Power-Law Behavior of Beat-Rate Variability in Monolayer Cultures of Neonatal Rat Ventricular Myocytes (original) (raw)
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Fractal Dynamics of Heartbeat Interval Fluctuations in Health and Disease
Non-linear fractal analysis of cardiac interbeat time series was performed in corticotropinreleasing factor receptor subtype 2 (CRFR2) deficient mice. Heart rate dynamics in mice constitutes a self-similar, scale-invariant, random fractal process with persistent intrinsic long-range correlations and inverse power-law properties. We hypothesized that the sustained tachycardic response elicited by intraperitoneal (ip) injection of human/rat CRF (h/ rCRF) is mediated by CRFR2. In wildtype control animals, heart rate was increased to about maximum levels (~ 750 bpm) while in CRFR2-deficient animals baseline values were retained (~ 580 bpm). The tachycardic response elicited by ip-application is mediated by CRFR2 and is interpreted to result from sympathetic stimulation. However, the functional integrity of CRFR2 would not present a prerequisite to maintaining the responsiveness and resiliency of cardiac control to external environmental perturbations experimentally induced by extrinsic ip-application of h/rCRF or under physiological conditions that may be associated with an increased peripheral release of CRF. Under stressful physiological conditions achieved by novelty exposure, CRFR2 is not involved in the cardiodynamic regulation to external short-term stress. While the hypothesis of involvement of CRFR2 in cardiac regulation upon pharmacological stimulation cannot be rejected, the present findings suggest that the mechanism of action is by sympathetic stimulation, but would not unambiguously allow to draw any conclusions as to the physiological role of CRFR2 in the control of cardiac dynamics.
Spontaneous Initiation and Termination of Complex Rhythms in Cardiac Cell Culture
Journal of Cardiovascular Electrophysiology, 2003
Complex Cardiac Rhythms. Introduction: Complex cardiac arrhythmias often start and stop spontaneously. These poorly understood behaviors frequently are associated with pathologic modification of the structural heterogeneity and functional connectivity of the myocardium. To evaluate underlying mechanisms, we modify heterogeneity by varying the confluence of embryonic chick monolayer cultures that display complex bursting behaviors. A simple mathematical model was developed that reproduces the experimental behaviors and reveals possible generic mechanisms for bursting dynamics in heterogeneous excitable systems.
Multiscale Aspects of Cardiac Control
We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. We first review recent progress using wavelet-based multifractal analysis, magnitude and sign decomposition analysis and a new segmentation algorithm to quantify multiscale features of heartbeat interval series. We then investigate how heartbeat dynamics change with circadian influences and under pathologic conditions, and we discuss their possible relation to the underlaying cardiac control mechanisms. The analytic tools we discuss may be used on a wider range of physiologic signals. r (P.Ch. Ivanov). biology. In particular, physiologic systems under autonomic regulation, such as heart rate, are good candidates for a statistical physics approach, since (i) physiologic systems often include many individual components, and (ii) physiologic systems usually are driven by competing forces, e.g., parasympathetic versus sympathetic stimuli. Physiologic systems often exhibit temporal structures which are similar to those found in physical systems driven away from an equilibrium state.
Frontiers in Physiology
Atrial fibrillation (AF) is a cardiac arrhythmia characterized by rapid and irregular atrial electrical activity with a high clinical impact on stroke incidence. Best available therapeutic strategies combine pharmacological and surgical means. But when successful, they do not always prevent long-term relapses. Initial success becomes all the more tricky to achieve as the arrhythmia maintains itself and the pathology evolves into sustained or chronic AF. This raises the open crucial issue of deciphering the mechanisms that govern the onset of AF as well as its perpetuation. In this study, we develop a wavelet-based multi-scale strategy to analyze the electrical activity of human hearts recorded by catheter electrodes, positioned in the coronary sinus (CS), during episodes of AF. We compute the so-called multifractal spectra using two variants of the wavelet transform modulus maxima method, the moment (partition function) method and the magnitude cumulant method. Application of these methods to long time series recorded in a patient with chronic AF provides quantitative evidence of the multifractal intermittent nature of the electric energy of passing cardiac impulses at low frequencies, i.e., for times (0.5 s) longer than the mean interbeat (≃ 10 −1 s). We also report the results of a two-point magnitude correlation analysis which infers the absence of a multiplicative timescale structure underlying multifractal scaling. The electric energy dynamics looks like a "multifractal white noise" with quadratic (log-normal) multifractal spectra. These observations challenge concepts of functional reentrant circuits in mechanistic theories of AF, still leaving open the role of the autonomic nervous system (ANS). A transition is indeed observed in the computed multifractal spectra which group according to two distinct areas, consistently with the anatomical substrate binding to the CS, namely the left atrial posterior wall, and the ligament of Marshall which is innervated by the ANS. In a companion paper (II. Modeling), we propose a mathematical model of a denervated heart where the kinetics of gap junction conductance alone induces a desynchronization of the myocardial excitable cells, accounting for the multifractal spectra found experimentally in the left atrial posterior wall area.
Journal of Clinical Investigation, 1997
We have presented evidence that ventricular fibrillation is deterministic chaos arising from quasiperiodicity. The purpose of this study was to determine whether the transition from chaos (ventricular fibrillation, VF) to periodicity (ventricular tachycardia) through quasiperiodicity could be produced by the progressive reduction of tissue mass. In isolated and perfused swine right ventricular free wall, recording of single cell transmembrane potentials and simultaneous mapping (477 bipolar electrodes, 1.6 mm resolution) were performed. The tissue mass was then progressively reduced by sequential cutting. All isolated tissues fibrillated spontaneously. The critical mass to sustain VF was 19.9 +/- 4.2 g. As tissue mass was decreased, the number of wave fronts decreased, the life-span of reentrant wave fronts increased, and the cycle length, the diastolic interval, and the duration of action potential lengthened. There was a parallel decrease in the dynamical complexity of VF as measured by Kolmogorov entropy and Poincaré plots. A period of quasiperiodicity became more evident before the conversion from VF (chaos) to a more regular arrhythmia (periodicity). In conclusion, a decrease in the number of wave fronts in ventricular fibrillation by tissue mass reduction causes a transition from chaotic to periodic dynamics via the quasiperiodic route.
Journal of theoretical biology, 2015
Variability in the action potential of isolated myocytes and tissue samples is observed in experimental studies. Variability is manifested as both differences in the action potential (AP) morphology between cells (extrinsic variability), and also 'intrinsic' or beat-to-beat variability of repolarization (BVR) in the AP duration of each cell. We studied the relative contributions of experimentally recorded intrinsic and extrinsic variability to dispersion of repolarization in tissue. We developed four cell-specific parameterizations of a phenomenological stochastic differential equation AP model exhibiting intrinsic variability using APs recorded from isolated guinea pig ventricular myocytes exhibiting BVR. We performed simulations in tissue using the four different model parameterizations in the presence and the absence of both intrinsic and extrinsic variability. We altered the coupling of the tissue to determine how inter-cellular coupling affected the dispersion of the AP...
Chaos: An Interdisciplinary Journal of Nonlinear Science
The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of $20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincar e plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (I Ks), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noisecurrent into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of timescales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channelnoise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.
PLoS Computational Biology, 2013
Beat-to-beat variability of repolarization duration (BVR) is an intrinsic characteristic of cardiac function and a better marker of proarrhythmia than repolarization prolongation alone. The ionic mechanisms underlying baseline BVR in physiological conditions, its rate dependence, and the factors contributing to increased BVR in pathologies remain incompletely understood. Here, we employed computer modeling to provide novel insights into the subcellular mechanisms of BVR under physiological conditions and during simulated drug-induced repolarization prolongation, mimicking long-QT syndromes type 1, 2, and 3. We developed stochastic implementations of 13 major ionic currents and fluxes in a model of canine ventricular-myocyte electrophysiology. Combined stochastic gating of these components resulted in short-and long-term variability, consistent with experimental data from isolated canine ventricular myocytes. The model indicated that the magnitude of stochastic fluctuations is rate dependent due to the rate dependence of action-potential (AP) duration (APD). This process (the ''active'' component) and the intrinsic nonlinear relationship between membrane current and APD (''intrinsic component'') contribute to the rate dependence of BVR. We identified a major role in physiological BVR for stochastic gating of the persistent Na + current (I Na ) and rapidly activating delayed-rectifier K + current (I Kr ). Inhibition of I Kr or augmentation of I Na significantly increased BVR, whereas subsequent b-adrenergic receptor stimulation reduced it, similar to experimental findings in isolated myocytes. In contrast, b-adrenergic stimulation increased BVR in simulated long-QT syndrome type 1. In addition to stochastic channel gating, AP morphology, APD, and beat-to-beat variations in Ca 2+ were found to modulate single-cell BVR. Cell-to-cell coupling decreased BVR and this was more pronounced when a model cell with increased BVR was coupled to a model cell with normal BVR. In conclusion, our results provide new insights into the ionic mechanisms underlying BVR and suggest that BVR reflects multiple potentially proarrhythmic parameters, including increased ion-channel stochasticity, prolonged APD, and abnormal Ca 2+ handling.
An ionic model for rhythmic activity in small clusters of embryonic chick ventricular cells
AJP: Heart and Circulatory Physiology, 2005
We recorded transmembrane potential in whole cell recording mode from small clusters (2–4 cells) of spontaneously beating 7-day embryonic chick ventricular cells after 1–3 days in culture and investigated effects of the blockers D-600, diltiazem, almokalant, and Ba2+. Electrical activity in small clusters is very different from that in reaggregates of several hundred embryonic chick ventricular cells, e.g., TTX-sensitive fast upstrokes in reaggregates vs. TTX-insensitive slow upstrokes in small clusters (maximum upstroke velocity ∼100 V/s vs. ∼10 V/s). On the basis of our voltage- and current-clamp results and data from the literature, we formulated a Hodgkin-Huxley-type ionic model for the electrical activity in these small clusters. The model contains a Ca2+ current ( ICa), three K+ currents ( IKs, IKr, and IK1), a background current, and a seal-leak current. ICa generates the slow upstroke, whereas IKs, IKr, and IK1 contribute to repolarization. All the currents contribute to spo...