Jan J. Zebrowski

Nonlinear oscillator model reproducing various phenomena in the dynamics of the conduction system of the heart.

A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained (models of the asystole). The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block (third degree). Finally, we demonstrate the possibility of introducing into the model a spatial dimension that creates exciting possibilities of simulating in the future the SA the AV nodes and the atrium including their true anatomical structure.

Dimensional analysis of HRV in hypertrophic cardiomyopathy patients

Hypertrophic cardiomyopathy (HCM) is an excessive thickening of the heart muscle in the absence of an apparent cause. This condition excludes individuals with high blood pressure or prolonged athletic training. It is characterized by left and/or right ventricular hypertrophy, which is usually asymmetric. It is a familial disease with autosomal dominant inheritance caused by mutations in the sarcomeric contractile protein gene [1]. The electrocardiogram (ECG) of those patients who have this pathology shows an abnormal electric signal due to the thickening of the heart and the loss of the normal alignment of heart muscle cells. Some H CM patients c an d evelop arrhythmias (ventricular tachycardia and atrial fibrillation), endocarditis, heart block, and also sudden cardiac death (SCD). In HCM patients there is an increased risk of premature death, which can occur with little or no warning. SCD can strike at any age [2]. However, stratification for sudden cardiac death on patients with HCM is highly difficult [3].

On the nature of heart rate variability in a breathing normal subject: A stochastic process analysis.

Human heart rate is moderated by the autonomous nervous system acting predominantly through the sinus node (the main cardiac physiological pacemaker). One of the dominant factors that determine the heart rate in physiological conditions is its coupling with the respiratory rhythm. Using the language of stochastic processes, we analyzed both rhythms simultaneously taking the data from polysomnographic recordings of two healthy individuals. Each rhythm was treated as a sum of a deterministic drift term and a diffusion term (Kramers-Moyal expansion). We found that normal heart rate variability may be considered as the result of a bidirectional coupling of two nonlinear oscillators: the heart itself and the respiratory system. On average, the diffusion (noise) component measured is comparable in magnitude to the oscillatory (deterministic) term for both signals investigated. The application of the Kramers-Moyal expansion may be useful for medical diagnostics providing information on the relation between respiration and heart rate variability. This interaction is mediated by the autonomous nervous system, including the baroreflex, and results in a commonly observed phenomenon--respiratory sinus arrhythmia which is typical for normal subjects and often impaired by pathology.

Local time properties of 24-hour Holter recordings of RR intervals: a nonlinear quantitative method through pattern entropy of 3-D return maps

An easy to implement, consistent new measure of the complexity of heart rate variability has been developed. It is well suited for nonstationary data such as that of Holter ECG recordings and allows to assess the risk of cardiac arrest.

On the effect of material inhomogeneities on the generation of vertical Bloch lines

The effects of inhomogeneities of the drive field Hz and of the in-plane anisotropy on the generation of vertical Bloch line pairs in the stripe domain wall were investigated numerically. It was found that the inhomogeneity of Hz does not cause the generation of vertical. Bloch line pairs in the linear range of wall motion (i.e. Hz<Hzcrit). In the case of the inhomogeneity of the in-plane anisotropy, however, the generation of vertical Bloch lines appears also for Hz<Hzcrit, provided that such an inhomogeneity is sufficiently large.

Nonlinear instabilities and nonstationarity in human heart-rate variability

The human cardiovascular system exhibits complex and interesting dynamics, including heart-rate fluctuations. The heart rate fluctuates irregularly - a phenomenon called heart-rate variability. Here, we present a short review of our experience with the analysis of heart-rate variability. Initially, we focused on the assessment of the risk of sudden cardiac death due to cardiac arrest. During this research, we became aware of intermittency in heart-rate variability. We identify the intermittency as type I and describe how simple models helped us understand the differences between our results and textbook properties of this phenomenon. We also mention the use of modified van der Pol oscillators for the modeling of heart-rate variability. Finally, we review our latest research on the modeling of the heart tissues properties using the true shape of the ventricles reconstructed from clinical electro-physiological measurement data.

3-dimensional Poincare plots of the QT intervals-an approach to nonlinear QT analysis

The Poincare plots-a simple graphical, nonlinear method was implemented to express 24-h QT interval changes. The group of 23 pts with hypertrophic cardiomyopathy was analyzed (11 pts. with higher and 12 with lower risk of sudden cardiac death). The control group consisted of 10 healthy subjects. 24-h Holter ECG recordings were analyzed and RR and QT intervals were measured beat by beat. 3 dimensional QT and RR plots were constructed in the time delay coordinates. Three main forms of QT plots were observed, highly different in cases with hypertrophic cardiomyopathy compared to normals. Different shapes of QT and RR plots revealed a complex nonlinear relation of the QT and RR intervals.

Dynamic behavior of domain walls in double layer self-biasing bubble garnet films

Radial expansion of bubbles and gradient bubble propagation experiments were conducted in a double layer garnet film with perpendicular anisotropy in both layers. Implanted and as-grown samples are compared. In radial expansion the side walls of the bubble exhibit a linear mobility much lower than calculated from γΔ/α. Saturation occurs at high drives (35 Oe). At drives above 50 Oe the saturation velocity of 27 m/s occurs only in the first 120 ns of the motion. After that the velocity drops to 17.5 m/s still independent of drive. This break in velocity does not occur in implanted samples, where the saturation velocity depends on implantation conditions. In gradient propagation saturation occurs at fields an order of magnitude smaller. The saturation velocity is independent of implantation, but overshoot depends strongly on it. No creep was detected. The 180° head-on domain wall between the two layers is found to have little effect on the dynamics of the side walls of the bubble. The motion of the head-on wall is also investigated and its velocity estimated. This head-on wall exhibits a linear mobility and a saturation velocity at high drives.

Dynamical non-linear analysis of heart rate variability in patients with aortic stenosis

In this study the 24-h Heart Variability Signals (HRV) of 206 patients with Aortic Stenosis (AS) and 68 healthy subjects (NRM) were analyzed, using dynamical nonlinear analysis to compare the complexity of the signals between these two groups during morning (7-12h), afternoon (15-20h) and night (0-5h). The dynamical analysis defines an initial window of 10,000 beats and calculates the Correlation Dimension (CD) as a non-linear index. Then the window is moved 2,500 beats on the time series and the CD of the new window is calculated. This process is repeated until the whole signal is analyzed. It was found that: 1) The CD of HRV has significant lower values in the morning than in the night for both groups. 2) The CD of males is lower than the CD values of females during morning for both groups. 3) The CD of NRM is lower than the CD of AS during the morning, while in the night the CD of NRM males is higher.

Observations and modeling of deterministic properties of human heart rate variability

Simple models show that in Type-I intermittency a characteristic U-shaped probability distribution is obtained for the laminar phase length. The laminar phase length distribution characteristic for Type-I intermittency may be obtained in human heart rate variability data for some cases of pathology. The heart and its regulatory systems are presumed to be both noisy and non-stationary. Although the effect of additive noise on the laminar phase distribution in Type-I intermittency is well-known, the effect of neither multiplicative noise nor non-stationarity have been studied. We first discuss the properties of two classes of models of Type-I intermittency: (a) the control parameter of the logistic map is changed dichotomously from a value within the intermittency range to just below the bifurcation point and back; (b) the control parameter is changed randomly within the same parameter range as in the model class (a). We show that the properties of both models are different from those obtained for Type-I intermittency in the presence of additive noise. The two models help to explain some of the features seen in the intermittency in human heart rate variability.