Slow potentials in the brain:
still little understood but gradually getting analytical attention

Theodore H. Bullock

Two classes of electrical activity in the central nervous system have been known for a long time: spikes with synaptic potentials and "slow" fluctuations (components mainly below ca. 100 Hz). Their relations to each other are still little known and an unfortunate schism persists in mutual disparagement by investigators who chiefly study one class or the other. The news I wish to highlight is that this schism is waning and this essay will be outmoded as more workers study both. I focus here on the class of slow potentials which in certain respects is the more neglected. This class should extend down into the less-known "infraslow" domain (power mainly below 0.1 Hz) - omnipresent, higher in amplitude and clearly significant functionally.

One view of our knowledge underlines the probability of many kinds of cellular sources, including, but not limited to neuron somata, axons and their terminals, dendrites and postsynaptic sites, neuroglia of more than one kind, ependyma and possibly blood vessels (including streaming potentials at the walls). Corresponding diversity of kinds of activity includes local, graded potentials of more than one kind, generator potentials of central sensory neurons, pacemaker potentials of more than one kind, such as quantal miniatures and extremely regular relaxation oscillations, spikes, after-potentials, classical synaptic potentials and subthreshold hyper- and depolarizations of longer duration with opposite membrane impedance change from the classical ones - and others. The intercellular fields of all these sources (more numerous than the sum of the cells and their synapses) add as vector sums, are dynamically interdependent and influence each other nonlinearly.

The long-standing question, whether brain waves could be causal or only epiphenomena should now be recast to read: Which of these kinds of activity can influence which others and in what ways? Pacemaker potentials, for example, must in the generalcase be influenced by the vector sum of local field potentials (LFPs) that alter transmembrane voltage gradients differently at dendritic arbors, somata and axon hillocks, at axon terminals and collateral branch points. Particularly important must be the multiple mechanisms of synchrony among populations of cells, both in firing and in subthreshold oscillations: these are most probably modulated by LFPs as well as chemical modulators.

The results to be expected from this view are observed: a great variety of manifestations of assembly activity, recorded from populations of different microstructure, connectivity, and cellular "personality" properties (e.g. facilitation, accomodation, iterativeness, burstiness, gap junction coupling, modulation by any of scores of substances). Even an extensive knowledge of single cell dynamics cannot, in general, predict the recorded microEEG seen by extracellular microelectrodes and wideband amplifiers. Likewise, even an extensive knowledge of such micro-fields, with multiple electrodes, cannot, in general, predict the macro-fields such as the scalp- recorded EEG. The three-dimensional spatial and temporal structure of the microEEG is probably information-rich about the vastly more complex activity of the distributed sources.

EEGs recorded from the scalp of humans show activity in all spectral frequencies between <0.1 and >200 Hz, with an amplitude maximum below 15 Hz and a steep amplitude decline above ca. 15 Hz. Amplitude is so small above ca. 50 Hz that these components are seldom studied outside the skull. Activity is generally rather similar at scalp loci four centimeters apart; coherence is quite significant out to some decimeters. Underlying strong local differentiation, fluctuations in coherence, with place as well as time, tend to occur in parallel at all frequencies, belying the Fourier assumption of independent oscillators.
EEGs recorded intracranially with macroelectrodes are similar but somewhat larger and decline in coherence, on average, to insignificant levels within 10 mm. Microelectrodes see much more variable activity, often with no appreciable coherence even at a fraction of a millimeter. They show neuronal spikes in some loci and these can be phase-related to some slow wave or not.

Rhythms or peaks in the power spectrum may become obvious in certain brain states or after adequate stimuli, for example delta, theta, alpha, beta or gamma waves at ca. 2, 5, 10, 20, or 40 Hz, respectively. Rarely do two or more of these rhythms, other than harmonics, occur together. A large literature has established correlations between the presence, or scalp distribution, of an oscillation and the behavioral or clinical state or the onset of an adequate stimulus or expectation. It is probable that during most of our waking hours, no rhythm is present in the scalp or subdural EEG - defining "rhythm" (in an abbreviated form, without discussion in this place) as more than just a component of a wide-band spectrum, such as as the spectrum seen by band- passing white noise.

A rhythm, for my purposes should be a distinct oscillation that maintains a periodicity within arbitrary, reasonable limits (e.g. ±25% of the mean) for more than a few cycles. Even when a clear rhythm is seen, wide-band energy is also present in EEGs and the resultant may not be equivalent to a stochastic time series. It can have a subtle temporal structure for example a nonlinear, quadratic phase coupling among the frequency components (bicoherence), and in addition a spatial fine or gross structure. Remarkable new analytical tools have come to hand for revealing temporal and spatial structure, such as "bispectrum", "independent component analysis", "mutual information" and the "additive periodogram", in addition to the battery of more classical methods.

Responses evoked by stimuli or expectations can be slow wave transients with a characteristic form or a succession of peaks or a more or less time-locked oscillation in addition to nerve impulse spikes. These "event-related potentials" and "induced rhythms" share many of the foregoing features of ongoing activity and are typically dependent on stimulus quality, intensity and repetition interval, locus in the brain and a number of modulating states.
Compound, local fields can be viewed heuristically as phenomena presented by nature that deserve adequate description and analysis at their own level, with the expectation of eventual clarification of the relations with other levels, such as single cell spiking. Long before such relations are well understood, empirical knowledge of the slow field potentials will undoubtedly reveal - and has already turned up - emergent phenomena, such as kindling, spindles, long range coherence, bicoherence and shifts in power spectra, in mutual information and in measures of chaos. Some of the emergents are useful, as in EEG diagnostic signs; others are the first neural and objective physical signs of cognitive processes such as expectation, attention, recognition and subtle mental discriminations; and some are the basic data for studying synchrony, microstructure and dynamical cooperativity..

In spite of over 70 years of research, major descriptive, as well as analytical and mechanistic questions remain. We do not know what differences in the EEG correlate with the vastly increased complexity of the cerebral mantle, comparing mammals with amphibians and fish, for example. Still less can we explain the differences between EEGs as well as evoked potentials from different parts of the brain, even in the best studied mammals. Insects, crustaceans, gastropods and annelids all show similar ongoing, unstimulated electrical activity in their higher centers that looks drastically different from activity of any vertebrate (or cephalopod!) higher center, but we have no understanding of the basis of the more conspicuous spikes and relatively much weaker slow waves from the invertebrates. A number of insects and gastropods can, under certain conditions, show repeatable slow (<1 to >40 Hz) rhythms and wide- band activity but dominated by spikey background. We have reason to expect wide variation in the degree and distribution of synchrony but lack quantitative data; this important variable can cause or enhance slow waves and hence LFPs. Such "induced rhythms" have attracted a great deal of recent interest, yet we have little understanding of what they do, especially in the majority of cases, where they have not been studied with adequate stimuli. These and other problems offer opportunities for discovery of new principles of system dynamics and organization.