Conditions for propagation and block of excitation in an asymptotic model of atrial tissue

Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction of the models. Earlier results have shown that the asymptotics of cardiac equations are non-standard. Here we apply such a novel asymptotic method to an ionic model of human atrial tissue in order to obtain a reduced but accurate model for the description of excitation fronts. Numerical simulations of spiral waves in atrial tissue show that wave fronts of propagating action potentials break-up and self-terminate. Our model, in particular, yields a simple analytical criterion of propagation block, which is similar in purpose but completely different in nature to the `Maxwell rule' in the FitzHugh-Nagumo type models. Our new criterion agrees with direct numerical simulations of break-up of re-entrant waves.Comment: Revised manuscript submitted to Biophysical Journal (30 pages incl. 10 figures

Asymptotic properties of mathematical models of excitability

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic timescales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially-extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for break-ups and self-termination of re-entrant waves in excitable media with Courtemanche et al. (1998) kinetics.Comment: 15 pages, 8 figures, to appear in Phil Trans Roy Soc London

Analytically Solvable Asymptotic Model of Atrial Excitability

We report a three-variable simplified model of excitation fronts in human atrial tissue. The model is derived by novel asymptotic techniques \new{from the biophysically realistic model of Courtemanche et al (1998) in extension of our previous similar models. An iterative analytical solution of the model is presented which is in excellent quantitative agreement with the realistic model. It opens new possibilities for analytical studies as well as for efficient numerical simulation of this and other cardiac models of similar structure

Asymptotic analysis and analytical solutions of a model of cardiac excitation.

The original publication is available at www.springerlink.com - http://link.springer.com/article/10.1007/s11538-007-9267-0Journal ArticleCopyright © SpringerWe describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape of action potential at repolarization. The proposed asymptotic description overcomes these deficiencies by allowing, among other non-Tikhonov features, that a dynamical variable may change its character from fast to slow within a single solution. The general asymptotic approach is best demonstrated on an example which should be both simple and generic. The classical model of Purkinje fibers (Noble in J. Physiol. 160:317-352, 1962) has the simplest functional form of all cardiac models but according to the current understanding it assigns a physiologically incorrect role to the Na current. This leads us to suggest an "Archetypal Model" with the simplicity of the Noble model but with a structure more typical to contemporary cardiac models. We demonstrate that the Archetypal Model admits a complete asymptotic solution in quadratures. To validate our asymptotic approach, we proceed to consider an exactly solvable "caricature" of the Archetypal Model and demonstrate that the asymptotic of its exact solution coincides with the solutions obtained by substituting the "caricature" right-hand sides into the asymptotic solution of the generic Archetypal Model. This is necessary, because, unlike in standard asymptotic descriptions, no general results exist which can guarantee the proximity of the non-Tikhonov asymptotic solutions to the solutions of the corresponding detailed ionic model

Electrophysiological mechanisms underlying T-wave alternans and their role in arrhythmogenesis

T-wave alternans (TWA) reflects every-other-beat alterations in the morphology of the electrocardiogram ST segment or T wave in the setting of a constant heart rate, hence, in the absence of heart rate variability. It is believed to be associated with the dispersion of repolarization and has been used as a non-invasive marker for predicting the risk of malignant cardiac arrhythmias and sudden cardiac death as numerous studies have shown. This review aims to provide up-to-date review on both experimental and simulation studies in elucidating possible mechanisms underlying the genesis of TWA at the cellular level, as well as the genesis of spatially concordant/discordant alternans at the tissue level, and their transition to cardiac arrhythmia. Recent progress and future perspectives in antiarrhythmic therapies associated with TWA are also discussed

The Wolff- Parkinson-White and related syndromes : an electrocardiographic appraisal

This is an electrocardiological study, based on electrocardiographic analysis of new cases as well as on a review of some features, hitherto unrecognized or not stressed, in subjects with these disorders, that may help throw more light on them. In six cases studied personally using intracardiac electrography - the technique of His bundle electrography - the contribution and relevance of this method will be analysed, and the results compared with the conclusions drawn from other contemporary work in this field. Thus, the clinical presentation of the cases, and of these syndromes, receives secondary attention, and more detailed analysis only when appropriate to substantiate the main burdens of the thesis. These case reports appear separately in Section c. The mechanism of production of arrhythmias is becoming much better understood, and some of the diagnostic measures that are discussed in this work provide a clearer picture of their genesis. It is not proposed to embark upon a detailed consideration of anti-arrhythmic therapy in these syndromes, but the general principles will be discussed, and special reference will also be made to some new developments in this field

Stories from different worlds in the universe of complex systems: A journey through microstructural dynamics and emergent behaviours in the human heart and financial markets

A physical system is said to be complex if it exhibits unpredictable structures, patterns or regularities emerging from microstructural dynamics involving a large number of components. The study of complex systems, known as complexity science, is maturing into an independent and multidisciplinary area of research seeking to understand microscopic interactions and macroscopic emergence across a broad spectrum systems, such as the human brain and the economy, by combining specific modelling techniques, data analytics, statistics and computer simulations. In this dissertation we examine two different complex systems, the human heart and financial markets, and present various research projects addressing specific problems in these areas. Cardiac fibrillation is a diffuse pathology in which the periodic planar electrical conduction across the cardiac tissue is disrupted and replaced by fast and disorganised electrical waves. In spite of a century-long history of research, numerous debates and disputes on the mechanisms of cardiac fibrillation are still unresolved while the outcomes of clinical treatments remain far from satisfactory. In this dissertation we use cellular automata and mean-field models to qualitatively replicate the onset and maintenance of cardiac fibrillation from the interactions among neighboring cells and the underlying topology of the cardiac tissue. We use these models to study the transition from paroxysmal to persistent atrial fibrillation, the mechanisms through which the gap-junction enhancer drug Rotigaptide terminates cardiac fibrillation and how focal and circuital drivers of fibrillation may co-exist as projections of transmural electrical activities. Financial markets are hubs in which heterogeneous participants, such as humans and algorithms, adopt different strategic behaviors to exchange financial assets. In recent decades the widespread adoption of algorithmic trading, the electronification of financial transactions, the increased competition among trading venues and the use of sophisticated financial instruments drove the transformation of financial markets into a global and interconnected complex system. In this thesis we introduce agent-based and state-space models to describe specific microstructural dynamics in the stock and foreign exchange markets. We use these models to replicate the emergence of cross-currency correlations from the interactions between heterogeneous participants in the currency market and to disentangle the relationships between price fluctuations, market liquidity and demand/supply imbalances in the stock market.Open Acces

HYSTERESIS IN REPOLARIZATION OF CARDIAC ACTION POTENTIALS: EFFECTS OF SPATIAL HETEROGENEITY AND SLOW REPOLARIZATION CURRENTS

Repolarization alternans, i.e. beat-to-beat variation of repolarization of action potential, is proposed as a predictor of life-threatening arrhythmias. Restitution relates repolarization duration with its previous relaxation time, i.e. diatstolic interval (DI), and is considered a dominant mechanism for alternans. Previously, we observed that different repolarization durations at the same DI during decelerating and accelerating pacing, i.e. restitution displays hysteresis, which is a measure of “cardiac memory”. Objective of the current study was to investigate in the pig 1) the mechanism for a previously observed hysteresis type phenomenon, where alternans, once started at higher heart rate, persists even when heart rate decreases below its initiating rate, 2) regional differences in expression of hysteresis, i.e. memory in restitution in the heart, and 3) changes in restitution and memory during manipulation of an important repolarization current, the slow delayed rectifier, IKs. Action potentials were recorded in pig ventricular tissues using microelectrodes. Regional differences were explored in endocardial and epicardial tissues from both ventricles. DIs were explicitly controlled in real time to separate restitution mechanism from non-restitution related effects. Stepwise protocols were used to explore the existence in hysteresis in alternans threshold, where DIs were held constant for each step and progressively decreased and then increased. Quantification of cardiac memory was achieved by sinusoidally changing DI protocols, which were used to investigate memory changes among myocytes from different regions of the heart and during IKs manipulation. Results show that during stepwise protocol, hysteresis in alternans still existed, which indicates that restitution is not the only mechanism underlying the hysteresis. When comparing hysteresis obtained from sinusoidally oscillatory DIs among different regions, results show memory is expressed differently with endocardium expressing the most and epicardium the least memory. This provides important implications about the location where arrhythmia would initiate. Results also show that measures for hysteresis loops obtained by sinusoidal DI protocols decreased (increased) after enhancement (attenuation) of IKs, suggesting decreased (increased) hysteresis, i.e. memory in restitution. This effect needs to be considered during drug development