mri image formation - aapm

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8/3/2016 1 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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8/3/2016

1

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

8/3/2016

2

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]

8/3/2016

3

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

8/3/2016

4

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

8/3/2016

5

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

8/3/2016

6

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

8/3/2016

7

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

8/3/2016

8

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

8/3/2016

9

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

8/3/2016

10

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

8/3/2016

11

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

8/3/2016

12

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]