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ME_SI.m
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ME_SI.m
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function ME_SI(fdwi,fbvec,fbval,ft2r,fmask,TE,outpath,options)
%{
░█▀▀█ ░█▀▀▀█ ░█▀▄▀█ ░█▀▀▀ ░█▀▀▄ ▀█▀
░█─── ░█──░█ ░█░█░█ ░█▀▀▀ ░█─░█ ░█─
░█▄▄█ ░█▄▄▄█ ░█──░█ ░█▄▄▄ ░█▄▄▀ ▄█▄
Multi-echo spectrum imaging (ME-SI)
Created by Ye Wu, PhD (dr.yewu@outlook.com)
- Nanjing University of Science and Technology, China
- University of North Carolina at Chapel Hill, USA
%}
arguments
fdwi (1,:) {mustBeNonzeroLengthText}
fbvec (1,:) {mustBeNonzeroLengthText}
fbval (1,:) {mustBeNonzeroLengthText}
ft2r (1,:) {mustBeNonzeroLengthText} % [restricted, hindered, free]
fmask string {mustBeFile}
TE (1,:) {mustBeNumeric}
outpath string {mustBeNonzeroLengthText}
options.normalizeToS0 (1,1) {mustBeNumericOrLogical} = true
options.useBshell (1,:) {mustBeNumericOrLogical} = false
options.lmax (1,1) {mustBeInteger,mustBeNonnegative} = 6
options.spectrum string {mustBeFile} = 'scheme/default_spectrum.mat'
end
addpath('third/osqp');
addpath('third/csd');
cellfun(@(x)assert(exist(x,'file'),'Input DWI %s does not exist', x),fdwi,'UniformOutput',false);
cellfun(@(x)assert(exist(x,'file'),'Input Bvec %s does not exist', x),fbvec,'UniformOutput',false);
cellfun(@(x)assert(exist(x,'file'),'Input Bval %s does not exist', x),fbval,'UniformOutput',false);
cellfun(@(x)assert(exist(x,'file'),'Input T2 relax %s does not exist', x),ft2r,'UniformOutput',false);
assert(exist(fmask,'file'),'Input mask %s does not exist', fmask);
assert(exist(options.spectrum,'file'),'Input spectrum %s does not exist', options.spectrum);
%% load multi-echo dMRI dataset
ME_dwi_info = cellfun(@(x)niftiinfo(x),fdwi,'UniformOutput',false);
ME_dwi = cellfun(@(x)niftiread(x),ME_dwi_info,'UniformOutput',false);
ME_bval = cellfun(@(x)round(importdata(x)'/100)*100,fbval,'UniformOutput',false);
ME_bvec = cellfun(@(x)importdata(x)',fbvec,'UniformOutput',false);
ME_mask_info = niftiinfo(fmask);
ME_mask = round(niftiread(ME_mask_info));
ME_t2r_info = cellfun(@(x)niftiinfo(x),ft2r,'UniformOutput',false);
ME_t2r = cellfun(@(x)niftiread(x),ME_t2r_info,'UniformOutput',false);
clear fdwi fbvec fbval fmask ft2r;
clear ME_t2r_info ME_mask_info
if options.useBshell
ind = cellfun(@(x)ismember(x,options.useBshell),fbval,'UniformOutput',false);
ME_dwi = cellfun(@(x,y)x(:,:,:,y),ME_dwi,ind,'UniformOutput',false);
ME_bvec = cellfun(@(x,y)x(y,:),ME_bvec,ind,'UniformOutput',false);
ME_bval = cellfun(@(x,y)x(y),ME_bval,ind,'UniformOutput',false);
clear ind
end
%% Normalization S/S0
if options.normalizeToS0
ind = cellfun(@(x)ismember(x,0),ME_bval,'UniformOutput',false);
ME_dwi_norm = cellfun(@(x,y)x(:,:,:,~y)./(mean(x(:,:,:,~y),4)+eps),ME_dwi,ind,'UniformOutput',false);
ME_bval_norm = cellfun(@(x,y)x(~y,:),ME_bval,ind,'UniformOutput',false);
ME_bvec_norm = cellfun(@(x,y)x(~y,:),ME_bvec,ind,'UniformOutput',false);
clear ind
ME_dwi = ME_dwi_norm; clear ME_dwi_norm;
ME_bval = ME_bval_norm; clear ME_bval_norm;
ME_bvec = ME_bvec_norm; clear ME_bvec_norm;
end
%% kernel
default_spectrum = load(options.spectrum);
adc_restricted = default_spectrum.adc_restricted;
adc_hindered = default_spectrum.adc_hindered;
adc_isotropic = default_spectrum.adc_isotropic;
num_restricted = size(adc_restricted,1);
num_hindered = size(adc_hindered,1);
num_isotropic = size(adc_isotropic,1);
kernel_restricted = cell(length(TE),num_restricted);
kernel_hindered = cell(length(TE),num_hindered);
kernel_isotropic = cell(length(TE),num_isotropic);
lmax = options.lmax;
nmax = lmax2nsh(lmax);
scheme = gen_scheme('scheme/sphere_362_vertices.txt',lmax);
for i = 1:length(TE)
bval = ME_bval{i};
bvec = ME_bvec{i};
bshell = unique(bval);
nvol = length(bval);
for j = 1:num_restricted
kernel_restricted{i,j} = zeros(nvol,nmax);
for k = 1:length(bshell)
order = min(floor(nsh2lmax(sum(bval==bshell(k)))),lmax);
DW_scheme = gen_scheme(bvec(bval==bshell(k),:),order);
R_amp = response(adc_restricted(j,1),adc_restricted(j,2),bshell(k),scheme);
R_SH = amp2SH(R_amp, scheme);
R_RH = SH2RH(R_SH);
m = [];
for l = 0:2:order
m = [ m R_RH(l/2+1)*ones(1,2*l+1) ];
end
fconv = DW_scheme.sh .* m(ones(size(DW_scheme.sh,1),1),:);
fconv(:,end+1:nmax) = 0;
kernel_restricted{i,j}(bval==bshell(k),:) = fconv;
clear DW_scheme R_amp R_SH R_RH fconv m;
end
end
for j = 1:num_hindered
kernel_hindered{i,j} = zeros(nvol,nmax);
for k = 1:length(bshell)
order = min(floor(nsh2lmax(sum(bval==bshell(k)))),lmax);
DW_scheme = gen_scheme(bvec(bval==bshell(k),:),order);
R_amp = response(adc_hindered(j,1),adc_hindered(j,2),bshell(k),scheme);
R_SH = amp2SH(R_amp, scheme);
R_RH = SH2RH(R_SH);
m = [];
for l = 0:2:order
m = [ m R_RH(l/2+1)*ones(1,2*l+1) ];
end
fconv = DW_scheme.sh .* m(ones(size(DW_scheme.sh,1),1),:);
fconv(:,end+1:nmax) = 0;
kernel_hindered{i,j}(bval==bshell(k),:) = fconv;
clear DW_scheme R_amp R_SH R_RH fconv m;
end
end
for j = 1:num_isotropic
kernel_isotropic{i,j} = zeros(nvol,1);
for k = 1:length(bshell)
kernel_isotropic{i,j}(bval==bshell(k),1) = exp(-bshell(k)*adc_isotropic(j));
end
kernel_isotropic{i,j} = kernel_isotropic{i,j} * (4*pi);
end
end
%% Vectorization & Masked & arrayed
ME_mask_ind = find(ME_mask>0.5);
ME_dwi_array = cellfun(@(x)reshape(x,size(x,1)*size(x,2)*size(x,3),size(x,4)),ME_dwi,'UniformOutput',false);
ME_dwi_array = cellfun(@(x)x(ME_mask_ind,:)',ME_dwi_array,'UniformOutput',false);
ME_dwi_array = cell2mat(ME_dwi_array');
ME_t2r_array = cellfun(@(x)reshape(x,size(x,1)*size(x,2)*size(x,3),1),ME_t2r,'UniformOutput',false);
ME_t2r_array = cellfun(@(x)x(ME_mask_ind,:)',ME_t2r_array,'UniformOutput',false);
clear ME_dwi ME_t2r
%% subject to
nv = size(scheme.vert,1);
ampbasis = repmat(scheme.sh,1,num_restricted + num_hindered);
ampbasis = mat2cell(ampbasis,nv,repmat(nmax,1,num_restricted + num_hindered));
ampbasis = blkdiag(ampbasis{:});
A1 = blkdiag(ampbasis,diag(ones(1,num_isotropic)));
A2 = zeros(size(A1,1),1);
alpha_coef = zeros(num_restricted*nmax+num_hindered*nmax+num_isotropic,size(ME_dwi_array,2));
ME_t2r_restricted = exp(-TE'./ME_t2r_array{1});
ME_t2r_hindered = exp(-TE'./ME_t2r_array{2});
ME_t2r_isotropic = exp(-TE'./ME_t2r_array{3});
clear ampbasis ME_t2r_array;
%% optimization
parfor i = 1:size(ME_dwi_array,2)
kernel = cell2mat([ cellfun(@(x,y) x.*y, kernel_restricted,num2cell(ME_t2r_restricted(:,i).*ones(1,num_restricted)), 'UniformOutput',false) ...
cellfun(@(x,y) x.*y, kernel_hindered,num2cell(ME_t2r_hindered(:,i).* ones(1,num_hindered)), 'UniformOutput',false) ...
cellfun(@(x,y) x.*y, kernel_isotropic,num2cell(ME_t2r_isotropic(:,i).* ones(1,num_isotropic)), 'UniformOutput',false)]);
dwi = ME_dwi_array(:,i);
try
H = double(kernel'*kernel);
f = -double(kernel'*dwi);
prob = osqp;
prob.setup(H,f,A1,A2,[],'alpha',0.1,'verbose',0);
res = prob.solve();
if max(res.x) > 100
continue;
end
alpha_coef(:,i) = res.x;
catch
continue;
end
end
%% save results
if ~exist(outpath,'dir')
mkdir(outpath)
end
% save FOD restricted
temp = single(zeros(nmax,size(ME_mask,1)*size(ME_mask,2)*size(ME_mask,3)));
info_fod = ME_dwi_info{1};
info_fod.Datatype = 'single';
info_fod.ImageSize(4) = nmax;
for i = 1:num_restricted+num_hindered
temp(:,ME_mask_ind) = alpha_coef((i-1)*nmax+1:i*nmax,:);
fod = reshape(temp',size(ME_mask,1),size(ME_mask,2),size(ME_mask,3),nmax);
if i <= num_restricted
niftiwrite(single(fod),fullfile(outpath,strcat('FOD_restricted_',num2str(i),'.nii')),info_fod,'Compressed', true);
else
niftiwrite(single(fod),fullfile(outpath,strcat('FOD_hindered_',num2str(i-num_restricted),'.nii')),info_fod,'Compressed', true);
end
end
temp = single(zeros(num_isotropic,size(ME_mask,1)*size(ME_mask,2)*size(ME_mask,3)));
info_fod.Datatype = 'single';
info_fod.ImageSize(4) = num_isotropic;
temp(:,ME_mask_ind) = alpha_coef(end-num_isotropic+1:end,:);
fod = reshape(temp',size(ME_mask,1),size(ME_mask,2),size(ME_mask,3),num_isotropic);
niftiwrite(fod,fullfile(outpath,'FOD_free.nii'),info_fod,'Compressed', true);
end
function nsh = lmax2nsh(lmax)
nsh = (lmax+1) * (lmax+2) / 2;
end
function lmax = nsh2lmax(nsh)
lmax = 2*(floor((sqrt(1+8*nsh)-3)/4));
end
function S = response(longitudinal,transverse,b,scheme)
D = [ transverse 0 0; 0 transverse 0; 0 0 longitudinal ];
C = s2c([ scheme.el scheme.az 1+0*scheme.az ]);
X = C(:,1);
Y = C(:,2);
Z = C(:,3);
S = exp(-b*[X.^2 Y.^2 Z.^2 2.*X.*Y 2.*X.*Z 2.*Y.*Z] * ...
[ D(1,1) D(2,2) D(3,3) D(1,2) D(1,3) D(2,3) ]');
end