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matRad_bioObjFunc.m
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matRad_bioObjFunc.m
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function [f, g] = matRad_bioObjFunc(w,dij,cst)
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% matRad optimization function based on the biologcial effect
%
% call
% [f, g] = matRad_bioObjFunc(w,dij,cst)
%
% input
% w: weight vector
% dij: matRad dij struct
% cst: cst file
%
% output
% f: objective function value
% g: gradient vector
%
% References
% [1] http://iopscience.iop.org/0031-9155/51/12/009
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Copyright 2015, Mark Bangert, on behalf of the matRad development team
%
%
% This file is part of matRad.
%
% matrad is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your option)
% any later version.
%
% matRad is distributed in the hope that it will be useful, but WITHOUT ANY
% WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
% details.
%
% You should have received a copy of the GNU General Public License in the
% file license.txt along with matRad. If not, see
% <http://www.gnu.org/licenses/>.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% calculate biological effect
linTerm = dij.mAlphaDose*w;
quadTerm = dij.mSqrtBetaDose*w;
e = linTerm + quadTerm.^2;
% Numbers of voxels
numVoxels = size(dij.physicalDose,1);
% Initializes f
f = 0;
% Initializes delta
delta_underdose = zeros(numVoxels,1);
delta_overdose = zeros(numVoxels,1);
delta_deviation = zeros(numVoxels,1);
delta_mean = zeros(numVoxels,1);
delta_EUD = zeros(numVoxels,1);
% Compute optimization function for every VOI.
for i = 1:size(cst,1)
% Only take OAR or target VOI.
if ~isempty(cst{i,4}) && ( isequal(cst{i,3},'OAR') || isequal(cst{i,3},'TARGET') )
% get effect vector in current VOI
e_i = e(cst{i,4});
% loop over the number of constraints for the current VOI
for j = 1:size(cst{i,6},1)
% get Penalty
rho = cst{i,6}(j).parameter(1);
% refernce effect
if ~isequal(cst{i,6}(j).type, 'mean') && ~isequal(cst{i,6}(j).type, 'EUD')
e_ref = dij.ax(cst{i,4}).*cst{i,6}(j).parameter(2)+dij.bx(cst{i,4})*cst{i,6}(j).parameter(2)^2;
end
if isequal(cst{i,6}(j).type, 'square underdosing')
if ~isequal(cst{i,3},'OAR')
% underdose : effect minus reference effect
underdose = e_i - e_ref;
% apply positive operator
underdose(underdose>0) = 0;
% calculate objective function
f = f + (rho/size(cst{i,4},1))*(underdose'*underdose);
% calculate delta
delta_underdose(cst{i,4}) = delta_underdose(cst{i,4}) + (rho/size(cst{i,4},1))*underdose;
else
disp(['square underdosing constraint for ' cst{i,2} ' will be skipped'])
end
elseif isequal(cst{i,6}(j).type, 'square overdosing')
% overdose : Dose minus prefered dose
overdose = e_i - e_ref;
% apply positive operator
overdose(overdose<0) = 0;
% calculate objective function
f = f + (rho/size(cst{i,4},1))*(overdose'*overdose);
%calculate delta
delta_overdose(cst{i,4}) = delta_overdose(cst{i,4}) + (rho/size(cst{i,4},1))*overdose;
elseif isequal(cst{i,6}(j).type, 'square deviation')
if ~isequal(cst{i,3},'OAR')
% deviation : Dose minus prefered dose
deviation = e_i - e_ref;
% claculate objective function
f = f + (rho/size(cst{i,4},1))*(deviation'*deviation);
% calculate delta
delta_deviation(cst{i,4}) = delta_deviation(cst{i,4}) + (rho/size(cst{i,4},1))*deviation;
else
disp(['square deviation constraint for ' cst{i,2} ' will be skipped'])
end
elseif isequal(cst{i,6}(j).type, 'mean')
if ~isequal(cst{i,3},'TARGET')
% calculate objective function
f = f + (rho/size(cst{i,4},1))*sum(e_i);
% calculate delta
delta_mean(cst{i,4}) = delta_mean(cst{i,4}) + ...
(rho/size(cst{i,4},1))*ones(size(cst{i,4},1),1);
else
disp(['mean constraint for ' cst{i,2} ' will be skipped'])
end
elseif isequal(cst{i,6}(j).type, 'EUD')
if ~isequal(cst{i,3},'TARGET')
% get exponent for EUD
exponent = cst{i,6}(j).parameter(2);
% calculate objective function and delta
if sum(e_i.^exponent)>0
f = f + rho*nthroot((1/size(cst{i,4},1))*sum(e_i.^exponent),exponent);
delta_EUD(cst{i,4}) = delta_EUD(cst{i,4}) + ...
rho*nthroot(1/size(cst{i,4},1),exponent) * sum(e_i.^exponent)^((1-exponent)/exponent) * (e_i.^(exponent-1));
if sum(~isfinite(delta_EUD)) > 0 % check for inf and nan for numerical stability
error(['EUD computation for ' cst{i,2} ' failed. Reduce exponent to resolve numerical problems.']);
end
end
else
disp(['EUD constraint for ' cst{i,2} ' will be skipped'])
end
else
error('undefined objective in cst struct');
end
end
end
end
% gradient calculation
if nargout > 1
delta = 2*(delta_underdose + delta_overdose + delta_deviation) + delta_mean + delta_EUD;
vBias= (delta' * dij.mAlphaDose)';
mPsi = (2*(delta.*quadTerm)'*dij.mSqrtBetaDose)';
g = vBias+mPsi ;
end