Chapter 3

Principles of nuclear magnetic resonance and MRI

Review

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.

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

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

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 proton density and 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

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 Tissues

Tissue 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

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.

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

Making an ImageMaking an Image k-space k-space (frequency domain) (frequency 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 = 00ttGGxx(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

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

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

Chapter 8

Quantitative Measurements Using fMRI

Review

T2* fMRI Signal

From Neural Activity to fMRI Signal

Neural activity Signalling Vascular response

Vascular tone (reactivity)Autoregulation

Metabolic signalling

BOLD signal

glia

arteriole

venule

B0 field

Synaptic signalling

Blood flow,oxygenationand volume

Complex relationship between change in neural activity and change in blood flow (CBF), oxygen consumption (CMRO2) and volume (CBV).

dendriteEnd bouton

fMRI Bold Response Model

time

BO

LD

res

pons

e, %

initialdip

positiveBOLD response

post stimulusundershootovershoot

1

2

3

0

stimulus

Figure 8.1. from textbook.

• Initial dip 0.5-1sec• Overshoot peak 5-8 sec• + BOLD response 2-3%• Final undershoot variable

Deoxyhemoglobin

BOLD signal

Graded BOLD Response

Figure 8.2. from textbook. N=12 subjects.

• Graded change in signal for a) BOLD and b) perfusion (CBF).• 3 minute visual pattern stimulation with different luminance levels.• Note max BOLD change of 2-3 % and max CBF change of 40-50 %.

Perfusion vs. Volume Change

Figure 8.4. from textbook.

• 30 second stimulation• 3-second intervals• CBF rapid• CBV slow

Mandeville et al., 1999

In rat experiments TC for CBV similar to that for BOLD overshoot.

BOLD volume assessed using exogenous tracer that remains in

blood.

Measurement of Cerebral Blood Flowwith PET or MRI (Arterial Spin Labeling - ASL)

• Uses magnetically labeled arterial blood water as an endogenous flow tracer

• Potentially provide quantifiable CBF in classical units (mL/min per 100 gm of tissue)

Detre et al., 1992

arteriallabeling

controllabeling

imagingslice

T1 relaxation

arterialspin labeling

O infusionor inhalation

15

αdecay

PET or SPECT Steady State Method

MRI PERFUSION Steady State Method

+

511 keV

511 keV

PET

Method

O-15 H20

Arterial Spin Labelling

• ASL is an example of a motion contrast• IMAGEperfusion = IMAGEuninverted – IMAGEinverted

• Perfusion is useful for clinical studies: how much blood is getting to a region, how long does it take to get there?

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

inversionslab

imagingplane

excitation

inversion

xy

z (=B0)

bloodblood

white matter = low perfusion

Gray matter = high perfusion

Chapter 5

Hardware for MRI

Review

3T Siemens Trio

• 60 cm patient bore60 cm patient bore• 40 mT/m max gradient amplitude per axis40 mT/m max gradient amplitude per axis• 200 T/m/sec slew rate200 T/m/sec slew rate• 22ndnd order active shimming order active shimming• ~0.30 ppm B~0.30 ppm B00 homogeneity over 40 cm sphere homogeneity over 40 cm sphere• self shieldedself shielded

• Shielding

• Shims

• Field Strength

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)

Figure 5.2 from textbook.

Magnet Shielding and Shimming

Iron Shielding

Shimssuperconductingstaticroom temperature

Magnet

Shim coil

Gradient coil

RF coil

Subject

Gradient Coils

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

Current and Gradient Pulse ShapeCurrent and Gradient Pulse Shape

a. gradient current supplied (short rise time induces eddy currents)a. gradient current supplied (short rise time induces eddy currents) b. eddy currents oppose changing field w/o compensationb. eddy currents oppose changing field w/o compensation c. gradient current supplied with eddy current compensationc. gradient current supplied with eddy current compensation d. potential field vs time with eddy current compensationd. potential field vs time with eddy current compensation

a

d

c

b

Jerry Allison.

dB/dt Effect (more eddy currents)

Peripheral Nerve Stimulation• dB/dt -- dE/dt• dt is gradient

ramp time• dB/dt largest

near ends of gradient coils

• spatial gradient of dE/dt also important

dB

dt

dB/dt / E-Field Characteristics of Stimulation

• Not dependent on B0

• Gradients - 40mT/m (larger Bmax for longer coil)• Gradient Coil Differences - strength (increases dB)

and length (head vs. body determines site)• Rise Time - shorter rise time means larger shorter dt

and therefore larger dB/dt• Other

– Disruption of nearby medical electronic devices– Subject Instructions

• Don’t clasp hands - closed circuit, lower threshold• Report tingling, muscle twitching, painful sensations

MRI Scanner Components

Figure 5.1b from textbook.

Exciter

Synthesizer

XMTR

T/Rswitch

RFCoil

PreampRCVR

A/P RAMHost

Pulseprogrammer Synthesizer, A/P

XMTR, RCVR, T/R

Shimdriver

Shim coils

Gradient coils

AmpsGx, Gy, Gz

Network

Schematic of MRI System

A/P - Array ProcessorRF, Shim, Gradient Coils inside magnetAll but Host, RAM, and A/P in equipment room

Same or different transmit and receive coil.

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

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

Surface CoilsSurface Coils

Figure 5.7 from textbook.

SN

R

0 50 100 150 200 2500

200

400

600

800

1000

1200

1400Surface coil/head coil comparison

1

2

3

4

17 cm spherical phantom

distance, mm

b

SNR

(1) two surface coils on opposite sides in phase.(2) two surface coils out of phase.(3) single surface coil on right side. (largest SNR)(4) head coil. (most uniform SNR)

RF Coil Uniformity and SNR

(1) (2)

(3) (4)

B1 directions indicated by color arrows.

Stimulus Presentation / Monitoring

Additional Equipment

• Software• Time-Line

– Control Stimulus

– Monitor Response

– Synchronize timing with MRI

E-PrimeE-Prime

fMRI Study Time

• New Design

• Scanning– Setup– Scans– Take down

• Preprocessing

• Statistical Analysis

1-1.5 hr/subject

4+ hr (one instance)

variable

<2 hr/ subject

15-20 min

45 min to 1 hr

15 min

fMRI Study – All Data

• Raw Data ~200 mBytes

• Motion Correction ~180 mBytes

• Other Corrections ~180 mBytes each possibly

• Spatial Normalization ~ 30 mBytes

• Statistical Analysis• Statistical Parametric Image (128x128x20) < 1 MByte

• Statistical Parametric Map (2x SPI) > 1 MByte

Total Data per subject can be 0.5-1.0 gBytesTotal Data per subject can be 0.5-1.0 gBytes

Chapter 7

Spatial and temporal resolution in fMRI

Review

Typical Paradigm

• Instruction• Presentation

– stimulation– timing

• Processing– sensing– decision

• Response– plan– motor

fMRI responses

time (s)

Trial #1

Trial #2

Presentation Response

Behaviour

time (s) 0 5 0 5

Figure 7.4 from textbook.

• BOLD signal time course• presentation (black)• processing (light grey)• response (dark grey)

Task

Behavior

Onset and Width of BOLD response as temporal measures.---- Not time to peak ----

Estimating Neural Processing Time From BOLD Response Onset

V1

SMA

M1

time

fMR

I re

spon

se a

mpi

tude

(a)

350300250200150-50

0

50

100

150

200

250

300

kinematic RT (ms)

BO

LD

ons

et d

iffe

renc

e (m

s)

(b)

Figure 7.5 from textbook.

Task – use joystick to move cursor from start box to target box as rapidly and accurately as possible (10 trials in multiple subjects). BOLD response – V1 (primary visual cortex), SMA (supplementary motor area), M1 (primary motor area)Analysis – but not increases with increasing reaction time (RT).Conclusion – Delay in reaction time from planning rather than execution of movement.

Estimating Neural Processing Time From from BOLD Response Width

fMR

I si

gnal

cha

nge

from

S

PL

Time after presentation (s)

0. 98

0. 99

1. 00

1. 01

1. 02

1. 03fMRI

(b)

20151050

Trial A

Trial B

RT(A) RT(B)

Task

(a)

(c)

16128400

4

8

12

16

Nor

mal

ized

wid

th o

f B

OL

D r

espo

nse

(s)

Reaction Time (s)

Figure 7.6 from textbook.

Task – determine if one object could be rotated to match a second. Rotation angle varied by design. Press button yes or no.BOLD response – Superior Parietal Lobule (SPL)Analysis – Normalized width of BOLD response correlated with reaction time (RT).Conclusion – SPL intimately involved in mental rotation of object.

Chapter 6

Selection of optimal pulse sequences for fMRI

Review

Advantages Disadvantages

BOLD Highest activation contrast 2x-4x over perfusion

complicated non-quantitative signal

easiest to implement no baseline information

multislice trivial susceptibility artifacts

can use very short TR

Perfusion unique and quantitative information low activation contrast

baseline information longer TR required

easy control over observed vasculature multislice is difficult

non-invasive slow mapping of baseline information

no susceptibility artifacts

Table 6.1a. Summary of practical advantages and disadvantages of pulse sequences (derived from textbook)

Venous outflow

Perfusion

NoVelocityNulling

VelocityNulling

ASLTI

Time/secs 1 2 40 3

Venous outflow

Figure 6.1a Signal is detected from water spins in the arterial-capillary region of the vasculature and from water in tissues surrounding the capillaries. Relative sensitivity controlled by adjusting TI and by incorporating velocity nulling gradients (also known as diffusion weighting). Nulling and TI~1 sec makes ASL sensitive to capillaries and surrounds.

Arteries Arterioles Capillaries Venules Veins

GE-BOLD

NoVelocityNulling

VelocityNulling

Figure 6.1b Gradient Echo BOLD is sensitive to susceptibility perturbers of all sizes, and are therefore sensitive to all intravasculature and extravascular effects in the capillary-venous portions of the vasculature. If a very short TR is used may show signal from arterial inflow, which can be removed by using a longer TR and/or outer volume saturation.

Arteries Arterioles Capillaries Venules Veins

Arterial inflow(BOLD TR < 500 ms)

Time/secs 1 2 40 3

SE-BOLD

NoVelocityNulling

VelocityNulling

Figure 6.1c Spin Echo BOLD is sensitive to susceptibility perturbers about the size of a red blood cell or capillary, making it predominantly sensitive to intravascular water spins in vessels of all sizes and to extravascular (tissue) water surrounding capillaries. Velocity nulling reduces the signals from larger vessesl.

Arteries Arterioles Capillaries Venules Veins

Arterial inflow(BOLD TR < 500 ms)

Time/secs 1 2 40 3

Figure 6.2 Pulse sequence diagrams of (a) gradient echo, (b) spin echo, and (c) asymmetric spin echo EPI. The TE is shown at the center of 9-line k-space (typically 64 or more lines). is the offset from center of k-space to echo. Additional pulses needed for ASL are indicated schematically.

Gradient-echo

RF

Gx

Gz

Gy

90°

TEASLpulse

TISpin-echo

180° TE

RF

Gx

Gz

Gy

ASLpulse

TI

90°

spin-echo

180° TE

RF

Gx

Gz

Gy

Chapter 4

Ultrafast fMRI

Review

Effects of Field Homogeneity

R2* = R2 + R2mi +R2ma

• R2 = transverse relaxation rate due to spin-spin interactions and diffusion through microscopic gradients

• R2mi = transverse relaxation rate due to microscopic changes, i.e. deoxyhemoglobin

• R2ma = transverse relaxation rate due to macroscopic field inhomogeneity

R2*a is relaxation rate during activationR2*r is relaxation rate at rest

Fig. 4.3 EPI obtained with TE= 60 and TR=3000 msec and 63 and 95 ky lines. Note recovery of signal loss in d vs c and ghosting in c.

Spin Echo

4x4x4 mm3

Gradient Echo EPI

2x2x2 mm3

Fig. 4.5 Gradient echo (GE) echo forms at center of readout window where area under rephasing gradient = area of dephasing gradient. Unlike spin echo dephasing is due to spatial difference in Larmor frequencies during application of gradients. First half of readout window is rephasing and second half is dephasing again. This process repeats at the center of readout window for each ky line in k-space for EPI.

gradient echo

readout window

r.f.

read gradient

TE

dephase

rephase dephase

For EPI where is the readout signal largest?

Fig. 4.7 GE EPI pulse sequence and k-space organization of samples.

RF

Slice

Read

Phase

a)

Read

Pha

se

b)

1

2 n

n-1

1

2

n-1

n

What flip angle is used for EPI?

Effect of system parameters on EPI images for fixed field of view.

Parameter Echo Spacing

Resolution SNR Geometric distortion

Increase gradient slew rate Reduced --- --- Reduced

Increase sampling bandwidth (kx)

Reduced --- Reduced Reduced

Increase number of shots (interleaving ky)

Reduced --- Increased Reduced

Use of ramp sampling (similar to slew rate effect)

Reduced --- --- Reduced

Increase read matrix (kx) Increased Increased Reduced Increased

Increase phase matrix (ky) --- Increased* Reduced ---

Increase field strength --- --- Increased Increased

Table 4.1 from text. * actual resolution increase less than expected due to smoothing effect of signal decay.

fMRI methods for reduced k-space coverage

• Keyhole

– acquire full k-space as reference

– acquire reduced low-frequency k-space fMRI study

– fill in missing k-space from reference

• Half-Fourier

– acquire 50-60% of k-space starting at highest ky

– theoretical symmetry used to fill in missing ky

fMRI methods for reduced k-space coverage

• Sensitivity encoding (SENSE)– Multiple RF coils with independent signal for each (parallel imaging)– Calibration maps from full k-space– each coil part of k-space– 2X improvement EPI, 4X for GE

• UNFOLD– Acquire k-space in sequential time segments

• time 1 acquire lines 1, 5, 9, 13 ...• time 2 acquire lines 2, 6, 10, 14 ...• time 3 acquire lines 3, 7, 11, 15 ...• time 4 acquire lines 4, 8, 12, 16 ...• reorder into k-space• 4x faster per segment reduces inter echo distortions