Magnetic Resonance Imaging:Magnetic Resonance Imaging:Physical PrinciplesPhysical Principles

,

Lewis Center forNeuroImaging

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Physics of MRI, An OverviewPhysics of MRI, An Overview Nuclear Magnetic

Resonance– Nuclear spins– Spin precession and the

Larmor equation– Static B0– RF excitation– RF detection

Spatial Encoding– Slice selective excitation– Frequency encoding– Phase encoding– Image reconstruction

Fourier Transforms– Continuous Fourier

Transform– Discrete Fourier Transform– Fourier properties– k-space representation in

MRI

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Physics of MRIPhysics of MRI Echo formation

– Vector summation– Phase dispersion– Phase refocus

2D Pulse Sequences– Spin echo– Gradient echo– Echo-Planar Imaging

Medical Applications– Contrast in MRI– Bloch equation

Tissue properties– T1 weighted imaging– T2 weighted imaging– Spin density imaging

Examples 3D Imaging Spectroscopy

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Many spins in a voxel: vector summationMany spins in a voxel: vector summation

spins in step spins not in step

Rotating frame

Lamor precession

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Phase dispersion due to perturbing B Phase dispersion due to perturbing B fieldsfields

Spin Phase Bt B = B0 + B0 + Bcs + Bpp

sometime after RF excitationImmediately after RF excitation

sampling

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Refocus spin phase – echo formationRefocus spin phase – echo formation

time

• Invert perturbing field: B -B

• Invert spin state: -

Phase 0 Bt -B(t-TE/2) 0

Phase 0 Bt -+B(t-TE/2) 0

Echo Time (TE)

(gradient echo, k-space sampling)

(spin echo)

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Spin EchoSpin Echo

Spins dephase with time

Rephase spins with a 180° pulse

Echo time, TE

Repeat time, TR

(Running analogy)

1 . E q u ilib riu m 2 . 9 0 P u lset= 0

3 . S p in D ep h a s in g

4 . 1 8 0 P u lset= T E /2

5 . S p in ech ot= T E

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Frequency encoding - 1D imaging Frequency encoding - 1D imaging

m(x)

Spatial-varying resonance frequency during RF detection

S(t) = m(x)eikxxdx = S(kx), m(x) = FT{S(kx)}

S(t) ~ eit

S(t) ~ m(x)eiGxxtdx

kx = Gxtx

B = B0 + Gxx

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Slice selectionSlice selectionSpatial-varying resonance frequency during RF excitation

z

B1 freq band

= 0 + Gzz

m+ = mx+imy ~ b1(t)e-iGzztdt = B1(Gzz)

Excited location

Slice profile

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Gradient Echo FT imagingGradient Echo FT imaging

y Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

z Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

RF

-35000

0

35000

0 2000 4000 6000 8000 10000Time (us)

Am

pli

tud

e (a

rb)

x Gradient

-35000

0

35000

Am

plit

ud

e (

arb

)

kx

ky

Readout

Repeat with different phase-encodingamplitudes to fill k-space

dttGtk )(2

)(

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Pulse sequence designPulse sequence design

y Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

z Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

RF

-35000

0

35000

0 2000 4000 6000 8000 10000Time (us)

Am

pli

tud

e (a

rb)

x Gradient

-35000

0

35000

Am

plit

ud

e (

arb

)

prewinderspoiler

rephasor

rewinderspoiler

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EPI (echo planar imaging)EPI (echo planar imaging)X

Y

Z

time

kx

ky

Quick, but very susceptible to artifacts, particularly B0 field inhomogeneity.Can acquire a whole image with one RF pulse – single shot EPI

RF

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Spin Echo FT imagingSpin Echo FT imagingx Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

y Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

z Gradient

-35000

0

35000

Am

pli

tud

e (a

rb)

RF

-35000

0

35000

0 5000 10000 15000 20000 25000Time (us)

Am

pli

tud

e (a

rb)

kx

ky

dttGtk )(2

)(

Readout

Repeat with different phase-encodingamplitudes to fill k-space

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Spin RelaxationSpin RelaxationSpins do not continue to precess foreverLongitudinal magnetization returns to equilibrium

due to spin-lattice interactions – T1 decay

Transverse magnetization is reduced due to both spin-lattice energy loss and local, random, spin dephasing – T2 decay

Additional dephasing is introduced by magnetic field inhomogeneities within a voxel – T2' decay. This can be reversible, unlike T2 decay

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Bloch EquationBloch EquationThe equation of MR physics

Summarizes the interaction of a nuclear spin with the external magnetic field B and its local environment (relaxation effects)

MT

zMMT

BMdt

Mdz

20

1

1ˆ

1

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Contrast - T1 DecayContrast - T1 Decay Longitudinal relaxation

due to spin-lattice interaction

Mz grows back towards its equilibrium value, M0

For short TR, equilibrium moment is reduced

)1()( 1/0

Ttz eMtM

0 1 2 3 4 5-1.0

-0.5

0.0

0.5

1.0180

o Pulse

Inversion Recovery

t/T1

Mz/M

0

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Contrast - T2 DecayContrast - T2 Decay Transverse relaxation due

to spin dephasing T2 irreversible dephasing T2/ reversible dephasing Combined effect

*2/

/22

*2

)0()(

111

TteMtM

TTT

0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

t/T2*M

x(t)

/Mx(

0)

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Free Induction Decay – Free Induction Decay – Gradient echo (GRE)Gradient echo (GRE)

Excite spins, then measure decay

Problems:– Rapid signal decay– Acquisition must be

disabled during RF– Don’t get central

“echo” data

time

e-t/T2*

90 RF0

MR signal

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Spin echo (SE)Spin echo (SE)

time

e-t/T2*

90 RF0

MR signal

180 RF0

e-t/T2

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MR Parameters: TE and TRMR Parameters: TE and TREcho time, TE is the time from the RF excitation

to the center of the echo being received. Shorter echo times allow less T2 signal decay

Repetition time, TR is the time between one acquisition and the next. Short TR values do not allow the spins to recover their longitudinal magnetization, so the net magnetization available is reduced, depending on the value of T1

Short TE and long TR give strong signals

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Contrast, Imaging ParametersContrast, Imaging Parameters

)GRE(e)e1(or

)SE(e)e1()TE,TR(S*21

21

T/TET/TR

T/TET/TR

TE TR Image WeightingShort Long ProtonShort Short T1Long Long T2, T2*

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Properties of Body TissuesProperties of Body TissuesTissue T1 (ms) T2 (ms)

Grey Matter (GM) 950 100

White Matter (WM) 600 80

Muscle 900 50

Cerebrospinal Fluid (CSF) 4500 2200

Fat 250 60

Blood 1200 100-200

MRI has high contrast for different tissue types!

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MRI of the Brain - SagittalMRI of the Brain - Sagittal

T1 ContrastTE = 14 msTR = 400 ms

T2 ContrastTE = 100 msTR = 1500 ms

Proton DensityTE = 14 msTR = 1500 ms

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MRI of the Brain - AxialMRI of the Brain - Axial

T1 ContrastTE = 14 msTR = 400 ms

T2 ContrastTE = 100 msTR = 1500 ms

Proton DensityTE = 14 msTR = 1500 ms

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Brain - Sagittal Multislice T1Brain - Sagittal Multislice T1

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Brain - Axial Multislice T1Brain - Axial Multislice T1

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Brain TumorBrain Tumor

Post-Gd T1

T1 T2

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3D Imaging3D ImagingInstead of exciting a thin slice, excite a thick slab

and phase encode along both ky and kz

Greater signal because more spins contribute to each acquisition

Easier to excite a uniform, thick slab than very thin slices

No gaps between slicesMotion during acquisition can be a problem

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2D Sequence (Gradient Echo)2D Sequence (Gradient Echo)

Gx

Gy

Gz

b1

acqky

kx

TR

TEScan time = NyTR

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3D Sequence (Gradient Echo)3D Sequence (Gradient Echo)

Gx

Gy

Gz

b1

acq

kx

ky

kz

Scan time = NyNzTR

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3D Imaging - example3D Imaging - example

•Contrast-enhanced MRA of the carotid arteries. Acquisition time ~25s.•160x128x32 acquisition (kxkykz).•3D volume may be reformatted in post-processing. Volume-of-interest rendering allows a feature to be isolated.•More on contrast-enhanced MRA later

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SpectroscopySpectroscopy Precession frequency depends on the chemical

environment (Bcs) e.g. Hydrogen in water and hydrogen in fat have a f = fwater – ffat = 220 Hz

Single voxel spectroscopy excites a small (~cm3) volume and measures signal as f(t). Different frequencies (chemicals) can be separated using Fourier transforms

Concentrations of chemicals other than water and fat tend to be very low, so signal strength is a problem

Creatine, lactate and NAA are useful indicators of tumor types

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Spectroscopy - ExampleSpectroscopy - Example

Intensity

Frequency

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Future lecturesFuture lectures Magnetization preparation

(phase and magnitude, pelc)

Fast imaging (fast sequences, epi, spiral…)

Motion (artifacts, compensation, correction, navigator…)

MR angiography (TOF, PC, CE)

Perfusion and diffusion Functional imaging

(fMRI) Cardiac imaging

(coronary MRA)

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33rdrd dimension – phase encoding dimension – phase encoding

Before frequency encoding and after slice selection, apply y-gradient pulse that makes spin phase varying linearly in y.

Repeat RF excitation and detection with different gradient area.

S(ky, t) = m+(x,y,z)dz)eikyyeiGxxtdxdy