Magnetic Resonance Imaging - Digital Signal Processing for Medical Imaging Using Matlab - page 45

gradient. But what we achived is the sampled value gives the information about
T 2 ( . (refer Sect. 3.2 ) for illustration.

10. Note that the sampled value corresponds to

x , y )

( G x , − G y ) , not ( G x , G y ) .

2.8.3 T 2 MRI Image Using Spin-Echo and Polar Scanning

1. Steps 1-3 are performed similar to the technique mentioned in the Sect. 2.8.1 .
2. Thus the currently obtained transverse component is given by

t
T 2 ( x , y )

−

e j ( − γ( B 0 )τ p + φ) e j ( − γ( B 0 ) t ) e M xy ( x , y , t ) = 2 M 0 sin (α τ p / 2 ) .

3. Apply both G x and G y gradient simulataneously for the time duration τ xy , so that

the transverse components become the following.

e j ( − γ( B 0 )τ p + φ) e j ( − γ( B 0 + G y y + G x x )τ xy ) M xy ( x , y , t ) = 2 M 0 sin (α τ p / 2 )

e j ( − γ( B 0 t )) e − ( t + τ xy ) ×

T 2 ( x , y )

4. The technique used in the steps 4-7 of the Sect. 2.8.2 are adopted.
5. Read-out phase starts immediate after some time (required time for rephasing)
after applying 180 ◦ pulse along with the positive x -gradient G x and positive y -
gradient G y for the duration of τ xy . The resultant transverse component during

read-out phase is given as

e j ( + γ( B 0 )τ p − φ n ( x , y , t ))

M xy ( x , y , t , n ) = 2 M 0 sin (α τ p / 2 )

n n

e j ( + γ( B 0 + G x x + G y y )τ xy ) e j ( − γ(( B 0 + G x x + G y y ) t )) . ×

6. After time duration of τ xy , there is the cancellation of the phase introduced due to

G x and G y gradient (upto step 4). This is gradient echo. This helps to synchronize
the hardware to sample the magnitude of s ( t ) at the end of the reading phase

2 τ x corresponding to the particular location in the K-space. This step is same as

that of the one used in phase gradient. But what we achived is the sampled value
gives the information about T 2 (

. (refer Sect. 3.3 ) for illustrations.
7. Note that the sample value corresponds to the point

x , y )

.
8. This is the polar version of the technique used in Sect. 2.8.2 . The main difference
is that the gradients are applied simultaneously. Also the value of G x and G y are
changed in such a way that the samples of the k-space (frequen cy domian ) are
uniformly scanned over the variables r and

( − G x , − G y )

G x + G y ) θ , where r = ( and

tan − 1 G y

G x .

θ =