Identification of cardiac rhythm features by mathematical analysis of vector fields

Automated techniques for locating cardiac arrhythmia features are limited, and cardiologists generally rely on isochronal maps to infer patterns in the cardiac activation sequence during an ablation procedure. Velocity vector mapping has been proposed as an alternative method to study cardiac activation in both clinical and research environments. In addition to the visual cues that vector maps can provide, vector fields can be analyzed using mathematical operators such as the divergence and curl. In the current study, conduction features were extracted from velocity vector fields computed from cardiac mapping data. The divergence was used to locate ectopic foci and wavefront collisions, and the curl to identify central obstacles in reentrant circuits. Both operators were applied to simulated rhythms created from a two-dimensional cellular automaton model, to measured data from an in situ experimental canine model, and to complex three-dimensional human cardiac mapping data sets. Analysis of simulated vector fields indicated that the divergence is useful in identifying ectopic foci, with a relatively small number of vectors and with errors of up to 30 degrees in the angle measurements. The curl was useful for identifying central obstacles in reentrant circuits, and the number of velocity vectors needed increased as the rhythm became more complex. The divergence was able to accurately identify canine in situ pacing sites, areas of breakthrough activation, and wavefront collisions. In data from human arrhythmias, the divergence reliably estimated origins of electrical activity and wavefront collisions, but the curl was less reliable at locating central obstacles in reentrant circuits, possibly due to the retrospective nature of data collection. The results indicate that the curl and divergence operators applied to velocity vector maps have the potential to add valuable information in cardiac mapping and can be used to supplement human pattern recognition.     

Automatic detection of conduction block based on time-frequencyanalysis of unipolar electrograms

It is commonly thought that lethal tachyarrhythmias, such as ventricular fibrillation (VF), are perpetuated by functional reentry, which occurs when an activation wave blocks and rotates around tissue that is excitable (i.e., functional block). Electrograms recorded near these regions typically contain two sequential deflections representing activation on either side of the block. By detecting these "double potentials," we hypothesize that functional block can be detected by a single electrode. METHODS: Unipolar electrograms were recorded from a 24 x 21 mapping array on the intact ventricular epicardium of five pigs during electrically-induced VF. The short time Fourier Transform (STFT) of each electrogram was analyzed to identify double potentials. To evaluate the performance of the STFT algorithm, conduction block was located in activation maps using a minimum conduction velocity criterion (10 cm/s) and then compared to the results of the STFT algorithm. RESULTS: The STFT algorithm detected conduction block with a sensitivity of 0.74 +/- 0.12 and a specificity of 0.99 +/- 0.00. CONCLUSION: We have developed an automated algorithm that can detect functional block during VF from a single electrode recording. Possible applications include fast, objective identification of block in mapping data and realtime localization of reentrant substrates using mapping catheters.     

Simulation analysis of conduction block in unmyelinated axons induced by high-frequency biphasic electrical currents

Nerve conduction block induced by high-frequency biphasic electrical currents is analyzed using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. Axons of different diameters (5-20 microm) can not be blocked completely when the stimulation frequency is between 2 kHz and 4 kHz. However, when the stimulation frequency is above 4 kHz, all axons can be blocked. At high-frequency a higher stimulation intensity is needed to block nerve conduction. The larger diameter axon has a lower threshold intensity for conduction block. The stimulation waveform in which the pulsewidth changes with frequency is more effective in blocking nerve conduction than the waveform in which the pulsewidth is fixed. The activation of potassium channels, rather than inactivation of sodium channels, is the possible mechanism underlying the nerve conduction block of the unmyelinated axon. This simulation study further increases our understanding of axonal conduction block induced by high-frequency biphasic currents, and can guide future animal experiments as well as optimize stimulation waveforms that might be used for electrical nerve block in clinical applications.     

A logical state model of reentrant ventricular activation

The ventricular surface of the heart was modeled as two-dimensional, 4096 element, network of cells connected logically to each other. An ischemic area was represented by a central core of prolonged refractoriness, distributed into eccentrically-layered elliptical contours such that refractoriness declined along varying gradients to the surrounding normal area. Propagation of cardiac action potentials was stimulated by five sequential states ranging from activation to inactivation. Reentrant activation was induced by premature stimulation of the network and resembled a "figure 8" type reentry seen experimentally. Activation patterns of reentry appeared as two propagation wavefronts which traveled around the ends of a continuous line of functional conduction block, merged into a single wavefront, then conducted slowly along a retrograde path to reactivate a region proximal to the block. Reentry could be prevented by modifying the distribution of recovery of excitability through stimulation at two strategically located sites during basic rhythm. Prevention occurred when the second site was situated in an area of prolonged refractoriness, just distal to the line of block. These simulations indicate that reentrant activation is characterized by the formation of long lines of conduction block which occur along a border of steeply graded refractoriness, and retrograde slow conduction which occurs along a more shallow refractory gradient. The occurrence of reentry is dependent on: 1) the coupling interval of the premature stimulus, 2) the location of the stimulus relative to the maximum refractory gradient, and 3) the activation sequence of the basic paced beats. Thus, this paper presents an efficient logical state model of cardiac activation which simulates experimentally observed activation patterns of reentry and its prevention.     

A computer model of human atria with reasonable computation loadand realistic anatomical properties

Atrial fibrillation is the most frequent arrhythmia, provoking discomfort, heart failure and arterial embolisms. The aim of this work is to develop a simplified anatomical computer model of human atria for the study of atrial arrhythmias and the understanding of electrical propagation mechanisms. With the model we propose, up to 40 s of real-time propagation have been simulated on a single-processor computer. The size and the electrophysiological properties of the simulated atria are within realistic values and information about anatomy has been taken into account in a three-dimensional structure. Besides normal sinus beat, pathological phenomena such as flutter and fibrillation have been induced using a programmed stimulation protocol. One important observation in our model is that atrial arrhythmias are a combination of functional and anatomical reentries and that the geometry plays an important role. This virtual atrium can reproduce electrophysiological observations made in humans but with the advantage of showing in great detail how arrhythmias are initiated and sustained. Such details are difficult or impossible to study in humans. This model will serve us as a tool to evaluate the impact of new therapeutic strategies and to improve them.     

The feasibility of endocardial propagation mapping using magnetic resonance guidance in a Swine model, and comparison with standard electroanatomic mapping

The introduction of electroanatomic mapping (EAM) has improved the understanding of the substrate of ventricular tachycardia. EAM systems are used to delineate scar regions responsible for the arrhythmia by creating voltage or activation time maps. Previous studies have identified the benefits of creating MR-guided voltage maps; however, in some cases voltage maps may not identify regions of slow propagation that can cause the reentrant tachycardia. In this study, we obtained local activation time maps and analyzed propagation properties by performing MR-guided mapping of the porcine left ventricle while pacing from the right ventricle. Anatomical and myocardial late gadolinium enhancement images were used for catheter navigation and identification of scar regions. Our MR-guided mapping procedure showed qualitative correspondence to conventional clinical EAM systems in healthy pigs and demonstrated altered propagation in endocardial infarct models.     

The Role of Slow Potassium Current in Nerve Conduction Block Induced by High-Frequency Biphasic Electrical Current

The role of slow potassium current in nerve conduction block induced by high-frequency biphasic electrical current was analyzed using a lumped circuit model of a myelinated axon based on the Schwarz–Reid–Bostock model. The results indicate that nerve conduction block at stimulation frequencies above 4 kHz is due to constant activation of both fast and slow potassium channels, but the block at stimulation frequencies below 4 kHz could be due to either anodal or cathodal dc block depending on the time of the action potiential arriving at the block electrode. When stimulation frequency was above 4 kHz, the slow potassium current was about 3.5 to 6.5 times greater than the fast potassium current at blocking threshold, indicating that the slow potassium current played a more dominant role than the fast potassium current. The blocking location moved from the node under the blocking electrode to a nearby node as the stimulation intensity increased. This simulation study reveals that in mammalian myelinated axons, the slow potassium current probably plays a critical role in the nerve conduction block induced by high-frequency biphasic electrical current.      

Construction of a computational anatomical model of the peripheral cardiac conduction system

A methodology is presented here for automatic construction of a ventricular model of the cardiac conduction system (CCS), which is currently a missing block in many multiscale cardiac electromechanic models. It includes the His bundle, left bundle branches, and the peripheral CCS. The algorithm is fundamentally an enhancement of a rule-based method known as the Lindenmayer systems (L-systems). The generative procedure has been divided into three consecutive independent stages, which subsequently build the CCS from proximal to distal sections. Each stage is governed by a set of user parameters together with anatomical and physiological constrains to direct the generation process and adhere to the structural observations derived from histology studies. Several parameters are defined using statistical distributions to introduce stochastic variability in the models. The CCS built with this approach can generate electrical activation sequences with physiological characteristics.     

A Tissue Framework for Simulating the Effects of Gastric Electrical Stimulation and In Vivo Validation

Gastric pacing is used to modulate normal or abnormal gastric slow-wave activity for therapeutic purposes. New protocols are required that are optimized for motility outcomes and energy efficiency. A computational tissue model was developed, incorporating smooth muscle and interstitial cell of Cajal layers, to enable predictive simulations of slow-wave entrainment efficacy under different pacing frequencies. Concurrent experimental validation was performed via high-resolution entrainment mapping in a porcine model (bipolar pacing protocol: 2 mA amplitude; 400 ms pulsewidth; 17-s period; midcorpus). Entrained gastric slow-wave activity was found to be anisotropic (circular direction: 8.51 mm${cdot}$s $^{-1}$; longitudinal: 4.58 mm${cdot}$s $^{-1}$), and the simulation velocities were specified accordingly. Simulated and experimental slow-wave activities demonstrated satisfactory agreement, showing similar propagation patterns and frequencies (3.5–3.6 cycles per minute), and comparable zones of entrainment (ZOEs; 64 cm $^2$). The area of ZOE achieved was found to depend on the phase interactions between the native and entrained activities. This model allows the predictions of phase interactions between native and entrained activities, and will be useful for determining optimal frequencies for gastric pacing, including multichannel pacing studies. The model provides a framework for the development of more sophisticated predictive gastric pacing simulations in future.      

Comparative simulation of excitation and body surfaceelectrocardiogram with isotropic and anisotropic computer heart models

Comparative simulations between isotropic and anisotropic computer heart models were conducted to study the effects of myocardial anisotropy on the excitation process of the heart and on body surface electrocardiogram. The isotropic heart model includes atria, ventricles, and a special conduction system, and is electrophysiologically specified by parameters relative to action potential, conduction velocity, automaticity, and pacing. The anisotropic heart model was created by incorporating rotating fiber directions into the ventricles of the isotropic heart model. The orientation of the myocardial fibers in the ventricles of the model was gradually rotated counterclockwise from the epicardial layer to the endocardial layer for a total rotation of 90°. The anisotropy of conduction velocity and intracellular electric conductivity was included in the simulation. Comparative simulations of the normal heart, LBBB, and RBBB showed no significant differences between the two models in the excitation processes of the whole heart or in the body surface electrocardiograms. However, it was easier to induce ventricular fibrillation in the anisotropic model than in the isotropic model. The comparative simulation is useful for investigating the effects of myocardial anisotropy at the whole heart level and for evaluating limitations of the isotropic heart model     

Equivalent Circuits for Small Symmetrical Longitudinal Apertures and Obstacles

Formulas based on small aperture and small obstacle theory are presented for the determination of equivalent circuits for symmetrical longitudinal apertures and obstacles. These formulas are then applied to several examples of practical interest, including aperture discontinuities in trough waveguide and an obstacle array of interest to anisotropic radomes.     

Extraction and analysis of T waves in electrocardiograms during atrial flutter

Analysis of T waves in the ECG is an essential clinical tool for diagnosis, monitoring, and follow-up of patients with heart dysfunction. During atrial flutter, this analysis has been so far limited by the perturbation of flutter waves superimposed over the T wave. This paper presents a method based on missing data interpolation for eliminating flutter waves from the ECG during atrial flutter. To cope with the correlation between atrial and ventricular electrical activations, the CLEAN deconvolution algorithm was applied to reconstruct the spectrum of the atrial component of the ECG from signal segments corresponding to TQ intervals. The locations of these TQ intervals, where the atrial contribution is presumably dominant, were identified iteratively. The algorithm yields the extracted atrial and ventricular contributions to the ECG. Standard T-wave morphology parameters (T-wave amplitude, T peak-T end duration, QT interval) were measured. This technique was validated using synthetic signals, compared to average beat subtraction in a patient with a pacemaker, and tested on pseudo-orthogonal ECGs from patients in atrial flutter. Results demonstrated improvements in accuracy and robustness of T-wave analysis as compared to current clinical practice.     

Cardiac anisotropy: is it negligible regarding noninvasive activation time imaging?

The aim of this study was to quantify the effect of cardiac anisotropy in the activation-based inverse problem of electrocardiography. Differences of the patterns of simulated body surface potential maps for isotropic and anisotropic conditions were investigated with regard to activation time (AT) imaging of ventricular depolarization. AT maps were estimated by solving the nonlinear inverse ill-posed problem employing spatio-temporal regularization. Four different reference AT maps (sinus rhythm, right-ventricular and septal pacing, accessory pathway) were calculated with a bidomain theory based anisotropic finite-element heart model in combination with a cellular automaton. In this heart model a realistic fiber architecture and conduction system was implemented. Although the anisotropy has some effects on forward solutions, effects on inverse solutions are small indicating that cardiac anisotropy might be negligible for some clinical applications (e.g., imaging of focal events) of our AT imaging approach. The main characteristic events of the AT maps were estimated despite neglected electrical anisotropy in the inverse formulation. The worst correlation coefficient of the estimated AT maps was 0.810 in case of sinus rhythm. However, all characteristic events of the activation pattern were found. The results of this study confirm our clinical validation studies of noninvasive AT imaging in which cardiac anisotropy was neglected.     

Quantification of regional left ventricular dyssynchrony by magnetic resonance imaging

Cardiac resynchronization therapy is an established treatment in patients with symptomatic heart failure and intraventricular conduction delay. Electrical dyssynchrony is typically adopted to represent myocardial activation dyssynchrony, which should be compensated by cardiac resynchronization therapy. One third of the patients, however, does not respond to the therapy. Therefore, imaging modalities aimed at the mechanical dyssynchrony estimation have been recently proposed to improve patient selection criteria. This paper presents a novel fully automated method for regional mechanical left ventricular dyssynchrony quantification in short-axis magnetic resonance imaging. The endocardial movement is described by time-displacement curves with respect to an automatically determined reference point. Different methods are proposed for time-displacement curve analysis aimed at the regional contraction timing estimation. These methods were evaluated in two groups of subjects with (nine patients) and without (six patients) left bundle branch block. The contraction timing standard deviation showed a significant increase for left bundle branch block patients with all the methods. A novel method based on phase spectrum analysis may be however preferred due to a better specificity (99.7%) and sensitivity (99.0%). In conclusion, this method provides a valuable prognostic indicator for heart failure patients with dyssynchronous ventricular contraction and it opens new possibilities for regional timing analysis.     

Model-based imaging of cardiac apparent conductivity and local conduction velocity for diagnosis and planning of therapy

We present an adaptive algorithm which uses a fast electrophysiological (EP) model to estimate apparent electrical conductivity and local conduction velocity from noncontact mapping of the endocardial surface potential. Development of such functional imaging revealing hidden parameters of the heart can be instrumental for improved diagnosis and planning of therapy for cardiac arrhythmia and heart failure, for example during procedures such as radio-frequency ablation and cardiac resynchronisation therapy. The proposed model is validated on synthetic data and applied to clinical data derived using hybrid X-ray/magnetic resonance imaging. We demonstrate a qualitative match between the estimated conductivity parameter and pathology locations in the human left ventricle. We also present a proof of concept for an electrophysiological model which utilizes the estimated apparent conductivity parameter to simulate the effect of pacing different ventricular sites. This approach opens up possibilities to directly integrate modelling in the cardiac EP laboratory.      

Model-based imaging of cardiac electrical excitation in humans

Activation time (AT) imaging from electrocardiographic (ECG) mapping data has been developing for several years. By coupling ECG mapping and three-dimensional (3-D) + time anatomical data, the electrical excitation sequence can be imaged completely noninvasively in the human heart. In this paper, a bidomain theory-based surface heart model AT imaging approach was applied to single-beat data of atrial and ventricular depolarization in two patients with structurally normal hearts. In both patients, the AT map was reconstructed from sinus and paced rhythm data. Pacing sites were the apex of the right ventricle and the coronary sinus (CS) ostium. For CS pacing, the reconstructed AT pattern on the endocardium of the right atrium was compared with the CARTO map in both patients. The localization errors of the origins of the initial endocardial breakthroughs were determined to be 6 and 12 mm. The sites of early activation and the areas with late activation were estimated with sufficient accuracy. The reconstructed sinus rhythm sequence was in good qualitative agreement with the pattern previously published for the isolated Langendorff-perfused human heart.     

无源网络导纳分析仪设计与实现

以AT89S52单片机和FPGA作为测量和数据处理核心,基于DDS技术,并结合I/V变换、A/D采样等外围电路,以及离散傅立叶变换(DFT)等数字信号处理方法,设计并实现了一种简易的无源网络导纳分析仪.另外,系统具有连续测量、频率特性测量及其绘制曲线等功能;还具有性能稳定、结构简单、测量方法巧妙,精度较高,人机交互界面友好等特点.     

Modulation of conduction at points of axonal bifurcation by appliedelectric fields

This study investigated how weak electric fields, on the order of 100 mV/cm, modulate action potential conduction through points of axonal bifurcation in leech touch sensory neurons. Axonal branch points in neurons are ubiquitous structures, and they are sites of low safety-factor for action potential propagation. In this study calibrated electric fields were applied around excised ganglia from the leech central nervous system. The electric fields were generated by 500 ms constant current square waves applied to the bath containing the tissue. Microelectrode penetration of the neurons was used to: 1) record transmembrane potential changes in the cell body of the neuron that resulted from the external field; 2) monitor conduction block when action potentials, evoked in the periphery, propagated into the ganglion; 3) inject current directly into the cell in an experimental analysis of the mechanism by which the externally applied field produced block. Conduction block was reliably induced by electric fields too weak to reach threshold for firing action potentials. In an experimental analysis where block was produced by the direct intracellular injection of negative current, a reversed polarity field relieved it. This indicates that when the external field induces block, it does so by membrane hyperpolarization at the branch point.     

Computer modeling of ventricular rhythm during atrial fibrillation and ventricular pacing

We propose a unified atrial fibrillation (AF)-ventricular pacing (VP) (AF-VP) model to demonstrate the effects of VP on the ventricular rhythm during atrial fibrillation AF. In this model, the AV junction (AVJ) is treated as a lumped structure characterized by refractoriness and automaticity. Bombarded by random AF impulses, the AVJ can also be invaded by the VP-induced retrograde wave. The model includes bidirectional conduction delays in the AVJ and ventricle. Both refractory period and conduction delay of the AVJ are dependent upon its recovery time. The electrotonic modulation by blocked impulses is also considered in the model. Our simulations show that, with proper parameter settings, the present model can account for most principal statistical properties of the RR intervals during AF. We further demonstrate that the AV conduction property and the ventricular rate in AF depend on both AF rate and the degree of electrotonic modulation in the AVJ. Finally, we show that multilevel interactions between AF and VP can generate various patterns of ventricular rhythm that are consistent with previous experimental observations.     

A technique for measurement of the extent of spatial organizationof atrial activation during atrial fibrillation in the intact humanheart

Atrial fibrillation (AF) is a common clinical problem, associated with considerable morbidity and motility, for which effective management strategies have yet to be devised. The absence of objective measures to guide selection of antiarrhythmic drug therapy for maintenance of sinus rhythm leaves only clinical endpoints (either beneficial or detrimental) for assessment of drug action, with occasional catastrophic consequences. As part of an attempt to provide an objective framework for the assessment of antiarrhythmic drug action on the electrophysiologic determinants of atrial fibrillation, the authors have developed a measure of the spatial organization of atrial activation processes during atrial fibrillation. By recording activation sequences at multiple equally spaced locations on the endocardial surface of the atrial during atrial fibrillation in humans and determining the degree of correlation between these activation sequences as a function of distance, the authors have been able to construct spatial correlation functions for atrial activation. They have found that atrial activation remains well-correlated, independent of distance during normal sinus rhythm and atrial flutter. During atrial fibrillation, correlation decays monotonically with distance and the space-constant for this decay may be used to describe the relative spatial organization of atrial fibrillation. The authors provide examples of the impact of antiarrhythmic agents on the space-constant and suggest that assessment of the relative spatial organization of atrial activation using this methodology may potentially provide an objective framework to guide therapy in patients with AF