Lead field theory and the spatial sensitivity of scalp EEG Thomas Ferree and Matthew Clay July 12, 2000

Transcription

1 Lead field theoy and the spatial sensitivity of scalp EEG Thomas Feee and Matthew Clay July 12, 2000 Intoduction Neuonal population activity in the human cotex geneates electic fields which ae measuable by scalp EEG. This noninvasive technology has essentially pefect tempoal esolution and povides physiological infomation which coelates closely with human sensation, behavio and cognition. Hee we eview the physical oigin of the scalp EEG and descibe ecent technological advances which simplify data acquisition and impove spatial esolution. We apply lead field theoy to quantify the sensitivity of scalp electodes to neuon electical activity. The ease of data collection and inceased spatial esolution pesents the oppotunity fo computational neuoscientists to study human cotical dynamics with an aim towad bette undestanding the elationship between population activity and highe bain function. Data acquisition Taditional EEG systems use only 20 electodes, each equiing scalp abasion and adhesion. It has ecently become clea that such a small numbe of electodes is not adequate to captue the spatial vaiations of the electic potential on the scalp suface (Sinivasan et al., 1998). Futhemoe, the pocess of scalp abasion is time consuming, uncomfotable to the subject, and inceases infection isk due to blood-bon pathogens. Figue 1 shows the application of the Geodesic Senso Net, a system of 130 sponge electodes which do not equie scalp abasion (Tucke, 1991). Basic engineeing pinciples and empiical studies show that, despite highe contact impedance between scalp and electodes, thee is no measuable loss of signal amplitude by not abading the scalp (Feee et al., 2000). Figue 1. The 128-channel Geodesic Senso Net. 1

2 Physical oigin of scalp EEG Scalp EEG is made possible by the cellula-level anatomy of the cotical tissue. The apical dendites of cotical pyamidal cells ae aligned along the local nomal to the cotical suface. Synchonously active cells geneate extacellula cuents which supeimpose to geneate electic and magnetic fields detectable at a distance. The electic potential Φ in the extacellula space is detemined by the solution to Poisson s equation 2 Φ = 1 σ J s whee Js is the local cuent density geneated by active neuons, and σ is the local tissue conductivity (Nunez, 1981). A multipole expansion of an abitay cuent distibution has the dipole as its leading ode tem. Hence the geneal solution fo potentials in the conductive head volume can be witten as the sum of solutions fo a single dipole souce. The lineaity of that solution allows the potential diffeence acoss two scalp electodes due to a single dipole to be witten as The lead field L is detemined entiely by the geomety and conductivity of the head volume. Spatial sensitivity of scalp EEG Φ = p L whee p is the cuent dipole moment, and L is called the lead field fo a paticula electode pai and dipole location. The ecipocity theoem fo volume conductos of abitay geomety (Helmholtz, 1853) shows that the lead field L can be computed in tems of the cuent density Ji which would be geneated at the dipole location if an extenal cuent I wee to be injected though the same electode pai. J L = i I σ A question commonly asked of scalp EEG is how much bain tissue contibutes to the potential diffeence acoss a paticula electode pai. This can be quantified by defining the so-called half-sensitivity volume (Malmivuo and Plonsey, 1995). Since the lead field fo a given electode pai weighs the contibution fom a single dipole at a paticula location, fixing the electode pai and computing the lead field as a function of dipole position shows the spatial vaiation of sensitivity. Since dipoles of inteest ae located exclusively in the bain, we estict ou attention to the bain volume. The half-sensitivity volume (HSV) is defined as the set of all points in the head fo which the magnitude o the lead field o scala sensitivity L is at least half its maximum value in the bain volume. Figue 2 shows the lead field vecto L as a 2

3 function of position thoughout the HSV fo electode sepaation angles of 10, 30 and 180 degees in a spheical head model. These angles wee chosen because fo 20 electode systems neaby electodes ae sepaated by about 30 degees, while fo 130 electode systems neaby electodes ae sepaated by about 10 degees. Clealy the HSV fo neaby electodes is moe focal than fo distant electodes, which esults in geate localization capability. Similaly, fo neaby electodes the lead field within the HSV is moe tangential than fo distant electodes, indicating that neaby electodes ae moe sensitive to tangential dipoles. Figue 2. Lead field vecto within the scala half-sensitivity volume (HSV) fo electode sepaations of 10, 30 and 180 degees. The lead field vecto and HSV quantify the spatial sensitivity of scalp electodes to a single dipole. Since bain activity is seldom so localized the single dipole should be viewed meely as a building block fom which abitay cuent distibutions can be constucted. The poblems of multiple-dipole and distibuted souce localization ae active eseach fields which ae beyond the scope of this pape, but we can say that by consideing all electode pais simultaneously it is possible to quantify the activity at many locations. Figue 3 shows the maximum sensitivity max( L ), the half-sensitivity volume o HSV, and the depth of the centoid of the HSV, as a function of electode sepaation in the same spheical head model. We use the maximum depth of the HSV because the location of maximum sensitivity is always neaest the bain suface, and as such is not a vey useful quantity fo compaison. The maximum sensitivity inceases apidly as a function of angle, neaing its maximum aound 60 degees and inceasing slowly to 180 degees. The HSV is nealy constant below 15 degees then inceases apidly as a function of angle, neaing its maximum aound 60 degees and deceasing slightly to 180 degees. The maximum depth of the HSV is nealy constant below 15 then inceases apidly as a function of angle, neaing its maximum nea 90 degees and emaining stable to 180 degees. 3

4 Figue 3. Maximum sensitivity (left), half-sensitivity volume (middle), and maximum depth of the HSV (ight) as a function of the angle between scalp electode sepaations, fo two values of skull conductivity. Regading the inceased esolution of 130 electode systems ove 20 electode systems, at 10 degees the spatial esolution is 6-8 cubic cm, while at 30 degees the spatial esolution is appoximately cubic cm, depending upon skull conductivity. While this incease in esolution may at fist seem maginal, with moe electodes the location of maximum esolution can be placed at many moe locations. This damatically inceases the oveall esolution of 130 electode systems vesus 20 electode systems. Conclusions Moden EEG systems with sponge electodes allow safe and convenient application of 130 electodes to the scalp. With 130 electodes, neaby pais have a maximum spatial esolution of appoximately 6-8 cubic cm. With 20 electodes, neaby pais have a maximum spatial esolution of appoximately cubic cm. In addition, with moe electodes the location of the maximum zoom can be placed in many moe locations, damatically inceasing the oveall spatial esolution of 130 electode systems. Since the lead field is a vecto quantity, dipole oientation is impotant. This implies that the HSV may not be contiguous when dipoles ae constained to lie along the local nomal to the convoluted cotical suface. Refeences Feee, T. C., P. L. Luu, G. S. Russell and D. M. Tucke (2000). Scalp electode impedance, infection isk and EEG data quality. Submitted to Electoencephalogaphy and Clinical Neuophysiology. 4

5 Helmholtz, H. L. F. (1853). Uebe einige Gesetze de Vetheilung elektische Stome in kopelichen Leiten mit Anwendung auf die thieisch-elektischen Vesuche. Ann. Physik und Chemie 89: , Malmivou, J. and R. Plonsey (1995). Bioelectomagnetism. Oxfod Univesity Pess. Nunez, P. L. (1981). Electic fields of the bain: the neuophysics of EEG. Oxfod Univesity Pess. Sinivasan, R., D. M. Tucke and M. Muias (1998). Estimating the spatial nyquist of the human EEG. Behavio Reseach Methods, Instuments, and Computes 30: Tucke, D. M. (1991). Spatial sampling of head electic fields: The geodesic senso net. Electoencephalogaphy and Clinical Neuophysiology 79: Acknowledgements This wok was suppoted by NIH gants R43-NS and R43-AG