Effects on Apparent T2 in Multi
Pulse Spin Echo
Bhairav B Mehta
Introduction
The transverse component of the magnetization decreases gradually to zero. This is an
exponential decay with the time constant as T
2
. T
2
relaxation time is time constant for spinning
protons to lose the phase coherence among the nuclei spinning perpendicular to the main field.
The value of T
2
depends on the mobility of the protons which is dependent on tissue property.
Thus by knowing the value of T
2
provides us the insight of the content of the voxel.
Due to off resonance the apparent value of T
2
decrease it follows a T
2
*
decay. To remove the
artifacts due off resonance we use spin echo which uses one 90
0
excitation and one 180
0
refocusing pulse.
Then to decrease the scan time they introduced Fast spin echo in which multiple refocusing
pulses were used to get multiple lines in kspace. Initially it was interpreted that echoes follow a
T
2
decay curve. But then it was observed there was some variation in the decay.
In this report I have tried to explain few possible reasons that affect the apparent decay or vary
the transverse magnetization. To support the argument I have attached few figures using
simulation of Bloch equation in matlab.
Dependency of steady state signal on T
1
as well as TR
In single pulse spin echo sequence the equation the steady state equation was assumed to be.
=
 

…
Msn
Mo1
e TRT1e TET2
1
where
M0
is the value of stable magnetization, TR is the repetition time, TE is echo time. The
slope of
(
loge Msn
) against TE gives T
2
.
But the actual steady state equation for spin echo is
=
Mse
Mo



+ 

…
1 2e TR TE2T1 e TRT1e TET2
2
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Thus we see that the slope of
(
loge Mse
) against TE is dependent on T
1
, T
2
, TE and TR, and T
2
cannot be determined without making a separate determination of T
1
. This dependency affects
the signal and produces an error. The relative error is given by the equation
=

=  
(
 ) 
(

εs
Mse MsnMse
2 e TRT1 eTE2T1 1 1 2e
TR
)
+ 
TE2 T1 e TET1
The exact equation (2) does reduce to equation (1) (i.e.
→
εs
0
) under the following condition:
≪
TE
T1
i.e. short echo time OR
≫
TR
T1
i.e. fully relaxed.
Similarly while applying multiple refocusing pulse the signal equation is not only function of T
2
but also T
1
, TR and TE. Let us consider a pulse sequence with two refocusing pulses one at
TE
1
/2 and other at (TE1 + TE
2
/2). The steady state signal equation is given as
=
( +






 
) 
Mse2
Mo 1 2e TR TE12T1 2e TR TE1
TE22T1 e TRT1 e
(
+
)
TE1
TE2 T2
The relative error changes to:
=
+
=


( 
εs2
Mse2 MsnMse2
2e TR TE12T1 1
+
) +






 
eTE1 TE22T1 1 2e TR TE12T1 2e TR TE1
TE22T1 e TRT1
If TE
1
=TE
2
=TE/2 the first echo will come at TE/2 and second echo will come at TE.
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 Fall '07
 Nayak
 Magnetic resonance imaging, Nuclear magnetic resonance, Bloch, slice profile, refocusing pulse, norm alised M

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