back	download MatLab source code		SphericalMidPoint.m	LineWithSphere.m	zip archive with all functions
				GetF3CoordinatesWithMirrorLocations.m
				GetCSD.m	CSD.m
		download Excel file with EEG montage (spherical and Cartesian coordinates)		Low Density (31-channel)	High Density (129-channel)	zip archive with both XLS tables
(Note: The CSD toolbox is a MatLab implementation of a spherical spline algorithm (Perrin et al., 1989) to compute scalp surface Laplacian or current source density (CSD) estimates for surface potentials (EEG/ERP). It was developed in May 2009 as an extension to this appendix to provide more functionality and a more detailed documentation.)

Appendix (Supplementary Data) published in Clinical Neurophysiology 2006;117(2):348-368.

Principal Components Analysis of Laplacian Waveforms as a Generic Method for Identifying ERP Generator Patterns: I. Evaluation with Auditory Oddball Tasks

Jürgen Kayser, Craig E. Tenke

Department of Biopsychology, Unit 50, New York State Psychiatric Institute, New York, USA

Received 11 February 2005; revised 8 August 2005; accepted 17 August 2005

Abstract

   Objective: To evaluate the effectiveness and comparability of PCA-based simplifications of ERP waveforms versus their reference-free Laplacian transformations for separating task- and response-related ERP generator patterns during auditory oddball tasks.

   Methods: Nose-referenced ERPs (31 sites total) were recorded from 66 right-handed adults during oddball tasks using syllables or tones. Response mode (left press, right press, silent count) and task was varied within subjects. Spherical spline current source density (CSD) waveforms were computed to sharpen ERP scalp topographies and eliminate volume-conducted contributions. ERP and CSD data were submitted to separate covariance-based, unrestricted temporal PCAs (Varimax) to disentangle temporally and spatially overlapping ERP and CSD components.

   Results: Corresponding ERP and CSD factors were unambiguously related to known ERP components. For example, the dipolar organization of a central N1 was evident from factorized anterior sinks and posterior sources encompassing the Sylvian fissure. Factors associated with N2 were characterized by asymmetric frontolateral (tonal: frontotemporal R>L) and parietotemporal (phonetic: parietotemporal L>R) sinks for targets. A single ERP factor summarized parietal P3 activity, along with an anterior negativity. In contrast, two CSD factors peaking at 360 and 560 ms distinguished a parietal P3 source with an anterior sink from a centroparietal P3 source with a sharply localized Fz sink. A smaller parietal but larger left temporal P3 source was found for silent count compared to button press. Left or right press produced opposite, region-specific asymmetries originating from central sites, modulating the N2/P3 complex.

   Conclusions: CSD transformation is shown to be a valuable preprocessing step for PCA of ERP data, providing a unique, physiologically meaningful solution to the ubiquitous reference problem. By reducing ERP redundancy and producing sharper, simpler topographies, and without losing or distorting any effects of interest, the CSD-PCA solution replicated and extended previous task- and response-related findings.

   Significance: Eliminating ambiguities of the recording reference, the combined CSD-PCA approach systematically bridges between montage-dependent scalp potentials and distinct, anatomically-relevant current generators, and shows promise as a comprehensive, generic strategy for ERP analysis.

Keywords: event-related potential (ERP); principal components analysis (PCA); current source density (CSD); oddball task; silent counting; response hand

Appendix

     The computation of current source density (CSD) estimates based on spherical splines (Perrin et al., 1989, 1990) may be compactly coded in high-level numerical languages, such as the widely-popular popular MatLab language (The MathWorks, Inc., 2002, MatLab Version 6.5, Release 13 [http://www.mathworks.com]). All crucial computational steps to transform surface potentials to CSD waveforms are exemplified by the MatLab routines provided below in section A2. As an initial step, any EEG montage has to be expressed in spatial coordinates of the electrode sites with respect to the underlying CSD model, which is a sphere for the Perrin et al. (1989, 1990) algorithm. In section A1, we explain a general procedure to derive these spatial locations for a unit sphere, and table the coordinates for our 31-channel EEG montage.

A1. Spatial coordinates of a unit sphere for 10-20 system EEG montages

     All notations are considered for a sphere with unit radius (1.0). For Cartesian coordinates, the x-y plane is marked by the great circle combining the locations Fpz, T7, Oz, and T8, with the x-axis running through T7 (-1.0) and T8 (+1.0), the y-axis running through Oz (-1.0) and Fpz (+1.0), and the z-axis running through the origin of the x-y plane (0) and Cz (+1.0). For spherical coordinates, the angle theta denotes the rotation of the x-axis towards the y-axis (positive poles, respectively), whereas phi denotes the angular displacement from the x-y plane towards the positive pole of the z-axis.

     The spherical coordinates for locations where the three great circles of the x-y, x-z, and y-z planes intersect are straightforward. As defined by the logic of the international 10-20 system (e.g., Oostenveld and Praamstra, 2001), intermediate locations on these great circles are quarter (22.5°) or quintile (18.0°) sections of the respective rectangular arcs (e.g., for Fp1, theta is 90 + 1*18 = 108; for Fz, phi is 2 * 22.5 = 45). Similarly, locations on the small circle combining nasion and inion are a quarter rectangular arc downwards (i.e., phi equals -22.5°) and on quintile sections with respect x-y plane angular displacement (e.g., for P10, theta is 2 * -18 = -36).

     The remaining locations, which are less straightforward, are located on small circles defined by two lateral and one midline base locations (Oostenveld and Praamstra, 2001). For instance, F3 is located on a small circle defined by the intersection of the sphere with the plane given by the base locations F7, F8, and Fz. Origin and radius of this small circle can easily be derived from the Cartesian coordinates of the three base locations. Halving the two vectors from this origin to F7 and Fz gives a mid-vector that intersects the sphere at F3. Once F3 has been derived, all mirror locations (i.e., F4, P3, and P4) are easily determined through their x-y plane displacements. By using these intermediate locations, this systematic can easily be extended to determine the coordinates of any montage based on the 10-20 system (see Functions 1 and 2, Example 1 for site F3, and Table A1 below).

     The “true” spatial location of the nose tip is obviously outside the sphere, which is in a strict sense incompatible with the assumed model. However, the inclusion of the nose reference in the EEG montage provides additional information, which is most important for determining the contributions of nearby anterior regions. As similar geometric simplifications were applied to all scalp coordinates, we modeled the effective location of the nose on the surface of the sphere as half of a quarter extension beyond nasion.

Function 1: SphericalMidPoint.m

% SphericalMidPoint - Determine a point on a unit sphere by assuming

% equal distance to two spherical points

% 

% (published in appendix of Kayser J, Tenke CE, Clin Neurophysiol 2006;117(2):348-368)

%

% Usage: [P] = SphericalPoint( Pl, Pr, Pm, P1, P2, lab);

%

% Implementation of simple linear geometric principles and algorithms

% (e.g., see documentation at http://mathworld.wolfram.com/Plane.html

% http://mathworld.wolfram.com/Sphere.html

% http://mathworld.wolfram.com/Line.html)

%

% Input parameters:

% Pl,Pr,Pm = point vectors with Cartesian x,y,z coordinates defining

% a small circle on a unit sphere, with Pl and Pr located

% on the x-y plane, and Pm on the y-z plane

% P1,P2 = point vectors indicating two locations on the small circle

% lab = electrode label string

%

% Output parameter:

% P = point vector/matrix with Cartesian x,y,z intersection(s)

%

% Copyright (C) 2003 by Jürgen Kayser (Email: kayserj@pi.cpmc.columbia.edu)

% GNU General Public License (http://www.gnu.org/licenses/gpl.txt)

% Updated: $Date: 2005/02/09 14:00:00 $ $Author: jk $

%

function [P] = SphericalPoint( Pl, Pr, Pm, P1, P2, lab);

M = Pl-(Pl-Pr)/2'; % use lateral points to determine their midpoint

d = abs(Pr(1)-Pl(1))/2; % ... in x-y plane on y-axis and its distance

V = Pm - M; % get vector from midline point Pm and midpoint M

m = sqrt(V(2)^2 + V(3)^2); % ... (V(1)=0) and determine the vector length m

q = (d^2 - m^2) / 2*m; % get extension q of vector V towards origin of

r = m + q; % ... small circle and compute its radius r

V = V * (m+q)/m; % extend vector V

O = Pm - V; % determine origin O of small circle

M1 = P1 - O; % translate first point vector to small circle

M2 = P2 - O; % translate second point vector to small circle

N = O + (M1-(M1-M2)/2); % determine mean vector and translate to unit sphere

P = LineWithSphere(N,O); % get intersection of vector O-N with unit sphere

R = 1.0; % set unit sphere radius

for i = 1:size(P,1) % test whether point P is really on the surface

    s = P(i,1).^2 + ... % ... of the sphere (s must be zero)

        P(i,2).^2 + ...

        P(i,3).^2 - R.^2;

    disp(sprintf('%5s %8.5f %8.5f %8.5f (off surface: %20.17f)', ...

         char(lab(:)),P(i,1),P(i,2),P(i,3),s));

end;

Function 2: LineWithSphere.m

% LineWithSphere - Determine intersection(s) of a line defined by

% two points in space with a sphere

% 

% (published in appendix of Kayser J, Tenke CE, Clin Neurophysiol 2006;117(2):348-368)

%

% Usage: [P] = LineWithSphere ( P1, P2, Os, r );

%

% Implementation of simple linear geometric principles and algorithms

% (e.g., see documentation at http://mathworld.wolfram.com/Plane.html

% http://mathworld.wolfram.com/Sphere.html

% http://mathworld.wolfram.com/Line.html)

%

% Input parameters:

% P1,P2 = point vectors with Cartesian x,y,z coordinates

% Os = point vector origin of sphere (default = [0 0 0])

% r = sphere radius (default = 1.0)

%

% Output parameter:

% P = point vector/matrix with Cartesian x,y,z intersection(s)

%

% Copyright (C) 2003 by Jürgen Kayser (Email: kayserj@pi.cpmc.columbia.edu)

% GNU General Public License (http://www.gnu.org/licenses/gpl.txt)

% Updated: $Date: 2005/02/09 14:00:00 $ $Author: jk $

%

function [P] = LineWithSphere ( P1, P2, Os, r );

if nargin < 4; r = 1.0; end; % use unit sphere (radius = 1) by default

if nargin < 3; Os = [0 0 0]; end; % use natural origin by default

x1 = P1(1); y1 = P1(2); z1 = P1(3); % x,y,z-coordinates for line point 1

x2 = P2(1); y2 = P2(2); z2 = P2(3); % x,y,z-coordinates for line point 2

x3 = Os(1); y3 = Os(2); z3 = Os(3); % x,y,z-coordinates for origin of sphere

a = (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2;

b = 2 * ( (x2-x1)*(x1-x3) + (y2-y1)*(y1-y3) + (z2-z1)*(z1-z3) );

c = x3^2 + y3^2 + z3^2 + x1^2 + y1^2 + z1^2 - 2 * (x3*x1 + y3*y1 + z3*z1) - r^2;

T = b^2 - 4 * a * c;

if T < 0 % no intersection

   P = [NaN NaN NaN];

   return

end

if T == 0 % one intersection

   u = -b / (2*a);

   P(1) = x1 + u * (x2 - x1);

   P(2) = y1 + u * (y2 - y1);

   P(3) = z1 + u * (z2 - z1);

   return

end

u = (-b + sqrt(T)) / (2 * a); % first intersection

P(1,1) = x1 + u * (x2 - x1);

P(1,2) = y1 + u * (y2 - y1);

P(1,3) = z1 + u * (z2 - z1);

u = (-b - sqrt(T)) / (2 * a); % second intersection

P(2,1) = x1 + u * (x2 - x1);

P(2,2) = y1 + u * (y2 - y1);

P(2,3) = z1 + u * (z2 - z1);

Example 1: GetF3CoordinatesWithMirrorLocations.m

% Example code to determine the spherical and Cartesian coordinates of

% four intermediate 10-20 locations (F3, F4, P3, P4) from a small circle

% given by three known 10-20 locations (F7, Fz, F8)

% 

% (published in appendix of Kayser J, Tenke CE, Clin Neurophysiol 2006;117(2):348-368)

%

ThetaPhi = [144.000 0.000; % F7 a priori known

             90.000 45.000; % Fz spherical coordinates

             36.000 0.000] ; % F8 [theta phi]

ThetaPhiRad = (2 * pi * ThetaPhi) / 360; % convert degrees to radians

[X,Y,Z] = sph2cart(ThetaPhiRad(:,1), ... % theta [radians] is in column 1

                   ThetaPhiRad(:,2), ... % phi [radians] is in column 2

                   1.0 ); % use unit radius

XYZ = [X Y Z]; % create Cartesian matrix

F7 = XYZ(1,:); % recover point vectors with

FZ = XYZ(2,:); % ... Cartesian x,y,z coordinates

F8 = XYZ(3,:); % ... for the three electrodes

P = SphericalMidPoint(F7,F8,FZ,F7,FZ,'F3'); % determine F3 as F7-Fz mid point

F3 = P(2,:); % use intersection above x-y plane

F4 = F3 .* [-1 1 1]; % mirror x-coordinate for F4

P3 = F3 .* [ 1 -1 1]; % mirror y-coordinate for P3

P4 = F3 .* [-1 -1 1]; % mirror x-,y-coordinates for P4

XYZext = [XYZ; F3; F4; P3; P4]; % extend XYZ matrix with new sites

[th,ph,ra] = cart2sph(XYZext(:,1), ... % convert Cartesian xyz coordinates

                      XYZext(:,2), ... % ... to spherical coordinates

                      XYZext(:,3)); % ... [radians]

ThetaPhiExt = [ [th * 360 / 2 / pi] ... % convert spherical coordinates from

                [ph * 360 / 2 / pi]]; % ... radians to degrees

Elab = ['F7';'Fz';'F8'; ... % create electrode label array

        'F3';'F4';'P3';'P4'];

disp(sprintf('%8s %10s %10s %12s %12s %12s', ...

    'Site','Theta','Phi','X','Y','Z'));

for i = 1:size(Elab,1) % table coordinates ...

  disp(sprintf('%8s %10.3f %10.3f %12.5f %12.5f %12.5f', ...

    char(Elab(i,:)), ... % ... electrode label

    ThetaPhiExt(i,1), ThetaPhiExt(i,2), ... % ... Theta, Phi [̊]

    XYZext(i,1),XYZext(i,2),XYZext(i,3)) ); % ... Cartesian x,y,z coordinates

end;

A2. Scalp current density estimates using spherical spline interpolation

     Given a complete EEG montage with spherical coordinates (i.e., angles theta and phi) for all recording sites, the computation of scalp current density estimates is exemplified by the two MatLab functions listed below. Two ASCII input files describing the EEG montage (e.g., consisting of the data rows in Table A1) and providing the recorded ERP data (i.e., arranging rows and columns as an electrodes-by-samples matrix) with an identical sequence of electrodes are needed. The initial iterative computations for the Legendre polynomial, the interelectrode cosine distances matrix, and g- and h-functions (Perrin et al., 1989) are rather time consuming (and more efficiently executed when using a compiler language), but need to be performed only once for any given montage. The actual sample-by-sample CSD transformations using these initial computations are very fast, even in an interpreter language. It should be noted that the last code line in Function 3 (GetCSD.m) evokes Function 4 (CSD.m) with implicit default settings for the smoothing constant (10^-5) and a head radius matching a unit sphere (1.0). The latter default provides larger and therefore more practical CSD values (μV/m²) compared with the smaller CSD values based on a more realistic head radius (10.0 cm; μV/cm²).

Function 3: GetCSD.m

% GetCSD - Compute Current Source Density (CSD) estimates using the spherical spline

% surface Laplacian algorithm suggested by Perrin et al. (1989, 1990)

% 

% (published in appendix of Kayser J, Tenke CE, Clin Neurophysiol 2006;117(2):348-368)

%

% Usage: [CE] = GetCSD(EEGmont, ERPdata);

%

% Implementation of algorithms described by Perrin, Pernier, Bertrand, and

% Echallier in Electroenceph Clin Neurophysiol 1989;72(2):184-187, and

% Corrigenda EEG 02274 in Electroenceph Clin Neurophysiol 1990;76:565.

%

% Input parameters:

% EEGmont = name of EEG montage spherical coordinates file in ASCII format,

% with rows consisting of seven columns: electrode label, two

% spherical angles (theta, phi), and Cartesian coordinates x,y,z

% ERPdata = name of ERP data file in ASCII format stored as

% electrodes-by-samples (rows-by-columns) matrix

%

% Output parameter:

% CE = CSD estimates as electrodes-by-samples matrix

%

% Copyright (C) 2003 by Jürgen Kayser (Email: kayserj@pi.cpmc.columbia.edu)

% GNU General Public License (http://www.gnu.org/licenses/gpl.txt)

% Updated: $Date: 2005/02/11 14:00:00 $ $Author: jk $

%

function [CE] = GetCSD(EEGmont, ERPdata)

ERP = load(ERPdata); % load electrodes-by-samples matrix

[Elab,Theta,Phi,X,Y,Z] = ... % read EEG montage

   textread(EEGmont,'%s%f%f%f%f%f');

ThetaRad = (2 * pi * Theta) / 360; % convert Theta and Phi to radians ...

PhiRad = (2 * pi * Phi) / 360; % ... and Cartesian coordinates ...

[X,Y,Z] = sph2cart(ThetaRad,PhiRad,1.0); % ... for optimal resolution

nElec = length(Elab); % determine size of EEG montage

EF(nElec,nElec) = 0; % initialize interelectrode matrix ...

for i = 1:nElec; for j = 1:nElec; % ... and compute all cosine distances

  EF(i,j) = 1 - ( ( (X(i) - X(j))^2 + ...

    (Y(i) - Y(j))^2 + (Z(i) - Z(j))^2 ) / 2 );

end; end;

m = 4; N = 50; % set m constant and N iterations

G(nElec,nElec) = 0; H(nElec,nElec) = 0; % claim memory for G- and H-matrices

for i = 1:nElec; for j = 1:nElec;

  P = zeros(N); % compute Legendre polynomial

  for n = 1:N;

    p = legendre(n,EF(i,j));

    P(n) = p(1);

  end;

  g = 0.0; h = 0.0; % compute h- and g-functions

  for n = 1:N;

    g = g + ( (( 2.0*n+1.0) * P(n)) / ((n*n+n)^m ) );

    h = h + ( ((-2.0*n-1.0) * P(n)) / ((n*n+n)^(m-1)) );

  end;

  G(i,j) = g / 4.0 / pi; % finalize cell of G-matrix

  H(i,j) = -h / 4.0 / pi; % finalize cell of H-matrix

end; end;

CE = CSD(ERP, G, H); % compute CSD for ERP data

Function 4: CSD.m

% CSD - Current Source Density (CSD) transformation based on spherical spline

% surface Laplacian as suggested by Perrin et al. (1989, 1990)

% 

% (published in appendix of Kayser J, Tenke CE, Clin Neurophysiol 2006;117(2):348-368)

%

% Usage: [X, Y] = CSD(Data, G, H, lamb, head);

%

% Implementation of algorithms described by Perrin, Pernier, Bertrand, and

% Echallier in Electroenceph Clin Neurophysiol 1989;72(2):184-187, and

% Corrigenda EEG 02274 in Electroenceph Clin Neurophysiol 1990;76:565.

%

% Input parameters:

% Data = surface potential electrodes-by-samples matrix

% G = g-function electrodes-by-electrodes matrix

% H = h-function electrodes-by-electrodes matrix

% lamb = smoothing constant lambda (default = 1.0e-5)

% head = head radius (default = no value for unit sphere [µV/m²])

% specify a value [cm] to rescale CSD data to smaller units [µV/cm²]

% (e.g., use 10.0 to scale to more realistic head size)

%

% Output parameter:

% X = current source density (CSD) transform electrodes-by-samples matrix

% Y = spherical spline surface potential (SP) interpolation electrodes-by-samples matrix (only if requested)

%

% Copyright (C) 2003 by Jürgen Kayser (Email: kayserj@pi.cpmc.columbia.edu)

% GNU General Public License (http://www.gnu.org/licenses/gpl.txt)

% Updated: $Date: 2005/02/11 14:00:00 $ $Author: jk $ - code compression and comments

% Updated: $Date: 2007/02/05 11:30:00 $ $Author: jk $ - recommented rescaling (unit sphere [µV/m²] to realistic head size [µV/cm²])

%

function [X, Y] = CSD(Data, G, H, lamb, head)

[nElec,nPnts] = size(Data); % get matrix dimensions

mu = mean(Data); % get grand mean

Z = (Data - repmat(mu,nElec,1)); % compute average reference

Y = G; X = H; % claim memory for output matrices

if nargin < 5; head = 1.0; end; % initialize scaling variable [µV/m²]

head = head * head; % or rescale data to head sphere [µV/cm²]

if nargin < 4; lamb = 1.0e-5; end; % initialize smoothing constant

for e = 1:size(G,1); % add smoothing constant to diagonale

  G(e,e) = G(e,e) + lamb;

end;

Gi = inv(G); % compute G inverse

for i = 1:size(Gi,1); % compute sums for each row

  TC(i) = sum(Gi(i,:));

end;

sgi = sum(TC); % compute sum total

for p = 1:nPnts

  Cp = Gi * Z(:,p); % compute preliminary C vector

  c0 = sum(Cp) / sgi; % common constant across electrodes

  C = Cp - (c0 * TC'); % compute final C vector

  for e = 1:nElec; % compute all CSDs ...

    X(e,p) = sum(C .* H(e,:)') / head; % ... and scale to head size

  end;

  if nargout > 1; for e = 1:nElec; % if requested ...

    Y(e,p) = c0 + sum(C .* G(e,:)'); % ... compute all SPs

  end; end;

end;

Appendix (Supplementary Data) published in Clinical Neurophysiology 2006;117(2):368-380.

Principal Components Analysis of Laplacian Waveforms as a Generic Method for Identifying ERP Generator Patterns: II. Adequacy of Low-Density Estimates

Jürgen Kayser, Craig E. Tenke

Department of Biopsychology, Unit 50, New York State Psychiatric Institute, New York, USA

Received 9 June 2005; revised 4 August 2005; accepted 23 August 2005

Abstract

   Objective: To evaluate the comparability of high- and low-density surface Laplacian estimates for determining ERP generator patterns of group data derived from a typical ERP sample size and paradigm.

   Methods: High-density ERP data (129 sites) recorded from 17 adults during tonal and phonetic oddball tasks were converted to a 10-20-system EEG montage (31 sites) using spherical spline interpolations. Current source density (CSD) waveforms were computed from the high- and low-density, but otherwise identical, ERPs, and correlated at corresponding locations. CSD data were submitted to separate covariance-based, unrestricted temporal PCAs (Varimax of covariance loadings) to identify and effectively summarize temporally and spatially overlapping CSD components. Solutions were compared by correlating factor loadings and scores, and by plotting ANOVA F statistics derived from corresponding high and low resolution factor scores using representative sites.

   Results: High- and low-density CSD waveforms, PCA solutions, and F statistics were remarkably similar, yielding correlations of .9 ≤ r ≤ .999 between waveforms, loadings, and scores for almost all comparisons at low-density locations except low-signal CSD waveforms at occipital sites. Each of the first 10 high-density factors corresponded precisely to one factor of the first 10 low-density factors, with each 10-factor set accounting for the meaningful CSD variance (> 91.6%).

   Conclusions: Low-density surface Laplacian estimates were shown to be accurate approximations of high-density CSDs at these locations, which adequately and quite sufficiently summarized group data. Moreover, reasonable approximations of many high-density scalp locations were obtained for group data from interpolations of low-density data. If group findings are the primary objective, as typical for cognitive ERP research, low-resolution CSD topographies may be as efficient, given the effective spatial smoothing when averaging across subjects and/or conditions.

   Significance: Conservative recommendations for restricting surface Laplacians to high-density recordings may not be appropriate for all ERP research applications, and should be reevaluated considering objective, costs and benefits.

Keywords: event-related potential (ERP); dense electrode array (DEA); current source density (CSD); low-density surface Laplacian; principal components analysis (PCA)

Appendix

     Table A1 lists the spatial coordinates for the 129-channel geodesic sensor net used in the current study based on sphere with unit radius (1.0) and the notation given in the appendix of our parallel report (Kayser and Tenke, in press). The spherical coordinates specified by the manufacturer (Electrical Geodesics, Inc.) were converted to angles theta, which denotes the rotation of the positive pole of the x-axis running through the 10-20 system locations T7 (-1.0) and T8 (+1.0) towards the positive pole of the y-axis running through Oz (-1.0) and Fpz (+1.0), and phi, which denotes the angular displacement from the x-y plane towards the positive pole of the z-axis running through the origin of the x-y plane (0) and Cz (+1.0). It should be noted that only sensors 129 (vertex) and 17 (displaced from the original mid-anterior scalp surface location to nose tip) have with sites Cz and Nose exact equivalents in our 31-channel EEG montage (see Tab. A1 in appendix of Kayser and Tenke, in press), which is based on the international 10-20 system (e.g., Oostenveld and Praamstra, 2001). However, most 10-20 system locations have approximate locations in the 129-channel layout (e.g., theta [174°] and phi [42°] of sensor 37 correspond roughly to the spherical coordinates of C3 [180° and 45°]; cf. Tab. A1 in appendix of Kayser and Tenke, in press; see Fig. 5 in Srinivasan et al., 1998).