Estimating the spatial Nyquist of the human EEG

Abstract

The discrete sampling of the brain's electrical field at the scalp surface with individual recording sensors is subject to the same sampling error as the discrete sampling of the time series at anyone sensor with analog-to-digital conversion. Unlike temporal sampling, spatial sampling is intrinsically discrete, so that the post hoc application of analog anti-aliasing filters is not possible. However, the skull acts as a low-pass spatial filter ofthe brain's electrical field, attenuating the high spatial frequency information. Because of the skull's spatial filtering, a discrete sampling of the spatial field with a reasonable number of scalp electrodes is possible. In this paper, we provide theoretical and experimental evidence that adequately sampling the human electroencephalograph (EEG) across the full surface of the head requires a minimum of 128 sensors. Further studies with each of the major EEG and event-related potential phenomena are required in order to determine the spatial frequency of these phenomena and in order to determine whether additional increases in sensor density beyond 128 channels will improve the spatial resolution of the scalp EEG.When the time series ofan electroencephalogram (EEG) channel is sampled discretely, the Nyquist theorem specifies that the highest measurable frequency is half the sampling rate. For example, with a 250 sample/sec analog-to-digital conversion rate, the highest frequency that can be resolved is 125 Hz. In actuality, because of phase alignment, it is necessary to discretely sample (digitize) the signal at a rate at least 2.5 times the highest frequency component ofthe signal (Bendat & Piersol, 1986). Signal frequencies higher than the Nyquist frequency are not only poorly characterized; they alias or appear misleadingly as increased energy at lower frequencies. To avoid aliasing, it is necessary to eliminate the frequency components of the signal that are higher than the Nyquist frequency through analog filtering.The electrical field of the brain generates a potential distribution that is continuous over the surface of the head. The discretization ofthis spatial EEG or averaged eventrelated potential (ERP) signal with scalp electrodes is also subject to the Nyquist theorem. Ifthe spatial sampling is Correspondence concerning this article should be addressed to D. M.Tucker, Electrical Geodesics, Inc., Riverfront Research Park, 1811 Garden Avenue, Suite 104, Eugene, OR 97403 (e-mail: dtucker@egi.com).Note: ElectricalGeodesics, Inc. sells 64-, 128-,and 256-channelEEG systems and thus has a commercial interest in promoting dense sensor array technology.-Editor

Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes

“…The spatial frequency of this point (~0.5-0.8 c/cm) is equivalent to a wavelength of 1.25-2 cm. Prior work analyzing PSDx from the adult scalp at a comparable temporal frequency range reported the corresponding spatial frequency to be~0.2-0.4 c/cm, equivalent to a wave length of 2.5-5 cm (Freeman et al, 2003;Srinivasan et al, 1998). Because the spatial texture of EEG is spatially mostly noncyclic, it would be more robust to have the sample frequency 3-5 times higher than the frequency limit (Barlow, 1993), which would yield interelectrode spacing of about 3-5 mm in neonates and 5-8 mm in adults.…”

“…The first step is to define the point in the spectrum where it reaches the noise floor (termed the "upper inflection point" in Results) and gives the upper end of the frequency range that should ideally be captured. The second step is to calculate the number of electrodes with the specified interelectrode spacing that are needed to sample the entire range of spatial frequency (Freeman et al, 2003;Srinivasan et al, 1998). The lower inflection point gives an estimate of the desired width of the array.…”

“…This richness in amplitude texture can be perceived as "spatial patterning" of the neonatal scalp EEG (hereafter referred to as "spatial patterning"), and it has been measured in adults by estimating the spatial frequency content of the scalp EEG (Freeman et al, 2003;Srinivasan et al, 1998). This would be a necessary piece of information to define the number of EEG electrodes that are needed to record the brain activity in full detail, to estimate the errors related to the conventional under-sampling of EEG (see also Grieve et al, 2004), as well as to aid in constructing realistic forward and inverse solutions for neonatal EEG source localization.…”

Scalp electrode impedance, infection risk, and EEG data quality

“…Without recording from sufficient scalp sites, the recording of the scalp potential misses meaningful spatial variations. Similar to what occurs in the time domain with inadequate spatial sampling, this shows up as aliasing in the spatial Fourier domain (Srinivasan, et al, 1998). Furthermore, individual site preparation precludes rapid application of an EEG sensor (electrode) array in emergency settings and field hospitals.…”

Evidence for Premotor Cortex Activity during Dynamic Visuospatial Imagery from Single-Trial Functional Magnetic Resonance Imaging and Event-Related Slow Cortical Potentials

“…CSD transformation was carried out in order to yield reference-free maps and to attenuate low spatial frequencies ("smearing") introduced into the scalp potential distribution due to volume conduction (Nunez, 1989;Nunez et al, 1994;Srinivasan et al, 1996). In order to map the activity distribution on the scalp surface with increased spatial sampling (Nunez et al, 1994;Srinivasan et al, 1998), the data of the two electrode sets were used simultaneously for the interpolation. SCP and CSD maps were visualized on individual head shapes reconstructed by using spline interpolation of the 3-D electrode and landmark coordinates acquired by the photogrammetric head digitizer.…”