Transcript No Slide Title

1D Pulse sequences
• We now have most of the tools to understand and start
analyzing pulse sequences. We’ll start with the most basic
ones and build from there. The simplest one, the sequence to
record a normal 1D spectrum, will serve to define notation:
Vectors:
Mo
z
z
x
x
90y
pulse
y
Mxy
y
acquisition
Shorthand:
90y
90y
n
• According to the direction of the pulse, we’ll use 90x or 90y
(or 90f if we use other phases) to indicate the relative
direction of the B1 field WRT Mo in the rotating frame.
• The acquisition period will always be represented by an FID
for the nucleus under observation (the triangle).
Inversion recovery
• Measurement of T1 is important, as the relaxation rate of
different nuclei in a molecule can tell us about their local
mobility. We cannot measure it directly on the signal or the
FID because T1 affects magnetization we don’t detect.
• We use the following pulse sequence:
180y (or x)
90y
tD
• If we analyze after the p pulse:
z
z
x
y
180y (or x)
x
tD
y
• Since we are letting the signal decay by different amounts
exclusively under the effect of longitudinal relaxation (T1),
we’ll see how different tD’s affect the intensity of the FID and
the signal after FT.
Inversion recovery (continued)
tD = 0
z
z
x
90y
y
tD > 0
z
x
FT
x
FT
z
90y
y
y
z
z
x
y
FT
y
x
tD >> 0
x
90y
y
• Depending on the tD delay we use we get signals with varying
intensity, which depends on the T1 relaxation time of the
nucleus (peak) we are looking at.
Inversion recovery (continued)
intensity
• If we plot the intensity versus time we get the following curve:
time
I(t) = I * ( 1 - 2 * e - t / T1 )
• It is an exponential with a time constant equal to the T1
relaxation time.
• In principle, measuring T2 would just involve calculating the
envelope of the FID, since the signal in Mxy decays only due
to transverse relaxation.
• The problem is that the decay we see on Mxy is not only due
to proper relaxation, but also to the inhomogeneity of Bo (the
fanning out or dephasing of the signal). The decay constant
of the FID is called T2*. To measure T2 properly we have to
use spin-echoes.
Spin-echoes
• The pulse sequence is the following:
90y
180y (or x)
tD
tD
• We do the analysis after the 90y pulse:
z
y
x
y
tD

x
x
y
y
dephasing
y
tD
x
x
180y (or x)
refocusing
Spin-echoes (continued)
• We now go back to the <xyz> coordinates:
z
y
x

y
• If we acquire the FID right after the spin-echo sequence, the
intensity of the signal after FT will only be affected by T2
relaxation and not by dephasing due to Bo imperfections.
• Upon repetition for different tD values, we plot the intensity
versus 2 * tD and get a graph similar to the one we got for
inversion recovery, but in this case the decay rate will be
equal to T2.
• Next class we will analyze the effects of spin-echoes under
different conditions:
• Chemical shift
• Heteronuclear coupling
• Homonuclear coupling