Illustrations on MRI Techniques Using Matlab - Digital Signal Processing for Medical Imaging Using Matlab - page 48

3.1.1 Proton-Density MRI Imaging

Let the image slice be represented as the matrix with the values filled up with proton-
density is as follows.

⎡
⎣

⎤
⎦

33979586994
559109551 7 910
69612992 6 9 6
56227822292
981109587101 5
61247378 1 3 9
99765479 034
53298946 5107
4138295109 4 6
59644217 8 9 7
48578314984

=

n

These are the magnitude of the resultant magnetic moment at t 0 (refer Fig. 3.4 ).

The following steps are followed to obtain the K-space corresponding to the proton-
density image. The identical transverse components are assumed to be available at
every pixel of the image slice, i.e. they are in-phase and are rotating in the Larmor
frequency.

=

1. Apply G y gradient for the duration of 0.0000000009.
2. Apply

G x gradient for the duration of 0.0000000009.
3. Apply G x gradient for the duration of 0.0000000018. During this phase, after the
time duration of 0.0000000009, there is the cancellation of phase introduced due
to G x . This is known as Gradient echo. This helps to synchronize the hardware
to sample at the particular instant during real time to choose the proper position
in the K-space.
4. Sample the real and imaginary component of the signal s

−

( t ) to obtain the sample

.
5. Proper scaling factor is used so that the final basis (to perform IFFT2) look like
the standard form e − j 2 π xG x

of the K-space at ( G x , G y )

e − j 2 π yG y

11 . This is the process of discretization.
6. The above steps are repeated for the complete scan in the K-space. For every
time, we have to wait for the longitudinal component to reach maximum before
applying 90 ◦ RF pulse. (This is illustrated by repeating the steps 1-5 by varying
the values of G x and G y ranging from

11

− 5 to 5 with the interval of 1.)

The resultant KSPACE is obtained as follows.