Investigation of Nonlinear ECoG Changes during Spontaneous Sleep State Changes and Cortical Arousal in Fetal Sheep

Matthias Schwab, Karin Schmidt1, Herbert Witte1 and Robert M. Abrams2

Department of Neurology, , 1 Institute for Medical Statistics, Computer Science and Documentation, Friedrich Schiller University, Jena, Germany and , 2 Perinatology Research Laboratory, Department of Obstetrics and Gynecology, College of Medicine, University of Florida, Gainesville, FL, USA


    Abstract
 Top
 Abstract
 Introduction
 Material and Methods
 Results
 Discussion
 References
 
We examined the processes of cortical activation and deactivation of the fetal brain during spontaneous sleep state transitions and during central nervous processing of vibroacoustic stimulations (VASs) using nonlinear analysis of the electrocorticogram (ECoG). Tests of nonlinearity and a random shuffling routine revealed deterministic and nonlinear portions in the fetal ECoG. As common nonlinear measures are not applicable to nonstationary time series, we developed an algorithm to estimate the predictability of the ECoG in its time course by means of a point prediction error (PPE). The ECoG was recorded before and during VAS from the maternal abdominal surface in seven chronically instrumented fetal sheep at 0.8 of gestation. The PPE during REM sleep was significantly higher than during NREM sleep. VAS in NREM sleep resulted in an abrupt increase of the PPE not reaching the level of REM sleep. The steep increase of the PPE at onset and its slow decrease after cessation of the stimulus were very similar to the dynamics of spontaneous sleep state transitions, suggesting the involvement of the same cortical activating mechanisms. In conclusion, the stage and the time course of fetal brain activation and deactivation patterns can be clearly shown by PPE techniques. The PPE is a useful complement to spectral analysis. Both techniques describe different properties of the ECoG.


    Introduction
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 Abstract
 Introduction
 Material and Methods
 Results
 Discussion
 References
 
Human babies develop distinct behavioral states with first signs of cyclicity in fetal heart rate pattern and body movements from ~32 weeks gestational age (Nijhuis et al., 1982Go; Okai et al., 1992Go). Vibroacoustic stimulation (VAS) of the surface of the maternal abdomen alters the behavioral states and is widely used by obstetricians as a test of fetal reactivity and thus, fetal health. If applied during the state 1F, corresponding to the postnatal quiet or NREM sleep, an increase of basal fetal heart rate, fetal heart rate variability, body movements and eye movements and a decrease of fetal breathing movements were found (Gagnon, 1989Go; Visser et al., 1989Go). These changes are interpreted as signs of fetal arousal. However, fetal electrocortical activity as a direct proof of this assumption cannot be measured easily in the human fetus.

The chronically instrumented fetal sheep has become a favorite animal model for investigations of brain function in utero. The fetal sheep brain develops cyclic electrocortical activity from ~115 day of gestation (term 146 days), alternating between a high-voltage, slow frequency electrocorticogram (ECoG) state, termed NREM sleep, and a low-voltage, high frequency ECoG state, termed REM sleep (Szeto et al., 1985Go), with a duration of the respective sleep state of up to 45 min. VAS alters the behavioral state organization in fetal sheep as well (Parkes et al., 1991Go; Bauer et al., 1997Go), and is accompanied by an ECoG desynchronization during stimulation in NREM sleep and an increase of beta activity during stimulation in REM sleep (Abrams et al., 1996Go; Bauer et al., 1997Go) typical for an arousal reaction (American Sleep Disorders Association, 1992Go).

The aims of the present study were to analyze the process of cortical activation and deactivation during spontaneous sleep state transitions from NREM to REM sleep and REM to NREM sleep in their time course and to study the central nervous processing of VAS in order to obtain more insights into the nature of the collective behavior of the neurons during cortical activation and deactivation. To our knowledge no analysis of changes of the ECoG in its time course during sleep state transitions and cortical activation has been reported yet. Although linear methods as power spectral analysis are often used to analyze the ECoG for practical reasons, there is a chance that relevant information may be lost because the ECoG is a highly complex signal that does not fit the criteria of ‘linearity’. Consequently, nonlinear analysis has recently been recognized as superior to linear analysis because it describes the properties of the ECoG in terms of information processing (Pritchard et al., 1995Go; Fell et al., 1996Go; Palus, 1996Go; Theiler and Rapp, 1996Go). Commonly used nonlinear measures such as Correlation dimension and leading Lyapunov exponent are applicable to steady state time series only and unsuited for revealing short time changes of the ECoG activity as they occur during spontaneous behavioral state changes and arousal reactions.

We have developed a nonlinear algorithm based on the Wolf algorithm (calculation of the leading Lyapunov exponent) (Wolf et al., 1985Go) which estimates a so-called point prediction error (PPE) regarding the course of the time series in the phase space. The PPE quantifies the predictability or causality of such a time series (Schmidt et al., 1997Go). A high prediction error stands for a low predictability or causality and vice versa. The PPE proved to be easily and successfully applicable and allows one to quantify instantaneously the nonlinear properties of a nonstationary times series (Schmidt et al., 1997Go). Thus, we were able to quantify not only the differences in complexity and predictability of the ECoG during REM sleep, NREM sleep and arousal but also the time course of their changes. To show the nonlinear character of the investigated ECoG epochs we examined a simulation of linear signal portions using an autoregressive (AR) modeling approach and a simulation of stochastic signal portions using a random shuffling routine. To demonstrate the usefulness of our nonlinear approach, this study compares the results of the estimation of the PPE with power spectral analysis. Results of spectral ECoG analysis have been published previously in part (Abrams et al., 1996Go).


    Material and Methods
 Top
 Abstract
 Introduction
 Material and Methods
 Results
 Discussion
 References
 
Surgery

The care and use of the animals reported on in this study were approved by the University of Florida Animal Care and Use Committee. Experiments were performed in seven chronically instrumented fetal lambs between 133 and 141 days of gestation (term 146 days). Animals underwent hysterotomy 5–12 days before the experiments in order to implant screw electrodes in the fetal skull over the parietal cortex for ECoG recordings, as well as electrodes for EOG and neck EMG recordings for exact determination of the behavioral states. A hydrophone was sutured to the skin near the ear in two of the seven fetuses to record the intrauterine sound pressure levels during VAS. Electrode wires were brought out of the uterus and the ewe through a small incision in the maternal flank.

Experimental Protocol and Data Acquisition

On the day of the experiment the unaesthesized ewes were brought into the laboratory and the electrode wires were connected to a physiograph (Gould Instruments, model 2400S, Dayton, OH) and a FM tape (Bruel and Kjaer, model 7005). Fetal ECoG, EOG and neck EMG signals were amplified, filtered (band-pass ranges: ECoG and EOG 0.3–30 Hz, EMG 30–300 Hz) and recorded continuously on the FM tape. After at least 1 h prestimulation time 6–10 VASs were performed alternately in NREM and REM sleep for 3 min using an industrial shaker (MB Electronics, model PM50, Cleveland, OH) pressed gently against the flank of the ewe. A complex sound pulsating at a rate of 7.7 pulses/s was generated by a wave-form generator (EDP Ltd, model GNAT, Oxford, UK) and drove the shaker. For a detailed description of the signal generation and the measurement of resulting intrauterine sound pressure see Abrams et al. (Abrams et al., 1996Go). Each stimulus was given 2 min after the beginning of the respective sleep state. At least one complete cycle of REM and NREM sleep was noted before the next stimulus was applied. The assessment of fetal sleep state was made by visual inspection of the strip chart recordings. NREM sleep was characterized by a high-voltage, slow frequency ECoG pattern, absence of sustained, rapid eye movements and occasional nuchal tone. REM sleep was distinguished by a low-voltage, high frequency ECoG, occurrence of rapid eye movements and general absence of nuchal tone.

Data Analysis

Data stored on FM tape were digitized using a 16 channel A/D board (Data Translation, DT2801F) with a sample rate of 128 Hz. In each animal we chose artifact-free 10 min epochs of unaffected REM and NREM sleep and 10 min epochs of the transitions between them from the digitized ECoG recordings before the onset of the first stimulation. Ten minute epochs during each stimulation were chosen such that they contained 1.5 min before, 3 min during and 5.5 min after stimulation.

For power spectral analysis, ECoG was quantified continuously over the chosen 10 min epochs using Fast Fourier Transformation. Spectral band power (total band 1.5–30 Hz, delta band 1.5–4 Hz, theta band 4–8 Hz, alpha band 8–13 Hz and beta band 13–30 Hz) and spectral edge frequency (95%) of the total band were calculated and summarized for every 4 s.

For the simulation of the pure linear signal portions an AR (25) model was fitted to unaffected 10 min ECoG epochs of NREM sleep and REM sleep, respectively. The obtained parameter of the AR models of either sleep state were used to simulate a spontaneous transition from NREM to REM sleep containing only the linear signal characteristics. White noise as the input signal of the adapted AR model leads to an AR signal which is statistically adequate to the original signal used for AR model fitting. The estimation of AR parameters and the simulation of the adequate AR model were done using MATLAB® routines contained in the Signal Identification Toolbox®. For the simulation of the pure stochastic signal portions we obtained surrogate data by a random shuffling of original data according to Theiler et al. (Theiler et al., 1992Go).

For nonlinear analysis, the data sets were filtered and sampled down to 64 Hz, the PPE was calculated for each time point and the received time series were smoothed over 257 data points (4 s).

Point Prediction Algorithm

The theoretical starting point of our algorithm is a one-dimensional time series {x(ti)}i=1,...,n as a projection of a measured biomedical process. According to Takens (1981), it is possible to transform such a time series in a multi-dimensional phase space by means of a time delay {tau}. The embedding in the phase space takes place as:

where i = 1,. . ., (De – 1){tau}, ti is the actual time point, {tau} is the time delay, De is the embedding dimension and {Y(ti)}i=1,...,n–(De–1) {tau} is the trajectory in the phase space.

For a one-to-one transformation of the measured time series De >= 2CD + 1 (where CD is the correlation dimension of the process) is necessary. The most frequently used approach to define the time lag {tau} is to use the autocorrelation function (ACF) or the mutual information. We choose a time lag {tau} depending on the first time point with ACF <= 1/e.

Our approach was based on the Wolf algorithm for the estimation of the leading Lyapunov exponent. However, it estimates the local exponential divergence similar to Gao and Zheng (Gao and Zheng, 1994Go) where this analysis is used not for single time points but for defined short-time windows.

Starting with any point y(ti) on a trajectory in the phase space we have to search for the nearest (Euclidean) neighbor in the phase space. The distance of this point to the starting point is D(ti). After a specific time step k the distance of the evolved points in the phase space is D'(ti+k). This procedure is repeated for every point y(ti) in the phase space. We are able to estimate single PPEs ({PPi}i=1,...,n–(De–1){tau}k) at every time point i according to:

where i = 1,...,n–(De–1){tau}k, ti = actual time point, D(ti) = smallest Euclidean distance at the time point ti, D'(ti+k) = evolved distance at the time point ti+k, k = evolving steps, f = sampling frequency, and {PPi}i=1,...,n–(De–1){tau}k = time series of PPEs. Subsequently a rectangular moving window was applied to the resulted time series of single PPEs. The window length was 257 data points (or 4 s accordingly).

The logarithmic relation (2) expresses the degree of interdependence of any defined time point on the initial conditions. It is a measure for the behavior of neighboring trajectories in the phase space. D'(ti+k) > D(ti) is equivalent to a divergence of the evaluated points in the phase space and results in PPi. > 0. Small changes in the initial conditions cause large changes over the time. Thus, a high positive value of PPi means a very low predictability and a high complexity. D'(ti+k) <= D(ti) corresponds to a convergence or no change over the time. It results in a PPi <= 0 and represents a quasiperiodic/periodic process or convergence to a steady state.

As in all nonlinear measures, the numerical values of the PPE depend on a sufficient number of data points and several other parameters as the embedding dimension, the time delays and the evolving time. These parameters must represent the entire range of activity contained in the ECoG signal. Especially for the examination of sleep state transitions, the different frequency distribution of the high-voltage, slow frequency ECoG during NREM and the low-voltage, high frequency ECoG during REM sleep needed to be taken into consideration. After testing all used parameters very careful, we chose an embedding dimension of 16, a time delay of 150 ms and an evolving time of 75 ms. ECoG epochs of 10 min containing 38400 data points proved to be sufficient for calculation of the PPE.

In order to compare the mean predictability of REM and NREM sleep during no stimulation with that during VAS, we averaged the PPEs resulting in a mean prediction error of the respective data set. All results are given as mean ± SD. Differences in the mean prediction errors were tested for significance by Wilcoxon's test for paired data. P values of <0.05 were considered to be significant.


    Results
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 Abstract
 Introduction
 Material and Methods
 Results
 Discussion
 References
 
Physiological Sleep States and Spontaneous Transitions

Physiological sleep states and spontaneous transitions were easy to recognize in the recorded ECoG signals of the examined animals (Fig. 1Go). The PPE was higher, i.e. the predictability of the ECoG was lower, in REM than in NREM sleep in all investigated animals. The mean prediction error as the average of the PPE over 10 min was 2.09 ± 0.62 s–1 in NREM sleep and 11.19 ± 2.04 s–1 in REM sleep (P < 0.01, Fig. 2Go). The higher prediction error revealed the higher complexity and lower causality of the ECoG during REM sleep and corresponded to the desynchronization of the ECoG. The interindividual variance of the predictability of the ECoG during NREM sleep was very low (Fig. 2Go). The higher standard deviation of the mean prediction error during REM than during NREM sleep is due to fluctuations of the predictability of the ECoG within the evaluated 10 min epochs and reveals the lower predictability of the ECoG in REM sleep as well (Figs 2 and 3GoGo).



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Figure 1.  Typical examples of the recorded ECoG signal during a spontaneous sleep state transition from REM to NREM sleep and during VAS in NREM sleep in a sheep fetus at 132 dGA (w230b).

 


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Figure 2.  Differences in the mean prediction error of the ECoG during NREM (filled bars), REM sleep (hatched bars) and VAS in NREM sleep (open bars). Average of 10 min ECoG epochs; mean ± SD, differences between NREM sleep, REM sleep and VAS in NREM sleep are significant at the 0.0001 level in each animal.

 


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Figure 3.  Time course of the changes of the point prediction error of the ECoG during transitions from NREM to REM sleep (left) and REM to NREM sleep (right). Arrows indicate the onset of transitions. Mean ± SD, five transitions in one fetus (w230b).

 
During spontaneous sleep state transitions the PPE changed markedly. However, the abrupt increase of the PPE during transitions from NREM to REM sleep was much steeper than the decrease during transitions from REM to NREM sleep (Fig. 3Go).

Vibroacoustic Stimulation

VAS led to sound pressures at the fetal head between 110 and 118 dB, exceeding the noise floor by at least 20 dB at all frequencies as shown elsewhere (Abrams et al., 1996Go). The maximum intrauterine sound pressure level ranged from 50 to 125 Hz and from 3.0 to 10.0 kHz.

VAS during NREM sleep provoked a disruption of the synchronized ECoG activity (Fig. 1Go) accompanied by an abrupt increase of the PPE (Fig. 4Go). The PPE rose from 2.09 ± 0.62 to 4.79 ± 1.61 s–1 (P < 0.05) and remained increased over the whole stimulation period. However, it did not reach the level of REM sleep (10.56 ± 2.50, P < 0.05; Figs 2 and 5GoGo). Thus, VAS in NREM sleep did not provoke a sleep state change from NREM to REM sleep. The time course of the abrupt increase of the PPE during VAS was very similar to that during spontaneous sleep state transitions from NREM to REM sleep (Fig. 5Go). The PPE returned within 2 min to prestimulation values. This decrease of the PPE after cessation of the VAS was much slower than the abrupt increase (Fig. 5Go). As in REM sleep, the less predictability of the ECoG during VAS in NREM sleep is also revealed by the higher fluctuations of the predictability of the ECoG in its time course and by the higher intraindividual variability of the predictability of the ECoG during VAS than during unaffected NREM sleep reflected by the higher standard deviation (Fig. 4Go).



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Figure 4.  Time course of changes of the point prediction error during VAS in NREM sleep. Average of five stimulations in one fetus (w230b), mean ± SD.

 


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Figure 5.  Comparison of the time course of changes of the point prediction error during spontaneous sleep state transitions from NREM to REM sleep and onset of VAS in NREM sleep (left) or during transitions from REM to NREM sleep and cessation of VAS (right). Mean of five spontaneous transitions and five stimulations in one fetus (w230b), VAS black line, spontaneous sleep state transitions dark gray line, unaffected REM sleep bright grayline.

 
In REM sleep, the PPE during VAS showed no changes (Fig. 6Go).



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Figure 6.  VAS in REM sleep. No changes of the point prediction error are visible. Average of five stimulations in one fetus (w230b), mean ± SD.

 
Test of Nonlinearity

During NREM sleep, the PPE of the simulated linear AR signal did not differ significantly from that of the original ECoG, revealing that there is only a small portion of nonlinearities in the NREM sleep ECoG (Fig. 7Go). The PPE of the simulated linear AR signal during REM sleep, however, was significantly lower than that of the original ECoG (Fig. 7Go). This reveals the lower predictability and higher complexity of the original REM sleep ECoG in comparison to the linear simulation and thus the high portion of nonlinear structure in the REM sleep ECoG. The lack of a difference between the PPE of the simulated linear AR model during NREM and REM sleep reflects a similar structure of the linear signal portion in both sleep states (Fig. 7Go).



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Figure 7.  Comparison of the PPE of the original signal (black line), the simulated linear AR signal (bright gray line) and the simulated random shuffled signal (dark gray line) during spontaneous sleep state transition from NREM to REM sleep. Mean of five spontaneous transitions in one fetus (w230b).

 
The PPE of the simulated random shuffling signal was significantly higher than the PPE of the original data sets and had almost the same high level in both sleep states (Fig. 7Go), revealing a clear deterministic portion in our original data and the nearunpredictability of our simulated random data sets.

Comparison to Power Spectral Analysis

Power spectral analysis of the ECoG during NREM sleep showed a frequency distribution with the maximal relative spectral power in the delta band (Fig. 8Go). During REM sleep, the frequency spectrum shifted to higher frequencies, the relative delta power decreased and the relative alpha and beta power increased, expressing the activation of the ECoG (Fig. 8Go). Relative theta band power remained unchanged. This frequency shift corresponded generally to a higher prediction error in REM than in NREM sleep.



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Figure 8.  Frequency distribution of ECoG power (relative band power) during NREM and REM sleep, and VAS in NREM and REM sleep (mean ± SD, n = 7; asterisks indicate significant differences, P < 0.05).

 
By means of power spectral analysis, VAS in NREM sleep provoked a clear arousal reaction of the fetus revealed by the shift of the ECoG power spectrum to higher frequencies (Fig. 8Go). In contrast to the clear differences between the prediction error during VAS in NREM sleep and unaffected REM sleep (Fig. 2Go), the power spectrum during arousal was much more similar to that of unaffected REM sleep than to that of NREM sleep (Fig. 8Go). Nevertheless, the ECoG power spectrum during VAS in NREM sleep still differed significantly from that of unaffected REM sleep power in the theta and beta bands as well as in the spectral edge frequency (Fig. 8Go, P < 0.05). Similar to the changes of the PPE, the power spectrum changed to prestimulation values within 2 min after cessation of the stimulus.

Power spectral analysis of the ECoG during VAS in REM sleep provoked a significant increase of the spectral power in the beta band, resulting in a slight but significant upward shift of spectral edge frequency from 21.22 ± 2.09 to 22.29 ± 1.75 Hz (Fig. 8Go, P < 0.05). The spectral power in the beta band dropped to the prestimulation values immediately after cessation of the stimulus. The PPE during REM sleep showed no changes following the stimulation, suggesting no further decrease in the predictability of the ECoG.


    Discussion
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 Abstract
 Introduction
 Material and Methods
 Results
 Discussion
 References
 
Our study was based on the concept that the ECoG is a highly complex signal (Pritchard et al., 1995Go; Micheloyannis et al., 1998bGo; Palus, 1996Go; Theiler and Rapp, 1996Go) containing information that cannot be described by linear approaches. The performed tests of nonlinearities in our data proved that the fetal ECoG is neither a superimposition of linear properties with nonstationarities nor a pure stochastic process. The fetal ECoG contains rather deterministic and nonlinear portions that need to be investigated with nonlinear methods. Changes of nonlinear measures of the EEG as correlation dimension, Kolmogorov entropy, leading Lyapunov exponent or mutual dimension were proved in several physiologic tasks (Aftanas et al., 1998Go; Micheloyannis et al., 1998aGo) or under pathological conditions (Röschke et al., 1994Go; Stam et al., 1997Go; Jeong et al., 1998Go; Sarnthein et al., 1998Go). Only a few attempts have been made to define a time variant nonlinear parameter to quantify the complexity and predictability of a time series (Gao and Zheng, 1994Go; Kowalik and Elbert, 1994Go; Pradhan et al., 1995Go). However, these attempts were not successful in quantifying short time changes of nonlinear properties of the EEG. Therefore, we developed an algorithm to calculate a PPE as a novel nonlinear approach in an attempt to better understand the physiological processes underlying the transitions between different functional states of the brain. Using this approach, we were able to quantify differences in the time course of the predictability of the ECoG during transitions between NREM and REM sleep, and during cortical activation induced by VAS.

The PPE revealed very clear differences in the predictability of the ECoG between unaffected REM and NREM sleep. The nonlinear properties of the signal within the respective sleep states were stable in their time course. A high predictability of the ECoG was found during NREM sleep and a lower predictability coincidental with poor organization of the rhythmic pattern during REM sleep (in other words, with a state of cortical activation).

The high predictability of the ECoG during NREM sleep shows that oscillations contained in the signal must be generated on a very regular basis. Indeed, during ECoG-synchronized NREM sleep, cortical and thalamic networks interact extensively, resulting in a coordinated occurrence of corticothalamocortical rhythms (Steriade et al., 1994Go; McCormick and Bal, 1997Go). Thalamocortical cells generate oscillatory, rhythmic bursts of action potentials in the frequency range of 0.5–4 Hz (McCarley et al., 1983Go) and intracortical circuits generate slow oscillations (<1 Hz) (Steriade et al., 1993Go). Spindle waves as a second thalamic rhythm of 7–14 Hz, which occur during synchronization of the ECoG in humans, monkeys and cats (McCarley et al., 1983Go; Steriade and Deschenes, 1984Go), are not seen in the fetal sheep ECoG.

During REM sleep, complex pontomedullary cholinergic neuronal circuits generate excitatory impulses (Jouvet, 1994Go) that are transferred over ascending cholinergic pathways to the thalamocortical systems (Francesconi et al., 1988Go; McCormick and Pape, 1988Go). The tonic input to the forebrain structures leads to an abolition of NREM sleep-related oscillations in the EEG visible as desynchronization (Steriade and McCarley, 1990Go). The steep, almost vertical increase of the PPE of the ECoG during the transition from NREM to REM sleep suggests a desynchronization of the thalamocortical activity in an all-or-none fashion. The much slower decrease of the PPE during the reverse transition from REM to NREM sleep and after cessation of VAS shows that the decreasing excitability of the ascending activating system does not disinhibit the generation of the corticothalamocortical slow wave rhythms in a threshold-like manner.

External VAS produced on the abdominal surface of a pregnant sheep induced an arousal reaction in the fetal electrocortical activity according to the criteria of the American Sleep Disorders Association (American Sleep Disorders Association, 1992Go) during both NREM and REM sleep. The EEG arousal criteria are based on a frequency shift to higher frequencies consistent with an activation of the EEG. There is no definition of EEG arousal using nonlinear measures. However, cortical activation could be proven by the increased PPE during VAS in NREM sleep, suggesting cerebral processing of the stimulus. The PPE showed that fetal cortical activation patterns in the state of arousal induced in NREM sleep were clearly different from that during unaffected REM sleep. Differences in frequency distribution between the state of arousal during stimulation in NREM sleep and unaffected REM sleep were less pronounced than that of the predictability of the ECoG.

On the other hand, VAS during REM sleep did not change the predictability of the ECoG although power spectral analysis revealed an arousal reaction by an increase of beta activity. Nonlinear properties of the state of arousal are probably concealed by that of the more complex REM sleep. The increase of beta activity does not mean necessarily a further ECoG activation and, thus, an increase of nonlinearity. Recent investigations have shown that fast ECoG rhythms in the frequency range of the beta band in a state of so-called desynchronization are in part synchronized (Steriade et al., 1996Go). Similar to the slow wave oscillations, they probably show no complex dynamic patterns.

Several studies in human and sheep fetuses have reported that the arousal threshold is higher in REM sleep than in NREM sleep (Gagnon, 1989Go; Parkes et al., 1991Go; Visser et al., 1989Go). In the human fetus, VAS applied during state 1F corresponding to NREM sleep induces frequently behavioral state changes (Visser et al., 1989Go). From the viewpoint of our results it is questionable whether the changes in human fetal behavior observed without access to the electrocortical activity are indeed sleep state changes or linked to the state of cortical arousal. On the other hand, fetal sheep might lack a true behavior state change because it is less sensitive to VAS than the human fetus (Bauer et al., 1997Go; Gagnon, 1989Go; Visser et al., 1989Go).

The equal dynamics of the decrease in the predictability of the ECoG during spontaneous transitions from NREM and REM sleep and during VAS support the view that similar mechanisms of functional brain activation are involved. The stimulus used in this study has been proven to be very effective in increasing the utilization of glucose along the auditory pathway, suggesting functional brain activation via the auditory system and not via vibration receptors in the skin (Abrams et al., 1989Go). It has been demonstrated by anatomical and electrophysiological methods that the auditory pathway sends projections to reticular neuronal groups of the brainstem participating in behavioral state-related effects such as changes in heart rate and heart rate variability (Bauer et al., 1997Go) and in mechanisms regulating REM sleep (Jones, 1994Go).

Our results prove that neither the knowledge of the unit properties nor the description of their interactions with linear methods is sufficient to explain the collective behavior of the neuronal network completely. Application of nonlinear measures to study the dynamics of the collective behavior has proven to be useful (Pritchard et al., 1995Go; Micheloyannis et al., 1998bGo; Palus, 1996Go; Theiler and Rapp, 1996Go). It seems that both the multiple interactions between several groups of neurons and an already nonlinear firing pattern of the individual neurons themselves create the characteristic dynamics of the EEG. Moreover, Ferri et al. (Ferri et al., 1996Go) showed that sleep regulation itself is a deterministic nonlinear process. Using the PPE, we could show for the first time short-term changes in nonlinear properties of the neuronal network in its time course.

Similar to other nonlinear measures, the PPE should be interpreted only as a relative measure to discriminate different states of functional brain activation (Palus, 1996Go). As all nonlinear measures that rely on phase space concepts, the absolute numerical values of the PPE depend on data length and input parameters. The uncritical use of these parameters and of the nonlinear algorithms themselves brought the reliability of chaos-based algorithms in general into question (Palus, 1996Go; Theiler and Rapp, 1996Go). Classic linear measures are more robust and more easily computed than nonlinear measures. Thus, it is useful from a pragmatic point of view to quantify first the phenomena under study with sophisticated measures from linear system theory. As we could show, both linear and nonlinear approaches give useful information but differ in terms of the information they provide. The PPE has gained importance in understanding mechanisms of time-related features of brain activation and yielded information that cannot be extracted by linear approaches. Estimation of the PPE leads to a single parameter which reflects a property of the whole dynamic system.

In conclusion, external VAS during NREM sleep did not alter the sleep state in fetal sheep but changed the functional state of the cerebral cortex significantly. These changes are mediated by an activation of brainstem structures, as inferred by estimation of the PPE. The PPE complements linear analysis methodology and is an elegant method for assessing and classifying the time courses of dynamic states of the brain.


    Notes
 
This study was supported by the Deutsche Akademir der Naturforscher Leopoldina.

Address correspondence to Dr Matthias Schwab, Department of Neurology, Friedrich Schiller University, D-07740 Jena, Germany. Email: schwab{at}landgraf.med.uni-jena.de.


    References
 Top
 Abstract
 Introduction
 Material and Methods
 Results
 Discussion
 References
 
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