Physics of MR Image AcquisitionHST-583, Fall 2002

• Review: - MRI: Overview - MRI: Spatial Encoding

• MRI Contrast: Basic sequences - Gradient Echo - Spin Echo - Inversion Recovery

HST.583: Functional Magnetic Resonance Imaging: Data Acquisition and Analysis Harvard-MIT Division of Health Sciences and Technology Dr. Jorge Jovicich

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Overview of an MRI procedure

Tissue protons align

IMAGE

(equilibrium state)

RF pulses

Protons absorb

(excited state)

processes

Protons emit RF energy )

detection

Relaxation processes

Repeat

using magnetic field gradients

Subject

Safety screening

RAW DATA MATRIX Fourier transform

00 Bγω = Larmor EquationMagnetic field with magnetic field

RF energy

Relaxation

(return to equilibrium state

NMR signal

Spatial encoding

HST.583 S(t1,t2) S(x1,x2)

Dynamics of the Magnetization

d r

M( t )

dt =

rM( t ) × γ

rBext ( t) −

( Mx i + My j) T2

* − (Mz − M0 )

T1

k

B0

M0

timeEquilibrium

RF

Equilibrium

signal 00 Bγω =

B0 B0 B0 B0

M0

M(t)M(t) M(t)

• Mathematical Description: precession + relaxation (Bloch equations)

NMR

• Geometrical description: damped precession

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Spatial Encoding in MRI

Key concept: ω( r ) = γ (B0 + G.r)

• Slice Selection

• Frequency Encoding

• Phase Encoding

- Location - Thickness - Rephasing/Refocussing

- Fourier Transform - FOV - Gradient Echo Formation

- Phase / Frequency Equivalency - FOV

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Slice Selection

• RF excitation (selective bandwidth) + magnetic field gradient

shape & duration bandwidth (bw)• RF pulse properties

frequency (wo)

∆z

z)

z

B Bo bw

w

zo

wo

Gz

ω( r ) = γ B0 + G.r( ) RF

Gz

Phase

• Magnetic field gradient (G • Schematically

Slice thickness (∆z): bw = γ Gz ∆z • Slice parameters Slice center (zo): wo = γ Gz zo

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‘Pulse sequence’ so far

RF

“slice select” Gz

MR signalfrom whole S(t)

Selected slice

Sample points

t

t

T2 *

t

HST.583 Courtesy of L. Wald

Frequency Encoding

• After slice selection all spins in the selected plane have the same frequency and phase (a)

• Signal is acquired while a magnetic field gradient Gx is on (b)

Gx

(a) (b) Gradient field y

63 MHz 64 MHz 65 MHz x

x

w(x) = γ Gx x

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‘Pulse sequence’ so far

RF

“slice select” Gz

“freq. encode” Gx(read-out)

S(t)

Sample points t

t

t

t Signal dephases rapidly

HST.583 Courtesy of L. Wald

More signal can be obtained:

RF

“slice select” Gz

“freq. encode” Gx(read-out)

S(t)

Sample pointst

-+

Acquisition window

Dephase

Rephase

We can save some time …HST.583

‘Pulse sequence’ so far

RF

“slice select” Gz

“freq. encode” Gx(read-out)

S(t)

Sample points

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t

-

+

Acquisition window

Gradient Echo

Frequency Encoding

Measured signal: Frequency spectrum: time domain 1D x-projection

S(t) Fourier transform

S(ω)

time

bw frequencyrec

δt Receiver bandwidth (bw )rec

Sampling time δt=1/ bwrec Nx: number of samples ω( r ) = γ (B0 + G.r)

Acquisition time (tacq): t = N δt = N / bwacq x x rec

• Relevant parameters Resolution (δx): δx = FOV / Nx x

Field of view (FOVx): bw = γ G FOVrec x x

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We could have measured ‘exactly’the same information differently:

RF

“slice select” Gz

“freq. encode” Gx(read-out)

S(t)

Sample points t

-

+

Acquisition window

RF excitation sampling points

Each

So far we’ve used ONE and we’ve acquired Nx

while the read-out gradient was ON

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Let’s look at one arbitrarysampled point in the MR signal

RF

Gz

Gx

S(t)

HST.583 dephasing during t Same net dephasing

-

+

t -

+ = -

-

RF

S(t)

Gz

Gx =

S(t) depends on net

We can do the same for all Nx sampled points:

-

RF

Gz

Gx RF

Gz

Gx

+

RF

Gz

Gx

Measure one point after dephasing gradient

Net negative dephasing

Net zero dephasingRepeat experiment Nx

times to sample all points Net positive dephasingHST.583

We could have measured ‘exactly’the same information differently:

S(t)

Measured signal: time domain

RF S(t)

slice Gzselect time

phase Gx FT

encode Frequency spectrum:

1D x-projection S(ω)

Repeat Nx times frequency

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Basic Gradient Echo Sequence

RF α α

TR TE

Gz Slice

Gy Phase

Gx Read

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Conventional spin-warpMRI sequence

θ Repeat Nphase times kphase

RF

GN

GNphase

slice

phase

phase

TE kreadGread

Signal Prephase

timet

0 acq

NNread TR Prephase

read

The signal we measure is in tγspatial frequency space (k-space) k(t ) = G(t ') dt '

2π ∫ 0 HST.583

Pulse Sequences & Image Contrast

Contents: • Definition of Contrast • Contrast parameters • Concept of MRI contrast weighting • Properties of pulse sequences &

sequence parameters

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Image Contrast Definition

• Goal: maximise the contrast ( USEFUL IMAGES! )

• Contrast: difference in MR signals between different tissues

Tissue 1 Tissue 2

Water protons’ T1, T2, T2*, ρ, T1, T2, T2*, ρ,mobility/environment: Diffusion, Flow Diffusion, Flow

MR signal: S1

noise

SSCNR σ

21 − =

S2

Some examples?Contrast to Noise ratio: HST.583

Image Contrast: What can we manipulate?

Tissue Properties: fixed Experimental Variables

Tissue T1 (ms) T2 (ms) ρ* Fat 260 84 0.90 White Matter 780 90 0.72 Gray Matter 920 100 0.84 CSF 3000 300 1.00

• Pulse sequence

• Pulse sequence parameters

- Repetition time: TR

- Echo time: TE

ρ*: % H2O relative to CSF - Inversion time: TI

- RF flip angle: α

• Contrast agent

What’s the effect of these variables?

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Image Contrast:Weighting the MR Signal

• General MRI pulse sequence: combination of contrasts

Signal Intensity: S(x,y) = k T1× ρ ×

× T2 × …

• Contrast Weighting: maximize one term, minimize the others

Example: T1-weighting T1

S(x,y) = k ρ× ×

× T2 × …

by choosing adequate sequence & sequence parameters

Some examples?HST.583

Typical MRI sequences

Gradient Echo:- Proton Density weighting - T1 weighting - T2* weighting

Spin Echo:- Proton Density weighting - T1 weighting - T2 weighting - Double echo: PD & T2 weighting

Inversion Recovery:- MP-RAGE: for high T1 contrast - FLAIR: for PD or T2 weighting without CSF signal

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Typical MRI sequences

Gradient Echo:- Proton Density weighting - T1 weighting - T2* weighting

Spin Echo:- Proton Density weighting - T1 weighting - T2 weighting - Double echo: PD & T2 weighting

Inversion Recovery:- MP-RAGE: for high T1 contrast - FLAIR: for PD or T2 weighting without CSF signal

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Basic Gradient Echo Sequence

RF

Slice

Phase

Read

α α

TR TE

−

−−= *

21 0 expexp1sin

T TE

T TRMSGRE αMR Signal:

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Repetition Time (TR): T1 contrast

TR encodeRF

Voltage(Signal)

Mxy

Mz

WM

GM

encode encode

GM: gray matter (long T1) time WM: white matter (short T1)

HST.583 Courtesy of L. Wald

Gradient Echo Sequence

−

−−= *

21 0 expexp1sin

T TE

T TRMSGRE α

*

*

Proton Density weighting T1 weighting T2* weighting ( TR >>T1, short TE, sin α ~ 1 ) ( TR ~ T1, short TE, sin α ~ 1 ) ( TR >>T1, TE ~ T2* )

Water density Gray / White matter / CSF Hemorrhage

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Gradient Echo Sequence

FA = 3o

FA = 5o

FA = 30o

FLASH

Courtesy of A. Dale and B. Fischl

Manipulating contrast with flip angle

Proton Density Weighting T1 Weighting

Typical MRI sequences

Gradient Echo:- Proton Density weighting - T1 weighting - T2* weighting

Spin Echo:- Proton Density weighting - T1 weighting - T2 weighting - Double echo: PD & T2 weighting

Inversion Recovery: - MP-RAGE: for high T1 contrast - FLAIR: for PD or T2 weighting without CSF signal

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Basic Spin-Echo Sequence

Excitation Pulse Refocusing Pulse

τ τ

180o

90o

RF

Slice

TE Phase

Read

Spin EchoHST.583

Spin-Echo Sequence: The MR Signal

τ τ

TE

TR

S TR TE

SE = M0 1 − exp − exp − T1 T2

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Spin Echo Sequence

−

−−=

21 0 expexp1sin

T TE

T TRMSGRE α

Proton Density weighting T1 weighting T2 weighting ( TR >>T1, short TE, sin α ~ 1 ) ( TR ~ T1, short TE, sin α ~ 1 ) ( TR >>T1, TE ~ T2 )

Water density Gray / White matter / CSF Hemorrhage

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Double Spin Echo Sequence

τ τ τ τ

180o 180o

90o

RF

Slice

TE1 TE2Phase

Read

Echo 1 Echo 2 HST.583

Typical MRI sequences

Gradient Echo:- Proton Density weighting - T1 weighting - T2* weighting

Spin Echo:- Proton Density weighting - T1 weighting - T2 weighting - Double echo: PD & T2 weighting

Inversion Recovery:- MP-RAGE: for high T1 contrast - FLAIR: for PD or T2 weighting without CSF signal

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Inversion Recovery

Excitation Pulse Refocusing Pulse Inversion Pulse

τ τ TI

180o 180o

90o

RF

Slice

TE Phase

Read

Magnetization Preparation Spin Echo

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Enhanced T1-weighting: Inversion Recovery

M0

-Mo

Spin Echo

TE

Mz(t)

90o

180o180o TI

CSF GM

180o Inversion: prepare magnetization prior to Spin Echo detection

2/1/1/ )21(Signal eee −−− +−∝ ρ T TE T TR T TI

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Fluid Attenuation Inversion Recovery (FLAIR)

M0

-Mo

Mz(t)

180o

TI

Spin Echo

TE

90o

180o

CSF

GM

Signal null at: TI = ln(2)* T1

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Physics of MR Image AcquisitionHST-583, Fall 2002

• Review: - MRI: Overview - MRI: Spatial Encoding

• MRI Contrast: Basic sequences - Gradient Echo - Spin Echo - Inversion Recovery

HST.583