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Figure3_pure_relaxation_model.m
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Figure3_pure_relaxation_model.m
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close all; clear; clc; warning off
% Load GT radius
Phantom1 = load('Histological_radius/ROI1.mat');
Phantom3 = load('Histological_radius/ROI3.mat');
Phantom4 = load('Histological_radius/ROI4.mat');
Phantom5 = load('Histological_radius/ROI5.mat');
Threshold = 40; % discard huge pores and convert to radius
R11 = Phantom1.ROI1.s1; R11 = R11(R11<Threshold)/2;
R12 = Phantom1.ROI1.s2; R12 = R12(R12<Threshold)/2;
R13 = Phantom1.ROI1.s3; R13 = R13(R13<Threshold)/2;
R14 = Phantom1.ROI1.s4; R14 = R14(R14<Threshold)/2;
R15 = Phantom1.ROI1.s5; R15 = R15(R15<Threshold)/2;
R31 = Phantom3.ROI3.s1; R31 = R31(R31<Threshold)/2;
R32 = Phantom3.ROI3.s2; R32 = R32(R32<Threshold)/2;
R33 = Phantom3.ROI3.s3; R33 = R33(R33<Threshold)/2;
R34 = Phantom3.ROI3.s4; R34 = R34(R34<Threshold)/2;
R35 = Phantom3.ROI3.s5; R35 = R35(R35<Threshold)/2;
R41 = Phantom4.ROI4.s1; R41 = R41(R41<Threshold)/2;
R42 = Phantom4.ROI4.s2; R42 = R42(R42<Threshold)/2;
R43 = Phantom4.ROI4.s3; R43 = R43(R43<Threshold)/2;
R44 = Phantom4.ROI4.s4; R44 = R44(R44<Threshold)/2;
R45 = Phantom4.ROI4.s5; R45 = R45(R45<Threshold)/2;
R51 = Phantom5.ROI5.s1; R51 = R51(R51<Threshold)/2;
R52 = Phantom5.ROI5.s2; R52 = R52(R52<Threshold)/2;
R53 = Phantom5.ROI5.s3; R53 = R53(R53<Threshold)/2;
R54 = Phantom5.ROI5.s4; R54 = R54(R54<Threshold)/2;
R55 = Phantom5.ROI5.s5; R55 = R55(R55<Threshold)/2;
R{1} = [R11; R12; R13; R14; R15];
R{2} = [R11; R12; R13; R14; R15];
R{3} = [R31; R32; R33; R34; R35];
R{4} = [R41; R42; R43; R44; R45];
R{5} = [R51; R52; R53; R54; R55];
% Load SMT of dMRI data
SM = load('SMT_relaxation_all_TEs/Spherical_mean_signal_perROI.txt');
SM_P1 = SM(6,:);
SM_P2 = SM(1,:);
SM_P3 = SM(2,:);
SM_P4 = SM(3,:);
SM_P5 = SM(4,:);
STD_dMRI = load('SMT_relaxation_all_TEs/STD_log_mean_signal_perROI.txt');
STD_dMRI_P1 = STD_dMRI(6,:);
STD_dMRI_P2 = STD_dMRI(1,:);
STD_dMRI_P3 = STD_dMRI(2,:);
STD_dMRI_P4 = STD_dMRI(3,:);
STD_dMRI_P5 = STD_dMRI(4,:);
% Create array structure
SM_P(:,1) = SM_P1;
SM_P(:,2) = SM_P2;
SM_P(:,3) = SM_P3;
SM_P(:,4) = SM_P4;
SM_P(:,5) = SM_P5;
STD_P(:,1) = STD_dMRI_P1;
STD_P(:,2) = STD_dMRI_P2;
STD_P(:,3) = STD_dMRI_P3;
STD_P(:,4) = STD_dMRI_P4;
STD_P(:,5) = STD_dMRI_P5;
% Rhos Estimated from previous analysis, we will use the mean value
Rho = [0.0039 0.0044 0.0020 0.0034 0.0029]; % all TEs
rho_j = mean(Rho([1,2,4,5])); std_j = std(Rho([1,2,4,5]));
% Define experimental parameters
TE = [51, 75, 100, 150, 200, 250]; % ms
Delta = 35;
delta = 9;
gyroMagnRatio = 267.5153151*10^(-6);
g = 166.8;
% bval = gyroMagnRatio^2 * g.^2 * delta^2 * (Delta - delta/3); %ms/um^2
bval = 5;
% Fixed parameters
T2csf = 3000;
for i=1:5 % For each ROI number
display(['Analysis for ROI #' num2str(i)])
Signal = SM_P(:,i);
R_i = R{i};
% Estimate the effective radius from the measured (spherical mean)
% dMRI-relaxation signal using a pure relaxation model
x0 = [1, 100];
lb = [0.1, 0];
ub = [10, 10000];
[x,resnorm,residual,exitflag,output] = lsqcurvefit(@VanGelderenS_mod_vect_pure_rel, x0, [TE(:); T2csf; rho_j], Signal(:), lb, ub);
disp('------------------------------------------')
display(['The effective radius is ', num2str(x(1))])
Rmean_exp(i) = x(1);
Signal_predicted(:,i) = VanGelderenS_mod_vect_pure_rel(x, [TE(:); T2csf; rho_j]);
beta(i) = x(2);
disp('------------------------------------------')
if i==1
Rxx = [R11; R12; R13; R14; R15];
elseif i==2
Rxx = [R11; R12; R13; R14; R15];
elseif i==3
Rxx = [R31; R32; R33; R34; R35];
elseif i==4
Rxx = [R41; R42; R43; R44; R45];
elseif i==5
Rxx = [R51; R52; R53; R54; R55];
end
% Generate the theoretical dMRI-relaxation signal from a distribution of cylinder radii (for each ROI)
S_theory = integrate_prop_signal([TE(:); T2csf; rho_j], Rxx);
x0 = 1;
lb = 0;
ub = 100000;
[scale,resnorm,residual,exitflag,output] = lsqcurvefit(@scale_factor, x0, S_theory(:), Signal(:), lb, ub);
S_theory = S_theory * scale;
S_theory_matrix(:,i) = S_theory(:);
% Estimate the effective radius from the generated theoretical (spherical mean)
% dMRI-relaxation signal using a pure relaxation model
x0 = [1, 100];
lb = [0.1, 0];
ub = [10, 10000];
[x,resnorm,residual,exitflag,output] = lsqcurvefit(@VanGelderenS_mod_vect_pure_rel, x0, [TE(:); T2csf; rho_j], S_theory(:), lb, ub);
disp('------------------------------------------')
display(['The (theoretical) effective radius is ', num2str(x(1))])
Hmean_exp(i) = x(1);
disp('------------------------------------------')
end
color(1,:) = [0 0.4470 0.7410];
color(2,:) = [0.9290 0.6940 0.1250];
color(3,:) = [0.4940 0.1840 0.5560];
color(4,:) = [0.4660 0.6740 0.1880];
color(5,:) = [0.6350 0.0780 0.1840];
% ------------------------------------------------------------------------
figure('Renderer', 'painters', 'Position', [200 200 600 600])
hold on
mdl = fitlm(Hmean_exp, Rmean_exp); % Fit Data
B = mdl.Coefficients.Estimate; % Coefficients
CI = coefCI(mdl);
% Coefficient Confidence Intervals
x = 0:0.1:6;
[Ypred,YCI] = predict(mdl, x'); % Fitted Regression Line & Confidence Intervals
figure(1)
for i=1:length(Rmean_exp)
h(i) = scatter(Hmean_exp(i), Rmean_exp(i), 200, 'p', 'MarkerFaceColor' , color(i,:), 'MarkerEdgeColor' , color(i,:));
end
hold on
pt = plot(x, Ypred,'-', x, YCI, '--r', 'LineWidth', 2, 'Color', [1, 0, 0, 0.5]);
hold off
grid
xlim([0, 6]); ylim([0, 6]);
hold on
axis('square')
plot(0:6,0:6, '-.k', 'LineWidth', 1)
xticks(1:6)
yticks(1:6)
xlabel('\it r_{eff-SEM-R} (\mu\itm)', 'FontSize',14)
ylabel('\it r_{eff-MRI-R} (\mu\itm)', 'FontSize',14)
title([' \it r_{eff-MRI-R}', ' ', 'vs' ' ', '\it r_{eff-SEM-R}'], 'fontsize', 16)
xl = xlim;
yl = ylim;
xt = 0.05 * (xl(2)-xl(1)) + xl(1);
yt = 0.92 * (yl(2)-yl(1)) + yl(1);
caption = sprintf('r_{eff-MRI-R} = %.2f + %.2f * r_{eff-SEM-R}', B(1), B(2));
text(xt, yt, caption, 'FontSize', 14, 'Color', 'red', 'FontAngle', 'italic');
xl = xlim;
yl = ylim;
xt = 0.06 * (xl(2)-xl(1)) + xl(1);
yt = 0.02 * (yl(2)-yl(1)) + yl(1);
str = texlabel('line: y=x');
txt = text(xt, yt, str, 'FontSize', 14, 'FontAngle', 'italic');
set(txt,'Rotation', 45);
ax = gca;
ax.XAxis.FontSize = 14;
ax.YAxis.FontSize = 14;
set(gca, ...
'TickDir' , 'out' , ...
'TickLength' , [.02 .02] , ...
'XMinorTick' , 'on' , ...
'YMinorTick' , 'on' , ...
'XColor' , [.3 .3 .3], ...
'YColor' , [.3 .3 .3], ...
'LineWidth' , 1.4 );
set( gca , ...
'FontName' , 'Helvetica' );
lgd = legend(h, {'Phantom 1','Phantom 2','Phantom 3', 'Phantom 4', 'Phantom 5', '', '', ''});
set(lgd,'Interpreter','latex', 'FontName', 'AvantGarde', 'Location', 'southeast');
lgd.FontSize = 14;
print('Figures/Figure3_A_pure_relaxation_mono_exp_constant_rho', '-dpng', '-r600')
% ------------------------------------------------------------------------
figure('Renderer', 'painters', 'Position', [200 200 600 600])
hold on
for i =1:5
pt(i) = errorbar(TE, log(SM_P(:,i)), STD_P(:,i), '.', 'color', color(i,:), 'MarkerSize', 20);
plot(TE, log(S_theory_matrix(:,i)),'--', 'color', color(i,:), 'LineWidth', 1.4);
end
axis('square')
xlabel('\it TE (ms)', 'FontSize',14)
ylabel('\it log(S) (a.u)', 'FontSize',14)
title('rMRI signal vs SEM-based signal', 'fontsize', 16)
ax = gca;
ax.XAxis.FontSize = 14;
ax.YAxis.FontSize = 14;
set(gca, ...
'TickDir' , 'out' , ...
'TickLength' , [.02 .02] , ...
'XMinorTick' , 'on' , ...
'YMinorTick' , 'on' , ...
'XColor' , [.3 .3 .3], ...
'YColor' , [.3 .3 .3], ...
'LineWidth' , 1.4 );
set( gca , ...
'FontName' , 'Helvetica' );
lgd = legend(pt, {'Phantom 1', 'Phantom 2', 'Phantom 3', 'Phantom 4', 'Phantom 5'});
set(lgd,'Interpreter','latex', 'FontName', 'AvantGarde', 'Location', 'southwest');
lgd.FontSize = 14;
set(lgd,'color','none');
title(lgd,'rMRI signal')
print('Figures/Figure3_B_logSignal_vs_TE_relaxation_mono_exp_constant_rho', '-dpng', '-r600')
% ---------------- private function --------------------------------%
function S = integrate_prop_signal(Data, Rxx)
% I am summing over all signals generated for each radius in the sample
r2m = sum(Rxx.^2);
S = 0;
%model = 'pure_relaxation';
model = 'relaxation_diffusion';
for i=1:length(Rxx)
r = Rxx(i);
if strcmp(model, 'pure_relaxation')
signal_r = VanGelderenS_mod_vect_pure_rel([r, 1], Data);
S = S + (r^2/r2m) .* Svg;
elseif strcmp(model, 'relaxation_diffusion')
signal_r = VanGelderenS_mod_vect_pure_rel([r, 1], Data);
b_vec = 5;
signal_d = VanGelderenS_mod_vect_pure_diff([r, 1], b_vec);
S = S + (r^2/r2m) .* signal_r * signal_d;
end
end
end
function Svg = scale_factor(x, S)
scale = x;
Svg = scale * S;
end