Illustrations on MRI Techniques Using Matlab - Digital Signal Processing for Medical Imaging Using Matlab - page 47

Chapter 3
Illustrations on MRI Techniques
Using Matlab

3.1 Illustration on the Steps Involved in Obtaining
Proton-Density MRI Image

Let the image slice in the z-direction is selected and 90 ◦ RF pulse is applied.
Refocussing gradient is also applied to compensate the phase introduced during
the slice selection. Let the size of the image slice be 11

× 11 in spatial domain.

Under this condition, every pixel of the image slice areassumedtohavethe

finite number of identical individual transverse magnetic moments n

( x , y )

( , )

.Alsothe
individual magnetic moment at every position is undergoing linear phase delay with
different rate k

x y

( x , y , i ) i.e. φ( t ) = 2 π k ( x , y , i ) t . Thus every pixel of the image slice

is characterized by the following factors.

• n ( x , y ) : Number of individual magnetic moments corresponding to proton density.

• k ( x , y , i ) : Phase constant associated with i th magnetic moment of the ( x , y ) posi-

tion of the image slice.

are under-
going random phase change, resultant magnitude of the magnetic moment at

When the individual magnetic moments of the particular position ( x , y )

)
gradually decreases at every pixel. This is known as dephasing. The rate at which the
magnitude is decreasing gives the characteristics of the image slice at

( x , y

( x , y ) . In case

of proton-density image, we try to record n and in the case of T 2 image, we try

to measure the magnitude of the resultant magnetic moment of every pixel

( x , y )

at
the particular instant to sense the rate at which the magnitude is decreasing i.e. T 2
imaging. The time instants mentioned in this chapter are arbitrarily chosen and are
represented in seconds.

( x , y )