonies. Western blotting results for EMT regulating protein expression, after TGF-β treatment showed, SAN inhibited cadherin switch in ER+ breast cancer. Moreover, expression of pathway proteins involved in EMT process after TGF-β treatment i.e. Smad, PI3K/Akt and MAP kinase were significantly masked against SAN treatment.In vivo resultsThe appearance of metastatic nodules in lung tissues of mice model, helps to study the effects of SAN against metastasis in bulb/c mice. The obtained results have confirmed that SAN impeded lung metastasis. The macroscopic examination has confirmed metastasis inhibitory role of SAN in breast cancer. The Hematoxylin and eosin (H&E) staining results further advocate anti-metastatic characteristics of SAN, presented by fewer metastatic nodule and lesions appearance in SAN treated mice compared to untreated metastasis mice.ConclusionIn summary, SAN displayed prominent anti-metastatic effects in animal model and anti-proliferation effects together with significant inhibitory potential on EMT regulating protein expression against TGF-β treatment in ER+ breast cancer. So, overall findings of our study highlighted the pre-clinical significance of SAN in animal model therefore, further studies in humans as a part of clinical trial will be needed to establish pharmacokinetics and other effects of SAN, so that it can be a potential candidate for future treatment of metastatic breast cancer (MBC).     

Low Energy Defibrillation in Human Cardiac Tissue: A Simulation Study

We aim to assess the effectiveness of feedback-controlled resonant drift pacing as a method for low energy defibrillation. Antitachycardia pacing is the only low energy defibrillation approach to have gained clinical significance, but it is still suboptimal. Low energy defibrillation would avoid adverse side effects associated with high voltage shocks and allow the application of implantable cardioverter defibrillator (ICD) therapy, in cases where such therapy is not tolerated today. We present results of computer simulations of a bidomain model of cardiac tissue with human atrial ionic kinetics. Reentry was initiated and low energy shocks were applied with the same period as the reentry, using feedback to maintain resonance. We demonstrate that such stimulation can move the core of reentrant patterns, in the direction that depends on the location of the electrodes and the time delay in the feedback. Termination of reentry is achieved with shock strength one-order-of-magnitude weaker than in conventional single-shock defibrillation. We conclude that resonant drift pacing can terminate reentry at a fraction of the shock strength currently used for defibrillation and can potentially work where antitachycardia pacing fails, due to the feedback mechanisms. Success depends on a number of details that these numerical simulations have uncovered.