Magnetic Resonance Imaging - Digital Signal Processing for Medical Imaging Using Matlab - page 34

y=[y 2*M0*sin(alpha1)*sin(-gamma*B0*t+phi)];
z=[z gamma*M0*sin(alpha1)*E0*sin(theta-phi)*t+2*M0*cos(alpha1)];
end
figure
plot3(x,y,z)
figure
subplot(1,2,1)
plot(x,y)
subplot(1,2,2)
plot(z)

2.4 Trick on MRI

E

The external magnetic moment is applied for the duration T π/ 2 to bring the

resultant magnetic moment to the transverse plane as described in the Sect. 2.3 .After
that, when E

( t )

is removed, the resultant magnetic moment has to rotate with constant
magnitude in the XY -plane with the larmor frequency. But in nature, transverse
component decreases and reaches zero after some time. This is called spin relaxation.
This is due to the spin-spin interactions between the micro-level magnetic moments
available in the human body. The time required to obtain

( t )

times the initial value
of the transverse component after the removal of the external magnetic moment
(represented as T 2 ) depends on the characteristics of the tissues of human body.
The resultant transverse magnetic moment during relaxation (free induction decay
(FID)) is recorded using the receiver antenna. This is used to obtain T 2 MRI and
proton-density MRI images.
In the same fashion, longituidanal component gradually increases and attains the
maximum value. This is due to spin-lattice interactions in the micro level magnetic
moments of the human body. The rate at which lognituidanal component reaches the
maximum value is described by the time constant T 1 (depends on the characteristics
of the tissues of the human body). Usually T 1

( 1 / e )

T 2 . After sufficient time (to nullify
the influence of existing transverse component), longitudanal component is flipped
to the transverse component and the corresponding FID is measured. This is used to
obtain the T 1 MRI image. Note that in all the cases ( T 1 , T 2 and proton-density) MRI

images, the receiver records only the transverse components of the magnetic field
during relaxation. The complete description is given in Sect. 2.8 .

2.5 Selecting the Human Slice and the Corresponding
External RF Pulse

When the external RF frequency is same as that of the larmour frequency, we are
able to get the transverse component of the magnetic field. When the complete
human body is kept under the identical strong magnetic moment B 0 , the recorded