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Effects on Apparent T2 in Multi Pulse Spin Echo

# Effects on Apparent T2 in Multi Pulse Spin Echo - Effects...

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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 k-space. 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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Effects on Apparent T2 in Multi Pulse Spin Echo - Effects...

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