4. Selforganization in the Brain

4.3 Function

Brain function can be studied at a number of different levels and with several techniques. It is not at all clear which approach will be most suitable for understanding higher brain functions. Electroencephalogram (EEG) recordings give information on the averaged electrical activity in a volume of cortical brain tissue, containing a large number of neurons. EEG records generally have a noise-like appearance indicating an ongoing erratic activity, which only seems to disappear in very deep anesthesia. This activity is aperiodic, although in certain conditions (e.g. during relaxation) it appears to be more 'rhythmic'. These rhythms, which have a specific dominant frequency and waveform, are used to classify the EEG. In the frequency domain, the EEG is characterized by a broad power spectrum, with a continuous distribution of power in the frequency range 0.5-100 Hz. When rhythmic components are present, they produce peaks in the spectrum, which are sitting on top of a broad background. Where does this noise-like background activity come from?


 Isolated neurons behave deterministically: pacemaker neurons fire action potentials periodically, while other neurons are silent unless they are synaptically activated. Usually a number of more or less simultaneous excitatory inputs are needed to cause such a neuron to file (Abeles, 1982). The response of a neuron to a specific synaptic input is predictable, because spontaneous fluctuations in membrane potential are small compared to the depolarization needed to reach the firing threshold. Still, when functioning in a neural network, the behaviour of neurons appears stochastic. This activity is caused by interactions in the network, as it disappears after blocking all synaptic transmission.


There is no noise source in the brain, as isolated neurons seem to operate deterministically. So, how can the noise-like character of the EEG be explained? The situation could be analogous to a gas, where the thermal movement of the molecules seems very erratic, although their movement is completely determined by physical laws. It is the lack of knowledge of all initial conditions, which forces a stochastic description. When their behaviour is averaged, deterministic macroscopic behaviour again appears. Only on the intermediate mesoscopic level stochastic behaviour dominates. This seems not to be the case in the brain, as a noise-like behaviour persists even on the macroscopic level of EEG measurements. The reason for this persistence is a large degree of coherence in the activity, which also becomes apparent when comparing EEG traces from different brain regions measured simultaneously. Although every individual trace has a noise­like appearance, there is often a great similarity between the traces. This spatial coherence is indicative of deterministic dynamics and it is therefore suggestive to explain the background EEG as chaotic activity, instead of random noise. Widespread spatial coherence is the most important argument used by Freeman (1985) to explain the background EEG activity in the rabbit olfactory bulb as chaotic. Chaotic dynamics as a basis for the EEG explains the broad power spectrum, without the need to assume an unknown noise source. It originates from the interplay of two conflicting forces: destabilizing positive feedback mechanisms (mutual inhibition and recurrent excitation) and stabilizing negative feedback. What results is an ever-changing macroscopic activity, which is very robust, because the dynamics are governed by a ('strange') attractor. The various rhythms mentioned above correspond to different chaotic attractors, probably with a relatively low fractal dimension. Such low-dimensional attractors are well known. An example is the Rossler-attractor, described by a set of three coupled nonlinear differential equations. For certain parameter settings, the solution is 'chaotic, but nevertheless it has a very 'rhythmic' appearance.


Transitions between various attractors ("modes of behaviour') are governed by control parameters. The brain is a hierarchical system, made of many subsystems controlling each other. This implies that the output variable of one subsystem can act as a control parameter of another subsystem (cf. Freeman, 1985). Such a mechanism seems to play a role in the regulation of the α-rhythm. The α-rhythm appears in the EEG of occipital brain regions, after cessation of visual input, either by closure of both eyes or by darkening the visual environment. It can be blocked abruptly by a flash of light. Termination of the visual input corresponds to a sort of functional deafferentiation of the visual cortex.  The α-rhythm apparently corresponds to the 'intrinsic' mode of behaviour of the visual cortex, which is disturbed by input from 'lower' visual centers. The output of these centers acts as control parameter for the visual cortex. The 'intrinsic' behaviour (α-rhythm) has a much lower fractal dimension then the fast erratic background EEG seen in the presence of visual input.


A similar mechanism seems to be operating during sleep-wakefulness transitions. Sleep is not a single physiological state, but instead consists of a sequence of stages, which differ in EEG activity and levels of vigilance. A common denominator seems to be a low level of sensory information processing. Focusing on EEG activity, deep sleep is characterized by a relatively high amplitude and abundance of lower frequencies, indicating a high degree of synchronization. When sleep becomes deeper, the degree of synchronization increases. In addition, there are periods with a fast, small amplitude EEG, which is difficult to distinguish from the waking EEG. In this stage rapid eye movements occur, giving rise to the term Rapid Eye Movement sleep. REM sleep is characterized by desynchronized EEG activity and a low muscular tone (paralysis). Four stages of non-REM sleep are distinguished, stage 3 and 4 corresponding to deep sleep. Babloyantz et al. (1985) presented evidence for chaotic dynamics of brain activity in the human EEG during sleep. Analyzing EEGs using recently developed techniques, they were able to estimate the fractal dimension for sleep stages 2 and 4. For neither REM sleep nor waking EEGs were they able to prove the existence of a chaotic attractor. Dimensionality was much higher in these cases. The increase in synchronization seen in non-REM sleep when going from stage 1 to 4 is paralleled by a decrease in dimensionality and an increase in coherence.


Non-REM sleep is also accompanied by a general reduction in metabolic activity as measured by the14C-deoxyglucose method (Kennedy et al., 1982). Moreover, characteristic dark markings (periodic spatial variations of metabolic activity) which were observed in nearly all major subdivisions of the cortex of waking animals, disappeared during sleep. In the same study, Kennedy et al. (1982) investigated 75 brain structures, in search for a structure in which activity would be selectively increased during non-REM sleep. However, in all structures glucose utilization dropped during non-REM sleep. These findings suggest that non-REM sleep and wakefulness are different functional states of the brain, which are intrinsic. Transitions between them are characterized by changes in the level of dissipation. Non-REM sleep could result from functional deafferentiation of the cortex. Deep structures, like the reticular formation, which are thought to be involved in regulation of sleep, could produce changes in the level of synchronization by a mechanism of general activation.


The most dramatic changes in brain activity occur during epileptic seizures. During a seizure, normal brain function is suddenly interrupted and the activity of the whole brain or part of it sharply increases and becomes very synchronized and nearly periodic. A recent classification (cf. Delgado-Escueta et al., 1986) distinguishes generalized epilepsies where the whole brain is involved in a seizure, from partial (a) epilepsies where the epileptogenic activity stays localized in a certain region. A second subdivision is made in idiopathic epilepsies (which are genetically determined) and symptomatic epilepsies (which are caused by a structural lesion). Idiopathic generalized epilepsies are least understood, both because no structural deficits can be shown and because the epileptogenic activity appears suddenly in several brain structures at once. No epileptogenic focus can be found which is primarily responsible for the onset of the seizures, as is the case for symptomatic epilepsies. For none of the epilepsies the primary cause has been established. Various animal and in vitro models are used to study the mechanisms involved. These investigations led to a variety of hypotheses of processes and compounds which could be of primary importance for seizure onset (Delgado-Escueta et al., 1986). The list of putative primary causes grows steadily and seems to keep in pace with advances in basic research. Various drugs with widely different mechanisms of action are known to promote convulsions. These observations lead to the conclusion that the same pathological state of the brain can be arrived at in a variety of ways. The sudden and unpredictable transition from normal brain function to epileptogenic behaviour seems to be universal and not dependent on primary cause.  It is proposed that a seizure corresponds to an intrinsic mode of behaviour where activity is highly synchronized, but unlike non-REM sleep stages, the level of activity is extremely high. Both excitatory and inhibitory neuron pools are highly activated. Negative feedback connections prevent simultaneous strong activation of both pools, but during a seizure periods of strong excitatory activity are alternated with period of strong inhibitory activity, giving rise to the characteristic periodic peak-wave complexes. That this seizure state also exists in non-epileptic subjects is shown by the results of electro-shock treatment, where the therapeutic effects are due to the seizure which results from it. In non-epileptic subjects, this seizure state can only be reached after a very strongly synchronizing stimulus like an electro-shock or with the aid of convulsants.


Normal brain function is characterized by a subtle balance in the levels of activity of excitatory and inhibitory neuron pools, allowing them to be simultaneously activated at a relatively moderate level. This gives rise to chaotic modes of behaviour on a variety of attractors with different dimensionality. Disturbance of this balance by a variety of causes can lead to the onset of a seizure, which corresponds either to a limit cycle attractor or a chaotic attractor of very low dimensionality. Babloyantz and Destexhe (1986) analyzed an EEG recording obtained during an absence (petit mal seizure) and found evidence for a chaotic attractor with a very low fractal dimension. Freeman (1986) showed that a seizure can result from runaway inhibition, thereby challenging the general view that epileptic activity always results from excessive excitation or failure of inhibition. In the same paper, Freeman also suggests a chaotic nature of seizure activity.


The above observations seem to suggest that the brain operates in a chaotic mode. Different functional states correspond to different strange attractors, the properties of which still need to be classified. During non-REM sleep stages bifurcations to low dimensional strange attractors take place, as a result of a drop in overall activity. In addition to this set of attractors with relatively high dimensionality and complexity, there exists at least one very low dimensional strange attractor, which corresponds to an epileptic mode of behaviour. Transitions to this attractor take place after one of the other attractors has become unstable. As a result, this transition can be abrupt and generalized. Probably a variety of causes can lead to the development of and instability of the high dimensional attractors governing normal brain function. Once a proper instability has developed, a bifurcation to a seizure state will result. The behaviour in this state does not depend on the initial cause, but will be universal.


Does a chaotic mode of operation make sense from a functional point of view? Chaos provides the opportunity to combine a high complexity (large dimensionality) with a high degree of organization (reflected by the fractal structure of the strange attractors). The high level of dissipation in the brain assures the stability of attractors, so that they can exist for prolonged periods of time and produce different modes of behaviour.


(a) The term 'partial' epilepsy/seizure has been replaced with 'focal' epilepsy/seizure.