delta = zhang_fit(berg,R,f)

ZHANG_FIT - Compute 'Berg' parameters for EEG multilayer sphere function delta = zhang_fit(berg,R,f) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MINIMIZATION FUNCTION FOR COMPUTING BERG PARAMETERS FOR EEG MULTILAYER SPHERICAL FORWARD MODEL (zhang_fit.m) This function serves as a minimization function for determining the Berg Eccentricity and Magnitude parameters associated with a series approximation of a Single Dipole in a Multilayer Sphere -by- multiple dipoles in a single shell. (Zhang: Eq 5i"). This function is intended to be called by the Matlab "fmins" function. This version has not been optimized for speed. (Ref: Z. Zhang "A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres" (Phys. Med. Biol. 40, pp335-349,1995) INPUTS: berg : Contains (2*J-1) x 1 R : Concentric Sphere Radii(in meters) from INNERMOST to OUTERMOST NL x 1 f: Weighting terms corresponding to sphere/conductivity profile of interest nmax x 1 where: NL = # of sphere layers; nmax = # of series terms; J = # of Berg Dipoles OUTPUTS: delta: Minimization function output. Best fit of Berg Eccentricity and Magnitude Paramters occurs when this value is minimized 1 x 1 External Functions and Files: None By John Ermer 5/5/99 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

- berg C:\BrainStorm_2001\Toolbox\berg.m

- berg C:\BrainStorm_2001\Toolbox\berg.m

function delta = zhang_fit(berg,R,f) %ZHANG_FIT - Compute 'Berg' parameters for EEG multilayer sphere % function delta = zhang_fit(berg,R,f) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % MINIMIZATION FUNCTION FOR COMPUTING BERG PARAMETERS FOR EEG MULTILAYER % SPHERICAL FORWARD MODEL (zhang_fit.m) % % This function serves as a minimization function for determining the Berg % Eccentricity and Magnitude parameters associated with a series approximation % of a Single Dipole in a Multilayer Sphere -by- multiple dipoles in a single shell. % (Zhang: Eq 5i"). This function is intended to be called by the Matlab "fmins" % function. This version has not been optimized for speed. % % (Ref: Z. Zhang "A fast method to compute surface potentials generated by dipoles % within multilayer anisotropic spheres" (Phys. Med. Biol. 40, pp335-349,1995) % % INPUTS: % berg : Contains (2*J-1) x 1 % R : Concentric Sphere Radii(in meters) from INNERMOST to % OUTERMOST NL x 1 % f: Weighting terms corresponding to sphere/conductivity % profile of interest nmax x 1 % % where: NL = # of sphere layers; nmax = # of series terms; J = # of Berg Dipoles % % OUTPUTS: % delta: Minimization function output. Best fit of % Berg Eccentricity and Magnitude Paramters occurs when % this value is minimized 1 x 1 % % External Functions and Files: None % % By John Ermer 5/5/99 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %<autobegin> ---------------------- 26-May-2004 11:34:43 ----------------------- % --------- Automatically Generated Comments Block Using AUTO_COMMENTS --------- % % CATEGORY: Forward Modeling % % At Check-in: $Author: Mosher $ $Revision: 13 $ $Date: 5/26/04 10:02a $ % % This software is part of BrainStorm Toolbox Version 2.0 (Alpha) 24-May-2004 % % Principal Investigators and Developers: % ** Richard M. Leahy, PhD, Signal & Image Processing Institute, % University of Southern California, Los Angeles, CA % ** John C. Mosher, PhD, Biophysics Group, % Los Alamos National Laboratory, Los Alamos, NM % ** Sylvain Baillet, PhD, Cognitive Neuroscience & Brain Imaging Laboratory, % CNRS, Hopital de la Salpetriere, Paris, France % % See BrainStorm website at http://neuroimage.usc.edu for further information. % % Copyright (c) 2004 BrainStorm by the University of Southern California % This software distributed under the terms of the GNU General Public License % as published by the Free Software Foundation. Further details on the GPL % license can be found at http://www.gnu.org/copyleft/gpl.html . % % FOR RESEARCH PURPOSES ONLY. THE SOFTWARE IS PROVIDED "AS IS," AND THE % UNIVERSITY OF SOUTHERN CALIFORNIA AND ITS COLLABORATORS DO NOT MAKE ANY % WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF % MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, NOR DO THEY ASSUME ANY % LIABILITY OR RESPONSIBILITY FOR THE USE OF THIS SOFTWARE. %<autoend> ------------------------ 26-May-2004 11:34:43 ----------------------- % History ------------------------------------------------ % Ermer 5-May-1999 creation % JCM 08-Sep-2003 Comments % --------------------------------------------------------- NL = length(R); % Number of Sphere Layers nmax = length(f); % Number of Legendre Series Terms J = (length(berg)+1)/2; % Infer Number of Berg Dipoles from Passed data mu_berg = berg(1:J); % Berg Eccentricity Factors 1->J lam_berg = [0.0 berg(J+1:2*J-1)]; % Berg Magnitude Factors 2->J % delta = 0.0; % Compute Factor to be minimized % for n = 2:nmax term0 = 0; for j=2:J term0 = term0 + lam_berg(j)*(mu_berg(j)^(n-1) - mu_berg(1)^(n-1)); end term1 = ( (R(1)/R(NL))^(n-1) )* ... ( f(n)-f(1)*mu_berg(1)^(n-1) - term0); delta = delta + term1*term1; end % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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