Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex

Cortical blood flow at the level of individual capillaries and the coupling of neuronal activity to flow in capillaries are fundamental aspects of homeostasis in the normal and the diseased brain. To probe the dynamics of blood flow at this level, we used two-photon laser scanning microscopy to image the motion of red blood cells (RBCs) in individual capillaries that lie as far as 600 μm below the pia mater of primary somatosensory cortex in rat; this depth encompassed the cortical layers with the highest density of neurons and capillaries. We observed that the flow was quite variable and exhibited temporal fluctuations around 0.1 Hz, as well as prolonged stalls and occasional reversals of direction. On average, the speed and flux (cells per unit time) of RBCs covaried linearly at low values of flux, with a linear density of ≈70 cells per mm, followed by a tendency for the speed to plateau at high values of flux. Thus, both the average velocity and density of RBCs are greater at high values of flux than at low values. Time-locked changes in flow, localized to the appropriate anatomical region of somatosensory cortex, were observed in response to stimulation of either multiple vibrissae or the hindlimb. Although we were able to detect stimulus-induced changes in the flux and speed of RBCs in some single trials, the amplitude of the stimulus-evoked changes in flow were largely masked by basal fluctuations. On average, the flux and the speed of RBCs increased transiently on stimulation, although the linear density of RBCs decreased slightly. These findings are consistent with a stimulus-induced decrease in capillary resistance to flow.