The human brain is arguably the most complex structure known to mankind and on the verge of starting to grasp its own inner workings. How do our brains compute? How fast do they compute? How do they store information? How universal is all of the above? Ever since the first electroencephalography (EEG) recordings in 1924, the study of the electrical activity of the human brain has focused on its prominent low-frequency features, in particular the excitatory and inhibitory rhythms at specific frequencies, like the α (10 Hz) and β (20 Hz) rhythms [1]. Traditional EEG studies are limited to f < 100 Hz. The fundamental processes at the individual neuron scale suggest a role of higher frequencies: the time of flight of a spike along an axon, the synaptic neuro-transmittor diffusion time, the integration time of the dendritic arbor. They are all near or sub 10 ms [2]. Synchronization and correlations associated with them are expected to exist at least up to 1 kHz.
Electrocorticographic (ECoG) recordings from the subdural surface of the cortex have recently made it possible to examine the electrical activity of the human neocortex with finer spatial and temporal fidelity than EEG. An array of electrodes is placed directly on the surface of the cortex, see Fig. 1. The absence of the skull and surrounding tissue increases the electrode voltage while the close proximity to the cortex means that ECoG records very local phenomena. For example, changes in the classical α&β rhythms appear spatially uniform for a given set of tasks in EEG, but vary strongly spatially within the ECoG array for the same tasks [3].
The cortical surface potentials from sub-dural arrays reported in this study were obtained from 20 participants receiving clinical monitoring for the localization of seizure foci prior to resection. Each was informed about, and consented to participate in, the University of Washington internal-review-board-approved experimental protocol. The voltage was sampled at 10 kHz (2 subjects) or 1 kHz (18 subjects) using Synamps2 amplifiers (Compumedics-Neuroscan, San Antonio, TX) in parallel with long term monitoring (Xltek, Oakville, ON) from 32 platinum electrodes, encased in silastic, in an 8x4 configuration (4 mm in diameter, with 2.3 mm exposed, separated by 1 cm, center-to-center, Ad-Tech, Racine, WI).
Our earlier studies [4] revealed the absence of distinct peaks in the power spectrum beyond f ≃ 60 Hz. We hypothesized the existence of a power-law of the form P (f ) ≃ Af -χ at these higher frequencies, and named it the χ-band/index, but the 1 kHz sampling rate truncated the signal at these high frequencies. The purpose of the study reported here was to determine, as accurately as possible, whether there is indeed such a power-law in the human cortical power spectrum, and how it might change with cortical activity (universality), by using a higher, 10 kHz sampling rate. Power-laws represent scale free behavior, the finding of which immediately evokes scale free networks, complexity, avalanches, and self-organized criticality (SOC). Unfortunately, many such networks and processes are not large enough or can not be monitored precisely long enough to establish the scale invariance convincingly [5,6]. The human brain is arguably the most com-FIG. 1: The electrode array locations are shown on a template brain for subject 1 (S1 -purple, temporal) and subject 2 (S2 -green, fronto-parietal). Potentials of all 32 channels are measured simultaneously with respect to a scalp reference and ground before pairwise re-referencing. FIG. 2: Illustration of the steps taken to remove the amplifier roll-off and noise floors from the raw power spectra (green to dark blue to black) The amplifier built-in amplitude attenuation was determined by scanning through 15-4000 Hz sine waves and fitting a smooth function to the attenuation at each frequency (light blue). A characteristic distribution of amplifier noise floors (current and potential noise) was generated by measuring the potential across an equivalent conformation of resistors (grey). The sharp line noise spikes at 60 Hz and its harmonics were excluded in our analysis.
plex and largest network available and may provide the best opportunity to observe scale free behavior in a natural setting. Each ECoG electrode measures the voltage power spectral density from a specific cortical surface area associated with a specific set of functions. An electrode pair probes about 10 6 neurons, and each neuron has up to 10 4 synapses [2]. This has not gone unnoticed, and the neuroscience literature is awash with attempts to interpret experimental low-frequency data with scale free concepts and models; with only limited success and leaving many questions [7]. In this paper we firmly establish the existence of the power-law in the χ-band and the actual value of the scaling index, χ. We obtain remarkable accuracy, particularly compared to many recent studies of power-law phenomena in nature [5]. Ou
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