Quasiperiodicity and chaos in cardiac fibrillation

Perspective on equal and cross-frequency neural coupling: Integration and segregation of the function of brain networks

We introduce a perspective that has not appeared before in the field of equal and multifrequency coupling derived from considering neuronal synchrony as a possible equivalence relation. The experimental results agree with the theoretical prediction that cross-frequency coupling results in a partition of the brain synchrony state space. We place these results in the framework of the integration and segregation of information in the processing of sensorimotor transformations by the brain cell circuits and propose that equal-frequency (1:1) connectivity favors integration of information in the brain whereas cross-frequency coupling (n:m) favors segregation. These observations may provide an outlook about how to reconcile the need for stability in the brain's operations with the requirement for diversity of activity in order to process many sensorimotor transformations simultaneously.

The calcium transient coupled to the L-type calcium current attenuates cardiac alternans

Cardiac action potential (AP) alternans have been linked to the development of arrhythmia. AP alternans may be driven by AP instabilities, Ca2+ transient (CaT) instabilities, or both. The mechanisms underlying CaT driven AP alternans is well-supported experimentally, but the ionic mechanism underlying alternans driven by AP instabilities remain incompletely understood. Here we used the Ca2+ buffer BAPTA to remove the CaT and generate a model of AP alternans driven primarily by AP instabilities. In isolated rabbit ventricle myocytes, AP alternans induced by rapid pacing were either critically damped and persisted over time, overdamped and ceased over seconds, or underdamped progressing to 2:1 capture. Control cells predominantly exhibited critically damped alternans. In contrast, removing CaT with BAPTA destabilized alternans formation in a concentration dependent manner. Importantly, alternans were easier to induce in CaT free cells as evidenced by a higher alternans threshold relative to control cells. While the L-type Ca2+ channel agonist Bay K 8644 had a minor effect on alternans formation in myocytes with conserved CaT, combining the agonist with BAPTA markedly promoted the formation of underdamped alternans and increased the alternans threshold more than four-fold as compared to controls. Our data support a mechanistic model in which AP alternans are a primary self-sustained event in which the CaT serves as a dampening cue that curbs alternans development, likely via a canonical negative feedback process involving Ca2+ induced inhibition of L-type Ca2+ current.

Review of chaos in hair-cell dynamics

The remarkable signal-detection capabilities of the auditory and vestibular systems have been studied for decades. Much of the conceptual framework that arose from this research has suggested that these sensory systems rest on the verge of instability, near a Hopf bifurcation, in order to explain the detection specifications. However, this paradigm contains several unresolved issues. Critical systems are not robust to stochastic fluctuations or imprecise tuning of the system parameters. Further, a system poised at criticality exhibits a phenomenon known in dynamical systems theory as critical slowing down, where the response time diverges as the system approaches the critical point. An alternative description of these sensory systems is based on the notion of chaotic dynamics, where the instabilities inherent to the dynamics produce high temporal acuity and sensitivity to weak signals, even in the presence of noise. This alternative description resolves the issues that arise in the criticality picture. We review the conceptual framework and experimental evidence that supports the use of chaos for signal detection by these systems, and propose future validation experiments.

Are physiological oscillations physiological?

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic β-cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re-thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory ('pacemaking') mechanisms at the cellular, tissue and system levels.

The Calcium Transient Coupled to the L-Type Calcium Current Attenuates Action Potential Alternans

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.

Meander pattern of spiral wave and the spatial distribution of its cycle length

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 T^{out} and inside T^{in} the meandering trajectory with a ratio of T^{in}/T^{out}=(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.

ECG Patient Simulator Based on Mathematical Models

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.

Understanding the origins of the basic equations of statistical fibrillatory dynamics

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with conservative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker's transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pattern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.

Cardiac and Autonomic Dysfunctions Assessed Through Recurrence Quantitative Analysis of Electrocardiogram Signals and an Application to the 6-Hydroxydopamine Parkinson's Disease Animal Model

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.

Reconceptualising Atrial Fibrillation Using Renewal Theory: A Novel Approach to the Assessment of Atrial Fibrillation Dynamics

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.

Complexus cordis

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.

Flickering of cardiac state before the onset and termination of atrial fibrillation

Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.

Early Signs of Critical Slowing Down in Heart Surface Electrograms of Ventricular Fibrillation Victims

Ventricular fibrillation (VF) is a dangerous type of cardiac arrhythmia which, without intervention, almost always results in sudden death. Implantable automatic defibrillators are among the most successful devices to prevent sudden death by automatically applying a shock to the heart when fibrillation occurs. However, the electric shock is very painful and could lead to dangerous situations when a patient is, for example, driving or biking. An early warning signal for VF could reduce the risk in such situations or, in the future, reduce the need for defibrillation altogether. Here, we test for the presence of critical slowing down (CSD), which has proven to be an early warning indicator for critical transitions in a range of different systems. CSD is characterized by a buildup of autocorrelation; we therefore study the residuals of heart surface electrocardiograms (ECGs) of patients that suffered VF to investigate if we can measure positive trends in autocorrelation. We consider several methods to extract these residuals from the original signals. For three out of four VF victims, we find a significant amount of positive autocorrelation trends in the residuals, which might be explained by CSD. We show that these positive trends may not be measurable from the original body surface ECGs, but only from certain areas around the heart surface. We argue that additional experimental studies involving heart surface ECG data of subjects that did not suffer VF are required to quantify the prediction accuracy of the promising results we get from the data of VF victims.

Generation of ECG signals from a reaction-diffusion model spatially discretized

We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is shown that under ventricular fibrillation, the electrocardiogram signal is chaotic and the transition from sinus rhythm to chaos is consistent with the Ruelle-Takens-Newhouse route to chaos, as experimental studies indicate. The proposed model constitutes a useful tool for research, medical education, and clinical testing purposes. An electronic device based on the model was built for these purposes

Renewal Theory as a Universal Quantitative Framework to Characterize Phase Singularity Regeneration in Mammalian Cardiac Fibrillation

BACKGROUND

Despite a century of research, no clear quantitative framework exists to model the fundamental processes responsible for the continuous formation and destruction of phase singularities (PS) in cardiac fibrillation. We hypothesized PS formation/destruction in fibrillation could be modeled as self-regenerating Poisson renewal processes, producing exponential distributions of interevent times governed by constant rate parameters defined by the prevailing properties of each system.

METHODS

PS formation/destruction were studied in 5 systems: (1) human persistent atrial fibrillation (n=20), (2) tachypaced sheep atrial fibrillation (n=5), (3) rat atrial fibrillation (n=4), (5) rat ventricular fibrillation (n=11), and (5) computer-simulated fibrillation. PS time-to-event data were fitted by exponential probability distribution functions computed using maximum entropy theory, and rates of PS formation and destruction (λ_f/λ_d) determined. A systematic review was conducted to cross-validate with source data from literature.

RESULTS

In all systems, PS lifetime and interformation times were consistent with underlying Poisson renewal processes (human: λ_f, 4.2%/ms±1.1 [95% CI, 4.0-5.0], λ_d, 4.6%/ms±1.5 [95% CI, 4.3-4.9]; sheep: λ_f, 4.4%/ms [95% CI, 4.1-4.7], λ_d, 4.6%/ms±1.4 [95% CI, 4.3-4.8]; rat atrial fibrillation: λ_f, 33%/ms±8.8 [95% CI, 11-55], λ_d, 38%/ms [95% CI, 22-55]; rat ventricular fibrillation: λ_f, 38%/ms±24 [95% CI, 22-55], λ_f, 46%/ms±21 [95% CI, 31-60]; simulated fibrillation λ_d, 6.6-8.97%/ms [95% CI, 4.1-6.7]; R²≥0.90 in all cases). All PS distributions identified through systematic review were also consistent with an underlying Poisson renewal process.

CONCLUSIONS

Poisson renewal theory provides an evolutionarily preserved universal framework to quantify formation and destruction of rotational events in cardiac fibrillation.

Chaotic Dynamics Enhance the Sensitivity of Inner Ear Hair Cells

Hair cells of the auditory and vestibular systems are capable of detecting sounds that induce sub-nanometer vibrations of the hair bundle, below the stochastic noise levels of the surrounding fluid. Furthermore, the auditory system exhibits a highly rapid response time, in the sub-millisecond regime. We propose that chaotic dynamics enhance the sensitivity and temporal resolution of the hair bundle response, and we provide experimental and theoretical evidence for this effect. We use the Kolmogorov entropy to measure the degree of chaos in the system and the transfer entropy to quantify the amount of stimulus information captured by the detector. By varying the viscosity and ionic composition of the surrounding fluid, we are able to experimentally modulate the degree of chaos observed in the hair bundle dynamics in vitro. We consistently find that the hair bundle is most sensitive to a stimulus of small amplitude when it is poised in the weakly chaotic regime. Further, we show that the response time to a force step decreases with increasing levels of chaos. These results agree well with our numerical simulations of a chaotic Hopf oscillator and suggest that chaos may be responsible for the high sensitivity and rapid temporal response of hair cells.

Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. Modeling

In a companion paper (I. Multifractal analysis of clinical data), we used a wavelet-based multiscale analysis to reveal and quantify the multifractal intermittent nature of the cardiac impulse energy in the low frequency range ≲ 2Hz during atrial fibrillation (AF). It demarcated two distinct areas within the coronary sinus (CS) with regionally stable multifractal spectra likely corresponding to different anatomical substrates. The electrical activity also showed no sign of the kind of temporal correlations typical of cascading processes across scales, thereby indicating that the multifractal scaling is carried by variations in the large amplitude oscillations of the recorded bipolar electric potential. In the present study, to account for these observations, we explore the role of the kinetics of gap junction channels (GJCs), in dynamically creating a new kind of imbalance between depolarizing and repolarizing currents. We propose a one-dimensional (1D) spatial model of a denervated myocardium, where the coupling of cardiac cells fails to synchronize the network of cardiac cells because of abnormal transjunctional capacitive charging of GJCs. We show that this non-ohmic nonlinear conduction 1D modeling accounts quantitatively well for the "multifractal random noise" dynamics of the electrical activity experimentally recorded in the left atrial posterior wall area. We further demonstrate that the multifractal properties of the numerical impulse energy are robust to changes in the model parameters.

Noise-induced chaos and signal detection by the nonisochronous Hopf oscillator

The Hopf oscillator has been shown to capture many phenomena of the auditory and vestibular systems. These systems exhibit remarkable temporal resolution and sensitivity to weak signals, as they are able to detect sounds that induce motion in the angstrom regime. In the present work, we find the analytic response function of a nonisochronous Hopf oscillator to a step stimulus and show that the system is most sensitive in the regime where noise induces chaotic dynamics. We show that this regime also provides a faster response and enhanced temporal resolution. Thus, the system can detect a very brief, low-amplitude pulse. Finally, we subject the oscillator to periodic delta-function forcing, mimicking a spike train, and find the exact analytic expressions for the stroboscopic maps. Using these maps, we find a period-doubling cascade to chaos with increasing force strength.

Analytical approaches for myocardial fibrillation signals

Atrial and ventricular fibrillation are complex arrhythmias, and their underlying mechanisms remain widely debated and incompletely understood. This is partly because the electrical signals recorded during myocardial fibrillation are themselves complex and difficult to interpret with simple analytical tools. There are currently a number of analytical approaches to handle fibrillation data. Some of these techniques focus on mapping putative drivers of myocardial fibrillation, such as dominant frequency, organizational index, Shannon entropy and phase mapping. Other techniques focus on mapping the underlying myocardial substrate sustaining fibrillation, such as voltage mapping and complex fractionated electrogram mapping. In this review, we discuss these techniques, their application and their limitations, with reference to our experimental and clinical data. We also describe novel tools including a new algorithm to map microreentrant circuits sustaining fibrillation.

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.

Characterization of human persistent atrial fibrillation electrograms using recurrence quantification analysis

Atrial fibrillation (AF) is regarded as a complex arrhythmia, with one or more co-existing mechanisms, resulting in an intricate structure of atrial activations. Fractionated atrial electrograms (AEGs) were thought to represent arrhythmogenic tissue and hence have been suggested as targets for radiofrequency ablation. However, current methods for ablation target identification have resulted in suboptimal outcomes for persistent AF (persAF) treatment, possibly due to the complex spatiotemporal dynamics of these mechanisms. In the present work, we sought to characterize the dynamics of atrial tissue activations from AEGs collected during persAF using recurrence plots (RPs) and recurrence quantification analysis (RQA). 797 bipolar AEGs were collected from 18 persAF patients undergoing pulmonary vein isolation (PVI). Automated AEG classification (normal vs. fractionated) was performed using the CARTO criteria (Biosense Webster). For each AEG, RPs were evaluated in a phase space estimated following Takens' theorem. Seven RQA variables were obtained from the RPs: recurrence rate; determinism; average diagonal line length; Shannon entropy of diagonal length distribution; laminarity; trapping time; and Shannon entropy of vertical length distribution. The results show that the RQA variables were significantly affected by PVI, and that the variables were effective in discriminating normal vs. fractionated AEGs. Additionally, diagonal structures associated with deterministic behavior were still present in the RPs from fractionated AEGs, leading to a high residual determinism, which could be related to unstable periodic orbits and suggesting a possible chaotic behavior. Therefore, these results contribute to a nonlinear perspective of the spatiotemporal dynamics of persAF.

Is human atrial fibrillation stochastic or deterministic?-Insights from missing ordinal patterns and causal entropy-complexity plane analysis

The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10^-3 vs. 7.79 × 10^-3, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.

Chaotic Dynamics of Inner Ear Hair Cells

Experimental records of active bundle motility are used to demonstrate the presence of a low-dimensional chaotic attractor in hair cell dynamics. Dimensionality tests from dynamic systems theory are applied to estimate the number of independent variables sufficient for modelling the hair cell response. Poincaré maps are constructed to observe a quasiperiodic transition from chaos to order with increasing amplitudes of mechanical forcing. The onset of this transition is accompanied by a reduction of Kolmogorov entropy in the system and an increase in transfer entropy between the stimulus and the hair bundle, indicative of signal detection. A simple theoretical model is used to describe the observed chaotic dynamics. The model exhibits an enhancement of sensitivity to weak stimuli when the system is poised in the chaotic regime. We propose that chaos may play a role in the hair cell's ability to detect low-amplitude sounds.

Chaos and hyperchaos in simple gene network with negative feedback and time delays

Today there are examples that prove the existence of chaotic dynamics at all levels of organization of living systems, except intracellular, although such a possibility has been theoretically predicted. The lack of experimental evidence of chaos generation at the intracellular level in vivo may indicate that during evolution the cell got rid of chaos. This work allows the hypothesis that one of the possible mechanisms for avoiding chaos in gene networks can be a negative evolutionary selection, which prevents fixation or realization of regulatory circuits, creating too mild, from the biological point of view, conditions for the emergence of chaos. It has been shown that one of such circuits may be a combination of negative autoregulation of expression of transcription factors at the level of their synthesis and degradation. The presence of such a circuit results in formation of multiple branches of chaotic solutions as well as formation of hyperchaos with equal and sufficiently low values of the delayed argument that can be implemented not only in eukaryotic, but in prokaryotic cells.

Cardiac pathology findings in 252 cats presented for necropsy; a comparison of cats with unexpected death versus other deaths

OBJECTIVES

To report necropsy and myocardial histopathology in cats with unexpected death and expected death/euthanasia, comparing findings in 4 groups of cats: unexpected death with noncardiac disease (UD-NC); unexpected death with cardiac disease (UD-C); expected death/euthanasia due to noncardiac disease with incidental cardiac disease (OD + HD); and expected death/euthanasia due to congestive heart failure (CHF).

ANIMALS

Two hundred fifty-two cats undergoing necropsy at a single centre.

METHODS

Signalment, history, body weight, heart weight and myocardial thickness were obtained from medical records. Cardiac histopathology slides were reviewed blindly by a single observer. Data were analysed using a Chi squared, Fisher's exact, Kruskal-Wallis tests or ANOVA as appropriate.

RESULTS

Death at a veterinary clinic and suspected poisoning were the most common reasons for necropsy in 158 cats with an unexpected death. No cause other than cardiac disease was found in 87/158 (55.1%), with hypertrophic cardiomyopathy identified in 68/87 (78%) of UD-C cats. Expected deaths or euthanasia occurred in 27 cats with CHF and 67 cats with concurrent heart disease (OD + HD). Myofiber disarray, interstitial fibrosis, subendocardial fibrosis and intramural arteriolosclerosis were more prevalent in UD-C cats than in UD-NC cats, and subendocardial fibrosis and arteriolosclerosis were more prevalent in UD-C cats than in CHF and OD + HD cats.

CONCLUSIONS

Cardiac disease, and hypertrophic cardiomyopathy in particular, was commonly present in cats that died unexpectedly in this study population. Subendocardial fibrosis and intramural arteriolosclerosis were more common in cats with unexpected death with cardiac disease than in other cats.

Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.

Drift of Scroll Wave Filaments in an Anisotropic Model of the Left Ventricle of the Human Heart

Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias.

Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.

Systems Medicine 2.0: potential benefits of combining electronic health care records with systems science models

Background

The global burden of disease is increasingly dominated by non-communicable diseases.These diseases are less amenable to curative and preventative interventions than communicable disease. This presents a challenge to medical practice and medical research, both of which are experiencing diminishing returns from increasing investment.

Objective

Our aim was to (1) review how medical knowledge is generated, and its limitations, (2) assess the potential for emerging technologies and ideas to improve medical research, and (3) suggest solutions and recommendations to increase medical research efficiency on non-communicable diseases.

Methods

We undertook an unsystematic review of peer-reviewed literature and technology websites.

Results

Our review generated the following conclusions and recommendations. (1) Medical knowledge continues to be generated in a reductionist paradigm. This oversimplifies our models of disease, rendering them ineffective to sufficiently understand the complex nature of non-communicable diseases. (2) Some of these failings may be overcome by adopting a “Systems Medicine” paradigm, where the human body is modeled as a complex adaptive system. That is, a system with multiple components and levels interacting in complex ways, wherein disease emerges from slow changes to the system set-up. Pursuing systems medicine research will require larger datasets. (3) Increased data sharing between researchers, patients, and clinicians could provide this unmet need for data. The recent emergence of electronic health care records (EHR) could potentially facilitate this in real-time and at a global level. (4) Efforts should continue to aggregate anonymous EHR data into large interoperable data silos and release this to researchers. However, international collaboration, data linkage, and obtaining additional information from patients will remain challenging. (5) Efforts should also continue towards “Medicine 2.0”. Patients should be given access to their personal EHR data. Subsequently, online communities can give researchers the opportunity to ask patients for direct access to the patient’s EHR data and request additional study-specific information. However, selection bias towards patients who use Web 2.0 technology may be difficult to overcome.

Conclusions

Systems medicine, when combined with large-scale data sharing, has the potential to raise our understanding of non-communicable diseases, foster personalized medicine, and make substantial progress towards halting, curing, and preventing non-communicable diseases. Large-scale data amalgamation remains a core challenge and needs to be supported. A synthesis of “Medicine 2.0” and “Systems Science” concepts into “Systems Medicine 2.0” could take decades to materialize but holds much promise.

Coexisting chaotic and multi-periodic dynamics in a model of cardiac alternans

The spatiotemporal dynamics of cardiac tissue is an active area of research for biologists, physicists, and mathematicians. Of particular interest is the study of period-doubling bifurcations and chaos due to their link with cardiac arrhythmogenesis. In this paper, we study the spatiotemporal dynamics of a recently developed model for calcium-driven alternans in a one dimensional cable of tissue. In particular, we observe in the cable coexistence of regions with chaotic and multi-periodic dynamics over wide ranges of parameters. We study these dynamics using global and local Lyapunov exponents and spatial trajectory correlations. Interestingly, near nodes-or phase reversals-low-periodic dynamics prevail, while away from the nodes, the dynamics tend to be higher-periodic and eventually chaotic. Finally, we show that similar coexisting multi-periodic and chaotic dynamics can also be observed in a detailed ionic model.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

ON THE CHAOS IN GENE NETWORKS

The methods for constructing "chaotic" nonlinear systems of differential equations modeling gene networks of arbitrary structure and dimensionality with various types of symmetry are considered. It has been shown that an increase in modality of the functions describing the control of gene expression efficiency allows for a decrease in the dimensionality of these systems with retention of their chaotic dynamics. Three-dimensional "chaotic" cyclic systems are considered. Symmetrical and asymmetrical attractors with "narrow" chaos having a Moebius-like structure have been detected in such systems. As has been demonstrated, a complete symmetry of the systems with respect to permutation of variables does not prevent the emergence of their chaotic dynamics.

Bifurcation theory and cardiac arrhythmias

In this paper we review two types of dynamic behaviors defined by the bifurcation theory that are found to be particularly useful in describing two forms of cardiac electrical instabilities that are of considerable importance in cardiac arrhythmogenesis. The first is action potential duration (APD) alternans with an underlying dynamics consistent with the period doubling bifurcation theory. This form of electrical instability could lead to spatially discordant APD alternans leading to wavebreak and reentrant form of tachyarrhythmias. Factors that modulate the APD alternans are discussed. The second form of bifurcation of importance to cardiac arrhythmogenesis is the Hopf-homoclinic bifurcation that adequately describes the dynamics of the onset of early afterdepolarization (EAD)-mediated triggered activity (Hopf) that may cause ventricular tachycardia and ventricular fibrillation (VT/VF respectively). The self-termination of the triggered activity is compatible with the homoclinic bifurcation. Ionic and intracellular calcium dynamics underlying these dynamics are discussed using available experimental and simulation data. The dynamic analysis provides novel insights into the mechanisms of VT/VF, a major cause of sudden cardiac death in the US.

Experimental study of firing death in a network of chaotic FitzHugh-Nagumo neurons

The FitzHugh-Nagumo neurons driven by a periodic forcing undergo a period-doubling route to chaos and a transition to mixed-mode oscillations. When coupled, their dynamics tend to be synchronized. We show that the chaotically spiking neurons change their internal dynamics to subthreshold oscillations, the phenomenon referred to as firing death. These dynamical changes are observed below the critical coupling strength at which the transition to full chaotic synchronization occurs. Moreover, we find various dynamical regimes in the subthreshold oscillations, namely, regular, quasiperiodic, and chaotic states. We show numerically that these dynamical states may coexist with large-amplitude spiking regimes and that this coexistence is characterized by riddled basins of attraction. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations. Finally, we comment on the possible scenarios where the coupling-induced firing death could play an important role in biological systems.

Effects of ganglionated plexi ablation on ventricular electrophysiological properties in normal hearts and after acute myocardial ischemia

BACKGROUND

Ganglionated plexi (GP) ablation has been shown to play an important role in atrial fibrillation (AF) initiation and maintenance. Also, GP ablation increases chances for prevention of AF recurrence. This study investigated the effects of GP ablation on ventricular electrophysiological properties in normal dog hearts and after acute myocardial ischemia (AMI).

METHODS

Fifty anesthetized dogs were assigned into normal heart group (n=16) and AMI heart group (n=34). Ventricular dynamic restitution, effective refractory period (ERP), electrical alternans and ventricular fibrillation threshold (VFT) were measured before and after GP ablation in the normal heart group. In the AMI heart group, the incidence of ventricular arrhythmias and VFT were determined.

RESULTS

In the normal heart group, GP ablation significantly prolonged ERP, facilitated electrical alternans but did not increase ERP dispersion, the slope of restitution curves and its spatial dispersion. Also, GP ablation did not cause significant change of VFT. In the AMI heart group, the incidence of ventricular arrhythmias after GP ablation was significantly higher than that in the control group or the GP plus stellate ganglion (SG) ablation group (P<0.05). Spontaneous VF occurred in 8/12, 1/10 and 2/12 dogs in the GP ablation group, the GP plus SG ablation group and the control group, respectively (P<0.05). VFT in the GP ablation group showed a decreased trend though a significant difference was not achieved compared with the control or the GP plus SG ablation group.

CONCLUSIONS

GP ablation increases the risk of ventricular arrhythmias in the AMI heart compared to the normal heart.

A method for analyzing temporal patterns of variability of a time series from Poincare plots

The Poincaré plot is a popular two-dimensional, time series analysis tool because of its intuitive display of dynamic system behavior. Poincaré plots have been used to visualize heart rate and respiratory pattern variabilities. However, conventional quantitative analysis relies primarily on statistical measurements of the cumulative distribution of points, making it difficult to interpret irregular or complex plots. Moreover, the plots are constructed to reflect highly correlated regions of the time series, reducing the amount of nonlinear information that is presented and thereby hiding potentially relevant features. We propose temporal Poincaré variability (TPV), a novel analysis methodology that uses standard techniques to quantify the temporal distribution of points and to detect nonlinear sources responsible for physiological variability. In addition, the analysis is applied across multiple time delays, yielding a richer insight into system dynamics than the traditional circle return plot. The method is applied to data sets of R-R intervals and to synthetic point process data extracted from the Lorenz time series. The results demonstrate that TPV complements the traditional analysis and can be applied more generally, including Poincaré plots with multiple clusters, and more consistently than the conventional measures and can address questions regarding potential structure underlying the variability of a data set.

Role of the alternans of action potential duration and aconitine-induced arrhythmias in isolated rabbit hearts

Under conditions of Na(+) channel hyperactivation with aconitine, the changes in action potential duration (APD) and the restitution characteristics have not been well defined in the context of aconitine-induced arrhythmogenesis. Optical mapping of voltage using RH237 was performed with eight extracted rabbit hearts that were perfused using the Langendorff system. The characteristics of APD restitution were assessed using the steady-state pacing protocol at baseline and 0.1 µM aconitine concentration. In addition, pseudo-ECG was analyzed at baseline, and with 0.1 and 1.0 µM of aconitine infusion respectively. Triggered activity was not shown in dose of 0.1 µM aconitine but overtly presented in 1.0 µM of aconitine. The slopes of the dynamic APD restitution curves were significantly steeper with 0.1 µM of aconitine than at baseline. With aconitine administration, the cycle length of initiation of APD alternans was significantly longer than at baseline (287.5 ± 9.6 vs 247.5 ± 15.0 msec, P = 0.016). The functional reentry following regional conduction block appears with the progression of APD alternans. Ventricular fibrillation is induced reproducibly at pacing cycle length showing a 2:1 conduction block. Low-dose aconitine produces arrhythmogenesis at an increasing restitution slope with APD alternans as well as regional conduction block that proceeds to functional reentry.

Suppression of re-entrant and multifocal ventricular fibrillation by the late sodium current blocker ranolazine

OBJECTIVES

The purpose of this study was to test the hypothesis that the late Na current blocker ranolazine suppresses re-entrant and multifocal ventricular fibrillation (VF).

BACKGROUND

VF can be caused by either re-entrant or focal mechanism.

METHODS

Simultaneous voltage and intracellular Ca(+)² optical mapping of the left ventricular epicardial surface along with microelectrode recordings was performed in 24 isolated-perfused aged rat hearts. Re-entrant VF was induced by rapid pacing and multifocal VF by exposure to oxidative stress with 0.1 mM hydrogen peroxide (H₂O₂).

RESULTS

Rapid pacing induced sustained VF in 7 of 8 aged rat hearts, characterized by 2 to 4 broad propagating wavefronts. Ranolazine significantly (p < 0.05) reduced the maximum slope of action potential duration restitution curve and converted sustained to nonsustained VF lasting 24 ± 8 s in all 7 hearts. Exposure to H₂O₂ initiated early afterdepolarization (EAD)-mediated triggered activity that led to sustained VF in 8 out of 8 aged hearts. VF was characterized by multiple foci, appearing at an average of 6.8 ± 3.2 every 100 ms, which remained confined to a small area averaging 2.8 ± 0.85 mm² and became extinct after a mean of 43 ± 16 ms. Ranolazine prevented (when given before H₂O₂) and suppressed H₂O₂-mediated EADs by reducing the number of foci, causing VF to terminate in 8 out of 8 hearts. Simulations in 2-dimensional tissue with EAD-mediated multifocal VF showed progressive reduction in the number of foci and VF termination by blocking the late Na current.

CONCLUSIONS

Late Na current blockade with ranolazine is effective at suppressing both pacing-induced re-entrant VF and EAD-mediated multifocal VF.

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria-Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations.

Spiral-wave turbulence and its control in the presence of inhomogeneities in four mathematical models of cardiac tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Intrinsic inhomogeneities and the coexistence of spirals with different periods of rotation

We propose a mechanism by which wave fronts emanating from a spiral may break far from the spiral core due to intrinsic spatial inhomogeneities. A series of computer simulations are presented to demonstrate how coupling domains, which on their own would not cause breakup, may cause a single spiral to break into many spirals.

Negative filament tension at high excitability in a model of cardiac tissue

One of the fundamental mechanisms for the onset of turbulence in 3D excitable media is negative filament tension. Thus far, negative tension has always been obtained in media under low excitability. For this reason, its application to normal (nonischemic) cardiac tissue has been questionable, as such cardiac turbulence typically occurs at high excitability. Here, we report expansion of scroll rings (low curvature negative filament tension) in a medium with high excitability by numerical integration of the Luo-Rudy model of cardiac tissue. We discuss the relation between negative tension and the meandering of 2D spiral waves and the possible applications to cardiac modeling.

Gastrointestinal arrhythmias are associated with statistically significant fluctuations in systemic information dimension

Although cardiac arrhythmias have been studied extensively, little is known about arrhythmic phenomena in the gastrointestinal (GI) system. In this study, we demonstrate for the first time that the onset of GI arrhythmias is associated with statistically significant fluctuations in the information dimension of the associated systems. We induced gastric and intestinal arrhythmias in pigs using surgical stomach division and mesenteric artery ligation, respectively. Both conditions lead to a decreased supply of blood to the GI tract, which is associated in humans with various potentially lethal conditions including chronic mesenteric ischemia, whose mortality rate is over 60%. During our experiments, we recorded simultaneous magnetocardiographic, magnetogastrographic and magnetoenterographic signals and concluded that, when GI circulation is compromised, the information dimensionality of the system fluctuates significantly. In conclusion, dimensionality may be an important diagnostic factor for the characterization of arrhythmias in the context of GI pathophysiology.

Serum transforming growth factor-beta1 as a risk stratifier of sudden cardiac death

Sudden cardiac death prematurely claims the lives of some 7 million each year worldwide. It occurs primarily in patients with an underlying structural cardiac abnormality, and regardless of the type of the underlying pathology (heart failure, dilated and hypertrophic cardiomyopathies, myocardial infarction and aging), death is almost always caused by ventricular tachycardia (VT) which rapidly degenerates to ventricular fibrillation (VF). Implantable cardioverter defibrillator is an effective but expensive therapy for preventing SCD, and finding a reasonably specific, sensitive and cost-effective risk stratification tool for patients at high risk of sudden cardiac death will have great clinical utility in preventing premature sudden cardiac death. Increased myocardial fibrosis has been shown to develop in a wide range of cardiac diseases all manifesting increased risk of VT and VF. Clinical and experimental studies attribute a major role for fibrosis in the initiation of VT, VF and sudden cardiac death. Transforming growth factor-beta1 (TGF-beta1) has been shown to promote myocardial tissue fibrosis and perhaps more importantly in cardiac conditions associated with increased myocardial fibrosis are shown to be positively correlated with increased serum levels of TGF-beta1. In the present hypothesis we suggest that monitoring the serum levels of TGF-beta1 may be a cost-effective risk stratifier to identify patients at high risk of sudden cardiac death caused by VT and VF.