Figure 5 - uploaded by Alan Garfinkel
Content may be subject to copyright.
Transition from periodic state (spiral-wave tachycardia) to a fibrillationlike state in epicardial sheets prepared from canine (A) and human right ventricle (B). A. After induction of sustained reentry in the presence of cromakalim (10 M), the extracellular electrogram showed stable period-1 behavior (beginning of trace), until an external pacing stimulus (at s) shortened the cycle length. After an initial transient instability (indicated by overlying box), the accelerated beats settled into an alternating (period-2) pattern in both the amplitude and period (52 ms alternating with 45 ms) of the spikes. The period-2 pattern continued for several minutes, evolving gradually with accentuation in the difference between amplitudes of the two spikes (right upper trace). However, at the second arrow (right upper trace), a slow modulation of the amplitude and period of the large spike began spontaneously (period-2 modulation), leading to a sudden transition to highly aperiodic fibrillationlike behavior (arrow, left lower trace). The fibrillation-like state persisted for several seconds before spontaneously reverting to the period-2 behavior (arrow, right lower trace). B. A similar sequence recorded from a human right ventricular epicardial sheet preparation in the presence of 10 M cromakalim. In this example, the initial transition (arrow, upper trace) occurred spontaneously, taking the period-1 reentrant tachycardia (cycle length 130 ms) into period-2 behavior through a transient unsettled period (indicated by the overlying box). The period-2 behavior then became progressively modulated (lower trace), reflected by a growing oscillation in the amplitude of the upward spikes (indicated by overlying box), leading to a sudden transition to the fibrillation-like state (arrow).
Source publication
In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillation-like activity in thin sheets of canine and huma...
Contexts in source publication
Context 1
... evidence of quasiperiodicity preceding fibrillation. Direct evidence linking quasiperiodicity and fibrillation came from the epicardial sheet preparations, in which we observed the onset of fibrillation in several instances (Fig. 5). In two cases, one from canine (Fig. 5 A) and one from human (Fig. 5 B) ventricular tissue, fibrillation was preceded by a long epoch of periodic behavior (period-2 or alternans), which then be- came unstable for a few seconds. The instability took the form of growing oscillatory modulations in both amplitude and pe- riod, followed by ...
Context 2
... evidence of quasiperiodicity preceding fibrillation. Direct evidence linking quasiperiodicity and fibrillation came from the epicardial sheet preparations, in which we observed the onset of fibrillation in several instances (Fig. 5). In two cases, one from canine (Fig. 5 A) and one from human (Fig. 5 B) ventricular tissue, fibrillation was preceded by a long epoch of periodic behavior (period-2 or alternans), which then be- came unstable for a few seconds. The instability took the form of growing oscillatory modulations in both amplitude and pe- riod, followed by an abrupt transition to fibrillation. ...
Context 3
... evidence of quasiperiodicity preceding fibrillation. Direct evidence linking quasiperiodicity and fibrillation came from the epicardial sheet preparations, in which we observed the onset of fibrillation in several instances (Fig. 5). In two cases, one from canine (Fig. 5 A) and one from human (Fig. 5 B) ventricular tissue, fibrillation was preceded by a long epoch of periodic behavior (period-2 or alternans), which then be- came unstable for a few seconds. The instability took the form of growing oscillatory modulations in both amplitude and pe- riod, followed by an abrupt transition to fibrillation. Because this modulated behavior ...
Context 4
... maps. In the examples in Fig. 5, detailed spatial activation maps were not obtained during the transition to fi- brillation. Fig. 6 shows another experiment in which the activa- tion sequence was mapped for 3.5 s during the transition from a stable spiral wave to a brief nonsustained fibrillation-like state. During the initial 2.3 s, the core of the spiral wave was ...
Context 5
... with the tip of the spiral wave tracing the trajectory indicated in red in Fig. 6 J. This hyperme- ander (28) led to termination of the spiral wave after only six additional rotations; during this stage the electrograms at all three sites became highly disordered, similar to those observed during the fibrillation-like state in the examples in Fig. 5. Hy- permeander of a single spiral wave has recently been shown in the isolated rabbit heart to produce the electrocardiographic pattern of fibrillation (29). Subsequent breakup of a single me- andering spiral wave into multiple spiral waves may also occur in sustained fibrillation. In the preparations in Fig. 5 B, crude activation ...
Context 6
... state in the examples in Fig. 5. Hy- permeander of a single spiral wave has recently been shown in the isolated rabbit heart to produce the electrocardiographic pattern of fibrillation (29). Subsequent breakup of a single me- andering spiral wave into multiple spiral waves may also occur in sustained fibrillation. In the preparations in Fig. 5 B, crude activation mapping during the fibrillation-like state showed the presence of multiple circulating wavefronts (data not shown). These experimental mapping results further support the relevance of spiral-wave hypermeander and breakup in the computer simulation to genuine cardiac ...
Similar publications
Ventricular fibrillation (VF) remains a major cause of death in the industrialized world. Alternans (a period-doubling bifurcation of cardiac electrical activity) have recently been causally linked to the progression from ventricular tachycardia (VT) to VF, a more spatiotemporally disorganized electrical activity. In this paper, we show how alterna...
Citations
... Cardiovascular and respiratory disorders Cardiac fibrillation, with its complex and disordered patterns, can be seen as a manifestation of Chaos in space and time within the heart muscle (Garfinkel et al. 1997;Cheffer et al. 2021). The chaotic electrical activity can disrupt the normal pumping function of the heart, leading to compromised blood circulation (Gupta et al. 2020(Gupta et al. , 2021Gupta 2023). ...
During the nineties, the Rössler’s have reported in their famous book “Chaos in Physiology,” that “physiology is the mother of Chaos.” Moreover, several researchers have proved that Chaos is a generic characteristic of systems in physiology. In the context of disease, like for example growth of cancer cell populations, Chaos often refers to irregular and unpredictable patterns. In such cases, Chaos signatures can be used to prove the existence of some pathologies. However, for other physiological behaviors, Chaos
is a form of order disguised as disorder and can be a signature of healthy physiological functions. This is for example the case of human brain behavior. As the boundary between health and disease is not always clear-cut in chaotic systems in physiology, some conditions may involve transitions between ordered and
chaotic states. Understanding these transitions and identifying critical points can be crucial for predicting Healthy vs. pathological Chaos. Using recent advances in physiological Chaos and disease dynamics, this survey paper tries to answer the crucial question: when Chaos be a sign of health or disease?
... 5 Additionally, AP alternans have been implicated as a cellular mechanism driving spiral wave break-up in simulations 6 and as a mechanism responsible for complex AP dynamics sustaining ventricular fibrillation. 7,8 Functionally linked to the development of AP alternans, hearts may also develop cytosolic Ca 2+ transient (CaT) alternans, 9 and these in turn mediate the development of mechanical and pulsus alternans. [10][11][12] The relationship between TWA, AP alternans, pulsus alternans, and CaT alternans is complex. ...
Background
Action potential (AP) alternans are linked to increased arrhythmogenesis. It is suggested that calcium (Ca ²⁺ ) transient (CaT) alternans cause AP alternans through bi-directional coupling feedback mechanisms because CaT alternans can precede AP alternans and develop in AP alternans free conditions. However, the CaT is an emergent response to intracellular Ca ²⁺ handling, and the mechanisms linking AP and CaT alternans are still a topic of investigation. This study investigated the development of AP alternans in the absence of CaT.
Methods
AP (patch clamp) and intracellular Ca ²⁺ (Fluo-4 epifluorescence) were recorded simultaneously from isolated rabbit ventricle myocytes perfused with the intracellular Ca ²⁺ buffer BAPTA (10-20 mM) to abolish CaT and/or the L-type Ca2+ channel activator Bay K 8644 (25 nM).
Results
After a rate change, alternans were critically damped and stable, overdamped and ceased over seconds, underdamped with longer scale harmonics, or unstably underdamped progressing to 2:1 capture. Alternans in control cells were predominantly critically damped, but after CaT ablation with 10 or 20 mM BAPTA, exhibited respectively increased overdamping or increased underdamping. Alternans were easier to induce in CaT free cells as evidenced by a higher alternans threshold (ALT-TH: at least 7 pairs of alternating beats) relative to control cells. Alternans in Bay K 8644 treated cells were often underdamped, but the ALT-TH was similar to control. In CaT ablated cells, Bay K 8644 prolonged AP duration (APD) leading predominantly to unstably underdamped alternans.
Conclusions
AP alternans occur more readily in the absence of CaT suggesting that the CaT dampens the development of AP alternans. The data further demonstrate that agonizing the L-type calcium current without the negative feedback of the CaT leads to unstable alternans. This negative feedback mechanism may be important for understanding treatments aimed at reducing CaT or its dynamic response to prevent arrhythmias.
... In the heart muscle, they underlie dangerous cardiac rhythm disturbances and usually have to be eliminated [3][4][5]. In the arrhythmia diagnostics and treatment, spiral wave cycle length (CL) and dynamics play an important role, as they can determine the type of arrhythmia [6,7]. ...
One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside Tout and inside Tin the meandering trajectory with a ratio of Tin/Tout=(n+1)/n for the inward and (n−1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.
... Recently, a model based on a discretized reaction-diffusion system to reproduce electrocardiograms from healthy hearts and various rhythm disorders was introduced [38]. Since the model presents chaotic behavior, it was associated with ventricular fibrillation, which arises from a normal rhythm through the so-called Ruelle-Takens-Newhouse scenario [49], as experimental studies suggest [50,51]. ...
In this work, we propose a versatile, low-cost, and tunable electronic device to generate realistic electrocardiogram (ECG) waveforms, capable of simulating ECG of patients within a wide range of possibilities. A visual analysis of the clinical ECG register provides the cardiologist with vital physiological information to determine the patient’s heart condition. Because of its clinical significance, there is a strong interest in algorithms and medical ECG measuring devices that acquire, preserve, and process ECG recordings with high fidelity. Bearing this in mind, the proposed electronic device is based on four different mathematical models describing macroscopic heartbeat dynamics with ordinary differential equations. Firstly, we produce full 12-lead ECG profiles by implementing a model comprising a network of heterogeneous oscillators. Then, we implement a discretized reaction–diffusion model in our electronic device to reproduce ECG waveforms from various rhythm disorders. Finally, in order to show the versatility and capabilities of our system, we include two additional models, a ring of three coupled oscillators and a model based on a quasiperiodic motion, which can reproduce a wide range of pathological conditions. With this, the proposed device can reproduce around thirty-two cardiac rhythms with the possibility of exploring different parameter values to simulate new arrhythmias with the same hardware. Our system, which is a hybrid analog–digital circuit, generates realistic ECG signals through digital-to-analog converters whose amplitudes and waveforms are controlled through an interactive and friendly graphic interface. Our ECG patient simulator arises as a promising platform for assessing the performance of electrocardiograph equipment and ECG signal processing software in clinical trials. Additionally the produced 12-lead profiles can be tested in patient monitoring systems.
... Heart rate variability (HRV) in paroxysmal or persistent AF is not well studied, and some studies describe HRV in AF as chaotic and unpredictable [1]- [3]. However, without any doubts, ECG of atrial fibrillation is unique for each patient, and ranges of HRV indices also differ between patients with AF. ...
Heart rate variability (HRV) indices describe properties of interbeat intervals in electrocardiogram (ECG). Usually HRV is measured exclusively in normal sinus rhythm (NSR) excluding any form of paroxysmal rhythm. Atrial fibrillation (AF) is the most widespread cardiac arrhythmia in human population. Usually such abnormal rhythm is not analyzed and assumed to be chaotic and unpredictable. Nonetheless, ranges of HRV indices differ between patients with AF, yet physiological characteristics which influence them are poorly understood. In this study, we propose a statistical model that describes relationship between HRV indices in NSR and AF. The model is based on Mahalanobis distance, the k-Nearest neighbour approach and multivariate normal distribution framework. Verification of the method was performed using 10 min intervals of NSR and AF that were extracted from long-term Holter ECGs. For validation we used Bhattacharyya distance and Kolmogorov-Smirnov 2-sample test in a k-fold procedure. The model is able to predict at least 7 HRV indices with high precision.
... Chaotic systems are nonlinear dynamical systems, whose outputs are pseudo-stochastic and quasi-periodic [8]. Therefore, introducing distinctive measures to distinguish between chaotic time-series and stochastic or periodic data could become quite challenging. ...
In this paper, the problem of entropy-based classification of time-series into stochastic, chaotic, and periodic is addressed, followed by proposing an alternative joint-entropy approach to time series classification. These data-driven methods describe the behavior of a signal, using the association of the entropy of a time-series with emergence and self-organization, as complex systems characteristics. First, we deduce that certain groups of entropies, namely Fuzzy entropy, and Distribution entropy, share more similarities with emergence, while permutation and dispersion entropies could be associated with self-organization. Then, we utilize these resemblances to propose a joint-entropy alternative approach, in which one of the specific entropies is presented for each characteristic. Further, in simulations, we evaluated the performance of our proposed approach, comparing with single entropy methods, using different classifiers and decision boundaries. The results reveal an excellent performance of 98% accuracy for simultaneous utilization of the Distribution and Permutation entropies as the input features of Random Forest classifier, while this value is at best 89% for when only a single entropy is fed to the classifier.
... We can see that the periodicity of the ECG signals is strongly modulated by the LF/HF ratio changes ( Figure 5C). As the LF/HF ratio increases, the RPs lose vertical dot structures, indicating an increase in stochasticity (Garfinkel et al., 1997;Schauerte et al., 2001;Chen et al., 2014). It is important to mention that a healthy heart does not exhibit a purely deterministic dynamic. ...
A classic method to evaluate autonomic dysfunction is through the evaluation of heart rate variability (HRV). HRV provides a series of coefficients, such as Standard Deviation of n-n intervals (SDNN) and Root Mean Square of Successive Differences (RMSSD), which have well-established physiological associations. However, using only electrocardiogram (ECG) signals, it is difficult to identify proper autonomic activity, and the standard techniques are not sensitive and robust enough to distinguish pure autonomic modulation in heart dynamics from cardiac dysfunctions. In this proof-of-concept study we propose the use of Poincaré mapping and Recurrence Quantification Analysis (RQA) to identify and characterize stochasticity and chaoticity dynamics in ECG recordings. By applying these non-linear techniques in the ECG signals recorded from a set of Parkinson’s disease (PD) animal model 6-hydroxydopamine (6-OHDA), we showed that they present less variability in long time epochs and more stochasticity in short-time epochs, in their autonomic dynamics, when compared with those of the sham group. These results suggest that PD animal models present more “rigid heart rate” associated with “trembling ECG” and bradycardia, which are direct expressions of Parkinsonian symptoms. We also compared the RQA factors calculated from the ECG of animal models using four computational ECG signals under different noise and autonomic modulatory conditions, emulating the main ECG features of atrial fibrillation and QT-long syndrome.
... Due to the difficulties for conducting myocardial conduction studies in vivo, in silico models have been developed, such as the Ten Tusscher-Noble-Noble-Panfilov (TNNP) model, which allows to reproduce myocardial initial excitable conditions and see the effect on wave front propagation, even on a three-dimensional plane (Fig. 5) 26 . Among other findings, ventricular tachycardia has been observed to be associated with the formation of a spiral wave front that propagates through the myocardium, while, in ventricular fibrillation, these patterns have a much more turbulent behavior, associated with heterogeneity in muscle fiber shape and ion concentrations [27][28][29][30][31] . ...
The science-based study of the heart has allowed us to know its structure and function deeply, through the fragmentation and analysis of its parts, following the guidelines that so many achievements have given to us. However, at the time of reassembling those analyzed fragments, we realize that something is missing; the simply sum of the parts is not equal to everything. Thus, for decades, numerous scientists have studied novel strategies that allow us understanding, every natural phenomena from a more inclusive, open and integrative models, which closely address to interactions rather than components. In this way, we can observe how, the behavior of many variables usually transgress the conventional plane and moves towards non-linearity and fractality, making a complex tissue that will maintain its structure while thermodynamically viable. Thus, this document shows the way how, the non-linear study of complex cardiovascular dynamics, begins to give us answers to many questions that the clinical cardiologist poses every day.
... We can see that the periodicity of the ECG signals is strongly modulated by the LF/HF ratio changes ( Fig. 4.C). As the LF/HF ratio increases, the RPs lose vertical dot structures, indicating an increase in stochasticity [51,55,56]. It is important to mention that a healthy heart does not exhibit a purely deterministic dynamic. ...
... corroborating Poincaré maps [26,27,50]. Furthermore, a decrease in heart rate tends to increase the periodicity of the signal, which can be promoted by PD bradycardia [51]. ...
A classic method to evaluate autonomic dysfunction is through the evaluation of heart rate variability (HRV). HRV provides a series of coefficients, such as SDNN (Standard Deviation of n-n intervals) and RMSSD (Root Mean Square of Successive Differences), which have well-established physiological associations. However, using only electrocardiogram (ECG) signals, it is difficult to identify proper autonomic activity, and the standard techniques are not sensitive and robust enough to distinguish pure autonomic modulation in heart dynamics from cardiac dysfunctions. By using Poincaré mapping and Recurrence Quantification Analysis (RQA), we were able to identify and characterize stochasticity and chaoticity dynamics in ECG recordings, using them to describe autonomic and heart dynamics. By applying these nonlinear techniques in the ECG signals recorded from a set of Parkinson disease animal model (6-OHDA), we show they present less variability in long time epochs and more stochasticity in short-time epochs, in their autonomic dynamics, when compared with those of the sham group. These results indicate that PD (Parkinson’s Disease) animal models present more “rigid heart rate” associated with “trembling ECG” and bradycardia, which are direct expressions of Parkinsonian symptoms. We also compared the RQA factors calculated from the ECG of animal models using four computational ECG signals under different noise and autonomic modulatory conditions, emulating atrial fibrillation and QT-long syndrome. We concluded, from Poincaré Map and RQA techniques, that PD animal models are more correlated with atrial fibrillation, with high variation according to autonomic modulation. As the Abstract should be able stand independantly of the main text, please do not abbreviate terms used only once in the Abstract.
... 50,51 This breakdown in coherence has been conceptualised as a conservative, non-dissipative form of chaos. [52][53][54] In our study, we reasoned that, given the highly disorganised nature of AF, the formation and destruction of re-entrant circuits in AF could reasonably be considered statistically independent events. 17 Our suggested rationale for this proposition is that because of the disorganised nature of AF, where wave propagation is disaggregated, events in one part of the chamber are effectively statistically independent of events in other parts of the atrial chamber. ...
Despite a century of research, the mechanisms of AF remain unresolved. A universal motif within AF research has been unstable re-entry, but this remains poorly characterised, with competing key conceptual paradigms of multiple wavelets and more driving rotors. Understanding the mechanisms of AF is clinically relevant, especially with regard to treatment and ablation of the more persistent forms of AF. Here, the authors outline the surprising but reproducible finding that unstable re-entrant circuits are born and destroyed at quasi-stationary rates, a finding based on a branch of mathematics known as renewal theory. Renewal theory may be a way to potentially unify the multiple wavelet and rotor theories. The renewal rate constants are potentially attractive because they are temporally stable parameters of a defined probability distribution (the exponential distribution) and can be estimated with precision and accuracy due to the principles of renewal theory. In this perspective review, this new representational architecture for AF is explained and placed into context, and the clinical and mechanistic implications are discussed.
