Nonlinear analysis of continuous ECG during sleep II. Dynamical measures

The hypothesis that cardiac rhythms are associated with chaotic dynamics implicating a healthy flexibility has motivated the investigation of continuous ECG with methods of nonlinear system theory. Sleep is known to be associated with modulations of the sympathetic and parasympathetic control of cardiac dynamics. Thus, the differentiation of ECG signals recorded during different sleep stages can serve to determine the usefulness of nonlinear measures in discriminating ECG states in general. For this purpose the following six nonlinear measures were implemented: correlation dimension D2, Lyapunov exponent L1. Kolmogorov entropy K2, as well as three measures derived from the analysis of unstable periodic orbits. Results of this study show that continuous ECG signals can be differentiated from linear stochastic surrogates by each of the nonlinear measures. The most significant finding with respect to the sleep-related differentiation of ECG signals is an increase in dominant chaoticity assessed by L1 and a reduction in the degrees of freedom estimated by D2 during REM sleep compared to slow wave sleep. Our findings suggest that the increase in dominant chaoticity during REM sleep with regard to time-continuous nonlinear analysis is comparable to an increased heart rate variability. The reduction in the correlation dimension may be interpreted as an expression of the withdrawal of respiratory influences during REM sleep. Received: 7 June 1999 / Accepted in revised form: 10 December 1999     

Neural net classification of REM sleep based on spectral measures as compared to nonlinear measures

 In various studies the implementation of nonlinear and nonconventional measures has significantly improved EEG (electroencephalogram) analyses as compared to using conventional parameters alone. A neural network algorithm well approved in our laboratory for the automatic recognition of rapid eye movement (REM) sleep was investigated in this regard. Originally based on a broad range of spectral power inputs, we additionally supplied the nonlinear measures of the largest Lyapunov exponent and correlation dimension as well as the nonconventional stochastic measures of spectral entropy and entropy of amplitudes. No improvement in the detection of REM sleep could be achieved by the inclusion of the new measures. The accuracy of the classification was significantly worse, however, when supplied with these variables alone. In view of results demonstrating the efficiency of nonconventional measures in EEG analysis, the benefit appears to depend on the nature of the problem. Received: 10 October 2000 / Accepted in revised form: 26 April 2001     

Nonlinearity in normal human EEG: cycles,temporal asymmetry,nonstationarity and randomness,not chaos

Two-hour vigilance and sleep electroencephalogram (EEG) recordings from five healthy volunteers were analyzed using a method for identifying nonlinearity and chaos which combines the redundancy–linear redundancy approach with the surrogate data technique. A nonlinear component in the EEG was detected, however, inconsistent with the hypothesis of low-dimensional chaos. A possibility that a temporally asymmetric process may underlie or influence the EEG dynamics was indicated. A process that merges nonstationary nonlinear deterministic oscillations with randomness is proposed for an explanation of observed properties of the analyzed EEG signals. Taking these results into consideration, the use of dimensional and related chaos-based algorithms in quantitative EEG analysis is critically discussed. Received: 25 September 1994 / Accepted in revised form: 10 July 1996     

Nonlinear analysis of continuous ECG during sleep I. Reconstruction

In recent years evidence has accumulated that ECG signals are of a nonlinear nature. It has been recognized that strictly periodic cardiac rhythms are not accompanied by healthy conditions but, on the contrary, by pathological states. Therefore, the application of methods from nonlinear system theory for the analysis of ECG signals has gained increasing interest. Crucial for the application of nonlinear methods is the reconstruction (embedding) of the time series in a phase space with appropriate dimension. In this study continuous ECG signals of 12 healthy subjects recorded during different sleep stages were analysed. Proper embedding dimension was determined by application of two techniques – the false nearest neighbours method and the saturation of the correlation dimension. Results for the ECG signals were compared with findings for simulated data (quasiperiodic dynamics, Lorenz data, white noise) and for phase randomized surrogates. Findings obtained with the two approaches suggest that embedding dimensions from 6 to 8 may be regarded as suitable for the topologically proper reconstruction of ECG signals. Received: 7 June 1999 / Accepted in revised form: 10 December 1999     

Membrane potential changes of skeletomotor neurons in response to random stretches of the triceps surae muscles in decerebrate cats

 The properties of membrane potential changes of skeletomotor neurons (S, FR, and FF) innervating triceps surae muscles during pseudorandom stretching of these muscles were studied in decerebrate cats. Peak amplitudes of pseudorandom muscle stretches ranged from 119 μm to 4.15 mm peak-to-peak. Sequences of ten identical stretching periods were applied for averaging. Shapes of membrane potential changes and probability density distribution of amplitudes of the input and output signals and power spectra suggest that the skeletomotor neuron membrane has nonlinear properties. First- and second-order Wiener kernels were determined by applying the cross-correlation (Lee-Schetzen) method. The results suggest that the transfer function between muscle stretches and subthreshold membrane potentials is a Wiener-type cascade. This cascade is consistent with a linear, second-order, underdamped transfer function followed by a simple quadratic nonlinearity [linear (L) system followed by nonlinear (N) system, or LN cascade]. Including the nonlinear component calculated from the second-order Wiener kernel improved the model significantly over its linear counterpart, especially in S-type motoneurons. Qualitatively similar results were obtained with all types of motoneurons studied. Received: 1 April 1993/Accepted in revised form: 24 March 1994     

On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data

 We discuss the estimation of the correlation dimension of optokinetic nystagmus (OKN), a type of reflexive eye movement. Parameters of the time-delay reconstruction of the attractor are investigated, including the number of data points, the time delay, the window duration, and the duration of the signal being analyzed. Adequate values are recommended. Digital low-pass filtering causes the dimension to increase as the filter cutoff frequency decreases, in accord with a previously published prediction. The stationarity of the correlation dimension is examined; the dimension appears to decrease over the course of 120 s of continuous stimulation. Implications for the reliable estimation of the dimension are considered. Several surrogate data sets are constructed, based on both early (0–30 s) and late (100–130 s) OKN segments. Most of the surrogate data sets randomize some aspect of the original OKN, while maintaining other aspects. Dimensions are found for all surrogates and for the original OKN. Evidence is found that is consistent with some amount of deterministic and nonlinear dynamics in OKN. When this structure is randomized in the surrogate, the dimension changes or the dimension algorithm ceases to converge to a finite value. Implications for further analysis and modeling of OKN are discussed. Received: 30 August 1996/Accepted in revised form: 13 November 1996     

Effect of light and zooplankton on skeletal δ13C values in the eastern Pacific corals Pavona clavus and Pavona gigantea

 Skeletal δ¹³C levels in symbiotic reef corals are believed to be predominantly influenced by metabolic fractionation. Therefore, environmental variables influencing coral metabolism should also affect skeletal δ¹³C levels. To test this hypothesis, we measured the effects of light (which drives photosynthesis) and relative zooplankton levels (heterotrophy) on skeletal δ¹³C values in the corals Pavona clavus and P. gigantea at two depths (1 m and 7 m). For both species, decreases in light or increases in zooplankton resulted in significant decreases in skeletal δ¹³C levels. A significant decrease in δ¹³C values with depth was observed in Pavona gigantea only. Thus, light and zooplankton directly affect coral skeletal δ¹³C values, supporting the hypothesis that metabolic fractionation significantly contributes to skeletal δ¹³C levels. Simultaneous decreases in both light and zooplankton resulted in decreases in skeletal δ¹³C values, reflecting decreases in light. In Pavona clavus, intra-annual variation in skeletal δ¹³C values over one year correlated with seasonal changes in irradiance. Further study is needed to resolve how skeletal δ¹³C values vary at intermediate levels of irradiance and zooplankton, and in other coral species. Accepted: 14 July 1998     

Nonlinear analysis of EEG signals: Surrogate data analysis

ObjectivesThe electroencephalogram (EEG) signal contains information about the state and condition of the brain. The aim of the study is to conduct a nonlinear analysis of the EEG signals and to compare the differences in the nonlinear characteristics of the EEG during normal state and the epileptic state.DataThe EEG data used for this study – which consisted of epileptic EEG and normal EEG – were obtained from the EEG database available with the Bonn University, Germany.ResultsThe attractors seen in normal and epileptic human brain dynamics were studied and compared. Surrogate data analyses were conducted on two nonlinear measures, namely the largest Lyapunov exponent and the correlation dimension, to test the hypothesis whether EEG signals were in accordance with linear stochastic models.DiscussionsThe existence of deterministic chaos in brain activity is confirmed by the existence of a chaotic attractor; also, saturation of the correlation dimension towards a definite value is the manifestation of a deterministic dynamics. Also a reduction is observed between the dimensionalities of the brain attractors from normal state to the epileptic state. The evaluation of the largest Lyapunov exponent also confirms the lowering of complexity during an episode of seizure.ConclusionIn case of Lyapunov exponent of EEG data, the change due to surrogating is small suggesting that it is not representing the system complexity properly but there is a marked change in the case of correlation dimension value due to surrogating.     

Nonlinear dynamics of the EEG separated by independent component analysis after sound and light stimulation

 The electroencephalogram (EEG) is a multiscaled signal consisting of several time-series components each with different dominant frequency ranges and different origins. Nonlinear measures of the EEG reflect the complexity of the overall EEG, but not of each component in it. The aim of this study is to examine effect of the sound and light (SL) stimulation on the complexity of each component of the EEG. We used independent component analysis to obtain independent components of the EEG. The first positive Lyapunov exponent (L1) was estimated as a nonlinear measure of complexity. Twelve subjects were administered photic and auditory stimuli with a frequency of 10 Hz, which corresponded to the alpha frequency of the EEG, by a sound and light entrainment device. We compared the L1 values of the EEGs and their independent components between baseline and after the SL stimulation. We detected that the L1 values of the EEG decreased after the SL stimulation in all channels except C3 and F4, indicating that the complexity of the EEG decreased. We showed that alpha components increased in proportion but decreased in complexity after the SL stimulation. The beta independent components were found to decrease in proportion and complexity. These results suggest that decreased complexity of the EEG after the SL stimulation may be principally caused by decreased complexity and increased proportion of the alpha independent components. We showed also that theta components increased in complexity after the SL stimulation. We propose that nonlinear dynamical analysis combined with independent component analysis may be helpful in understanding the temporal characteristics of the EEG, which cannot be detected by conventional linear or nonlinear methods. Received: 12 March 2001 / Accepted in revised form: 27 November 2001     

Respiratory influences on non-linear dynamics of heart rate variability in humans

 The goal of our study was to determine whether evidence for chaos in heart rate variability (HRV) can be observed when the respiratory input to the autonomic controller of heart rate is forced by the deterministic pattern associated with periodic breathing. We simultaneously recorded, in supine healthy volunteers, RR intervals and breathing volumes for 20 to 30 min (1024 data point series) during three protocols: rest (control), fixed breathing (15 breath/min) and voluntary periodic breathing (3 breaths with 2 s inspiration and 2 s expiration followed by an 8 s breath hold). On both the RR interval and breathing volume series we applied the non-linear prediction method (Sugihara and May algorithm) to the original time series and to distribution-conserved isospectral surrogate data. Our results showed that, in contrast to the control test, during both fixed and voluntary periodic breathing the variability of breathing volumes was clearly deterministic non-chaotic. During all the three protocols, the RR-interval series’ non-linear predictability was consistent with one of a chaotic series. However, at rest, no clear difference was observed between the RR-interval series and their surrogates, which means that no clear chaos was observed. During fixed breathing a difference appeared, and this difference seemed clearer during voluntary periodic breathing. We concluded that HRV dynamics were chaotic when respiration was forced with a deterministic non-chaotic pattern and that normal spontaneous respiratory influences might mask the normally chaotic pattern in HRV. Received: 7 August 1995 / Accepted in revised form: 20 March 1997     

Sleep EEG as a nonlinear dynamic process: a comparison of global correlation dimension of human EEG and measures of linear interdependence between channels

The goal of this work was to study (1) whether the estimation of correlation dimension (D2) using spatial embedding distinguishes between sleep stages and (2) whether information gained from the application of global D2 is redundant to measures of linear interdependence between channels. Twenty one-channel EEG segments of 12 healthy male subjects recorded during waking and sleep stages REM, I, II, and III-IV (according to the Rechtshaffen and Kales criteria) were analyzed with global (multichannel) D2, mean square correlation coefficients (MS) and proportion of variance accounted for by the first principal component (PC1). D2 was found to decrease progressively from stage I to stage III-IV with D2 values of waking and REM being close to those of stages I and II. MS and PC1 did not distinguish among sleep stages but yielded significant differences between waking and sleep. The results suggest that global D2 extracts information from human EEG. That sort of evidence cannot be obtained with measures of linear interdependence between channels.     

Analysis and automatic identification of sleep stages using higher order spectra

Electroencephalogram (EEG) signals are widely used to study the activity of the brain, such as to determine sleep stages. These EEG signals are nonlinear and non-stationary in nature. It is difficult to perform sleep staging by visual interpretation and linear techniques. Thus, we use a nonlinear technique, higher order spectra (HOS), to extract hidden information in the sleep EEG signal. In this study, unique bispectrum and bicoherence plots for various sleep stages were proposed. These can be used as visual aid for various diagnostics application. A number of HOS based features were extracted from these plots during the various sleep stages (Wakefulness, Rapid Eye Movement (REM), Stage 1-4 Non-REM) and they were found to be statistically significant with p-value lower than 0.001 using ANOVA test. These features were fed to a Gaussian mixture model (GMM) classifier for automatic identification. Our results indicate that the proposed system is able to identify sleep stages with an accuracy of 88.7%.     

Hydraulic Lift in Cork Oak Trees in a Savannah-Type Mediterranean Ecosystem and its Contribution to the Local Water Balance

The aim of this study was to identify the sources and depth of water uptake by 15-years old Quercus suber L. trees in southern Portugal under a Mediterranean climate, measuring δ¹⁸O and δD in the soil–plant-atmosphere continuum. Evidence for hydraulic lift was substantiated by the daily fluctuations observed in Ψ_s at 0.4 and 1 m depth and supported by similar δ¹⁸O values found in tree xylem sap, soil water in the rhizosphere and groundwater. From 0.25 m down to a depth of 1 m, δD trends differed according to vegetation type, showing a more depleted value in soil water collected under the evergreen trees (−47‰) than under dead grasses (−35‰). The hypothesis of a fractionation process occurring in the soil due to diffusion of water vapour in the dry soil is proposed to explain the more depleted soil δD signature observed under trees. Hydraulically lifted water was estimated to account for 17–81% of the water used during the following day by tree transpiration at the peak of the drought season, i.e., 0.1–14 L tree⁻¹ day⁻¹. Significant relationships found between xylem sap isotopic composition and leaf water potential in early September emphasized the positive impact of the redistribution of groundwater in the rhizosphere on tree water status.     

In vitro versus in vivo genetic divergence in potato

 The objective of this study was to compare the genetic divergence pattern in potato (Solanum tuberosum L.) under in vitro and in vivo conditions. Twenty two potato genotypes were evaluated for ten morphological characters under four in vitro conditions, and for 20 characters under four in vivo seasons. Mahalanobis’ generalized intra- and inter-group genetic distances, and the distribution of genotypes into different clusters, led to the same conclusions under both in vitro and in vivo conditions: (1) genetic diversity was not related to geographic diversity, (2) genetic distances were higher between Tuberosum and Andigena than within Tuberosum and Andigena, and (3) present-day Indian varieties have more resemblance to Tuberosum than to the Andigena group. The in vitro approach was more effective than the in vivo approach for differentiating the genotypes per se, although its effectiveness for cross prediction is known to be low. Received: 15 September 1997 / Accepted: 15 July 1998     

Diving behavior of immature hawksbill turtles (Eretmochelys imbricata) in a caribbean reef habitat

 Time-depth recorders were deployed on immature hawksbill turtles at the southwestern reefs of Mona Island, Puerto Rico, to examine patterns of diving behavior. Diving profiles of 10–12 day duration were obtained from five turtles ranging in carapace length from 27–52 cm. Turtles exhibited contrasting diurnal and nocturnal diving behaviors. During daylight hours, dives were made 92% of the time, featured continuous depth variation and were attributed to foraging activity. Foraging dive duration increased with turtle size; individual mean dive durations ranged from 19–26 min; mean post-dive surface intervals ranged from 37–64 s; mean depths ranged from 8–10 m. At night, dives were made 86% of the time to constant depths and were interpreted as resting behavior. Resting dive durations were not dependent on turtle size; individual mean dive durations ranged from 35–47 min; mean post-dive surface intervals ranged from 36–60 s; and mean depths from 7–10 m. Immature hawksbill turtles maintained short term home ranges several hundred meters in extension. Accepted: 2 July 1996     

Sleep and EEG spectra in the Syrian hamster (Mesocricetus auratus) under baseline conditions and following sleep deprivation

Summary Sleep was studied by continuous 24-h recordings in adult male Syrian hamsters, chronically implanted with EEG and EMG electrodes. Three vigilance states were determined using visual scoring and EEG power spectra (0.25–25 Hz) computed for 4-s episodes.The effects of two methods of total sleep deprivation (SD) were examined on vigilance states and the EEG power spectrum. The animals were subjected to 24 h SD by: (1) forced locomotion in a slowly rotating drum, (2) gentle handling whenever the hamsters attempted a sleeping posture. In addition, the hamsters were subjected to SD by handling during the first 3 h of the L period.Sleep predominated in the L period (78.2% of 12 h) and the D period (51.2%). The power spectra of the 3 vigilance states were similar during the L and D period. In NREM sleep, power density values in the low frequency range (0.25–6.0 Hz) exceeded those of REM sleep and W by a maximum factor of 8.3 and 2.8, respectively. At frequencies above 16 Hz, NREM and REM sleep power density values were significantly lower than during W. A progressive decrease in power density for low EEG frequencies (0.25–7 Hz) during NREM sleep was seen in the course of the L period. Power density values of higher frequencies (8–25 Hz) increased at the end of the L period and remained high during the first hours of the D period.The effect of prolonged SD on vigilance states and EEG spectra was similar by both methods and strikingly small compared to similar results in rats. In contrast, 3 h SD induced a large and more prolonged effect. The similarities and differences of sleep and sleep regulation are summarized for the hamster, rat and man.Abbreviations EEG electroencephalogram - LD light dark - REM rapid eye movements - NREM sleep non REM sleep - W waking - SD sleep deprivation - TST total sleep time - L light - D dark     

Importance of epiphytic cyanobacteria as food sources for heterotrophs in a tropical seagrass bed

 The natural carbon and nitrogen stable isotope ratios (δ¹³C, δ¹⁵N) of various autotrophs and heterotrophs were measured in a Syringodium isoetifolium-dominated seagrass bed at Dravuni Island, Fiji to define carbon and nitrogen sources for heterotrophic organisms in a system where few animals graze directly on seagrass leaves. The organic carbon, nitrogen, and phosphorus content of organisms was also determined. The δ¹³C and δ¹⁵N data suggest that herbivorous heterotrophs in this seagrass bed depend significantly on epiphytic cyanobacteria rather than seagrass leaves and its detritus. This can be attributed to relative differences in nitrogen content of those organic materials. The cyanobacteria nitrogen content (3.6–4.8% of DW) is nearly half that of heterotrophs (7.0–8.6% N of DW) while that of S. isoetifolium origin (0.6–1.1% N of DW) is less than one third of the cyanobacteria nitrogen content. Phosphorus content was similar among cyanobacteria (0.8–1.1 mg g^-1) and S. isoetifolium (0.4–1.4 mg g^-1). These results suggest that cyanobacteria are important food sources for heterotrophs at the study site, and that inorganic nitrogen released through breakdown of cyanobacteria by heterotrophs may support the continued production of S. isoetifolium. Accepted: 24 May 1999     

Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep

The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant degree of nonlinear RRI dynamics in all subjects. A parametric model, consisting of a nonlinear delayed-feedback system with stochastic noise as the perturbing input, was employed to estimate the relative contributions of linear and nonlinear deterministic dynamics in the data. Both infant groups showed similar proportional contributions in linear, nonlinear, and stochastic dynamics. However, approximate entropy, correlation dimension, and nonlinear prediction error were all decreased in active versus quiet sleep; in addition, the parametric model revealed a doubling of the linear component and a halving of the nonlinear contribution to overall heart rate variability. Spectral analysis indicated a shift in relative power toward lower frequencies. We conclude that 1) RRI dynamics in infants with PCE and normal controls are similar; and 2) in both groups, sympathetic dominance during active sleep produces primarily periodic low-frequency oscillations in RRI, whereas in quiet sleep vagal modulation leads to RRI fluctuations that are broadband and dynamically more complex.     

CMS sources in sunflower: different origin but same mechanism?

 The presence of orfH522, orfH708 and orfH873 in the mtDNA, as well as the expression of mitochondrially encoded proteins, were investigated for 28 sources of cytoplasmic male sterility (CMS) and HA89, a fertile line of Helianthus annuus. The whole 5-kb insertion, found in PET1, is also present in all PET1-like CMS sources. However, with regard to the 11-kb inversion ANO1 demonstrated a different organization at the cob locus from the other PET1-like CMS sources. Only orfH873 gave hybridization patterns in all investigated cytoplasms. For the fertile cytoplasm, as well as ANN4, ANN5, ANL1, ANL2, ARG2 and MAX1, hybridizations obtained with orfH708 were highly polymorphic. Hybridization signals with orfH522 were only detectable in the PET1-like CMS sources and MAX1. Comparing the mitochondrially encoded proteins of the CMS sources characteristic patterns could be detected for seven cytoplasms in addition to the PET1-like CMS sources expressing the 16-kDa protein. For ANN1 and ANN3 three CMS-associated proteins of 16.3 kDa, 16.9 kDa and 34.0 kDa could be identified among the in organello translation products. Also ANT1 expressed three additional proteins of 13.4 kDa, 17.8 kDa and 19.7 kDa, respectively. In ARG3 and RIG1 one protein of 17.5 kDa was missing and instead a new protein of 16.9 kDa appeared. In addition, in GIG1 and PET2 a unique protein of 12.4 kDa could be identified. These results indicate that certain types of cytoplasmic male sterility are preferentially present in sunflower. Received: 15 June 1998 / Accepted: 13 July 1998     

Microbial sensors for naphthalene using Sphingomonas sp. B1 or Pseudomonas fluorescens WW4

 Amperometric biosensors for naphthalene were developed using either immobilized Sphingomonas sp. B1 or Pseudomonas fluorescens WW4 cells. The microorganisms were immobilized within a polyurethane-based hydrogel, which was used for a microbial biosensor for the first time. Both strains were shown to be equally suited for the quantification of naphthalene in aqueous solutions. The biosensors were tested in a flow-through system and a stirred cell (batch method). In both systems a linear response down to the detection limit was obtained. Measurements in the flow-through system gave sensitivities of up to 1.2 nA mg⁻¹ l⁻¹ and a linear range from 0.03 mg/l to 2.0 mg/l. The response time (t ₉₅) was 2 min and the sample throughput six per hour; the repeatability was within ±5 %. With the batch method, sensitivities of between 3 nA mg⁻¹ l⁻¹ and 5 nA mg⁻¹l⁻¹ and a linear range of 0.01–3.0 mg/l were obtained; the response time was between 3 min and 5 min. The sensors reached an operational lifetime of up to 20 days. The sensitivity of both sensors for naphthalene was, in most cases, more than four times higher than for various other substrates. Received: 18 October 1995/Received revision: 22 December 1995/Accepted: 22 January 1996