Chapter 14:Physics of Magnetic Resonance - Human … · IAEA Diagnostic Radiology Physics: A Handbook for Teachers and Students -14 (02/141) CHAPTER 14 TABLE OF CONTENTS 14.1. Introduction

IAEAInternational Atomic Energy Agency

Slide set of 141 slides based on the chapter authored by

Hee Kwon Song

of the IAEA publication (ISBN 978-92-0-131010-1):

Diagnostic Radiology Physics:

A Handbook for Teachers and Students

Objective:

To familiarize the student with the fundamental concepts of

MRI.

Chapter 14: Physics of Magnetic

Resonance

Slide set prepared

by E. Berry (Leeds, UK and

The Open University in

London)

IAEA Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14 (02/141)

CHAPTER 14 TABLE OF CONTENTS

14.1. Introduction

14.2. Nuclear magnetic resonance

14.3. Relaxation and tissue contrast

14.4. MR spectroscopy

14.5. Spatial encoding and basic pulse sequences

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14.1 INTRODUCTION14.1

Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14.1 Slide 1 (03/141)

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Nuclear magnetic resonance (NMR)

� Nuclei in a magnetic field absorb applied radiofrequency

(RF) energy and later release it with a specific frequency

� 1920s – Stern and Gerlach

• particles have intrinsic quantum properties

� 1938 – Rabi

• discovered phenomenon of NMR (Nobel prize 1944)

� 1946 – Bloch and Purcell

• measured NMR signal from liquids and solids (Nobel prize 1952)

� But no imaging yet 9


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Magnetic resonance imaging (MRI)

� 1973 – Lauterbur

• method to spatially encode the NMR signal using linear magnetic

field gradients

� 1973 – Mansfield

• method to determine spatial structure of solids by introducing

linear gradient across the object

� i.e apply magnetic field gradients to induce spatially

varying resonance frequencies to resolve spatial

distribution of magnetization

� Milestone – the beginning of MR Imaging

� Nobel prize in medicine in 2003

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Characteristics of MRI

� No ionizing radiation

• unlike x-rays and CT

� Superior soft tissue contrast compared with other

modalities

� Can control image contrast among different tissues by

adjusting acquisition timing parameters

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14.2 NUCLEAR MAGNETIC

RESONANCE14.2


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14.2 NUCLEAR MAGNETIC RESONANCE14.2

Nuclear magnetic resonance

� 14.2.1 The nucleus: spin, angular and magnetic

momentum

� 14.2.2 External magnetic field and magnetization

� 14.2.3 Excitation and detection


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RESONANCE14.2.1 THE NUCLEUS: SPIN, ANGULAR AND MAGNETIC

MOMENTUM

Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14.2.1 Slide 1 (09/141)

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14.2 NUCLEAR MAGNETIC RESONANCE14.2.1 The nucleus: spin, angular and magnetic momentum

Nuclei used for MRI

� MRI involves imaging the nucleus of hydrogen atom

• = proton

� Hydrogen abundant in human body in water and fat

• Water is 50-70% of total body weight

• Fat is 10-20% of total body weight

� Other nuclei are used in research

• carbon (13C), phosphorus (31P), fluorine (19F), sodium (23Na)

• relatively low abundance in vivo

• limited signal available


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14.2 NUCLEAR MAGNETIC RESONANCE

14.2.1 The nucleus: spin, angular and magnetic

momentum

Properties of the nucleus

� Angular momentum

where h is Planck’s constant and I

is the nuclear spin (or quantum

number)

• for the hydrogen nucleus, I =

½

� Because the proton is positively

charged, the angular

momentum also produces a

nuclear magnetic moment

where γ is the gyromagnetic ratio


hIp =

pγµ =

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14.2 NUCLEAR MAGNETIC RESONANCE

14.2.1 The nucleus: spin, angular and magnetic

momentum

Gyromagnetic ratio

� Specific to each type of nucleus

� For proton, roughly 42.57 MHz T-1


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14.2 NUCLEAR MAGNETIC RESONANCE14.2.1 The nucleus: spin, angular and magnetic momentum

Nucleus Relative

Abundance (%)

Spin (I) Gyromagnetic

ratio (Hz/G)

Relative

sensitivity*

Abundance

in human

body (% of

atoms)1H 99.98 1/2 4258 1 6313C 1.11 1/2 1071 0.016 0.1319F 100 1/2 4005 0.83 0.0012

23Na 100 3/2 1126 0.093 0.03731P 100 1/2 1723 0.066 0.1439K 93.1 3/2 199 5.08 x 10-4 0.031

* PER EQUAL NUMBER OF NUCLEI


Common nuclei for MR

Adapted from Stark & Bradley, Magnetic Resonance Imaging, 2nd edition

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RESONANCE14.2.2 EXTERNAL MAGNETIC FIELD AND

MAGNETIZATION

Diagnostic Radiology Physics: A Handbook for Teachers and Students – 14.2.2 Slide 1 (14/141)

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14.2 NUCLEAR MAGNETIC RESONANCE14.2.2 External magnetic field and magnetization

Boltzmann distribution

� Consider a collection of these magnetic moments

• or spins

� No external magnetic field

• random alignment: zero net magnetization

� In external magnetic field B0

• each spin aligns parallel or anti-parallel to direction of applied field

• i.e. polarized

• parallel orientation has lower energy state

• slightly greater number of spins align along that direction


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No external magnetic field

� Random alignment of

spins

� Zero net magnetization

In external magnetic field B0

� Each spin aligns parallel

or anti-parallel to

direction of applied field

� i.e. polarized



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Boltzmann distribution

� Parallel orientation has lower energy state

� Slightly greater number of spins align along that direction

Where

• N+ is number of spins aligned parallel to direction of applied field

• N- is number of spins aligned anti-parallel to direction of applied field

• ∆E is energy difference between the two states

• k is Boltzmann constant

• T is absolute temperature

• ω0 is Larmor, or resonance, frequency


kTktE oeeN

N // ωh== ∆

−

+

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Precession and Bloch Equation

� Torque on magnetization causes it to precess about the

direction of the magnetic field

� Will precess at the Larmor frequency,

� Analogous to precession of spinning top about the

direction of gravitational field

• top has angular momentum due to its spin

• precession arises from a torque acting on the top


B×= µ µ

γdt

d

oo Bγω =

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Larmor frequency

� Under the influence of an

external magnetic field Bo,

the spins precess about

the direction of the field at

the Larmor frequency

which is proportional to Bo

� e.g. at 1.5 T, ω0 = 64 MHz


oo Bγω =

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Rotating frame of reference

� In stationary (or laboratory) frame of reference,

precession:

• at Larmor frequency ω0

• about the direction of B0 (z-axis)

� In rotating frame of reference, which rotates at Larmor

frequency, precession:

• at Larmor frequency appears to be stationary

• at a different frequency ω in stationary frame, appears to precess

at ωr , where


or ωωω −=

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Net magnetization

� Total magnetization within a voxel

• net magnetization

• vector sum of all spins within the voxel

• aligned along +z direction, the direction of B0

� **add diagram**

� Henceforth

• “Magnetization” = net magnetization of a collection of spins

• i.e. not magnetization of a single spin


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Bloch equation for net magnetization M

� In the presence of a constant external magnetic field B0

• net magnetization is aligned along the z-axis, remains stationary

and does not precess about any axis

• magnetization is at its equilibrium magnetizationM0.

� When additional fields applied, including time varying

fields

• magnetization may deviate from equilibrium position

• magnetization may precess about an effective magnetic field


BMM

×= γdt

d

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Perturbation from equilibrium

� Arises from applied additional magnetic fields

� Such a perturbation is needed for signal detection


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RESONANCE14.2.3 EXCITATION AND DETECTION


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14.2 NUCLEAR MAGNETIC RESONANCE14.2.3 Excitation and detection

Effect of external radiofrequency (RF) field B1(t)

� Spins are in a magnetic field B0

� B1(t) is resonating at the Larmor frequency

� From Bloch equation

• magnetization will precess about effective magnetic field

• given by vector sum of static B0 field and time varying B1 field

� In the rotating frame

• B1 field appears stationary

• magnetization is initially aligned along z-axis

• magnetization precesses about the direction of the B1 field

• will continue to do so as long as B1 is applied


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� If RF field B1 lies along the x-axis

• magnetization precesses, or

nutates, about the x-axis

� Typically, apply B1 field just long

enough to cause a 90° rotation

� At end of the RF pulse, (2-3 ms),

magnetization is aligned with y-

axis

• note that diagram shows rotating

frame with axes (xr, yr, zr)




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� Once magnetization is rotated into the transverse (x, y)

plane

� RF is removed

� Precession is again

• about B0

• at the Larmor frequency (in stationary frame of reference)

• according to Bloch equation

� Can detect the rotating magnetization


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Detection of a signal from

rotating magnetization

� Use an RF coil

� By Faraday’s law,

changing magnetic flux

through coil induces

voltage changes

� Changes are detected

by receiver



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Detection of a signal from rotating magnetization

� Overall strength of received signal depends on

• type and size of RF coil used for signal reception

• proximity of coil to the imaged object

• voxel size

� More in Chapter 15


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14.3 RELAXATION AND

TISSUE CONTRAST14.3


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14.3 RELAXATION AND TISSUE CONTRAST14.3

Relaxation and tissue contrast

� 14.3.1 T1 and T2 relaxation

� 14.3.2 Bloch equations with relaxation terms

� 14.3.3 T2* relaxation

� 14.3.4 Contrast agents

� 14.3.5 Free-induction decay (FID)


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14.3 RELAXATION AND

TISSUE CONTRAST14.3.1 T1 AND T2 RELAXATION


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14.3 RELAXATION AND TISSUE CONTRAST14.3.1 T1 and T2 relaxation


Spin-lattice, or T1, relaxation

� One of two mechanisms that drive magnetization back to

its equilibrium state

� Some of energy absorbed by spins from RF pulse is lost to

their surroundings - the lattice

� Time constant for this phenomenon is T1

• depends on the mobility of the lattice

• efficiency of energy transfer from excited spins to the lattice

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Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14. 3.1 Slide 3 (34/141)


� The longitudinal component (z-component) of the

magnetization returns to its equilibrium state M0 in an

exponential fashion

where Mz(0) is the longitudinal magnetization immediately

following RF excitation

� For a 90° excitation, Mz(0) is zero

� After a time period of several T1s, the magnetization has

nearly fully returned to its equilibrium state

( ) ( ) ( )11 // 10 Tt

o

Tt

zz eMeMtM −− −+=

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� Light gray component

� After a time period of several T1s, the magnetization has

nearly fully returned to its equilibrium state:

• amplitude M0

• aligned with z-axis


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Spin-spin, or T2, relaxation

� In addition to interactions with the lattice, spins interact

with each other – “spin-spin”

� Each spin is essentially a magnetic dipole

• creates a magnetic field of its own

• slightly alters the field of its surroundings

� Any spin close to another will experience the additional

field

• which slightly alters its precessional frequency

� Spins are in constant motion, so precessional frequency of

each spin changes continuously


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� Result is a loss of phase coherence

� Leading to an exponential decay of signal in the

transverse plane

� With time constant T2

where Mxy(0) is the transverse magnetization immediately

following RF excitation


( ) ( ) 2/0 Tt

xyxy eMtM −=

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� Dark gray component

� T2 relaxation reduces the transverse component towards

zero


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Typical T1 and T2 values in human tissues at 1.5 T

� T1 and T2 differ between tissue types

� T1 and T2 are field-strength dependent

Adapted from Bernstein, King and Zhou, Handbook of MRI pulse sequences, 2004

Tissue T1 (ms) T2 (ms)

Muscle 870 50

Fat 260 80

Liver 490 40

Blood (oxygenated) 1200 200

Blood (deoxygenated) 1200 125

White matter 790 90

Gray matter 920 100

Cerebrospinal fluid (CSF) 4000 2000

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TR and image creation

� Repeat process of excitation and signal detection many

times until have sufficient data for image reconstruction

� Time between successive excitations is repetition time

(TR)

� From

value of TR determines the extent to which tissues with

various T1s have returned to their equilibrium state


( ) ( ) ( )11 // 10 Tt

o

Tt

zz eMeMtM −− −+=

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TR and image creation

� If TR is short

• tissues with short T1s which relax more quickly will appear brighter

than those with longer T1 values

• differences in T1 between tissues will be emphasized


( ) ( ) ( )11 //10

Tt

o

Tt

zz eMeMtM−− −+=

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TE and image creation

� Time between excitation and data acquisition is echo time

(TE)

� If TE is long

• tissues with short T2s which relax more quickly will appear darker

than those with longer T2 values

• differences in T2 between tissues will be emphasized

� More in Section 14.5.4


( ) ( ) 2/0 Tt

xyxy eMtM −=

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14.3 RELAXATION AND

TISSUE CONTRAST14.3.2 BLOCH EQUATIONS WITH RELAXATION TERMS


IAEA Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14.3.2 Slide 2 (44/141)

14.3 RELAXATION AND TISSUE CONTRAST14.3.2 Bloch equations with relaxation terms

Bloch equations

� If the T1 and T2 relaxation constants are incorporated into

the Bloch equation (slide 17/141)

� Now includes

• effects of both static (B0) and dynamic (B1) magnetic fields

• relaxation of spins due to T1 and T2 relaxation

21

ˆˆˆ

T

yMxMz

T

MM

dt

d yxzo+

−−

+×= BMM

γ

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14.3 RELAXATION AND

TISSUE CONTRAST14.3.3 T2* RELAXATION



14.3 RELAXATION AND TISSUE CONTRAST14.3.3 T2* relaxation

Effect of magnetic field inhomogeneities

� In a homogeneous field, the transverse signal decays

• exponentially

• with intrinsic T2 time constant

� Magnetic field inhomogeneities may arise from

• imperfect magnet shimming

• induced field perturbations (e.g. due to susceptibility differences at

tissue boundaries)

� These lead to additional loss of coherence among the

spins

� In an inhomogeneous field, the transverse signal may

decay more rapidly



Effect of magnetic field inhomogeneities

� Approximation for signal loss within a voxel

� Exponential decay with time constant T2*

• pronounced “T- two star”

• T2* < T2

• represents total transverse relaxation time

• i.e. both intrinsic T2 and the component due to inhomogeneous

field, T2′ “T- two prime”



T2* relaxation

where

� ∆B is the field inhomogeneity across a voxel

� γ is the gyromagnetic ratio

� T2* is the total transverse relaxation time constant

� T2 is the intrinsic transverse relaxation time constant

� T2′ is the transverse relaxation time constant due to the

inhomogeneous field

′+=∆+=

222

*

2

1111

TTB

TTγ



Most common incidences of field perturbations in vivo

� Near regions of air-tissue boundaries

� Sinus cavity in the head

� In trabecular (spongy) bone

• susceptibility difference between bone and bone marrow induces

local field inhomogeneities within the marrow



Reversal of signal loss

� Signal loss due to intrinsic T2 relaxation cannot be

avoided

� Signal loss due to field inhomogeneities can be reversed

� Apply a second RF pulse

• known as a refocusing pulse

� This is basis of spin echo imaging

� Section 14.5.5

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14.3 RELAXATION AND

TISSUE CONTRAST14.3.4 CONTRAST AGENTS


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14.3 RELAXATION AND TISSUE CONTRAST14.3.4 Contrast agents

Contrast Agents

� Further enhance contrast among tissues

� Highly paramagnetic

• enhance the spin-lattice interaction

• shorten T1 time constant

• longitudinal signal restored more rapidly following excitation

� Commonly based on gadolinium 3+ ion

• seven unpaired electrons

• strongly paramagnetic


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Relaxation rate R1

where

� T10 is the intrinsic tissue T1 without contrast agent

� r is relaxivity of contrast agent

� [C] is concentration of contrast agent


[ ]CrTT

R +==101

1

11

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Relaxivity

� Specific property of each type of contrast agent

� Varies significantly from one agent to another

� Both T1 and T2 are affected by contrast agents

• relaxivities roughly the same for both

� But, T10 >> T20

� i.e. R1 << R2

� So, for a given concentration of contrast agent, relative

effect is greater on longitudinal time constant(T1) than on

transverse (T2) time constant.


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Imaging sequences in contrast-enhanced MRI

� Highlight enhancing structures by using short TR

� Most tissues do not recover sufficiently after excitation

� Only those tissues affected by contrast agent will recover

sufficiently to produce a high signal

• as they have drastically shortened T1 values


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Clinical applications of contrast-enhanced MRI

� Tumour detection

• inject contrast agent into blood stream through vein in arm

• most tumours have a rich blood supply

• contrast agent diffuses from vessels into extra vascular space

• local reduction in T1

• enhance lesion signal intensity compared with surrounding tissue

• degree of signal enhancement may be used to assess tumour

perfusion

� MR angiography

� Imaging of myocardial infarction


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Example of tumour detection

� Pre-contrast, no lesion is visible

� Post-contrast (intra-vascular administration), the lesion is

enhanced due to high vascularity within the lesion


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14.3 RELAXATION AND

TISSUE CONTRAST14.3.5 FREE-INDUCTION DECAY (FID)


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14.3 RELAXATION AND TISSUE CONTRAST14.3.5 Free-induction decay (FID)

Free induction decay (FID)

� Occurs following excitation with an RF pulse

� Evolution of the signal in the transverse plane

• exponential decay with T2 time constant (ignoring the T2* effect)

• spins precess at Larmor frequency in laboratory frame of reference

� In homogeneous field, detected signal is

• perfectly sinusoidal

• modulated by exponential decay with T2 time constant


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14.3 RELAXATION AND TISSUE CONTRAST14.3.5 Free-induction decay (FID)

Frequency spectrum of free induction decay

� Take Fourier transform of the FID

� Result is a function, whose real component is a Lorentzian

• peak of Lorentzian function centred at the Larmor frequency

• full-width-at-half-maximum =

� Rapidly decaying signal

• broader spectrum

� Longer T2

• sharper peak in spectrum


21 Tπ

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14.4 MR SPECTROSCOPY14.4 MR SPECTROSCOPY


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14.4 MR SPECTROSCOPY14.4 MR spectroscopy

Proton spectroscopy

� All hydrogen nuclei (protons) have same properties

• spin number, angular moment

� In a homogeneous magnetic field expect to precess at

same frequency

� But local magnetic field differs for hydrogen nuclei of

different chemical species

• different magnetic shielding from electron clouds

� So even if a homogeneous external field

• slight difference in precessional frequency for hydrogen nuclei in

different molecules


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Proton spectroscopy – water and fat

� e.g. water and fat, frequency difference of

• 3.35 ppm (parts-per-million)

• 215 Hz at 1.5 T

� FID for an object containing both water and fat

• sum of two decaying sinusoids

• slightly different resonant frequencies

• different T2 time constants

� Fourier transform of FID – frequency spectrum

• superposition of two Lorentzians

• separated by 3.35 ppm


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MR spectroscopy

� Within single molecule such as fat

• hydrogen nuclei resonate at different frequencies

• protons bound to carbon atom with single bonds vs. carbon atom

with double bonds

• T2 values could also vary

� Complex frequency spectrum

• multiple peaks of different amplitudes and widths

� MR spectroscopy

• use the information in spectrum to determine the chemical and

structural properties of molecules


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Chemical shift

� Separations between resonant peaks of different protons

proportional to external magnetic field strength

• high field systems advantageous for MR spectroscopy

• higher spectral resolution

� Frequency shift due to different electronic environments

• known as chemical shift

Diagnostic Radiology Physics: A Handbook for Teachers and Students – 14.4 Slide 5 (65/141)

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Clinical applications of MR spectroscopy

� Monitor biochemical changes in tumours, stroke, metabolic

disorders

� Commonly used nuclei

• proton, phosphorous, carbon

� Higher peak in spectrum associated with higher

concentration of a compound or molecule

� E.g. in proton spectroscopy

• increased ratio of choline:creatine may indicate malignant disease

• high lactate levels may indicate cell death and tissue necrosis

� More in Chapter 15


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14.5 SPATIAL ENCODING AND

BASIC PULSE SEQUENCES14.5


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14.5 SPATIAL ENCODING AND BASIC PULSE

SEQUENCES14.5

Spatial encoding and basic pulse sequences

� 14.5.1 Slice-selection

� 14.5.2 Frequency and phase encoding

� 14.5.3 Field-of-view and spatial resolution

� 14.5.4 Gradient echo imaging

� 14.5.5 Spin echo imaging

� 14.5.6 Multi-slice imaging

� 14.5.7 Three-dimensional imaging


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BASIC PULSE SEQUENCES14.5.1 SLICE-SELECTION


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SEQUENCES14.5.1 Slice-selection

Slice selection

� In previous discussion RF pulse caused entire imaging

volume to be excited

� In most applications though, an image of a thin slice of

object is desired

� Achieve thin slice by

• applying a linear magnetic field gradient across the object during

the RF pulse

• shaping the RF pulse to give desired slice profile


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Slice profile

� RF pulse applied simultaneously with linear magnetic field

gradient

� Excited slice profile in direction of gradient resembles

Fourier transform of the shape of the RF pulse

• most accurate for small flip angles (< 30°)

• acceptable for 90° excitation

• deviates at larger flip angles, but often assumed to hold


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Slice profile

� To get rectangular slice profile

� Use sinc-shaped RF pulse

� The dotted box (left) indicates how the sinc pulse is often

truncated to limit its width, and the ends may be tapered to

create a smooth transition region in the slice profile


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Shaping the excitation pulse

� Sinc pulse is infinitely long, so is truncated in practice

• usually include only one or two lobes on either side of main lobe

� To taper to zero at the ends, apply low pass smoothing

• Hanning or Hamming filter

� Without a low pass filter get abrupt truncations

• can lead to Gibbs ringing

• and excitation outside the desired slice

� Gaussian RF pulse shape could be used too


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Slice thickness

� The thickness of the excited slice ∆z is a function of

• bandwidth of the sinc pulse, BW

• amplitude of slice selection gradient, Gz


zG

BWz

γ=∆

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Slice selection gradient

� In MRI have three sets of linear gradient coils

• used for spatial encoding

• Gx, Gy and Gz

• provide linear gradients long the x, y and z axes respectively

� Slice selection gradient may be any one of these

� Or can obtain a slice plane in any spatial orientation by

using more than one of the gradients

� Excited plane is perpendicular to the direction of the net

gradient


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BASIC PULSE SEQUENCES14.5.2 FREQUENCY AND PHASE ENCODING


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SEQUENCES14.5.2 Frequency and phase encoding

Spatial encoding within the selected slice

� After exciting desired slice

• use linear gradients along the two perpendicular in-plane directions

• Gx and Gy for an axial slice plane from Gz gradient

� Linear gradient field will cause spins at different positions

along direction of gradient

• to precess at different frequencies

� Frequency of precession varies linearly with position

where Gx is the applied magnetic field gradient along x axis and ωx

is the resonance frequency of the spins at position x


xGxx γω =

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Rotating frame of reference

� The precession frequency in the equation is relative to the

rotating frame

• the additive frequency term due to the static B0 field is not included

� Note that this also applies to subsequent equations


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Frequency-encoding

� During MRI data acquisition

• spatial gradient applied

• along x-axis by convention

• spins resonate at linearly varying frequencies

� This is frequency-encoding

� Applied gradient is called readout gradient

• since data points are acquired while gradient is applied


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Phase-encoding

� Arises from spatial gradient applied along y-axis by

convention

� Applied gradient is called phase-encoding gradient


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The detected signal, frequency encoding only

� The detected signal S(t) is the sum of all the excited spins

in the imaging volume

� Each spin is resonating at a frequency corresponding with

its position along gradient direction

where ρ(x) is the spin density

• T1 and T2 dependence have been ignored for simplicity

� Term in the exponent is a phase term


( ) ( ) ( ) dxexdxextSxtGjtj xx ∫∫ == γω ρρ

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The phase term in the detected signal

� The phase term represents the relative phase

accumulated

• in the rotating frame

• due to the frequency encoding gradient

� Typically, readout gradient is constant

� More generally, readout gradient may be time varying

• so the accumulated phase term must be replaced by a time

integral of the readout gradient


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The phase term in the detected signal for a time varying

readout gradient

� Define

� Then

� i.e. position variable x and the variable kx are a Fourier pair

� kx represents spatial frequency, in “k-space”

� Thus image space and k-space are a Fourier pair


( ) ( ) ( ) dxexkStSxjk

xx∫== ρ

( ) dttGk xx ⋅= ∫γ

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Extend to 2D, i.e. both frequency and phase encoding

� Define

� Then

� Image space and k-space are a Fourier pair

� Once a sufficient amount of data are acquired in k-

space

� Can obtain imaging object by Fourier

transformation


( ) dttGk yy ⋅= ∫γ

( ) ( ) ( )dxdyeyxkkS

ykxkj

yx

yx∫+= ,, ρ


( )yx kkS ,

( )yx,ρ

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Data acquisition in 2D k-space

� Desired k-space data, , acquired by navigating

through k-space

� Use Gx and Gy gradients, where


( )yx kkS ,


( ) dttGk yy ⋅= ∫γ

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Data acquisition in 2D k-space


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Data acquisition strategies in 2D k-space

� Can acquire data to fill k-space after a single excitation

• but signal may be small during data acquisition due to T2 or T2*

decay

• leading to blurring or other image artefacts

� Instead use multiple TRs

� Acquire data for a single line of k-space following each

excitation

� Details of typical data acquisition strategies in sections

14.5.4, 14.5.5, 14.5.6


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BASIC PULSE SEQUENCES14.5.3 FIELD-OF-VIEW AND SPATIAL RESOLUTION


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SEQUENCES14.5.3 Field-of-view and spatial resolution

Field of view (FOV)

� Determined by manner in which k-space is sampled

� Image space and k-space are

• Fourier pair

• have an inverse relationship

• image space, units of distance – spatial position

• k-space, units of 1/distance – spatial frequency

� Larger FOV: finer sampling in k-space

� Smaller FOV: coarser sampling in k-space


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Field of view (FOV)

� FOV given by inverse of the distance between adjacent

sampled k-space points

� Can be different for the two in-plane directions

where ∆kx and ∆ky are the spacing between adjacent k-

space points along kx and ky


x

xk

FOV∆

=1

y

yk

FOV∆

=1

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Spatial resolution / pixel width

� The range of the sampled k-space region is important

� High spatial resolution requires larger region of k-space to

be sampled

� Expressed in terms of pixel widths ∆x and ∆y

where kx, max and ky, max are the maximum positions, along kx

and ky respectively, that are sampled


max,2

1

xkx =∆

max,2

1

yky =∆

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BASIC PULSE SEQUENCES14.5.4 GRADIENT ECHO IMAGING


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SEQUENCES14.5.4 Gradient echo imaging

Pulse sequences

� Set of instructions that control how MRI data are acquired

• application of Gx, Gy and Gz magnetic field gradients

• the RF pulse

• data acquisition

� Many available

� Some optimized e.g. for

• rapid imaging

• estimating diffusion or flow

• robustness against motion


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Gradient echo pulse sequence

� One of the simplest imaging pulse sequences

• Slice-selective RF pulse which rotates the magnetization into the

transverse plane (conventionally along the z-axis)

• Frequency-encoding, or readout, gradient (x-axis)

• Phase-encoding gradient (y-axis)

� Plus

• Slice “rewinder”

• Readout pre-phase gradient


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Gradient echo pulse sequence

� Following slice excitation,

phase-encoding and readout

pre-phase gradients are

applied.

� Data acquisition subsequently

follows in which one line of k-

space data is acquired.

� The phase encoding gradient

amplitude is linearly increased

from one TR to the next in

order to fill different ky lines of

k-space.


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Slice “rewinder”

� Opposite polarity to slice-selection gradient amplitude

� Needed to undo the phase accumulation that occurs

during RF pulse when a slice-selection gradient present

• spins at different positions along the z-axis will accumulate

different amounts of phase during the RF pulse

� Apply rewinder gradient with area approximately half that

of slice selection gradient

• reverses undesired phase dispersion

• aligns spins along same direction in the transverse plane


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Readout pre-phase gradient

� For reconstruction of an MR image, require k-space to be

filled symmetrically about its centre

• i.e. about kx = ky = 0

� Can be achieved efficiently by acquiring a full line of data

in a single readout

� Pre-phase gradient moves the k-space location to –kx, max

prior to each data acquisition

• position in k-space is the integral of the spatial gradients

• a negative Gx pre-phase gradient will move k-space position along

negative kx direction


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a) The pre-phase gradient of the readout axis moves the current k-space

position to –kx, max

b) Subsequently, one complete line of data is acquired during readout

c) Also apply the various phase-encoding gradients prior to readout to

move along the ky axis

• two different phase-encoded acquisitions are shown, one positive and one negative

Continue until the desired k-space region is filled (gray box).


a) b) c)

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� Without a pre-phase gradient

• data readout would begin at kx = 0

• to fill the other half of k-space would need second readout in

opposite direction

� Pre-phase gradient causes de-phasing of spins

• that element of de-phasing is then reversed by the readout

gradient

• spins come back into phase and result in the “echo” signal


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When to apply gradients

� One line of data acquired during each TR

� During each TR apply different phase-encoding

amplitudes to sample different lines along ky axis

� Phase-encoding, pre-phase and slice rewinders must be

applied

• after the end of the excitation pulse

• prior to beginning of readout window

� Could be applied simultaneously


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Gradient amplitude and duration

� Total area under pulses is important

• since k is time integral of the gradient

� Area under the readout pre-phase gradient should be one-

half of the area of the readout gradient

• echo will occur midway through the readout window

� Achieve using

• same amplitude, but opposite polarity and half pulse width

or

• maximum possible amplitude and a shorter pulse width

• good if short TE is desired


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Image reconstruction

� Acquire desired data

• e.g.

• 256 phase-encoding lines

• 256 readout points per line

� Apply 2D discrete fast Fourier transform to k-space data


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TE, echo time

� Time between peak of excitation pulse and centre of

readout window (kx=0)

• above a certain minimum, can select value of TE to achieve

desired image contrast

� During TE

• transverse magnetization decays with instrinsic T2 relaxation time

constant

• also loss of phase coherence among the spins from field

inhomogeneity

• result is T2* decay of signal

• the gradient echo image is weighted by the factor exp(-TE/T2*)


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T1-weighted imaging

� T1 relaxation takes place following each excitation and

longitudinal magnetization recovers

� If TR short

• longitudinal magnetization for tissue with relatively long T1s

remains low (insufficient time for recovery)

• lower signal in tissues with long T1s

• longitudinal magnetization greater for tissue with shorter T1s

• higher signal in tissues with short T1s

� T1-weighted images


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T1-weighted imaging

� Image contrast results from difference in T1 among the

tissues

� TE kept to a minimum in T1-weighted imaging to minimise

contrast from T2 or T2*

� Both TR and TE are short


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Fast imaging

� Applications such as dynamic imaging

� Multiple images are acquired rapidly to detect changes in

the images over time

� TR needs to be short

• but short TR reduces time available for magnetization to recover

� So, use small excitation angles (e.g., 5o – 30o) so that

acquired signal is maximised


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Ernst angle

� θE

� Flip angle that yields highest signal intensity for

• given TR

• known or approximate tissue T1

� Obtained by solving Bloch equation


( )1/1cosTTR

E e−−=θ

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Drawback of gradient echo imaging

� Sensitive to magnetic field inhomogeneities

• imperfect shimming of main B0 field

• along air tissue boundaries where susceptibility difference between

regions distorts the local magnetic field

� Leads to additional signal loss from dephasing of spins

(T2* decay) within affected voxels

� Results in reduced signal

� Or even complete loss of signal at long TE


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BASIC PULSE SEQUENCES14.5.5 SPIN ECHO IMAGING


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SEQUENCES14.5.5 Spin echo imaging

Spin echo imaging

� Avoids reduction of signal due to magnetic field

inhomogeneities

� A second RF pulse is applied following the initial 90°

excitation pulse

• at time TE/2

• 180° flip angle

� Called a “refocusing pulse”

� Effect is to reverse the phase that a spin may have

accumulated due to the inhomogeneous field


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After the refocusing pulse

� After 180° refocusing pulse, magnetization again

accumulates phase

� But, because of the phase reversal from the refocusing

pulse, the total phase is reduced

� At the echo time TE the phase accumulated after the

refocusing pulse cancels the phase accumulated before


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Spin echo pulse sequence

� The spin echo sequence is

similar to the gradient echo

sequence

• phase-encoding, rewinder and pre-

phase gradients

� Plus a 180° refocusing pulse

• to refocus any spin that may have

dephased due to magnetic field

inhomogeneities

� The refocusing pulse reverses

any accumulated phase• so polarities of both the phase

encoding gradient and the pre-

phase gradient of the readout are

reversed


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Spin echo pulse sequence in

k-space

� Effect of refocusing pulse

is

• to move current k-space

location to its conjugate

position

• i.e. to reflect the point about

the k-space origin


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Acquired signal at TE

� Spin echo imaging

• evolves with the intrinsic T2 time constant

• not affected by inhomogeneous fields

� Gradient echo imaging

• evolves with T2*

• is affected by inhomogeneous fields


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Fast imaging

� In gradient echo, use short TR and small angle excitation

� In spin echo, short TR not recommended due to rapid

reduction of available magnetization

• 180° refocusing pulse inverts any positive longitudinal

magnetization to –z direction

• a short TR does not allow sufficient time for recovery

� Instead, reduce scan time by acquiring multiple lines of

data following a single excitation pulse

� “Fast spin echo” or “turbo spin echo”


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“Fast spin echo” or “turbo spin echo”

� For each excitation pulse

• apply multiple refocusing pulses

• acquire multiple lines of data

� Typically 16, 32 or more lines of data per TR

� Single shot acquisitions possible

• e.g. 128 refocusing pulses and 128 readout lines following a single

excitation pulse


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BASIC PULSE SEQUENCES14.5.6 MULTI-SLICE IMAGING


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SEQUENCES14.5.6 Multi-slice imaging

Two approaches to get more than one slice

� Acquire multiple 2D slices by

• repeating the single slice strategy

• at shifted slice positions

� Use 3D imaging


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Multiple slice technique

� All gradient waveforms, including slice selection gradients,

remain unchanged

� Vary location of each slice by modulating frequency of the

excitation RF pulse

• modify the carrier frequency of the RF pulse


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� Centre location of excited slice with respect to scanner

isocentre, zslice, given by

where ∆f is the offset frequency of the RF pulse relative to

resonance frequency at isocentre and Gsl is the slice

selection gradient amplitude


sl

sliceG

fz

γ∆

=

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� Typically acquire multiple 2D slices in an interleaved

fashion

� Do not need to wait until the end of a TR following data

acquisition from one slice before acquiring data from other

slices

• there is “dead time” between end of data acquisition and next

excitation pulse for a given slice

• excite a different slice, and acquire data, during “dead time” of the

previous slice


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Interleaved slice acquisition

� Three slices S1, S2 and S3 are acquired

� Each box can represent any imaging sequence

� Effective TR for each slice is period between acquisitions

of the same slice

• corresponds to the time between excitations for any given spin


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Interleaved slice acquisition

� Total scan time can be equal to scan time for a single slice

if the dead time is sufficiently long

� Otherwise, repeat scan until all remaining slices are

acquired

� Following data acquisition, images are reconstructed by

applying separate 2D Fourier transforms for each slice


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BASIC PULSE SEQUENCES14.5.7 THREE-DIMENSIONAL IMAGING


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SEQUENCES14.5.7 Three-dimensional imaging

3D imaging

� Alternative approach to acquisition of multiple slices

� Excite a single large volume (instead of a single slice)

� Add phase encoding along slice direction

� Now have phase encoding in

• in-plane, and

• through-plane (slice) directions

� Just as in-slice spatial information is encoded using

phase-encoding along y-axis

� Slice information is encoded using phase-encoding along

z-direction


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3D gradient echo sequence

� Similar to 2D sequence

� But has additional phase

encoding along the slice-

encoding direction, Gz


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3D imaging

� After data acquisition, images are obtained by 3D Fourier

transform of the acquired k-space data

� Data for all slices acquired simultaneously

• in 2D scheme each data acquisition window receives data from

only one slice

� Scan time in 3D is greater than that for 2D (for a single

slice with the same TR) by a factor equal to the number of

slices


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Advantages/Disadvantages of 3D imaging

� 3D imaging preferred when multiple contiguous slices

needed

• because slices are contiguous

� 3D imaging preferred if thin slices required

• because excitation of a large 3D volume requires much lower

gradient amplitude than needed to excite individual thin slices

� 2D imaging preferred if arbitrary slice positions desired


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BASIC PULSE SEQUENCES14.5.8 MEASUREMENT OF RELAXATION TIME

CONSTANTS


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SEQUENCES14.5.8 Measurement of relaxation time constants

Why measure T1 and T2?

� Determine disease status

� Track disease progress following treatment


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Measurement of T1

� Several approaches

� One example is the inversion recovery (IR) technique

• accurate and widely used

� Apply 180° pulse

• inverts spins from equilibrium position into the –z axis

� Magnetization recovers from its inverted state towards

equilibrium magnetization

• in exponential fashion, with longitudinal time constant T1

• according to

where


( ) ( ) ( )11 //10

Tt

o

Tt


( ) 00 MM z −=

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Inversion recovery (IR)

sequence

� Invert magnetization to the –z

axis by a 180° pulse

� Acquire data following an

inversion time (TI)

� Repeat for different TI values

(open circles)

� Fit data to equation to find T1

� Typically a fast imaging

technique used

• such as turbo spin echo


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Measurement of T1

� Series of images acquired, each with different inversion

time TI

� Measure signal intensity and fit to

� Derive T1


( ) ( ) ( )11 //10

Tt

o

Tt


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Measurement of T1

� Any imaging sequence could be used

� Rapid sequence preferred to reduce total scan time

• e.g. turbo spin echo

� Long TR used

• ensures spins are nearly fully relaxed prior to subsequent TRs

• ideally TR


15 T×≈

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Measurement of T2

� Two approaches

� Use a spin echo sequence

1. repeatedly with different TEs

2. with one excitation and multiple refocusing pulses


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Measurement of T2, first approach

� Spin echo sequence

• expect signal to decay exponentially with T2 time constant

� Repeat using increasing echo times

� Fit measured signal intensities to decaying exponential

� Could use just two different echo times, but four or five

more typical

� TR >> T1

• ensures magnetization returns to equilibrium state

• magnetization at start of each excitation is identical and not a

function of TR or TE


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Measurement of T2, second approach

� Spin echo sequence

• expect signal to decay exponentially with T2 time constant

� Use one excitation and multiple refocusing pulses

� e.g. 90° excitation followed by

• 6 refocusing pulses (180°)

• 6 data acquisition periods

• so get set of images with different TEs within the same TR

� Sequence similar to fast spin echo

• except acquired echoes used to reconstruct different images

� Method is efficient


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Measurement of T2 - Inaccuracies in the 180° refocusing

pulses

� Do not affect T2 measurement accuracy in single echo spin

echo sequences

• signal at different echo times is equally affected by the

inaccuracies, so signal amplitudes are scaled in the same way for

all echoes

� Do affect T2 measurement accuracy in multiple echo spin

echo sequences


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Measurement of T2*

� Similar to measurement of T2, but use gradient echo

sequence in lieu of spin echo

• multiple gradient echoes follow a single excitation pulse

• each echo at a different TE

� No concerns about accuracy of RF pulse affecting

accuracy of measurement

• as no refocusing pulses used in gradient echo


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14. BIBLIOGRAPHY14.

Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14. Bibliography Slide 1 (140/141)

IAEA Diagnostic Radiology Physics: A Handbook for Teachers and Students - 14. Bibliography Slide 2 (141/141)

14. BIBLIOGRAPHY14.

� BERNSTEIN, M.A., KING, K.F., ZHOU, X.J., Handbook of MRI pulse

sequences, Elsevier Inc, Amsterdam (2004).

� BUSHBERG, J.T., SEIBERT, J.A., LEIDHOLDT, E.M.J., BOONE, J.M., The

Essential Physics of Medical Imaging, 2nd Ed edn, Williams and Wilkins.

(2002).

� HAACKE, E.M., BROWN, R.W., THOMPSON, M.R., VENKATESAN, R.,

Magnetic resonance imaging: Physical principles and sequence design, John

Wiley & Sons, Inc, New York (1999).

� PAULY, J., NISHIMURA, D., MACOVSKI, A., A k-space analysis of small-tip-

angle excitation, J. Magn. Reson. 81 43-56 (1989).

� SPRAWLS, P., Magnetic Resonance Imaging: Principles, Methods, and

Techniques, 2nd edn, Medical Physics Publishing, Madison, Wisconsin

(2000).

� STARK, D.D., BRADLEY, W.G., Magnetic resonance imaging, 2nd edn,

Mosby-Year Book, St. Louis (1992).

Documents

Chapter 14:Physics of Magnetic Resonance - Human … · IAEA Diagnostic Radiology Physics: A Handbook for Teachers and Students -14 (02/141) CHAPTER 14 TABLE OF CONTENTS 14.1. Introduction