Deterministic nonlinearity in ventricular fibrillation

We provide numerical evidence that the electrocardiogram data collected from pigs during induced ventricular fibrillation cannot be described by a monotonic nonlinear transformation of linearly filtered noise. To establish this we use surrogate techniques and apply two test statistics: (1) the Takens' maximum likelihood estimator of the Grassberger-Procaccia correlation dimension and (2) an improved correlation dimension estimation routine. The improved dimension estimates provide evidence that the correlation dimension of the underlying dynamics during the episode of VF in the first 30 s is slightly less than 6. This result is consistent and reproducible among subjects. (c) 2000 American Institute of Physics.     

Symbolic dynamics of ventricular tachycardia and ventricular fibrillation

In this paper, the symbolic dynamics analysis was used to analyze the complexity of normal heartbeat signal (NSR), Ventricular tachycardia (VT) and ventricular fibrillation (VF) signals. By calculating the information entropy value of symbolic sequences, the complexities were quantified. Based on different information entropy values, NSR, VT and VF signals were distinguished with satisfactory results. The study showed that a sudden drop of symbolic sequence’s entropy value indicated that the patients most likely entered the episode of ventricular tachycardia and this was a crucial episode for the clinical treatment of patients. It had important clinical significance for the automatic diagnosis.     

Spatial organization in two-species annihilation

The spatial structure of reactants in the two-species annihilation reaction A+B0 is described. In one dimension, we investigate the distribution of domain sizes and the distributions of nearest-neighbor distances between particles of the same and of opposite species. The latter two quantities are characterized by a new length scale which is intermediate to the domain size t^1/2 and the typical interparticle spacing t^1/4. A scaling argument suggests that the typical distance between particles of opposite species, or equivalently the gaps between domains, grows ast , with = 3/8 and 1/3, respectively, in spatial dimensiond=1 and 2. The average density profile of a single domain is spatially nonuniform, with the density decaying to zero linearly as the domain edge is approached. This behavior permits a determination of the distribution of nearest-neighbor distances of same-species reactants. The corresponding moments of this distribution exhibit multiscaling which involves geometric averages of different powers of the domain size and the interparticle spacing.     

Vulnerability to ventricular fibrillation

One of the factors that favors the development of ventricular fibrillation is an increase in the dispersion of refractoriness. Experiments will be described in which an increase in dispersion in the recovery of excitability was determined during brief episodes of enhanced sympathetic nerve activity, known to increase the risk of fibrillation. Whereas in the normal heart ventricular fibrillation can be induced by a strong electrical shock, a premature stimulus of moderate intensity only induces fibrillation in the presence of regional ischemia, which greatly increases the dispersion of refractoriness. One factor that is of importance for the transition of reentrant ventricular tachycardia to ventricular fibrillation during acute regional ischemia is the subendocardial Purkinje system. After selective destruction of the Purkinje network by lugol, reentrant tachycardias still develop in the ischemic region, but they do not degenerate into fibrillation. Finally, attempts were made to determine the minimal mass of thin ventricular myocardium required to sustain fibrillation induced by burst pacing. This was done by freezing of subendocardial and midmural layers. The rim of surviving epicardial muscle had to be larger than 20 g. Extracellular electrograms during fibrillation in both the intact and the "frozen" left ventricle were indistinguishable, but activation patterns were markedly different. In the intact ventricle epicardial activation was compatible with multiple wavelet reentry, in the "frozen" heart a single, or at most two wandering reentrant waves were seen. (c) 1998 American Institute of Physics.     

Faux-boolean algebras,classical probability,and determinism

It is possible to define, for any quantum system, an algebra of definite-valued events—those events that are definitely occurrent or non-occurrent. It is shown that two different sets of constraints on the algebra of definite-valued events are each equivalent to the definition of that set as a certain pseudo-Boolean algebra.     

Computerized mapping of fibrillation in normal ventricular myocardium

It is well known that the ability to fibrillate is intrinsic to a normal ventricle that exceeds a critical mass. The questions we address are how is ventricular fibrillation (VF) initiated and perpetuated in normal myocardium, and why is VF not seen more often in the general population if all ventricles have the ability to fibrillate. To study the mechanisms of VF, we used computerized mapping techniques with up to 512 channels of simultaneous multisite recordings for data acquisition. The data were then processed for dynamic display of the activation patterns and for mathematical analyses of the activation intervals. The results show that in normal ventricles, VF can be initiated by a single strong premature stimulus given during the vulnerable period of the cardiac cycle. The initial activations form a figure-eight pattern. Afterward, VF will perpetuate itself without any outside help. The self-perpetuation itself is due to at least two factors. One is that single wave fronts spontaneously break up into two or more wavelets. The second is that when two wavelets intersect perpendicular to each other, the second wavelet is broken by the residual refractoriness left over from the first wavelet. Mathematical analyses of the patterns of activation during VF revealed that VF is a form of chaos, and that transition from ventricular tachycardia (VT) to VF occurs via the quasiperiodic route. In separate experiments, we found that we can convert VF to VT by tissue size reduction. The physiological mechanism associated with the latter transition appears to be the reduction of the number of reentrant wave fronts and wandering wavelets. Based on these findings, we propose that the reentrant wave fronts and the wandering wavelets serve as the physiological equivalent of coupled oscillators. A minimal number of oscillators is needed for VF to perpetuate itself, and to generate chaotic dynamics; hence a critical mass is required to perpetuate VF. We conclude that VF in normal myocardium is a form of reentrant cardiac arrhythmia. A strong electrical stimulus initiates single or dual reentrant wave fronts that break up into multiple wavelets. Sometimes short-lived reentry is also generated during the course of VF. These organized reentrant and broken wavelets serve as coupled oscillators that perpetuate VF and maintain chaos. Although the ability to support these oscillators exists in a normal ventricle, the triggers required to generate them are nonexistent in the normal heart. Therefore, VF and sudden death do not happen to most people with normal ventricular myocardium. (c) 1998 American Institute of Physics.     

Self-organization and the dynamical nature of ventricular fibrillation

This article reviews recent data supporting the conjecture that, in the structurally and electrophysiologically normal heart, cardiac fibrillation is not a totally random phenomenon. Experimental and numerical studies based on the theory of excitable media suggest that fibrillation in the mammalian ventricles is the result of self-organized three-dimensional (3-D) electrical rotors giving rise to scroll waves that move continuously (i.e., drift) throughout the heart at varying speeds. A brief review of studies on the dynamics of rotors in two-dimensional (2-D) and 3-D excitable media is presented with emphasis on the experimental demonstration of such dynamics in cardiac muscle of various species. The discussion is centered on rotor dynamics in the presence and the absence of structural heterogeneities, and in the phenomena of drifting and anchoring, which in the electrocardiogram (ECG) may manifest as life-threatening cardiac rhythm disturbances. For instance, in the rabbit heart, a single electrical rotor that drifts rapidly throughout the ventricles gives rise to complex patterns of excitation. In the ECG such patterns are indistinguishable from ventricular fibrillation. On the other hand, a rotor that anchors to a discontinuity or defect in the muscle (e.g., a scar, a large artery or a bundle of connective tissue) may result in stationary rotating activity, which in the ECG is manifested as a form of so-called "monomorphic" ventricular tachycardia. More recent data show that ventricular fibrillation occurs in mammals irrespective of size or species. While in small hearts, such as those of mice and rabbits, a single drifting or meandering rotor can result in fibrillation, in larger hearts, such as the sheep and possibly the human, fibrillation occurs in the form of a relatively small number of coexisting but short-lived rotors. Overall, the work discussed here has paved the way for a better understanding of the mechanisms of fibrillation in the normal, as well as diseased human heart. (c) 1998 American Institute of Physics.     

Atomicity and determinism in Boolean systems

The logic of a Boolean system of finite degrees of freedom is shown to be atomic if and only if the system obeys a deterministic theory. This is, therefore, the physical meaning of atomicity. Furthermore, it is proved that nondeterminacy of such a system implies the nonexistence of phase space.     

Spiral breakup as a model of ventricular fibrillation

The phenomenon of spiral breakup in a 2D and a 3D excitable medium is described. Differences between breakup in two dimensions and in three dimensions are discussed. Spiral breakup in an anatomical model of the ventricles of the heart is also studied. The patterns of excitation in the heart are presented at different wavelengths together with their electrocardiograms. Finally it is suggested that the phenomenon of spiral breakup is a possible mechanism of the ventricular fibrillation (VF). (c) 1998 American Institute of Physics.     

Test for low-dimensional determinism in electroencephalograms

We tested low-dimensional determinism in an electroencephalogram (EEG), based on the fact that smoothness (continuity) on an embedded phase space is enough to imply determinism within time series. A modified version of the method developed by Salvino and Cawley [Phys. Rev. Lett. 73, 1091 (1994)] was used. In our method, we chose a box randomly and then estimated the mean directional element in the box containing the d+1 data points, where d is the embedding dimension. The global average for the mean local directional elements over the boxes, W, is a measure for smoothness. The nonlinear noise reduction method developed by Sauer [Physica D 58, 193 (1992)] is then applied to the EEG. We also compared the results for the EEG with those for its surrogate data. We found that the W values for the noise-reduced EEG had stable values around 0.35, which means that the EEG is not a low-dimensional deterministic signal. However, this method may not be applicable to the time series generated from high-dimensional deterministic systems. We cannot exclude the possibility that the determinism in the EEG may be too high-dimensional to be detected with current methods.     

Reply to “determinism,realism, and Stapp's 1985 proof of nonlocality”

It is shown that the objections raised in the cited paper are to features not present in my proof.     

Comments on “determinism,realism, and Stapp's 1985 proof of nonlocality”

An earlier argument by the author, that Stapp's 1985 proof of quantum locality contains an implicit element of realism, is elaborated. Refuted thereby is Clifton's criticism that the author's argument was based on a misinterpretation of counterfactual analysis.     

Investigation of determinism in heart rate variability

The article searches for the possible presence of determinism in heart rate variability (HRV) signals by using a new approach based on NARMA (nonlinear autoregressive moving average) modeling and free-run prediction. Thirty-three 256-point HRV time series obtained from Wistar rats submitted to different autonomic blockade protocols are considered, and a collection of surrogate data sets are generated from each one of them. These surrogate sequences are assumed to be nondeterministic and therefore they may not be predictable. The original HRV time series and related surrogates are submitted to NARMA modeling and prediction. Special attention has been paid to the problem of stationarity. The results consistently show that the surrogate data sets cannot be predicted better than the trivial predictor-the mean-while most of the HRV control sequences are predictable to a certain degree. This suggests that the normal HRV signals have a deterministic signature. The HRV time series derived from the autonomic blockade segments of the experimental protocols do not show the same predictability performance, albeit the physiological interpretation is not obvious. These results have important implications to the methodology of HRV analysis, indicating that techniques from nonlinear dynamics and deterministic chaos may be applied to elicit more information about the autonomic modulation of the cardiovascular activity. (c) 2000 American Institute of Physics.     

Bistability,basins of attraction and predictability in a forced mass-reaction model

A simple mass-reaction model with periodically forced contact rate is considered. It is shown that the forced differential equation exhibits at least two distinct periodic orbits for several ranges of forcing amplitude. Basins of attraction are computed for co-existing stable periodic orbits and are shown to be intertwined in a complex manner. Dimension (capacity) of the basin is computed, and it is shown how the basin structure affects final state predictability.     

Local order, entropy and predictability of financial time series

We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea is that in spite of the high stochasticity in average there might be special local situations where there local order exist and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the uncertainty/predictability and the distribution of these quantities. Received 19 January 2000