Illustrations on MRI Techniques Using Matlab - Digital Signal Processing for Medical Imaging Using Matlab - page 50

In this procedure, it is noted that at the time of sampling the K-space, there is no
significant dephasing experienced by the individual magneticmoments at every pixel.
Hence the reconstructed imagemainly contributes the proton-density at every pixel. It
is observed from the matrix FINALPROTONDENSITYIMAGE that the pixel values
are exactly the number of individual magnetic moments ( n ) at every pixel

( x , y ) .This

type of MRI imaging technique is known as proton-density MRI imaging.

3.1.1.1 protondensity.m

siz=11;
K=0.2; %Initial phase
Mxyit=[];
gamma=2*pi*42.58*(10ˆ6);
d1=((10ˆ3)/(11*42.58*(10ˆ6)*0.0000000009));
d2=((10ˆ3)/(11*42.58*(10ˆ6)*0.0000000009));
B0=1;
n=round(rand(siz,siz)*9+1);
for x=1:1:siz
for y=1:1:siz
for i=1:1:n(x,y)
k(x,y,i)=rand*2-1;
end

end

end
KSPACE=zeros(11,11);
for Gx=-5:1:5;
for Gy=-5:1:5;
Gy1=Gy/(10ˆ3);%This is to indicate that B0 is high compared with y-gradient
Gx1=Gx/(10ˆ3);%This is to indicate that B0 is high compared with x-gradient
for x=0:1:siz-1
for y=0:1:siz-1
for i=1:1:n(x+1,y+1)
phi1=k(x+1,y+1,i)*0.0000000009*2*pi;
%The magnetic moments after applying y-gradient for the duration of
%0.0000000009
temp1(x+1,y+1,i)=exp(-j*((B0*gamma+gamma*y*d2*Gy1)*0.0000000009-phi1+K));
%The magnetic moments after applying x-gradient for the duration of
%0.0000000009 after applying the y-gradient for the duration of
%0.0000000009
phi2=k(x+1,y+1,i)*0.0000000009*2*pi;
temp2(x+1,y+1,i)=exp(-j*((B0*gamma+d2*gamma*y*Gy1)*0.0000000009-phi1+K))...
*exp(-j*((B0*gamma-gamma*d1*x*Gx1)*0.0000000009-phi2));
%The magnetic moments after applying x-gradient for the duration of
%0.0000000018 after applying the y-gradient for the duration of
%0.0000000009 and negative x-gradient for the duration of 0.0000000009
phi3=k(x+1,y+1,i)*0.0000000018*2*pi;
temp3(x+1,y+1,i)=exp(-j*((B0*gamma+gamma*d2*y*Gy1)*0.0000000009-phi1+K))...
*exp(-j*((B0*gamma-gamma*d1*x*Gx1)*0.0000000009-phi2))*...
exp(-j*((B0*gamma+gamma*d1*x*Gx1)*0.0000000018-phi3));
end
end
end

for x=0:1:siz-1
for y=0:1:siz-1
for i=1:1:n(x+1,y+1)