Steven J. Evans

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the hearts natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.

Use of P-wave-triggered, P-wave signal-averaged electrocardiogram to predict atrial fibrillation after coronary artery bypass surgery

Atrial fibrillation occurs commonly after coronary artery bypass surgery. However, despite numerous attempts at prediction, no accurate and generally accepted method exists to predict its occurrence. P-wave-triggered P-wave signal averaging was performed on 54 patients before coronary artery bypass surgery to evaluate the utility of this method to predict atrial fibrillation after coronary artery bypass surgery. After excluding six patients with unevaluable P-wave signal averages and three patients with postoperative arrhythmias other than atrial fibrillation, the P-wave signal averages of 45 patients were analyzed. Sixteen patients had postoperative atrial fibrillation and 29 did not. The mean P-wave duration of the filtered, signal-averaged P wave was 163 +/- 19 msec in the 16 patients with atrial fibrillation and 144 +/- 16 msec in the 29 patients without (p < 0.005). Left atrial enlargement on the surface electrocardiogram (ECG) was the only other statistically significant variable that correlated weakly with the onset of postoperative atrial fibrillation (p = 0.04). Other clinical variables such as P-wave duration in ECG lead II, left ventricular hypertrophy on ECG, age, sex, hypertension, and left ventricular ejection fraction were not significantly different between the two groups. With a cut point of 155 msec, chi-squared analysis revealed a p value of < 0.005, yielding a sensitivity of 69%, a specificity of 79%, a positive predictive value of 65%, and a negative predictive value of 82%. Signal-averaging of the P wave in patients before coronary artery bypass surgery provides a good predictor of postoperative atrial fibrillation.

Electroanatomical mapping of the heart: basic concepts and implications for the treatment of cardiac arrhythmias.

The CARTO electroanatomical mapping system represents a paradigm shift in the ability to map the three‐dimensional anatomy of the heart and determine the cardiac electrical activity at any given mapped point. The system associates anatomical structure and electrophysiological data and displays the combined information in an easily readable, visual fashion. The system consists of a roving mapping catheter with small magnetic sensors in the tip, a fixed sensor that acts as a reference point, a low magnetic field generating pad, and a data acquisition and display system. When the roving catheter is moved in three‐dimensional space, its location in relation to the fixed sensor is monitored by the system, with a resolution of < 1 mm. By gating the acquisition of points in space to the cardiac electrical activity, points that represent both location and electrical activity at that location can be acquired and displayed on a computer screen. After acquiring a number of points, a three‐dimensional representation is constructed, and may be displayed from any viewing projection. Clinical applications of the system include defining the mechanisms of arrhythmias, designing ablation strategies, guiding ablations, and improving the safety of mapping and ablation procedures by allowing localization of critical cardiac structures such as the atrioventricular node and His bundle. The system holds the potential to both further our understanding of arrhythmias and increase the safety, efficacy, and efficiency of catheter ablation.

Efficient integration of a realistic two-dimensional cardiac tissue model by domain decomposition

The size of realistic cardiac tissue models has been limited by their high computational demands. In particular, the Luo-Rudy phase II membrane model, used to simulate a thin sheet of ventricular tissue with arrays of coupled ventricular myocytes, is usually limited to 100/spl times/100 arrays. The authors introduce a new numerical method based on domain decomposition and a priority queue integration scheme which reduces the computational cost by a factor of 3-17. In the standard algorithm all the nodes advance with the same time step /spl Delta/t, whose size Is limited by the time scale of activation. However, at any given time, many regions may he inactive and do not require the same small /spl Delta/t and consequent extensive computations. Hence, adjusting /spl Delta/t locally is a key factor in improving computational efficiency, since most of the computing time is spent calculating ionic currents. This paper proposes an efficient adaptive numerical scheme for integrating a two-dimensional (2-D) propagation model, by incorporating local adjustments of /spl Delta/t. In this method, alternating direction Cooley-Dodge and Rush-Larsen methods were used for numerical integration. Between consecutive integrations over the whole domain using an implicit method, the model was spatially decomposed into many subdomains, and /spl Delta/t adjusted locally. The Euler method was used for numerical integration in the subdomains. Local boundary values were determined from the boundary mesh elements of the neighboring subdomains using linear interpolation. Because /spl Delta/t was defined locally, a priority queue was used to store and order nest update times for each subdomain. The subdomain with the earliest update time was given the highest priority and advanced first. This new method yielded stable solutions with relative errors less than 1% and reduced computation time by a factor of 3-17 and will allow much larger (e.g. 500/spl times/500) models based on realistic membrane kinetics and realistic dimensions to simulate reentry, triggered activity, and their interactions.

Properties of two human atrial cell models in tissue: Restitution, memory, propagation, and reentry

To date, two detailed ionic models of human atrial cell electrophysiology have been developed, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models draw from similar experimental data, they have vastly different properties. This paper provides the first systematic analysis and comparison of the dynamics of these models in spatially extended systems including one-dimensional cables and rings, two-dimensional sheets, and a realistic three-dimensional human atrial geometry. We observe that, as in single cells, the CM adapts to rate changes primarily by changes in action potential duration (APD) and morphology, while for the NM rate changes affect resting membrane potential (RMP) more than APD. The models also exhibit different memory properties as assessed through S1-S2 APD and conduction velocity (CV) restitution curves with different S1 cycle lengths. Reentrant wave dynamics also differ, with the NM exhibiting stable, non-breaking spirals and the CM exhibiting frequent transient wave breaks. The realistic atrial geometry modifies dynamics in some cases through drift, transient pinning, and breakup. Previously proposed modifications to represent atrial fibrillation-remodeled electrophysiology produce altered dynamics, including reduced rate adaptation and memory for both models and conversion to stable reentry for the CM. Furthermore, proposed variations to the NM to reproduce action potentials more closely resembling those of the CM do not substantially alter the underlying dynamics of the model, so that tissue simulations using these modifications still behave more like the unmodified NM. Finally, interchanging the transmembrane current formulations of the two models suggests that currents contribute more strongly to RMP and CV, intracellular calcium dynamics primarily determine reentrant wave dynamics, and both are important in APD restitution and memory in these models. This finding implies that the formulation of intracellular calcium processes is as important to producing realistic models as transmembrane currents.

Dynamics of human atrial cell models: restitution, memory, and intracellular calcium dynamics in single cells.

Mathematical models of cardiac cells have become important tools for investigating the electrophysiological properties and behavior of the heart. As the number of published models increases, it becomes more difficult to choose a model appropriate for the conditions to be studied, especially when multiple models describing the species and region of the heart of interest are available. In this paper, we will review and compare two detailed ionic models of human atrial myocytes, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models include the same transmembrane currents and are largely based on the same experimental data from human atrial cells, the two models exhibit vastly different properties, especially in their dynamical behavior, including restitution and memory effects. The CM produces pronounced rate adaptation of action potential duration (APD) with limited memory effects, while the NM exhibits strong rate dependence of resting membrane potential (RMP), limited APD restitution, and stronger memory, as well as delayed afterdepolarizations and auto-oscillatory behavior upon cessation of rapid pacing. Channel conductance modifications based on experimentally measured changes during atrial fibrillation modify rate adaptation and memory in both models, but do not change the primary rate-dependent properties of APD and RMP for the CM and NM, respectively. Two sets of proposed changes to the NM that yield a spike-and-dome action potential morphology qualitatively similar to the CM at slow pacing rates similarly do not change the underlying dynamics of the model. Moreover, interchanging the formulations of all transmembrane currents between the two models while leaving calcium handling and ionic concentrations intact indicates that the currents strongly influence memory and the rate adaptation of RMP, while intracellular calcium dynamics primarily determine APD rate adaptation. Our results suggest that differences in intracellular calcium handling between the two human atrial myocyte models are responsible for marked dynamical differences and may prevent reconciliation between the models by straightforward channel conductance modifications.

Echocardiographically guided electrophysiologic testing in pregnancy.

Electrophysiologic testing is usually performed with fluoroscopy to guide catheter positioning. This method of visualizing catheter placement may not be ideal for patients who are pregnant. We report four cases of echocardiographically guided placement of catheters for electrophysiologic testing because of the consideration of pregnancy. Adequate visualization of catheters was possible, allowing for proper catheter positioning and complete electrophysiologic testing, including the recording of atrial, His-bundle, and ventricular potentials, as well as cardiac stimulation and induction of tachycardia. This method holds promise for patients in whom fluoroscopy may be relatively contraindicated, such as pregnant patients, as well as patients in whom it is desirable to avoid x-ray exposure such as women of childbearing age and young children.

Real-time computer simulations of excitable media: JAVA as a scientific language and as a wrapper for C and FORTRAN programs

We describe a useful setting for interactive, real-time study of mathematical models of cardiac electrical activity, using implicit and explicit integration schemes implemented in JAVA. These programs are intended as a teaching aid for the study and understanding of general excitable media. Particularly for cardiac cell models and the ionic currents underlying their basic electrical dynamics. Within the programs, excitable media properties such as thresholds and refractoriness and their dependence on parameter values can be analyzed. In addition, the cardiac model applets allow the study of reentrant tachyarrhythmias using premature stimuli and conduction blocks to induce or to terminate reentrant waves of electrical activation in one and two dimensions. The role of some physiological parameters in the transition from tachycardia to fibrillation also can be analyzed by varying the maximum conductances of ion channels associated with a given model in real time during the simulations. These applets are available for download at http://arrhythmia.hofstra.edu or its mirror site http://stardec.ascc.neu.edu/~fenton.

Differentiation of Beats of Ventricular and Sinus Origin Using a Self‐Training Neural Network

Despite advances in the computerized detection of arrhythmias, arrhythmia recognition by morphological waveform analysis still poses a difficult problem. Artificial neural networks, computer algorithms that are self‐trained by an analog of biological synaptic modification to perform pattern recognition, hold great promise for the differentiation of various cardiac rhythms. The goal of this study was to differentiate beats of sinus and ventricular origin on a global basis and on a patient‐specific basis by the use of artificial neural network analysis. Neural networks were trained to recognize digitized intracardiac electrograms (9 patients) and surface electrocardiograms (11 patients) obtained during sinus rhythm and ventricular tachycardia. After training, sinus rhythm or ventricular tachycardia beats were input into the neural network, and classified as to their origin. By the use of modified receiver operating characteristic curve plots, it was possible to differentiate with high sensitivity and specificity between beats of sinus origin and ventricular origin in all patients. The addition of high amounts of noise to the beats did not markedly degrade the performance of the surface ECG neural networks, and still allowed high sensitivity in differentiating beats of sinus origin from beats of ventricular origin, especially when noise was added to the training set. Neural networks provided sensitive and specific detection of cardiac electrical activity during sinus rhythm and ventricular tachycardia, and may play an important role in allowing development of improved arrhythmia recognition and management systems.

Clinical Heterogeneity in Sodium Channelopathies

Background: Mutations in the SCN5A gene have been linked to a variety of diseases causing sudden cardiac death, with important variability in expressivity and phenotypic overlap. With the availability of genetic testing family members may now be diagnosed as carriers based solely on the presence of the genetic defect. Clinical decision making in this situation is complex and generates important ethical and medicolegal issues.Methods:Wedescribe two families, 24-328 and 24-588, originally diagnosed with Brugada syndrome after the probands experienced cardiac arrest and we performed clinical and genetic analysis in their members. Results: Both families had members with various electrocardiographic abnormalities including some with Brugada syndrome, long QT syndrome and conduction system disease. Both families had an important family history of sudden cardiac death. Direct sequencing of exons and exon-intron boundaries of the sodium channel gene SCN5A identified mutations in both families. Conclusions: These two families illustrate an increasingly common scenario when encountering families with ion channelopathies. Because a defibrillator is the only available therapeutic option at present in Brugada syndrome, physicians will be faced with extremely difficult therapeutic decisions that also have important legal, social and ethical implications, especially in children. These data indicate the need to develop guidelines on how to approach the results of genetic testing, especially in asymptomatic individuals.