©2016 m.s. cohen all rights [email protected] reserved · proton precession applied magnetic ......

©2016 M.S. Cohen all rights reserved

[email protected]

©2016 M.S. Cohen all rights reserved [email protected]

AN MRI PRIMER


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,…}


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


PROTON PRECESSION

Applied Magnetic Field: B

Precession: ω

Spin

ω = γ X B γH ≈ 267.52 Rad/sec/Tesla≈ 42.577 MHz/Tesla


PROTONS IN APPLIED FIELD

Applied Magnetic Field


TRANSITION TO EQUILIBRIUM

Zero Field Field Applied

Up/Down state transitions require quantized energy input

Energy


T1

CSF

BrainFat

Time (seconds)

Magnetization(signal)

1

0.5

01 2 3 40

�

M (t) = M 0 (1− e− tr

T1)


PROTONS IN APPLIED FIELD

Applied MagneticField

Due to their angular momentum, Protons precess in the magnetic field.


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


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


AN RF PULSE CONVERTS LONGITUDINAL MAGNETIZATION INTO SIGNAL

90° RF Pulse

LongitudinalMagnetization

MR Signal

Precession


IN-PHASE PRECESSIONN

S

Receiver

NMR Signal

N

S


OUT OF PHASE PRECESSIONN

S

Receiver

NMR Signal


T2:

The Characteristic Time forTransverse Decay


SUMMARY ANIMATION


HAHN SPIN ECHO2. 90° Pulse

3. T2* Relaxation

4. 180° Pulse

5. Spin Rephasing

6. Spin Echo

1. Equilibrium


SUMMARY ANIMATION


T2 AND TE

0

1

0.5

060 120Time (milliseconds)

Signal

CSF

Brain

Fat

�

S(t) = M xy (t) = M 0e− te

T 2


PARTIAL SATURATION

NMR Signal

Sequence of 90° Pulses

tr tr


EFFECTS OF TE AT LONG TR


CONTRAST, TR AND TE

TRLong

Short

Short LongTE

T2-Weighted

T1-Weighted

ProtonDensity

�

S = kρM 0 (1− e− tr

T1)e− te

T 2


CONTRAST, TR AND TE

TR

Long

Short

Short LongTE

Density

T1

T2


SAMPLE DATA SET (NORMAL)

Sample Data Set (normal)

Fast Spin Echo3 mm Slices

3D IR-SPGR TE = 3.2, TI = 700


SPIN ECHO


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


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


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


1T2*

1T2

1T2

1T2

= + +D’

Molecular Field Inhomogeneity

Diffusion

The Observed Transverse Relaxation Rate, T2*, is the sum of

several components:


MR IMAGE FORMATION


FREQUENCY SELECTIVE EXCITATION

RF

Grad 0

Sir Peter Mansfield


MAGNETIC FIELD GRADIENTS

MRI Instrument in Cross Section

Position

Field Strength

Magnet

Gradient Coil

Physicist


A 1D IMAGE

Position

Field Strength /Frequency


FOURIER PROJECTIONS

MR ImageRaw Data FFT of Raw Data


realimaginary

BACK PROJECTION

Image Domain

Fourier Domain

GradientEncoding

2D FourierTransform

Paul Lauterbur


CONVENTIONAL SPATIAL ENCODING

Grad 1

Samples

A2

A1

Grad 2A2

A1

A2

A1

RF

Grad 0

tr

…

…

…

…

…

te


CONVENTIONAL K-SPACE TRAJECTORY

+K

-Kfrequency

phase

tr


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.


3D K-SPACE

Gz

Gy

Gx

tr

Imaging time = tr * Nz * Ny


t slice

Gz

Gy

Gx

RF

te

MULTI-SLICE MRISlice 1

tr

N =slices tr / tslice

Slice 1Slice 2Slice 3 Slice 4

Readout


SPATIAL ENCODING

Grad 1

Samples

A2

A1

Grad 2A2

A1

A2

A1

RF

Grad 0

tr

…

…

…

…

…

te


CONTRAST ENCODING

Grad 1

Samples

A2

A1

Grad 2A2

A1 A1

RF

Grad 0

tr

…

…

…

…

…

te

tr

te

A2


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


DIFFUSION AND MOTION


GRADIENTS AND PHASE

0 T/2 T

Phase with respect to

center

+

–


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


PHASE AND MOTION

Stationary

Moving

phas

e

0 T/2 T

0 T/2 T


α°

Gz

Gy

Gx

RF

te


Motion Encoding

α°

Gz

Gy

Gx

RF

te


ϕ = γ vT 2

4 + 23aT 3

24 +…⎡⎣

⎤⎦


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


�

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


DIFFUSION & SIGNAL

Denis Le Bihan, Nature Reviews in Neuroscience 4:469, 2003


BRAIN DIFFUSION IS ANISOTROPIC

Schaefer, P. W. et al. Radiology 2000;217:331-345


ISOTROPIC VS. ANISOTROPIC DIFFUSION


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


DETERMINANTS OF IMAGING TIME

Scan Time =

Repetition Time (TR)x Number of Phase Encodes

x NEX (Averages)x Number of 3D Steps


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:


SIGNAL AND FLIP ANGLE

Small Flip Angle Large Flip Angle

α°α°


SMALL AND LARGE FLIP ANGLE

Loss of Longitudinal Magnetization

Small Flip Angle Large Flip Angle


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)


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


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


T2 AND T2*

T2: Transverse Magnetization Decay from Spin-Spin Interactions

T2*: Transverse Magnetization Decay from Local Magnetic Field

Variations


SIGNAL AND TE GRADIENT ECHO

TE=20 TE=40 TE=60

TE=80 TE=100


MAGNETIC SUSCEPTIBILITY

The Extent to Which a Substance Becomes “MAGNETIZED” when Placed Within a Magnetic Field


MAGNETIC SUSCEPTIBILITY

Applied Magnetic

Field

Objects with Susceptibility Different than Air Distort the Magnetic Field


T2*

100ms

0ms


SPIN ECHO

Gz

Gy

Gx

RF180°90°

te

10 msec


FLASH

10 msec

α°

Gz

Gy

Gx

RF

te


FLASH MAGNETIZATION CYCLE1. 2.

3.

α°

Longitudinal Recovery α° RF pulse followedby data collection

Spoiling of transversemagnetization


SSFPα°

Gz

Gy

Gx

α°RF

te


α°

Gz

Gy

Gx

RF

te

α°

Gz

Gy

Gx

α°RF

te

“FLASH” “GRASS” “SSFP”

α°

Gz

Gy

Gx

RF

te


3D MP-RAGE

Gz

Gy

Gx

trti tr tr

RF

…

…

…

…

…

Repeat Ny times

180°α° α° α°


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


TRADEOFFS

Volume Coveragetrslice thicknesste


TRADEOFFS

SNRtrteflip anglevoxel volumecontrastimaging time (e.g., averaging)


TRADEOFFS

Imaging Timetrresolutiontotal slices (due to vendor optimization)


TRADEOFFS

SARflip angleecho train lengthnumber of slices / trtotal scan duration

©2016 m.s. cohen all rights [email protected] reserved · proton precession applied magnetic ......

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