A characterization of HRV's nonlinear hidden dynamics by means of Markov models

Relation of Various Parameters Used to Estimate Cardiac Vagal Activity and Validity of pNN50 in Anesthetized Humans

Objectives Analysis of heart rate variability (HRV) has been used as a measure of cardiac autonomic function. According to the pNN50 statistic, the percentage of differences between successive normal RR intervals (RRI) that exceed 50 ms, has been known to reflect cardiac vagal modulation. Relatively little is known about the validity of pNN50 during general anesthesia (GA). Therefore, we evaluated the correlation of pNN50 with other variables such as HF, RMSSD, SD1 of HRV reflecting the vagal tone, and examined the validity of pNN50 in anesthetized patients. Methods: We assessed changes in RRI, pNN50, root mean square of successive differences of RRI (RMSSD), high frequency (HF) and standard deviation 1 (SD1) of Poincaré plots after GA using sevoflurane anesthesia. We also calculated the probability distributions for the family of pNNx statistics (x: 2-50 ms). Results All HRV variables were significantly decreased during GA. HF power was not correlated with pNN50 during GA (r = 0.096, P = 0.392). Less than pNN47 was shown to have a correlation with other variables. Conclusions These data suggest that pNN50 can not reflect the level of vagal tone during GA.

Robust sleep apnea monitoring using heart rate variability and extended Kalman classification based on single lead ECG

Sleep apnea diagnosis requires analysis of long term polysomnographic signal during one period of night sleep. Limited access to sleep laboratories, various required devices and dedicated assistants made the diagnosis of sleep apnea underestimated and not easily accessible to the general population. In this work, a classification method based on modified Kalman filter which uses heart rate variability (HRV) wavelet signal obtained from a single electrocardiogram (ECG) lead is proposed. A pre-filtering was performed on wavelet transform to improve the correlation of extracted features. Sample entropy was used to enhance the convergence rate and accuracy of classification. The performance of the proposed method was evaluated in terms of accuracy, sensitivity and specificity. The classifier overcomes these methods by 5.3% to 7.2% improvements in accuracy.

NONLINEAR ANALYSIS OF PHYSIOLOGICAL SIGNALS: A REVIEW

This paper reviews various nonlinear analysis methods for physiological signals. The assessment is based on a discussion of chaos-inspired methods, such as fractal dimension (FD), correlation dimension (D2), largest Lyapunov exponet (LLE), Renyi's entropy (REN), Shannon spectral entropy (SEN), and approximate entropy (ApEn). We document that these methods are used to extract discriminative features from electroencephalograph (EEG) and heart rate variability (HRV) signals by reviewing the relevant scientific literature. EEG features can be used to support the diagnosis of epilepsy and HRV features can be used to support the diagnosis of cardiovascular diseases as well as diabetes. Documenting the widespread use of these and other nonlinear methods supports our thesis that the study of feature extraction methods, based on the chaos theory, is an important subject which has been gaining more and significance in biomedical engineering. We adopt the position that pursuing research in the field of biomedical engineering is ultimately a progmatic activity, where it is necessary to engage in features that work. In this case, the nonlinear features are working well, even if we do not have conclusive evidence that the underlying physiological phenomena are indeed chaotic.

Detection of Nonlinearity in Cardiovascular Variability Signals using Cyclostationary Analysis

A novel approach for detection of polynomial nonlinearity in the neuro-cardiovascular system based on cyclostationary analysis is presented. Metronome breathing is employed to provide a sinusoidal input to the neuro-cardiovascular system in which Heart Rate Variability (HRV) and Blood Pressure Variation (BPV) are considered as its outputs. The presence of new harmonics of the main respiratory rate in the HRV and BPV is investigated by using the concept of (self) phase and (self) frequency coupling. It is shown that a second order polynomial nonlinear system is actually involved in producing the HRV and BPV. The strength of this nonlinearity decreases with increasing the breathing rate.

Hidden markov models and mutual information analysis to characterize nonlinear dynamics in heart rate variability

A study of nonlinear dynamics of the heart rate variability (HRV) was performed using hidden Markov models (HMM) and Mutual Information (MI). A methodology based on HMM has been developed in the present work. Cardiac RR series were analyzed in the three frequency bands: HF (0.15-0.45Hz), high frequency band; LF (0.04-0.15Hz), low frequency band; VLF (0.003-0.04Hz), very low frequency band. These series (0, observations) were modeled using HMM. The model λ=(A,B,∏) was selected so that P(O/λ) was locally maximized. Ergodic topology and N=10 states were also considered for this analysis. Different measures based on HMM were defined and obtained from RR time series of 37 Idiopathic Dilated Crdiomyopathy (IDC) patients and 46 healthy subjects (NRM), during awake and sleep stages. Two groups of IDC patients were considered: 11 high risk (HR) patients, after aborted sudden cardiac death (SCD) or who died during the follow up; 26 low risk (LR) patients, without SCD. Some HMM measures showed high percentages (up to 100%) of well classified subjects in all groups.

Evaluation of different rhythms by hidden Markov models in heart rate variability of hypertrophic cardiomyopathy patients

Synchronization and regularity between different rhythms were evaluated in the HRV using hidden Markov models (HMMs) at very low (VLF), low (LF) and high (HF) frequency bands. Phase synchronization of these rhythms was studied in RR series of hypertrophic cardiomyopathy (HCM) patients during the sleeping period. Two groups of patients were considered in the HCM group: high risk (HR), patients after aborted sudden death (SCD) or that died during follow up, and low risk (LR), patients without SCD. RR time-series were filtered in the following frequency-bands, VLF, LF and HF. The RR phase differences of HF vs. VLF, HF vs. LF and LF vs. VLF were calculated and then the amplitude range partitioned into 8 bins. Finally, these series (O, observations) were modeled using HMM. The models lambda = (A,B,pi) were selected such that P(O/lambda) was locally maximized. Ergodic topology and N = {5,10,15,20} states were considered also for this analysis. Ergodic HMMs with 10 states were found to be sufficient to characterize the HRV rhythms of HR and LR patients. Different synchronization strength was observed studying the phase entropies. However, only the parameters obtained from the HMM were able to differentiate the different groups, with p-value < 0.0005.

Hidden Markov Models Based on Symbolic Dynamics for Statistical Modeling of Cardiovascular Control in Hypertensive Pregnancy Disorders

Discrete hidden Markov models (HMMs) were applied to classify pregnancy disorders. The observation sequence was generated by transforming RR and systolic blood pressure time series using symbolic dynamics. Time series were recorded from 15 women with pregnancy-induced hypertension, 34 with preeclampsia and 41 controls beyond 30th gestational week. HMMs with five to ten hidden states were found to be sufficient to characterize different blood pressure variability, whereas significant classification in RR-based HMMs was found using fifteen hidden states. Pregnancy disorders preeclampsia and pregnancy induced hypertension revealed different patho-physiological autonomous regulation supposing different etiology of both disorders.

Robustness of support vector machine-based classification of heart rate signals

In this study, we discuss the use of support vector machine (SVM) learning to classify heart rate signals. Each signal is represented by an attribute vector containing a set of statistical measures for the respective signal. At first, the SVM classifier is trained by data (attribute vectors) with known ground truth. Then, the classifier learnt parameters can be used for the categorization of new signals not belonging to the training set. We have experimented with both real and artificial signals and the SVM classifier performs very well even with signals exhibiting very low signal to noise ratio which is not the case for other standard methods proposed by the literature.

Statistics and graphs for heart rate variability: pNN50 or pNN20?

Two measures of heart rate variability, pNN50 and pNN20, are compared. A non-linear transformation of these measures is proposed, that is helpful in understanding their interrelationship. Provided a valid statistical test is employed, results from analysing pNN20 are likely to be equivalent to those from analysing pNN50. Arguments recently made by Mietus et al (2002 Heart 88 378-80) against the commonly used pNN50 are unconvincing.

Nonlinear measures of QT interval series: novel indices of cardiac repolarization lability: MEDqthr and LLEqthr

In this study, we investigated nonlinear measures of chaos of QT interval time series in 28 normal control subjects, 36 patients with panic disorder and 18 patients with major depression in supine and standing postures. We obtained the minimum embedding dimension (MED) and the largest Lyapunov exponent (LLE) of instantaneous heart rate (HR) and QT interval series. MED quantifies the system's complexity and LLE predictability. There was a significantly lower MED and a significantly increased LLE of QT interval time series in patients. Most importantly, nonlinear indices of QT/HR time series, MEDqthr (MED of QT/HR) and LLEqthr (LLE of QT/HR), were highly significantly different between controls and both patient groups in either posture. Results remained the same even after adjusting for age. The increased LLE of QT interval time series in patients with anxiety and depression is in line with our previous findings of higher QTvi (QT variability index, a log ratio of QT variability corrected for mean QT squared divided by heart rate variability corrected for mean heart rate squared) in these patients, using linear techniques. Increased LLEqthr (LLE of QT/HR) may be a more sensitive tool to study cardiac repolarization and a valuable addition to the time domain measures such as QTvi. This is especially important in light of the finding that LLEqthr correlated poorly and nonsignificantly with QTvi. These findings suggest an increase in relative cardiac sympathetic activity and a decrease in certain aspects of cardiac vagal function in patients with anxiety as well as depression. The lack of correlation between QTvi and LLEqthr suggests that this nonlinear index is a valuable addition to the linear measures. These findings may also help to explain the higher incidence of cardiovascular mortality in patients with anxiety and depressive disorders.

Diminished chaos of heart rate time series in patients with major depression

BACKGROUND

Depression and anxiety have been linked to serious cardiovascular events in patients with preexisting cardiac illness. A decrease in cardiac vagal function as suggested by a decrease in heart rate (HR) variability has been linked to sudden death.

METHODS

We compared LLE and nonlinearity scores of the unfiltered (UF) and filtered time series (very low, low, and high frequency; VLF, LF and HF) of HR between patients with depression (n = 14) and healthy control subjects (n = 18).

RESULTS

We found significantly lower LLE of the unfiltered series in either posture, and HF series in patients with major depression in supine posture (p <.002). LLE (LF/UF), which may indicate relative sympathetic activity was also significantly higher in supine and standing postures in patients (p <.05); LF/HF (LLE) was also higher in patients (p <.05) in either posture.

CONCLUSIONS

These findings suggest that major depression is associated with decreased cardiac vagal function and a relative increase in sympathetic function, which may be related to the higher risk of cardiovascular mortality in this group and illustrates the usefulness of nonlinear measures of chaos such as LLE in addition to the commonly used spectral measures.

Heart rate time series: decreased chaos after intravenous lactate and increased non-linearity after isoproterenol in normal subjects

In this study, we reanalyzed our previous heart rate time series data on the effects of intravenous sodium lactate (n=9) and intravenous isoproterenol (n=11) using non-linear techniques. Our prior findings of significantly higher baseline non-linear scores (NL: S(netGS)) and significantly lower largest Lyapunov exponents in supine posture in patients with panic disorder compared to control subjects prompted this study. We obtained the largest Lyapunov exponent (LLE), and a measure of non-linearity (NL: S(netGS)) of heart rate time series. LLE quantifies predictability and NL quantifies the deviation from linear processes. There was a significant increase in NL score, (S(netGS)) after isoproterenol infusions and a significant decrease in LLE (an increase in predictability indicating decreased chaos), after intravenous lactate in supine posture in normal control subjects. Increased NL scores in supine posture after intravenous isoproterenol may be due to a relative increase in cardiac sympathetic activity or a decrease in vagal activity at least in certain circumstances, and an overall decrease in LLE may indicate an impaired cardiac autonomic flexibility after intravenous sodium lactate, as LLE is diminished by autonomic blockade by atropine. Band analysis of LLE (LF/HF) (LF: 0.04-0.15 Hz and HF: 0.15-0.5 Hz) showed an increase of these ratios during either condition with a higher sympathovagal interaction after the drug administration. These findings may throw new light on the association of anxiety and significant cardiovascular events.

Decreased chaos and increased nonlinearity of heart rate time series in patients with panic disorder

In this study, we investigated measures of nonlinear dynamics and chaos of heart rate time series in 30 normal control subjects and 36 age-matched patients with panic disorder in supine and standing postures. We obtained minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies system's complexity, LLE predictability and NL, deviation from linear processes. There was a significant increase in complexity (p < 0.00001), an increase in predictability (decreased chaos) (p < 0.00001) and an increase in nonlinearity (Snet GS) (p = 0.00001), especially in supine posture in patients with panic disorder. Increased NL score in supine posture may be due to a relative increase in cardiac sympathetic activity and an overall decrease in LLE may indicate an impaired cardiac autonomic flexibility in these patients due possibly to a decrease in cardiac vagal activity. These findings may further explain the reported higher incidence of cardiovascular mortality in patients with anxiety disorders.

Nonlinear measures of heart rate time series: influence of posture and controlled breathing

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P < 0.00001), a decrease in predictability (P < 0.00001) and an increase in nonlinearity (P = 0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component.