Illustrations on MRI Techniques Using Matlab - Digital Signal Processing for Medical Imaging Using Matlab - page 51

KSPACE(Gx+6,Gy+6)=KSPACE(Gx+6,Gy+6)+temp3(x+1,y+1,i);

end
end

end
end
end

KSPACEREARRANGED=KSPACE(6:1:11,6:1:11);
KSPACEREARRANGED=[KSPACEREARRANGED KSPACE(6:1:11,1:1:5)];
KSPACEREARRANGED=[KSPACEREARRANGED; KSPACE(1:1:5,6:1:11) KSPACE(1:1:5,1:1:5) ];
RECONSTRUCTED=ifft2(KSPACEREARRANGED)
%Hence the measured image is the proton density image.

3.2 Illustrtion on the Steps Involved in Obtaining the T 2 MRI
Image Using Cartesian Scanning

Let the image slice be represented as the matrix with the values filled up with proton-
density (number of individual magnetic moments available at every pixel) is as
follows.

⎡
⎣

⎤
⎦

3593 74721033
8553 9162949
8394 2365366
38497647689
7876 2687857
29687347663
7624 7771722
43551292636
769108948845
431210289257
75425488538

=

n

Every magnetic moments at every pixel are assumed to be identical (magnitude and
phase) at t 0. Initial phase of every individual magnetic moments are assumed

to be identically equal to K

=

2. Individual magnetic moments of every pixel
undergoes phase change, which varies linearly as 2

= 0 .

π k ( x , y , i ) t , where k ( x , y , i ) is

the linear phase constant associated with i th magnetic moment at the position .

Phase constants of the individual magnetic moments at every pixel are illustrated in
the Fig. 3.2 . Every subplot of the Fig. 3.2 belongs to the individual pixel. For instant
(

( x , y )

1 , 1 ) subplot corresponds to ( 1 , 1 ) pixel. The phase constants associated with the

three (note that n ( 1 , 1 ) = 3) individual magnetic moments at the position ( 1 , 1 ) is

shown as the three stems in the subplot ( 1 , 1 ) . The following steps are followed to

obtain T 2 image.

1. Apply G y gradient for the duration of 0.1.
2. Apply G x gradient for the duration of 0.1.