Textbook for the

Statistical Parametric Mapping

(SPM) class

Statistical Parametric Statistical Parametric MappingMapping

Chapter 3

Principles of Nuclear Magnetic Resonance and MRI

Many thanks to those that share their MRI slides online

Methodology

Interpretation Applications

Physical ScienceTechnology

MedicineMedicinePhysiologyPhysiology

Physics

Engineering

Computer Science

CognitiveCognitiveScienceScience

Statistics

NeuroscienceNeuroscience

Peter Bandettini NIH

MRI Has Many Layers Of Complexity

…

Physics … Engineering … Technology … Applications … Interpretation …

Even subdivisions below have multiple layers of complexity

History: MRI

• Paul Lauterbur and Peter Mansfield won the Nobel Prize in Physiology/Medicine (2003) for their pioneering work in MRI

• 1940s – Bloch & Purcell: Nuclear Magnetic Resonance

• 1990s - Discovery that MRI can be used to distinguish oxygenated blood from deoxygenated blood. Leads to Functional Magnetic Resonance imaging (fMRI)

• 1973 - Lauterbur: gradients for spatial localization of images

• 1977 – Mansfield: first image of human anatomy, first echo planar image (a fast imaging technique)

Fiber Track Imaging

Angiography

Venography

Anatomy

Perfusion

Peter Bandettini NIH

fMRIfMRI

Peter Bandettini NIH

P

R

Basic Physics of MRI

• Why does neutron have magnetic properties?• What about electron(s) magnetic properties?

• All magnetic fields are the result of charge in motion• Nucleus of an atom has a magnetic moment when it

has an odd number of protons (or neutrons). Single proton in Hydrogen yields strongest magnetic effect.

Model of spin as motion

Basic Physics of MRI• The orientation of nuclear magnetic moments are

affected by an external magnetic field (that not due to the local nuclear magnetic moments).

No external magnetic field. Orientation is

random.

External magnetic field B0. Orientation follows

direction of external magnetic field.

Basic Physics of MRI• Nuclei line up with magnetic moments either in a parallel or

anti-parallel configuration.• In body tissues more line up in parallel creating a small

additional magnetization M in the direction of B0.

Nuclear magnetic moments precess

about B0.

Nuclei spin axis not parallel to B0 field

direction.

Field Strength and the Net Magnetization (M)

NL

NU = 1,000,000

~ 1,000,000 + 10

1.5 T

~ 1,000,000 + 15

= 1,000,000 - 5

...

...

NL

NU

ΔE3.0T = 2*ΔE1.5T ΔE1.5T

..

...

NNLL = # /volume in low energy state = # /volume in low energy state

NNUU = # /volume high energy state = # /volume high energy stateM (N(NLL - N - NUU))

Lowering temperature increases M – Any volunteers?

MM3.0 T

Basic Physics of MRI• Frequency of precession of magnetic moments given

by Larmor relationship

~ 43 mHz/Tesla

Larmor frequencies of RICs MRIs

3T ~ 130 mHZ7T ~ 300 mHz

11.7T ~ 500 mHz

f = f = x B x B00

f = Larmor frequency (mHz) = Gyromagnetic ratio (mHz/Tesla)B0 = Magnetic field strength (Tesla)

NMRable Nuclei

Basic Physics of MRI

Body Body 11H content is high due to water (>67%)H content is high due to water (>67%) Hydrogen protons in mobile water are primary Hydrogen protons in mobile water are primary

source of signals in fMRI and aMRIsource of signals in fMRI and aMRI

• M is parallel to B0 since transverse components of magnetic moments are randomly oriented.

• The difference between the numbers of protons in the parallel (up here) and anti-parallel states leads to the net magnetization (M).

• Proton density relates to the number of parallel states per unit volume.

• Signal producing capability depends on proton density.

Basic Physics of MRI

B0

Proton Signal

• 6.023x1023 molecules in 18 gm of H2O

• 3.35x1022 molecules in 1 gm (1 cc ~ cm3)

• 3.35x1019 molecules in 1 mg (1 mm3)

• 7.70x1019 hydrogen atoms/mm3

• 7.70x1014 signal producing protons/mm3

So the approximately 1 in 105 signal producing protons is still a lot.

Note: The number of protons contributing to signal will depend on volume from which the signal arises (voxel size).

Basic Physics of MRI

• Radio Frequency (RF)• B1(f) is magnetic field

rotating at frequency = f• Resonance Condition:

f = Larmor frequency

B1 is rotating magnetic field

associated with the RF pulse.

RF at Larmor frequency will cause M to rotate

about B1 in rotating frame of reference.

Rotating B1 Rotating B1 from RF pulse?from RF pulse?

NOTE: coordinate system

Basic Physics of MRI

RF pulse duration and strength determine flip

angle

duration

strength

RF Pulse

Frequency of rotation of M about B1 determined by the magnitude (strength)

of B1.

Basic RF Pulse Concepts

Flip AngleRotation of Net Magnetization (M)

Mo

x’

Bo

α

B1

Bo: magnetic fieldB1: generated by the RF coilα : flip angle

When α = 90° then Mxy = M0 and Mz = 0When α = 180° then Mxy = 0 and Mz = - M0

y’RF coil

Sample

M0 : depends on proton density

Basic Physics of MRI

FID magnitude decays in an exponential manner with a time constant T2. Decay due to ‘spin-spin’ relaxation.

• 90° RF pulse rotates M into transverse (x-y) plane

• Rotation of M within transverse plane induces signal in receiver coil at Larmor frequency.

• Magnitude signal dependent on Mxy. )2sin()( 2

0 fteStS Tt

π⋅=−

FID = Free Induction Decay

Need for 180° Pulse - Spin Echo

90°

180°0

TE

TE/2 -

timeTE/2+

• FID also diminishes due to local static FID also diminishes due to local static magnetic field inhomogeneitymagnetic field inhomogeneity

• Some spins precess faster and some Some spins precess faster and some slower than those due to Bslower than those due to B00

• 180 180 ° RF pulse reverses RF pulse reverses dephasing at TE (echo time)dephasing at TE (echo time)

• Residual decay due to T2Residual decay due to T2 Spin Echo Signal

Nuclear Magnetic Resonance (NMR) Signal: Spin Echo (SE)

TE/2 TE/2

90o

TR (repetition time) = time between RF excitation pulses

90o 180o

FID Spin Echo

TE = time from 90o pulse to center of spin echo

MRI Scanner Anatomy

• A helium-cooled superconducting magnet generates the static field.– Always on: only quench

field in emergency.– niobium titanium wire.

• Coils allow us to – Make static field

homogenous (shims: solenoid coils)

– Briefly adjust magnetic field (gradients: solenoid coils)

– Transmit, record RF signal (RF coils: antennas)

Superconductor Magnet

Necessary Equipment

Magnet

Gradient Coils RF Coil

RF Coil

3T magnet

gradient coils(inside)

Gradient Coils

Sounds generated during imaging due to mechanical stress within gradient coils.

MRI Scanner Components

RF Coil• RF Coils can transmit and receive RF signals

(i.e. apply B1 and monitor Mxy)• A typical coil is a tuned LC circuit and may be

considered a near-field antenna

RF Coils or Antennas

Volume coil

• The MRI antenna is called a coil.• Use different coils for different body parts.• For brains, the most common antenna is the head coil

(surrounds the volume of interest)• S coils: better signal for a small region near the coil.

Surface coilHead coil

www.fmrib.ox.ac.uk/~karla/

Surface coil

NS

M-P

035

Per

man

ent

Mag

net

MR

I

Comprehensive Receiving coils

7 standard configuration：QD head coil QD Neck Coil QD Body Coil

QD Extremity Coil Flat Spine Coil Breast Coil

Signal and Field Strength• In theory:

– Signal increases with square of field strength

– Noise increases linearly with field strength

– A 3T scanner should have twice SNR of 1.5T scanner; 7T should have ~4.7 times SNR of 1.5T.

• Unfortunately, physiological artifacts also increase, so advantage is less in practice.

• Benefits: speed, resolution• Costs: Artifacts, RF heating,

wavelength effects, auditory noise, $

Making Images of the NMR Making Images of the NMR SignalSignal

• Uniform magnetic field to set the stage (Main Magnet)

• Gradient coils for positional information• RF transceiver (excite and receive)• Digitizer (convert received analog to digital)• Pulse sequencer (controls timing of gradients,

RF, and digitizer)• Computer (FFT to form images, store pulse

sequences, display results, archive, etc.)

Role of Gradient Coils

• Coils that produce magnetic field gradients along x-,y-,and z-directions to encode spatial information

• Selective excitation: (during RF) excite those spins within a thin “slice” of the subject

• Frequency encoding: (during readout) make the signal’s frequency depend on position

• Phase encodingPhase encoding: (between excitation and readout) make the signal’s phase depend on position

Gradient Magnetic Fields for Gz

• Field Characteristics• Gradient field direction parallel to B0

• Created by Maxwell Pair —currents are anti-parallel (opposite direction)

Coil 1

Coil 2

BG

Total Field• Total Field

• Sum of Main Magnet and Gradient Fields• In practice a “shim” field is also used to “flatten” the field.

B0=BM+BG

Gradient field decreases total

Gradient field increases total

B0 ~ 1mT

Spatial Encoding by Gradient Fields

• Field varies (almost) linearly• Field magnitude changes with z

here

• Frequency changes with z

• Delta B0 = 0 at z = 0 for balanced system

• Gradient units (T/m)

€

B0 =G z⋅z

f ≅ γ B0 + ΔB0( )

B= 0.001 T z = 0.25 m B/ z = 0.004 T/m

~ 172 kHz/m

Slice SelectionDuring RF excitation, a linear gradient is applied. Only a “slice” of the sample is excited.

Slice Location

center of RF frequency range

f=(B0 + Gsss)

Thickness

TH = BWRF/ Gs

s

f

• RF Coils Transmit RF Field (B1)

—Transmitter at frequency f0 with bandwidth

ff Receive signal from Mxy

—Receiver tuned to frequency f0

RF Field Generation

tt

ffoo

ff = 1/ t= 1/ t

FTFT

ffoo

Body Transmitter/Receiver

Head Transmitter/Receiver

Frequency encoding

Mxy

f(x)

B(x) = B0 + Gxx

f(x) = {B0 + Gxx}

f(x) = Gxx

The precession frequency of the net magnetization Mxy depends on x-location. A Fourier transform of the time signal can determine where the nuclei are along the x-direction.

During signal readout, a gradient is applied in one direction:

Phase encoding

Mxy

f (y)

B(y) = B0 + Gyyf(y) = {B0 + Gyy}

f (y) = Gyy

The phase difference depends on y-location. When phase encoding is complete a Fourier transform of the signal tells us where the nuclei are along the y-direction.

Between excitation and readout a gradient is applied in one direction. This is done in small increments (once per TR) such that the summed effect is similar to frequency encoding.

Frequency and Phase Encoding for a 2D MRI

Select slice (Gs)

Phase Encode (Gp)

Frequency encode (Gf)

Repeat this many times with Gp changed each time

Slice Select for Brain Orientation: GSlice Select for Brain Orientation: Gxx – sagittal; G – sagittal; Gyy – coronal; G – coronal; Gzz - axial - axial

RF Excitation

Readout

Making an ImageMaking an Image k-space k-space (frequency (frequency

domain)domain)

A k-space domain image is formed using

frequency and phase encoding

Two Spaces

FTFT

FTFT-1-1

k-spacek-space

kkxx

kkyy

Acquired DataAcquired Data

Image spaceImage space

xx

yy

Final ImageFinal Image

MRI task is to acquire k-space image then transform to a spatial-domain image. kx is sampled (read out) in real time to give N samples. ky is adjusted before each readout.

MR image is the magnitude of the Fourier transform of the k-space image

The k-space Trajectory

kx = kx = 00tt GGxx(t) dt(t) dt

ky = ky = 00t’t’ GGyy(t) dt(t) dt

if Gif Gyy is constant is constant ky = ky = GGyyt’t’

Equations that govern 2D k-space trajectoryEquations that govern 2D k-space trajectory

The kx, ky frequency coordinates are established by durations (t) and strength of gradients (G).

if Gif Gxx is constant is constant kx = kx = GGxxtt

Simple MRI Frequency Encoding:

digitizer ondigitizer on

RF ExcitationRF Excitation

SliceSliceSelection (GSelection (Gzz))

FrequencyFrequency Encoding (GEncoding (Gxx))

ReadoutReadout

Exercise drawing k-space manipulationExercise drawing k-space manipulation

The k-space Trajectory

Frequency Frequency Encoding Encoding Gradient Gradient

((GGxx))

kx

ky

(0,0)

Digitizer records N samples along kx where ky = 0

Move to left side of k-space.

Simple MRI Frequency Encoding: Spin Echo

digitizer ondigitizer on

ExcitationExcitation

SliceSliceSelectionSelection

FrequencyFrequency Encoding (GEncoding (Gxx))

ReadoutReadout

Exercise drawing k-space representationExercise drawing k-space representation

The K-space Trajectory

180 pulse

Digitizer records N samples of kx where ky = 0

Frequency and Phase Encoding for 2D Spin Echo Imaging

digitizer ondigitizer on

ExciteExcite

SliceSliceSelectSelect

FrequencyFrequencyEncodeEncode

PhasePhaseEncodeEncode

ReadoutReadout

9090 180180

kx

ky

The 2D K-space Trajectory

180 pulse

Digitizer records N samples of kx and N samples of ky

2D Fourier Imaging

Magnitude of Fourier transform

Raw 2D k-space data Processed data

Imaging time - Np TR

Calculation of the Field of View (FOV)along frequency encoding direction

FOVFOVff = BW/( = BW/(*G*Gff ) )

Using Gx for frequency encoding let the readout FOV range from -xm to +xm

Within this FOV frequencies range from (B(B00 - G - Gx x xm) to + ) to + (B(B00 + G + Gx x xm))

Frequency change is 2 Frequency change is 2 G Gx x xm.

Since 2 xm = FOV then the frequency range is G Gxx FOV FOV

RF receiver bandwidth (BW) is adjusted to cover this range of frequencies. RF receiver bandwidth (BW) is adjusted to cover this range of frequencies. Therefore BW = Therefore BW = G Gxx FOV. FOV.

Same as equation for slice thickness seen before

• If BW is fixed increasing Gf reduces FOV• If Gf is fixed increasing BW increases FOV

RF Receiver Bandwidth and Digitizer RF Receiver Bandwidth and Digitizer Sampling RateSampling Rate

Example: For receiver with BW = 32 kHzExample: For receiver with BW = 32 kHz

With RWith Rss = 32K samples/second what is time to acquire = 32K samples/second what is time to acquire

one line of 256 samples along kx?one line of 256 samples along kx? 256 samples/32K samples/sec = 8 msec.256 samples/32K samples/sec = 8 msec.

BW = 2 fBW = 2 fmaxmax in MRI (-f in MRI (-fmaxmax to +f to +fmaxmax))

Digitizer must sample at rate RDigitizer must sample at rate Rss = 2 f = 2 fmaxmax to to

avoid aliasing so avoid aliasing so RRss = BW = BW..

Calculation of the Field of View (FOV)Calculation of the Field of View (FOV)along phase encoding directionalong phase encoding direction

GGp p FOV FOVpp = N = Npp / T / Tpp

where Twhere Tpp is the duration and N is the duration and Npp the number the number

of the phase encoding gradients, Gp is theof the phase encoding gradients, Gp is themaximum amplitude of the phase encodingmaximum amplitude of the phase encodinggradient.gradient.

FOVFOVpp = (N = (Npp / T / Tpp)/ ()/ (GGpp ) )

More Example CalculationsMore Example CalculationsWhat is BW/pixel if BW = 32 kHZ in 256x256 image?What is BW/pixel if BW = 32 kHZ in 256x256 image?

32 kHz/256 pixels = 125 Hz/sample.32 kHz/256 pixels = 125 Hz/sample.

What is spread in Larmor frequencies for a 3T magnet What is spread in Larmor frequencies for a 3T magnet with 0.1 ppm range in Bwith 0.1 ppm range in B00 within a voxel? within a voxel?

3T x 43 mHz/T = 129 MHz3T x 43 mHz/T = 129 MHz129 x10129 x1066 Hz x 0.1/1x10 Hz x 0.1/1x1066 = 12.9 Hz = 12.9 Hz

What is potential phase shift at TE = 20 msec due to this What is potential phase shift at TE = 20 msec due to this inhomogeneity?inhomogeneity?

12.9 cycles/sec12.9 cycles/sec-1-1 x 20 x10 x 20 x10-3-3 sec = 0.258 of a cycle sec = 0.258 of a cycle

kx

ky

256

256

256

256

128

Decreases y-direction spatial resolution.

Partial Fourier or K-Space Imaging to Shorten Scan Time

Decreasing number of phase (ky) lines reduces scan time proportionally.

Half Fourier Imaging

kx

ky

256

256

kx

ky

256

128

Retains resolution but decreased SNR

Developing Contrast Using Weighting

• Contrast = difference in image values between different tissues

• T1 weighted example: gray-white contrast is possible because T1 differs between these two types of tissue

T1 and T2• T1-Relaxation: Recovery

– Recovery of longitudinal orientation of M along z-axis.

– ‘T1 time’ refers to time interval for 63% recovery of longitudinal magnetization.

– Spin-Lattice interactions.• T2-Relaxation: Dephasing

– Loss of transverse magnetization Mxy.

– ‘T2 time’ refers to time interval for 37% loss of original transverse magnetization.

– Spin-spin interactions,and more.

Properties 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

T1 values for B0 ~ 1Tesla.T2 ~ 1/10th T1 for soft tissues

Average Values of T1 and T2 in the Average Values of T1 and T2 in the Human BrainHuman Brain

Relaxation Times (msec)

Tissue 1.5T 3.0T 4.0T

WM-T1 640 860 1040

GM-T1 880 1200 1410

WM-T2 80 80 50

GM-T2 80 110 50

Large frequency dependence for T1 values. Data from textbook.

Basic Physics of MRI: T1 and T2

T1 is shorter in fat (large molecules) and longer in

CSF (small molecules). T1 contrast is higher for lower

TRs.

T2 is shorter in fat and longer in CSF. Signal

contrast increased with TE.

• TR determines T1 contrast

• TE determines T2 contrast.

(msec)

(sec)

T1 & T2 Weighting – Spin Echo

• T1W Contrast Echo (TE) at T2 contrast min Repeat (TR) at T1 contrast max

• T2W Contrast Echo (TE) at T2 contrast max Repeat (TR) at T1 contrast min

T1 Contrast Weighting

T2 Contrast Weighting

TE

TR TE

TR

Min T2 Contrast Max T1 Contrast

Max T2 Contrast Min T1 Contrast

3214 34 21decay

T

TE

eryre

T

TR

eeSS ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−−2

cov

10 1

Contrast, Imaging Parameters

- proton density- proton densitySE – spin echo imagingSE – spin echo imagingGRE – gradient echo imagingGRE – gradient echo imaging

Short TEs reduce T2WShort TEs reduce T2WLong TRs reduce T1WLong TRs reduce T1W

€

S(TR,TE)∝ ρ 1− e−TR /T1{ } e−TE /T2{ } SE

or ρ 1− e−TR /T1{ } e−TE /T2*

{ } GRE

T1W T2W

PDWPDW

T1WT1W

T2WT2W

Three Common Clinical MRIsThree Common Clinical MRIs

Note: Display contrast adjusted for best viewing of each.

Largest SignalLargest Signal

Good GM-WM ContrastGood GM-WM Contrast

Fluids are bright

Inversion Recovery T1 ContrastInversion Recovery T1 Contrast

-S-So

SSo

S = SS = Soo * (1 – 2 e * (1 – 2 e –t/T1–t/T1))

S = SS = Soo * (1 – 2 e * (1 – 2 e –t/T1’–t/T1’))

Sampling signal at this time suppresses tissue with T1’

                                                        

        

T2WT2W Inversion RecoveryInversion Recovery(CSF Attenuated)(CSF Attenuated)

Gradient Echo Imaging

• Signal is generated by magnetic field refocusing mechanism only (the use of negative and positive gradient)

• Signal intensity is governed by

S = So e-TE/T2*

• Can be used to measure T2* value of the tissue

• R2* = R2 + R2ih +R2ph (R2=1/T2)• Used in 3D and BOLD fMRI

ph – other phase related

MRI Pulse Sequence for Gradient Echo Imaging

digitizer ondigitizer on

ExcitationExcitation

SliceSliceSelectionSelection

FrequencyFrequency EncodingEncoding

PhasePhase EncodingEncoding

ReadoutReadout

€

cos(θE ) = e− TRT1Ernst angle (E) for optimum SNR .

E.

crus

her

crus

her

crus

her

crus

her

B1

Gz

Gx

Gy

B1

Gz

Gx

Gy

TR1 TR2

TRN/2 TRN

TR1

TR2

TRN/2

TRN

Fig. 3.19. Courtesy of Peter Jezzard.

refocus

acquire

FLASH Pulse Sequence

2D Gradient EchoRF (10-15 degrees)Short TR (10-50 msec)N= 256 (2.5-13 sec per slice)

3D Sequence (Gradient Echo)

Gx

Gy

Gz

B1

acq

kx

ky

kz

Scan time = NyNzTRGood for high resolution T1W images of brain

Select& phase

phase

read

RF

3D T1W brain image 0.8mm spacing

Time = 25 min

B1

Gz

Gx

Gy

Fig. 3.20. Courtesy of Peter Jezzard.

refocus

acquire

a) b)

2D Echo Planar Imaging (EPI)

2d Gradient EchoEntire 2D slice within one TR64x64 or 128x128Time per slice (30-50 msec)Whole volume (2-4 sec)Good for fMRI studies

Fig. 3.23 courtesy of Peter Jezzard.

FLASH Image T2* Weighted

TE = 30 msecCSF is bright

Signal loss and distortions due to local differences in magnetic field

Sources of Contrast in Brain- Endogenous - BOLD- Exogenous - could be contrast agent (Gd based)- Other - Susceptibility

R2* = net T2 relaxation rate = 1/T2*

R2* = R2tis + R2ih + R2BOLD + R2suc

BOLD EPI Functional MRIBOLD EPI Functional MRI

RestTask

Subtraction converted to t- or z-values

3 %

0

R L

z = (Task - Rest)/SDTask-Rest

(Task - Rest)

fMRI (BOLD EPI) – With Statistical Parametric fMRI (BOLD EPI) – With Statistical Parametric MappingMapping

R Finger

Tongue

z-values > 3

3D Surface Views

R Finger Movement

Tongue Movement