The aim of this study was to find spatial patterns of EEG amplitude in the gamma range of the EEGs from multiple sensory and limbic areas that demonstrated multisensory convergence and integration. 64 electrodes spread in small arrays were fixed on or in the olfactory, visual, auditory, somatomotor and entorhinal areas of cats and rabbits. The subjects were trained to discriminate 2 visual and then 2 auditory conditioned stimuli, one reinforced (CS+), the other not (CS-). A moving window was applied to the 6-s records from 20 trials of each CS including a 3-s prestimulus control (CS0). The root mean square amplitude was calculated for each signal in the gamma range, so each window gave a point in 64-space. EEG patterns from the CS+, CS- and CS0 conditions gave 3 clusters of points in 64-space. The Euclidean distance of each point to the nearest center of gravity of a cluster served for classification and estimation of the probability of correct classification. The results showed that the gamma activity (35-60 Hz in cats, 20-80 Hz in rabbits) in all five areas formed global patterns of amplitude modulation (AM) in time windows lasting ~100-200 ms and recurring at 2-4 Hz, which were correctly classified above chance levels (p < .01). All areas contributed information to the AM patterns that served to classify the EEG epochs in the windows with respect to the conditioned stimuli. In conclusion, multisensory integration took place over the greater part of the hemisphere, despite lack of phase coherence among the gamma waves. The integration occurred rapidly enough that, within 300 ms of CS onset, activity in every sensory area was modified by what took place in every other sensory area.

We present a general connectionist model for an olfactory system. The dynamical behavior of each node (neural ensemble) of the model is governed by a second-order ordinary differential equation (ODE) followed by an asymmetric sigmoidal function, relating the aggregate activity of neurons to system parameters and stimuli from an outside environment. A digital implementation of the general connectionist model simulates the characteristics of a mammalian olfactory system having modifiable synaptic connections and spatio-temporal interactions among neural ensembles. Each of four distributed delay terms is represented by a second-order ODE. A parameter optimization algorithm is an integral component of the model. The parameter optimization discussed in this paper results in aperiodic oscillations having a near 1/f-type power spectrum with a peak in the gamma range, simulating the electro-encephalographic (EEG) potentials from the neural olfactory system. Random optimization is used for a rough search in a global parameter domain and the parameter self-adaptation rule serves for fine tuning within a local domain after the global search. By design the model is started from an unstable zero point by an external impulse input. It requires 650-850ms to pass through an initializing transient before settling into a strange attractor. The attractor persists for at least 1500ms, which is 7.5-20 times longer than the duration of the maximal stationary states observed in the EEGs and it is stable under perturbation by simulated sensory inputs giving response amplitudes less than 2 times the basal aperiodic activity. However, the optimization to 1/f-type activity reveals an inherent limit on digital simulation of chaotic states, owing to attractor crowding such that the size of basins decreases with increasing size of the model, until it approaches the size of digitizing step in computation, here a 64-bit word ( approximately 10(-16)). Outputs that are not optimized to approach 1/f-type power spectra transit earlier to limit cycle activity, usually well before 2000ms. The duration of stationarity is increased by randomizing the terminal bit of the 64-bit words representing the state variables. The 1/f-type solutions are also exquisitely sensitive to parameter truncation; parameter values must be saved in their full binary form for re-starting. The implications in terms of numerical instability, chaos, attractor crowding and the shadowing theorem are discussed.

We evaluated the rapid changes in regional scalp EEG synchronization in normal subjects with spatial and temporal resolution exceeding prior art 10-fold with a high spatial density array and the Hilbert transform. A curvilinear array of 64 electrodes 3 mm apart extending 18.9 cm across the scalp was used to record EEG at 200/sec. Analytic amplitude (AA) and phase (AP) were calculated at each time step for the 64 traces in the analog pass band of 0.5-120 Hz. AP differences approximated the AP derivative (instantaneous frequency). The AP from unfiltered EEG revealed no reproducible patterns. Filtering was necessary in the beta and gamma ranges according to a technique that optimized the correlation of the AP differences with the activity band pass filtered in the alpha range. The sizes of temporal AP differences were usually within +/-0.5 radian from the average step corresponding to the center frequency of the pass band. Large AP differences were often synchronized over distances of 6 to 19 cm. An optimal pass band to detect and measure these recurring jumps in AP in the beta and gamma ranges was found by maximizing the alpha peak in the cospectrum of the correlation between unfiltered EEG and the band pass AP differences. Synchronized AP jumps recurred in clusters (CAP) at alpha and theta rates in resting subjects and with EMG. Cortex functions by serial changes in state. The Hilbert transform of EEG from high-density arrays can visualize these state transitions with high temporal and spatial resolution and should be useful in relating EEG to cognition.

Objective: To evaluate rapid changes in regional EEG synchronization in normal subjects with spatial and temporal resolution exceeding prior art 10-fold.

Methods: A curvilinear array of 64 electrodes 3 mm apart extending 18.9 cm across the scalp was used to record EEG at 200/s. Analytic amplitude (AA) and phase (AP) were calculated at each time step for the 64 traces in the analog pass band of 0.5-120 Hz. AP differences approximated the AP derivative (instantaneous frequency). The AP from unfiltered EEG revealed no reproducible patterns. Filtering was necessary in the beta and gamma ranges according to a technique that optimized the correlation of the AP differences with the activity band pass filtered in the alpha range.

Results: The sizes of temporal AP differences were usually within ±0.5 radian from the average step corresponding to the center frequency of the pass band. Large AP differences were often synchronized over distances of 6 to 19 cm. An optimal pass band to detect and measure these recurring jumps in AP in the beta and gamma ranges was found by maximizing the alpha peak in the cospectrum of the correlation between unfiltered EEG and the band pass AP differences. Synchronized AP jumps recurred in clusters (CAP) at alpha rates in resting subjects and with EMG.

Conclusion: Cortex functions by serial changes in state. The Hilbert transform of EEG from high density arrays can visualize these state transitions with high temporal and spatial resolution and should be useful in relating EEG to cognition.