Conduction Velocity Restitution Curves Research Articles

Autonomic modulation impacts conduction velocity dynamics and wavefront propagation in the left atrium.

Atrial fibrosis and autonomic remodelling are proposed pathophysiological mechanisms in atrial fibrillation (AF). Their impact on conduction velocity (CV) dynamics and wavefront propagation was evaluated. Local activation times (LATs), voltage, and geometry data were obtained from patients undergoing ablation for persistent AF. LATs were obtained at three pacing intervals (PIs) in sinus rhythm (SR). LATs were used to determine CV dynamics and their relationship to local voltage amplitude. The impact of autonomic modulation- pharmacologically and with ganglionated plexi (GP) stimulation, on CV dynamics, wavefront propagation, and pivot points (change in wavefront propagation of ≥90°) was determined in SR. Fifty-four patients were included. Voltage impacted CV dynamics whereby at non-low voltage zones (LVZs) (≥0.5 mV) the CV restitution curves are steeper [0.03 ± 0.03 m/s ΔCV PI 600-400 ms (PI1), 0.54 ± 0.09 m/s ΔCV PI 400-250 ms (PI2)], broader at LVZ (0.2-0.49 mV) (0.17 ± 0.09 m/s ΔCV PI1, 0.25 ± 0.11 m/s ΔCV PI2), and flat at very LVZ (<0.2 mV) (0.03 ± 0.01 m/s ΔCV PI1, 0.04 ± 0.02 m/s ΔCV PI2). Atropine did not change CV dynamics, while isoprenaline and GP stimulation resulted in greater CV slowing with rate. Isoprenaline (2.7 ± 1.1 increase/patient) and GP stimulation (2.8 ± 1.3 increase/patient) promoted CV heterogeneity, i.e. rate-dependent CV (RDCV) slowing sites. Most pivot points co-located to RDCV slowing sites (80.2%). Isoprenaline (1.3 ± 1.1 pivot increase/patient) and GP stimulation (1.5 ± 1.1 increase/patient) also enhanced the number of pivot points identified. Atrial CV dynamics is affected by fibrosis burden and influenced by autonomic modulation which enhances CV heterogeneity and distribution of pivot points. This study provides further insight into the impact of autonomic remodelling in AF.

BS-516-02 OPTICAL MAPPING OF EXPLANTED HUMAN HEARTS ENABLES REFINED IONIC MODELS OF ACTION POTENTIAL AND CONDUCTION VELOCITY RESTITUTION CURVES FOR ARRHYTHMIA SIMULATION

Dynamics and stability of electrical waves in the heart has been attributed to the action potential duration (APD) restitution curve, which is a measure of how the tissue responds to a given cycle length (CL) and the conduction velocity (CV). The restitution curves have been used to investigate how changes in stimulation CL can lead to the induction of alternans and arrhythmias. Only few restitution curves are available from clinical measurements in human hearts, and they were generated using monophasic action potential measurements or from single human cardiomyocytes. To obtain APD and CV restitution curves from explanted human hearts with optical mapping, and take advantage of the experimental data to refine the dynamics of an ionic model, which can be valuable for arrhythmia simulation studies. Optical mapping of membrane potentials was performed on explanted human hearts (n=2 from recipient patients and n=1 from a rejected donor) at high resolutions (256x256 pixels, at 500 Hz) and a large field of view of 8 x 8 cm2. Action potential was measured across the anterior epicardial RV and LV and the endocardium LV, paced at CLs from 3 sec and shorter, until conduction block or VF induction. APD and CV restitution were obtained across the mapped tissue. Optical voltage signals were obtained by pacing the heart at different CLs (Panel A). APDs and CVs were calculated, and restitution curves for APD and CV were calculated for different regions in the hearts. APD alternans, between even and odd beats, were observed and quantified (panels B and C). A human ventricular cardiomyocyte model was fitted to the experimentally obtained APD and CV restitution curves to reproduce AP duration (APD restitution) and conduction velocity (CV restitution) at all CLs. The resultant ionic model recapitulates the experimental data including the bifurcation period and magnitude of alternans as well as the wave propagations. Optical mapping of action potential from explanted human hearts were used to refine the dynamics of an ionic model of human ventricular myocytes. The refined model reproduced the experimental wave propagations at all CLs, including alternans. Our study presents a clinically relevant in silico model to study the induction and dynamics of arrhythmias in whole heart simulations.

A computationally efficient dynamic model of human epicardial tissue.

We present a new phenomenological model of human ventricular epicardial cells and we test its reentry dynamics. The model is derived from the Rogers-McCulloch formulation of the FitzHugh-Nagumo equations and represents the total ionic current divided into three contributions corresponding to the excitatory, recovery and transient outward currents. Our model reproduces the main characteristics of human epicardial tissue, including action potential amplitude and morphology, upstroke velocity, and action potential duration and conduction velocity restitution curves. The reentry dynamics is stable, and the dominant period is about 270 ms, which is comparable to clinical values. The proposed model is the first phenomenological model able to accurately resemble human experimental data by using only 3 state variables and 17 parameters. Indeed, it is more computationally efficient than existing models (i.e., almost two times faster than the minimal ventricular model). Beyond the computational efficiency, the low number of parameters facilitates the process of fitting the model to the experimental data.

Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue.

Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20cm during one-to-one responses and it decreases to a specific value of about 3cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.

A work flow to build and validate patient specific left atrium electrophysiology models from catheter measurements.

Biophysical models of the atrium provide a physically constrained framework for describing the current state of an atrium and allow predictions of how that atrium will respond to therapy. We propose a work flow to simulate patient specific electrophysiological heterogeneity from clinical data and validate the resulting biophysical models. In 7 patients, we recorded the atrial anatomy with an electroanatomical mapping system (St Jude Velocity); we then applied an S1-S2 electrical stimulation protocol from the coronary sinus (CS) and the high right atrium (HRA) whilst recording the activation patterns using a PentaRay catheter with 10 bipolar electrodes at 12 ± 2 sites across the atrium. Using only the activation times measured with a PentaRay catheter and caused by a stimulus applied in the CS with a remote catheter we fitted the four parameters for a modified Mitchell-Schaeffer model and the tissue conductivity to the recorded local conduction velocity restitution curve and estimated local effective refractory period. Model parameters were then interpolated across each atrium. The fitted model recapitulated the S1-S2 activation times for CS pacing giving a correlation ranging between 0.81 and 0.98. The model was validated by comparing simulated activations times with the independently recorded HRA pacing S1-S2 activation times, giving a correlation ranging between 0.65 and 0.96. The resulting work flow provides the first validated cohort of models that capture clinically measured patient specific electrophysiological heterogeneity.

Optical Mapping Approaches on Muscleblind‐Like Compound Knockout Mice for Understanding Mechanistic Insights Into Ventricular Arrhythmias in Myotonic Dystrophy

BackgroundCardiac arrhythmias are common causes of death in patients with myotonic dystrophy (dystrophia myotonica [DM]). Evidence shows that atrial tachyarrhythmia is an independent risk factor for sudden death; however, the relationship is unclear.Methods and ResultsControl wild‐type (Mbnl1+/+; Mbnl2+/+) and DM mutant (Mbnl1−/−; Mbnl2+/−) mice were generated by crossing double heterozygous knockout (Mbnl1+/−; Mbnl2+/−) mice. In vivo electrophysiological study and optical mapping technique were performed to investigate mechanisms of ventricular tachyarrhythmias. Transmission electron microscopy scanning was performed for myocardium ultrastructural analysis. DM mutant mice were more vulnerable to anesthesia medications and program electrical pacing: 2 of 12 mice had sudden apnea and cardiac arrest during premedication of general anesthesia; 9 of the remaining 10 had atrial tachycardia and/or atrioventricular block, but none of the wild‐type mice had spontaneous arrhythmias; and 9 of 10 mice had pacing‐induced ventricular tachyarrhythmias, but only 1 of 14 of the wild‐type mice. Optical mapping studies revealed prolonged action potential duration, slower conduction velocity, and steeper conduction velocity restitution curves in the DM mutant mice than in the wild‐type group. Spatially discordant alternans was more easily inducible in DM mutant than wild‐type mice. Transmission electron microscopy showed disarranged myofibrils with enlarged vacuole‐occupying mitochondria in the DM mutant group.ConclusionsThis DM mutant mouse model presented with clinical myofibril ultrastructural abnormality and cardiac arrhythmias, including atrial tachyarrhythmias, atrioventricular block, and ventricular tachyarrhythmias. Optical mapping studies revealed prolonged action potential duration and slow conduction velocity in the DM mice, leading to vulnerability of spatially discordant alternans and ventricular arrhythmia induction to pacing.

Supernormal Conduction and Suppression of Spatially Discordant Alternans of Cardiac Action Potentials.

Spatially discordant alternans (DA) of action potential durations (APD) is thought to be more pro-arrhythmic than concordant alternans. Super normal conduction (SNC) has been reported to suppress formation of DA. An increase in conduction velocity (CV) as activation rate increases, i.e., a negative CV restitution, is widely considered as hallmark of SNC. Our aim in this study is to show that it is not an increase in CV for faster rates that prevents formation of DA, rather, it is the ratio of the CV for the short relative to the long activation that is critical in DA suppression. To illustrate this subtlety, we simulated this phenomenon using two approaches; (1) by using the standard, i.e., S1S2 protocol to quantify restitution and disabling the slow inactivation gate j of the sodium current (INa), and (2) by using the dynamic, i.e., S1S1 protocol for quantification of restitution and increasing INa at different cycle lengths (CL). Even though both approaches produced similar CV restitution curves, DA was suppressed only during the first approach, where the CV of the short of the long-short action potential (AP) pattern was selectively increased. These results show that negative CV restitution, which is considered characteristic of SNC, per se, is not causal in suppressing DA, rather, the critical factor is a change in the ratio of the velocities of the short and the long APs.

Cardiac contraction induces discordant alternans and localized block.

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e., alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be proarrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e., from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.

Dynamics of propagation of premature impulses in structurally remodeled infarcted myocardium: a computational analysis.

Initiation of cardiac arrhythmias typically follows one or more premature impulses either occurring spontaneously or applied externally. In this study, we characterize the dynamics of propagation of single (S2) and double premature impulses (S3), and the mechanisms of block of premature impulses at structural heterogeneities caused by remodeling of gap junctional conductance (Gj) in infarcted myocardium. Using a sub-cellular computer model of infarcted tissue, we found that |INa,max|, prematurity (coupling interval with the previous impulse), and conduction velocity (CV) of premature impulses change dynamically as they propagate away from the site of initiation. There are fundamental differences between the dynamics of propagation of S2 and S3 premature impulses: for S2 impulses |INa,max| recovers fast, prematurity decreases and CV increases as propagation proceeds; for S3 impulses low values of |INa,max| persist, prematurity could increase, and CV could decrease as impulses propagate away from the site of initiation. As a consequence it is more likely that S3 impulses block at sites of structural heterogeneities causing source/sink mismatch than S2 impulses block. Whether premature impulses block at Gj heterogeneities or not is also determined by the values of Gj (and the space constant λ) in the regions proximal and distal to the heterogeneity: when λ in the direction of propagation increases >40%, premature impulses could block. The maximum slope of CV restitution curves for S2 impulses is larger than for S3 impulses. In conclusion: (1) The dynamics of propagation of premature impulses make more likely that S3 impulses block at sites of structural heterogeneities than S2 impulses block; (2) Structural heterogeneities causing an increase in λ (or CV) of >40% could result in block of premature impulses; (3) A decrease in the maximum slope of CV restitution curves of propagating premature impulses is indicative of an increased potential for block at structural heterogeneities.

Select Articles Published on the Topic of Arrhythmia and Electrophysiogy in 2013

Select Articles Published on the Topic of Arrhythmia and Electrophysiogy in 2013

A Quantitative Comparison of the Behavior of Human Ventricular Cardiac Electrophysiology Models in Tissue

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O'Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1–S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work.

Circulation : Clinical Summaries

<i>Circulation</i> : Clinical Summaries

A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics.

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.

The Effect of Low Extracellular Potassium on Cardiac Arrhythmia Vulnerability: A Computer Simulation Study

Unidirectional conduction block of cardiac excitation wave is one of the necessary conditions leading to initiation of reentrant arrhythmia. Temporal vulnerable window (VWtime) is an important measure for arrhythmia vulnerability. In this study, we examine theoretically how low extracellular K concentration ([K]o) control the VWtime by a single premature extrasystole. A numerical modified LR91 one dimensional heterogeneous ventricular model is used to quantitatively investigate the relation of low [K]o with conduction velocity (CV), VWtime, and electrical dynamic factor CV restitution. Morever, we characterize the distribution of Na channel conductance (gNa) and gating factors of premature beat applied at different time of the VWtime with different [K]o. The results show that lowering [K]o enlarge the VWtime magnitude gradually. The CV of S1 beat slows down with the [K]o in a reverse-[K]o dependent manner. Low [K]o promote the recovery of maximum Na conductance (GNa) from inactivation. However, decreasing [K]o can increase heterogeneity of gNa along the cable, and modulate CV restitution curve, which induce larger transmural dispersion of refratoriness for the premature beat and enlarge the VWtime.

Asymptotics of Conduction Velocity Restitution in Models of Electrical Excitation in the Heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh-Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified "caricature" of Noble (J. Physiol. Lond. 160:317-352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177-210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler-Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.

Evidence of a Pro-Arrhythmic Substrate in the Failing Right Ventricle of Pulmonary Hypertensive Rats

Arrhythmic risk is increased in patients with heart failure. We have investigated the arrhythmic state of the failing right ventricle in a model of pulmonary hypertension (PAH).Wistar rats were injected intraperitoneally with monocrotaline (MCT, 60 mg/kg) to induce PAH and right ventricular failure within 3-4 weeks and compared to age-matched saline-injected animals (CON).In vivo measurement of ECG parameters using radiotelemetry indicated modification of T wave-parameters in MCT treated animals e.g. a prolonged QT interval (CON 49.7±2.0 vs. MCT 76.2±2.5 ms, P<0.001) and time from the peak to the end of the T-wave (Tpe, CON 25±1.8 vs. MCT 33.1±1.7 ms, P = 0.007) (CON n = 6, MCT n = 7).Animals were humanely killed upon showing clinical symptoms of HF. Monophasic action potentials (MAPs) were recorded at the right ventricular epicardial surface of isolated hearts and a S1-S2 protocol used to construct standard APD restitution curves. MAP duration was significantly prolonged in failing hearts (MAP90, 39.9±1.9 ms in CON vs. 80.7±3.5 ms in MCT, P<0.001) and standard restitution slopes were steeper (mean maximum slope was 0.18±0.02 CON vs. 0.73±0.28 MCT, P<0.001).Optical action potentials were recorded at stimulation frequencies between 5-12 Hz using the voltage-sensitive dye di-4-ANEPPS and dynamic APD and conduction velocity restitution curves measured. The failing right ventricle exhibited steeper restitution and conduction velocity restitution curves (mean maximum slope for conduction velocity was 0.013±0.004 MCT vs. 0.002±0.001 CON, P<0.001). At high pacing frequencies, arrhythmias were induced in failing but not in control hearts.T-wave modification, APD prolongation, steeper APD and conduction velocity restitution curves are typically associated with a pro-arrhythmic state. We conclude that the failing right ventricle of pulmonary hypertensive rats have an elevated risk of developing arrhythmias. The underlying mechanisms are under investigation.

Atrial proarrhythmia due to increased inward rectifier current (IK1) arising from KCNJ2 mutation – A simulation study

Atrial fibrillation (AF) has been linked to increased inward rectifier potassium current, IK1, either due to AF-induced electrical remodelling, or from functional changes due to the Kir2.1 V93I mutation. The aim of this simulation study was to identify at cell and tissue levels' mechanisms by which increased IK1 facilitates and perpetuates AF. The Courtemanche et al. human atrial cell action potential (AP) model was modified to incorporate reported changes in IK1 induced by the Kir2.1 V93I mutation in both heterozygous (Het) and homozygous (Hom) mutant forms. The modified models for wild type (WT), Het and Hom conditions were incorporated into homogeneous 1D, 2D and 3D tissue models. Restitution curves of AP duration (APD), effective refractory period (ERP) and conduction velocity (CV) were computed and both the temporal and the spatial vulnerability of atrial tissue to re-entry were measured. The lifespan and tip meandering pattern of re-entry were also characterised. For comparison, parallel simulations were performed by incorporating into the Courtmanche et al. model a linear increase in maximal IK1 conductance. It was found that the gain-in-function of V93I ‘mutant’IK1 led to abbreviated atrial APs and flattened APD, ERP and CV restitution curves. It also hyperpolarised atrial resting membrane potential and slowed down intra-atrial conduction. V93I ‘mutant’IK1 reduced the tissue's temporal vulnerability but increased spatial vulnerability to initiate and sustain re-entry, resulting in an increased overall susceptibility of atrial tissue to arrhythmogenesis. In the 2D model, spiral waves self-terminated for WT (lifespan < 3.3 s) tissue, but persisted in Het and Hom tissues for the whole simulation period (lifespan > 10 s). The tip of the spiral wave meandered more in WT tissue than in Het and Hom tissues. Increased IK1 due to augmented maximal conductance produced similar results to those of Het and Hom Kir2.1 V93I mutant conditions. In the 3D model the dynamic behaviour of scroll waves was stabilized by increased IK1. In conclusion, increased IK1 current, either by the Kir2.1 V93I mutation or by augmented maximal conductance, increases atrial susceptibility to arrhythmia by increasing the lifespan of re-entrant spiral waves and the stability of scroll waves in 3D tissue, thereby facilitating initiation and maintenance of re-entrant circuits.

Global Endocardial Electrical Restitution in Human Right and Left Ventricles Determined by Noncontact Mapping

This study was aimed at evaluating global characteristics of electrical restitution in the human ventricle using noncontact mapping. Steep action potential restitution (slope >1) and conduction velocity (CV) restitution have been linked with propensity to ventricular fibrillation, but clinical measurement of global electrical restitution had not been feasible. Activation-recovery interval (ARI) and CV restitution curves were simultaneously constructed from 16 regional segments of the left and right ventricles in 8 patients (6 male, 2 female, age 42 +/- 17 years) following successful ablation of idiopathic ventricular tachycardia in the absence of structural disease guided by the Ensite 3000 system (Endocardial Solutions Inc., St. Paul, Minnesota). The ARIs were determined from reconstructed unipolar electrograms as validated with monophasic action potential recordings. The ARI restitution slopes were determined using the overlapping least-squares linear segments. Global electrical restitution curves were heterogeneous in shape and distribution. ARI restitution slope was >1 at 25% of 128 sites. The overall mean slope was 0.79 and was greater in the left than the right ventricle (0.93 +/- 0.49 vs. 0.65 +/- 0.26, p < 0.001). Dispersion of ARI restitution slopes increased with decreasing diastolic intervals. The CV restitution operated over a narrower range of diastolic intervals compared with ARI restitution, reaching a plateau (10 +/- 6 ms vs. 38 +/- 13 ms, p < 0.001) after refractoriness. The magnitude of CV restitution was also greater (steeper) than ARI restitution (25 +/- 10% vs. 18 +/- 9%, p < 0.001). Noncontact mapping can be used to examine global electrical restitution in the human ventricle. The ARI restitution is heterogeneous, with a slope >1 at 25% of all sites. The heterogeneity of ARI and CV restitution may be important in determining myocardial electrical stability.

Head-tail interactions in numerical simulations of reentry in a ring of cardiac tissue

The relationships between action potential duration (APD) and conduction velocity (CV) to the previous diastolic interval (DI) are known as the APD and CV restitution relationships. There is considerable debate regarding the importance of these relationships in the development and stability of reentry. The purpose of this study was to increase the understanding of the ionic basis for restitution during reentry. APD and CV were studied numerically during one-dimensional reentry as ring length (L) was shortened. A three-state variable model (u, v, w) was used to analyze the effect of gating variables of the fast (v) and slow (w) currents on the spatial and temporal dynamics of transmembrane potential (u). Three parameter sets were used corresponding to three APD and CV restitution curves. Sustained spatial oscillations of APD and CV larger than the ring length were observed in two of the parameter sets (cytochalasin-D model [CYTO] and model 3 [M3]) before block occurred at L = 6 cm. The last model (diacetyl monoxime [DAM]) resulted in uniform APD and CV for all L until block occurred at L = 3 cm. Multivalued APD and CV restitution relationships due to "dephasing" of w and v with DI were observed in M3 and CYTO simulations. Overall, these dynamics could be explained by the wavelength-to-ring length ratio and the sensitivity of APD on the value of the gating variables w and v. Propagation stability is mostly controlled by APD sensitivity to w, but the APD restitution slope does not always reflect this sensitivity. The interaction of the dynamic history (i.e., memory) of the fast and slow currents and electrotonic effects resulted in multivalued restitution curves.