Indeterminacy of Spatiotemporal Cardiac Alternans

Cardiac alternans, a beat-to-beat alternation in action potential duration (at the cellular level) or in ECG morphology (at the whole heart level), is a marker of ventricular fibrillation, a fatal heart rhythm that kills hundreds of thousands of people in the US each year. Investigating cardiac alternans may lead to a better understanding of the mechanisms of cardiac arrhythmias and eventually better algorithms for the prediction and prevention of such dreadful diseases. In paced cardiac tissue, alternans develops under increasingly shorter pacing period. Existing experimental and theoretical studies adopt the assumption that alternans in homogeneous cardiac tissue is exclusively determined by the pacing period. In contrast, we find that, when calcium-driven alternans develops in cardiac fibers, it may take different spatiotemporal patterns depending on the pacing history. Because there coexist multiple alternans solutions for a given pacing period, the alternans pattern on a fiber becomes unpredictable. Using numerical simulation and theoretical analysis, we show that the coexistence of multiple alternans patterns is induced by the interaction between electrotonic coupling and an instability in calcium cycling.Comment: 20 pages, 10 figures, to be published in Phys. Rev.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Minimal model for calcium alternans due to SR release refractoriness

In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion, and release conductance for the onset of alternans. We find that the development of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.Postprint (author's final draft

On complex dynamics in a Purkinje and a ventricular cardiac cell model

Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the occurrence of such phenomena and to decode their mechanisms. The focus of this paper is the investigation of dynamics of cardiac muscle cells described by systems of ordinary differential equations. This is generically performed by studying a Purkinje cell model and a modified ventricular cell model. We find chaotic dynamics with respect to the leak current in the Purkinje cell model, and EADs and chaos with respect to a reduced fast potassium current and an enhanced calcium current in the ventricular cell model -- features that have been experimentally observed and are known to exist in some models, but are new to the models under present consideration. We also investigate the related monodomain models of both systems to study synchronisation and the behaviour of the cells on macro-scale in connection with the discovered features. The models show qualitatively the same behaviour to what has been experimentally observed. However, for certain parameter settings the dynamics occur within a non-physiological range

On complex dynamics in a Purkinje and a ventricular cardiac cell model

Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the occurrence of such phenomena and to decode their mechanisms. The focus of this paper is the investigation of dynamics of cardiac muscle cells described by systems of ordinary differential equations. This is generically performed by studying a Purkinje cell model and a modified ventricular cell model. We find chaotic dynamics with respect to the leak current in the Purkinje cell model, and EADs and chaos with respect to a reduced fast potassium current and an enhanced calcium current in the ventricular cell model — features that have been experimentally observed and are known to exist in some models, but are new to the models under present consideration. We also investigate the related monodomain models of both systems to study synchronisation and the behaviour of the cells on macro-scale in connection with the discovered features. The models show qualitatively the same behaviour to what has been experimentally observed. However, for certain parameter settings the dynamics occur within a non-physiological range

A statistical index for early diagnosis of ventricular arrhythmia from the trend analysis of ECG phase-portraits

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record.In this paper, we propose a novel statistical index for the early diagnosis of ventricular arrhythmia (VA) using the time delay phase-space reconstruction (PSR) technique, from the electrocardiogram (ECG) signal. Patients with two classes of fatal VA-with preceding ventricular premature beats (VPBs) and with no VPBs-have been analysed using extensive simulations. Three subclasses of VA with VPBs viz. ventricular tachycardia (VT), ventricular fibrillation (VF) and VT followed by VF are analyzed using the proposed technique. Measures of descriptive statistics like mean (µ), standard deviation (σ), coefficient of variation (CV = σ/µ), skewness (γ) and kurtosis (β) in phase-space diagrams are studied for a sliding window of 10 beats of the ECG signal using the box-counting technique. Subsequently, a hybrid prediction index which is composed of a weighted sum of CV and kurtosis has been proposed for predicting the impending arrhythmia before its actual occurrence. The early diagnosis involves crossing the upper bound of a hybrid index which is capable of predicting an impending arrhythmia 356 ECG beats, on average (with 192 beats standard deviation) before its onset when tested with 32 VA patients (both with and without VPBs). The early diagnosis result is also verified using a leave one out cross-validation (LOOCV) scheme with 96.88% sensitivity, 100% specificity and 98.44% accuracy.This work was supported by the E.U. ARTEMIS Joint Undertaking under the Cyclic and person-centric Health management: Integrated appRoach for hOme, mobile and clinical eNvironments—(CHIRON) Project, Grant Agreement # 2009-1-100228

Mitochondrial chaotic dynamics: Redox-energetic behavior at the edge of stability

Mitochondria serve multiple key cellular functions, including energy generation, redox balance, and regulation of apoptotic cell death, thus making a major impact on healthy and diseased states. Increasingly recognized is that biological network stability/instability can play critical roles in determining health and disease. We report for the first-time mitochondrial chaotic dynamics, characterizing the conditions leading from stability to chaos in this organelle. Using an experimentally validated computational model of mitochondrial function, we show that complex oscillatory dynamics in key metabolic variables, arising at the “edge” between fully functional and pathological behavior, sets the stage for chaos. Under these conditions, a mild, regular sinusoidal redox forcing perturbation triggers chaotic dynamics with main signature traits such as sensitivity to initial conditions, positive Lyapunov exponents, and strange attractors. At the “edge” mitochondrial chaos is exquisitely sensitive to the antioxidant capacity of matrix Mn superoxide dismutase as well as to the amplitude and frequency of the redox perturbation. These results have potential implications both for mitochondrial signaling determining health maintenance, and pathological transformation, including abnormal cardiac rhythms.publishedVersionKembro, Jackelyn Melissa. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales; Argentina.Kembro, Jackelyn Melissa. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones Biológicas y Tecnológicas; Argentina.Cortassa, Sonia. National Institutes of Health. NIH · NIA Intramural Research Program; Estados Unidos.Lloyd, David. Cardiff University. School of Biosciences 1; Inglaterra.Sollot, Steven. Johns Hopkins University. Laboratory of Cardiovascular Science; Estados Unidos.Sollot, Steven. Johns Hopkins University. Laboratory of Cardiovascular Science; Estados Unidos

Border-Collision Bifurcations of Cardiac Calcium Cycling

In this thesis, we study the nonlinear dynamics of calcium cycling within a cardiac cell. We develop piecewise smooth mapping models to describe intracellular calcium cycling in cardiac myocyte. Then, border-collision bifurcations that arise in these piecewise maps are investigated. These studies are carried out using both one-dimensional and two-dimensional models. Studies in this work lead to interesting insights on the stability of cardiac dynamics, suggesting possible mechanisms for cardiac alternans. Alternans is the precursor of sudden cardiac arrests, a leading cause of death in the United States