Private Weakly-Random Sequences from Human Heart Rate for Quantum Amplification.

We investigate whether the heart rate can be treated as a semi-random source with the aim of amplification by quantum devices. We use a semi-random source model called ε-Santha-Vazirani source, which can be amplified via quantum protocols to obtain a fully private random sequence. We analyze time intervals between consecutive heartbeats obtained from Holter electrocardiogram (ECG) recordings of people of different sex and age. We propose several transformations of the original time series into binary sequences. We have performed different statistical randomness tests and estimated quality parameters. We find that the heart can be treated as a good enough, and private by its nature, source of randomness that every human possesses. As such, in principle, it can be used as input to quantum device-independent randomness amplification protocols. The properly interpreted ε parameter can potentially serve as a new characteristic of the human heart from the perspective of medicine.

Dynamical Landscape of Heart Rhythm in Long-Term Heart Transplant Recipients: A Way to Discern Erratic Rhythms.

It is commonly believed that higher values of heart rate variability (HRV) indices account for better organization of the network of feedback reflexes driving an organism's response to actual bodily needs. In order to evaluate this organization in heart transplant (HTX) recipients, 58 nocturnal Holter signals of 14 HTX patients were analyzed. Their dynamical properties were evaluated by short-term HRV indices and measures grounded on entropy. Estimates grouped according to the patients' clinical progress: free of complications versus with complications, and arranged in order of the length of time since the HTX, lead us to the conclusion that higher HRV is associated with a worse outcome for HTX patients. Moreover, short-term HRV indices that are constant, rather than increasing over time, serve well in the prognosis of the future state of a HTX patient. These findings suggest that increases observed in HRV indices are related to erratic rhythms resulting from remodeling of the cardiac tissue (including heterogeneous innervation) in long-term HTX patients. Therefore, we hypothesize that dynamical landscape markers (entropy and fragmentation measures together with the short-term HRV indices) can serve as a tool in the exploration of the genesis of (non-respiratory sinus) arrhythmia.

Dynamical Pattern Representation of Cardiovascular Couplings Evoked by Head-up Tilt Test.

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human underwent a provocation test using the head-up tilt (HUT) protocol. The information provided by ShE and TE is evaluated from two aspects: that of the algorithmic stability and that of the recognised physiology of the cardiovascular response to the HUT test. To address both of these aspects, two types of symbolization of three-element subsequent values of a signal are considered: one, well established in heart rate research, referring to the variability in a signal, and a novel one, revealing primarily the dynamical trends. The interpretation of ShE shows a strong dependence on the method that was used in signal pre-processing. In particular, results obtained from normalized signals turn out to be less conclusive than results obtained from non-normalized signals. Systematic investigations based on surrogate data tests are employed to discriminate between genuine properties-in particular inter-system coupling-and random, incidental fluctuations. These properties appear to determine the occurrence of a high percentage of zero values of TE, which strongly limits the reliability of the couplings measured. Nevertheless, supported by statistical corroboration, we identify distinct timings when: (i) evoking cardiac impact on the vascular system, and (ii) evoking vascular impact on the cardiac system, within both the principal sub-systems of the baroreflex loop.

Heart Rhythm Insights Into Structural Remodeling in Atrial Tissue: Timed Automata Approach.

The heart rhythm of a person following heart transplantation (HTX) is assumed to display an intrinsic cardiac rhythm because it is significantly less influenced by the autonomic nervous system-the main source of heart rate variability in healthy people. Therefore, such a rhythm provides evidence for arrhythmogenic processes developing, usually silently, in the cardiac tissue. A model is proposed to simulate alterations in the cardiac tissue and to observe the effects of these changes on the resulting heart rhythm. The hybrid automata framework used makes it possible to represent reliably and simulate efficiently both the electrophysiology of a cardiac cell and the tissue organization. The curve fitting method used in the design of the hybrid automaton cycle follows the well-recognized physiological phases of the atrial myocyte membrane excitation. Moreover, knowledge of the complex architecture of the right atrium, the ability of the almost free design of intercellular connections makes the automata approach the only one possible. Two particular aspects are investigated: impairment of the impulse transmission between cells and structural changes in intercellular connections. The first aspect models the observed fatigue of cells due to specific cardiac tissue diseases. The second aspect simulates the increase in collagen deposition with aging. Finally, heart rhythms arising from the model are validated with the sinus heart rhythms recorded in HTX patients. The modulation in the impairment of the impulse transmission between cells reveals qualitatively the abnormally high heart rate variability observed in patients living long after HTX.

Complexity of cardiovascular rhythms during head-up tilt test by entropy of patterns.

OBJECTIVE: The head-up tilt (HUT) test, which provokes transient dynamical alterations in the regulation of cardiovascular system, provides insights into complex organization of this system. Based on signals with heart period intervals (RR-intervals) and/or systolic blood pressure (SBP), differences in the cardiovascular regulation between vasovagal patients (VVS) and the healthy people group (CG) are investigated. APPROACH: Short-term relations among signal data represented symbolically by three-beat patterns allow to qualify and quantify the complexity of the cardiovascular regulation by Shannon entropy. Four types of patterns: permutation, ordinal, deterministic and dynamical, are used, and different resolutions of signal values in the the symbolization are applied in order to verify how entropy of patterns depends on a way in which values of signals are preprocessed. MAIN RESULTS: At rest, in the physiologically important signal resolution ranges, independently of the type of patterns used in estimates, the complexity of SBP signals in VVS is different from the complexity found in CG. Entropy of VVS is higher than CG what could be interpreted as substantial presence of noisy ingredients in SBP of VVS. After tilting this relation switches. Entropy of CG occurs significantly higher than VVS for SBP signals. In the case of RR-intervals and large resolutions, the complexity after the tilt becomes reduced when compared to the complexity of RR-intervals at rest for both groups. However, in the case of VVS patients this reduction is significantly stronger than in CG. SIGNIFICANCE: Our observations about opposite switches in entropy between CG and VVS might support a hypothesis that baroreflex in VVS affects stronger the heart rate because of the inefficient regulation (possibly impaired local vascular tone alternations) of the blood pressure.

Multistructure index characterization of heart rate and systolic blood pressure reveals precursory signs of syncope.

Recurrent syncope - abrupt loss of consciousness - can have a serious impact on patients' quality of life, comparable with chronic illnesses. Vasovagal syncope (VVS) is a specific reflex syncope, in which an inappropriate reaction of the autonomic nervous system (ANS) plays a key role in the pathophysiology. In syncope diagnosis, an ideal diagnostic method should positively identify vasovagal sensitive patients, without the need to perform a specialised head-up tilt table (HUTT) test. We apply a novel methodology of multistructure index (MI) statistics for seamlessly evaluating the size spectrum of the asymmetry properties of magnitudes of neural reflexes responsible for maintaining the homeostatic dynamics of autonomic control. Simultaneous evaluation using the MI of the effects on heart rate and blood pressure involved in achieving homeostasis of contrasting properties of the dynamics of slow and fast neural regulation reveals a clear distinction between vasovagal patients and healthy subjects, who are/are not susceptible to spontaneous fainting. Remarkably, a healthy cardiovascular response to the HUTT test is indeed evident prior to the test, making the MI a robust novel indicator, clearly distinguishing the cardiovascular autonomic regulation of healthy people from that of vasovagal patients without the need to perform an actual HUTT test.

Visualization of Heart Rate Variability of Long-Term Heart Transplant Patient by Transition Networks: A Case Report.

We present a heart transplant patient at his 17th year of uncomplicated follow-up. Within a frame of routine check out several tests were performed. With such a long and uneventful follow-up some degree of graft reinnervation could be anticipated. However, the patient's electrocardiogram and exercise parameters seemed largely inconclusive in this regard. The exercise heart rate dynamics were suggestive of only mild, if any parasympathetic reinnervation of the graft with persisting sympathetic activation. On the other hand, traditional heart rate variability (HRV) indices were inadequately high, due to erratic rhythm resulting from interference of the persisting recipient sinus node or non-conducted atrial parasystole. New tools, originated from network representation of time series, by visualization short-term dynamical patterns, provided a method to discern HRV increase due to reinnervation from other reasons.

Chronographic Imprint of Age-Induced Alterations in Heart Rate Dynamical Organization.

Beat-to-beat changes in the heart period are transformed into a network of increments between subsequent RR-intervals, which enables graphical descriptions of short-term heart period variability. Three types of such descriptions are considered: (1) network graphs arising from a set of vertices and directed edges, (2) contour plots of adjacency matrices A, representing the networks and transition matrices T, resulting from A, and (3) vector plots of gradients of the matrices A and T. Two indices are considered which summarize properties of A and T: the approximate deceleration capacity and the entropy rate. The method, applied to time series of nocturnal RR-intervals recorded from healthy subjects of different ages, reveals important aspect of changes in the autonomic activity caused by biological aging. Independent of the subject's age, following accelerations, a pendulum-like dynamics appears. With decelerations, this dynamics develops in line with the subject's age. This aging transition can be graphically visualized by vectors connecting the maxima of the transition probabilities of T, which, metaphorically, resemble a chronometer or the hands of a clock.

Causal relationships in the variability of cardiovascular system evoked by orthostatic stress by transfer entropy.

The coupling between cardiac and vascular systems in healthy volunteers, elicited by the head-up tilt test is estimated by means of transfer entropy with non-uniform embedding. The method applied to beat-to-beat recordings with heart periods and systolic blood pressure, supports the commonly accepted model, that baroreflex is the key factor in maintaining homeostatic blood distribution after tilting. However the method applied to changes of heart periods and changes of blood pressure, display switches in the driving system, from vascular in the early tilt, to cardiac just after the early tilt and back to vascular in the late tilt.

Complexity of the heart rhythm after heart transplantation by entropy of transition network for RR-increments of RR time intervals between heartbeats.

Network models have been used to capture, represent and analyse characteristics of living organisms and general properties of complex systems. The use of network representations in the characterization of time series complexity is a relatively new but quickly developing branch of time series analysis. In particular, beat-to-beat heart rate variability can be mapped out in a network of RR-increments, which is a directed and weighted graph with vertices representing RR-increments and the edges of which correspond to subsequent increments. We evaluate entropy measures selected from these network representations in records of healthy subjects and heart transplant patients, and provide an interpretation of the results.

Aging in autonomic control by multifractal studies of cardiac interbeat intervals in the VLF band.

The heart rate responds dynamically to various intrinsic and environmental stimuli. The autonomic nervous system is said to play a major role in this response. Multifractal analysis offers a novel method to assess the response of cardiac interbeat intervals. Twenty-four hour ECG recordings of RR interbeat intervals (of 48 elderly volunteers (age 65-94), 40 middle-aged persons (age 45-53) and 36 young adults (age 18-26)) were investigated to study the effect of aging on autonomic regulation during normal activity in healthy adults. Heart RR-interval variability in the very low frequency (VLF) band (32-420 RR intervals) was evaluated by multifractal tools. The nocturnal and diurnal signals of 6 h duration were studied separately. For each signal, the analysis was performed twice: for a given signal and for the integrated signal. A multifractal spectrum was quantified by the h(max) value at which a multifractal spectrum attained its maximum, width of a spectrum, Hurst exponent, extreme events h(left) and distance between the maxima of a signal and its integrated counterpart. The following seven characteristics are suggested as quantifying the age-related decrease in the autonomic function ('int' refers to the integrated signal): (a) h(sleep)(max) - h(max)(wake) > 0.05 for a signal; (b) h(int)(max) > 1.15 for wake; (c) h(int)(max) - h(max) > 0.85 for sleep; (d) Hurst(wake) - Hurst(sleep) < 0.01; (e) width(wake) > 0.07; (f) width(int) < 0.30 for sleep; (g) h(int)(left) > 0.75. Eighty-one percent of elderly people had at least four of these properties, and ninety-two percent of young people had three or less. This shows that the multifractal approach offers a concise and reliable index of healthy aging for each individual. Additionally, the applied method yielded insights into dynamical changes in the autonomic regulation due to the circadian cycle and aging. Our observations support the hypothesis that imbalance in the autonomic control due to healthy aging could be related to changes emerging from the vagal function (Struzik et al 2006 IEEE Trans. Biomed. Eng. 53 89-94).

Comparison of wavelet transform modulus maxima and multifractal detrended fluctuation analysis of heart rate in patients with systolic dysfunction of left ventricle.

BACKGROUND: In recent years the WTMM (wavelet transform modulus maxima) and MDFA (multifractal detrended fluctuation analysis) methods have become widely used techniques for the determination of nonlinear, multifractal heart rate (HR) dynamics. The purpose of our study was to compare multifractal parameters of heart rate calculated using both methods in a group of 90 patients with reduced left ventricular systolic function (rlvs group) and in a group of 39 healthy persons (nsr group). METHODS: For each subject from the rlvs group (LVEF < or =40%) and the nsr group, a 24-hour ECG Holter monitoring was performed. The width of the multifractal spectrum and global Hurst exponent were calculated by means of WTMM and MDFA methods for 5-hour daytime and nighttime subsets. RESULTS: The width of the multifractal spectrum was significantly lower and the Hurst exponent was significantly higher in rlvs group in comparison to nsr group both during diurnal activity and nocturnal rest according to MDFA and only during diurnal activity according to WTMM method. In both groups we observed significant differences of the multifractal spectrum width and the global Hurst exponent between the nighttime and daytime recordings. CONCLUSIONS: MDFA seems to be more sensitive as compared with WTMM method in differentiation between multifractal properties of the heart rate in healthy subjects and patients with left ventricular systolic dysfunction.

Seidel-Herzel model of human baroreflex in cardiorespiratory system with stochastic delays.

The stochastic versus deterministic solution of the Seidel-Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to sustained oscillatory solutions if time delays in transfer of signals by sympathetic nervous system to the heart and vasculature are changed. Oscillations in the heart rate and blood pressure are physiologically crucial since they are recognized as Mayer waves. We test the role of delays of the sympathetic stimulation in reconstruction of the known features of the heart rate. It appears that realistic histograms and return plots are attainable if sympathetic time delays are stochastically perturbed, namely, we consider a perturbation by a white noise. Moreover, in the case of stochastic model the bifurcation points vanish and Mayer oscillations in heart period and blood pressure are observed for whole considered space of sympathetic time delays.