©2016 M.S. Cohen all rights [email protected] reserved · PROTON PRECESSION Applied Magnetic ......
Transcript of ©2016 M.S. Cohen all rights [email protected] reserved · PROTON PRECESSION Applied Magnetic ......
©2016 M.S. Cohen all rights reserved
©2016 M.S. Cohen all rights reserved [email protected]
AN MRI PRIMER
©2016 M.S. Cohen all rights reserved [email protected]
NUCLEAR SPIN
“Spin” is a property of many particles. It is a type of angular momentum.Angular momentum is a vector quantity.Quantum properties prohibit knowing both magnitude and three-dimensional orientation. We can know both the z-component and magnitude.
ħ = 1.0546 X 10-34 J-s S = ! s(s +1), where s = {0, 1
2,1, 32,2,…}
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SPIN STATES
A Spin 1/2 particle has two states (“up/down”, “1 and 2”, α/β)In a magnetic field, B0, the two states have different energies
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PROTON PRECESSION
Applied Magnetic Field: B
Precession: ω
Spin
ω = γ X B γH ≈ 267.52 Rad/sec/Tesla≈ 42.577 MHz/Tesla
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PROTONS IN APPLIED FIELD
Applied Magnetic Field
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TRANSITION TO EQUILIBRIUM
Zero Field Field Applied
Up/Down state transitions require quantized energy input
Energy
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T1
CSF
BrainFat
Time (seconds)
Magnetization(signal)
1
0.5
01 2 3 40
�
M (t) = M 0 (1− e− tr
T1)
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PROTONS IN APPLIED FIELD
Applied MagneticField
Due to their angular momentum, Protons precess in the magnetic field.
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PROTON RESPONSES TO APPLIED MAGNETIC FIELD
Spin Alignment Along Net Applied Field spins align parallel or anti-parallel to the applied field
Precession About the Magnetic Field at a precession frequency of: γ × B, known as the Larmor frequency
Spin Alignment Occurs at the Rate, T1
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THE RESONANCE PHENOMENON
When a second magnetic field (B1) is applied, rotating at the Larmor rate, the proton will precess about it.
B1 Field Axis
Precession Angle About RF Field
Static Magnetic Field: B0
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AN RF PULSE CONVERTS LONGITUDINAL MAGNETIZATION INTO SIGNAL
90° RF Pulse
LongitudinalMagnetization
MR Signal
Precession
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IN-PHASE PRECESSIONN
S
Receiver
NMR Signal
N
S
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OUT OF PHASE PRECESSIONN
S
Receiver
NMR Signal
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T2:
The Characteristic Time forTransverse Decay
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SUMMARY ANIMATION
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HAHN SPIN ECHO2. 90° Pulse
3. T2* Relaxation
4. 180° Pulse
5. Spin Rephasing
6. Spin Echo
1. Equilibrium
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SUMMARY ANIMATION
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T2 AND TE
0
1
0.5
060 120Time (milliseconds)
Signal
CSF
Brain
Fat
�
S(t) = M xy (t) = M 0e− te
T 2
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PARTIAL SATURATION
NMR Signal
Sequence of 90° Pulses
tr tr
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EFFECTS OF TE AT LONG TR
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CONTRAST, TR AND TE
TRLong
Short
Short LongTE
T2-Weighted
T1-Weighted
ProtonDensity
�
S = kρM 0 (1− e− tr
T1)e− te
T 2
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CONTRAST, TR AND TE
TR
Long
Short
Short LongTE
Density
T1
T2
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SAMPLE DATA SET (NORMAL)
Sample Data Set (normal)
Fast Spin Echo3 mm Slices
3D IR-SPGR TE = 3.2, TI = 700
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SPIN ECHO
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MR FORMULÆ
Contrast Summary:
Spin Echo Signal = kρΜ0(1 - e-tr/T1)e-te/T2
ρ is the proton densityk represents instrument effects
The “Bloch” Equation:
dM/dt = γM X B1 + (M0 - Mz)/T1 - (Mx + My)/T2
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CONTRAST TO NOISE RATIO (GRAY-WHITE)
trte
0
0.2
0.13 6
tr, te in seconds
-5% +3%0%
�
Contrast = [(1− e− tr /1.2 )e− te /.08 ], gray matter−[(1− e− tr /1.0 )e− te /.07 ], white matter
Gray – White
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CONTRAST OPTIMIZATION
TE
Cont
rast
>> T2a=40; T2b=45; te=0:150;>> contrast = exp(-te/T2b) - exp(-te/T2a);>> plot(te,contrast,'linewidth',3);>> find(contrast==max(contrast))ans = 43
43 ms
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1T2*
1T2
1T2
1T2
= + +D’
Molecular Field Inhomogeneity
Diffusion
The Observed Transverse Relaxation Rate, T2*, is the sum of
several components:
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MR IMAGE FORMATION
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FREQUENCY SELECTIVE EXCITATION
RF
Grad 0
Sir Peter Mansfield
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MAGNETIC FIELD GRADIENTS
MRI Instrument in Cross Section
Position
Field Strength
Magnet
Gradient Coil
Physicist
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A 1D IMAGE
Position
Field Strength /Frequency
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FOURIER PROJECTIONS
MR ImageRaw Data FFT of Raw Data
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realimaginary
BACK PROJECTION
Image Domain
Fourier Domain
GradientEncoding
2D FourierTransform
Paul Lauterbur
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CONVENTIONAL SPATIAL ENCODING
Grad 1
Samples
A2
A1
Grad 2A2
A1
A2
A1
RF
Grad 0
tr
…
…
…
…
…
te
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CONVENTIONAL K-SPACE TRAJECTORY
+K
-Kfrequency
phase
tr
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k(x,y,t ) = γ G(x,y,t )dt
0
T
∫
EPI K-SPACE TRAJECTORY
k-phase
k-frequency
k-space plots the integral of the
gradient encoding.
Its Fourier transform is the
image.
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3D K-SPACE
Gz
Gy
Gx
tr
Imaging time = tr * Nz * Ny
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t slice
Gz
Gy
Gx
RF
te
MULTI-SLICE MRISlice 1
tr
N =slices tr / tslice
Slice 1Slice 2Slice 3 Slice 4
Readout
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SPATIAL ENCODING
Grad 1
Samples
A2
A1
Grad 2A2
A1
A2
A1
RF
Grad 0
tr
…
…
…
…
…
te
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CONTRAST ENCODING
Grad 1
Samples
A2
A1
Grad 2A2
A1 A1
RF
Grad 0
tr
…
…
…
…
…
te
tr
te
A2
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INVERSION RECOVERY
−500 0 500 1000 1500 2000 2500 3000 3500 4000−1
−0.5
0
0.5
1
Time (ms)
Mz
−500 0 500 1000 1500 2000 2500 3000 3500 4000−1
−0.5
0
0.5
1
Time (ms)
Mxy
CSFBrainFat
180° 90°
TI=700ms
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DIFFUSION AND MOTION
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GRADIENTS AND PHASE
0 T/2 T
Phase with respect to
center
+
–
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x(t) = x0 + vt + at 2
2 +…
ϕ = γ G(t)x(t)dt0
T
∫
= γ G(t) x0 + vt + at 2
2 +…⎡⎣
⎤⎦dt
0
T
∫
= γ vT 2
4 + 23aT 3
24 +…⎡⎣
⎤⎦
GRADIENTS AND PHASE
0 T/2 T
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PHASE AND MOTION
Stationary
Moving
phas
e
0 T/2 T
0 T/2 T
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1.5
1
0.5
0
-0.5
-1
-1.5
Velo
city
(mm
/sec
)
Cephalic
Caudal
0 100 200 300 400 500 600 700
Delay from R-Wave (msec)Total Frontal Pole MotionCorrected Frontal Pole MotionHead Motion
0 2 mm/sec-2
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�
SID = k exp(−te /T2) ⋅exp[−γ2G2δ2 (Δ−δ)]
DIFFUSION GRADIENTS
Gδ
Δ
δ
RF
RF
�
SI0 = k exp(−te /T2) Make Image
Make Image
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DIFFUSION & SIGNAL
Denis Le Bihan, Nature Reviews in Neuroscience 4:469, 2003
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BRAIN DIFFUSION IS ANISOTROPIC
Schaefer, P. W. et al. Radiology 2000;217:331-345
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ISOTROPIC VS. ANISOTROPIC DIFFUSION
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REDUCED FLIP ANGLE IMAGING
• Determinants of Imaging Time
• TR, Saturation and Image Quality
• Reduced Flip Angle Techniques
FLASH (=SPGR)
FISP (=GRASS)
• Gradient Echoes
• Applications of Shallow Flip Imaging
• Ultra-Fast Imaging
Outline
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DETERMINANTS OF IMAGING TIME
Scan Time =
Repetition Time (TR)x Number of Phase Encodes
x NEX (Averages)x Number of 3D Steps
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TR AND IMAGE QUALITY
• Decreased Scan Time • Increased T1 Contrast • Reduced (Useable) T2 Contrast • Reduced Signal to Noise Ratio • Increased Power Deposition • Reduced Slice Coverage
Reduced TR Yields:
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SIGNAL AND FLIP ANGLE
Small Flip Angle Large Flip Angle
α°α°
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SMALL AND LARGE FLIP ANGLE
Loss of Longitudinal Magnetization
Small Flip Angle Large Flip Angle
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FLIP ANGLE AND TR/T1
90°
45°
10°5°
0 1 2 3 40
0.2
0.4
0.6
0.8
1
20°
0 0.02 0.04 0.06 0.08 0.10
0.05
0.1
0.15
0.2
0.25
5°
10°
20°45°
90°
αErnst = arccos(e− tr/T 1)
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Contrast and Flip AngleLarge Flip Angles Short Long
Long Proton Density T2* Weighted
Short T1 Weighted
Small Flip Angles Short Long
Long Proton Density T2* Weighted
Short Proton Density T2* Weighted
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A 180° PULSE IS NOT USED IN FLASH IMAGING
InitialMagnetization After
SmallRF Pulse
After 180°Pulse
x
y
z
x
y
z
x
y
z
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T2 AND T2*
T2: Transverse Magnetization Decay from Spin-Spin Interactions
T2*: Transverse Magnetization Decay from Local Magnetic Field
Variations
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SIGNAL AND TE GRADIENT ECHO
TE=20 TE=40 TE=60
TE=80 TE=100
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MAGNETIC SUSCEPTIBILITY
The Extent to Which a Substance Becomes “MAGNETIZED” when Placed Within a Magnetic Field
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MAGNETIC SUSCEPTIBILITY
Applied Magnetic
Field
Objects with Susceptibility Different than Air Distort the Magnetic Field
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FLASH MAGNETIZATION CYCLE1. 2.
3.
α°
Longitudinal Recovery α° RF pulse followedby data collection
Spoiling of transversemagnetization
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α°
Gz
Gy
Gx
RF
te
α°
Gz
Gy
Gx
α°RF
te
“FLASH” “GRASS” “SSFP”
α°
Gz
Gy
Gx
RF
te
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3D MP-RAGE
Gz
Gy
Gx
trti tr tr
RF
…
…
…
…
…
Repeat Ny times
180°α° α° α°
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PHASE MAPS
readout
RF
slice select
te
• Time shift in data collection amounts to a phase offset• Spins precessing at different rates (different magnetic fields) will
acquire different phase shifts
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TRADEOFFS
SNRtrteflip anglevoxel volumecontrastimaging time (e.g., averaging)
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TRADEOFFS
Imaging Timetrresolutiontotal slices (due to vendor optimization)
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TRADEOFFS
SARflip angleecho train lengthnumber of slices / trtotal scan duration