vb_eeg_multi_shell

 EEG potential for dipoles in multilayer spherical model 
        eeg = vb_eeg_multi_shell(P, Q, Robs, R, sigma)
 INPUTS 
 P    : current dipole position (in meters)          ( NP x 3 )
 Q    : current dipole moment (direction)            ( NP x 3 )
 Robs : EEG sensors (in meters) on the scalp         ( NS x 3 )
 R    : Radii of sphere from innermost to outermost  ( NL x 1 )
 sigma: Conductivity    from innermost to outermost  ( NL x 1 )
 NJ   : # of Berg Dipoles     (Default: 3)

 OUTPUT
   eeg : EEG Lead field matrix   ( NP x NS )

 Single Dipole in a multilayer sphere can be approximated 
        by multiple dipoles in a single shell. 
 Z. Zhang,  Phys. Med. Biol., vol.40, pp. 335-349, 1995.


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

0001 function eeg = vb_eeg_multi_shell(P, Q, Robs, R, sigma, NJ)
0002 % EEG potential for dipoles in multilayer spherical model
0003 %        eeg = vb_eeg_multi_shell(P, Q, Robs, R, sigma)
0004 % INPUTS
0005 % P    : current dipole position (in meters)          ( NP x 3 )
0006 % Q    : current dipole moment (direction)            ( NP x 3 )
0007 % Robs : EEG sensors (in meters) on the scalp         ( NS x 3 )
0008 % R    : Radii of sphere from innermost to outermost  ( NL x 1 )
0009 % sigma: Conductivity    from innermost to outermost  ( NL x 1 )
0010 % NJ   : # of Berg Dipoles     (Default: 3)
0011 %
0012 % OUTPUT
0013 %   eeg : EEG Lead field matrix   ( NP x NS )
0014 %
0015 % Single Dipole in a multilayer sphere can be approximated
0016 %        by multiple dipoles in a single shell.
0017 % Z. Zhang,  Phys. Med. Biol., vol.40, pp. 335-349, 1995.
0018 %
0019 %
0020 % Copyright (C) 2011, ATR All Rights Reserved.
0021 % License : New BSD License(see VBMEG_LICENSE.txt)
0022 
0023 NL     = length(R);        % # of sphere layers
0024 NV     = size(P,1);        % # of dipoles
0025 Nobs = size(Robs,1);    % # of EEG sensors
0026 
0027 sigmaL  = sigma(NL);        % Conductivity in outermost sphere
0028 eeg     = zeros(NV,Nobs);    % EEG Lead field matrix
0029 
0030 if NL==1,
0031     for n=1:Nobs
0032         Rn   = Robs(n,:);        % n-th EEG sensor position
0033         eeg(:,n) = vb_eeg_one_shell(P, Q, Rn, sigmaL);
0034     end
0035     
0036     return
0037 end
0038 
0039 if nargin < 6  
0040     % Default # of Berg dipoles
0041     NJ=3;       
0042 end
0043 
0044 %  mu: Berg radial factors            ( NJ x 1 )
0045 % lam: Berg magnitude factors         ( NJ x 1 )
0046 [mu,lam] = vb_berg_param(R, sigma, NJ);
0047 
0048 for n=1:Nobs
0049     Rn   = Robs(n,:);        % n-th EEG sensor position
0050     eeg0 = zeros(NV,1);
0051     
0052     % Approximation by NJ dipoles in a single shell
0053     for j=1:NJ
0054         eeg0 = eeg0 + vb_eeg_one_shell(mu(j)*P, lam(j)*Q, Rn, sigmaL);
0055     end;
0056     
0057     eeg(:,n) = eeg0;
0058 end
0059