The "Chaos Theory" and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease?

Fractal dimension based geographical clustering of COVID-19 time series data

Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

Dynamical behavior analysis of the heart system by the bifurcation structures

The functioning of the heart rhythm can exhibit a wide variety of dynamic behaviours under certain conditions. In the case of rhythm disorders or cardiac arrhythmias, the natural rhythm of the heart is usually involved in the sinoatrial node, the atrioventricular node, the atria of the carotid sinus, etc. The study of heart related disorders requires an important analysis of its rhythm because the regularity of cardiac activity is conditioned by a large number of factors. The cardiac system is made up of a combination of nodes ranging from the sinus node, the atrioventricular node to its Purkinje bundles, which interact with each other via communicative aspects. Due to the nature of their respective dynamics, the above are treated as self-oscillating elements and modelled by nonlinear oscillators. By modelling the cardiac conduction system as a model of three nonlinear oscillators coupled by delayed connections and subjected to external stimuli depicting the behavior of a pacemaker, its dynamic behavior is studied in this paper by nonlinear analysis tools. From an electrocardiogram (ECG) assessment, the heart rhythm reveals normal and pathological rhythms. Three forms of ventricular fibrillation, ventricular flutter, ventricular tachycardia and atrial fibrillation are observed. The results are confirmed by the respective maximum Lyapunov exponents. Considering the cardiac nodes as microchips, using microcontroller simulation technology, the cardiac conduction system was modelled as a network of four ATmega 328P microcontrollers. A similarity with the results obtained numerically can be observed.

Heart Rate Variability in Healthy Subjects During Monitored, Short-Term Stress Followed by 24-hour Cardiac Monitoring

Heart Rate Variability (HRV) can be a useful metric to capture meaningful information about heart function. One of the non-linear indices used to analyze HRV, Detrended Fluctuation Analysis (DFA), finds short and long-term correlations in RR intervals to capture quantitative information about variability. This study focuses on the impact of visual and mental stimulation on HRV as expressed via DFA within healthy adults. Visual stimulation can activate the automatic nervous system to directly impact physiological behavior such as heart rate. In this investigation of HRV, 70 participants (21 males) viewed images on a screen followed by a math and recall task. Each viewing segment lasted 2 min and 18 s. The math and memory recall task segment lasted 4 min total. This process was repeated 9 times during which the participants' electrocardiogram was recorded. 37 participants (12 males) opted in for an additional 24-h Holter recording after the viewing and task segments of the study were complete. Participants were randomly assigned to either a pure (organized image presentation) or mixed (random image presentation) image regime for the viewing portion of the study to investigate the impact of the external environment on HRV. DFA α1 was extracted from the RR intervals. Our findings suggest that DFA α1 can differentiate between the viewing [DFA α1 range from 0.96 (SD = 0.25) to 1.08 (SD = 0.22)] and the task segments [DFA α1 range from 1.17 (SD = 0.21) to 1.26 (SD = 0.25)], p < 0.0006 for all comparisons. However, DFA α1 was not able to distinguish between the two image regimes. During the 24-hour follow up, participants had an average DFA α1 = 1.09 (SD = 0.14). In conclusion, our findings suggest a graded response in DFA during short term stimulation and a responsiveness in participants to adjust physiologically to their external environment expressed through the DFA exponent.

Psychophysiological and Psychosocial Profile of Patients Attending Drug Addiction Centers

Drug treatment centres provide the highest level of rehab services for patients diagnosed with drug addictions. Most inpatient drug rehab programs focus on medical detox and mental health interventions. However, how to optimize the later remains a challenge. The aim of this study was to examine the psychophysiological and psychosocial profile of patients attending drug addiction centres in comparation with the general population. A total of 105 inpatient drug rehab patients and 50 participants from the general population were compared based on standardized psychophysiological and psychosocial measures. Results of this study suggest that patients attending drug addiction centers differ from general population in several different psychophysiological and psychosocial factors. Patients reported significantly lower levels of physical activity and increased sympathetic responsiveness, and significantly higher levels in loneliness, psychologically inflexibility and neuroticism. The results of this study highlight the importance of address healthy lifestyle behaviors such as sport practice and psychological variables such as loneliness, psychological (in)flexibility and neuroticism to improve current programs aim to prevent or reduce problematic drug consumptions.

Heart Rate Variability During a Standard Dive: A Role for Inspired Oxygen Pressure?

Introduction: Heart rate variability (HRV) during underwater diving has been infrequently investigated because of environment limitations and technical challenges. This study aims to analyze HRV changes while diving at variable hyperoxia when using open circuit (OC) air diving apparatus or at constant hyperoxia using a closed-circuit rebreather (CCR). We used HRV analysis in time and frequency domain adding nonlinear analysis which is more adapted to short-time analysis and less dependent on respiratory rate (Sinus respiratory arrhythmia). Materials and Methods: 18 males, 12 using OC (30 mfw for 20 min) and 6 using CCR (30 mfw for 40 min.). HRV was recorded using a polar recorder. Four samples of R-R intervals representing the dive were saved for HRV analysis. Standard deviation of normal-to-normal intervals (SDNN), square root of the mean squared differences between successive RR intervals (rMSSD), and average RR intervals (RR) in time-domain; low frequency (LF) and high frequency (HF) in frequency domain were investigated. Nonlinear analysis included fractal dimension (FrD). Results: SDNN and rMSSD were significantly increased during descent and at depth with OC, not with CCR. Mean RR interval was longer at depth with OC, but only during ascent and after the dive with CCR. HF power was higher than baseline during the descent both with OC and CCR and remained elevated at depth for OC. The LF/HF ratio was significantly lower than baseline for descent and at depth with both OC and CCR. After 30 min of recovery, the LF/HF ratio was higher than baseline with both OC and CCR. Nonlinear analysis detected differences at depth for OC and CCR. Discussion: Increased parasympathetic tone was present during diving. RR duration, SDNN; rMSSD, HF spectral power all increased during the dive above pre-dive levels. Conversely, HF power decreased (and the LF/HF increased) 30 min after the dive. Using FrD, a difference was detected between OC and CCR, which may be related to differences in partial pressure of oxygen breathed during the dive.

Heart Rate Variability Analysis to Predict Onset of Ventricular Tachyarrhythmias in Implantable Cardioverter Defibrillators

Implantable cardioverter defibrillators (ICDs) are commonly used in patients at high risk of sudden cardiac death (SCD) to help prevent and treat life-threatening arrhythmia. Up to 80% of cases of sudden cardiac death are caused by ventricular tachyarrhythmias (VTA) and the accurate prediction of VTA in patients with ICDs can help prevent SCD. Early prediction allows tiered and less invasive therapies to be used to help prevent VTA which are more easily tolerated by the patient and are less battery intensive. In this work, a comparative study of three types of frequency domain features (spectral, bispectrum, and Fourier-Bessel) for VTA prediction is presented based on heart rate variability (HRV) signals between one and five minutes prior to known SCD. Using Fourier-Bessel features and a standard classification approach resulted in the best performance of 87.5% accuracy, 89.3% sensitivity and 85.7% specificity. These results suggest that Fourier-Bessel features are a promising approach for SCD prediction, and that new feature development can help improve both the sensitivity and specificity of SCD prediction in ICDs.

Investigation of Linear and Nonlinear Properties of a Heartbeat Time Series Using Multiscale Rényi Entropy

The time series of interbeat intervals of the heart reveals much information about disease and disease progression. An area of intense research has been associated with cardiac autonomic neuropathy (CAN). In this work we have investigated the value of additional information derived from the magnitude, sign and acceleration of the RR intervals. When quantified using an entropy measure, these time series show statistically significant differences between disease classes of Normal, Early CAN and Definite CAN. In addition, pathophysiological characteristics of heartbeat dynamics provide information not only on the change in the system using the first difference but also the magnitude and direction of the change measured by the second difference (acceleration) with respect to sequence length. These additional measures provide disease categories to be discriminated and could prove useful for non-invasive diagnosis and understanding changes in heart rhythm associated with CAN.

Impact of functional training on geometric indices and fractal correlation property of heart rate variability in postmenopausal women

BACKGROUND

To evaluate the influence of functional training on the geometric indices of heart rate variability (HRV) and fractal correlation properties of the dynamics of heart rate in menopausal women.

METHODS

Of 39 women who were in the period of menopause for more than a year and who did not practice any regular physical activity were divided into: Functional training group (FTG = 50 ± 4.5 years; 67.64 ± 11.64 kg; 1.5 ± 0.05 m) that executed the functional training (FT) and all proposals by reviews and the Control group (58.45 ± 4.8 years; 66.91 ± 13.24 kg; 1.55 ± 0.05 m) who performed all assessments but not FT. The training consisted of 18 weeks (three times a week) and the volunteers performed three sets of 11 functional exercises followed by a walk in each of the sessions. The autonomic nervous system modulation was evaluated by analysis of HRV and the indices obtained were: RR intervals, RRTRI, TINN, SD1, SD2, SD1/SD2, qualitative analysis of Poincaré plot and DFA (alfa-1, alfa-2 and alfa-1/alfa-2). The Student's t-test for unpaired samples (normal data) or Mann-Whitney test nonnormal data) were used to compare the differences obtained between the final moment and the initial moment of the studied groups (p < .05).

CONCLUSION

Were observed in the FTG: increased SD1 (CG 0.13 ± 4.00 vs. 3.60 ± 8.43), beat-to-beat global dispersion much greater as an increased in the dispersion of long-term RR intervals and increased fractal properties of short-term (α1) (CG -0.04 ± 0.13 vs. 0.07 ± 0.21). FT promoted a beneficial impact on cardiac autonomic modulation, characterized by increased parasympathetic activity and short-term fractal properties of the dynamics of the heart rate.

Effects of guided breath exercise on complex behaviour of heart rate dynamics

INTRODUCTION

Cardiac autonomic regulation is influenced by changes in respiratory rate, which has been demonstrated by linear analysis of heart rate variability (HRV). Conversely, the complex behaviour is not well defined for HRV during this physiological state. In this sense, Higuchi Fractal Dimension is applied directly to the time series. It analyses the fractal dimension of discrete time sequences and is simpler and faster than correlation dimension and many other classical measures derived from chaos theory. We investigated chaotic behaviour of heart rate dynamics during guided breath exercises.

METHOD

We investigated 21 healthy male volunteers aged between 18 and 30 years. HRV was analysed 10 min before and 10 min during guided breath exercises. HRV was analysed in the time and frequency domain for linear analysis and through HFD for non-linear analysis.

RESULTS

Linear analysis indicated that SDNN, pNN50, RMSSD, LF, HF and LF/HF increased during guided breath exercises. HFD analysis illustrated that between K_max 20 to K_max 120 intervals, was enhanced during guided breath exercises.

CONCLUSION

Guided breath exercises acutely increased chaotic behaviour of HRV measured by HFD.

Influence of bilevel positive airway pressure on autonomic tone in hospitalized patients with decompensated heart failure

[Purpose] This study evaluated the effect of Bilevel Positive Airway (BiPAP) on the autonomic control of heart rate, assessed by heart rate variability (HRV), in patients hospitalized with decompensated heart failure. [Subjects and Methods] This prospective cross-sectional study included 20 subjects (age: 69±8 years, 12 male, left ventricular ejection fraction: 36 ±8%) diagnosed with heart failure who were admitted to a semi-intensive care unit with acute decompensation. Date was collected for HRV analysis during: 10 minutes spontaneous breathing in the resting supine position; 30 minutes breathing with BiPAP application (inspiratory pressure = 20 cmH2O and expiratory pressure = 10 cmH2O); and 10 minutes immediately after removal of BiPAP, during the return to spontaneous breathing. [Results] Significantly higher values for indices representative of increased parasympathetic activity were found in the time and frequency domains as well as in nonlinear Poincaré analysis during and after BiPAP in comparison to baseline. Linear HRV analysis: standard deviation of the average of all R-R intervals in milliseconds = 30.99±4.4 pre, 40.3±6.2 during, and 53.3±12.5 post BiPAP. Non-linear HRV analysis: standard deviations parallel in milliseconds = 8.31±4.3 pre, 12.9±5.8 during, and 22.8 ±6.3 post BiPAP. [Conclusion] The present findings demonstrate that BiPAP enhances vagal tone in patients with heart failure, which is beneficial for patients suffering from acute decompensation.

Heart rate variability and critical flicker fusion frequency changes during and after parachute jumping in experienced skydivers

PURPOSE

The purpose of this study was (1) to further explore the heart rate dynamics and assess a potential cardiovascular risk in response to 4000 m jumps in experienced skydivers; (2) to assess whether there is an impact of such jumps on skydivers' cortical arousal or not, which may impact their decision making processes.

METHOD

18 experienced skydivers performed successive jumps from a plane at 4000 m of height. Heart rate dynamics and cortical arousal were assessed by the use of heart rate variability and Critical Flicker Fusion Frequency (CFFF), respectively.

RESULTS

CFFF did not differ between the three measurement time points (p > 0.05). Mean heart rate increased during the jump (p < 0.001) and came back to pre-jump values after the jump (p < 0.001). Percentage of the differences of successive NN intervals greater than 50 ms (pNN50) decreased during the jump (p < 0.001) and kept lower values after the jump compared to pre-jump (p < 0.05). High-frequency power (HF) did not differ during the jump (p > 0.05) but decreased after the jump compared to both pre-jump (p < 0.01) and jump (p < 0.05). Sample entropy decreased during the jump (p < 0.001) and came back to pre-jump values after the jump (p > 0.05).

CONCLUSION

These results confirm a vagal input reduction associated with a rise of the sympathetic tone during the jump and suggests that the experienced skydiver is not exposed to a high cardiovascular risk. This study also shows that environmental stresses induced by free fall could not hamper the perceptual vigilance of experienced skydivers.

Multifractality in heartbeat dynamics in patients undergoing beating-heart myocardial revascularization

BACKGROUND

The multifractal approach of HRV analysis offers new insight into the mechanisms of autonomic modulation of the diseased hearts and has a potential to depict subtle changes in cardiac autonomic nervous control not revealed by conventional linear and non-linear analyses in various conditions like heart failure or stable angina pectoris. The aim of this study was to employ the multifractality approach in cardiac surgery patients and evaluate the multifractality before and after beating-heart myocardial revascularization (off-pump CABG).

METHODS

Twenty-four hour Holter recordings were performed pre- and postoperatively in 60 patients undergoing off-pump CABG. Selected conventional time- and frequency-domain linear HRV indices were calculated from the 24h and 5 min ECG segments, and preselected multifractal parameters τ(q=2), τ(q=3), h_top and Δh were determined for daytime (12:00-18:00) and nighttime (00:00-06:00) periods of the ECG recordings using Ivanov's method. Mean differences over time were tested using paired-samples t-test and exact Wilcoxon matched-pairs test. The results are reported as mean ± SD and median with interquartile range. A p value of <0.05 was considered statistically significant.

RESULTS

All selected conventional linear HRV parameters decreased significantly after off pump CABG (p from <0.001-0.015). Preoperatively, multifractal parameter τ(q=2) was -0.60 ± 0.12 and -0.54 ± 0.12, τ(q=3) -0.52 ± 0.18 and -0.49 ± 0.17, h_top 0.20 ± 0.07 and 0.15 ± 0.07 and Δh 0.31 ± 0.14 and 0.17 ± 0.14 for daytime and nighttime periods, respectively. Postoperatively, τ(q=2) and τ(q=3) were significantly higher for daytime (-0.49 ± 0.15, p<0.001 and -0.43 ± 0.23, p=0.015), whereas h_top and Δh were significantly higher for both daytime and nighttime (0.25 ± 0.07, p<0.001 and 0.19 ± 0.06, p=0.002 for h_top and 0.41 ± 0.20, p=0.003 and 0.31 ± 0.19, p < 0.001 for Δh, respectively). All pre- and postoperative parameters, except τ(q=2) and τ(q=3) preoperatively, were significantly lower for nighttime as compared to daytime periods.

CONCLUSIONS

A significant breakdown of multifractal complexity and anti-correlation behavior with a significant sympathetic overdrive and a concomitant parasympathetic withdrawal occurs after off-pump CABG. The circadian pattern of multifractality regains its day-night variation in the first week after the surgical procedure.

Risk stratification of cardiac autonomic neuropathy based on multi-lag Tone-Entropy

Cardiac autonomic neuropathy (CAN) is an irreversible condition affecting the autonomic nervous system, which leads to abnormal functioning of the visceral organs and affects critical body functions such as blood pressure, heart rate and kidney filtration. This study presents multi-lag Tone-Entropy (T-E) analysis of heart rate variability (HRV) at multiple lags as a screening tool for CAN. A total of 41 ECG recordings were acquired from diabetic subjects with definite CAN (CAN+) and without CAN (CAN-) and analyzed. Tone and entropy values of each patient were calculated for different beat sequence lengths (len: 50-900) and lags (m: 1-8). The CAN- group was found to have a lower mean tone value compared to that of CAN+ group for all m and len, whereas the mean entropy value was higher in CAN- than that in CAN+ group. Leave-one-out (LOO) cross-validation tests using a quadratic discriminant (QD) classifier were applied to investigate the performance of multi-lag T-E features. We obtained 100 % accuracy for tone and entropy with len = 250 and m = {2, 3} settings, which is better than the performance of T-E technique based on lag m = 1. The results demonstrate the usefulness of multi-lag T-E analysis over single lag analysis in CAN diagnosis for risk stratification and highlight the change in autonomic nervous system modulation of the heart rate associated with cardiac autonomic neuropathy.

Linear and nonlinear analysis of heart rate variability in healthy subjects and after acute myocardial infarction in patients

The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.

Fractal properties of human heart period variability: physiological and methodological implications

Fractal frequency scaling of heart period variability is used as a concise index of overall cardiac control. However, no prior study has assessed within-individual reproducibility of fractal indices of heart period, or reported how the estimated indices respond to autonomic blockade. Therefore, we examined fractal properties of the heart period from ten young, healthy individuals during three separate experimental sessions under control (saline) conditions and twice under combined autonomic blockade (atenolol and atropine sulfate) conditions. Under each condition, R-R intervals were recorded with the subject in the supine and the 40 deg upright tilt positions during 20 min of controlled breathing in each position. We calculated the fractal scaling exponent using detrended fluctuation analysis and estimated confidence intervals of the scaling exponents for each R-R interval time series within each individual. In the control condition, upright tilt significantly increased the scaling exponents (from 0.73 +/- 0.11 (+/-S.D., session 1), 0.72 +/- 0.10 (session 2) and 0.75 +/- 0.13 (session 3) to 0.82 +/- 0.12, 0.82 +/- 0.11 and 0.84 +/- 0.10; Student's paired t-test, t = 2.79, P = 0.02; t = 2.80, P = 0.02; and t = 2.07, P = 0.07). However, neither the absolute scaling exponents nor their change in response to upright tilt were reproducible (Lin's concordance coefficient less than 0.9, P > 0.1 for all comparisons). Following autonomic blockade, the scaling exponents were significantly increased (supine: 1.08 +/- 0.13 and 1.08 +/- 0.14; tilt: 1.07 +/- 0.21 and 1.08 +/- 0.14) for both experimental sessions (two-way repeated-measures ANOVA; F(17,1) = 40.89, P < 0.001 and F(17,1) = 42.72, P < 0.001) regardless of position. However, within individuals, the scaling exponents failed to distinguish between control and blockade for half of the subjects in at least one experimental session. Thus, fractal scaling exponents are not reproducible within individuals and do not reliably reflect the autonomic mechanisms responsible for heart period variability. In fact, data from combined blockade suggest that physiological effects of autonomic outflow may mask intrinsic fractal behaviour of the sinoatrial node.

Cortical thickness abnormalities in cocaine addiction--a reflection of both drug use and a pre-existing disposition to drug abuse?

The structural effects of cocaine on neural systems mediating cognition and motivation are not well known. By comparing the thickness of neocortical and paralimbic brain regions between cocaine-dependent and matched control subjects, we found that four of 18 a priori regions involved with executive regulation of reward and attention were significantly thinner in addicts. Correlations were significant between thinner prefrontal cortex and reduced keypresses during judgment and decision making of relative preference in addicts, suggesting one basis for restricted behavioral repertoires in drug dependence. Reduced effortful attention performance in addicts also correlated with thinner paralimbic cortices. Some thickness differences in addicts were correlated with cocaine use independent of nicotine and alcohol, but addicts also showed diminished thickness heterogeneity and altered hemispheric thickness asymmetry. These observations suggest that brain structure abnormalities in addicts are related in part to drug use and in part to predisposition toward addiction.

Errors in the estimation of approximate entropy and other recurrence-plot-derived indices due to the finite resolution of RR time series

An analysis of the errors due to the finite resolution of RR time series in the estimation of the approximate entropy (ApEn) is described. The quantification errors in the discrete RR time series produce considerable errors in the ApEn estimation (bias and variance) when the signal variability or the sampling frequency is low. Similar errors can be found in indices related to the quantification of recurrence plots. An easy way to calculate a figure of merit [the signal to resolution of the neighborhood ratio (SRN)] is proposed in order to predict when the bias in the indices could be high. When SRN is close to an integer value n, the bias is higher than when near n - 1/2 or n + 1/2. Moreover, if SRN is close to an integer value, the lower this value, the greater the bias is.