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Basic Concepts for Spatial Analysis

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Imaging Brain Function With EEG

Abstract

In order to embark on the study of so complex organ as the brain, we select, observe, and measure one of the various forms of energy produced and used by the brain—electric, magnetic, chemical, thermal, and metabolic—and a hierarchical level of analysis—microscopic, mesoscopic, and macroscopic—each with its characteristic space-time scales. By choosing to read our book, we infer that readers have chosen to analyze the electroencephalogram from the scalp (EEG), the electrocorticogram from cortical surfaces (ECoG, Fig. 6.1), and the local field potentials from the depth of the brain (LFP) in any or all accessible forms and locations (Lopes da Silva 1993; Basar 1998). Then we characterize and classify the phenomena that we want to analyze and understand. We have begun with time series analysis of single channel recordings; now we undertake the spatial analysis of signals from arrays of channels. To that end, we require some basic concepts that we introduce in this chapter, with references to detailed treatments in other chapters.

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Notes

  1. 1.

    More details are given, Sect. 9.5 and in Freeman (2007). From a real ECoG signal, the Hilbert transform basically generates a complex signal. The original (real) signal together with its imaginary counterpart (obtained with the Hilbert transform) forms a complex analytic signal, in the sense that its Fourier transform is strictly positive. Using Euler’s theorem, the analytic signal is plotted as a vector (Fig. 9.8c) rotating counterclockwise. The length of the vector gives the analytic amplitude; the angle from the real axis gives the analytic phase.

  2. 2.

    We band-pass filter the 64 signals in the 20–80-Hz range and compute the spatial ensemble average signal A(t). We then construct a window twice the wavelength of the peak frequency in the mean PSDT of each 6 s trial and step it along the 64 signals and the spatial ensemble average at intervals of the wavelength. At each step we calculate the mean SD of the 64 standard deviations, SD T (t), and the SD of the average waveform, SDT(t), in the window.

  3. 3.

    Experimental demonstration of the mechanism for stabilization of positive feedback in mutual excitation requires use of an excitatory population with no effective inhibitory neurons. The illustration is from periglomerular interneurons in the outer layer of the olfactory bulb (Section 5.2.3 in Freeman 1975). They are GABAergic and therefore mistakenly regarded as inhibitory. In fact they have a high intracellular concentration of chloride ions (Siklós et al. 1995). The action of GABA is to allow chloride ions to exit the neurons, causing depolarization and therefore excitation.

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Authors and Affiliations

  1. Molecular and Cell Biology, University of California at Berkeley, Berkeley, CA, USA

    Walter J. Freeman

  2. Centre for Systems Neuroscience, University of Leicester, Leicester, UK

    Rodrigo Quian Quiroga

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  1. Walter J. Freeman
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  2. Rodrigo Quian Quiroga
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Freeman, W.J., Quiroga, R.Q. (2013). Basic Concepts for Spatial Analysis. In: Imaging Brain Function With EEG. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4984-3_6

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