Home > functions > leadfield > eeg > vb_bem_eeg.m

vb_bem_eeg

PURPOSE ^

EEG potential for multilayer model by BEM

SYNOPSIS ^

function P = vb_bem_eeg(D,Sout,Vhead,Fhead,V,J,Xeeg,BEM)

DESCRIPTION ^

 EEG potential for multilayer model by BEM 
 多層境界面モデルのポテンシャルと磁場
  P = vb_bem_eeg(D,Sout,Vhead,Fhead,V,J,Xeeg,BEM)
 OUTPUTS:
  P : EEG Lead field matrix   ( Neeg x NP)
  P : 多層モデルのEEG センサポテンシャル

 INPUTS (Required):
   V   : dipole location(in meters)               NP x 3
   J   : dipole moment                            NP x 3
  Xeeg : EEG sensors(in meters) on the scalp      Neeg x 3
 D     : solid angle matrix for boundary surfaces
 Vhead : vertex coordinate for boundary surfaces
 Fhead : patch index for boundary surfaces
 Sout  : normal vector for boundary surfaces

 D     : 境界面係数行列
 Vhead : 境界三角面の座標
 Fhead : 境界三角面頂点インデックス
 Sout  : 三角面の外向き面積法線
 V     : 電流双極子座標        (m)
 J     : 電流双極子モーメント  (A)
 Xeeg  : EEG センサ座標

 BEM.Nvertex   = 各境界面の頂点インデックス
               = [ start_id(1)     end_id(1)     ; 
                             ...                 ;
                   start_id(Nsurf) end_id(Nsurf) ]
               = [開始インデックス, 終了インデックス]
                 innermost to outermost 

 BEM.Npatch    = 各境界面の三角面インデックス 
               = [開始インデックス, 終了インデックス]
 BEM.sigma     = 各領域の伝導率 
               = [sigma(1), ..., sigma(Nsurf), 0]

 2004-12-26 M. Sato
 2007-12-6  M. Sato 
   EEG positions are mapped to outermost head surface first
 2007-12-25  M. Sato 
   EEG = Weighted average of potentials at nearest head positions
 2008-10-8  M. Sato 
   Multisurface correction & Auto solid angle calculation 
   are done before saving omega

 Copyright (C) 2011, ATR All Rights Reserved.
 License : New BSD License(see VBMEG_LICENSE.txt)

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function    P = vb_bem_eeg(D,Sout,Vhead,Fhead,V,J,Xeeg,BEM)
0002 % EEG potential for multilayer model by BEM
0003 % 多層境界面モデルのポテンシャルと磁場
0004 %  P = vb_bem_eeg(D,Sout,Vhead,Fhead,V,J,Xeeg,BEM)
0005 % OUTPUTS:
0006 %  P : EEG Lead field matrix   ( Neeg x NP)
0007 %  P : 多層モデルのEEG センサポテンシャル
0008 %
0009 % INPUTS (Required):
0010 %   V   : dipole location(in meters)               NP x 3
0011 %   J   : dipole moment                            NP x 3
0012 %  Xeeg : EEG sensors(in meters) on the scalp      Neeg x 3
0013 % D     : solid angle matrix for boundary surfaces
0014 % Vhead : vertex coordinate for boundary surfaces
0015 % Fhead : patch index for boundary surfaces
0016 % Sout  : normal vector for boundary surfaces
0017 %
0018 % D     : 境界面係数行列
0019 % Vhead : 境界三角面の座標
0020 % Fhead : 境界三角面頂点インデックス
0021 % Sout  : 三角面の外向き面積法線
0022 % V     : 電流双極子座標        (m)
0023 % J     : 電流双極子モーメント  (A)
0024 % Xeeg  : EEG センサ座標
0025 %
0026 % BEM.Nvertex   = 各境界面の頂点インデックス
0027 %               = [ start_id(1)     end_id(1)     ;
0028 %                             ...                 ;
0029 %                   start_id(Nsurf) end_id(Nsurf) ]
0030 %               = [開始インデックス, 終了インデックス]
0031 %                 innermost to outermost
0032 %
0033 % BEM.Npatch    = 各境界面の三角面インデックス
0034 %               = [開始インデックス, 終了インデックス]
0035 % BEM.sigma     = 各領域の伝導率
0036 %               = [sigma(1), ..., sigma(Nsurf), 0]
0037 %
0038 % 2004-12-26 M. Sato
0039 % 2007-12-6  M. Sato
0040 %   EEG positions are mapped to outermost head surface first
0041 % 2007-12-25  M. Sato
0042 %   EEG = Weighted average of potentials at nearest head positions
0043 % 2008-10-8  M. Sato
0044 %   Multisurface correction & Auto solid angle calculation
0045 %   are done before saving omega
0046 %
0047 % Copyright (C) 2011, ATR All Rights Reserved.
0048 % License : New BSD License(see VBMEG_LICENSE.txt)
0049 
0050 
0051 %% 多層モデル補正
0052 %fprintf('--- Multisurface correction\n');
0053 %[D, Keeg] = vb_bem_matrix(D,BEM);
0054 %
0055 %% 自己重み係数:基底関数を三角面上で積分した寄与を加える
0056 %fprintf('--- Auto solid angle calculation\n');
0057 %D = vb_solid_auto_grk(D,Fhead,Sout);
0058 
0059 % Inter-vertex distance of head surface
0060 dnext = vb_next_vertex_distance(Fhead,Vhead);
0061 dmax  = max(dnext);
0062 dmean = mean(dnext);
0063 
0064 fprintf('Mean inter-vertex distance of head surface = %f\n',dmean);
0065 fprintf('MAX  inter-vertex distance of head surface = %f\n',dmax);
0066 
0067 % EEG positions are mapped to outermost head surface
0068 % IXeeg    : Vertex index nearest to EEG sensor [Neeg x Np]
0069 % distance : Distance from EEG sensor to head vertex [Neeg x Np]
0070 Np = 3; % number of close surface points for each sensor
0071 [Xeeg, IXeeg, distance] = vb_map_eeg_to_head(Xeeg, Vhead, BEM, dmax, Np);
0072 
0073 fprintf('Mean EEG-Vertex minimum distance = %f\n', mean(distance(:,1)));
0074 
0075 % Extract valid vertex
0076 ix_next = find( IXeeg > 0 );
0077 
0078 fprintf('# of neighbor vertex for EEG = %d\n', length(ix_next))
0079 fprintf('Mean EEG-Vertex distance = %f\n', mean(distance(ix_next)));
0080 
0081 tic
0082 % Peeg : 双極子ポテンシャルからEEGポテンシャルへの変換行列
0083 fprintf('--- EEG transfer matrix calculation\n');
0084 [Peeg] = vb_bem_inverse_eeg(D, IXeeg(ix_next), BEM);
0085 
0086 vb_ptime(toc);
0087 tic
0088 
0089 % ポテンシャル計算
0090 fprintf('--- EEG potential calculation\n');
0091 Phead = vb_bem_eeg_linear_grk(Peeg,Vhead,Fhead,V,J);
0092 
0093 vb_ptime(toc);
0094 
0095 % EEG = Weighted average of potentials at close head positions
0096 %  Phead : head vertex potential  (Nhead x Ndipole)
0097 %  P     : EEG Lead field matrix  ( Neeg x Ndipole)
0098 
0099 fprintf('--- Interpolate head potential to EEG sensor position\n');
0100 
0101 [Neeg, Np] = size(IXeeg); % Neeg = # of EEG sensor
0102 NP = size(V,1); % # of dipoles
0103 P  = zeros(Neeg,NP);
0104 
0105 % Weight factor for average
0106 Ptemp  = zeros(Neeg, Np);
0107 weight = vb_linear_interpolate3(distance);
0108 
0109 for n = 1:NP
0110     Ptemp(ix_next) = Phead(:,n);
0111     P(:,n) = sum(Ptemp .* weight , 2);
0112 end

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