Andreas Voss

Nonlinear analysis of complex phenomena in cardiological data

Zusammenfassung Das Hauptanliegen dieses Beitrages ist es, verschiedene Ansätze in der Herzfrequenz- und Blutdruckvariabilität zu diskutieren und damit das Verständnis der kardiovaskulären Regulation zu verbessern. Wir betrachten Komplexitätsmaße basierend auf der symbolischen Dynamik, die renormierte Entropie und die ,finite-time’ Wachstumsraten. Weiterhin werden die duale Sequenzmethode zur Bestimmung der Baroreflexsensitivität sowie die Maximalkorrelationsmethode zur Schätzung der nichtlinearen Kopplung in bivariaten Daten vorgestellt. Letztere stellt eine geeignete Methode zur Bestimmung der Kopplungsstärke und –richtung dar. Herzfrequenz- und Blutdruckvariabilitätsdaten einer klinischen Pilotstudie und einer großangelegten klinischen Studie werden analysiert. Wir demonstrieren in diesem Beitrag, dass Methoden der nichtlinearen Dynamik nützlich sind für die Risikostratifizierung nach Herzinfarkt, für die Vorhersage von lebensbedrohlichen Rhythmusstörungen sowie für die Modellierung der Herzfrequenz- und Blutdruckregulation. Diese Ergebnisse könnten in der klinischen Diagnostik sowie für therapeutische und präventive Zwecke von implantierbaren Defibrillatoren der nächsten Generation von Bedeutung sein.Summary The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators.

Multiparametric Analysis of Heart Rate Variability Used for Risk Stratification Among Survivors of Acute Myocardial Infarction

A multiparametric heart rate variability analysis was performed to prove if combined heart rate variability (HRV) measures of different domains improve the result of risk stratification in patients after myocardial infarction. In this study, standard time domain, frequency domain and non‐linear dynamics measures of HRV assessment were applied to 572 survivors of acute myocardial infarction. Three parameter sets each consisting of 4 parameters were applied and compared with the standard measurement of global heart rate variability HRVi. Discriminant analysis technique and t‐test were performed to separate the high risk groups from the survivors. The predictive value of this approach was evaluated with receiver operator (ROC) and positive predictive accuracy (PPA) curves. Results ‐ The discriminant analysis shows a separation of patients suffered by all cause mortality in 80% (best single parameter 74%) and sudden arrhythmic death in 86% (73%). All parameters of set I show a high significant difference (p<0.001) between survivors and non‐survivors based on two‐tailed t‐test. The specificity level of the multivariate parameter sets is at the 70% sensitivity level (ROC) about 85–90%, whereas HRVi shows maximum levels of 70%. The PPA in the all cause mortality group is at the 70% sensitivity level twice as high as the univarihate HRV measure and increases to more than fourfold as high within the VT/VF group. In conclusion, in this population, the multiparametric approach with the combination of four parameters from all domains especially from NLD seems to be a better predictor of high arrhythmia risk than the standard measurement of global heart rate variability.

Baroreflex sensitivity, heart rate, and blood pressure variability in normal pregnancy

Heart rate variability is a relevant predictor of cardiovascular risk in humans. However, to use heart and blood pressure (BP) variability or baroreflex sensitivity as markers for hypertensive pregnancy disorders, it is first necessary to describe these parameters in normal pregnancy. To accommodate the complexities of autonomic cardiovascular control we added parameter domains of nonlinear dynamics to conventional linear methods of time and frequency domains. The BP of 27 women with normal pregnancy and 14 nonpregnant women were monitored at a high resolution (200 Hz sampling frequency) using a Portapres for 30 min. The pregnant women were divided into groups of 32 or less or greater than 32 weeks of gestation. Pregnant and nonpregnant women were classified into subclasses of maternal age of less than 28 or 28 or more years. Except for two single parameter domains, we found no significant differences in heart rate and BP variability for pregnant women with different gestational age or different maternal age. Moreover, no significant differences in spontaneous baroreflex sensitivity could be found between pregnant women regardless of either their age or gestational age. In contrast, all measures of nonlinear dynamics of heart rate variability as well as all parameter domains of spontaneous baroreflex sensitivity showed significant changes between pregnant and nonpregnant women, whereas BP variability did not differ between those groups. This complex assessment of autonomic cardiovascular regulation has shown that the parameters tested are stable in the second half of normal pregnancy, and might have the potential to be excellent indicators of pathophysiologic conditions.

Angiotensin-Converting Enzyme and Angiotensinogen Gene Polymorphisms and Heart Rate Variability in Twins

Decreased heart rate variability (HRV) is associated with congestive heart failure, post-myocardial infarction, ventricular arrhythmias, sudden cardiac death, and advancing age. A deletion/insertion polymorphism in the angiotensin-converting enzyme (ACE) gene and a substitution (M235T) in the angiotensinogen gene have been associated with risk for heart disease. The aim of this study was to determine the heritability of HRV and related parameters in monozygotic and dizygotic twins and to assess the influence of ACE and angiotensinogen polymorphisms. We studied 95 MZ pairs and 46 DZ pairs. We measured HRV and related parameters, ACE and angiotensinogen levels, plasma norepinephrine, ACE, and angiotensinogen genotypes. We found that HRV and related parameters were significantly influenced by genetic variability, although nonshared genetic effects were also important. Angiotensinogen and plasma norepinephrine were generally correlated with decreased HRV, whereas ACE was correlated with perturbances of normal rhythmic HRV. Nevertheless, the DD ACE genotype was associated with increased HRV (p <0.05), whereas angiotensinogen polymorphisms had no effect. We conclude that HRV and related parameters are in part heritable. Interestingly, the DD ACE genotype is associated with increased HRV.

Comparison of nonlinear methods symbolic dynamics, detrended fluctuation, and Poincaré plot analysis in risk stratification in patients with dilated cardiomyopathy

Dilated cardiomyopathy (DCM) has an incidence of about 20100 000 new cases per annum and accounts for nearly 10 000 deaths per year in the United States. Approximately 36% of patients with dilated cardiomyopathy (DCM) suffer from cardiac death within five years after diagnosis. Currently applied methods for an early risk prediction in DCM patients are rather insufficient. The objective of this study was to investigate the suitability of short-term nonlinear methods symbolic dynamics (STSD), detrended fluctuation (DFA), and Poincare plot analysis (PPA) for risk stratification in these patients. From 91 DCM patients and 30 healthy subjects (REF), heart rate and blood pressure variability (HRV, BPV), STSD, DFA, and PPA were analyzed. Measures from BPV analysis, DFA, and PPA revealed highly significant differences (p<0.0011) discriminating REF and DCM. For risk stratification in DCM patients, four parameters from BPV analysis, STSD, and PPA revealed significant differences between low and high risk (maximum sensitivity: 90%, specificity: 90%). These results suggest that STSD and PPA are useful nonlinear methods for enhanced risk stratification in DCM patients.

Analysis of cardiovascular oscillations: A new approach to the early prediction of pre-eclampsia

Pre-eclampsia (PE) is a serious disorder with high morbidity and mortality occurring during pregnancy; 3%-5% of all pregnant women are affected. Early prediction is still insufficient in clinical practice. Although most pre-eclamptic patients show pathological uterine perfusion in the second trimester, this parameter has a positive predictive accuracy of only 30%, which makes it unsuitable for early, reliable prediction. The study is based on the hypothesis that alterations in cardiovascular regulatory behavior can be used to predict PE. Ninety-six pregnant women in whom Doppler investigation detected perfusion disorders of the uterine arteries were included in the study. Twenty-four of these pregnant women developed PE after the 30th week of gestation. During pregnancy, additional several noninvasive continuous blood pressure recordings were made over 30 min under resting conditions by means of a finger cuff. The time series extracted of systolic as well as diastolic beat-to-beat pressures and the heart rate were studied by variability and coupling analysis to find predictive factors preceding genesis of the disease. In the period between the 18th and 26th weeks of pregnancy, three special variability and baroreflex parameters were able to predict PE several weeks before clinical manifestation. Discriminant function analysis of these parameters was able to predict PE with a sensitivity and specificity of 87.5% and a positive predictive value of 70%. The combined clinical assessment of uterine perfusion and cardiovascular variability demonstrates the best current prediction several weeks before clinical manifestation of PE.

Evaluation of renormalised entropy for risk stratification using heart rate variability data.

Standard time and frequency parameters of heart rate variability (HRV) describe only linear and periodic behaviour, whereas more complex relationships cannot be recognised. A method that may be capable of assessing more complex properties is the non-linear measure of ‘renormalised entropy’. A new concept of the method, REAR, has been developed, based on a non-linear renormalisation of autoregressive spectral distributions. To test the hypothesis that renormalised entropy may improve the result of high-risk stratification after myocardial infarction, it is applied to a clinical pilot study (41 subjects) and to prospective data of the St Georges Hospital post-infarction database (572 patients). The study shows that the new REAR method is more reproducible and more stable in time than a previously introduced method (p<0.001). Moreover, the results of the study confirm the hypothesis that on average, the survivors have negative values of REAR (−0.11±0.18), whereas the non-survivors have positive values (0.03±0.22, p<0.01). Further, the study shows that the combination of an HRV triangular index and REAR leads to a better prediction of sudden arrhythmic death than standard measurements of HRV. In summary, the new REAR method is an independent measure in HRV analysis that may be suitable for risk stratification in patients after myocardial infarction.

Familial and genetic influences on heart rate variability

The authors tested the hypothesis of a genetic influence on heart rate variability (HRV). This genetic influence was assessed in 62, twin pairs (30 monozygotic, 32 dizygotic). From all twins, long-term electrocardiographic records were obtained, edited, and analyzed. Heart rate variability analysis was performed on the basis of parameters from time-domain, frequency-domain, and nonlinear dynamics. First, the parameter distances between the two twins of a pair and between one of the two and a third randomly selected person of another age-matched twin pair (ST1) were compared. Second, the parameter distances between the two twins and the averaged parameter distances of these two twins to all other age-matched persons (ST2) were compared. Finally, the averaged differences in parameter values between monozygotic and dizygotic age-matched twin pairs were compared. For statistical analysis, the nonparametric Wilcoxons matched-pair signed rank test and parametric t-test for paired samples were used. Twin pairs show a significant lower difference in parameter values than other randomly selected and age-matched couples (P < .001 in ST1 and ST2). This reflects a considerable familial influence. Most parameters of the time-domain, none of the frequency-domain, and half of the nonlinear dynamics show significant differences between twin pairs and nontwin pairs. As a result of the comparison between monozygotic and dizygotic twin pairs, a significant lower parameter difference in the monozygotic pairs (P < .05) is found. These results suggest that there is a genetic component in heart rate generation and HRV, in addition to family environmental influences. Analysis of HRV might become a useful method in phenotyping severe genetic changes in cardiovascular diseases.

Alternans of blood pressure and heart rate in dilated cardiomyopathy.

LEDER, U., et al.: Alternans of Blood Pressure and Heart Rate in Dilated Cardiomyopathy. Impaired myocardial performance is known to be associated with electrical and mechanical beat‐to‐beat alternans phenomena. The alternans in blood pressure and heart rate and their interdependency in idiopathic dilated cardiomyopathy (IDC) were studied. The arterial blood pressure and the electrocardiograph (ECG) were continuously recorded in 22 patients suffering from IDC (age 49 ± 13 years, ejection fraction 0.33 ± 0.13, left ventricular diameter of 67 ± 8 mm) and in 21 healthy controls (age 52 ± 15 years). The beat‐to‐beat variations of the interbeat intervals (IBI) and of the blood pressure amplitudes (AMP) were measured. An alternans beat was defined as a beat preceded and followed by beats that had higher or lower values in the respective modality. The percentages of singular and repetitive alternans patterns, and the interdependency of the alternans patterns in AMP and IBI were assessed. The study found significantly more singular and repetitive alternans patterns in the IDC group compared to the control group both in the analysis of AMP and IBI (singular alternans in IBI: 55 ± 11 vs 47 ± 7%, P < 0.01; singular alternans in AMP: 61 ± 15 vs 45 ± 6%, P < 0.01; triple alternans in IBI: 29 ± 18 vs 16 ± 9%, P < 0.01; triple alternans in AMP: 34 ± 24 vs 12 ± 7%, P < 0.01). The amplitudes of the AMP alternans patterns were higher in IDC compared to controls (9 ± 7 vs 4 ± 2% of AMP, P = 0.01) whereas they did not differ in IBI. The correlation analysis revealed a significant interdependency of the alternans pattern in IBI and AMP in 18 of 22 IDC patients and in 12 of 21 controls (r = 0.50 ± 0.21 [IDC]; r = 0.26 ± 0.05 [controls]). The slope of the linear regression (ΔAMP vs ΔIBI) was steeper in the IDC group compared to the control group (62 ± 50 vs 20 ± 22 mmHg/s, P < 0.01). The percentages of alternans patterns appearing in IBI and AMP were positively correlated to the left ventricular diameter (r = 0.70 in the IBI, and r = 0.30 in the AMP). The blood pressure amplitude and the heart rate did not differ between the two groups. Patients suffering from IDC have a higher prevalence, stability, amplitude, and interdependency of alternans patterns in IBI and AMP compared to the control group. The amount of alternans patterns indicates the stage of disease. The alternans analysis may have impact on the functional assessment of patients suffering from heart failure.

Scaling graphs of heart rate time series in athletes demonstrating the VLF, LF and HF regions

Scaling analysis of heart rate time series has emerged as a useful tool for the assessment of autonomic cardiac control. We investigate the heart rate time series of ten athletes (five males and five females), by applying detrended fluctuation analysis (DFA). High resolution ECGs are recorded under standardized resting conditions over 30 min and subsequently heart rate time series are extracted and artifacts filtered. We find three distinct regions of scale invariance, which correspond to the well-known VLF, LF and HF bands in the power spectra of heart rate variability. The scaling exponents alpha are alpha(HF): 1.15 [0.96-1.22], alpha(LF): 0.68 [0.57-0.84], alpha(VLF): 0.83[0.82-0.99], p < 10(-5)). In conclusion, DFA scaling exponents of heart rate time series should be fitted to the VLF, LF and HF ranges, respectively.