introduction to mri requirements for mriintroduction to mri daniel b. ennis, ph.d. requirements for...

UCLA – Radiology – DCVI

Introduction to MRIDaniel B. Ennis, Ph.D. Requirements for MRI

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Requirements for MRI

• NMR Active Nuclei– e.g. 1H in H20

• Cryogen– Liquid He and N2

• Magnetic Field (B0)– Polarizer

• RF System (B1)– Exciter

• Coil– Receiver

• Gradients (GX, GY, GZ)– Spatial Encoding X-gradY-grad

Z-grad

Main Coil (B0)

Cryostat

Body Coil (B1)

Image Adapted From: http://www.ee.duke.edu/~jshorey R a d i o l o g y

µ Magnetic Moment }� B0 Mz Bulk Magnetization }� B1 Mxy Transverse Magnetization }� Coil

S (t) Received Signal }� GradientsS

� k⇥

k -space signal }� FFTI ( x) Image

Dipoles to Images

Main Field – B0

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� k⇥


Dipoles to Images

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Main Field (B0) - Principles

• B0 is a strong magnetic field– 1.5T, 3.0T, 7.0T, etc.– Z-oriented

• B0 forces to precess– Larmor Equation

• B0 generates – More B0, more

�B0 = B0�k

⇥ = �B

�M =N

totalX

n=1

�µn

�M

�M�M

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Magnetic Dipoles & Larmor

Movie from Don Plewes

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Bulk Magnetization

�M =N

totalX

n=1

�µn

Ntotal=0.24x1023 spins in a 2x2x10mm voxelR a d i o l o g y

}Zeeman Splitting

N� = Spin-Up State, Low EnergyN� = Spin-Down State, High Energy

B0 is o� B0 is on

N�

N�E = � 1

2��B0

E = +12��B0

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

SN

S

N

S

N

S

N

S

N

S

N S

N

S

N

S

N

S

N

S }N

S

N

S

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Zeeman Splitting

N⇥ �N⇤Ntotal

⌅ 42.58⇤ 106 · 6.6⇤ 10�34 · 1.52 · 1.38⇤ 10�23 · 300

⌅ 4.5⇤ 10�6

�� = 42.58⇤ 106 Hz/Th = 6.6⇤ 10�34 J · s [Planck’ Constant]T = 300K (room temperature)K = 1.38⇤ 10�23 J/K [Boltzmann Constant]B0 = 1.5T

N� �N⇥Ntotal

⇥ ��hB0

2KT

~4.5ppm @ 1.5T

RF Pulses – B1

09

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� k⇥


Dipoles to Images

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B1 Field - RF Pulse

• B1 is a – radiofrequency (RF)

• 42.58MHz/T (63MHz at 1.5T) – short duration pulse (~0.1 to 5ms)– small amplitude

• <30 µT– circularly polarized

• rotates at Larmor frequency– magnetic field – perpendicular to B0

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B1 Field

⇤B1 = 2Be1(t) cos(⇥RF t+ �)⇤i

t = ⌧pt = 0

t

t = ⌧pt = 0

t

Hard RF Pulse Soft Sinc RF Pulse

Envelope Function

Carrier Frequency

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Lab vs. Rotating Frame

X Y

Z

X’ Y’

Z=Z’

A lot of the math can be done more easily in the rotating frame.

Laboratory Frame Rotating Frame

RF↵✓ RF↵

✓

Coils

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� k⇥


Dipoles to Images

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Coils

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Faraday’s Law of Induction“The induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.” --http://en.wikipedia.org/wiki/Faraday's_law_of_induction

Time-varying

Magnetic Field

Loop of

Wire

Voltage

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NMR Signal Detection• Coil only detects Mxy

• Coil does not detect Mz

• Coil must be properly oriented

Mxy

✓ V (t) / sin �

Faraday’s Law of Induction

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8-Channel Head CoilEach coil element has a unique sensitivity profile.

Gradients – Gx, Gy, & Gz




� k⇥


Dipoles to Images

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Gradients

• Gradients are a:– Small

• <5G/cm (<0.0075T @ edge of 30cm FOV)– Spatially varying

• Linear gradients• Adds to B0 only in Z-direction

– Time varying• Slewrate Max. ~150-200mT/m/ms

– Magnetic fields• Adds/Subtracts to the B0 field

– Parallel to B0

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MRI InstrumentationY-Gradient

Transceiver

Patient

Z-Gradient

X-Gradient

http://www.magnet.fsu.edu

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Z Gradients

B0

B0 � �B0

MaxwellPair Coil

I

I

B0 + �B0

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Z-Gradients

Z

X

B0 + �B0

B0 � �B0

B0

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X-Gradients

B0B0��B0 B0+�B0

Z

X

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X+Z-Gradients

Z

X

Z

X

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X+Z-Gradients

Spin IsochromatGroup of spins with the same resonance

frequency.

Possible Slice

Z

X

k-space

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What is k-space?

• Spatial Frequency Mapping– Each echo measures some of the spatial

frequencies that comprise the object– k-space has units of cm-1 or mm-1

– Audio signals have units of Hertz (s-1)

• A line of k-space is filled by an echo• 2D FT of k-space produces the image

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1D k-space

time-or-

space

Any signal/image can be decomposed into a summation of sine waves of appropriate amplitude.

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1D k-space

time-or-

space


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1D k-space

time-or-

space


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1D k-space

time-or-

space


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1D k-space

time-or-

space


time-or-

space

Fourier Representation

low highfrequency

FFT➠R a d i o l o g y

What is k-space?

➠FFT

k-space image space

k-space is the raw data collected by the scanner.

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What is k-space?

➠FFT

Contrast

➠FFT

Edges

Center

Edges

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What is k-space?

ContrastInformation

Points in k-space represent different patterns in an image.

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k-space spikes

➠FFT

k-space image space

A k-space spike creates a banding artifact.

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k-space and Field of View

FFT➠

ky

kx

ky

kx FFT➠

Uniformly skipping lines in k-space causes aliasing.

FOV =1

�k

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k-space and Resolution

FFT➠

ky

kx

ky

kx FFT➠

Acquiring fewer phase encodes decreases resolution.

Image Contrast

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Why Image Contrast?Visual Area

of the Thalamus

Visual Cortex

Retina

Opticnerve

Optictract

Opticchiasm

The human visual system is more sensitive to contrast than absolute luminance.

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Why Image Contrast?

Bloch Equations with Relaxation

DCVI

1952 Nobel Prize in Physics

Felix Bloch b. 23 Oct 1905 d. 10 Sep 1983

Edward Purcell b. 30 Sep 1912 d. 07 Mar 1997

“for their development of new methods for nuclear magnetic

precision measurements and discoveries in connection therewith“

DCVI

Bloch Equations

• Precession– Magnitude of unchanged– Phase (rotation) of changes due to

• Relaxation– T1 changes are slow O(100ms)– T2 changes are fast O(10ms)– Magnitude of M can be ZERO

• Diffusion– Spins are thermodynamically driven to

exchange positions.

{

Precession TransverseRelaxation

LongitudinalRelaxation

Diffusion

{ { {d~M

dt= ~M⇥ �~B� M

x

i +My

j

T2� (M

z

�M0) k

T1+Dr2 ~M

~M~B~M

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Longitudinal & Transverse Relaxation

Mxy

(t) = M0xy

e�t/T2{Initial Condition

Return to Equilibrium

General solutions to the Bloch equations with relaxation in the rotating frame during free precession.

Mz (t) = M0z e

� tT1 +M0

⇣1� e�

tT1

⌘{ {

Initial Condition Return to Equilibrium

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T1 & T2 RelaxationM0

A.U.

Time [ms]

M0xy

M0z

MzMxy

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T1 and T2 Values @ 1.5T

Tissue T1 [ms] T2 [ms]

gray matter 925 100

white matter 790 92

muscle 875 47

fat 260 85

kidney 650 58

liver 500 43

CSF 2400 180

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T1 Relaxation

• Longitudinal or spin-lattice relaxation• Typically, (10s ms)<T1< (100s ms)• T1 is long for

– Small molecules (water)– Large molecules (proteins)

• T1 is short for– Fats and intermediate-sized molecules

• T1 increases with increasing B0

• T1 decreases with contrast agents • Short T1s are bright on T1-weighted image

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T1 Relaxation

0 1000 2000 3000 4000 5000

1.00

0.75

0.50

0.25

0.00

Fat – 260ms Liver – 500ms CSF – 2400ms

Decay Time [ms]

Fraction of M0

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T2 Relaxation• Transverse or spin-spin relaxation

– Molecular interaction causes spin dephasing

• Typically, T2<(10s ms)• T2 increases with

– Decreasing molecular size• Large molecules have a short T2

– Fat has a short T2

– Increasing molecular mobility• Liquids have long T2s

– CSF, edema

– Decreasing molecular interactions• Solids have short T2s

• T2 relatively independent of B0

• T2 always < T1

• Long T2 is bright on T2 weighted imageR a d i o l o g y

T2 Relaxation

0 200 400 600 800

100

75

50

25

00

Liver – 43ms Fat – 85msCSF – 180ms

Decay Time [ms]

Percent Signal [a.u.]

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T2* Relaxation

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T2* Relaxation• The “observed” transverse relaxation time constant• Spin-spin (T2) dephasing combined with...

– Irreversible

• Intravoxel field inhomogeneity– B0

• Typically a few PPM over DSV (40-50cm)• 1PPM = 640Hz = 1.5µT

– Susceptibility differences (macro and micro)• Induce small field perturbations, therefore dephasing

– Reversible• Can be rephased with a spin echo

– Not with a gradient echo!

• Diffusion– Irreversible

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T2* Relaxation

ReversibleLosses

IrreversibleLosses

1T ⇤

2

=1T2

+ ��B0

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T2* Relaxation

ReversibleLosses

IrreversibleLosses

1

T ⇤2

=1

T2+

1

T02

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T2* Relaxation

ReversibleLosses

IrreversibleLosses

1

T ⇤2

=1

T2+

1

T02

+1

TD2

+ · · ·

IrreversibleLosses

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0 125 250 375 500

100

75

50

25

00

T2 – 125ms T2* – 90ms

Decay Time [ms]

Percent Signal [a.u.]

T2* vs T2

T2*<T2 (always!)

What are echoes?


What are echoes?

• Two-sided NMR signals– First half from re-focusing– Second half from de-phasing

• Spin Echoes– Arise from multiple RF-pulses

• Gradient Echoes– Arise from magnetic field gradient reversal

• Line of k-space

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Why echoes?• Free Induction Decay

– NMR signal immediate after an RF pulse– Signal decays rapidly

• T2*(<T2)+Spectral distribution

• Imaging requires certain “delays”– Slice-selective re-phasing– Phase encoding– Readout pre-phasing

• Echoes let us buy some time

RF

Free Induction Decay (FID)R a d i o l o g y

Pulse Sequences

Contrast Module Imaging Module

Saturation RecoveryInversion Recovery

T2-preparation

(Fast) Spin Echo(Spoiled) Gradient Echoaka “Host Sequence”

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Pulse Sequence Definitions

• TR - Repetition Time– Duration of basic pulse sequence repeating block– At least one echo acquired per TR

• TE - Echo Time– Time from excitation to the maximum of the echo

Spin Echo Imaging

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Spin Echo

• Advantages– All spins within voxel rephased

• Insensitive to off-resonance– B0 inhomogeneity– Intravoxel Chemical shift signal loss– Susceptibility

– Great for T1, T2, ρ contrast• Not T2*

– High SNR

• Disadvantages– TR can be long– SAR can be high

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Spin Echo

RF

Signal

90°

Some T2* signal losses are reversible.

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Spin Echo

RF

Signal

90°180°

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Spin Echo

TE

RF

Signal

90°180°

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Spin EchoTR

TE

RF

Signal

90°180°

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Spin Echo - ContrastTR

TE

RF

Signal

90°180°

e� t

T⇤2

e� t

T2

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Spin EchoTR

TE

RF

Signal

90°180°

How do you adjust the TR?How do you adjust the TE? R a d i o l o g y

Spin Echo - Refocusing

http://en.wikipedia.org/wiki/File:HahnEcho_GWM.gif

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Spin Echo ContrastSpin Density Short LongT1-Weighted Short IntermediateT2-Weighted Intermediate Long

Spin Echo Parameters

AEcho

/ ⇢⇣1� e�TR/T1

⌘e�TE/T2

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Spin Echo ContrastSpin Density 10-30ms >2000msT1-Weighted 10-30ms 450-850msT2-Weighted >60ms >2000ms

Spin Echo Parameters

Images Courtesy of Mark Cohen

TR

Short

Long

TEShort Long

T2

T1

ρ

X

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Spin Echo - Contrast

http://en.wikipedia.org/wiki/File:HahnEcho_GWM.gif R a d i o l o g y

Spin Echo - Variable TE T2 Contrast

TE=13ms TE=26ms TE=53ms

TE=106ms TE=145ms TE=172ms

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Echo-3

Fast Spin Echo90°

180°

RF

GSlice

GPhase

GReadout

Signal

180° 180°

T2-decay

Echo-2Echo-1

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Fast Spin Echo• Advantages

– Turbo factor accelerates imaging– Can be used with 2D slice interleaving– Allows T2 weighted imaging in a breath hold

• Disadvantages– High turbo factors (ETL>4):

• Blur images• Alter image contrast

– Fat & Water are both bright on T2-weighted• Water/CSF T2 is long• Repeated 180s reduce spin-spin interaction

– This lengthens the moderate T2 of fat

– SAR can be high

Inversion Recovery


Inversion Recovery• Key Features

– Signal Preparation Block• 180° RF Inversion Pulse• TI – Inversion Time [ms]

– Signal Measurement Block• Spin Echo or Gradient Echo

• Signal during imaging is dependent on– T1 and TI

• TR is typically long (>2000ms)– Better for 2D sequences

• Can null a single T1 species if– TI=ln(2)T1=0.69T1

• Can be used for quantitative T1 mapping

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Inversion Pulses

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Inversion Recovery

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180°

Inversion Recovery

Contrast

180°

ContrastRelaxImaging

TITR

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180°

Inversion Recovery

TE

180°

90°

180°

Contrast

TRTI

Relax Contrast

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180°

Inversion Recovery180°

90°

180°

TRTI

Mz

Contrast Relax

TE

Contrast

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180°

Inversion Recovery180°

90°

180°

TRTI

Mz

Contrast Relax

TE

Contrast

Gradient Echo Imaging


Basic Gradient Echo Sequence

RF

Slice Select

PhaseEncode

Freq.Encode

Free Induction Decay (FID)

e� t

T⇤2

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RF

Slice Select

PhaseEncode

Freq.Encode

Free Induction Decay (FID)

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RF

Slice Select

PhaseEncode

Freq.Encode

Gradient Echo!

e� t

T⇤2

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RF

Slice Select

PhaseEncode

Freq.Encode

TETR

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WastedTime


RF

Slice Select

PhaseEncode

Freq.Encode

TETR

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Gradient Echo + Spoiling

RF

Slice Select

PhaseEncode

Freq.Encode

SpoilerGradient

RF PhaseCycling

SpoilerGradient

Gradient Echoes & Contrast

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Spoiled Gradient Echo Contrast

Aecho

/⇢

�1� e�TR/T1

�

1� cos ↵e�TR/T1sin ↵e�TE/T

⇤2

Contrast adjusted by changing TR, flip angle, and TE.

Type of Contrast TE TR Flip AngleSpin Density Short Long SmallT1-Weighted Short Intermediate LargeT2*-Weighted Intermediate Long Small

Gradient Echo Parameters

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T2*-weighted Gradient Echo Imaging

TE=9ms TE=30msSusceptibility Weighting (darker with longer TE)

Bright fluid signal (long T2* is brighter with longer TE)

Axial Shoulder Axial Shoulder

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Spoiled GRE & Ernst Angle

�Ernst = arccos�e�

T RT1

⇥

Tissue T1 [ms] T2 [ms]

muscle 875 47fat 260 85

Produces the largest MRI signal for a given TR and T1.

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10° 20° 30° 40° 50° 60° 70° 80° 90°Flip Angle

MR

I Sig

nal [

A.U

.]

FatMuscle

Contrast

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1° 5° 10° 20°

30° 45° 60° 90°

High Muscle Signal High Fat Signal

Highest Contrast

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Spin Echo EPI90°

180°

RF

GSlice

GPhase

GReadout

Signal

TE

90°

TR

T2*-decay

Off Resonance Effects Accumulate

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Spin Echo EPI• Advantages

– Can acquire data in a “single shot”– Can be used with 2D slice interleaving– Allows fast T2* weighted imaging

• Disadvantages– Single Shot EPI

• Ghosting • Blur images• Image distortion• Alter image contrast

– Multi-shot EPI• Slower than single shot

– Faster than SE

• Applications– DWI, Perfusion, fMRI

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� k⇥


Dipoles to Images

UCLA – Radiology – DCVI

Daniel B. Ennis, [email protected] (Office)http://ennis.bol.ucla.edu

Peter V. Ueberroth Bldg.Suite 1417, Room C10945 Le Conte Avenue

Thanks

introduction to mri requirements for mriintroduction to mri daniel b. ennis, ph.d. requirements for...

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