Magnetic Resonance Imaging - Digital Signal Processing for Medical Imaging Using Matlab - page 43

9. The steps 1-7 are repeated for the complete range of G x and G y (refer Sect. 2.7 )
and hence discrete MRI image in the frequency domain is obtained.
10. Apply the inverse 2D-DFT to obtain MRI image. The image thus obtained cor-
responds to proton-density image. This gives the proton-density (refer Sect. 3.1
for illustration) of every pixel of the image slice.

2.8.2 T 2 MRI Image Using Spin-Echo and Carteisian Scanning

T 2 MRI principles are explained with the micro-level behaviour of the randomly ori-
ented individual magneticmoments (with various rate at which the phase is changing)
at every point ( x , y ) across the slice. Due to the slice selection (along the z -axis) by
applying the z -gradient, followed by RF exitation and refocussing gradient we are
able to obtain the in-phase resultant magnetic moment making an angle

with the
z -axis (measured anti-clockwise when viewed along the z -axis). The corresponding
transverse component is making an angle

α

φ

with the x -axis (measured anti-clockwise

when viewed along the z -axis).
The individual magnetic moments at the particular position

( , )

after the release
of RF exitation, starts to experience different phase (even though it was made inphase
due to external RF exitation). This is the natural phenomenon due to spin-spin
interaction. The phase achived by the individul magnetic moment over the time helps
in decreasing the resultant transverse component. The rate at whcich the the phase
of the individual magnetic moment is changing purely depends on the tissue. The
rate at which the resultant transverse magnetic moment is decreasing is described
by the factor T 2 (

x y

plays the important role in knowing the
characteristics of the tissue and hence image is obtained. But in practice the rate at
which the resultant transverse component is characterized by the factor T 2 .Even
after the transverse component becomes zero due to the factor T 2 , the dephasing
operation still continuos. This leads to the technique called spin echo (described
below) to obtain the non-zero transverse component, (even after reaching zero due
to T 2 ). This in further helps to obtain the frequency sample of the MRI image
highlighting the T 2 values as described below.
1. Steps 1-4 are performed similar to the technique mentioned in the Sect. 2.8.1 .
2. Thus the currently obtained transverse component is given by
M xy (

x , y ) and hence T 2 ( x , y )

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

T 2 ( x , y ) .

3. Apply the G x gradient for the duration of τ x , so that the transverse component

e j ( − γ( B 0 )τ p + φ) e j ( − γ( B 0 + G y y )τ y ) ...

becomes (2.65). M xy ( x , y , t ) = 2 M 0 sin (α τ p / 2 )

e j ( − γ( B 0 + G x x )τ x ) e j ( − γ( B 0 t )) e − ( t + τ y + τ x ) (2.64)

T 2 ( x , y )

It is assumed that there is no significant change in α value.