903 Clinical Neurology and Neurosurgery, 94 (Suppl.) (1992) S103-S105 Q 1992 Elsevier Science Publishers B.V. All rights reserved 0303~8467/92/$05.00 CNN 00132
Cerebral information processing estimated by unpredictability of the EEG Bob Kemp Department of Neurology and Clinical Neurophysiology, UniversityHospital, Leiden (The Netherlands)
Key words: EEG
EEG model; EEG analysis
Summary Processing of complex information by the brain desynchronizes neuronal cells and therefore increases the unpredictability of the EEG, rather than its amplitude or power. A model of this mechanism describes the EEG as being composed of both an unpredictable fraction and a fraction that can be predicted from the past EEG. The model realistically simulates EEG of several behavioural states and suggests a simple algorithm for the computation of EEG predictability (values between 0% and 100%). Applications in sleep analysis and event-related desynchronization demonstrated that the algorithm is more accurate and artifact-resistant than the usual (spectral) power methods.
Introduction A neural network handles (or creates) complex streams of new information by having many cells perform different tasks. Also, new tasks will be engaged as soon as the previous ones are finished. The gross network activity will therefore be a sum of many independent sources and change relatively fast and irregular. These changes are usually not predictable. If, on the contrary, the network is not in such an efficiently organized state, the cells can only diffuse ‘old information amongst each other. In this case, the activity of many cells can become synchronized. The resulting group activity will tend to echo through the cell network and repeat itself. The gross EEG is then, therefore, largely predictable from its own recent past, up to some seconds ago. This mechanism has been described for the hippocampal theta rhythm as well as for the thalamic alpha rhythm [1,2]. Epileptic and slow-wave sleep activity are also periodic to some extent and may therefore also fit into this concept. In this view, the intensity of information processing by a neural network is proportional to the fraction of the EEG that can not be predicted from its own past. It is probably not proportional to EEG amplitude or power
Correspondence to: Dr. Ir. B. Kemp, Department of Neurology and Clinical Neurophysiology, University Hospital, P.O. Box 9600,230O RC Leiden, The Netherlands. Tel.: (71) 262188 / 263960; Fax: (71) 213152.
because, although some electrical activity must accompany information processing, the largest powers will occur during synchronized, idle, states. Therefore, the predictability of EEG components would be a more relevant parameter for analysis of brain functioning than the usually applied power of these components (e.g., based on Fourier analysis). Available methods for predictability analysis are based on two types of models that describe how the brain generates both predictable and unpredictable activity. These models are known as “deterministic chaos” and “noise driven feedback”, respectively . The latter type includes Auto Regressive and Kalman filter models. Both types of models contain a causal, deterministic feedback mechanism that produces the predictable part of future activity by echoing current and past activity. In chaos models, this mechanism is extremely sensitive to small disturbances, so that it can generate erratic signals that are partially unpredictable. In the noise models, the feedback is not very sensitive to small disturbances and an independent noise source was added in order to account for the unpredictable part. Until now, we have designed and applied only noise model based analysis, because of the following arguments. Any cerebral system is influenced by membrane noise and by undescribed complex activity from connected systems. The feedback mechanism in noise models can be chosen in such a way that the models produce realistic simulations of EEG signals (next section), while
s104 chaos models cannot. The noise model-based algorithms
are relatively clear and simple. The algorithms offer good time resolution: the results reflect the dynamics of the state of synchronization, including short-lasting event-related responses. This paper describes how to compute EEG predictability based on the noise model. We also compared some practical results to results obtained by power computa-
EEG (y) can be computed from the present of s, which is indeed echoed to the future EEG (depending on the degree of synchronization), is our EEG predictability parameter,p. It can be estimated as follows:
of the future
and past EEG. The percentage
Methods and results
We have proposed  an EEG generator model in which the feedback loop consists of a simple causal bandpass filter. In this way, the EEG contains a rhythmic component which is almost completely determined by the past EEG. A random noise drives the model, thus producing the unpredictable component. The rhythmic component waxes and wanes because it is randomly enhanced and attenuated by the noise. When the feedback is maximally active (so the network is in the idle state, just diffusing ‘old’ activity to all cells), 100% of the predictable, rhythmic component is echoed to the future EEG. When the feedback is fully inhibited (so the network is processing new information and not passing around ‘old’ activity), 0% of the rhythmic component is echoed to the future. We adopted this model because an electronic version realistically simulates (Fig. 1) desynchronized background EEG, as well as K-complexes, alpha rhythms, sleep spindles and slow-wave sleep [4,5]. Based on the 0
where the summation is over time or over equivalent experiments [3,6,7]. Simply check the formula by substituting the EEG generator equationy = p’s + noise into this formula and note that the random noise contribution will average out of the numerator. Note that p ranges from 0 to 1, i.e. from 0% to 100% . Instead of estimating p, it is also possible to test between (e.g.) hypothesesp = 0% andp = 100% by computing the test statistic
Due to the limited frequency response of the cells (i.e., action potentials, PSPs, refractory period), the brain needs a little time to be able to generate completely unpredictable EEG, even if we compensate for the low-pass filter effect of volume conduction. In practice therefore, the EEG is predicted about 5 or 10 ms ahead and then compared to the actual EEG, using the above formulas. In the first application  of the predictability estimator, light flashes made the occipital cortex of 9 volunteers switch from a relatively idle state with about 80% predictable alpha rhythm to an active state with about 20% 0
Fig. 1. Simulations by the noise-driven feedback model of A: 100% desynchronized EEG with event responses every 2.5 s. B: 70% synchronization around 14 Hz with responses every 4 s. C: 70% synchronization around 1 Hz with random responses. Each trace fasts 25 s. Note that the event resonses are variable, although caused by identical events, i.e. identical input pulses to the model at each dot.
s105 predictability. The latency from flash to the first decrease of predictability ranged (between subjects) from 70 to 120 ms, estimated with a 4-ms time resolution. The best time resolution that can be obtained by classical (power) methods is about 50 ms. In later applications, the predictability test statistic, L, accurately detected sleep spindles, K-complexes and slow sleep waves [9-111. Recently, we demonstrated  that the predictability parameters distinguish high-frequency EEG (such as sleep spindles) much better from EMG artifacts than classical power analysis (e.g., based on Fourier transform) methods.
On a quite different time scale, ameter offers an accurate tool for lated responses of EEG rhythms, tion. In particular time resolutions can easily be realized. References
Conclusions The concept of an EEG that becomes predictable during idle states, due to unspecific coupling between cells, is not only supported by structural/physiological reasoning, but also by the fact that only structures like these have been able to produce realistic EEG simulations. The predictability parameter therefore is more likely to reflect the intensity, or efficiency, of information processing by the brain than the classical (spectral) power methods. Since maturation and ageing of the brain influences its capacity for information processing, this parameter should also be considered for the assessment of brain development and degeneration.
the predictability parthe study of event-ree.g. (de)synchronizain the order of 10 ms
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