eeg_lap2scd

 eeg_lap2scd - scalp current density from Laplacian of scalp potential

 Useage: [scd] = eeg_lap2scd(lap,conductivity)

 where     'lap' is a scalp Laplacian matrix (ie, del^2(V)).
           'conductivity' (> 0) is a scalp estimate. Commercial software 
           (EMSE, SourceSignal; CURRY, Neuroscan) use 0.33 Siemens/m, 
           which is the default here.  The conductivity units depend 
           on the Laplacian units; V/m^2, uV/m^2, ?/m^2 is assumed.

 notes:    Current density is proportional to *minus* the Laplacian
           of electric potential, so it has an opposite polarity to 
           the Laplacian. This function employs the following equation:

           div( current density ) = -1 ( conductivity * Laplacian(potential) )

           div( current density ) = -1 * 0.33{S/m} * Laplacian {V/m^2}

           The resulting values are Ampere/m^3 {A/m^3}.  If lap in uV/m^2, 
           the result is in uA/m^3.  This result is often referred to as 
           'scalp current density' or 'current source density' in the 
           EEG literature.

 refs:     Geddes L, Baker L (1967) Med Biol Engr 5:271-293
           Oostendorp T, van Oosterom A (1996) IEEE Trans Biomed Eng 43: 394-405
           Perrin et al : http://www.lyon151.inserm.fr/unites/280_angl.html

0001 function [scd] = eeg_lap2scd(lap,conductivity)
0002 
0003 % eeg_lap2scd - scalp current density from Laplacian of scalp potential
0004 %
0005 % Useage: [scd] = eeg_lap2scd(lap,conductivity)
0006 %
0007 % where     'lap' is a scalp Laplacian matrix (ie, del^2(V)).
0008 %           'conductivity' (> 0) is a scalp estimate. Commercial software
0009 %           (EMSE, SourceSignal; CURRY, Neuroscan) use 0.33 Siemens/m,
0010 %           which is the default here.  The conductivity units depend
0011 %           on the Laplacian units; V/m^2, uV/m^2, ?/m^2 is assumed.
0012 %
0013 % notes:    Current density is proportional to *minus* the Laplacian
0014 %           of electric potential, so it has an opposite polarity to
0015 %           the Laplacian. This function employs the following equation:
0016 %
0017 %           div( current density ) = -1 ( conductivity * Laplacian(potential) )
0018 %
0019 %           div( current density ) = -1 * 0.33{S/m} * Laplacian {V/m^2}
0020 %
0021 %           The resulting values are Ampere/m^3 {A/m^3}.  If lap in uV/m^2,
0022 %           the result is in uA/m^3.  This result is often referred to as
0023 %           'scalp current density' or 'current source density' in the
0024 %           EEG literature.
0025 %
0026 % refs:     Geddes L, Baker L (1967) Med Biol Engr 5:271-293
0027 %           Oostendorp T, van Oosterom A (1996) IEEE Trans Biomed Eng 43: 394-405
0028 %           Perrin et al : http://www.lyon151.inserm.fr/unites/280_angl.html
0029 %
0030 
0031 % $Revision: 1.1 $ $Date: 2004/11/12 01:32:33 $
0032 
0033 % Licence:  GNU GPL, no implied or express warranties
0034 % History:  06/2001, Darren.Weber_at_radiology.ucsf.edu
0035 %
0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0037 
0038 if ~exist( 'conductivity', 'var' )
0039     conductivity = 0.33; % Siemens/meter
0040     fprintf ('Note: Scalp conductivity = %6.4f S/m; assume Laplacian in ?/m^2.\n', conductivity)
0041 end
0042 
0043 fprintf ('Scalp Current Density = -%6.4f * Laplacian(elec potential)\n', conductivity)
0044 scd = -1 * conductivity * lap;
0045 
0046 return