Jan Gieraltowski

Development of multiscale complexity and multifractality of fetal heart rate variability.

During fetal development a complex system grows and coordination over multiple time scales is formed towards an integrated behavior of the organism. Since essential cardiovascular and associated coordination is mediated by the autonomic nervous system (ANS) and the ANS activity is reflected in recordable heart rate patterns, multiscale heart rate analysis is a tool predestined for the diagnosis of prenatal maturation. The analyses over multiple time scales requires sufficiently long data sets while the recordings of fetal heart rate as well as the behavioral states studied are themselves short. Care must be taken that the analysis methods used are appropriate for short data lengths. We investigated multiscale entropy and multifractal scaling exponents from 30 minute recordings of 27 normal fetuses, aged between 23 and 38 weeks of gestational age (WGA) during the quiet state. In multiscale entropy, we found complexity lower than that of non-correlated white noise over all 20 coarse graining time scales investigated. Significant maturation age related complexity increase was strongest expressed at scale 2, both using sample entropy and generalized mutual information as complexity estimates. Multiscale multifractal analysis (MMA) in which the Hurst surface h(q,s) is calculated, where q is the multifractal parameter and s is the scale, was applied to the fetal heart rate data. MMA is a method derived from detrended fluctuation analysis (DFA). We modified the base algorithm of MMA to be applicable for short time series analysis using overlapping data windows and a reduction of the scale range. We looked for such q and s for which the Hurst exponent h(q,s) is most correlated with gestational age. We used this value of the Hurst exponent to predict the gestational age based only on fetal heart rate variability properties. Comparison with the true age of the fetus gave satisfying results (error 2.17±3.29 weeks; p<0.001; R(2)=0.52). In addition, we found that the normally used DFA scale range is non-optimal for fetal age evaluation. We conclude that 30 min recordings are appropriate and sufficient for assessing fetal age by multiscale entropy and multiscale multifractal analysis. The predominant prognostic role of scale 2 heart beats for MSE and scale 39 heart beats (at q=-0.7) for MMA cannot be explored neither by single scale complexity measures nor by standard detrended fluctuation analysis.

RS slope detection algorithm for extraction of heart rate from noisy, multimodal recordings.

Current gold-standard algorithms for heart beat detection do not work properly in the case of high noise levels and do not make use of multichannel data collected by modern patient monitors. The main idea behind the method presented in this paper is to detect the most prominent part of the QRS complex, i.e. the RS slope. We localize the RS slope based on the consistency of its characteristics, i.e. adequate, automatically determined amplitude and duration. It is a very simple and non-standard, yet very effective, solution. Minor data pre-processing and parameter adaptations make our algorithm fast and noise-resistant. As one of a few algorithms in the PhysioNet/Computing in Cardiology Challenge 2014, our algorithm uses more than two channels (i.e. ECG, BP, EEG, EOG and EMG). Simple fundamental working rules make the algorithm universal: it is able to work on all of these channels with no or only little changes. The final result of our algorithm in phase III of the Challenge was 86.38 (88.07 for a 200 record test set), which gave us fourth place. Our algorithm shows that current standards for heart beat detection could be improved significantly by taking a multichannel approach. This is an open-source algorithm available through the PhysioNet library.

Modeling heart rate variability including the effect of sleep stages

We propose a model for heart rate variability (HRV) of a healthy individual during sleep with the assumption that the heart rate variability is predominantly a random process. Autonomic nervous system activity has different properties during different sleep stages, and this affects many physiological systems including the cardiovascular system. Different properties of HRV can be observed during each particular sleep stage. We believe that taking into account the sleep architecture is crucial for modeling the human nighttime HRV. The stochastic model of HRV introduced by Kantelhardt et al. was used as the initial starting point. We studied the statistical properties of sleep in healthy adults, analyzing 30 polysomnographic recordings, which provided realistic information about sleep architecture. Next, we generated synthetic hypnograms and included them in the modeling of nighttime RR interval series. The results of standard HRV linear analysis and of nonlinear analysis (Shannon entropy, Poincaré plots, and multiscale multifractal analysis) show that-in comparison with real data-the HRV signals obtained from our model have very similar properties, in particular including the multifractal characteristics at different time scales. The model described in this paper is discussed in the context of normal sleep. However, its construction is such that it should allow to model heart rate variability in sleep disorders. This possibility is briefly discussed.

On the risk of aortic valve replacement surgery assessed by heart rate variability parameters.

In recent years the number of arterial stenosis (AS) patients has grown rapidly and valvular disease is expected to be the next great epidemic. We studied a group of 385 arterial valve replacement (AVR) surgery patients, of whom 16 had died in the postoperational period (up to 30 d after the operation). Each patient had a heart rate variability (HRV) recording made prior to the operation in addition to a full set of medical diagnostics including echocardiography. We formed 16 age, sex, New York Heart Association (NYHA) class, and BMI adjusted control pairs for each person who died in the perioperative period. Our aim was to find indications of the risk from AVR surgery based on the medical data and HRV properties. Besides standard, linear HRV methods, we used indexes of time irreversibility introduced by Guzik (G%), Porta (P%), Ehlers (index E) and Hou (index D). In addition, we analyzed the multiscale multifractal properties of HRV calculating the Hurst surface. The nonlinear analysis methods show statistically significant indications of the risk of AVR surgery in an increase of multifractality and an increase of time irreversibility of the HRV measured prior to the operation.

Formation of functional associations across time scales in the fetal autonomic control system — A multifractal analysis

During fetal development, different control systems mediated by the autonomic nervous system form functional connections over a wide range of time scales. Using multiscale multifractal analysis (MMA) of fetal heart rate variability (HRV), we describe fundamental relationships in the developing scale-wide adjustments within fetal behavior states as well as across state changes. MMA yields the local Hurst exponent surface h(q,s) with q as the multifractal parameter and s as the scale. In 30-minute recordings of healthy fetuses between 24 and 36weeks of gestation (n=25 in quiet sleep, n=29 in active sleep, n=30 changing sleep state) we investigated the dependency of h(q,s) on gestation age. In univariate models, we found a decreasing persistence for short scales and small amplitudes in the quiet (s1=39, q1=-0.7, R(2)=0.52) and in the active (s1=69, q1=-1.4, R(2)=0.23) sleep in contrast to an increasing persistency for long scales and large amplitudes (s1=147, q1=2.4, R(2)=0.29) in the mixed state. Bivariate models (additional scales considered) presented increased coefficients of determination R(2)=0.56, 0.4, and 0.43, respectively. Persistency increasing with age in connection with the sleep state changes (independent of the age related short range dependencies within the separate homogeneous sleep states) is reported here for the first time. The MMA indices obtained for the fetal HRV represent characteristics of the maturating scale-wide cardiovascular control in the context of the evolving sleep state dynamics, which have so far not been considered. They should be incorporated in the search for HRV indices for prenatal diagnosis of developmental disorders and risk assessment.

Fractal pattern of heart rate variability revealing unknown very low frequency properties

The subject of our research was an analysis of heart rate variability based on non-linear method Multiscale Multifractal Analysis (MMA). The analysis of HRV night-time recordings involved 5 groups of patients (285 subjects): 38 healthy patients, 103 with aortic valve stenosis, 36 with hypertrophic cardiomyopathy, 32 with atrial fibrillation, 59 coronary disease and 17 with congestive heart failure. The end result of MMA is the Hurst surface h(q,s) measuring a persistence. This is the 3D plot of the local Hurst exponent h describing the scaling of the variance of the signal as a function of q, which is a magnitude of the fluctuations and the parameter s - a measure of the time scale (convertible to frequency). In our research, we assessed the shape and form of the Hurst surface and based on the differences of these features we constructed 6 criteria. These criteria intended as a diagnostic tool for screening examination, allow to classify patients as healthy when all the criteria were fulfilled or ill when at least one criterion was negative. We also prepared an additional criterion, distinguishing group of patients with atrial fibrillation and detecting heart rate variability pattern for this group. In general for all of groups (285 patients), we obtained 76% of correct results (i.e. the accuracy). The percent of correct results for coronary disease: 70%, for hypertrophic cardiomyopathy: 61% patients, for atrial fibrillation: 86%, for aortic valve stenosis: 79% and 80% - for congestive heart failure patients. These results allow us to draw a conclusion that Multiscale Multifractal Analysis can be used as an effective screening examination method (general 6 criteria) as well as there are clear heart rate variability multifractal pattern, which we can detect using our criteria. This multifractal pattern can reflect a variety of physio-pathological processes, which at this stage of our research is not able to specify, so need further research.

Heart rate variability, multifractal multiscale patterns and their assessment criteria

OBJECTIVE Both the central nervous system and the autonomic nervous system are complex physiological networks which modulate the heart rate. They are spatially extended, have built-in delays and work on many time scales simultaneously-nonhomogeneous networks with multifractal dynamics. The object of our research was the analysis of human heart rate variability (HRV) using the nonlinear multiscale multifractal analysis (MMA) method for several cardiovascular diseases. The analysis of HRV (night-time recordings) involved six groups of patients: 61 healthy persons, 104 cases with aortic valve stenosis, 42 with hypertrophic cardiomyopathy, 36 with atrial fibrillation, 70 patients with coronary artery disease and 19 with congestive heart failure. 85% of patients formed a training data set (282 subjects) and 15% formed a test data set (50 subjects). APPROACH Multiscale multifractal analysis allows one to analyze the complexity of HRV and find the scaling properties of its fluctuations. The main result of MMA is the Hurst surface, the shape of which changes depending on the medical case analyzed. We prepared six criteria to distinguish a multifractal pattern for healthy subjects. We also prepared additional criteria, enabling one to recognize atrial fibrillation. MAIN RESULTS For the training data set, we obtained the following accuracy statistics in distinguishing the patients from the healthy: 68% for coronary artery disease, 67% for hypertrophic cardiomyopathy, 88% for atrial fibrillation, 74% for aortic valve stenosis and 83% for congestive heart failure. For the complete training data set we obtained an accuracy of 73%, and 80% for the test data set (mean for ten random selections of the test data set). SIGNIFICANCE The results of MMA presented here provide an additional input into the diagnostic process and may help to create a paradigm for future studies on medical screening methods, especially in that MMA focuses on very low frequencies of HRV not easily accessible by standard medical techniques. Satisfactory statistics for screening using both MMA and the unfiltered version of LF/HF indicate that the nature of the complete network moderating heart rhythm needs to be studied and that sinus rhythm in clinical patients may not always be separated from arrhythmia when its incidence is large.

Role of autonomic nervous system in the pathomechanism of hypertension

Due to high prevalence of hypertension (HT) in worldwide population, all aspects of this disease are studied in order to understand its pathogenesis and the influence on human body, as well as in order to find proper treatment. Impaired balance of autonomic nervous system (ANS) is taken into account as one of the main causes elevating blood pressure (BP). It seems that over-activation of sympathetic nervous system (SNS) is the most important factor in pathogenesis of HT. There are some methods which allow us to measure the sympathetic and parasympathetic nervous system activity. Some of them are described below and the influence of impaired ANS balance on HT development is presented. Many different, natural and pathologic factors can cause SNS response, so the measurement of the sole ANS activity cannot fully answer the question about the pathomechanism underlying HT. In this paper, we present some hypotheses regarding possible mechanisms of the disease progression. In primary HT, impairment of baroreceptors response is considered one of such mechanisms. Another one is the influence of hyperinsulinemia on the activation of SNS in insulin resistant patients. A few other factors are considered, like obesity, salt intake, sodium retention and alcohol intake and they are described briefly in our paper. In secondary hypertension, SNS can be activated indirectly by comorbidities, and this pathomechanism is also discussed.