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Waveform_ToolBox.m
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classdef Waveform_ToolBox
methods(Static)
function [F]= Fcalc(Dn,Handle,dT,Gmax)
% G in mT/m
% dT in us
% This give a b-value in s/mm^2
equpu =@(d) d^3/3;
equpu0=@(d) d^2;
equv =@(d) 0;
equpu(1000e-3)+equpu0(1000e-3)*(1000e-3)+equpu(1000e-3)
bfact=[];
GammaH= 267.513e6; % Hz/T
Gmax=Gmax*1e-3*1e-3; % mT/m -> T/mm
Handle = {@equh1, @equh2, @equh3};
dT=dT*1e-6;
Tn=cumsum(Dn);
F=[];
for cpt=1:1:length(Dn)
Tn=0;
if cpt==1
Tn=linspace(0,Dn(cpt),Dn(cpt)/dT)
else
Tn=linspace(Dn(cpt-1),Dn(cpt),(Dn(cpt)-Dn(cpt-1))/dT)
end
F=[F Handle{cpt}(Tn)];
end
end
function [bval, M1, Grad, Slope]= AddBvalEvent(bval, M1, Grad, Slope,Sn,TimeStep)
dTimeStep = TimeStep;
dTimeStep2 = dTimeStep * dTimeStep;
dTimeStep3 = dTimeStep2 * dTimeStep;
dTimeStep4 = dTimeStep2 * dTimeStep2;
dTimeStep5 = dTimeStep2 * dTimeStep3;
% Calculate change of b-value
% (unit: (mT/m)^2 us^3)
bval = bval + M1 * M1 * dTimeStep ...
+ 1./2. * (M1 * Grad + M1 * Grad) * dTimeStep2 ...
+ 1./6. * (M1 * Slope + M1 * Slope + 2. * Grad * Grad) * dTimeStep3 ...
+ 1./8. * (Grad * Slope + Grad * Slope) * dTimeStep4 ...
+ 1./20. * (Slope * Slope) * dTimeStep5;
% Calculate change of 0th moment (time-integral of gradient)
% (unit: mT/m us)
M1 = M1 + Grad * dTimeStep + 1./2. * Slope * dTimeStep2;
% Calculate change of gradient amplitude
% (unit: mT/m)
Grad = Grad + Slope * dTimeStep;
Slope=Slope+Sn;
end
function [bval] = Biter(Dn,Gn,Rt)
tmp_time=0;
bval=0;
M1=0;
Grad=0;
Slope=0;
cG=0;
for cpt=1:1:length(Dn)
if Dn(cpt)>0 && Dn(cpt)>2*Rt && Gn(cpt)~=0 % Trapezoid
% Ramp Up
[bval, M1, Grad, Slope]= Waveform_ToolBox.AddBvalEvent(bval, M1, Grad, Slope,Gn(cpt)*1/Rt,0);
cG=[cG Grad];
% Flatop
[bval, M1, Grad, Slope]= Waveform_ToolBox.AddBvalEvent(bval, M1, Grad, Slope,-Gn(cpt)*1/Rt,Rt);
cG=[cG Grad];
% Ramp Dowm
[bval, M1, Grad, Slope]= Waveform_ToolBox.AddBvalEvent(bval, M1, Grad, Slope,-Gn(cpt)*1/Rt,Dn(cpt)-2*Rt);
cG=[cG Grad];
% zero
[bval, M1, Grad, Slope]= Waveform_ToolBox.AddBvalEvent(bval, M1, Grad, Slope,Gn(cpt)*1/Rt,Rt);
cG=[cG Grad];
tmp_time=tmp_time+Dn(cpt);
elseif Dn(cpt)>0 && Dn(cpt)<=2*Rt && Gn(cpt)~=0 % Triangle
GM(cpt).StartTime=tmp_time;
GM(cpt).RampTime=Dn(cpt)/2;
GM(cpt).FlapTop=0;
GM(cpt).StopTime=GM(cpt).StartTime+GM(cpt).FlapTop+2*GM(cpt).RampTime;
GM(cpt).EffectiveTime=GM(cpt).FlapTop+GM(cpt).RampTime;
GM(cpt).Ampl=Gn(cpt)*GM(cpt).RampTime/Rt;
tmp_time=GM(cpt).StopTime;
else % Blank
% zero
[bval, M1, Grad, Slope]= Waveform_ToolBox.AddBvalEvent(bval, M1, Grad, Slope,0,Dn(cpt));
cG=[cG Grad];
tmp_time=tmp_time+Dn(cpt);
end
end
GammaH= 267.513e6; % Hz/T
bval=GammaH*GammaH*bval;
end
function [bval, bfact]= Bcalc(G,dT)
% G in mT/m
% dT in us
% This give a b-value in in s/mm^2
bfact=[];
GammaH= 267.513e6; % Hz/T
G=G*1e-3*1e-3; % mT/m -> T/mm
dT=dT*1e-6; % us -> s
% btmp=0;
% bfunc=zeros(1,length(G));
%
% for cpt=1:1:length(G)
% bfunc(cpt)=btmp+G(cpt)*G(cpt)*dT;
% btmp=bfunc(cpt);
% end
%
% TimeFact=(GammaH*GammaH * dT * dT ); %1e-18 * 1e-6
% bfact = bfunc*TimeFact;
% bval = btmp*TimeFact;
%
Integration1 = cumsum(G.*dT); % First integral
bfact=Integration1.*Integration1; % Square of the First integral
bval = (GammaH^2)*sum(bfact* dT); % Second integral
bfact=(GammaH^2)*cumsum(bfact*dT);
end
function [bval]= BValue_Mono_ref(delta,DELTA,Gmax,rT)
%
% Calculate reference b-value for a monopolar waveform
% delta (Ramptime +Plateau)in s
% DELTA in S
% Gmax could be a 1D vector waveform or an amplitude both in mT/m
% ramptime rT in s
% This give a b-value in s/mm^2
Gmax=Gmax*1e-3*1e-3; % Convert mT/m to T/mm
GammaH= 267.513e6; %% Hz/T
bval = (GammaH^2)* (max(Gmax)^2) * ( delta* delta*(DELTA - delta/3) + rT*rT*rT/30 - delta *rT*rT/6); % s/mm^2
end
function [M]= M0(G,dT)
t=(0:1:(length(G)-1))*dT;
M=cumsum(G)*dT;
end
function [M]= M1(G,dT)
t=(0:1:(length(G)-1))*dT;
M=cumsum(G.*t')*dT;
end
function [M]= M2(G,dT)
t=(0:1:(length(G)-1))*dT;
M=cumsum(G.*t'.*t')*dT;
end
function [M]= M3(G,dT)
t=(0:1:(length(G)-1))*dT;
M=cumsum(G.*t'.*t'.*t')*dT;
end
function [M]= MomentN(G,dT,N)
t=(0:1:(length(G)-1))*dT;
M=cumsum(G.*(t.^N)')*dT;
end
function [M0,M1,M2,M3]= Moment(G,dT)
M0=Waveform_ToolBox.M0(G,dT);
M1=Waveform_ToolBox.M1(G,dT);
M2=Waveform_ToolBox.M2(G,dT);
M3=Waveform_ToolBox.M3(G,dT);
end
% function [M0]=M0iter( G, G2, t0, t1, mode)
%
% t=t1-t0;
% if(mode==1) %'RampUp'
%
% M0=(G2*t/2);
%
% elseif(mode==2) %'FlapTop'
%
% M0=(G*t);
%
% elseif(mode==3) %'RampDown'
%
% M0= G*t/2;
%
% elseif(mode==4) %'BridGe'
%
% M0= t*(G+G2)/2;
%
% else
%
% M0= 0.0;
%
% end
% end
%
% function [M1]=M1iter( G, G2, t0, t1, mode, scale)
%
% t=t1-t0;
% if(mode==1) %'RampUp'
%
% M1=(G2*t*t/3+scale*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% elseif(mode==2) %'FlapTop'
%
% M1=(G*t*t/2+scale*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% elseif(mode==3) %'RampDown'
%
% M1=(G*t*t/6+scale*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% elseif(mode==4) %'BridGe'
%
% M1=(t*t*(G/6+G2/3)+scale*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% else
% M1=0.0;
% end
% end
%
% function [M2]=M2iter(G, G2,t0, t1,mode,scale)
%
% t=t1-t0;
% if(mode==1) %'RampUp'
%
% M2=(G2*t*t*t/4+scale*2*t0*Waveform_ToolBox.M1iter(G,G2,0,t,mode,0)+scale*t0*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% elseif(mode==2) %'FlapTop'
%
% M2=(G*t*t*t/3+scale*2*t0*Waveform_ToolBox.M1iter(G,G2,0,t,mode,0)+scale*t0*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% elseif(mode==3) %'RampDown'
%
% M2=(G*t*t*t/12+scale*2*t0*Waveform_ToolBox.M1iter(G,G2,0,t,mode,0)+scale*t0*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% elseif(mode==4) %'BridGe'
%
% M2=(t*t*t*(G/12+G2/4)+scale*2*t0*Waveform_ToolBox.M1iter(G,G2,0,t,mode,1/2)+scale*t0*t0*Waveform_ToolBox.M0iter(G,G2,0,t,mode));
%
% else
% M2=0;
% end
% end
function [M0]=M0iter(G1, G2,t0,t1)
t=t1-t0;
M0=Waveform_ToolBox.Mniter_0(G1, G2,t,0);
end
function [M1]=M1iter(G1, G2,t0,t1)
t=t1-t0;
M1=Waveform_ToolBox.Mniter_0(G1, G2,t,0)*t0+Waveform_ToolBox.Mniter_0(G1, G2,t,1);
end
function [M2]=M2iter(G1, G2,t0,t1)
t=t1-t0;
M2=Waveform_ToolBox.Mniter_0(G1, G2,t,0)*t0^2+2*Waveform_ToolBox.Mniter_0(G1, G2,t,1)*t0+Waveform_ToolBox.Mniter_0(G1, G2,t,2);
end
function [M3]=M3iter(G1, G2,t0,t1)
t=t1-t0;
M3=Waveform_ToolBox.Mniter_0(G1, G2,t,0)*t0^3+3*Waveform_ToolBox.Mniter_0(G1, G2,t,1)*t0^2+3*Waveform_ToolBox.Mniter_0(G1, G2,t,2)*t0+Waveform_ToolBox.Mniter_0(G1, G2,t,3);
end
function [M4]=M4iter(G1, G2,t0,t1)
t=t1-t0;
M4=Waveform_ToolBox.Mniter_0(G1, G2,t,0)*t0^4+4*Waveform_ToolBox.Mniter_0(G1, G2,t,1)*t0^3+6*Waveform_ToolBox.Mniter_0(G1, G2,t,2)*t0^2+4*Waveform_ToolBox.Mniter_0(G1, G2,t,3)*t0^3+Waveform_ToolBox.Mniter_0(G1, G2,t,4);
end
function [Mn]=Mniter_0(G1, G2,t,n)
Mn=t^(n+1)*(G1/(n+1)+G2)/(n+2);
end
function [M0,M1,M2,M3,M4] = Momentiter(Dn,Gn,Rt)
t0=0;
t1=0;
M0=0;
M1=0;
M2=0;
M3=0;
M4=0;
for cpt=1:1:length(Dn)
if Dn(cpt)>0 && Dn(cpt)>2*Rt && Gn(cpt)~=0 % Trapezoid
t0=t1;
t1=t0+Rt; % RampUp
G0=0;
G1=Gn(cpt);
M0=M0+Waveform_ToolBox.M0iter(G0,G1,t0,t1);
M1=M1+Waveform_ToolBox.M1iter(G0,G1,t0,t1);
M2=M2+Waveform_ToolBox.M2iter(G0,G1,t0,t1);
M3=M3+Waveform_ToolBox.M3iter(G0,G1,t0,t1);
M4=M4+Waveform_ToolBox.M4iter(G0,G1,t0,t1);
t0=t1;
t1=t0+Dn(cpt)-2*Rt; % Flaptop
G0=Gn(cpt);
G1=Gn(cpt);
M0=M0+Waveform_ToolBox.M0iter(G0,G1,t0,t1);
M1=M1+Waveform_ToolBox.M1iter(G0,G1,t0,t1);
M2=M2+Waveform_ToolBox.M2iter(G0,G1,t0,t1);
M3=M3+Waveform_ToolBox.M3iter(G0,G1,t0,t1);
M4=M4+Waveform_ToolBox.M4iter(G0,G1,t0,t1);
t0=t1;
t1=t0+Rt; % RampDown
G0=Gn(cpt);
G1=0;
M0=M0+Waveform_ToolBox.M0iter(G0,G1,t0,t1);
M1=M1+Waveform_ToolBox.M1iter(G0,G1,t0,t1);
M2=M2+Waveform_ToolBox.M2iter(G0,G1,t0,t1);
M3=M3+Waveform_ToolBox.M3iter(G0,G1,t0,t1);
M4=M4+Waveform_ToolBox.M4iter(G0,G1,t0,t1);
elseif Dn(cpt)>0 && Dn(cpt)<=2*Rt && Gn(cpt)~=0 % Triangle
Ampl=Gn(cpt)*Dn(cpt)/Rt/2;
t0=t1;
t1=t0+Dn(cpt)/2; % RampUp
G0=0;
G1=Gn(cpt);
M0=M0+Waveform_ToolBox.M0iter(G0,G1,t0,t1);
M1=M1+Waveform_ToolBox.M1iter(G0,G1,t0,t1);
M2=M2+Waveform_ToolBox.M2iter(G0,G1,t0,t1);
M3=M3+Waveform_ToolBox.M3iter(G0,G1,t0,t1);
M4=M4+Waveform_ToolBox.M4iter(G0,G1,t0,t1);
t0=t1;
t1=t0+Dn(cpt)/2; % RampDown
G0=Gn(cpt);
G1=0;
M0=M0+Waveform_ToolBox.M0iter(G0,G1,t0,t1);
M1=M1+Waveform_ToolBox.M1iter(G0,G1,t0,t1);
M2=M2+Waveform_ToolBox.M2iter(G0,G1,t0,t1);
M3=M3+Waveform_ToolBox.M3iter(G0,G1,t0,t1);
M4=M4+Waveform_ToolBox.M4iter(G0,G1,t0,t1);
else % Blank
% zero
t0=t1;
t1=t0+Dn(cpt); % Flaptop
G0=0;
G1=0;
M0=M0+Waveform_ToolBox.M0iter(G0,G1,t0,t1);
M1=M1+Waveform_ToolBox.M1iter(G0,G1,t0,t1);
M2=M2+Waveform_ToolBox.M2iter(G0,G1,t0,t1);
M3=M3+Waveform_ToolBox.M3iter(G0,G1,t0,t1);
M4=M4+Waveform_ToolBox.M4iter(G0,G1,t0,t1);
end
end
end
% function [Ed_rsp]= EddyCurrent2(G,dT,lambda)
% Ed_rsp=[];
% N_lam = 200;
% all_lam = linspace(1e-4,lambda,N_lam);
% all_e = zeros(1, N_lam);
% ii = 1;
% for lam = all_lam
% lam_s = lam * 1.0e-3;
% r = diff(exp(-[1:numel(G)+1].*dT./lam_s));
% r = r(end:-1:1);
% e = dot(r,G);
% all_e(ii) = e;
% ii = ii + 1;
% end
%
% if all_e(2) < 0
% all_e = -all_e;
% end
% end
function [Ed_rsp]= EddyCurrent(G,dT,lambda)
t=(0:1:length(G)-1)*dT;
dG=diff(G);
dG=[0; dG];
% calculate time course of eddy currents for chosen lambda
% eddy_response = exp(-(1:length(dGdt))/(LAMBDA0*(1e-3)/dt));
% eddy_plot = conv(dGdt,eddy_response);
% eddy_plot = eddy_plot(1:n);
dExpL=exp(-t./lambda)';
Ed_rsp=conv(dG,dExpL);
Ed_rsp=Ed_rsp(1:length(G));
end
function [Ed_rsp]= EddySprectrum(G,dT,lam_vect)
Ed_rsp=[];
for cpt=1:1:length(lam_vect)
Ed_rsp(:,cpt)=Waveform_ToolBox.EddyCurrent(G,dT,lam_vect(cpt)) ;
end
end
function [Stm]= PNS(G,dT)
alpha = 0.333;
r = 23.4;
c = 334e-6;
Smin = 60;
coeff = zeros(numel(G), 1);
for cpt = 1:(numel(G))
coeff(cpt) = ( c / ((c + dT*(numel(G)-1) - dT*(cpt-1))^2.0) / Smin );
end
Stm = zeros(numel(G), 1);
for cpt2 = 1:(numel(G)-2)
ss = 0;
for cpt = 1:(cpt2+1)
ss = ss + coeff( numel(coeff)-cpt2+cpt-1 ) * (G(cpt+1)-G(cpt));
end
Stm(cpt2) = ss;
end
end
function [G,t]= Balanced_Factory(Dn,Gn,Rt,dT,Bval)
%%% Build a Structure with all the information we need
[GM] = Waveform_ToolBox.BuildGStruct(Dn,Gn,Rt)
[GM, M0b, M0a] =Waveform_ToolBox.Balancer(GM);
RTfunction=@(t)t/Rt;
%%% Generate a vector of gradient
[G_tmp] = Waveform_ToolBox.GStruct2GVect(GM,RTfunction);
G=G_tmp(1:dT:end); % T/m
t=1:dT: GM(end).StopTime;
if ~(nargin<5||isempty(Bval))
b_fact=Waveform_ToolBox.Bcalc(G,dT);
Ampl=sqrt(Bval./b_fact); % mT/m
G=repmat(G,1,length(Ampl)).*Ampl;
end
end
function [Dn,Gn]= Revert_Factory(G,Rt,dT)
% This function is a copy paste (converted to matlab) to the code
% implemented in the sequence to estimate the gradient from the waveform vector.
% If it buggy here the sequence is too.
Dn=[];
Gn=[];
cpt_gr=1;
Save_Grad=[];
Grad_tmp=[];
Grad_tmp_n=[];
Grad_tmp_z=[];
trig=false;
trig_n=false;
trig_z=false;
dMaxG=0;
MaxAmpl=max(abs(G));
for cpt=1:1:length(G)
dNegG=0;
dPosG=0;
if G(cpt)>0
dPosG=1;
elseif G(cpt)<0
dNegG=1;
end
if abs(G(cpt))>dMaxG
dMaxG=abs(G(cpt));
end
% ////////// Positive Gradient ////////////
if (~trig)&&(dPosG~=0) %%% Rampup from 0
Grad_tmp.dStart=(cpt-1)*dT;
trig=true;
end
if (trig&&(dPosG==0||cpt==length(G))) %%% End of pulse
Grad_tmp.dStop=(cpt-1)*dT;
Grad_tmp.lSign=1;
Grad_tmp.dAmpl=1;
Grad_tmp.dDuration=Grad_tmp.dStop-Grad_tmp.dStart;
% Grad_tmp.lDuration_us=fSDSRoundDownGRT(static_cast<long>(Grad_tmp.dDuration*1e6));
Grad_tmp.lRampTime=Rt;
if(Grad_tmp.dDuration<(2*Rt)) % Triangle case
Grad_tmp.dAmpl=dMaxG/MaxAmpl;
%Grad_tmp.lRampTime=fSDSRoundDownGRT(Grad_tmp.lDuration_us/2);
end
Save_Grad(cpt_gr).grad=Grad_tmp;
cpt_gr=cpt_gr+1;
Grad_tmp=[];
trig=false;
dMaxG=0;
end
% ////////// Negative Gradient ////////////
if ((~trig_n)&&(dNegG~=0)) %%% Rampup from 0
Grad_tmp_n.dStart=(cpt-1)*dT;
trig_n=true;
end
if (trig_n&&(dNegG==0||cpt==length(G))) %%% End of pulse
Grad_tmp_n.dStop=(cpt-1)*dT;
Grad_tmp_n.lSign=-1;
Grad_tmp_n.dAmpl=-1;
Grad_tmp_n.dDuration=Grad_tmp_n.dStop-Grad_tmp_n.dStart;
%Grad_tmp_n.lDuration_us=fSDSRoundDownGRT(static_cast<long>(Grad_tmp_n.dDuration*1e6));
Grad_tmp_n.lRampTime=Rt;
if(Grad_tmp_n.dDuration<(2*Rt))
Grad_tmp_n.dAmpl=-dMaxG/MaxAmpl;
%Grad_tmp_n.lRampTime=fSDSRoundDownGRT(Grad_tmp_n.lDuration_us/2);
end
Save_Grad(cpt_gr).grad=Grad_tmp_n;
cpt_gr=cpt_gr+1;
Grad_tmp_n=[];
trig_n=false;
dMaxG=0;
end
% ////////// Fill Time ////////////
if (~trig_z)&&(dNegG==0)&&(dPosG==0) %%% Trig 0
Grad_tmp_z.dStart=(cpt-1)*dT;
trig_z=true;
end
if trig_z&&(trig_n||trig||cpt==length(G)) %%% End of fill time
Grad_tmp_z.dStop=(cpt-1)*dT;
Grad_tmp_z.lSign=0;
Grad_tmp_z.dAmpl=0;
Grad_tmp_z.dDuration=Grad_tmp_z.dStop-Grad_tmp_z.dStart;
Save_Grad(cpt_gr).grad=Grad_tmp_z;
cpt_gr=cpt_gr+1;
Grad_tmp_z=[];
trig_z=false;
end
end
%%%% Save into the struct format
for cpt_g=1:1:length(Save_Grad)
Dn=[Dn; Save_Grad(cpt_g).grad.dDuration];
Gn=[Gn; Save_Grad(cpt_g).grad.dAmpl];
end
end
function [G,t]= Factory(Dn,Gn,Rt,dT,Bval,RTfunction)
% This function build a waveform base on the timing and in mT/m
% dT in us
% This give a b-value in in s/mm^2
%
%
%
% Example :
%
% Dn=[7000 273000 7000]; % us
% Gn=[1 0 -1]; % Normalized or mT/m
% RampTime=1520; % us
% dT=10; % us
% Bval=[200 350]; % s/mm^2
% RTfunction=@(t)(1 -1*exp(-0.002*t-0.000001*t.*t-0.000000001*t.*t.*t));
%
% [G,t]= Waveform_ToolBox.Factory(Dn,Gn,RT,dT,Bval,RTfunction);
%
%%% The user can define it's own Ramp function, otherwise linear %%%
if nargin<6 || isempty(RTfunction)
RTfunction=@(t)t/Rt;
end
%%% Build a Structure with all the information we need
[GM] = Waveform_ToolBox.BuildGStruct(Dn,Gn,Rt);
%%% Generate a vector of gradient
[G_tmp] = Waveform_ToolBox.GStruct2GVect(GM,RTfunction);
G=G_tmp(1:dT:end); % mT/m
t=1:dT: GM(end).StopTime;
if ~(nargin<5||isempty(Bval))
b_fact=Waveform_ToolBox.Bcalc(G,dT);
Ampl=sqrt(Bval./b_fact); % mT/m
G=repmat(G,1,length(Ampl)).*Ampl;
end
end
function [G,t]= Factory2(Dn,Gn,Rst,Rt,dT,Bval,RTfunction)
% This function build a waveform base on the timing and in mT/m
% dT in us
% This give a b-value in in s/mm^2
%
%
%
% Example :
%
% Dn=[7000 273000 7000]; % us
% Gn=[1 0 -1]; % Normalized or mT/m
% RampTime=1520; % us
% dT=10; % us
% Bval=[200 350]; % s/mm^2
% RTfunction=@(t)(1 -1*exp(-0.002*t-0.000001*t.*t-0.000000001*t.*t.*t));
%
% [G,t]= Waveform_ToolBox.Factory(Dn,Gn,RT,dT,Bval,RTfunction);
%
%%% The user can define it's own Ramp function, otherwise linear %%%
if nargin<7 || isempty(RTfunction)
RTfunction=@(t)t/Rt;
end
%%% Build a Structure with all the information we need
[GM] = Waveform_ToolBox.BuildGStruct(Dn,Gn,Rt);
%%% Generate a vector of gradient
[G_tmp] = Waveform_ToolBox.GStruct2GVect(GM,RTfunction);
G1=G_tmp(1:dT:end); % mT/m
%%% Regenare only the relevant gradients
Dn2=Dn(find(Rst));
Gn2=Gn(find(Rst));
[GM] = Waveform_ToolBox.BuildGStruct(Dn2,Gn2,Rt);
%%% Generate a vector of gradient
[G_tmp] = Waveform_ToolBox.GStruct2GVect(GM,RTfunction);
G=G_tmp(1:dT:end); % mT/m
t=1:dT: GM(end).StopTime;
if ~(nargin<6||isempty(Bval))
b_fact=Waveform_ToolBox.Bcalc(G1,dT);
Ampl=sqrt(Bval./b_fact); % mT/m
G=repmat(G,1,length(Ampl)).*Ampl;
end
end
function [GM] = BuildGStruct(Dn,Gn,Rt)
tmp_time=0;
GM=[];
for cpt=1:1:length(Dn)
if Dn(cpt)>0 && Dn(cpt)>2*Rt % Trapezoid
GM(cpt).StartTime=tmp_time;
GM(cpt).RampTime=Rt;
GM(cpt).FlapTop=Dn(cpt)-2*GM(cpt).RampTime;
GM(cpt).StopTime=GM(cpt).StartTime+GM(cpt).FlapTop+2*GM(cpt).RampTime;
GM(cpt).EffectiveTime=GM(cpt).FlapTop+GM(cpt).RampTime;
GM(cpt).Ampl=Gn(cpt);
tmp_time=GM(cpt).StopTime;
elseif Dn(cpt)>0 && Dn(cpt)<=2*Rt % Triangle
GM(cpt).StartTime=tmp_time;
GM(cpt).RampTime=Dn(cpt)/2;
GM(cpt).FlapTop=0;
GM(cpt).StopTime=GM(cpt).StartTime+GM(cpt).FlapTop+2*GM(cpt).RampTime;
GM(cpt).EffectiveTime=GM(cpt).FlapTop+GM(cpt).RampTime;
GM(cpt).Ampl=Gn(cpt)*GM(cpt).RampTime/Rt;
tmp_time=GM(cpt).StopTime;
else % Blank
GM(cpt).StartTime=tmp_time;
GM(cpt).RampTime=0;
GM(cpt).FlapTop=0;
GM(cpt).StopTime=GM(cpt).StartTime;
GM(cpt).EffectiveTime=0;
GM(cpt).Ampl=0;
end
end
end
function [G] = GStruct2GVect(GM,RTfunction)
G=zeros(round(GM(end).StopTime),1);
for cpt=1:1:length(GM)
if GM(cpt).EffectiveTime~=0
t1=GM(cpt).StartTime+1;
t2=GM(cpt).StartTime+GM(cpt).RampTime;
%G(t1:1:t2)=GM(cpt).Ampl*RTfunction(1:1:GM(cpt).RampTime); % Ramp1
G(t1:1:t2)=GM(cpt).Ampl*RTfunction(1:1:GM(cpt).RampTime)./RTfunction(GM(cpt).RampTime); % Ramp1
t1=t2+1;
t2=t2+GM(cpt).FlapTop;
G(t1:1:t2)=GM(cpt).Ampl; % G
t1=t2+1;
t2=t2+GM(cpt).RampTime;
G(t1:1:t2)=GM(cpt).Ampl*RTfunction(GM(cpt).RampTime:-1:1)./RTfunction(GM(cpt).RampTime); % Ram
%G(t1:1:t2)=GM(cpt).Ampl*(RTfunction(GM(cpt).RampTime:-1:1)); % Ramp1
end
end
end
function [GM,M0b,M0a] = Balancer(GM)
%Todo
M0b=0;
M0a=0;
for cpt=1:1:length(GM)
M0b=M0b+(GM(cpt).FlapTop+GM(cpt).RampTime)*GM(cpt).Ampl;
end
M0b
for cpt=1:1:length(GM)
if (GM(cpt).Ampl>0)
if M0b>0
GM(cpt).Ampl=GM(cpt).Ampl-M0b/(GM(cpt).FlapTop+GM(cpt).RampTime);
break;
end
elseif (GM(cpt).Ampl<0)
if M0b<0
GM(cpt).Ampl=GM(cpt).Ampl-M0b/(GM(cpt).FlapTop+GM(cpt).RampTime);
break;
end
end
end
for cpt=1:1:length(GM)
M0a=M0a+(GM(cpt).FlapTop+GM(cpt).RampTime)*GM(cpt).Ampl;
end
M0a
end
function [G,Bmax, TEmin]=WaveformTEMin(Btarget, T90,T180,TEepi,Rt,Gmax,dT,Type)
% Find the TE by bisection, we stop when we have the b-value
% +/- 10
eps=10; % bvalue
err=999999999;
TE1=30000;
TE2=250000;
% TE_prev1=TE1;
% TE_prev2=TE2;
% itermax=1000;
% iter=1;
% tmpTE=[];
% tmpb=[];
% while (err >= eps)&(iter<=itermax)
%
%
% [~, b1]= Waveform_ToolBox.WaveformComposer(TE1,T90,T180,TEepi,Rt,Gmax,dT,Type) ;
% [~, b2]= Waveform_ToolBox.WaveformComposer(TE2,T90,T180,TEepi,Rt,Gmax,dT,Type) ;
%
% if abs(b1-Btarget)>abs(b2-Btarget) % change the low limit
% TE1=TE1+abs(TE2-TE1)/4;
% err=abs(b2-Btarget);
% TEmin=TE2;
% else % change the high limit
% TE2=TE2-abs(TE2-TE1)/4;
% err=abs(b1-Btarget);
% TEmin=TE1;
% end
% iter=iter+1;
% end
% [G, Bmax]= Waveform_ToolBox.WaveformComposer(TEmin,T90,T180,TEepi,Rt,Gmax,dT,Type) ;
tmpTE=linspace(0,TE2,100);
for cpt=1:1:100
[G, Bmax]= Waveform_ToolBox.WaveformComposer(tmpTE(cpt),T90,T180,TEepi,Rt,Gmax,dT,Type) ;
tmpb(cpt)=Bmax;
end
idx=find(tmpb~=0);
TEmin = interp1(tmpb(idx),tmpTE(idx),Btarget);
TEmin=ceil(TEmin/10)*10; % round to dT=10;
[G, Bmax]= Waveform_ToolBox.WaveformComposer(TEmin,T90,T180,TEepi,Rt,Gmax,dT,Type) ;
% figure,plot(tmpb,tmpTE);
end
function [G,Bmax]=WaveformComposer(TE,T90,T180,TEepi,Rt,Gmax,dT,Type,Bval,RTfunction)
lt = ceil( (TE/2 - T180/2 - max(T90, TEepi)) /10 )*10 ;
FillPre=TE/2- T90 - T180/2 -lt;
FillPost=TE/2- TEepi - T180/2 -lt;
Delta=lt+FillPre+T180+FillPost;
[FillPre FillPost Delta];
if Type==1 % AMC
[D1 D2]=Waveform_ToolBox.M2Solver(Delta,lt,Rt);
Dn=[T90 D1 D2 FillPre T180 FillPost D2 D1];
Gn=[0 Gmax -Gmax 0 0 0 Gmax -Gmax ];
elseif Type==2 %Bip
Dn=[T90 lt/2 lt/2 FillPre T180 FillPost lt/2 lt/2];
Gn=[0 Gmax -Gmax 0 0 0 -Gmax Gmax ];
elseif Type==3 % AMC inv
[D1 D2]=Waveform_ToolBox.M2Solver(Delta,lt,Rt);
Dn=[T90 D2 D1 FillPre T180 FillPost D1 D2];
Gn=[0 Gmax -Gmax 0 0 0 Gmax -Gmax ];
else %Mono
Dn=[T90 lt FillPre T180 FillPost lt];
Gn=[0 Gmax 0 0 0 -Gmax ];
end
if nargin<9 || isempty(Bval)
Bval=[];
end
if nargin<10 || isempty(RTfunction)
RTfunction=@(t)t/Rt;
end
[G,t]= Waveform_ToolBox.Factory(Dn,Gn,Rt,dT,Bval,RTfunction);
Bmax =Waveform_ToolBox.Bcalc(G,dT);
end
function [D1 D2]=M2Solver(Delta,lt,rt)
dT=10;
Ratio=999999999;
Delt2=0;
check=0;
for Delt1=0:dT:lt/2
Delt2=Delt1*(Delta-rt)/(Delta+rt-2*Delt1);
if(Ratio>abs((Delt1+Delt2)-lt))
Ratio= abs((Delt1+Delt2)-lt);
D1=Delt1;
D2=Delt2;
check=1;
end
end
if check
D2=ceil(D2/dT)*dT;
else
D2=0;
D1=0;
end
end
function [G]=EPIComposer(n,G,D,rt)
sign =1;
Dn=[];
Gn=[];
for cpt=1:1:n
if mod(cpt,2)==0 % Even
sign=1;
else % Odd
sign=-1;
end
Dn=[Dn D];
Gn=[Gn sign*G];
end
%%% Build a Structure with all the information we need
[GM] = Waveform_ToolBox.BuildGStruct(Dn,Gn,rt);
RTfunction=@(t)t/rt;
G=Waveform_ToolBox.GStruct2GVect(GM,RTfunction);
end
end
end