chapter 14: physics ofmagnetic...

Diagnostic Radiology Physics:A Handbook for Teachers and Students

Special topics 1

Dr. khitam Y. Elwasife

Objective:

To familiarize the student with the fundamental concepts of

MRI.

Chapter 14: Physics of Magnetic

Resonance

CHAPTER 14 TABLE OF CONTENTS

1. Introduction

2. Nuclear magnetic resonance

3. Relaxation and tissue contrast

4. MR spectroscopy

5. Spatial encoding and basic pulse sequences

14.1 INTRODUCTION14.1

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 pure 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 …


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 انحدار 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


Characteristics of MRI

No ionizing radiation

• unlike x-rays and CT

soft tissue are clear compared with other

method

Can control image between different tissues

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

2. NUCLEAR MAGNETIC

RESONANCE1.THE NUCLEUS: SPIN, ANGULAR AND MAGNETIC

MOMENTUM

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 present in more quantity in human body in

water and fat

• Water is 50-70% of total body weight

• Fat is 10-20% of total body weight

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

momentum

Properties of the nucleus Angular momentum p I

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

p

2. NUCLEAR MAGNETIC RESONANCE

1.The nucleus: spin, angular and magnetic

momentum

Gyromagnetic ratio is the ratio of its magnetic moment to its angular momentum

Specific to each type of nucleus

For proton, roughly 42.57 MHz T-1

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*

Abundanin huma

body (%

atoms)

cen

of

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

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 alignmentانتقام : 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

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



Boltzmann distribution

Parallel orientation has lower energy state

Slightly greater number of spins align along that direction

N eE / kt eo / kT

N

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

• 0 is Larmor, or resonance, frequency

What are the Bloch equations?

Bloch began with the assumption that the millions of individual nuclei

in a sample could be represented by a single vector M. (Bloch

called M the "polarization" but today it is more frequently known as

the net magnetization.) Just as individual nuclei possess spin

angular momentum, so does the vector M. As Joseph Larmor

showed a half century before, an external field (B) produces

a torque (τ) or "twisting force" on M resulting in its precession at

angular frequency ω = γ B.

Since M is a vector rotating in space it can be resolved into have

three components — Mx(t), My(t), and Mz(t) — each a function of

time. Mx(t) and My(t) are the transverse components; Mz(t) is

the longitudinal component.

In 1946 Felix Bloch published a mathematical analysis of the "Nuclear Induction" phenomenon

including a set of equations explaining the origin and properties of the NMR signal. This paper

is very readable and does not require a high level of mathematics or physics background


Bloch Equation

Torque on magnetization causes it to precessمعالجة

about the direction of the magnetic field

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

dt

Will precess at the Larmor frequency,

d B

o Bo


Larmor frequency

o Bo

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, 0 = 64 MHz


Rotating frame of reference

In stationary (or laboratory) frame of reference,

precession:

• at Larmor frequency 0

• 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 in stationary frame, appears toprecess

at r , where

r o

14.2 NUCLEAR MAGNETIC RESONANCE

14.2.2 External magnetic field and magnetization

Net magnetization

Total magnetization

net magnetization vector sum of all spins within the voxel

• aligned along +z direction, the direction of B0

“Magnetization” = net magnetization of a collection of spins


Bloch equation for net magnetization M

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

and does not precess about any axis

• magnetization is at its equilibrium magnetization M0.

When additional fields applied, including time varying

fields

• magnetization may deviate from equilibrium position

• magnetization may precess about an effective magnetic field

dt

In the presence of a constant external magnetic field B0

dM MB

At equilibrium (i.e., when no scanning is taking

place) M is aligned with the main magnetic field

(Bo). However, during the MR imaging M is

purposely headed out of collection allowing it to

precess around the direction of Bo .The direction of

the Bo field is commonly designated as the z-

axis. Using this coordinate system, M can be

considered to have both longitudinal (Mz) and transverse (Mxy) components

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

Effect of external radiofrequency (RF)

field B1(t)

The radiofrequency field (B1) is applied perpendicular to the main magnetic field (Bo). The B1 field is produced either by a local coil (as shown in the picture) or more commonly, from windings in the walls of the scanner itself. Initially, M is aligned with Bo but will be tipped out of alignment during application by the rotating/oscillating B1 field. Like pushing a child on a swing, the B1 field must be applied near the Larmor frequency for this to occur.



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

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


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


Detection of a signal from rotating magnetization

Overall strength of received signal depends on

• type and size of RF coil used for signal reception

More in Chapter 15

3. RELAXATION AND

TISSUE CONTRAST1. T1 AND T2 RELAXATION

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


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

o


The longitudinal component (z-component) of the

magnetization returns to its equilibrium state M0 in an

exponential fashion

Mz t Mz 0e 1 M 1e 1t /T t /T



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


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



Result is a loss of phase coherence

Leading to an exponential decay of signal in the

transverse plane

With time constant T2

Mxy t Mxy 0e 2

t /T

where Mxy(0) is the transverse magnetization immediately

following RF excitation



Dark gray component

T2 relaxation reduces the transverse component towards

zero


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

3. RELAXATION AND TISSUE CONTRAST1. T1 and T2 relaxation

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

z z o

t /Tt /TM 1 e M t M 0e


TR and image creation

Mz t Mz 0e 1 Mo 1e 1t /T t /T

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


TE and image creation

Time between excitation and data acquisition is echo time

(TE)

Mxy t Mxy 0e 2

t /T

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

14.3 RELAXATION AND

TISSUE CONTRAST14.3.2 BLOCH EQUATIONS WITH RELAXATION TERMS

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

dt T1 T2

M z zM x x M y ydM

MB Mo

14.3 RELAXATION AND

TISSUE CONTRAST14.3.3 T2* RELAXATION

T2 Relaxation: Definition

T2 relaxation is the process by which the transverse

components of magnetization (Mxy) decay or dephase. ...

Thus T2 is the time required for the transverse

magnetization to fall to approximately 37% (1/e) of its initial value

14.3 RELAXATION AND

TISSUE CONTRAST14.3.4 CONTRAST AGENTS

14.3 RELAXATION AND

TISSUE CONTRAST14.3.5 FREE-INDUCTION DECAY (FID)

MRI=Magnetic Resonance Imaging

Allows the clinician to see high quality images of the

inside of the body:

• Brain

• Heart

• Lungs

• Spine

• Knees

• Etc.

MRI machines look like a large block with a

tube running through the middle of the

machine, called the bore of the magnet.

The bore is where the patient is located for the

duration of the scan.

The MRI machine picks points in the patients body, decides what type of

tissue the points define, then compiles the points into 2 dimensional and

3 dimensional images.

Once the 3 dimensional image is created, the MRI

machine creates a model of the tissue. This allows

the clinician to diagnose without the use of surgery.

The magnet strength is measured in units of Tesla or

Gauss (1 Tesla = 10,000 Gauss).

Today’s MRI machines have magnets with strengths

from 5000 to 20,000 Gauss.

To give the strength of these magnets, the earth’s

magnetic field is about .5 Gauss, making the MRI

machine 10,000 to 30,000 times stronger.

Magnetic resonance imaging (MRI) is a spectroscopic imaging technique used in medical settings to produce images of the inside of the human body.MRI is based on the principles of nuclear magnetic resonance (NMR), which is a spectroscopic technique used to obtain microscopic chemical and physical data about molecules

MRI

• The magnetic resonance imaging is accomplished through the absorption and emission of energy of the radio frequency (RF) range of the electromagnetic spectrum.

The Components

A magnet which produces a very powerful uniform magnetic field.

Gradient Magnets which are much lower in strength.

Equipment to transmit radio frequency (RF).

A very powerful computer system, which translates the signals transmitted by the coils.

to stimulate the protons in the atoms of the elements present in the body to

release a signal, and then picked up and determine its location in the body and

displayed on the gradation of gray colors refers to the strength of the signal, and

the gradient is different tissues in the body.

- More of these elements is the stimulation of hydrogen so as to its presence in

abundance in living organisms and the presence of a proton & one in the atomic

nucleus, giving it more power than the rest of the items on the issuance of the

signals used in magnetic resonance imaging.

2- MRIThere are many different types today many ideas for magnetic resonance

devices , in general, there are three main types of magnetic resonance imaging

devices ( Permanent Resistant And anti- resistance)

- MRI generally contain part gives a strong magnetic field & part issued radio

waves to stimulate the protons and captures the incoming signal and a portion of

them & tiered system .

- The survey , which is used in medical fields will cost a million dollars per Tesla

and several hundreds of thousands of dollars are spent annually on maintenance .

- Used computers mainly in MRI scans and programs developed effectively help to

give the best results.

1- The idea of magnetic resonance

1- The resistive magnet has many coils of wire that wrap around the bore, through

which electrical currents are passed, creating a magnetic field. This particular magnet

requires a large amount of electricity to run, but are quite cheap to produce.

2- The permanent magnet is one that delivers a magnetic field, which is always on at full

strength and therefore, does not require electricity. The cost to run the machine is low

due to the constant magnetic force. However, the major drawback of these magnets is

the weight in relation to the magnetic field they produce.

types of magnetic resonance imagin devices

3- The superconducting magnets are very similar to the design of the

resistive magnets, in that they too have coils through which electricity is

passed creating a magnetic field. However, the major difference between the

resistive magnet and the superconducting magnet is the fact that the coils are

constantly bathed in liquid helium at -452.4ºC. This cold temperature causes

the resistance of the wire to be near zero, therefore reducing the electrical

requirement of the system. All of these factors allow for the machine to remain

a manageable size, have the ability to create high quality images, and still

operate at a reasonable cost. The superconducting magnet is the most

commonly used in machines today, giving the highest quality images of all

three magnet types.

The device consists of an electromagnet huge spiral for the formation of a

magnetic field around the patient produces a magnetic field of 2 Tesla ,

equivalent to 20,000 Gauss .

-This area makes hydrogen atoms Taatmgnt and moving all of its Part to

magnetic north Vtaatouhd in one direction .

- After that displays the body to radiation Mveaih lead to increased capacity of

the atoms and the piece will be tacking a certain degree , leaving us an iota of

every million corn is the process of magnetic resonance imaging , a large

number of atoms is sufficient for the emergence of a clear picture of the part to

be photographed and sending much of the energy reverse .

-This energy is the inverse of the receiving device are calculated and composed

in the form of a photo This picture shows the intensity of the hydrogen in every

region of the body. Using this image doctors can discover a lot of diseases .

-

The physics of magnetic resonance

When provoked atoms in the body are protons movement with & against the

direction of the magnetic field the main growing protons approval of the thrust

for protons anti small amount but it is very important to get the picture later ,

and disturbed these protons especially radio waves altering the status of the

vertical to the horizontal , but what would soon return to equilibrium situation ,

but for its return to put the equilibrium position.

is for the purpose of diagnostic imaging such as veins and arteries , or

photographing neurological changes in the brain , and magnetic resonance

imaging is better to clarify the types of tissues and body fluids , and is also used

for planning treatment plans based on radiation therapy. Before MRI screening

should review medical history and ensure fully the absence of previous surgery

or accidents have led to the presence of metals in the body such as shrapnel ,

and be sure that cross- examination of public -ray & routine patient passing

through the metal detector . The patient often gives a special dye is injected into

the body in order to increase the contrast and clarify parts converged

The use of magnetic resonance

Composed image of magnetic resonance imaging of multiple columns and rows are

called in English matrix, each column description contains the boxes called pixel,.

-the distribution of the signals captured from the body on these boxes so arranged in

order of the body, and this mechanism relies on a graded gives each segment of the

body force specific signal , and the signal strength captured give color to grayscale ,

consists us a picture magnetic resonance image grayscale . - Clear your equation is :

The number of squares per cm = 1 / box size

- The contrast in the image depends on the horizontal and vertical timings and proton

density and called ( internal influences ) , the echo time and repetition are considered (

external influences ) .

Magnetic resonance image

- More MRIs consists of two dimensions, each dimension is divided into a network of rectangular elements called sham (pixels) pixels. The intensity of each pixel in the image depends on the strength of magnetic resonance wave emitted by the region that they contain. The size of the image depends on the number Baksalat, and Medm images consist of 265 Peixalat vertically and horizontally Peixalat 256.

Clarity (IMAGE RESOLUTION)

MRI’s of the heart can be done to look at many different areas including: vessels,

chambers, and valves.

The MRI can detect problems associated with different heart

diseases including plaque build up and other blockages in blood

vessels due to coronary artery disease or heart attacks.

MRI’s of the brain can evaluate how the brain is working,

whether normal or abnormal.

Brain MRI’s can show damage resulting from different

problems such as: damage due to stroke,

abnormalities associated with dementia and/or

Alzheimer’s, seizures, and tumors.

fMRI are done prior to brain surgery, to give a map of

the brain, and help plan the procedure.

MRI’s can be done on the knee to evaluate damage to the meniscus,

ligaments, and tendons.

Tears in the ligaments are given a grade 1-3 depending on their

severity:

1-fluid around the ligament

2-fluid around the ligament with partial disruption of the ligament fibers

3-complete disruption of the ligament fibers

a primary magnet: creates the magnetic field by coiling electrical wire and running a current through the wire

gradient magnets: allow for the magnetic field to be altered and allow image slices of the body to be created.

a coil: emits the radiofrequency pulse allowing for the alignment of the protons.

An MRI consists of:

Once the contrast dye has been injected, the patient enters the bore of the MRI

machine on their back lying on a special table.

The patient will enter the machine head first or feet first, depending on the area to

be scanned. Once the target is centered, the scan can begin

.

•The scan can last anywhere from 20-30 minutes.

•The patient has a coil that is placed in the target area, to be scanned.

•A radio frequency is passed through the coils that excites the

hydrogen protons in the target area.

•The gradient magnets are then activated in the main magnet and alter

the magnetic field in the area that is being scanned.

•

•The patient must hold completely still in order to get a high quality

image. (This is hard for patients with claustrophobia)

•The radio frequency is then turned-off and the hydrogen protons

slowly begin to return to their natural state.

The atoms that compose the human body have a property known as spin (a fundamental property of all atoms in nature like mass or charge).Spin can be thought of as a small magnetic field and can be given a + or – sign and a mathematical value of multiples of ½.Components of an atom such as protons, electrons and neutrons all have spin.

Spin:

Protons and neutron spins are known as nuclear spins.

An unpaired component has a spin of ½ and two particles with opposite spins cancel one another.

• In NMR it is the unpaired nuclear spins that produce a signal in a magnetic field.

Human body is mainly composed of fat and water, which makes the human body composed of about 63% hydrogen.

Why Are Protons Important to MRI?

positively charged

spin about a central axis

a moving (spinning) charge creates a magnetic field.

When placed in a large magnetic field, hydrogen atoms have a strong tendency

to align in the direction of the magnetic filed

Inside the bore of the scanner, the magnetic field runs down the center of the

tube in which the patient is placed, so the hydrogen protons will line up in either

the direction of the feet or the head.

•The majority will cancel each other, but the net number of protons is sufficient

to produce an image.

Energy Absorption:

The MRI machine applies radio frequency (RF) pulse that is specific to hydrogen.

• The RF pulses are applied through a coil that is specific to the part of the body being scanned.

The gradient magnets are rapidly turned on and off which alters the main magnetic field.

The pulse directed to a specific area of the body causes the protons to absorb energy and spin in different direction, which is known as resonance

• Frequency (Hz) of energy absorption depends on strength of external magnetic field.

Fig: 2. A) The protons spinning in the nature, without an external strong field. The directions of spins are random and cancel out each other. The net magnetization is nearly 0. B) In the presence of a large external magnetic field Bo the spins align themselves either against (low energy state) or along (low energy state). There is a slight abundance of spins aligned in the low energy state.

Fig:1 A) The top spinning in the earth's gravity.

The gravity tries to pull it down but it stays

upright due to its fast rotation. B) A charge

spinning in the magnetic field Bo.

Spin

Spin is a fundamental property of nature like electrical

charge or mass. Spin comes in multiples of 1/2 and can

be + or -. Protons, electrons, and neutrons possess spin.

Individual unpaired electrons, protons, and neutrons each

possesses a spin of 1/2.

In the deuterium atom ( 2H ), with one unpaired electron,

one unpaired proton, and one unpaired neutron, the total

electronic spin = 1/2 and the total nuclear spin = 1.

Two or more particles with spins having opposite signs

can pair up to eliminate the observable manifestations of

spin. An example is helium. In nuclear magnetic

resonance, it is unpaired nuclear spins that are of

importance.= electron

= neutron

= proton

Properties of Spin

When placed in a magnetic field of strength B, a particle with a net spin can absorb a

photon, of frequency . The frequency depends on the gyromagnetic ratio, of the

particle

The magnetic field runs down the center of the patient, causing the slowing hydrogen

protons to line-up

.

The protons either align themselves pointed towards the head or the feet of the patient,

and most cancel each other out.

The protons that are not cancelled create a signal and are the ones responsible for the

image.

The contrast dye is what makes the target area stand out and show any irregularities

that are present.

The dye blocks the X-Ray photons from reaching the film, showing different densities

in the tissue.

The tissue is classified as normal or abnormal based on its response to the magnetic

field

The tissues with the help of the magnetic field send a signal to the computer.

The different signals are sent and modified into images that the clinician can evaluate,

and label as normal or abnormal. If the tissue is considered abnormal, the clinician can

often detect the abnormality, and monitor progress and treatment of the abnormality.

The MRI has allowed clinicians to treat, monitor, and learn about many different diseases

and problems. As well as, to learn how the body functions, normally, without needing to

resort to more invasive methods like surgery.

relaxation

When the RF pulse is turned off the hydrogen protons slowly return to their natural alignment within the magnetic field and release their excess stored energy. This is known as

relaxation.

What happens to the released energy?Released as heat

ORExchanged and absorbed by other protons

ORReleased as Radio Waves.

MagLab - MRI Tutorial - National High Magnetic Field ...(show)

http://www.magnet.fsu.edu/education/tutorials/java/mri/

http://www.magnet.fsu.edu/education/tutorials/java/mri/(show)

It is important to describe NMR on a microscopic scale. A macroscopic

picture is more convenient. The first step in developing the macroscopic

picture is to define the spin packet. A spin packet is a group of spins

experiencing the same magnetic field strength. In this example, the spins

within each grid section represent a spin packet. At any instant in time,

the magnetic field due to the spins in each spin packet can be

represented by a magnetization vector. The size of each vector is

proportional to (N+ - N-).

The vector sum of the magnetization vectors from all of the spin packets

is the net magnetization. In order to describe pulsed NMR is necessary

from here on to talk in terms of the net magnetization, the external

magnetic field and the net magnetization vector at equilibrium are both

along the Z axis

Spin Packets

For every unit volume of tissue, there is a number of cells, these cells contain water molecules, each water molecule contain one oxygen and two hydrogen atoms., Each hydrogen atom contains one proton in its nucleus. Different tissues thus produce different images based on the amount of their hydrogen atoms producing a signal

T1 Processes

At equilibrium, the net magnetization vector lies along the

direction of the applied magnetic field Bo and is called the

equilibrium magnetization Mo. In this configuration, the Z

component of magnetization MZ equals Mo. MZ is referred to as

the longitudinal magnetization. There is no transverse (MX or

MY) magnetization here. It is possible to change the net

magnetization by exposing the nuclear spin system to energy of

a frequency equal to the energy difference between the spin

states. If enough energy is put into the system, it is possible to

saturate the spin system and make MZ=0. The time constant

which describes how MZ returns to its equilibrium value is called

the spin lattice relaxation time (T1). The equation governing this

behavior as a function of the time t after its displacement is:

Mz = Mo ( 1 - e-t/T1 )

T1 is therefore defined as the time required to change the Z

component of magnetization by a factor of e.

Precession

If the net magnetization is placed in the XY plane it will

rotate about the Z axis at a frequency equal to the

frequency of the photon which would cause a transition

between the two energy levels of the spin. This

frequency is called the Larmor frequency.

T1 and T2 time constants:Consider the net magnetisation vector of a group of

spins. At thermal equilibrium (M = M0), it is aligned with

the external magnetic field, B0. Now consider the

rotation of the net magnetisation vector by 90° (π/2

radians). The net magnetisation will precess around

the external magnetic field direction (diagrams are

drawn in the rotating frame of precession). Eventually,

the net magnetisation vector will return to its thermal

equilibrium position. The T1 and T2 time constants

(measured in milliseconds) describe how this happens;

the T1 time constant describes the recovery of the

Mz component of the net magnetisation vector, and the

T2 time constant describes the decay of the

Mxy component of the net magnetisation vector

(M does not simply "rotate" back to M0, because the T1

and T2 processes are separate, and the T1 and T2 times

for a tissue type are not the same.

The T2 time is related to the effect of nuclear spins on

each other. This may sound alot like the T1 process

described above, but it is slightly different. The spin-spin

interation purely refers to the loss of phase 6as they

interact with each other via their own oscillating magnetic

fields. (Phase coherence means spins are all precessing

together.) The slight changes in magnetic field which a

proton experiences causes its Larmor frequency to

change. As a result, the precession of spins moves out of

phase and the overall net magnetisation is reduced. This

T2 "relaxation" can occur without loss of energy to the spin

system (spins going out of phase only), and it can

occur withloss of energy to the spin system at the same

time (which is T1 relaxation, see above).

Larmor precession is the precession of the magnetic

moments of electrons move with magnetic moments .

The magnetic field exerts a torque on the magnetic moment,

Where is the torque, is the magnetic dipole moment, J is the angular

momentum vector, B is the external magnetic field, and is the gyromagnetic

ratio which gives the proportionality constant between the magnetic moment

and the angular momentum.

Remark :How do protons interact with a magnetic field?

Moving (spinning) charged particle generates its own little magnetic field

Such particles will tend to line up with external magnetic field lines (think of iron filings around a magnet)

Spinning particles with mass have angular momentum

Angular momentum resists attempts to change the spin orientation (think of a gyroscope)

http://en.wikipedia.org/wiki/Gyromagnetic_ratio

The angular momentum vector precesses about the external field axis with an angular frequency

known as the Larmor frequency,

where is the Larmor frequency, m is mass, e is charge, and B is applied field. For a given nucleus, the g-factor includes the effects of the spin of the nucleons as well as their orbital angular momentum and the coupling between the two. Because the nucleus is so complicated, g factors are very difficult to calculate, but they have been measured to high precision for most nuclei.

is the gyromagnetic ratio. [the ratio of the magnetic moment of a spinning

charged particle to its angular momentum]

Many factors contribute to MR imaging

-Quantum properties of nuclear spins

-Radio frequency (RF) excitation

properties

-Tissue relaxation properties

-Magnetic field strength and gradients

-Timing of gradients, RF pulses, and

signal detection

1) Put subject in big magnetic field

2) Transmit radio waves into subject [2~10 ms]

3) Turn off radio wave transmitter

4) Receive radio waves re-transmitted by subject0

5) Convert measured RF data to image

Procedure of MRI

There is electric charge on the surface of the proton, thus creating a small current loop and generating magnetic moment .

The proton also has mass which generates an angular momentum when it is spinning.

What kinds of nuclei can be used for NMR?

Nucleus needs to have 2 properties:Spincharge

Nuclei are made of protons and neutronsBoth have spin ½Protons have charge

Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin

Hydrogen atom is the only major species that is MR sensitive

Hydrogen is the most abundant atom in the body

The majority of hydrogen is in water (H2O)

Essentially all MRI is hydrogen (proton) imaging

MRI

X-Ray, CT

Electromagnetic Radiation Energy

14.4 MR SPECTROSCOPY14.4 MR SPECTROSCOPY

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


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 chemicaland

structural properties of molecules


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


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

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).

chapter 14: physics ofmagnetic...

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