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MRI image formation
Chen Lin, PhD DABR
Indiana University School of Medicine
and
Indiana University Health
Disclosure • No conflict of interest for this presentation
Chen Lin, PhD DABR 2 AAPM 2016
Outlines • Data acquisition
– Spatial (Slice/Slab) selection
– Spatial encoding (using frequency and phase)
• Image reconstruction – K-space
– Fourier Transform
• Signal-to-noise ratio – Signal intensity
– Source of noise
Chen Lin, PhD DABR 3 AAPM 2016
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Free Precession
Chen Lin, PhD DABR
𝒇 = 𝛾𝐵0
4 AAPM 2016
Z
Y
X
MZ
B0
Excitation
Chen Lin, PhD DABR
B1
𝒇RF = 𝒇
5 AAPM 2016
Z
Y
X
MXY
MZ
B1
B0
Signal
Chen Lin, PhD DABR
𝒇 = 𝛾𝐵0
6 AAPM 2016
Z
Y
X
MXY
B0
t
T2*
S(t) = A𝑒𝑖[2𝜋𝑓𝑡+𝜑0]
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Chemical Shift (CS)
Chen Lin, PhD DABR
𝒇 = 𝛾𝐵0+ CS
7 AAPM 2016
Z
Y
X
MXY
B0
t
SPATIAL SELECTION AND ENCODING
Chen Lin, PhD DABR 8 AAPM 2016
Slice/Slab Selection Gradient
Chen Lin, PhD DABR
Tx Frequency
Z Water
9 AAPM 2016
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Slice/Slab Selection Gradient
Chen Lin, PhD DABR
Tx Frequency
Z Water
10 AAPM 2016
RF TxBW
Slice/Slab Selection Gradient
Chen Lin, PhD DABR
Tx Frequency
Z Water
11 AAPM 2016
Fat
Slice/Slab Selective Excitation
Chen Lin, PhD DABR 12
Tx Frequency
Z
Thin Slice
AAPM 2016
TxBW (~ 2kHz)
Tx Offset
Thick Slice
Gz
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Slice Selective Excitation and Refocusing
Chen Lin, PhD DABR 13
https://www.imaios.com/en/e-Courses/e-MRI/Magnetic-Resonance-Spectroscopy-MRS/single-voxel-spectroscopy
AAPM 2016
Frequency Encoding Gradient
Chen Lin, PhD DABR
Rx Frequency
X
Rx
Ban
d W
idth
(R
xBW
)
14 AAPM 2016
Water
S(t) = ΣAx𝑒𝑖(2𝝿𝞬𝑥𝐺𝑥𝑡)
t
Frequency Encoding Gradient
Chen Lin, PhD DABR
Rx Frequency
X
Rx
Ban
d W
idth
(R
xBW
)
15 AAPM 2016
Water
Fat
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Frequency Encoding Implementation
Chen Lin, PhD DABR 16
FOVx (in Frequency Encoding direction)
Rx Frequency
RxBW (+/- 8 – 128 kHz) X
RxBW / FOVx -> Gx
AAPM 2016
Phase Encoding
Chen Lin, PhD DABR
Y
17 AAPM 2016
Precession Frequency
Phase diff.
∆𝜙 = 0 | t=0
Phase Encoding Gradient
Chen Lin, PhD DABR
Y
18 AAPM 2016
Precession Frequency
Phase diff.
∆𝜙 = 0 | t=0
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Phase Encoding Gradient
Chen Lin, PhD DABR
Y
19 AAPM 2016
t
Gy
Phase diff ∆𝜙 | t = 𝞽 S(t ) = ΣAy𝑒
𝑖(2𝝿𝞬𝑦𝐺𝑦𝞽)
Ph
ase
Ran
ge
(0 –
2p
)
∆𝜙(y) = g y Gy t
Fat
Phase Encoding Implementation
AAPM 2016 Chen Lin, PhD DABR 20
S = 𝑆𝑘𝑒𝑖𝜑𝑘(𝜏𝐺𝑦1)
𝜏𝐺𝑦1
𝜏𝐺𝑦𝑛
S = 𝑆𝑘𝑒𝑖𝜑𝑘(𝜏𝐺𝑦𝑛)
Spatial Selection and Encoding in 2D MRI
Chen Lin, PhD DABR
Frequency Encoded Points (NFreq = 8)
ky
Ph
ase
En
co
din
g S
tep
s (N
phase =
4)
kx
Gy Gx Gz
21 AAPM 2016
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Chemical Shift Artifact
Chen Lin, PhD DABR 22
http://mri-q.com/chemical-shift-artifact.html
Frequency Encoding
AAPM 2016
Chen Lin, PhD DABR
With FatSat
Chemical Shift Artifact in SS-EPI
23 AAPM 2016
GRE Train (~64) Gy
Gx
E1 E2 E3 E4 E5 E6
Phase Encoding Blips
Without FatSat
Frequency and Phase Encoding • Each encoded data point is a Fourier series.
• Frequency encoding – More efficient, no aliasing (using a low pass filter)
– Frequency Encoding typically used in the direction of higher resolution or greater coverage
– Chemical shift artifact (can be minimized with high RxBW)
• Phase encoding – More time consuming (NPE * TR), does improve SNR
– Can be used more than once
Chen Lin, PhD DABR 24 AAPM 2016
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Spatial Selection & Encoding
• Heavily rely on the imaging gradients
– Gradient non-linearity -> Spatial distortion
– Gradient performance -> Acquisition time and min. FOV
– Gradient stability -> Artifacts
• Any combinations of the three orthogonal physical gradients can be used for spatial selection or encoding
AAPM 2016 Chen Lin, PhD DABR 25
K-SPACE AND FOURIER TRANSFORMATION
Chen Lin, PhD DABR 26 AAPM 2016
K: Wave Number or Wave Index
Chen Lin, PhD DABR
0 1 2 3 4 K=
x
I
x
I
x
I
x
I
x
I
0 1 27 AAPM 2016
Kx
I
1
K Space
x
I Image Space
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2D Image <-> 2D K-space
Chen Lin, PhD DABR
Kx
Ky
Y
X
Y
X
X
Y Y
X
28 AAPM 2016
Magnitude
Phase
K-space Image space FT
k-space <-> Image space
Chen Lin, PhD DABR 29 AAPM 2016
Information in K-space • Inner k-space (Low spatial freq.) -> Intensity/Contrast.
• Outer k-space (High spatial freq.) -> Edges/Details.
• K-space resolution (DK) -> Image FOV.
• K-space range (Kmax) -> Image resolution.
• Symmetry -> Allows partial k-space acquisition. Chen Lin, PhD DABR 30 AAPM 2016
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SIGNAL-TO-NOISE RATIO (SNR)
Chen Lin, PhD DABR 31 AAPM 2016
Signal and Noise
• Proton Density (PD)
• Voxel size (Dx Dy Dz)
• Field Strength (B0)
• Receiver coil sensitivity
• Sequence type and parameters
• Relaxation Properties.
• Averages (NEX)
• Patient / Object.
• Components (receiver coils & electronic components) in receiving chain.
Chen Lin, PhD DABR 32 AAPM 2016
Noise and K-space filter
Noise in MRI • Stochastic Process /
thermal motion of electrons
• “White noise”
Chen Lin, PhD DABR 33
Noise (Wide BW)
K
Intensity
0
Signal (Limited BW) High SNR
Low SNR
AAPM 2016
Low-pass filter
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Signal to Noise Ratio (SNR) • SNR: Signal / Noise
Signal: Average of pixel intensity (in a signal region) Noise: Fluctuation (Stdev ) of pixel intensity (in a noise region)
SNR ~ f(Sequence Type, FA, TR, TE, TI …) *
PD B0 Dx Dy Dz ( Nphase * NEX / rBW )1/2
• Scan time = Nphase * NEX * TR • SNR Efficiency = SNR / Scan Time • Contrast to Noise Ratio (CNR) = |STissue1 – STissue2| / Noise
Chen Lin, PhD DABR 34 AAPM 2016
Thank you !
[email protected]