Niels Wessel

Recurrence-plot-based measures of complexity and their application to heart-rate-variability data

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.

The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death

OBJECTIVES This study introduces new methods of non-linear dynamics (NLD) and compares these with traditional methods of heart rate variability (HRV) and high resolution ECG (HRECG) analysis in order to improve the reliability of high risk stratification. METHODS Simultaneous 30 min high resolution ECGs and long-term ECGs were recorded from 26 cardiac patients after myocardial infarction (MI). They were divided into two groups depending upon the electrical risk, a low risk group (group 2, n = 10) and a high risk group (group 3, n = 16). The control group consisted of 35 healthy persons (group 1). From these electrocardiograms we extracted standard measures in time and frequency domain as well as measures from the new non-linear methods of symbolic dynamics and renormalized entropy. RESULTS Applying discriminant function techniques on HRV analysis the parameters of non-linear dynamics led to an acceptable differentiation between healthy persons and high risk patients of 96%. The time domain and frequency domain parameters were successful in less than 90%. The combination of parameters from all domains and a stepwise discriminant function separated these groups completely (100%). Use of this discriminant function classified three patients with apparently low (no) risk into the same cluster as high risk patients. The combination of the HRECG and HRV analysis showed the same individual clustering but increased the positive value of separation. CONCLUSIONS The methods of NLD describe complex rhythm fluctuations and separate structures of non-linear behavior in the heart rate time series more successfully than classical methods of time and frequency domains. This leads to an improved discrimination between a normal (healthy persons) and an abnormal (high risk patients) type of heart beat generation. Some patients with an unknown risk exhibit similar patterns to high risk patients and this suggests a hidden high risk. The methods of symbolic dynamics and renormalized entropy were particularly useful measures for classifying the dynamics of HRV.

Quantitative analysis of heart rate variability

In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, noninvasive diagnostic tools like Holter monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyze the HRV. Especially, some complexity measures that are based on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. (c) 1995 American Institute of Physics.

Predictive Value of Maternal Angiogenic Factors in Second Trimester Pregnancies With Abnormal Uterine Perfusion

Angiogenic factors like placental growth factor and its antiangiogenic antagonist soluble fms-like tyrosine kinase 1 (sFlt1) are closely related to the pathogenesis of preeclampsia and intrauterine growth restriction. Because it is known that altered maternal sFlt1 and placental growth factor levels are detectable weeks before the onset of these pregnancy complications, it was the aim of the study to investigate the predictive value of these markers in high-risk second trimester pregnancies characterized by abnormal uterine perfusion. This prospective study includes 63 second trimester pregnant women with abnormal uterine perfusion. Twenty five of them developed a later complication (12 with preeclampsia, 11 with intrauterine growth restriction, and 2 with intrauterine death), whereas 38 had a normal course of pregnancy. Pregnancies with adverse pregnancy outcome showed in the second trimester significantly higher sFlt1 (1403.6±555 versus 451.8±42 pg/mL; P<0.05) and lower placental growth factor (139.6±24 versus 184.1±21 pg/mL) levels compared with those with normal outcome. These alterations were more pronounced in pregnancies with subsequent preeclampsia compared with intrauterine growth restriction and early onset diseases (delivery <34 weeks) compared with late-onset diseases. The combination of Doppler and sFlt1 increases the sensitivity of Doppler alone for iatrogenic preterm delivery from 64% up to 79% and the specificity from 63% up to 80%. Using both factors, sFlt1 and placental growth factor, early onset preeclampsia can be predicted with 83% sensitivity and 95% specificity. We conclude that the concurrent measurement of uterine perfusion and angiogenic factors allows an efficient prediction of early onset pregnancy complications, particularly preeclampsia.

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.

Circulatory soluble endoglin and its predictive value for preeclampsia in second-trimester pregnancies with abnormal uterine perfusion

OBJECTIVE Soluble endoglin (sEng) is increased dramatically in preeclampsia and acts synergistically with soluble fms-like tyrosine kinase 1 (sFlt1) to promote the preeclamptic phenotype. The aim of this study was to investigate whether the sEng increase was present already in second-trimester pregnancies with abnormal uterine perfusion and whether the pregnancy was at risk for preeclampsia. STUDY DESIGN This prospective study includes 77 second-trimester pregnant women with abnormal uterine perfusion. sEng and sFlt1 were measured with an enzyme-linked immunosorbent assay. RESULTS Adverse pregnancy outcome was associated with higher sEng levels in the second trimester. SEng was highest in those pregnancies with early-onset preeclampsia. Combined analysis of sEng and sFlt1 is able to predict early-onset preeclampsia with a sensitivity of 100% and a specificity of 93.3%. CONCLUSION Elevated sEng levels are detectable in second-trimester pregnancies with abnormal uterine perfusion and subsequent pregnancy complications. The concurrent measurement of uterine perfusion and angiogenic factors allows a highly efficient prediction of early-onset preeclampsia.

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.

Dietary omega-3 fatty acids modulate the eicosanoid profile in man primarily via the CYP-epoxygenase pathway

Cytochrome P450 (CYP)-dependent metabolites of arachidonic acid (AA) contribute to the regulation of cardiovascular function. CYP enzymes also accept EPA and DHA to yield more potent vasodilatory and potentially anti-arrhythmic metabolites, suggesting that the endogenous CYP-eicosanoid profile can be favorably shifted by dietary omega-3 fatty acids. To test this hypothesis, 20 healthy volunteers were treated with an EPA/DHA supplement and analyzed for concomitant changes in the circulatory and urinary levels of AA-, EPA-, and DHA-derived metabolites produced by the cyclooxygenase-, lipoxygenase (LOX)-, and CYP-dependent pathways. Raising the Omega-3 Index from about four to eight primarily resulted in a large increase of EPA-derived CYP-dependent epoxy-metabolites followed by increases of EPA- and DHA-derived LOX-dependent monohydroxy-metabolites including the precursors of the resolvin E and D families; resolvins themselves were not detected. The metabolite/precursor fatty acid ratios indicated that CYP epoxygenases metabolized EPA with an 8.6-fold higher efficiency and DHA with a 2.2-fold higher efficiency than AA. Effects on leukotriene, prostaglandin E, prostacyclin, and thromboxane formation remained rather weak. We propose that CYP-dependent epoxy-metabolites of EPA and DHA may function as mediators of the vasodilatory and cardioprotective effects of omega-3 fatty acids and could serve as biomarkers in clinical studies investigating the cardiovascular effects of EPA/DHA supplementation.

Classifying cardiac biosignals using ordinal pattern statistics and symbolic dynamics

The performance of (bio-)signal classification strongly depends on the choice of suitable features (also called parameters or biomarkers). In this article we evaluate the discriminative power of ordinal pattern statistics and symbolic dynamics in comparison with established heart rate variability parameters applied to beat-to-beat intervals. As an illustrative example we distinguish patients suffering from congestive heart failure from a (healthy) control group using beat-to-beat time series. We assess the discriminative power of individual features as well as pairs of features. These comparisons show that ordinal patterns sampled with an additional time lag are promising features for efficient classification.

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.