Transcript Lecture 5: Imaging Theory (3/6) – One

Quiz
In a 2D spin warp or FT MR scan, aliasing should only occur
a) in the slice select direction
b) in the readout direction
c) in the phase encoding direction
Between adjacent phase encodes, the larger phase encode has
an additional p phase wrap across the FOV in the y direction.
Between k-space samples in the readout direction, there is a
relative 2 p phase wrap across the FOV in the x direction.
Imaging Considerations
We have touched earlier on some the effects that make the imaged slice
magnetization look complex. Let’s quantify some of them.
Main field inhomogeneity
Bo inhomogeneity ( also know as shim)
a) magnet
1.5 T shim specifications to 1/3 ppm (parts per
million)
over a 20 cm diameter sphere
~ 20 Hz at 1.5 T
Is this significant?
Patient-Induced Inhomogeneity
Main field inhomogeneity
Tissue’s bulk magnetic susceptibility, , can vary.
 varies by 10-6 to 10-5
1 ppm to 12 ppm
Worst areas: tissue-air interface
lung / abdomen
sinus
intestines
Chemical Shift:
Electronic shielding reduces the magnetic field seen by the fat
molecules.
Bshielded  Bo (1   )
f  ?
  3.5 ppm for fat
Patient-Induced Inhomogeneity
T2*

z component of magnetic field
 Bo  E(r )

E(r ) is the field inhomogeneity term.
 iωE (rt ) t / T2 (r )
s(t )   m(r )  e
e
dV
volume
- unintended
- T2 effect
- due to local
neighborhood
inhomogeneity
T2*
Varying magnetic field in immediate neighborhood (within a
voxel) causes in-plane spins to dephase earlier than intended T2
decay. The faster decay has a decay constant referred to as T2*
T2* Equation
• T2* is actual decay in gradient echo
experiment.
• T2 is actual spin-spin decay of material. We
will see how to easily measure this today.
• Last term is decay due to local magnetic
environment
1
1 1


*
'
T2 T2 T2
Causes of Phase Error
Main field inhomogeneity,
patient-induced inhomogeneity,
gradient non-linearity,
and blood flow
all cause phase errors (or frequency errors, depending on your
point of view). That is, spins will resonate faster or slower than
our basic formula predicts.
 
ω  γ(Bo  G  r )
Chemical shift is another type of phase error.
Let’s study the effects of these phenomena on the two major classes
of MR imaging sequences.
Gradient Echo
This is what we have studied to date:
90º
RF
t
Gx
t
s(t)
t
t
0
t

2
 ( x, y, z, t )   ω( x, y, z, )d
0
t 

 ωE ( x, y, z )t   cst  γ  G ( )  r d
0
Where does the gradient echo form?
What happens when we push the echo time out?
2D Fourier Transform (2)
2D Fourier Transform: (2D FT or Spin Warp)
1)
RF
t
6GRADECH.AVI
Gx(t)
Susceptibility Artifacts
Short echo time
Water /plastic interface
has large susceptibility.
Notice dropout of signal
around water discs in bottom image.
Longer echo time
Note: Not exactly the same slice and
so bottom slice has some water signal
also around discs.
Perils of Gradient Echo Imaging and
T2*
TE = 8 ms
TE = 24 ms
0.17 T GE Orthopedic Scanner
Spin Echo Phenomenon
Spin Echo Generation

90º
(a)
(b)

180º
(c)
(d)
Spin Echo Generation:
Following a 90º excitation pulse, (a -b)
the spin vectors begin to fan out and dephase because of
precessional frequency differences (c) at time ,
a 180º excitation rotates all the spins about the x’ axis (d)
The spin vectors continue to precess at their slightly different
frequencies, rephasing at time 2 (e).
Image Copyright Nishimura
(e)
Tip Bulk Magnetization
z'
M
y'
x'
Tip Bulk Magnetization
z'
M
y'
x'
B1
Tip Bulk Magnetization
z'
y'
x'
B1
Tip Bulk Magnetization
z'
y'
x'
B1
Tip Bulk Magnetization
z'
y'
x'
B1
Transverse Magnetization
z'
Mtrans
x'
y'
T2 Decay
z'
s
y'
f
x'
T2 relaxation is dephasing of transverse magnetizati
T2 Decay
z'
s
y'
f
x'
T2 relaxation is dephasing of transverse magnetizati
T2 Decay
z'
s
y'
f
x'
T2 relaxation is dephasing of transverse magnetizati
Refocusing Pulse
z'
s
y'
f
x'
B1
Refocusing Pulse
z'
s
y'
f
x'
B1
Refocusing Pulse
z'
s
y'
f
x'
B1
Rephasing
z'
s
y'
f
x'
Rephasing
z'
s
y'
f
x'
Rephasing
z'
s
y'
f
x'
Echo Formation
z'
y'
Mtrans
x'
Spin Echoes
 ( x, y, z, t )  
t
0
t 

ω( x, y, z, )d  ωE ( x, y, z)t  cst  γ G( )  r d
0
The phase errors E are for the most part out of our control, but there
is a method around them called a spin echo.
Chemical shift, CS , can be compensated with techniques beyond the
scope of this class. But these require more scan time also..
However, we can use a “spin echo” to correct for both effects. Spin
echoes form the second major class of pulse sequences.
Spin echoes use a 90º pulse as we have seen, but also a second RF
pulse, a 180º pulse. Let’s first consider just the effects of offresonance and ignore the imaging gradients.
180º
90º
RF
0

2
t
Spin Echo Generation in Rotating Frame
90º
180º

(a)
(b)
(c)

(d)
(e)
The phase error just prior to the 180º pulse is  ( _ )  ωE ( x, y, z )

_
Just after the 180º pulse, it is  ( )  p   ( )
 p   E ( x, y, z )
Then we let the spins progress for another .

2
 (2 )   ( )    E ( x, y, z, t )dt'

 p   E ( x, y, z, )   E ( x, y, z )(2   )
p
A “spin echo” is said to be formed at t=2
Image Copyright Nishimura
Effect of echo delay on signal loss
Effect of echo delay on susceptibility-induced signal losses:
(a) TE = 15 ms
(b) TE = 10 ms
Notice homogeneity of water discs
and air bubble appearance.
(c) TE = 5 ms
Note artifactual signal reduction in the region
of the nasal and mastoid sinuses.
Spin Echo Pulse Sequence


Echo Time (TE) = 2 
Z grad
90
180
90
RF
X Grad
Gy
TE
Y Grad
TR
Spin Echo Signal Plus X Readout
Gradient
6SPINECH.AVI
Left plot experiences no refocusing pulse. Right plot experiences
refocusing pulse half way through time series. Sum of magnitude of
spins given on top. Time series ends at echo time.
Spin Echo RF Sequence
T2
T2*
TE
TR
1
1
=
+ B0
*
T2
T2
Spin Echo Sequence with 180 y pulse
Spin Echo Sequence – Long Versus Short
T2
long T2
long T2
short T2
short T2
T2-weighting: long TE, long TR
PD-weighting: short TE, long TR
T1, T2, and Density-Weighted Images
T1-weighted
T2-weighted
r-weighted
Scan Duration
Scan Time = TR  PE  NEX
TR = repetition time
PE = number of phase encoding values
NEX = number of excitations (averages)
Spin Echo Formation
• For spins to be refocused, they must
experience the same magnetic field after the
180 refocusing pulse as they experienced
before the 180 refocusing pulse.
• Thus, only dephasing due to macroscopic
inhomogeneities (B0) is refocused.
Dephasing due to microscopic
inhomogenieties (T2) is not refocused.
Spin Echo Parameters
TR
T1-weighting short (400 msec)
TE
short (20 msec)
T2-weighting long (3000 msec) long (100 msec)
r-weighting long (3000 msec) short (20 msec)
Signal vs Weighting
T1-weighted
T2-weighted
r-weighted
T1-weighting
long T1, small signal
short T1, large signal
T2-weighting
long T2, large signal
short T2, small signal
r-weighting
high r, large signal
low r, small signal
Images of the Knee
r-weighted
T2-weighted
Needs longer TE
T2 & T2* Relaxation: Image Contrast Sources
T2
Mxy
T2 *
1
1
=
+ B0
*
T2
T2
Time
FSE Pulse Sequence Timing Diagram
90°
180°
180°
180°
180°
rf
Slice
Select
Phase
Encode
Freq.
Encode
ETL=4
Signal
ESP
Filling k-space FSE
Phase
Direction
Frequency Direction
Scan Duration
Scan Time = TR  PE/ETL  NEX
TR = repetition time
PE = number of phase encoding values
NEX = number of excitations (averages)
ETL = echo train length
T2 Weighting (Various Sequences)
TR = 2500
TE = 116
ETL = 16
NEX = 2
24 slices
17 slices/pass
2 passes
Time = 2:51
FSE
SE
TR = 2500
TE = 112
ETL = N/A
NEX = 1
24 slices
20 slices/pass
2 passes
Time = 22:21
Inversion Recovery RF Sequence
Inversion Recovery (IR) Sequence & Spin
Behavior
Inversion Recovery
TI
180°
rf
Slice
Select
Phase
Encode
Freq.
Encode
Signal
90°
180°
IR Sequence – Short Versus Long T1
Inversion Recovery Signal
Mlong
short T1
longer T1
Short T1 = brighter
Long T1 = darker
TI
Inversion Recovery Signal
Mlong
short T1
longer T1
Short T1 = brighter
Long T1 = null
TI
Short Tau Inversion Recovery (Fat
Nulled)
STIR
Mlong
Short T1 = null
Long T1 = brighter
TI
short T1 (fat)
longer T1
Spine: T1 versus T2 versus
STIR
T1
T2
STIR
Inversion Recovery II
IR pulse precedes
T2-weighted sequence
Coronal Tumor
Here the inversion recovery delay is very long ( ~2 s). Here the idea
is to null CSF so one can distinguish tumor from CSF. Notice tumor
still has positive contrast.
MR: SNR vs Field Strength
Signal
M o  Bo
- energy separation of Zeeman levels
M
  o  Bo
t
2
Signal amplitude is  Bo
sreceive 
- Faraday’s Law of Induction
Noise Power
Receiver  Bo
Patient  Bo
2
- electronics
- patient electrons in Brownian motion
Patient noise dominates at most field strengths ( Bo  .1 T )
SNR 
Bo 2
Bo 2
 Bo
SNR
• We will first consider the case where we
ignore T1 and T2 of the tissue involved.
– leave sequence dependent effects for later
SNR
Noise Power
Study for impulse at x=0, y = 0
Each k-space point has signal A, noise power 2
Each sampled point is independent with respect to noise.
ky
Amplitude of Signal = NxNyA
Ny
kx
Noise Power = NxNy 2   2
Ny Nx
SNR 
Nx
2 
1
T
Nx Ny A
Nx N y

Nx Ny A

T  sampling interval in time
SNR  A N x N y T  A Time A/D on
SNR
SNR  A N x N y T  A Time A/D on
SNR  voxel size since this determines the
# of protons per voxel
Replace A above by voxel size
Together,
SNR  voxelsize  TimeA/D on
SNR
Time
Resolution
Scan Time
Image b) has twice the SNR as a)
at an expense of four times the scan time
Axial Forearm T2-Weighted
TE = 15 ms
TE = 45 ms
TR = 4000 ms for all
Notice appearance of supinator
Muscle ( arrow) on all images.
One arm had an exercise protocol.
Which one? What is in between arms?
TE = 75 ms
TE = 105 ms
M z,n 1  M z,n Steady statecondition
After tipping q , Mz is reduced by cosq
q
q
q
M z,n1 M z,n
q
M z
M z,n  M z,n 1 cosq
Mz recoveryequation
M z,n  M z,n e TR / T 1  M 0 (1  e TR / T 1 )
P lug in for M z,n
TR
M z,n  M z,n 1 cosqe TR / T 1  M 0 (1  e TR / T 1 )
Use steady-statecondition
During each TR, Mz will recover. M   M  cosqe TR / T 1  M (1  e TR / T 1 )
z ,n
z ,n
0
When in steady-state,
M z,n (1  cosq )  M 0 (1  e TR / T 1 )
M z,n1  M z,n
Where n-1 is the n-1th RF pulse
and n is the nth RF pulse.
M

z ,n
M 0 (1  e TR / T 1 )

(1  cosq )
M 0 (1  e TR / T 1 )
Mxy 
sin(q )
(1  cosq )
For q  p/2,
Mxy  M 0 (1  e TR / T 1 )