Magnetic Resonance Imaging - Digital Signal Processing for Medical Imaging Using Matlab - page 39

2.6.1 Observation on ( 2.47 )-( 2.50 )

1. The time instant t 0in( 2.47 ) is the starting time at which the receiver starts

receiving the signal. This is otherwise called as the starting time instance of the
readout phase.
2. Note that the transverse component is rotating with identical larmour frequency
at all (x,y) positions. This is achieved with the identical strong magnetic field (in
the z -axis) throughout the slice.
3. The amplitude M xy (

=

0 + ) x , y , is the function of ( x , y ) as it involves the hidden

t
T 2 ( x , y ) from the time instance of the middle of the RF pulse.
4. Hence if the receiver is designed to receive the transverse component as the
function of

−

term e

( x , y ) , the image completely describes the T 2 ( x , y ) characteristics of

the sliced tissue.

2.6.2 Receiver to Receive the Transverse Component

The transverse component M . Usually

M x , t component is sensed as the voltage induced in the the receiver coil as described
below. When the receiver coil is excited with the external source to generate the
transverse magnetic moment represented as the vector

( x , y , t ) is represented as the vector [ M x , t M y , t ]

and are kept in the
transverse magnetic moment (to be sensed) represented as the vector

[ 10 ]

[ M x , t M y , t ] ,the

voltage is induced in the coil as follows.

d
dt

( ) =− [

M x , t M y , t ]·[

]

v t 10 dxdy (2.51)

x y

The generalized expression for the transverse component of the magnetic moment
is given as

e − j (γ B 0 t − φ) M ( x , y , t ) = ( M r + jM i ) (2.52)

d
dt

⇒ v ( t ) =− [ ( M r cos (γ B 0 t − φ) + M i sin (γ B 0 t − φ))

x y

( − M r sin (γ B 0 t − φ) + M i cos (γ B 0 t − φ)) ]·[ 10 ] dxdy (2.53)

B 0
x

⇒ v ( t ) = γ ( M r sin (γ B 0 t − φ) − M i cos (γ B 0 t − φ)) dxdy (2.54)

y

It is possible to obtain M r and M i as follows.