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Functions/PowerLawFit.m

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+function beta = PowerLawFit(y,x);
+% function beta = PowerLawFit(y,x);
+% fits the model y = beta(1) * x .^ beta(2)
+% using a reweighted linearized form
+
+logy = y.*log(y);
+sol = pinv(cat(1,y.*ones(size(x)),y.*log(x))')*logy';
+beta = [exp(sol(1)), sol(2)];

Functions/fontScale.m

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+function fontScale(scale)
+% function fontScale(scale)
+
+H = gcf;
+allText   = findall(H, 'type', 'text');
+allAxes   = findall(H, 'type', 'axes');
+allFont   = [allText; allAxes];
+fontSize = get(allFont,'FontSize');
+
+newFontSize = LocalScale(fontSize, scale, 2);
+set(allFont,{'FontSize'},newFontSize);
+
+function newArray = LocalScale(inArray, scale, minValue)
+n = length(inArray);
+newArray = cell(n,1);
+for k=1:n
+  newArray{k} = max(minValue,scale*inArray{k}(1));
+end

Functions/simContrastvFlip.m

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+function [OptimumTheta MaxContrast]=simContrastvFlip(T1pair,TR,varargin)
+%%
+% function [OptimumTheta MaxContrast]=simContrastvFlip(T1pair,TR)
+% T1pair should be a vector with 2 T1 values
+% TR should be the value of the repetition time used
+%
+% this function plots the signal of a GRE sequence run with repetition time
+% TR as a function of the flip angle
+% additionally it calculates and plots the contrast that can be generated between
+% these two sample and its optimum flip angle
+%
+% the ouptput from the function are OptimumTheta and MaxContrast
+
+
+if ~exist('T1pair','var') || ~exist('TR','var')
+    disp('ERROR: T1pair and TR must be specified')
+    return
+end
+
+if length(T1pair)~=2
+    disp('ERROR: T1pair must contain 2 values')
+    return
+end
+
+if ~exist('tColours','var')
+    tColours = {[66 122 223]/255,[108 158 80]/255,[223 76 76]/255};
+end
+
+if nargin>2
+    ShowFigure=varargin{1};
+else
+    ShowFigure=1;
+end;
+
+%% doing all the calculations
+
+theta = linspace(0,180,1000);
+sig = zeros(length(theta),2);
+for iT1 = 1:2
+    sig(:,iT1) = (1-exp(-TR/T1pair(iT1))).*sin(theta*pi/180)./(1-cos(theta*pi/180)*exp(-TR/T1pair(iT1)));
+end
+contrast=abs(sig(:,1)-sig(:,2));
+[maximum position]=max(contrast);
+OptimumTheta=theta(position);
+MaxContrast=maximum;
+
+
+%% plotting the results
+if ShowFigure
+    figure
+    % set(gcf,'Position',[    50   679   740   409])
+    set(gcf,'Position',[   36   719   517   400])
+    set(gcf,'Color',[1 1 1]);
+    plot(theta,sig(:,1),'linewidth',2,'color',tColours{1}); hold all
+    plot(theta,sig(:,2),'linewidth',2,'color',tColours{2});
+    h1 = plot(theta,contrast);
+    set(h1,'linewidth',2,'color','k')
+    xlabel('Flip Angle (degrees)')
+    ylabel('Relative signal')
+    grid on
+    title(['TR = ' num2str(TR) 'ms'])
+    legend(['T1 = ' num2str(T1pair(1)) 'ms'], ['T1 = ' num2str(T1pair(2)) 'ms'], 'Contrast');
+    xlim([0 180])
+    text(45 ,maximum,['Optimum Flip=',num2str(round(OptimumTheta)),'degrees'])
+    text(45 ,maximum*2,['Max Contrast=',num2str(round(maximum*1000)/1000),' '])
+    fontScale(1.2)
+end

Functions/simContrastvTE.m

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+function OptimumTE=simContrastvTE(T2pair,varargin)
+%% usage function OptimumTE=simContrastvTE(T2pair,varargin)
+% T2pair should be a vector with 2 T2 values
+%
+% this function plots the signal as a function of the echo time for two
+% samples with different T2s 
+% additionally it calculates the contrast as a function of TE and finds the
+% optimum echo time
+
+
+%% check if the correct variables exist
+if ~exist('T2pair','var') 
+    disp('ERROR: T2pair must be specified')
+    return
+end
+
+if length(T2pair)~=2
+    disp('ERROR: T2pair must contain 2 values')
+    return
+end
+
+if ~exist('tColours','var')
+    tColours = {[66 122 223]/255,[108 158 80]/255,[223 76 76]/255};
+end
+if nargin>1
+    ShowFigure=varargin{1};
+else
+    ShowFigure=1;
+end;
+
+%% compute signal evolution as function of echo time
+
+TE_vals = linspace(0,200,1000);
+sig = zeros(length(TE_vals),2);
+for iT2 = 1:2
+    sig(:,iT2) = (exp(-TE_vals/T2pair(iT2)));
+end
+contrast=abs(sig(:,1)-sig(:,2));
+[maximum position]=max(contrast);
+OptimumTE=TE_vals(position);
+
+
+
+
+%% plot results
+if ShowFigure
+figure
+% set(gcf,'Position',[    50   679   740   409])
+set(gcf,'Position',[ 75   306   400   400])
+set(gcf,'Color',[1 1 1]);
+
+plot(TE_vals,sig(:,1),'linewidth',2,'color',tColours{1}); hold all
+plot(TE_vals,sig(:,2),'linewidth',2,'color',tColours{2}); 
+h1 = plot(TE_vals,contrast);
+set(h1,'linewidth',2,'color','k')
+xlabel('TE (ms)')
+ylabel('Relative signal')
+grid on
+legend(['T2 = ' num2str(T2pair(1)) 'ms'], ['T2 = ' num2str(T2pair(2)) 'ms'], 'Contrast');
+text(OptimumTE ,0.5,['Optimum TE=',num2str(round(OptimumTE)),'ms'])
+
+fontScale(1.2)
+end;