Lecture 6: Spin-echo and related techniques/file/PHY411-Lectu… · Spin-echo and related...
Transcript of Lecture 6: Spin-echo and related techniques/file/PHY411-Lectu… · Spin-echo and related...
Lecture 6: Spin-echo and related techniques
Lecture aims to explain: 1. Free induction decay and T2* time
2. The spin-echo method and T2 measurements
Free induction decay and T2* time
FID method: Apply a π/2-pulse with oscillating field H1 along y-axis (oscillating with ω=γH0 ) and observe spin evolution in the xy-plane due to precession about the external field H0 (along z). Important assumption: all
pulses are very short compared to T2*
π/2-pulse excitation: laboratory frame
Laboratory frame: helical motion of magnetization
-1-0.5
00.5
1
-1-0.5
00.5
10
0.2
0.4
0.6
0.8
1
Mx
Evolution of magnetization due to Pi/2 - pulse, H1= 3mT, H0=0.1T
My
MztH0plane-in γθ =
tH1z γθ =
Let’s consider evolution during a π/2-pulse: oscillating H1 along y-axis, observe spin evolution in the xy-plane due to precession about the external field H0 (along z)
In the figure the π/2-pulse calculated for proton takes only about 2 µs
π/2-pulse excitation: rotating frame
Rotating frame: arch-like motion from z-direction to x-direction
constantplane-in =θ
tH1z γθ =
The frame is rotating clock-wise with a frequency γH0 . Effectively precession around the external field is accounted for already. Direction of the oscillating field is also fixed along negative y-axis (note: opposite to previous slide for convenience).
y'
x'
z‘
1H
0zM
Free induction decay: measured signal
Example of a stationary coil immersed in a rotating, fixed magnitude field H(t)
After rotation into the plane, H1 is switched off and the spins precess around the external field H0 (in the laboratory frame)
dtdΦEMF −= ∫ ⋅=
area coildSBΦ
tcosHtsinH(t) ωω yzH ˆˆ +−=For H(t):
H(t)
ωtHωLEMF 2 cos=
It is possible to show that:
Free induction decay in the presence of inhomogeneities: T2*
Spins will gradually spread in-plane leading to reduction of the net magnetisation. The “spread angle” is given by
constantplane-in ≠θ
tH0plane-in ∆∆ γθ =
Consider the frame rotating clock-wise with ω=γH0 and spins flipped along x-axis by a π/2-pulse
Due to the inhomogeneity of the magnetic field or presence of chemical shifts):
y'
x'
z‘
'T1
T1
T1
22*2
+=This will result in an additional decay with T2’. Total magnetisation decay measured in an FID experiment is described with T2*:
Spin-echo techniques and measurements of T2
Spin-echo pulse sequence
The main task is to reverse the spread of spins in the xy-plane (in the rotating frame) which occurs due to the inhomogeneities of γ in the spin ensemble
Spin-echo pulse sequence: A π/2-pulse is applied along the positive x’-axis at t=0 and then π-pulse is applied along the positive y’-axis at t=τ
On the graph TE – the spin-echo time, when an increase in magnetisation will be observed due to re-focussing effect.
Spin evolution due to spin-echo pulse excitation
Laboratory signal in the spin-echo experiment
Using the spin-echo sequence, revival of the signal is observed after time TE=2τ
Note: The signal (magnetisation) still decays due to irreversible loss in fluctuating local fields described with a characteristic demagnetisation time T2
Multiple spin-echo experiments Rather than repeating an experiment with a different echo time to measure T2, it is common to collect data for more than one echo of the original rf excitation. This is accomplished using the pulse-sequence shown in the figure
Typical magnitudes of transverse spin relaxation time T2
Material/Tissue T1 (ms) T2 (ms)
Gray matter 950 100
White matter 600 80
Muscle 900 50
Cerebrospinal fluid 4500 2200
Fat 250 60
Blood 1200 100-200
GaAs crystal ~1000 ~0.1
Self-assembled semiconductor quantum dot
>106 ~1
Limitations of spin-echo
The spin echo does not reduce the effect of T2 on the magnetisation decay. The reason lies in the rapid time fluctuations in the intrinsic local fields
Example 6.1 Estimate the smallest magnetic field required for a “useful” ‘π/2’ pulse in (i) a GaAs crystal with T2~100 µs, (ii) grey matter with T2~100 ms. State the assumptions, which you made. Use 69Ga with γGa=6.44×107 rad s-1 T-1 and protons with γp=26.75×107 rad s-1 T-1 for GaAs and grey matter, respectively.
SUMMARY FID method: Apply a π/2-pulse with oscillating field H1 along y-axis (oscillating with ω=γH0 ) and observe spin evolution in the xy-plane due to precession about the external field H0 (along z). Important assumption: all pulses are very short compared to T2*. Signal will decay with a characteristic time T2* including effects of local fields (described with T2) and ensemble inhomogeneities. T2* may be much shorter than T2
Spin-echo: Apply a π/2-pulse followed with a refocussing π-pulse after a time τ. Revival of the signal (i.e. spin-echo) is observed after TE=2τ. The spin-echo amplitude still decays irreversibly with T2. Multiple echo experiments can be used for faster data acquisition.