Applying fractal analysis to short sets of heart rate variability data

Heart rate variability-based prediction of early cardiotoxicity in breast-cancer patients treated with anthracyclines and trastuzumab

BACKGROUND

Cardiotoxicity is a recognized complication in breast cancer (BC) patients undergoing chemotherapy with anthracyclines with or without trastuzumab. However, the prognostic value of heart rate variability (HRV) indexes for early cardiotoxicity development remains unknown.

METHODS

Fifty BC patients underwent TTE assessment before and three months after chemotherapy. HRV indexes were obtained from continuous electrocardiograms in supine position with spontaneous breathing, active standing, and supine position with controlled breathing. The magnitude of change (Δ) between supine-standing and supine-controlled breathing was calculated. Variables were compared using t-test or ANOVA. Cardiotoxicity predictive value was assessed by ROC curve analysis. A p value of < 0.05 was considered significant.

RESULTS

TTE revealed reduced left atrial conduit strain in the cardiotoxicity group. Mean heart rate increased during all maneuvers at follow-up, with no differences in HRV indexes between patients with or without cardiotoxicity. However, a lower Δ in supine-controlled breathing of several HRV indexes predicted early cardiotoxicity identified by echocardiography (e.g. SDNN ≤ -8.44 ms: Sensitivity = 75%, Specificity = 69%).

CONCLUSIONS

BC patients treated with chemotherapy maintain cardiac autonomic responses to physiological stimuli after 3 months of chemotherapy. However, a lower Δ during active standing and controlled breathing before chemotherapy may predict early cardiotoxicity.

Temporal complexity in photoplethysmography and its influence on blood pressure

Objective: The temporal complexity of photoplethysmography (PPG) provides valuable information about blood pressure (BP). In this study, we aim to interpret the stochastic PPG patterns with a model-based simulation, which may help optimize the BP estimation algorithms. Methods: The classic four-element Windkessel model is adapted in this study to incorporate BP-dependent compliance profiles. Simulations are performed to generate PPG responses to pulse and continuous stimuli at various timescales, aiming to mimic sudden or gradual hemodynamic changes observed in real-life scenarios. To quantify the temporal complexity of PPG, we utilize the Higuchi fractal dimension (HFD) and autocorrelation function (ACF). These measures provide insights into the intricate temporal patterns exhibited by PPG. To validate the simulation results, continuous recordings of BP, PPG, and stroke volume from 40 healthy subjects were used. Results: Pulse simulations showed that central vascular compliance variation during a cardiac cycle, peripheral resistance, and cardiac output (CO) collectively contributed to the time delay, amplitude overshoot, and phase shift of PPG responses. Continuous simulations showed that the PPG complexity could be generated by random stimuli, which were subsequently influenced by the autocorrelation patterns of the stimuli. Importantly, the relationship between complexity and hemodynamics as predicted by our model aligned well with the experimental analysis. HFD and ACF had significant contributions to BP, displaying stability even in the presence of high CO fluctuations. In contrast, morphological features exhibited reduced contribution in unstable hemodynamic conditions. Conclusion: Temporal complexity patterns are essential to single-site PPG-based BP estimation. Understanding the physiological implications of these patterns can aid in the development of algorithms with clear interpretability and optimal structures.

Cardiac Autonomic Response to Active Standing in Calcific Aortic Valve Stenosis

Aortic stenosis is a progressive heart valve disorder characterized by calcification of the leaflets. Heart rate variability (HRV) analysis has been proposed for assessing the heart response to autonomic activity, which is documented to be altered in different cardiac diseases. The objective of the study was to evaluate changes of HRV in patients with aortic stenosis by an active standing challenge. Twenty-two volunteers without alterations in the aortic valve (NAV) and twenty-five patients diagnosed with moderate and severe calcific aortic valve stenosis (AVS) participated in this cross-sectional study. Ten minute electrocardiograms were performed in a supine position and in active standing positions afterwards, to obtain temporal, spectral, and scaling HRV indices: mean value of all NN intervals (meanNN), low-frequency (LF) and high-frequency (HF) bands spectral power, and the short-term scaling indices (α1 and αsign1). The AVS group showed higher values of LF, LF/HF and αsign1 compared with the NAV group at supine position. These patients also expressed smaller changes in meanNN, LF, HF, LF/HF, α1, and αsign1 between positions. In conclusion, we confirmed from short-term recordings that patients with moderate and severe calcific AVS have a decreased cardiac parasympathetic supine response and that the dynamic of heart rate fluctuations is modified compared to NAV subjects, but we also evidenced that they manifest reduced autonomic adjustments caused by the active standing challenge.

Effect of gender-related depression on heart rate variability during an autonomic nervous test

Patients with depression have lower heart rate variability (HRV) compared with controls. However, studies have indicated HRV difference between male and female controls. The gender effect might be interactive with the depression effect on the HRV, resulting in a low accuracy of recognising the patients with depression from the controls. Our study explores the effect of gender-related depression on HRV. Four ANS tests including resting, deep breathing, Valsalva, and orthostatic test are employed as stimuli. HRV were collected from 182 subjects comprising 91 depressive patients (33 females/58 males) and 91 controls (33 females/58 males) in the four tests. Time and frequency domains and nonlinear parameters are employed to quantify HRV. Two-way ANOVA is applied to evaluate the effect of gender-related depression. Most HRV parameters of the patients significantly differ from those of the controls, but some parameters indicate different depression effect between the males and females in the deep breathing and Valsalva test. Some HRV parameters illustrate significant difference between the male and female controls. Therefore, the effect of depression on HRV of each gender should be investigated.

Multifractal Analysis Reveals Decreased Non-linearity and Stronger Anticorrelations in Heart Period Fluctuations of Fibromyalgia Patients

Objective: To characterize the multifractal behavior of the beat to beat heart-period or RR fluctuations in fibromyalgia patients (FM) in comparison with healthy-matched subjects.

Methods: Multifractral detrended fluctuation analysis (MDFA) was used to study multifractality in heartbeat times-series from 30 female healthy subjects and 30 female patients with fibromyalgia during day and night periods.The multifractal changes as derived from the magnitude and sign analysis of these RR fluctuations were also assessed.

Results: The RR fluctuations dynamics of healthy subjects showed a broad multifractal spectrum. By contrast, a noticeable decrease in multifractality and non-linearity was observed for patients with fibromyalgia. In addition, the spectra corresponding to FM subjects were located on the average to the right of the spectra of healthy individuals, indicating that the local scaling exponents reflect a smoother behavior compared to healthy dynamics. Moreover, the multifractal analysis as applied to the magnitude and sign heartbeat series confirmed that, in addition to a decreased nonlinearity, fibromyalgia patients presented stronger anticorrelation in directionality, which did not remain invariant for small or rather larger fluctuations as it occurred in healthy subjects.

Conclusion: When compared to healthy controls, fibromyalgia patients display decreased nonlinearity and stronger anticorrelations in heart period fluctuations. These findings reinforce the hypothesis of the potential role of the dysfunctional autonomic nervous system in the pathogenesis of fibromyalgia.

Sign and magnitude scaling properties of heart rate variability in patients with end-stage renal failure: Are these properties useful to identify pathophysiological adaptations?

The scaling properties of heart rate variability data are reliable dynamical features to predict mortality and for the assessment of cardiovascular risk. The aim of this manuscript was to determine if the scaling properties, as provided by the sign and magnitude analysis, can be used to differentiate between pathological changes and those adaptations basically introduced by modifications of the mean heart rate in distinct manoeuvres (active standing or hemodialysis treatment, HD), as well as clinical conditions (end stage renal disease, ESRD). We found that in response to active standing, the short-term scaling index (α₁) increased in healthy subjects and in ESRD patients only after HD. The sign short-term scaling exponent (α_1sign) increased in healthy subjects and ESRD patients, showing a less anticorrelated behavior in active standing. Both α₁ and α_1sign did show covariance with the mean heart rate in healthy subjects, while in ESRD patients, this covariance was observed only after HD. A reliable estimation of the magnitude short-term scaling exponent (α_1magn) required the analysis of time series with a large number of samples (>3000 data points). This exponent was similar for both groups and conditions and did not show covariance with the mean heart rate. A surrogate analysis confirmed the presence of multifractal properties (α_1magn > 0.5) in the time series of healthy subjects and ESDR patients. In conclusion, α₁ and α_1sign provided insights into the physiological adaptations during active standing, which revealed a transitory impairment before HD in ESRD patients. The presence of multifractal properties indicated that a reduced short-term variability does not necessarily imply a declined regulatory complexity in these patients.

Correlations in magnitude series to assess nonlinearities: Application to multifractal models and heartbeat fluctuations

The correlation properties of the magnitude of a time series are associated with nonlinear and multifractal properties and have been applied in a great variety of fields. Here we have obtained the analytical expression of the autocorrelation of the magnitude series (C_{|x|}) of a linear Gaussian noise as a function of its autocorrelation (C_{x}). For both, models and natural signals, the deviation of C_{|x|} from its expectation in linear Gaussian noises can be used as an index of nonlinearity that can be applied to relatively short records and does not require the presence of scaling in the time series under study. In a model of artificial Gaussian multifractal signal we use this approach to analyze the relation between nonlinearity and multifractallity and show that the former implies the latter but the reverse is not true. We also apply this approach to analyze experimental data: heart-beat records during rest and moderate exercise. For each individual subject, we observe higher nonlinearities during rest. This behavior is also achieved on average for the analyzed set of 10 semiprofessional soccer players. This result agrees with the fact that other measures of complexity are dramatically reduced during exercise and can shed light on its relationship with the withdrawal of parasympathetic tone and/or the activation of sympathetic activity during physical activity.

Cardiorespiratory dynamics measured from continuous ECG monitoring improves detection of deterioration in acute care patients: A retrospective cohort study

Background

Charted vital signs and laboratory results represent intermittent samples of a patient’s dynamic physiologic state and have been used to calculate early warning scores to identify patients at risk of clinical deterioration. We hypothesized that the addition of cardiorespiratory dynamics measured from continuous electrocardiography (ECG) monitoring to intermittently sampled data improves the predictive validity of models trained to detect clinical deterioration prior to intensive care unit (ICU) transfer or unanticipated death.

Methods and findings

We analyzed 63 patient-years of ECG data from 8,105 acute care patient admissions at a tertiary care academic medical center. We developed models to predict deterioration resulting in ICU transfer or unanticipated death within the next 24 hours using either vital signs, laboratory results, or cardiorespiratory dynamics from continuous ECG monitoring and also evaluated models using all available data sources. We calculated the predictive validity (C-statistic), the net reclassification improvement, and the probability of achieving the difference in likelihood ratio χ² for the additional degrees of freedom. The primary outcome occurred 755 times in 586 admissions (7%). We analyzed 395 clinical deteriorations with continuous ECG data in the 24 hours prior to an event. Using only continuous ECG measures resulted in a C-statistic of 0.65, similar to models using only laboratory results and vital signs (0.63 and 0.69 respectively). Addition of continuous ECG measures to models using conventional measurements improved the C-statistic by 0.01 and 0.07; a model integrating all data sources had a C-statistic of 0.73 with categorical net reclassification improvement of 0.09 for a change of 1 decile in risk. The difference in likelihood ratio χ² between integrated models with and without cardiorespiratory dynamics was 2158 (p value: <0.001).

Conclusions

Cardiorespiratory dynamics from continuous ECG monitoring detect clinical deterioration in acute care patients and improve performance of conventional models that use only laboratory results and vital signs.

Effects of Orthostatism and Hemodialysis on Mean Heart Period and Fractal Heart Rate Properties of Chronic Renal Failure Patients

The aim of this work was to evaluate the short-term fractal index (α₁ ) of heart rate variability (HRV) in chronic renal failure (CRF) patients by identifying the effects of orthostatism and hemodialysis (HD), and by evaluating the correlation between α₁ and the mean RR interval from sinus beats (meanNN). HRV time series were derived from ECG data of 19 CRF patients and 20 age-matched healthy subjects obtained at supine and orthostatic positions (lasting 5 min each). Data from CRF patients were collected before and after HD. α₁ was calculated from each time series and compared by analysis of variance. Pearson's correlations between meanNN and α₁ were calculated using the data from both positions by considering three groups: healthy subjects, CRF before HD and CRF after HD. At supine position, α₁ of CRF patients after HD (1.17 ± 0.30) was larger (P < 0.05) than in healthy subjects (0.89 ± 0.28) but not before HD (1.10 ± 0.34). α₁ increased (P < 0.05) in response to orthostatism in healthy subjects (1.29 ± 0.26) and CRF patients after HD (1.34 ± 0.31), but not before HD (1.25 ± 0.37). Whereas α₁ was correlated (P < 0.05) with the meanNN of healthy subjects (r = -0.562) and CRF patients after HD (r = -0.388), no significance in CRF patients before HD was identified (r = 0.003). Multiple regression analysis confirmed that α₁ was mainly predicted by the orthostatic position (in all groups) and meanNN (healthy subjects and patients after HD), showing no association with the renal disease condition in itself. In conclusion, as in healthy subjects, α₁ of CRF patients correlates with meanNN after HD (indicating a more irregular-like HRV behavior at slower heart rates). This suggests that CRF patients with stable blood pressure preserve a regulatory adaptability despite a shifted setting point of the heart period (i.e., higher heart rate) in comparison with healthy subjects.

Relationship in Pacemaker Neurons Between the Long-Term Correlations of Membrane Voltage Fluctuations and the Corresponding Duration of the Inter-Spike Interval

Several studies of the behavior in the voltage and frequency fluctuations of the neural electrical activity have been performed. Here, we explored the particular association between behavior of the voltage fluctuations in the inter-spike segment (VFIS) and the inter-spike intervals (ISI) of F1 pacemaker neurons from H. aspersa, by disturbing the intracellular calcium handling with cadmium and caffeine. The scaling exponent α of the VFIS, as provided by detrended fluctuations analysis, in conjunction with the corresponding duration of ISI to estimate the determination coefficient R ² (48-50 intervals per neuron, N = 5) were all evaluated. The time-varying scaling exponent α(t) of VFIS was also studied (20 segments per neuron, N = 11). The R ² obtained in control conditions was 0.683 ([0.647 0.776] lower and upper quartiles), 0.405 [0.381 0.495] by using cadmium, and 0.151 [0.118 0.222] with caffeine (P < 0.05). A non-uniform scaling exponent α(t) showing a profile throughout the duration of the VFIS was further identified. A significant reduction of long-term correlations by cadmium was confirmed in the first part of this profile (P = 0.0001), but no significant reductions were detected by using caffeine. Our findings endorse that the behavior of the VFIS appears associated to the activation of different populations of ionic channels, which establish the neural membrane potential and are mediated by the intracellular calcium handling. Thus, we provide evidence to consider that the behavior of the VFIS, as determined by the scaling exponent α, conveys insights into mechanisms regulating the excitability of pacemaker neurons.

Design of wireless multi-parameter monitoring system for oral feeding of premature infants

Premature infants often cannot successfully and coordinately complete their oral feeding. Mature sucking, swallowing, and respiration activities are crucial indicators for the survival of newborn infants. Due to the vulnerability and unobvious muscle activities of premature infants, current clinical care givers mainly depend on the subjective behavioral observation of infants during oral feeding. There is still lack of an integrated oral feeding monitoring system to objectively and quantifiably monitor the related physiological parameters of premature infants. In this study, a wireless multi-parameter monitoring system for oral feeding of premature infants was proposed to monitor the sucking-swallowing-respiratory activities and the heart rate variability to provide quantitative indices of oral feeding. Here, a novel sucking pressure sensing module was also developed to monitor the premature infant's sucking pressure under oral feeding to avoid the immersion influence of milk. The experimental results showed that the proposed system detected the related physiological parameters of premature infants during oral feeding effectively and may provide an objective clinical evaluation tool for oral feeding ability and safety of premature infants in the future.

Heart rate dynamics distinguish among atrial fibrillation, normal sinus rhythm and sinus rhythm with frequent ectopy

Atrial fibrillation (AF) is usually detected by inspection of the electrocardiogram waveform, a task made difficult when the signal is distorted by noise. The RR interval time series is more frequently available and accurate, yet linear and nonlinear time series analyses that detect highly varying and irregular AF are vulnerable to the common finding of frequent ectopy. We hypothesized that different nonlinear measures might capture characteristic features of AF, normal sinus rhythm (NSR), and sinus rhythm (SR) with frequent ectopy in ways that linear measures might not. To test this, we studied 2722 patients with 24 h ECG recordings in the University of Virginia Holter database. We found dynamical phenotypes for the three rhythm classifications. As expected, AF records had the highest variability and entropy, and NSR the lowest. SR with ectopy could be distinguished from AF, which had higher entropy, and from NSR, which had different fractal scaling, measured as higher detrended fluctuation analysis slope. With these dynamical phenotypes, we developed successful classification strategies, and the nonlinear measures improved on the use of mean and variability alone, even after adjusting for age. Final models using all variables had excellent performance, with positive predictive values for AF, NSR and SR with ectopy as high as 97, 98 and 90%, respectively. Since these classifiers can reliably detect rhythm changes utilizing segments as short as 10 min, we envision their application in noisy settings and in personal monitoring devices where only RR interval time series may be available.

Heart rate dynamics preceding hemorrhage in the intensive care unit

Occult hemorrhage in surgical/trauma intensive care unit (STICU) patients is common and may lead to circulatory collapse. Continuous electrocardiography (ECG) monitoring may allow for early identification and treatment, and could improve outcomes. We studied 4,259 consecutive admissions to the STICU at the University of Virginia Health System. We collected ECG waveform data captured by bedside monitors and calculated linear and non-linear measures of the RR interbeat intervals. We tested the hypothesis that a transfusion requirement of 3 or more PRBC transfusions in a 24 hour period is preceded by dynamical changes in these heart rate measures and performed logistic regression modeling. We identified 308 hemorrhage events. A multivariate model including heart rate, standard deviation of the RR intervals, detrended fluctuation analysis, and local dynamics density had a C-statistic of 0.62. Earlier detection of hemorrhage might improve outcomes by allowing earlier resuscitation in STICU patients.

Classification of cardiac rhythm using heart rate dynamical measures: validation in MIT-BIH databases

BACKGROUND

Identification of atrial fibrillation (AF) is a clinical imperative. Heartbeat interval time series are increasingly available from personal monitors, allowing new opportunity for AF diagnosis.

GOAL

Previously, we devised numerical algorithms for identification of normal sinus rhythm (NSR), AF, and SR with frequent ectopy using dynamical measures of heart rate. Here, we wished to validate them in the canonical MIT-BIH ECG databases.

METHODS

We tested algorithms on the NSR, AF and arrhythmia databases.

RESULTS

When the databases were combined, the positive predictive value of the new algorithms exceeded 95% for NSR and AF, and was 40% for SR with ectopy. Further, dynamical measures did not distinguish atrial from ventricular ectopy. Inspection of individual 24hour records showed good correlation of observed and predicted rhythms.

CONCLUSION

Heart rate dynamical measures are effective ingredients in numerical algorithms to classify cardiac rhythm from the heartbeat intervals time series alone.

Fractal-like correlations of the fluctuating inter-spike membrane potential of a Helix aspersa pacemaker neuron

We analyzed the voltage fluctuations of the membrane potential manifested along the inter-spike segment of a pacemaker neuron. Time series of intracellular inter-spike voltage fluctuations were obtained in the current-clamp configuration from the F1 neuron of 12 Helix aspersa specimens. To assess the dynamic or stochastic nature of the voltage fluctuations these series were analyzed by Detrended Fluctuation Analysis (DFA), providing the scaling exponent α. The median α result obtained for the inter-spike segments was 0.971 ([0.963, 0.995] lower and upper quartiles). Our results indicate a critical-like dynamic behavior in the inter-spike membrane potential that, far from being random, shows long-term correlations probably linked to the dynamics of the mechanisms involved in the regulation of the membrane potential, thereby endorsing the occurrence of critical-like phenomena at a single-neuron level.

Heart rate variability during sleep and subsequent sleepiness in patients with chronic fatigue syndrome

We determined whether alterations in heart rate dynamics during sleep in patients with chronic fatigue syndrome (CFS) differed from controls and/or correlated with changes of sleepiness before and after a night in the sleep laboratory. We compared beat-to-beat RR intervals (RRI) during nocturnal sleep, sleep structure, and subjective scores on visual analog scale for sleepiness in 18 CFS patients with 19 healthy controls aged 25-55 after excluding subjects with sleep disorders. A short-term fractal scaling exponent (α1) of RRI dynamics, analyzed by the detrended fluctuation analysis (DFA) method, was assessed after stratifying patients into those who reported more or less sleepiness after the night's sleep (a.m. sleepier or a.m. less sleepy, respectively). Patients in the a.m. sleepier group showed significantly (p<0.05) higher fractal scaling index α1 during non-rapid eye movement (non-REM) sleep (Stages 1, 2, and 3 sleep) than healthy controls, although standard polysomnographic measures did not differ between the groups. The fractal scaling index α1 during non-REM sleep was significantly (p<0.05) higher than that during awake periods after sleep onset for healthy controls and patients in the a.m. less sleepy group, but did not differ between sleep stages for patients in the a.m. sleepier group. For patients, changes in self-reported sleepiness before and after the night correlated positively with the fractal scaling index α1 during non-REM sleep (p<0.05). These results suggest that RRI dynamics or autonomic nervous system activity during non-REM sleep might be associated with disrupted sleep in patients with CFS.

Effects of fetal respiratory movements on the short-term fractal properties of heart rate variability

We evaluated the effect of fetal respiratory movements (RM) on the heart rate (HR) fractal dynamics.Abdominal ECG recordings were collected from low-middle-risk pregnant woman at rest. Mean gestational age was 34.8 ± 3.7 weeks. Ultrasound images were simultaneously acquired determining if RM were exhibited by fetuses. 13 pairs of HR series were compared. Each pair included 5 min of data from the same fetus either during the manifestation of RM or when there was no persistent indication of them. Detrended fluctuation analysis was applied to these series for obtaining the scaling exponent α1. HR series were also assessed using the conventional parameters RMSSD and HF power.The main findings of this contribution were the lack of significant changes in the scaling exponent α1 of fetal HR fluctuations as a result of RM. By contrast, HF power and RMSSD did show significant changes associated with the manifestation of fetal RM (p < 0.001 and p < 0.05, respectively). Yet the scaling exponent was the only parameter showing a significant relationship with the particular frequency of fetal RM (r s  = 0.6, p < 0.03). Given the invariability of α1 regarding the manifestation of fetal RM, we consider that the HR short-term fractal properties are convenient for assessing the cardiovascular prenatal regulation.

Complexity of the autonomic heart rate control in coronary artery occlusion in patients with and without prior myocardial infarction

Autonomic nervous system (ANS) is governed by complex interactions arising from feedback loops of nonlinear systems that operate over a wide range of temporal and spatial scales, enabling the organism to adapt to stress, metabolic changes and diseases. This study is aimed to assess multifractal and nonlinear characteristics of the ANS during ischemic events provoked by a prolonged percutaneous coronary intervention (PCI) procedure. Eighty-seven patients from the STAFF III database were used. Patients were classified into 2 groups: (1) with prior myocardial infarction (MI) and (2) without MI (noMI). R-R signals during three 3-min stages of the procedures were analyzed using multifractal and surrogate data techniques. Multifractal indices increased significantly from the pre-inflation stage to the post-deflation stage. These variations were more marked for the noMI group. Multifractal changes significantly correlated with both the decreased parasympathetic and the increased sympathetic modulations accounted by classical linear indices. Multifractal measures resulted to be a more powerful indicator than linear HRV indices in quantifying the ischemia-induced changes. Right coronary artery (RCA) occlusions provoke greater multifractal reactions throughout the PCI procedure. Our findings suggest reduced complex multifractal and nonlinear reactions of ANS activity in patients with prior MI in comparison to the noMI group, possibly due to degradation in the complexity of control mechanism of heart rate generation.

Adaptive time-varying detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a technique commonly used to assess and quantify the presence of long-range temporal correlations (LRTCs) in neurophysiological time series. Convergence of the method is asymptotic only and therefore its application assumes a constant scaling exponent. However, most neurophysiological data are likely to involve either spontaneous or experimentally induced scaling exponent changes. We present a novel extension of the DFA method that permits the characterisation of time-varying scaling exponents. The effectiveness of the methodology in recovering known changes in scaling exponents is demonstrated through its application to synthetic data. The dependence of the method on its free parameters is systematically explored. Finally, application of the methodology to neurophysiological data demonstrates that it provides experimenters with a way to identify previously un-recognised changes in the scaling exponent in the data. We suggest that this methodology will make it possible to go beyond a simple demonstration of the presence of scaling to an appreciation of how it may vary in response to either intrinsic changes or experimental perturbations.

Modified permutation-entropy analysis of heartbeat dynamics

Heart rate variability (HRV) contains important information about the modulation of the cardiovascular system. Various methods of nonlinear dynamics (e.g., estimating Lyapunov exponents) and complexity measures (e.g., correlation dimension or entropies) have been applied to HRV analysis. Permutation entropy, which was proposed recently, has been widely used in many fields due to its conceptual and computational simplicity. It maps a time series onto a symbolic sequence of permutation ranks. The original permutation entropy assumes the time series under study has a continuous distribution, thus equal values are rare and can be ignored by ranking them according to their order of emergence, or broken by adding small random perturbations to ensure every symbol in a sequence is different. However, when the observed time series is digitized with lower resolution leading to a greater number of equal values, or the equalities represent certain characteristic sequential patterns of the system, it may not be rational to simply ignore or break them. In the present paper, a modified permutation entropy is proposed that, by mapping the equal value onto the same symbol (rank), allows for a more accurate characterization of system states. The application of the modified permutation entropy to the analysis of HRV is investigated using clinically collected data. Results show that modified permutation entropy can greatly improve the ability to distinguish the HRV signals under different physiological and pathological conditions. It can characterize the complexity of HRV more effectively than the original permutation entropy.

Asymmetric properties of long-term and total heart rate variability

We report on two new physiological phenomena: the long-term and total heart rate asymmetry, which describe a significantly larger contribution of heart rate accelerations to long-term and total heart rate variability. In addition to the existing pair of indices, SD1(d); SD1(a); which are based on partitioning short-term variance, we introduce two other pairs of descriptors based on partitioning longterm (SD2(d); SD2(a)) and total (SDNN(d); SDNN(a)) heart rate variability. The new asymmetric descriptors are used to analyze RR intervals time series derived from the 30-min ECG recordings of 241 healthy subjects resting in supine position. It is shown that both new types of asymmetry are present in 76% of the subjects. The new phenomena reported here are real physiological findings rather than artifacts of the method since they vanish after data shuffling.

Multivariate short-term heart rate variability: a pre-diagnostic tool for screening heart disease

This study has aimed to develop a novel pre-diagnostic tool for primary care screening of heart disease based on multivariate short-term heart rate variability (HRV) analyzed by linear (time and frequency domain) and nonlinear methods (compression entropy (CE), detrended fluctuation analysis (DFA), Poincaré plot analysis, symbolic dynamics) applied to 5-min ECG segments. Firstly, we applied HRV analysis to separate healthy subjects (REF) from heart disease patients (PAT). Then to optimize the results, we subdivided both groups according to gender: REF (♂ = 78, ♀ = 53) versus PAT (♂ = 378, ♀ = 115). Finally, we divided REF and PAT into two age subgroups (30-50 years vs. 51-70 years of age) to consider the influence of age on HRV. Heart disease patients were classified using a scoring system based on cut-off values calculated from all HRV indices obtained from the REF. After combining the optimum indices from all different analyzing methods, sensitivities of more than 72% and a specificity of 100% in all subgroups were revealed. Nonlinear indices proved to be better for discriminating heart disease patients from healthy subjects. Multivariate short-term HRV, analyzed by both linear and nonlinear methods appears to be a suitable pre-diagnostic tool for screening heart disease in primary care settings.

Short-term heart rate dynamics of pregnant women

Aiming to detect the stage of gestation where dynamical changes of the RR fluctuations may occur, we assessed short-term fluctuations of low risk pregnant women. Ninety six, 10min ECG recordings were collected along gestation (7 to 39 weeks). Corresponding RR fluctuations series were analysed to obtain the RMSSD, α(1), α(1(mag)) and α(1(sign)) parameters. Four groups covering first, second and last trimesters of gestation were conformed. No significant changes in α(1), which was close to unit, and α(1(sign)) among gestational groups were identified. But, in accordance with previous findings, we did find a significant reduction of RMSSD along gestation, and significant short-term changes that indicate a higher degree of nonlinearity after about 26 weeks of gestation (α(1(mag))>0.5)). These results suggest that the short-term heart rate dynamics of low risk pregnant women do not become compromised during gestation, despite the increased haemodynamic demands and other ongoing adaptations. Yet the complexity of the mechanisms involved in the cardiac regulation of pregnant women does seem to increase from mid-pregnancy, possibly owing to new short-term control influences or to modifications regardless the strength of the regulatory interactions.